Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Tully, Alexandra Bennett
Doctor of Philosophy - PhD
University of British Columbia
Organic photovoltaics (OPVs) have the potential to serve as flexible and transparent solar cells, comprised of inexpensive materials and created through scalable and energy efficient processes. However, poor power conversion efficiency (largely due to inefficient charge separation) prevents them from being a commercial competitor to today’s conventional solar cells. This thesis marks the first results of a collaborative research project at the University of British Columbia’s Stewart Blusson Quantum Matter Institute investigating the physics underlying poor charge transfer in OPVs. The first step in engineering more efficient charge separation is understanding the fundamentals of the charge transfer process. When an electron is excited in an OPV, it remains coulombically bound with its hole, forming an exciton. Excitons in organic solar cells are more tightly bound with larger binding energies than those in conventional solar cells, making them harder to dissociate into free charges. The nature of these excitons plays a role in the generation of free carriers in OPVs, but it remains an open question that can benefit from the temporal and spatial information provided by time- and angle-resolved photoemission spectroscopy (TR-ARPES). We work with neat C60 thin films due to the material’s foundational status as a prototypical OPV electron-acceptor material and because it is a photo-absorbing excitonic semiconductor, with a manifold of optically-accessible excitonic states. The importance of long-range order to conducting spectroscopic analysis of a thin film’s electronic structure prompted our development of a generalizable growth technique that consistently results in single-domain C60 films of controllable thicknesses, using Au(111) as an epitaxially well-matched substrate. To better understand the evolution of the optically-excited carriers, we use TR-ARPES (supported by low-energy electron diffraction and scanning tunneling microscopy) to investigate and to map the energy landscape of C₆₀ thin films in both space and time (with ångström and femto- to picosecond resolution, respectively). This thesis presents the time-evolution of excitonic states and their angular dispersion. Our results include what is, to our knowledge, the first angular-resolved data within the first Brillouin zone of the excited states of C₆₀.
From Growth to TR-ARPES of C60:a Prototypical OPV SystembyAlexandra Bennett TullyB.Sc., Yale University, 2014M.Sc., The University of British Columbia, 2019A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)December 2023© Alexandra Bennett Tully 2023The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the thesisentitled:From Growth to TR-ARPES of C60:a Prototypical OPV Systemsubmitted by Alexandra Bennett Tully in partial fulfillment of therequirements for the degree of Doctor of Philosophy in Physics.Examining Committee:Sarah Burke, Associate Professor, Physics and Astronomy, Chemistry, UBCSupervisorDavid Jones, Professor, Physics and Astronomy, UBCCo-supervisorCarlos Silva-Acun˜a, Professor, Physics, Universite´ de Montre´alExternal ExaminerTakamasa Momose, Professor, Chemistry, UBCUniversity ExaminerAlireza Nojeh, Professor, Electrical and Computer Engineering, UBCUniversity ExaminerMona Berciu, Professor, Physics and Astronomy, UBCSupervisory Committee MemberAdditional Supervisory Committee Members:Jeremy Heyl, Professor, Physics and Astronomy, UBCSupervisory Committee MemberiiAbstractOrganic photovoltaics (OPVs) have the potential to serve as flexible and trans-parent solar cells, comprised of inexpensive materials and created throughscalable and energy efficient processes. However, poor power conversionefficiency (largely due to inefficient charge separation) prevents them frombeing a commercial competitor to today’s conventional solar cells. This thesismarks the first results of a collaborative research project at the University ofBritish Columbia’s Stewart Blusson Quantum Matter Institute investigatingthe physics underlying poor charge transfer in OPVs.The first step in engineering more efficient charge separation is under-standing the fundamentals of the charge transfer process. When an electronis excited in an OPV, it remains coulombically bound with its hole, formingan exciton. Excitons in organic solar cells are more tightly bound with largerbinding energies than those in conventional solar cells, making them harderto dissociate into free charges. The nature of these excitons plays a role inthe generation of free carriers in OPVs, but it remains an open question thatcan benefit from the temporal and spatial information provided by time- andangle-resolved photoemission spectroscopy (TR-ARPES).We work with neat C60 thin films due to the material’s foundationalstatus as a prototypical OPV electron-acceptor material and because it isa photo-absorbing excitonic semiconductor, with a manifold of optically-accessible excitonic states. The importance of long-range order to conductingspectroscopic analysis of a thin film’s electronic structure prompted ourdevelopment of a generalizable growth technique that consistently resultsin single-domain C60 films of controllable thicknesses, using Au(111) as anepitaxially well-matched substrate.To better understand the evolution of the optically-excited carriers, weiiiAbstractuse TR-ARPES (supported by low-energy electron diffraction and scanningtunneling microscopy) to investigate and to map the energy landscape of C60thin films in both space and time (with A˚ngstro¨m and femto- to picosecondresolution, respectively). This thesis presents the time-evolution of excitonicstates and their angular dispersion. Our results include what is, to ourknowledge, the first angular-resolved data within the first Brillouin zone ofthe excited states of C60.ivLay SummaryOrganic photovoltaic (OPV) materials have the capability to fundamen-tally alter our engagement with solar energy: the solar-harvesting devicesthese materials enable can be thin, flexible, light-weight, semitransparent(transparent to visible light), low-cost, and take relatively little energy toproduce. However, poor power conversion efficiency (largely due to inefficientcharge separation) prevents them from being a commercial competitor totoday’s conventional solar cells. In order to better understand the physics ofcharge transfer in these materials, we use a spectroscopic technique calledTR-ARPES to map the energy landscape of our thin films in both space andtime (with A˚ngstro¨m and femto- to picosecond resolution, respectively). Thisexperiment requires extremely pure sample films, which we grow in-house.This thesis marks the first results of a collaborative research project at theUniversity of British Columbia’s Stewart Blusson Quantum Matter Institute,investigating the physics underlying poor charge transfer in OPVs.vPrefaceThis thesis is representative of my scientific research during my PhD atthe University of British Columbia – work for which I was the primaryinvestigator. However, experimental physics is highly collaborative field, andthis work in particular was undertaken as part of a joint research projectat the University of British Columbia’s Stewart Blusson Quantum MatterInstitute involving the groups of Dr. Sarah Burke, Dr. David Jones, and Dr.Andrea Damascelli. Here, I will detail the contributions made by myself andothers to the experiments reported in this thesis.Chapter 3 provides an overview of some of the experimental develop-ments that were required for the experiments reported in this thesis. Thetechnical developments were conceived of over the course of conversationsbetween A. Tully, R. Greenwood, E. Ma˚rsell (now at MAX IV Laboratory),S. Burke, and D. Jones. The experimental procedures delineated in thischapter were performed by A. Tully with assistance from R. Greenwood.The machining was performed by A. Tully and H. Gautam. Data analysiswas performed by A. Tully.Chapter 4 describes the growth recipe developed for C60 thin filmson Au(111) that promotes long-range order. A version of this chapter isin preparation for submission, entitled Two-stage growth for highly orderedepitaxial C60 films on Au(111). The concept of a two-stage growth methodcame out of discussions that included A. Tully, R. Greenwood, S. Burke, D.Jones, and G. Sawatzky. The experimental methodology was determined byA. Tully with assistance from R. Greenwood. The growth and low-energyelectron diffraction measurements were led by A. Tully with assistance from R.Greenwood. Film growth and LEED data was analyzed by A. Tully. Scanningtunneling microscopy data was acquired and analyzed by R. GreenwoodviPrefacewith assistance from V. King and J. Yu. Low-energy electron microscopydata (and the LEED data included in the LEEM figure) was acquired andanalyzed by our collaborator, E. Ma˚rsell. Ellipsometry data was acquiredand analyzed by S. Kung with assistance from A. Tully. The preliminarymanuscript was written by A. Tully with assistance from S. Burke and R.Greenwood. S. Burke was responsible for project direction and management.Chapter 5 reports ARPES data collected on 1, 5, and 10 ML C60 films.Film growth was conducted by A. Tully and R. Greenwood. ARPES datacollection was led by A. Tully and performed by A. Tully and R. Greenwood,with assistance from M. X. Na, G. Levy, and A. K. Mills. Data was analyzedby A. Tully with assistance from R. Greenwood and M. X. Na. M. Michiardiand S. Kung were valuable sources of ARPES insight throughout. S. Burkeand D. Jones were responsible for project direction and management.Chapter 6 reports TR-ARPES data collected on C60 thin films. Filmgrowth was conducted by A. Tully and R. Greenwood. ARPES data wascollected by A. Tully, R. Greenwood, and M. X. Na, with assistance fromS. Zhdanovich, S. Dufresne, and B. Guislain. Data was analyzed by A.Tully with assistance from R. Greenwood and advice from M. X. Na. Datacollection has been informed by discussions with M. Berciu and L. Kemper. S.Burke and D. Jones were responsible for project direction and management.Appendix B describes a growth recipe developed for C60 thin films on Cu-intercalated graphene/SiC. The experiment was proposed by A. Tully. Theexperiment was conducted by A. Tully with assistance from R. Greenwood.viiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . liAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . lii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation: The Bigger Picture . . . . . . . . . . . . . . . . 11.2 The Role of Excitons in OPV Materials . . . . . . . . . . . . 21.2.1 Excitonic vs. Conventional Solar Cells . . . . . . . . 21.2.2 Exciton Dissociation in OPVs . . . . . . . . . . . . . 41.3 Introduction to Buckminsterfullerenes . . . . . . . . . . . . . 91.3.1 The Discovery of C60 . . . . . . . . . . . . . . . . . . 91.3.2 Form and Phases of C60 . . . . . . . . . . . . . . . . 101.3.3 Excitons in C60 . . . . . . . . . . . . . . . . . . . . . 142 Experimental and Analysis Techniques . . . . . . . . . . . . 202.1 Molecular Beam Epitaxy (MBE) . . . . . . . . . . . . . . . . 21viiiTable of Contents2.2 Low Energy Electron Diffraction (LEED) . . . . . . . . . . . 242.3 Angle-Resolved Photoemission Spectroscopy (ARPES) . . . 292.4 Time- and Angle-Resolved Photoemission Spectroscopy (TR-ARPES) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.5 Denoising Convolutional Neural Network (CNN) . . . . . . . 473 Experimental Background: Technical Details . . . . . . . . 583.1 Sample Mounting Procedure . . . . . . . . . . . . . . . . . . 583.2 Updated Sample Holder Design . . . . . . . . . . . . . . . . 593.3 Temperature Calibration Experiment . . . . . . . . . . . . . 614 C60/Au(111): System Description and Growth Techniques 634.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.2 Motivation for Growth Recipe . . . . . . . . . . . . . . . . . 664.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.4 Film Growth Procedure . . . . . . . . . . . . . . . . . . . . . 714.5 LEED and LEEM . . . . . . . . . . . . . . . . . . . . . . . . 724.6 STM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745 ARPES on C60/Au(111) . . . . . . . . . . . . . . . . . . . . . 775.1 Au(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2 1 ML C60/Au(111) . . . . . . . . . . . . . . . . . . . . . . . . 815.2.1 ARPES Data . . . . . . . . . . . . . . . . . . . . . . . 815.2.2 Band Folding Model . . . . . . . . . . . . . . . . . . . 895.2.3 Denoised Data Analysis . . . . . . . . . . . . . . . . . 995.2.4 Summary of Section 5.2 . . . . . . . . . . . . . . . . . 1035.3 5 ML C60/Au(111) . . . . . . . . . . . . . . . . . . . . . . . 1035.3.1 ARPES Data . . . . . . . . . . . . . . . . . . . . . . . 1035.3.2 Denoised Data Analysis . . . . . . . . . . . . . . . . . 1115.4 10 ML C60/Au(111) . . . . . . . . . . . . . . . . . . . . . . . 1125.5 Summary of Static ARPES Results . . . . . . . . . . . . . . 114ixTable of Contents6 TR-ARPES on C60/Au(111) . . . . . . . . . . . . . . . . . . . 1166.1 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1186.1.1 Pump Effect & Identifying Excitonic States . . . . . . 1186.1.2 States in Energy . . . . . . . . . . . . . . . . . . . . . 1226.1.3 Exciton Decays . . . . . . . . . . . . . . . . . . . . . 1346.1.4 Summary of Dynamics . . . . . . . . . . . . . . . . . 1516.2 Angular Dispersion . . . . . . . . . . . . . . . . . . . . . . . 1586.2.1 Constant Energy Cuts . . . . . . . . . . . . . . . . . 1586.2.2 High Symmetry Cuts . . . . . . . . . . . . . . . . . . 1616.3 Considerations for Future Measurements . . . . . . . . . . . 1676.3.1 Damage Thresholds . . . . . . . . . . . . . . . . . . . 1676.3.2 Polarization Effects . . . . . . . . . . . . . . . . . . . 1686.3.3 Pre-pulse Effects . . . . . . . . . . . . . . . . . . . . . 1696.3.4 Pulse Width Effects . . . . . . . . . . . . . . . . . . . 1717 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . 1747.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1747.2 Advancements & Outlook . . . . . . . . . . . . . . . . . . . . 176Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178AppendicesA Supplementary TR-ARPES Data and Analysis . . . . . . . 200A.1 Comparison of TR-ARPES CECs across Experiments . . . . 200A.2 Mystery Feature . . . . . . . . . . . . . . . . . . . . . . . . . 203A.3 Application of the Durban-Watson Test . . . . . . . . . . . . 204B C60/Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211C Ellipsometry on C60 . . . . . . . . . . . . . . . . . . . . . . . . 215D C60 Band Structure Streak-Correction . . . . . . . . . . . . 218E Experiment Timeline . . . . . . . . . . . . . . . . . . . . . . . 221xTable of ContentsF Relevant DFT Calculations: a brief how-to . . . . . . . . . 225F.1 Introductory Information . . . . . . . . . . . . . . . . . . . . 225F.2 Bulk High Symmetry Cut Calculation . . . . . . . . . . . . . 225F.3 Fermi Energy Corrections . . . . . . . . . . . . . . . . . . . . 227F.4 Self-Consistency Check . . . . . . . . . . . . . . . . . . . . . 228F.5 Au(111) Slab Calculation . . . . . . . . . . . . . . . . . . . . 231F.6 Fermi Surface Calculation . . . . . . . . . . . . . . . . . . . . 237F.7 Adding a Potential . . . . . . . . . . . . . . . . . . . . . . . . 238xiList of Tables1.1 Lattice Parameters of C60. . . . . . . . . . . . . . . . . . . . . 122.1 Photon Sources in the Damascelli Lab . . . . . . . . . . . . . 474.1 Disorder in C60 Films. . . . . . . . . . . . . . . . . . . . . . . 685.1 Thickness Dependence of C60 Band Positions . . . . . . . . . 1156.1 Summary of TR-ARPES Experiments . . . . . . . . . . . . . 1186.2 Summary of Peak Values for CT2 across Fits . . . . . . . . . 1336.3 Summary of Peak Values for S1 and CT1 across Fits . . . . . 1336.4 Photon Source Comparison . . . . . . . . . . . . . . . . . . . 1526.5 Excitonic States in 15 ML C60/Ag(111). . . . . . . . . . . . . 1536.6 Exciton States in 5 ML C60/Ag(111). . . . . . . . . . . . . . 1536.7 Excitonic States in Multilayer C60/Cu(111). . . . . . . . . . . 1536.8 Excitonic States in 10 ML C60/Au(111) (this work) . . . . . . 1536.9 Excitonic States from up to 3.0 eV: fit vs calculated . . . . . 157xiiList of Figures1.1 A representative illustration of an exciton with the hole lo-cated at the top of the highest occupied molecular orbital(HOMO) and the electron located at the bottom of the lowestunoccupied molecular orbital (LUMO). The electronic bandgap, optical band gap, and the binding energy of the exciton(EB) are depicted. . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Illustration of canonical exciton dissociation across a donor(grey)/acceptor (purple) interface. Step 1: the electron isphotoexcited from the HOMO to the (in this case) LUMO andforms an exciton with its hole. Step 2: the exciton diffusesto the D/A interface. Step 3: the electron is attracted tothe higher electron affinity acceptor material and the excitonstraddles the D/A interface. Step 4: the exciton dissociatesacross the interface resulting in free charge carriers. . . . . . . 51.3 An illustration of the local lattice distortions created by iso-lated excess charge carriers or a delocalized exciton (left)versus those created by a tightly bound exciton (right). (Left)An excess charge carrier like an electron (blue) or a hole (red)will result in a local lattice distortion that dresses the carrier,forming a polaron. The opposite charges result in correspond-ing opposite local lattice distortions. (Right) When oppositecharges are tightly bound in a Frenkel exciton, their chargeclouds will partially cancel, resulting in a weaker electric po-tential and a smaller local lattice distortion. . . . . . . . . . . 8xiiiList of Figures1.4 Model of C60, also known as a buckyball: a truncated icosa-hedron with 12 pentagons, 20 hexagons, and a total of 90covalent bonds. C60 is a common acceptor molecule used inOPVs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5 Model of phase transition from fcc to sc lattice. (a) Anfcc lattice with a 1 unit basis; face-centered atoms (or inthis case, C60 molecules) are delineated with a black outlineand all sites are equivalent. (b) A sc lattice with a 4 unitbasis, where a corner site and 3 of the face-centered sites areinequivalent (indicated with grey, purple, orange, and pink).(c) Extension of lattice to illustrate how each basis forms itsown sc lattice (example shown for orange basis). Color (shade)gradient goes from left (darker) to right (lighter) and servesas a visualization aid. (d) Top-down view of the sc C60 lattice,with the 4 inequivalent orientations of C60 shown and circledin the corresponding color. Image (d) is adapted from Davidet al.’s 1991 Letter to Nature. . . . . . . . . . . . . . . . . . . 131.6 Cascade of exciton states in C60. HOMO refers to the highestoccupied molecular orbital, and CT refers to the charge trans-fer states. Center energies and bandwidths are based on datadiscussed in this thesis. . . . . . . . . . . . . . . . . . . . . . 151.7 An illustration of the possible localization of the S1, CT1, andCT2 excitons in C60. Here the S1 (Frenkel) exciton has LUMOcharacter and is located on a single C60 molecule. The charge-transfer (CT) excitons are of LUMO (CT1) and LUMO+1(CT2) character, and are distributed across neighbouring C60molecules. The extent of the delocalization in the CT excitonsremains an open question in the field, and a very recent paperclaims that the CT1 and CT2 are actually singlets (the S2 andS3, respectively)! . . . . . . . . . . . . . . . . . . . . . . . . . 16xivList of Figures2.1 Image of lab system set up, including our MBE, LEED cham-ber, and ARPES chamber. This set up facilitates in-situsample growth, characterization, and analysis, while maintain-ing an ultra-high vacuum (UHV) environment. Our ARPESexperiments can be performed at temperatures as low as 4 K. 202.2 Schematic of Scienta Omicron customized Lab10 MBE system.Does not include our home-built characterization chamber.Figure from my MSc thesis and adapted from the ScientaOmicron Lab10 system manual. . . . . . . . . . . . . . . . . . 222.3 Depiction of a basic MBE set up, including crucibles for sampledeposition, QCM growth monitors, a retractable shutter toprecisely control deposition time, and the sample plate andheater. Image taken from my MSc thesis. . . . . . . . . . . . 242.4 Schematic of OMBE’s LEED configuration. Figure adaptedfrom my MSc thesis. . . . . . . . . . . . . . . . . . . . . . . . 262.5 LEED image of ordered monolayer C60 on Au(111), takenwith an electron beam energy of 77 eV. Example diffractionspots are indicated as nth order (green) and (n+1)th order(blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.6 Illustration of how the observed LEED pattern depends onthe configuration of the LEED optics. Figure obtained frommy MSc thesis and adapted from Arthur T. Hubbard’s TheHandbook of Surface Imaging and Visualization, p. 291. . . . 28xvList of Figures2.7 Geometry of an ARPES experiment; in our system, the θmotor can be varied from -40◦ to 40◦ (as long as the He lampis retracted), and the ϕ motor from -40◦ to 10◦. The θ slitaccepts photoelectrons from 30◦ of emission angle (-15◦ to+15◦). In this figure, the black arrow represents incomingphotons, and the blue beam represents the electrons emittedfrom the sample. This figure provides a 2D top view schematic(left), which shows the ability to move the sample in theta(with example θ motor positions of 0◦ and 20◦), and a 3D sideview schematic (right), which shows the sample’s movement inϕ as well as gives a sense of the structure of the chamber. Theimage of the DA30 hemispherical analyzer (inset) is reproducedfrom the ScientaOmicron website. . . . . . . . . . . . . . . . . 312.8 Illustration of the photoemission process, where EV is thevacuum energy, EF is the Fermi energy, Φ is the work functionof the material, E0 is the bottom of the valence band relative toEF , V0 is the inner potential, and EK is the maximum kineticenergy of electrons that will be photoemitted with a givenphoton energy hν. Figure adapted from Damascelli’s Probingthe Low-Energy Electronic Structure of Complex Systems byARPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.9 Illustration of photoemission geometry as described by thederivations in this section. Figure adapted from Damascelli’sProbing the Low-Energy Electronic Structure of Complex Sys-tems by ARPES . . . . . . . . . . . . . . . . . . . . . . . . . 332.10 Shown at motor values of θ = ϕ = 0 with our finite θslit of±15◦ (left) and at maximum θ (for our experimental setup) of±55◦ (θmax slit + θmax motor = 55◦). Taking into account theexperimental restrictions of ϕ will result in further limiting ofthese accessible regions. Note that even at extreme θ values,the 6.2 eV laser cannot reach the edges of the Au(111) BZ. . 35xviList of Figures2.11 ARPES data of bilayer C60 on Au(111) depicting the dispersionof kinetic energy as a function of kx. Distinct, sharp bandsare Au(111) bands; C60 HOMO (between -1 and -2 eV) andHOMO-1 (between -2.5 and -3.5 eV) are fuzzy and broad. Γand K points of the C60 Brillouin zone are indicated (for anexplanation of these high symmetry points, see Fig. 2.13).Taking a constant energy cut of our data cube immediatelybelow EF results in the image shown in Fig. 2.12. . . . . . . 412.12 A constant energy cut showing the dispersion of energy throughboth kx and ky at E −EF = −0.2 eV, integrated over 0.1 eV.The ky = 0 line is indicated in purple; taking a slice throughthe data cube holding ky = 0 results in the image shown inFig. 2.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.13 Depiction of the Brillouin zone of the bulk fcc crystal (highsymmetry points depicted in blue but labelled in black) pro-jected in the (111) direction, resulting in the surface Brillouinzone for fcc(111) (high symmetry points depicted and labelledin blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.14 Negative delay (probe before pump): the probe photoemitselectrons from their ground state (akin to equilibrium ARPES).Zero delay (probe and pump overlap): the probe photoemitselectrons the directly accessible (or nearly immediately occu-pied through decay channels) electronic states. Positive delay(probe after pump): first the pump photoexcites the electronsand then the probe subsequently photoemits the electronsfrom the excited states. By varying the delay time (includingmultiple positive delays), we can discern the lifetimes of theexcited states. . . . . . . . . . . . . . . . . . . . . . . . . . . . 46xviiList of Figures2.15 CNNs are a type of deep learning that specializes in patternrecognition. Practical applications include the optical charac-ter recognition (OCR) in your smartphone, facial recognitionsoftware, and automatic tumor detection in medical imagery.A denoising CNN takes a noisy input image and producesa denoised output image. It does this through a procedurewhich combines a series of layers and filters. The CNN con-tains a number of layers. Each layer can be associated withmultiple filters. Filters are where the parameters for patternrecognition get defined. Each filter is convolved with the orig-inal image in their given layer. The result of this convolutionis a numerical array that describes the extent to which thevarious pixels of the original image match the filter(s) in thatlayer. These numerical arrays are then combined in a processknown as ‘pooling.’ Once pooled, the (new) numerical arrayis the output image for that layer of the CNN. A few commonmethods of pooling (shown in this figure) are max pooling,average pooling, and mixed pooling. In max pooling, themaximum value for a given index of the numerical arrays iskept; in average pooling, the average of the values for eachindex is kept; in mixed pooling, a linear combination of themaximum and the average value is kept. . . . . . . . . . . . . 492.16 (a) Raw ARPES FS data, taken with our XUV source. (b)ARPES data enhanced by increasing the contrast by a factorof 2. (c) ARPES data with a Gaussian filter applied. (d)Denoised ARPES data, using Kim et al.’s neural network. . . 532.17 (a) Raw ARPES high symmetry slice data, taken with ourXUV source. (b) ARPES data enhanced by increasing thecontrast by a factor of 2. (c) ARPES data with a Gaussianfilter applied. (d) Denoised ARPES data, using Kim et al.’sneural network. . . . . . . . . . . . . . . . . . . . . . . . . . . 54xviiiList of Figures2.18 (a) Raw ARPES FS data, taken with our He lamp source. (b)ARPES data enhanced by increasing the contrast by a factorof 2. (c) ARPES data with a Gaussian filter applied. (d)Denoised ARPES data, using Kim et al.’s neural network. . . 552.19 A comparison of the constant ky high symmetry slices of theangular data taken with our XUV (a) and He lamp (d) sourceson 1 ML films. The resulting raw data is depicted in panels(b) and (e). Note that the sharp, linearly-dispersing featuresvisible in (b) are barely visible in (e). However, once thedenoising CNN has been applied, the right cone-like featurebecomes obvious in the lamp data (f) as well as the XUV data(c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.1 Standard sample plate/holder mechanisms for (a) ScientaOmi-cron systems (including our MBE) and (b) the custom ScientaARPES system. (a) The sample is either clamped or epoxiedto the surface of the flag-style sample plate. (b) The sampleis typically epoxied to the top of the molybdenum post. Thebullet and post can be made from a variety of UHV-safe mate-rials; Copper and Molybdenum are used in this figure becausethose are the materials used for the experiments described inthis thesis. This figure is adapted from my MSc thesis. . . . . 593.2 This design is a foil clamp, made of 0.125 mm thick molyb-denum. It is intended to be placed over the crystal (withthe crystal surface inside the 3.5 mm hole), and then havethe prongs folded around the crystal and post, thereby me-chanically securing the crystal to the post. In practice, themolybdenum foil was too brittle to allow for tight clampingof such small components. . . . . . . . . . . . . . . . . . . . . 60xixList of Figures3.3 Side view of sample in sample holder. Au(111) crystal ismounted to the molybdenum post using tantalum wires. Notethe copper block installed in the double-decker sample holder:the block facilitates adequate thermal conductivity to thesample as discussed in Section 3.2. . . . . . . . . . . . . . . . 603.4 Top-down view of the Au(111) crystal, mounted on a molyb-denum post, fastened in the double-decker sample holder.Tantalum wires can be seen using the “brim” of the tophatcrystal to secure the crystal to the post. . . . . . . . . . . . . 613.5 Plot shows temperature of the manipulator vs temperature ofthe sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.1 Introduction to the 2√3 x 2√3 R30◦ superstructure of C60/Au(111).(a) Schematic of one of C60’s preferential epitaxial growthson Au(111) (the 2√3 x 2√3 R30◦ superstructure) in realspace. Unit cells are delineated with dashed lines, and exam-ple lattice vectors are illustrated. (b) Schematic of epitaxialrelationship between C60 Brillouin zone (BZ) and Au(111) BZin momentum space. (c) LEED image of Au(111) substrateprepared for growth. Inset shows LEED image of herringbonestructure of clean Au(111). (d) LEED image of ML C60 onAu(111), grown with stage 1 process. Note the 30◦ rotationrelative to the gold structure in (c) (between grey hexagonand gold hexagon, respectively). . . . . . . . . . . . . . . . . 654.2 Depiction of our multi-stage film growth procedure, beginningwith a clean substrate, followed by growth of the first ML,and finally growth of the desired number of additional layers.Note that the first ML is grown at 300◦ C, and the subsequentlayers are grown at 155◦ C. . . . . . . . . . . . . . . . . . . . 66xxList of Figures4.3 Comparison of C60’s 2√3 x 2√3 R30◦ and in-phase epitaxialgrowths on Au(111). Unit cells are delineated with dashedlines, and example lattice vectors are illustrated with arrows.Note that in the 2√3 superstructure, the C60 molecules oc-cupy identical lattice sites relative to the Au substrate. Injuxtaposition, the in-phase superstructure results in moleculessitting atop a variety of different Au lattice sites. This isillustrated in the schematic by the different configurationsof Au atoms visible within the C60 molecules (circles) in thein-phase diagram (note that although some configurationsappear similar, they are not identical). . . . . . . . . . . . . . 694.4 LEED data comparing the results of a typical one-stage growthrecipe (a) to films grown using our two-stage growth recipe(b) and (c). LEED images are taken with a beam energy ofapproximately 10 eV, to best illustrate the presence or lackof domains (note that both penetration depth and beam areaare a function of energy). (a) Film A was grown with thesubstrate held at 155◦ C for the entire duration. LEED imagesshow that the single-stage growth film A contains significantmultiple domains and is of lesser quality than films B and C.(b) Film B is of similar thickness to film A, but it was grownin two stages. The first ML was grown with the substrateheld at 300◦ C. The subsequent 4 layers were grown with thesubstrate held at 155◦ C. Film B shows no signs of multipledomains. (c) Like film B, film C (10 ML) was grown usinga two-stage growth method and shows no signs of multipledomains. The self-contained, ordered growth described in thischapter results in films up to 10 ML thick with long-rangeordered domains. . . . . . . . . . . . . . . . . . . . . . . . . . 73xxiList of Figures4.5 LEEM results of 1.5 ML C60 single-stage growth showing mul-tidomain diffraction (a) typical of single stage growth recipes,bright-field LEEM image showing contrast between first andsecond layer (b), and dark-field LEEM images correspondingto R30◦ (c), +14◦ (d), in-phase (e), -14◦ (f) domains relativeto the Au(111) lattice. Examples of locations where grainsappear to be nucleated at step edges are indicated by arrowsin (d), including a 60◦ bend at the right-most arrow indicativeof the underlying Au(111) surface. . . . . . . . . . . . . . . . 754.6 Data from STM experiment on 1 ML C60/Au(111) using thefirst stage of our growth recipe. Film grown in OMBE andtransferred to STM chamber under vacuum (≤ 1×10−5 mbar).(a) STM image of 1 ML film. The step edge through the centerof the image is a step in the Au substrate (∼ 0.24 nm). TheC60 overlayer ‘blankets’ the step edge with no change in therotational or translational domain. The dark spot is a pit inthe Au substrate confirmed by its height. Single bright spotindicates surface contamination, likely incurred during thetransfer. (b) Fine electronic structure of fullerene molecules(taken on a different sample than in (a)). C60 is oriented intwo configurations: hexagon down (“dogbones”) or C-C bonddown (“cheerios”). This data is consistent with the preferentialorientation of C60 on Au(111) described in literature. (c) FFTof (a), confirming a single rotational domain. . . . . . . . . . 765.1 ARPES spectra of clean Au(111) taken with He lamp (hν =22.1 eV, T = 10.5 K). (Left) Fermi surface of Au(111) substrateafter being prepared for growth. Area enclosed by grey dottedline is original data; outside data is generated by symmetrizing(rotating) original data. (Right) High symmetry cut at ky = 0(gold dashed line in (a)), showing Rashba splitting of theAu(111) surface state. Quality of data indicates clean, flatsingle-crystal Au(111). . . . . . . . . . . . . . . . . . . . . . . 78xxiiList of Figures5.2 ARPES spectra of clean Au(111) taken with the p-polarizedXUV source (hν = 22.8 eV, T = 20 K), EB = (−10, EF ). . . 795.3 ARPES spectra of clean Au(111) taken with the unpolarizedHe lamp source (hν = 22.1 eV, T = 20 K), EB = (−6, EF ).Note that surface state contrast has been enhanced for visual-ization purposes. . . . . . . . . . . . . . . . . . . . . . . . . . 805.4 ARPES spectra (ky = 0) and EDC of 1 ML C60/Au(111)taken with our XUV source (hν = 22.8 eV, T = 12 K). (Top)C60 HOMO and HOMO-1 as well as some prominent Au(111)bands are labelled. (Bottom) EDC plot including the fit, withpeak center and FWHM values. The location of the HOMOrelative to EF is determined by a Gaussian fit to the EDC. . 825.5 ARPES spectra (ky = 0) and EDC of 1 ML C60/Au(111)taken with our He lamp source (hν = 22.1 eV, T = 9 K).(Top) C60 HOMO and HOMO-1 as well as some prominentAu(111) bands are labelled. (Bottom) EDC plot including thefit, with peak center and FWHM values. The location of theHOMO relative to EF is determined by a Gaussian fit to theEDC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.6 Unexpected bands not obviously attributable to Au(111). Al-though the ARPES spectra on ML C60/Au(111) does notobviously show bands above the C60 HOMO, by adjusting theXUV source photon-energy from hν = 22.8 eV to hν = 25 eV,we are able to discern a linearly-dispersing band that extendsthrough the C60 HOMO and all the way to EF (pink boxeddata; light pink dashed line serves as a guide to the eye). Thisdispersion is clearly different from the surface state that isapparent in this energy range on pure Au(111) (gold boxeddata). Note that all data is normalized within its respectiveplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84xxiiiList of Figures5.7 High symmetry cuts taken at ky = 0 show a linearly-dispersingfeature extending through the C60 HOMO and band gap toEF . (a) (left) Region above HOMO shows no obvious features,but (right) normalized data in that isolated region showsmultiple linearly-dispersing features. (b) An example linearly-dispersing feature extends several eV below EF but does notdisperse in kz, indicating that it is a surface-resonant bulkband. (Pink dashed lines serve as a guide to the eye.) Datataken at T = 9 K. . . . . . . . . . . . . . . . . . . . . . . . . 855.8 Comparison of constant energy cuts of 1 ML C60/Au(111),taken with XUV (left) vs He lamp (right) light sources. CECsare taken near EF at equivalent binding energies (EB). Photonenergies were approximately 22.8 eV (XUV) and 22.1 eV (Helamp). Data taken at T = 9 K. . . . . . . . . . . . . . . . . . 875.9 Comparison of a CEC taken at 0.2 eV below EF on 1 MLC60/Au(111) with DFT and experimental data on pristineAu(111). (a) DFT 5-layer slab calculation of the Au FermiSurface. (b) A Fermi Surface contour of an Au(111) surfacemeasured with a momentum microscope is included as anadditional point of comparison (image adapted from Tusche etal.). (c) CEC of 1 ML film at E−EF = −0.2 with XUV source(hν = 22.8 eV). The relevant (experimentally accessible) regionof the calculation is indicated by the blue rectangle. The lightgreen circle and rounded hexagon highlight the Au surfacestate and the sp band. The light green highlights are overlaidon only half of the data, to avoid obscuring all of the data.The spectral features overlaid by the light green highlightscould be attributed to the surface state and the sp band ofthe Au; the dispersion that is visible in the region betweenthe light green overlay is clearly inconsistent with the spectralfeatures expected from an Au(111) FS, and thus cannot beattributed solely to the Au(111) substrate. . . . . . . . . . . . 88xxivList of Figures5.10 Constant energy cut of 1 ML C60 on Au(111), taken at E −EF = −0.2 eV (XUV, hν = 22.8 eV). Grey dashed hexagonsdemarcate the C60 Brillouin zone. Note that these hexagonsare located approximately 1 eV closer to EF than the top ofthe C60 HOMO (Fig. 5.4). . . . . . . . . . . . . . . . . . . . . 895.11 ARPES spectra of linearly-dispersing features found at Kpoints of C60 BZ. (Left) Constant energy cut at E−EF = −0.2eV shows diffracted replica of the surface resonance Au spband, with the C60 BZ overlaid in dashed grey lines; thesereplicas are due to the epitaxial C60 supercell and are onlyvisible on a highly ordered sample. Purple and red dashedlines indicate the constant ky slices that are taken to producethe images to the right. (Right) linearly-dispersing features,formed by the crossing of replica bands at the K and K’ pointsof the C60 BZ (see circular inset at top left). Note that hereprime denotes the second BZ. . . . . . . . . . . . . . . . . . . 905.12 A comparison of the C60/Au(111) system in real space (left)and reciprocal space (right). A superstructure in real-spaceleads to a new periodicity and new (smaller) Brillouin zone inreciprocal-space; because of the new periodic potential, theoriginal bands get folded into this new BZ. . . . . . . . . . . 915.13 A model of how the C60 2√3-type superstructure’s Brillouinzones tile to fill the Au(111) BZ at the Fermi surface (theAu sp band and surface state are delineated in green). Fourtimes the Γ− M C60 cut is equivalent to the Γ− K cut for Au.Three times the Γ− K C60 cut is equivalent to the Γ− M cutfor Au. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925.14 Illustration of first fold of the Au sp band given the C60superstructure. (a) Au BZ (yellow) and sp band at the FermiSurface (green) are folded across the edge (dashed purple) ofthe C60 BZ (dashed black) resulting in a new band (purple).(b) Folding of the Au sp band into the C60 BZ, taking intoaccount the system’s 6-fold symmetry. . . . . . . . . . . . . . 93xxvList of Figures5.15 Illustration of second fold of the Au sp band given the C60superstructure. (a) Au BZ (yellow) and sp band at the FermiSurface (green) are folded across the 2 edges (dashed purpleand dashed blue) of the C60 BZ (dashed black) resulting innew bands (purple and blue). (b) Folding of the Au sp bandfully into the C60 BZ, taking into account the system’s 6-foldsymmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.16 Constant energy cut of 1 ML C60/Au(111), taken at E−EF =−0.2 eV, with band folding model overlaid. Bands not seendue to matrix element effects not shown in this model. . . . . 955.17 This series of images shows our complete band folding model,comprising 12 bands (left), the 2 bands that are removed (mid-dle), and the remaining 10 bands that we use for comparison toour XUV (p-polarized, hν = 22.8 eV) data. Because ARPESspectra intensity fluctuates as a function of photoemissionselection rules, in is unsurprising that we do not see all 12bands in our data. For clarity in comparison, we remove these2 bands and keep the relevant 10. Rest assured, the other 2bands are visible in data collected with an alternate photonsource (Fig. 5.18). . . . . . . . . . . . . . . . . . . . . . . . . 965.18 Comparison of Fermi Surface spectra taken on monolayer C60with unpolarized 22.1 eV He lamp light source (left) vs. p-polarized 22.8 eV XUV light source (right). ARPES spectraintensity fluctuates as a function of photoemission selectionrules; relevant parameters include light source polarizationand photon energy. In this case, 10/12 bands from our modelfit the XUV data on the right, and the other 2 bands arevisible in the He lamp data on the left. . . . . . . . . . . . . . 97xxviList of Figures5.19 Comparison of slope of replica band with Au sp band. (Left)High symmetry cut at ky = −0.36 A˚−1 on 1 ML C60/Au(111)showing replica bands (taken with XUV, hν = 25 eV, T =9 K). Data was passed through the denoising convolutionalneural network described in Section 2.5. Lorentzian peakswere fit to the right side of the left cone-like feature using arolling fit (see Fig. 5.22 for further information); centers offit results are indicated by turquoise dots. A linear fit to thecenters of those peaks results in the purple dashed line. Thisline has a slope of -7.9 ± 0.2 and matches our replica banddata well. (Middle) Fit is plotted on, and agrees with, ourraw data. (Right) High symmetry cut at ky = −0.72 A˚−1 onpristine Au(111) showing sp band (taken with He lamp, hν =22.1 eV, T = 10.5 K). This value of ky contains the portionof the sp band equivalent to the section that results in therelevant replica band, assuming band folding has occurred.The purple dashed line has the same slope as the fit result fromthe replica band with a constant offset chosen to allow the lineto overlay the sp band. The fit result from our replica banddata matches the slope of the sp band in pristine Au(111),further supporting agreement between our model and data. . 985.20 Linearly-dispersing features that lie at the K points of the 1stBZ (ky = −0.36) with linear fits on both the (a) raw and (b)denoised XUV data, along with (c) a comparison of the 2 fitsoverlaid on top of both the raw and denoised data. . . . . . . 100xxviiList of Figures5.21 Comparison of raw and denoised data of linearly-dispersingfeature with fits. a) Raw data with fits: (i) raw data, (ii)initial fit, (iii) datapoints to be discarded marked in blue (forthe purposes of generating a better fit), (iv) final fit on rawdata, excluding some data points. (b) Denoised with fits usingthe same initial parameters as in a (ii) and a (iv) (for b (ii)and b (iii), respectively). (c) (i) Denoised data with the rawdata fit in purple (a (ii)) and the denoised fit in turquoise(b (ii)). Note that not only is the fit from the denoised databetter when compared to the underlying data in (i), but thefits cannot easily be visibly compared to the raw data, becausethe feature is so faint (ii). . . . . . . . . . . . . . . . . . . . . 1015.22 Description of fitting procedure: Lorentzian peaks are fit inthree discrete sections (bottom, middle, and top of “cone”);the number of peaks expected is specified per section (2, 2,and 1, respectively). For each section, data is sliced in y anda “rolling fit” is applied. For example: We fit the (a) top ofour cone with (b) a y range of 0.1 eV (bracket), a window of+/- 0.02 eV, and 20 steps. These parameters mean that eachy center value is 0.1 / 20 = 0.005 eV apart. For each y centervalue, we get an average y slice (where, for every x value, they center +/- 0.02 eV values are averaged, and thus a line plotof eV vs intensity can be made). (c) We then fit a singleLorentzian peak to that line data. (d) Finally, we add the(x=Lorentzian peak center, y=y center value) (circled withblack arrow pointing to it) to our list of coordinates, whichwe use to find our best fit lines. . . . . . . . . . . . . . . . . . 1025.23 ARPES spectra and EDC of 5 ML C60/Au(111) taken withour XUV source (hν = 22.8 eV, T = 10 K). The location ofthe HOMO and HOMO-1 relative to EF is determined by twoGaussians fit to the EDC. The (bottom) EDC plot includesthe fit, reporting the peak center and FWHM values. . . . . . 104xxviiiList of Figures5.24 ARPES spectra and EDC of 5 ML C60/Au(111) taken withour He lamp source (hν = 22.1 eV, T = 27 K). The location ofthe HOMO and HOMO-1 relative to EF is determined by twoGaussians fit to the EDC. The (bottom) EDC plot includesthe fit, reporting the peak center and FWHM values. . . . . . 1055.25 Comparison of our 5 ML C60 band structure data with pub-lished experimental data and calculations. (a) Bandstructureof our 5 ML C60/Au(111) film (XUV, hν = 22.8 eV, T =10 K). (b) Latzke and Ojeda-Aristizabal et al.’s publishedwork of 5 ML C60/Bi2Se3. (c) Adaptation of Latzke andOjeda-Aristizabal et al.’s figure depicting (left) the curvatureof their experimental data and (right) their calculated resultsfor single layer C60/Bi2Se3 band structure. The lines from thecalculation that best fit the curvature data are highlighted inred (right) and plotted over the data (left). (d) Schematics ofthe C60 BZ and the relevant HS cuts for (left) our data and(right) Latzke and Ojeda-Aristizabal’s data. . . . . . . . . . . 1065.26 Comparison of the HOMO and HOMO-1 peak positions andwidths at high symmetry points in a 5 ML C60 sample. (Top)High symmetry cut of C60 band structure including HOMOand HOMO-1. Integration windows are indicated around eachhigh symmetry point. (Bottom) EDCs with Gaussian fitsreveal that the peak location and bandwidths of the HOMOand HOMO-1 remain quite consistent across high symmetrypoints K, Γ, M, Γ′, and M′. . . . . . . . . . . . . . . . . . . . 108xxixList of Figures5.27 Comparison of high symmetry cut data of a 5 ML C60/Au(111)film to band structure calculations. (a) HS data of our film,taken with the XUV source (hν = 22.8 eV), including centerenergies and fwhm. (b) Band structure calculation for fcc C60(applicable to bulk C60 at room temperature). Black dashedline indicates top of HOMO in (b), which is considered EF inJalali-Asadabadi’s calculation. For easier comparison with ourdata, an offset was applied to (b)’s y-axis such that the centerof the calculated HOMO at Γ is at -2.08 eV (grey dottedline). (c) Band structure calculation for C60 with 4 distinctorientations (applicable to our low-temperature sc phase witha 4 unit basis). Note that the dispersion in the HOMO atthe Γ point the data better agrees with Laouini’s calculateddispersion at Γ than Jalali-Asadabadi’s calculation. This isunsurprising given that our data was taken at T = 10 K andthe C60 would be in the sc phase. . . . . . . . . . . . . . . . . 1095.28 ARPES spectra of 5 ML C60/Au(111) taken with XUV (hν =22.8 eV, T = 10 K). (a) Constant energy cuts of C60 at energiesapproximating the top, middle, and bottom of the HOMOand HOMO-1. (b) The high symmetry points and relativeBrillouin zones of C60 and Au(111). (c) Vertical slice taken atkx = Γ (depicted by the dashed purple lines) illustrating thedispersion of the C60 band manifolds; the top (green), middle(dark red), and bottom (brown) energies of the HOMO andHOMO-1 are shown with minor ticks and labels. . . . . . . . 110xxxList of Figures5.29 ARPES spectra of 5 ML C60/Au(111) taken with He lamp(hν = 22.1 eV, T = 27 K). (a) Constant energy cuts of C60at energies approximating the top, middle, and bottom ofthe HOMO and HOMO-1. (b) The high symmetry pointsand relative Brillouin zones of C60 and Au(111). (c) Verticalslice taken at kx = Γ (depicted by the dashed purple lines)illustrating the dispersion of the C60 band manifolds; the top(green), middle (dark red), and bottom (brown) energies ofthe HOMO and HOMO-1 are shown with minor ticks and labels.1115.30 Comparison of raw and denoised data of the C60 band structure(taken with the XUV source). Top plots illustrate raw (left)and denoised (right) data, while bottom plots present thecurvature of each. Data is smoothed using a Gaussian filterbefore taking the curvature (the 2nd derivative along the y-axis). Although the curvature of the denoised data crisplydepicts the prominent doubled structure at the top of eachband, it appears to wash out some of the lower structurevisible in the curvature of the raw data. . . . . . . . . . . . . 1125.31 ARPES spectra (ky = 0) of 10 ML C60/Au(111) taken withour He lamp source (hν = 22.1 eV, T = 10.5 K). . . . . . . . 1135.32 EDC of 10 ML C60/Au(111) band structure, including theHOMO and HOMO-1. The location of the peaks relative toEF is determined by a fit with 2 Gaussian peaks. . . . . . . . 1145.33 Summary of band structure data taken with XUV source onpristine Au(111) (gold, hν = 25 eV), 1 ML C60 (green, hν= 22.65 eV), and 5 ML C60 (grey, hν = 22.8 eV). (a) Datacovers EB = (−4.4, EF ). Each data set is normalized. (b)Same data as in (a) but EB = (−1.2, EF ). This illustrates thedistinct spectral features visible only in the 1 ML C60/Au(111)(described further in Section 5.2.2), in juxtaposition with theAu ss and the 5 ML C60 band gap. Each newly-limited dataset is normalized and maximum intensity is set to 0.8 for thesake of feature visibility. . . . . . . . . . . . . . . . . . . . . . 115xxxiList of Figures6.1 Artistic rendering of TR-ARPES experiment on C60/Au(111),using ScientaOmicron’s DA30 hemispherical analyzer andconducted with UBC’s 3.1/6.2 eV pump-probe set up. Imageshows a 1.55 eV seed pulse passing through a barium boratenonlinear optic crystal used for frequency doubling. Datadisplayed in the analyzer is from the work described in thischapter. This image is an adaptation of a figure created by acolleague for Science 366, 1231-1236 (2019). . . . . . . . . . . 1176.2 Time-resolved and angle-integrated scan of the dynamics ofour 10 ML C60/Au(111) film, taken with our 6 eV source inFeb. 2023 (T = 10.6 K). This plot illustrates the pump effect(dark is signal intensity), where we expect pumped signal onlyat or after zero delay. In our case, the CT1 (red) and CT2(yellow) are visible beginning at a delay of up to -0.5 ps, dueto our having a time resolution of ∼ 500 fs. The pump effectof the S1 is not visible in this plot due to the oversaturatedsignal up to the Au(111) Fermi energy. Visibility of the CT2signal is achieved by taking a log plot of the heatmap data(colorbar inset) and is necessary because the excitonic signalsare very weak; this is also why the signal below EF appearsoversaturated. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119xxxiiList of Figures6.3 Time-resolved and angle-integrated scan of the dynamics ofour 10 ML C60/Au(111) film, taken with our 6 eV sourcein Feb. 2023 (T = 10.6 K). This plot illustrates the pumpeffect, where we expect signal above EF only at or after zerodelay. This plot has not been oversaturated, therefore the CT2(yellow) is close to invisible (in comparison to the discernibleintensity in the 2.4 - 3.0 eV region of Fig. 6.2). We can,however, detect some increase in pumped signal in the S1. Itis perhaps slightly more obvious in the inset image, whichillustrates all three states with different saturation levels (the3 excitonic states are indicated by a yellow, red, and greybar on the left axis). Note how the S1 state gets brighter atpositive delay. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1206.4 Energy distribution curves (EDCs) of the S1, CT1 and CT2states integrated over negative delay (-1 to -0.5 ps, blue), zerodelay (-0.5 to 0.5 ps, orange), and positive delay (0.5 to 1 ps,green). (Top) Linear plot shows the S1 state is least prominentat negative delay, more prominent at zero delay (-0.5 to 0.5ps), and most prominent at positive delay. (Bottom) Logplot highlights the dynamics of the CT states, with the CT1displaying the same dynamics pattern as the S1, in contrast tothe CT2 that is almost uniquely populated at time zero. Thesedynamics agree with literature that suggests direct populationof the CT2 and subsequent decay into the longer-lived CT1and S1 states. . . . . . . . . . . . . . . . . . . . . . . . . . . . 121xxxiiiList of Figures6.5 TR-ARPES spectra and EDC of the CT2 at Γ taken in Febru-ary 2023. Data integrated in θ approximating kx = (-0.13,0.13) A˚−1 as illustrated in the inset image of hexagonal BZ:purple line represents available data, pink line indicates inte-gration window. (Top) Time-resolved and angle-integratedheatmap of the CT2. (Bottom) EDC at zero delay (integratedfrom -0.5 to 0.5 ps). Three peaks are visible in both images;the EDC is fit with three Gaussians, allowing for a constantoffset. Peaks are found to be at 2.57 eV, 2.76 eV, and 2.96 eV.1236.6 TR-ARPES spectra and EDC of the CT2 along Γ - K takenin June 2023. Data integrated in θ approximating kx =(0.02, 0.27) A˚−1 as illustrated in the inset image of hexagonalBZ: purple line represents available data, pink line indicatesintegration window. (Top) Time-resolved and angle-integratedheatmap of the CT2. (Bottom) EDC at zero delay (integratedfrom -0.5 to 0.5 ps). Three peaks are visible in both images;the EDC is fit with three Gaussians, allowing for a constantoffset. Peaks are found to be at 2.58 eV, 2.78 eV, and 3.04 eV.1246.7 TR-ARPES spectra and EDC of the CT2 along M - K taken inJune 2023, with data spanning -1 to 1 ps delay. Data integratedin θ approximating kx = (0.02, 0.27) A˚−1 as illustrated in theinset image of hexagonal BZ: purple line represents availabledata, pink line indicates integration window. (Top) Time-resolved and angle-integrated heatmap of the CT2. (Middle)EDC at zero delay (integrated from -0.5 to 0.5 ps) with fitwhere peak values and FWHMs are allowed to vary. (Bottom)EDC at zero delay (-0.5 to 0.5 ps) with fit where lowest peakvalue is fixed at 2.57 eV. All other parameters are allowed tovary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126xxxivList of Figures6.8 TR-ARPES spectra and EDC of the CT2 along M - K taken inJune 2023, with data spanning -0.5 to 0.5 ps delay. Data inte-grated in θ approximating kx = (0.02, 0.27) A˚−1 as illustratedin the inset image of hexagonal BZ: purple line representsavailable data, pink line indicates integration window. (Top)Time-resolved and angle-integrated heatmap of the CT2. (Mid-dle) EDC at zero delay (integrated from -0.5 to 0.5 ps) with fitwhere peak values and FWHMs are allowed to vary. (Bottom)EDC at zero delay (-0.5 to 0.5 ps) with fit where lowest peakvalue is fixed at 2.57 eV. All other parameters are allowed tovary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.9 EDC of the full energy range acquired at Γ in February 2023showing our best fit and the fit components. (Initial angularintegration in θ approximating kx = (-0.13, 0.13) A˚−1.) (Top)EDC of all three excited states, taken at Γ and integrated from0.25 to 0.5 ps. The best fit of this data includes seven Gaussianpeaks, a Fermi-Dirac (which takes into account the Au(111)signal), and allows for a constant offset. This represents theminimum number of contributions that enable an accuratefit. (Bottom) Plot of the fit components along with peakenergies and FWHMs. The seven peaks are found to be atthe following locations: (S1) 1.63 eV, 1.8 eV, (CT1) 1.98 eV,2.12 eV, (CT2) 2.5 eV, 2.75 eV, 2.96 eV. . . . . . . . . . . . . 1296.10 Log plot of the EDC and fit from Fig. 6.9 including labels ofthe relevant states and residuals of the fit, showing no obviousanisotropy or structure. . . . . . . . . . . . . . . . . . . . . . 130xxxvList of Figures6.11 TR-ARPES spectra and EDC centered on the CT1 along Γ - Ktaken in June 2023. Data integrated in θ approximating kx =(0.02, 0.27) A˚−1 as illustrated in the inset image of hexagonalBZ: purple line represents available data, pink line indicatesintegration window. (Top) Time-resolved and angle-integratedheatmap centered on the CT1. (Bottom) EDC integrated from0 to 1 ps and fit with 3 Gaussian peaks as well as a Fermi-Diracfunction (and allowing for a constant offset). Peaks are foundat (inferred S1 peak below data minimum) 1.87 eV, (CT1)2.12 eV, and (bottom of CT2) 2.48 eV. . . . . . . . . . . . . . 1316.12 TR-ARPES spectra and EDC centered on the CT1 along M - Ktaken in June 2023. Data integrated in θ approximating kx =(0.02, 0.27) A˚−1 as illustrated in the inset image of hexagonalBZ: purple line represents available data, pink line indicatesintegration window. (Top) Time-resolved and angle-integratedheatmap centered on the CT1. (Bottom) EDC integrated from0 to 1 ps and fit with three Gaussian peaks as well as a Fermi-Dirac function (and allowing for a constant offset). Peaksare found at (inferred S1 peak below data minimum) 1.68 eV,(CT1) 2.21 eV, and (bottom of CT2) 2.52 eV. . . . . . . . . . 1326.13 TR-ARPES spectra and TDC with (decay constant) fit ofthe CT2 along Γ - K taken in June 2023. Data integrated inθ approximating kx = (0.02, 0.27) A˚−1 (see inset hexagon).(Top) Time-resolved and angle-integrated heatmap of theCT2 with a source time resolution of 225 fs. (Middle) TDCintegrated across full energy range and fit with a Gaussianconvolved with an exponential (and allowing for a constantoffset), resulting in a decay constant of 119 fs. (Bottom)Residuals of the fit. . . . . . . . . . . . . . . . . . . . . . . . . 135xxxviList of Figures6.14 TR-ARPES spectra and TDC with (decay constant) fit ofthe CT2 along Γ - M taken in June 2023. Data integrated inθ approximating kx = (0.02, 0.27) A˚−1 (see inset hexagon).(Top) Time-resolved and angle-integrated heatmap of theCT2 with a source time resolution of 225 fs. (Middle) TDCintegrated across full energy range and fit with a Gaussianconvolved with an exponential (and allowing for a constantoffset), resulting in a decay constant of 124 fs. (Bottom)Residuals of the fit. . . . . . . . . . . . . . . . . . . . . . . . . 1366.15 TR-ARPES spectra and TDC with (decay constant) fit ofthe CT2 at Γ taken in February 2023. Data integrated inθ approximating kx = (-0.13, 0.13) A˚−1 (see inset hexagon).(Top) Time-resolved and angle-integrated heatmap of theCT2 with a source time resolution of 500 fs. (Bottom) TDCintegrated across full energy range and fit with a Gaussianconvolved with an exponential (and allowing for a constantoffset), resulting in a decay constant of 204 fs. (Bottom)Residuals of the fit. . . . . . . . . . . . . . . . . . . . . . . . . 1376.16 Comparison of the CT2 decay constant for each energy peak.(Top) Time-resolved and angle-integrated heatmap of the CT2taken at Γ in February 2023 (time resolution: 500 fs), dividedinto three energy regions containing the top (green), middle(orange), and bottom (blue) CT2 peaks. (Middle) TDCsintegrated across the three distinct energy ranges and each fitwith a Gaussian convolved with an exponential (and allowingfor a constant offset). The resultant decay constants are 204fs, 181 fs, and 232 fs. (Bottom) Table reporting the relevantenergy regions and results of fits where τ is the decay constant,t0 is the location relative to time zero of the peak, and ∆tis the time-resolution in the fit (the FWHM of the Gaussiancomponent). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138xxxviiList of Figures6.17 Difference map of the time-resolved and angle-integrated scanof the dynamics of our 10 ML C60/Au(111) film, taken at Γ(February 2023). Data integrated in θ approximating kx =(-0.13, 0.13) A˚−1. The first four columns of the data wereaveraged and then subtracted from the rest; pumped signal isshown in red, unpumped signal is white, and depletion is blue.Horizontal red streaks indicate multi-peak structure in theS1 and CT1. The approximate energy regions of the excitedstates are indicated by the grey (S1) and red (CT1) verticalbars to the left of the plot. This plot has been oversaturated(by capping the intensities) to better illustrate this structure.It is worth noting that the depletion visible below EF at laterdelays (blue) may be attributable to the pre-pulse at -20 pspresent in our February measurement. . . . . . . . . . . . . . 1396.18 Difference map of the time-resolved and angle-integrated scanof the dynamics of the CT1 and CT2. Scan taken along Γ - Kon a 10 ML C60/Au(111) film, taken with our 6 eV source inJune 2023 (T = 10.6 K). Data integrated in θ approximatingkx = (0.02, 0.27) A˚−1 as illustrated next to the title: purpleline represents available data, pink line indicates integrationwindow. The first four columns of the data were averaged andthen subtracted from the rest; pumped signal is shown in red,unpumped signal is white, and depletion is blue (see Fig. 6.17for scale bar). There may be some multi-peak structure in theCT1, but higher statistics are needed to confirm. . . . . . . . 140xxxviiiList of Figures6.19 Pump effect and dynamics of the CT1 and CT2 along M - Kon a 10 ML C60/Au(111) film, taken with our 6 eV source inJune 2023 (T = 10.6 K). Data integrated in θ approximatingkx = (0.02, 0.27) A˚−1 as illustrated next to the title: purpleline represents available data, pink line indicates integrationwindow. (Upper) Difference map of the time-resolved andangle-integrated scan of the dynamics. The first four columnsof the data were averaged and then subtracted from the rest;pumped signal is shown in red, unpumped signal is white, anddepletion is blue. (Lower) EDC of the raw data, integratedfrom -1 to 0 ps delay (blue), from 0 to 1 ps delay (gold), andfrom 1 to 5 ps delay (green). Although the heatmap suggestsmultiple peaks in the CT1 (similar to Fig. 6.17), the lack ofdiscernible peak structure in the EDC plot integrated from1 to 5 ps (green line) implies a need for better statistics tofacilitating fitting to these peaks. . . . . . . . . . . . . . . . . 1416.20 EDCs of the CT1 and S1 states integrated over 5 ps, 10 ps, and20 ps rolling integration windows. Data is from our Februarymeasurement, taken at Γ (integrated in θ approximating kx =(-0.13, 0.13) A˚−1). Note that the 20 ps plot shows less noisewhile preserving the peak dynamics visible in the smallerintegration windows. . . . . . . . . . . . . . . . . . . . . . . . 1436.21 EDCs of the CT1 and S1 states integrated over 20 ps with afit overlaid. Bottom panels display the fit results, includingthe peak centers, FWHMs, and heights for the CT1 (orange)and S1 (blue) states over time. . . . . . . . . . . . . . . . . . 1446.22 EDCs of the CT1 and CT2 states integrated over 10 ps witha fit overlaid. Bottom panels display fit results for the peakcenters, and heights for the CT1 (orange) and CT2 (green)states over time. Data from our June measurement, takenalong Γ - K (integrated in θ approximating kx = (0.02, 0.27)A˚−1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145xxxixList of Figures6.23 EDCs of the CT1 and CT2 states integrated over 10 ps witha fit overlaid. Bottom panels display fit results for the peakcenters, and heights for the CT1 (orange) and CT2 (green)states over time. Data from our June measurement, takenalong M - K (integrated in θ approximating kx = (0.02, 0.27)A˚−1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1466.24 Comparison of TDCs of the CT1 (integrated from E - EHOMO= 2.0 - 2.3 eV) from normalized data collected with 500 fs and225 fs time-resolution. The resolution of the data (particularlyat later delays in the 225 fs data) is insufficient to supporta conclusive comparison of decay constants. However, thedata loosely substantiates a shorter decay constant for the225 fs data. Additionally, all three plots show the CT1 statepopulated for longer than the 1 - 1.5 ps previously reported.The decays in this plot are generated by fitting an exponentialto the normalized data at delays > 0. Note that a moreaccurate fitting technique for decay constants involves fittingfor peaks and then subsequently fitting for the amplitudesover time; this exponential fit is helpful for getting a bettersense of the data. . . . . . . . . . . . . . . . . . . . . . . . . . 1476.25 Comparison of decay constants for the CT1 from data collectedwith 500 fs and 225 fs time-resolution. These fits are the resultsof taking EDCs of the CT1 with a rolling integration window of10 ps and then fitting the heights of those peaks (as a functionof delay) with a Gaussian convolved with an exponential. TheFebruary data was limited to a range of delays similar to thedata acquired in June. The decay constants are comparableacross measurements. . . . . . . . . . . . . . . . . . . . . . . 148xlList of Figures6.26 Analysis of decay constants assuming a decay from the CT1into the S1. The top image shows the pumped signal dueto both the CT1 and S1 (integrated from 1.7 to 2.3 eV).Data is shown for delays from -1 ps to 100 ps, with -1 to1 ps shown in the inset. The bottom image illustrates a fitusing a model that assumes a decay from the CT1 into theS1. Here, the upper state (CT1) is modeled with a simpleexponential (upper state model = Aue−(x−t0)/τu) while thelower state (S1)’s model incorporates a rise time that is fixedto the decay constant of the upper state (lower state model =Ale−(x−t0)/τl(1− e−(x−t0)/τu)). Note that τu is allowed to varyduring the fit. The full model (upper state model + lowerstate model) is fit to the data resulting in the green line anddecay constants of 5.28 ± 0.90 ps for the CT1 and 38.06 ±4.95 ps for the S1. . . . . . . . . . . . . . . . . . . . . . . . . 1506.27 Summary of exciton energies for different C60 film thicknessesand different substrates. . . . . . . . . . . . . . . . . . . . . . 1546.28 Summary of exciton decay constants for different C60 filmthicknesses and different substrates. . . . . . . . . . . . . . . 1556.29 CECs throughout the CT1, with a red box around the plottaken at the CT1 fitted peak value (the relevant EDC plotis included for reference at the top of the figure). Raw datais enclosed by the gray dashed line and used to reconstructthe full first BZ (yellow dashed line). Scans were taken at apositive delay of 600 fs. Heatmap data is linear and normalized.1596.30 CECs throughout the CT2, with orange boxes around the plottaken at the CT2 fitted peak values (the relevant EDC plot isincluded for reference at the top of the figure). Raw data isenclosed by the gray dashed line and used to reconstruct thefull first BZ (yellow dashed line). Scans were taken at zerodelay. Heatmap data is linear and normalized. . . . . . . . . . 160xliList of Figures6.31 Dispersion at various HS points throughout the BZ, takenat zero delay. Top image shows dispersion across the K - Γ- K cut, including dispersion in the CT2 energy range at Γ.Middle image shows the slice taken across opposing M points.Bottom image shows slice taken at the bottom of the BZ.Inset images display relevant slices. HS points have not beenlabelled because the k-correction of this data is still beingfinalized. Recall: Γ - K ∼ 0.42 A˚−1 and Γ - M ∼ 0.36 A˚−1. . 1626.32 Comparison of angular dispersion at Γ of both the CT2 andCT1 from our February (left) and June (right) experiments.Both images show a parabolic feature that extends throughthe CT2, with 3 flat bands at energies of 2.53/2.51 eV, 2.8eV, and 2.99 eV. The highest peak is too faint to be fit inthe June data presented here; however, the three flat bandscorrespond to the peaks visible in Figures 6.5 to 6.8, whichincludes three-peak fits to the June data. The CT1 is presentin both images at very similar energies: 2.11 eV and 2.16 eV.An M-like dispersion is visible in the CT1 in February, butnot obviously in June. The side branches of the M may havebroadened into the two large regions of intensity (in the CT1and symmetric around Γ) visible in June. There is a regionof intensity right at Γ in February (the point of the M) thatcoincides with a lack of signal in June; possible explanationsfor this include the unintentional change in the polarization ofthe probe between experiments or a slight difference in offsetangle (in ky). The discontinuities in both datasets (obvious inFebruary image, less apparent but at 2.5 eV in June image)occurs where datasets are stitched. In February data, the CT2taken at zero delay with the CT1 at 0.6 ps positive delay. InJune, all data was acquired at zero delay. . . . . . . . . . . . 163xliiList of Figures6.33 Comparison of the pumped angular dispersion centered at Γ(Γ - K orientation) with a tight-binding-style calculated CTexcitonic band structure of the low-temperature simple cubicC60 and the high-temperature fcc structure, as published byPac et al. Data has been oversaturated (by capping the inten-sities) to better illustrate the band structure, and includes anEDC with a three-peak fit, where peaks are likely attributableto the manifold of excitonic states. Red dashed lines illustratelocation of calculated exciton bands at Γ on our data. Energyaxes are comparable across images; however, our data (andpeak values) may be overestimated by as much as 0.3 eVrelative to the calculations. This is because our data is plottedrelative to the middle of the HOMO and calculations are oftenplotted relative to the top of the valence band. See Table 6.9for a quantitative comparison of fit and calculated energies. . 1656.34 Comparison of the pumped angular dispersion centered atΓ (Γ - K orientation) with the calculated band structure forthe LUMO of the low-temperature simple cubic C60 and thehigh-temperature fcc structure, as published by Laouini et al.Data has been oversaturated (by capping the intensities) tobetter illustrate the band structure, and includes an EDC witha three-peak fit, where peaks are likely attributable to themanifold of excitonic states depicted in Fig. 6.33. Note thatthe sc calculation does indicate the presence of some parabolicbands centered along Γ, although they are depicted in the Γ -M and Γ - R bulk HS cuts, making direct comparison difficult.As a reminder, K points would be expected at approximately0.42 A˚−1 in our data. . . . . . . . . . . . . . . . . . . . . . . . 166xliiiList of Figures6.35 CEC of a damaged film at a binding energy of 0.7 eV belowEF . The original film was 5 ML C60/Au(111) film. Afterapplying the XUV source (2.4 eV) pump at various powers upto 840 mW, the band structure of the resulting film (shownhere) resembles the replica structure in single ML C60/Au(111)films described in Ch. 5. Signs of sample damage, such as anincrease in background counts, began after applying 500 mWof pump power to the sample. . . . . . . . . . . . . . . . . . . 1686.36 Population of excitonic states illustrating pre-pulse effect atzero delay (data is from February 2023). (a) Plot of thepopulation of the CT2 (integrated from 2.3 to 2.6 eV), CT1(2.0 to 2.3 eV), and S1 (1.7 to 2.0 eV) from -1 to 100 ps.Inset image shows same data from -1 to 1 ps (region to theleft of the black dashed line in the principal image). Thegrey intensity at negative delay indicates (pre-)population ofthe S1, likely due to the pre-pulse at -20 ps (note that thelifetime of the S1 is expected to be > 20 ps. (b) Integratingover narrower ranges in energy allows us to determine whichenergies show signs of pre-population. Above 2.05 eV, signsof pre-population abruptly vanish, indicating that excitonicstates above 2.05 eV have lifetimes < 20 ps. . . . . . . . . . . 1706.37 EDCs integrated over negative (blue), zero (orange), andpositive (green) delays along the Γ (February), Γ - K (June),and Γ - M (June) slices. Although the excited states (andFermi edge) are visible in all 3 scans, note the relative intensityof the CT2 to the CT1 in the February data as opposed tothe June data. All angular integration windows were in θapproximating kx = (-0.13, 0.13) and (0.02, 0.27) A˚−1 andare illustrated by the pink line relative to the BZ, consistentwith the rest of this chapter. . . . . . . . . . . . . . . . . . . 173xlivList of FiguresA.1 Compilation of CECs through excited states from differentexperiment runs (February, May, and June 2023). Energiesassociated with the CT1 are boxed in red, energies associatedwith the CT2 are boxed in orange. Raw data is enclosed bythe gray dashed line and used to reconstruct the full first BZ(yellow dashed line; distance from Γ to K = 0.42 A˚−1). Datais normalized, and the scale bar applies to all images. Forexperiment parameters associated with each measurement, seeTable 6.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201A.2 Comparison of CECs taken at 2.96/3.0 eV from February andJune data. The intensity in the two images appears rotated 60degrees relative to one another. Yellow hexagon delineates BZedges; Red hexagon scale was chosen to align with intensityfor the purpose of illustrating the 60 degree rotation. Rawdata is enclosed by the gray dashed line. . . . . . . . . . . . . 202A.3 Comparison of CECs taken at 2.2 eV from February andMay data. The intensity in the February data appears at theedges of the BZ (yellow dashed line; distance from Γ to K= 0.42 A˚−1); the intensity in the May data appears furtherinside the BZ. This may be a real effect, or it is possible thatthere is an error in the k-correction of this data. Analysis isongoing. Additionally, the February data shows a star-likepattern around Γ, while the May data does not. (See text forexplanation.) . . . . . . . . . . . . . . . . . . . . . . . . . . . 202A.4 Cone-like feature that appears just above the Fermi energy ofAu(111) after 3 to 7 days of TR-ARPES measurement withthe 3.1/6.2 eV pump-probe source. This image was taken inFebruary with the pump blocked. . . . . . . . . . . . . . . . . 203xlvList of FiguresA.5 Comparison of two different fits to an EDC (integrated from0.25 to 0.5 ps) that includes all three excitonic states (S1, CT1,and CT2). Both fits include a fixed number of Gaussians aswell as a Fermi-Dirac to account for the Au(111) signal, andthey allow for a constant offset. The first fit (left) includesthree peaks, one for each excitonic state. The fitted peaklocations are 1.7, 2.11, and 2.68 eV. The residuals (plottedbelow) show substantial structure, and the DW score is 0.670.The second fit (right) includes seven peaks. The fitted peaklocations are 1.63, 1.8, 1.98, 2.12, 2.5, 2.75, and 2.96 eV. Theresiduals (plotted below) show much less structure, and theDW score is 1.097, indicating improved model accuracy. Datais from February 2023. . . . . . . . . . . . . . . . . . . . . . . 205A.6 Comparison of two different fits to an EDC (integrated from0.25 to 0.5 ps) that includes the lower two excitonic states (S1,CT1). Both fits include a fixed number of Gaussians as wellas a Fermi-Dirac to account for the Au(111) signal, and theyallow for a constant offset. The first fit (left) includes twopeaks, one for each excitonic state. The fitted peak locationsare 1.72, and 2.10 eV. The residuals (plotted below) showsubstantial structure, and the DW score is 0.343. The secondfit (right) includes four peaks. The fitted peak locations are1.63, 1.8, 1.98, and 2.12 eV. These peak results match thelower four peaks found in the more accurate fit of Fig. A.5.The residuals (plotted below) show much less structure, andthe DW score is 0.671, indicating improved model accuracy.Data is from February 2023. . . . . . . . . . . . . . . . . . . . 206xlviList of FiguresA.7 Comparison of two different fits to an EDC (integrated from-0.5 to 0.5 ps) that includes the upper excitonic state (CT2).Both fits include a fixed number of Gaussians as well as aFermi-Dirac to account for the Au(111) signal, and they allowfor a constant offset. The first fit (left) includes one single peakfor the excitonic state. The fitted peak location is 2.69 eV(with a FWHM of 3.33 eV). The residuals (plotted below) showsubstantial structure, and the DW score is 0.137. The secondfit (right) includes three peaks. The fitted peak locations are2.57, 2.76, and 2.96 eV. The residuals (plotted below) showmuch less structure, and the improved DW score is 0.383. Itis worth noting that this DW score, though improved, stillindicates that our model may not fully describe our data.Data is from February 2023. . . . . . . . . . . . . . . . . . . . 207A.8 Comparison of two different fits to an angle-integrated TDCof the CT2. The upper plot shows the time-resolved and angle-integrated heatmap of the state; the TDC data is generatedby integrating over the full energy range. Both fits are aGaussian convolved with an exponential; the first fit (left)allows for a constant offset, and the second fit (right) allowsfor a linear offset. The DW test gives scores of 1.113 and1.673, respectively, indicating that including a linear offsetresults in a model that better describes the data. The physicaljustification of a linear offset is not currently known, butshould be investigated. It is also worth considering to whatextent the DW test results should be relied upon within the[1, 3] result interval. Data is from February 2023. . . . . . . . 209xlviiList of FiguresA.9 Comparison of two EDCs integrated over different delays ((-0.5, 1) and (0.25, 0.5) ps) fit with the same three-peak model.The EDCs cover the same energy range that includes all threeexcitonic states (S1, CT1, and CT2). The fit is a sum of threeGaussians as well as a Fermi-Dirac to account for the Au(111)signal and allows for a constant offset. The DW scores are0.334 and 0.670, respectively. The discrepancy in scores maybe attributable to the prominence of the CT2 in the first EDC(which includes zero delay) relative to the second EDC (whichexcludes zero delay). The CT2 intensity is fairly localized tozero delay and the state contains three visible peaks that weare fitting with a single Gaussian in this model. This figureillustrates the importance of the integration window whenbuilding a fit model, pariticularly near zero delay in our TRdata. Data is from February 2023. . . . . . . . . . . . . . . . 210B.1 LEED image of graphene/H/SiC. Image taken at beam energyof 130 eV. Brightest spots are SiC, blurry spots are graphene.Graphene-SiC reconstruction not visible due to inadequatesample quality. Image taken after 7 (cumulative) hours ofannealing at 475◦ C. This graphene sample is inadequate andmust be replaced. . . . . . . . . . . . . . . . . . . . . . . . . . 211B.2 LEED image of graphene/Cu/SiC. Image taken at beam en-ergy of 131 eV. Brightest spots in outer ring are graphene (bluearrow), surrounded by 6 spots that are due to the graphene-SiCreconstruction (green arrow). Additional spots surroundingthose 6 are due to the Cu-intercalation, causing a 6√3 x 6√3reconstruction (yellow arrow). SiC (1 x 1) shows up as faintspots between the more complex patterns (orange arrow). . . 212xlviiiList of FiguresB.3 LEED image of C60 on graphene/Cu/SiC taken at beam en-ergy of 24 eV. The 6 bright spots in each ring suggest a(reproducible) dominant domain, however the rings illustratethe multi-domained nature of this sample. The 3 rings corre-spond to the first 3 orders of C60 spots. The dark oval in thisimage – to the top-right of the electron gun – is an artifact ofour LEED set up and is not related to the sample. . . . . . . 213C.1 A polarization ellipse that illustrates the ellipsometric anglesΨ and ∆. In this image, the electromagnetic (elliptically po-larized) wave propagates out of the page towards the reader(along the positive z-axis). Elliptic polarization can be de-scribed by the phase shift ∆ (the relative phase of the vibra-tions along the x and y directions) and the relative amplitudeX/Y , which can be expressed as tan(Ψ) = XY . If the beamis linearly polarized, ∆ = 0 or π. In this case, the vibrationsalong x and y are either in-phase or have the opposite phase,and the ellipse will collapse into a straight line that connectsopposite corners of the purple rectangle. If a beam is circularlypolarized, Ψ = π4 and ∆ =π2 or −π2 . This implies that the xand y vibrations have the same amplitude, and the polariza-tion ellipse becomes a circle. This figure is adapted from theHandbook of Ellipsometry (Chapter 1, Figure 1.1). . . . . . . 216C.2 Example of ellipsometry data with fit overlaid. Data plottedas eV vs. Ψ (red) and eV vs. ∆ (green). Film thickness wasdetermined to be 4.29 ± 0.005 nm. Data analyzed on August24, 2022. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217xlixList of FiguresD.1 Streak-correction of the HOMO of a 5 ML C60/Au(111) film,integrated over all Φ. Top image shows the streaked raw datawith the MDC (integrated over all EK) overlayed. Middle im-age shows the MDC with a 4th-order polynomial fit overlayed.The streak-correction ratio array is generated by dividing thefit by the data. Bottom image shows the HOMO data afterthe streak-correction ratio array has been applied to each rowof the data (in EK). . . . . . . . . . . . . . . . . . . . . . . . 219D.2 CECs of the raw data compared to the streak-corrected datafor the HOMO (left set of panels) and the HOMO-1 (right setof panels). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220E.1 Timeline of my PhD including significant experimental issues,solutions, and successes. . . . . . . . . . . . . . . . . . . . . . 224F.1 Transformation matrix for a slab of 4 layers with hexagonalsymmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232F.2 Slab of 4 layers with hexagonal symmetry shown in xcrysden. 233F.3 Example slab with vacuum layer added shown in xcrysden. . 234F.4 Example slab with extended number of unit cells drawn toillustrate hexagonal structure. . . . . . . . . . . . . . . . . . . 234lList of AbbreviationsA˚ A˚ngstro¨mARPES Angle-resolved photoemission spectroscopyCT Charge transferCuPc Copper phthalocyanineD/A (electron-) Donor-acceptoreV Electron voltsfcc Face-centered cubicℏ Plank constantHOMO Highest occupied molecular orbitalLEED Low energy electron diffractionLN2 Liquid nitrogenLUMO Lowest unoccupied molecular orbitalMBE Molecular beam epitaxyOMBE Organic molecular beam epitaxyOPV Organic photovoltaicsQCM Quartz crystal monitorsc Simple cubicSTM Scanning tunneling microscopy/eSTS Scanning tunneling spectroscopyTR-ARPES Time- and angle-resolved photoemission spectroscopyTSP Titanium sublimation pumpUHV Ultrahigh vacuumZnPc Zinc phthalocyanineliAcknowledgementsThe straightforward and structurally-imposed linearity of a dissertationbelies the pervasive ambiguity and sometimes circuitous path that leadsto a doctorate. The route is replete with adventure and pitfalls, and I amimmensely grateful for the company I have had along the way:Sarah and David – Thank you for serving as my guides, for supportingme, and for always finding time when there is none.LAIR, Ultrafast, and 479 – You are the best mix of kind and competent,of helpful and driven. Thank you for your patience in answering a plethoraof questions, and for the time all of you were willing to contribute to helpingwith this project.Rysa and Ketty – The long nights in the lab were better because of you;I am so excited to see what you both accomplish next.Stepan – I will forever be thankful for the boon of a great friendship.Deborah and Alan – You have done more for me than I could ever recount,repay, or even know. All of the adventures are thanks to you.Tim – You are the most unexpected and extraordinary turn of my life sofar. There is no one I would rather have by my side, for this journey or anyother.liiChapter 1Introduction1.1 Motivation: The Bigger PictureIn 2016, a Nature review article described photovoltaics as “the most elegantdemonstration of renewable energy generation,” calling organic photovoltaics“arguably the most radical approach” [1]. While conventional silicon-basedsolar cells (CSCs) currently dominate the photovoltaic industry [2], organicphotovoltaics (OPVs) are nearing commercial-viability with private compa-nies [3, 4] working on this technology alongside countless academic institutionsand research groups throughout the globe [5, 6]. OPV materials have the ca-pability to fundamentally alter our engagement with solar energy: the devicesthese materials comprise can be thin, flexible, light-weight, semi-transparentand of tunable colour [7], and perform better under lower light intensitiesand at higher temperatures [8]; they are low-cost and take relatively littleenergy to produce. The combination of these qualities enables a degreeof adaptation and integration of solar harvesting capabilities into commoninfrastructure, that appeals to architects, commercial construction firms,the automobile industry, environmental policy groups, and your averagehomeowner alike. However, increases in efficiency are required before OPVdevices can become a viable alternative to CSCs. It’s worth noting thatincreases in film longevity would also contribute to commercial viability;however, it is likely that solving efficient charge extraction may help increaselongevity as well. This is because most of the detrimental processes in OPVsare side reactions from the excited state: if the excited states efficientlytransfer into separable charges that are extracted, they will not create thedetrimental side reactions.This work marks the first results from a collaborative research project11.2. The Role of Excitons in OPV Materialsat the University of British Columbia’s Stewart Blusson Quantum MatterInstitute (SBQMI), established to investigate the physics underlying poorcharge transfer – one of the principal causes of OPV’s inefficiency. Theoverarching goal of this project is to use a combination of scanning tunnelingmicroscopy and spectroscopy (STM and STS) and time- and angle-resolvedphotoemission spectroscopy (TR-ARPES) to detail the spatial and temporalenergy landscape and electronic structure of our OPV films, grown in-housein our organic molecular-beam epitaxy (OMBE) growth chamber.1.2 The Role of Excitons in OPV MaterialsIn order to better understand charge transfer and separation in OPVs, itis important to consider excitons in the context of OPV materials. Whenan electron is excited in an OPV, it remains coulombically bound with itshole, forming an exciton. The state of an exciton depends on the incomingphoton energy, the allowed transitions of the system, and the electron (e−)and hole (h+) wavefunctions. Figure 1.1 provides a representative exampleof an exciton of HOMO-LUMO character, where the exciton state residesbelow the single particle transport gap. Excitons in organic solar cells aremore tightly bound with larger binding energies (∼ 100 to 500 meV) thanthose in conventional solar cells (10 meV) [9, 10], making them harder todissociate into free charges.1.2.1 Excitonic vs. Conventional Solar CellsIn a conventional solar cell, the Wannier excitons produced through photoex-citation have binding energies of ∼ 10 meV [9] and are able to spontaneouslydissociate at room temperature (kBT ∼ 25 meV). An excitonic solar cell[11, 12], on the other hand, is typically composed of organic semiconductors,such as planar or bulk heterojunction cells [13, 14] and small molecule solarcells [15], or it is made up of a hybrid structure (containing both organic andinorganic materials) like in dye-sensitized solar cells [16]. It is worth notingthat some purely inorganic photovoltaics are also excitonic, for example21.2. The Role of Excitons in OPV MaterialsFigure 1.1: A representative illustration of an exciton with the hole located atthe top of the highest occupied molecular orbital (HOMO) and the electronlocated at the bottom of the lowest unoccupied molecular orbital (LUMO).The electronic band gap, optical band gap, and the binding energy of theexciton (EB) are depicted.certain perovskite solar cells [17], but the unelaborated term “excitonic solarcell” likely implies an organic component. The organic semiconductors inexcitonic solar cells have weaker (non-covalent) intermolecular interactionsand more localized electrons. Localized electrons with higher effective massesare unable to screen charges as effectively, resulting in a lower dielectricmaterial [11] (and thus less effective screening and a greater Coulomb po-tential well around the charges). More localized electrons also results in alarger electron/hole wavefunction overlap [18]. This combination results inan exciton with a Coulomb binding energy that is greater than the averagethermal energy of the charge carrier (E > kBT ); therefore the Frenkel exci-tons photoexcited in OPVs require additional input energy (typically on theorder of a few hundred meV) to separate [10, 19].11Excitonic solar cells can also contain more delocalized charge-transfer (CT) excitons(to be discussed in more detail in Section 1.3.3): CT excitons have lower binding energiesthan Frenkel excitons (10 to 100 meV [19]) but are still often > kBT .31.2. The Role of Excitons in OPV MaterialsTo understand this quantitatively, consider the following: In a conven-tional solar cell, the effective mass of an electron in the semiconductor, meffis less than the mass of an electron in vacuum, me. In an excitonic semi-conductor, however, the lower dielectric constant (and the correspondinglyhigher binding energy of the exciton) results in the charge carrier becomingmore localized, with a higher effective mass. Thus, in an excitonic solar cell,meff > me. We can see the relationship between the effective mass of theelectron and the localization of the charge carrier by calculating its Bohrradius:rB = r0ϵmemeff(1.1)In order to generate free charge carriers, the Coulomb potential energyof the exciton must be less than its average thermal energy:E = (q24πϵϵ0)(1rc) < kBT, (1.2)where q is the electronic charge and ϵ0 is the permittivity of free space.Solving for rc allows us to define the critical distance between charges – whenrc > rB, excitonic behaviour is observed. Thus, whether a material behavesas a conventional (γ < 1) or an excitonic (γ > 1) semiconductor can bedefined by the following ratio [20]:γ =rcrB≈ ( q24πϵ0kBr0me)(meffϵ2T). (1.3)1.2.2 Exciton Dissociation in OPVsIn the context of OPVs, excitons are typically discussed in the frameworkof (electron-) donor/acceptor (D/A) heterojunctions. These type-II [21]D/A heterojunctions are comprised of two materials with different electronaffinities. The donor material (e.g. ZnPc) has a lower electron affinity, andthe acceptor material (e.g. C60) has a higher electron affinity. The canonicaldescription of exciton dissociation in a D/A heterojunction involves thefollowing 4-step process, and is illustrated in Fig. 1.2:41.2. The Role of Excitons in OPV MaterialsFigure 1.2: Illustration of canonical exciton dissociation across a donor(grey)/acceptor (purple) interface. Step 1: the electron is photoexcited fromthe HOMO to the (in this case) LUMO and forms an exciton with its hole.Step 2: the exciton diffuses to the D/A interface. Step 3: the electron isattracted to the higher electron affinity acceptor material and the excitonstraddles the D/A interface. Step 4: the exciton dissociates across theinterface resulting in free charge carriers.1. Photoabsorption and exciton generation primarily in the donor mate-rial.2. (Neutral) exciton diffusion to the D/A interface.3. Electron is attracted to the higher electron affinity acceptor material;the electron and hole form a geminate pair (still held by Coulombattraction) across the D/A interface. The exciton is now in what iscalled a “charge-transfer” (CT) exciton state across the junction.4. Exciton dissociates across the interface resulting in free charge carriers.In 1986, Tang proposed that the difference in LUMO levels betweenthe donor and acceptor materials could serve as the driving force for initial51.2. The Role of Excitons in OPV Materialsexciton dissociation [22], but extensive subsequent research in this field hasleft the precise mechanism of exciton dissociation in OPVs an open question.Recent hypotheses include the following:• Deibel et al.’s (2009) suggestion that charge delocalization occurs overmultiple polymer segments and/or fullerene molecules [23].• Lee, J. et al.’s (2010) determination that hot exciton processes (wherebythe CT exciton is located at or across a heterojunction interface) donot contribute to photogenerated charge carriers at all [24].• Bakulin et al.’s and Grancini et al.’s (2012) conclusion (contradictoryto Lee’s) that hot interfacial CT states with delocalized wave functionsincrease free polaron generation [25, 26].2• Jailaubekov et al.’s (2012) slightly different take that the hot interfacialCT exciton’s electron and/or hole wave functions are localized onmolecules far away from the interface [28].• Ge´linas et al.’s (2014) suggestion of a model that assumes delocalizedπ-electron states over the entire ordered fullerene domain [29].• Lee, M. H. et al.’s (2015) use of a hybrid model to describe inter-facial CT state dynamics, in which semiclassical quantum dynamicsdescribes charge dissociation (on a shorter timescale) and Redfieldtheory describes relaxation (on a longer timescale) [30].3• Smith et al.’s (2015) discussion of phonon-assisted ultrafast chargeseparation in PCBM. Smith argues that the highest CT state is reso-nant with lower delocalized states, which provides a bridge across thedonor/acceptor interface. Vibrational fluctuations facilitate electronictransitions across this bridge, enabling the exciton to avoid decayinginto the lower, trapped CT states [31].2For further discussion of Bakulin and Grancini’s reports on hot CT states, see Ref.[27].3Lee suggests that a CT state evolves into a charge-separated state due to quantumdiffusion, but these charge-separated states eventually relax to low-energy CT states as aresult of their interaction with the thermal bath.61.2. The Role of Excitons in OPV MaterialsAlthough today the canonical description of OPV systems typicallyincludes both donor and acceptor, certain materials operate as an OPV ontheir own. In such a case, charge transfer states might span across multiplemolecules rather than bridging a heterojunction interface, and a phenomenonintrinsic to the material would be responsible for exciton dissociation. Forexample, pure C60 thin films, when optically excited, produce a cascade ofexcitonic states [32, 33] and (with a metal/organic Schottky contact) generatea photocurrent [34, 35].A recent paper by Fomichev,∗ Ruocco,∗ Tully, and Berciu discusses therole of electron-phonon coupling in directly facilitating exciton dissociationin C60-like materials [36].4 This phenomenon may be driven by the so-called carrier-lattice interaction: this interaction is a consequence of theCoulomb force between the carrier and the lattice, and it can lead to ionsbeing displaced from their equilibrium positions (particularly in polarizablematerials like C60) with carriers of different charge (e.g. electron and hole)distorting the lattice in opposite directions [37]. If one considers an excitonan electron-hole pair that can be separated by a range of distances (i.e.delocalized to varying extents depending on, for example, the excitonicstate), then a tightly bound (Frenkel) exciton and a more delocalized (CT)exciton will have differing effects on lattice distortion. An excess chargecarrier (e.g. an isolated electron or hole) will result in a local lattice distortionthat dresses the carrier, forming a polaron. Because electrons and holes haveopposite charges, however, the local lattice distortion formed by each of themwill also be opposite to one another. This means that the more closely boundthe electron and hole, the more their charge clouds will cancel each otherout, and the smaller the local lattice distortion will be. Correspondingly, amore delocalized exciton contains an electron and hole that are further apart,resulting in a stronger electric potential around each carrier and inducing alarger local lattice distortion that produces polarons. For a more intuitive,pictorial description, see Fig. 1.3.Carrier-lattice coupling lowers the energy of the delocalized state throughpolaron formation: the electron-phonon interaction can potentially overscreen4(∗) denotes equal contributions by Fomichev and Ruocco.71.2. The Role of Excitons in OPV MaterialsFigure 1.3: An illustration of the local lattice distortions created by isolatedexcess charge carriers or a delocalized exciton (left) versus those created by atightly bound exciton (right). (Left) An excess charge carrier like an electron(blue) or a hole (red) will result in a local lattice distortion that dresses thecarrier, forming a polaron. The opposite charges result in correspondingopposite local lattice distortions. (Right) When opposite charges are tightlybound in a Frenkel exciton, their charge clouds will partially cancel, resultingin a weaker electric potential and a smaller local lattice distortion. Figurepublished in Ref. [36].the electron-hole attraction, turning it repulsive at short distances and drivingexciton dissociation under certain circumstances. This may explain whyoptically exciting OPV materials such as C60 – polarizable and with strongly-bound excitons – generates a photocurrent even in the absence of D/Aheterojunction architecture.In OPV heterojunction devices, fullerene derivatives are nearly ubiquitousacceptor materials, due in part to their high electron affinities and their longexciton diffusion lengths (the characteristic distance travelled prior to anexciton’s recombination) [33, 38]. In order to understand exciton dissociationin more complex heterojunctions – often with disordered interfaces andmultiple materials – it is helpful to first consider a simplified model systemlike neat (i.e. pure) C60 films. In the research covered in this thesis, we workwith neat C60 due to its foundational status as a prototypical OPV acceptormaterial and because it is a photo-absorbing excitonic semiconductor, withboth Frenkel and CT excitonic states.5 Using a single material OPV to5CuPc/C60 was also the sample material for the hot-charge transfer hypothesis described81.3. Introduction to Buckminsterfullerenesbetter understand these systems has several advantages: it enables us toavoid complications arising from disordered interfaces, fewer materials maybe easier to model, and (given the number of unknowns in this project) asingle-material system serves as an excellent experimental foundation forfuture experiments involving more complex systems.1.3 Introduction to Buckminsterfullerenes1.3.1 The Discovery of C60In 1984, Harry Kroto (from the University of Sussex) reached out to fellowchemist Richard Smalley, asking to use his lab’s cluster beam apparatus6at Rice University to study linear chain molecules of carbon – moleculesthat he thought had been created in the atmospheres of carbon-rich redgiant stars. It took a year, but Smalley finally decided to grant Kroto somebeamtime. In 1985, Kroto, Smalley, and Robert Curl (a collaborator ofSmalley’s studying semiconductor clusters), together with graduate studentsJames Heath and Sean O’Brien, discovered that carbon will make truncatedicosahedral molecules when one makes a vapour of carbon atoms and allowsit to condense in helium [39]. These molecules resemble the geodesic domespopularized by an American architect of the 20th century, Richard Buckmin-ster Fuller (a perhaps more colloquial example of the fullerene molecule’sshape in the macroscopic world is a soccer ball). In 1996, Curl, Kroto, andSmalley were awarded the Nobel Prize in Chemistry for this discovery [40].While their work was built on the foundation of many – Archimedes (whois acknowledged as the first to conceive of a truncated icosahedron), E. G.Osawa (a Japanese physical-organic chemist who determined that carbonin such a structure would likely be stable [41]), D. Jones7 (who conceivedof closed spheroidal cages made of graphene sheets [42]), and Bochvar andearlier and discussed in Ref [28].6A laser pulse is fired at a sample, creating a plume of vaporized material. A subsequentstream of helium causes the cooling and clustering of the material, which is then collectedfor analysis by a mass spectrometer.7A scientific journalist writing as ‘Daedalus’ in the New Scientist in 1966; not mysupervisor!91.3. Introduction to BuckminsterfullerenesFigure 1.4: Model of C60, also known as a buckyball: a truncated icosahedronwith 12 pentagons, 20 hexagons, and a total of 90 covalent bonds. C60 is acommon acceptor molecule used in OPVs [49].Galpern [43] as well as Stankevich et al. [44] (who performed the relevanttheoretical calculations over a decade before Curl, Kroto, and Smalley’sdiscovery), to name but a few – the discovery of fullerenes has paved theway for novel research in various fields from advanced materials (carbonnanotubes, as an example) to pharmaceutical science (where buckyballs havebeen considered as a multifunctional system for drug and gene delivery)[40, 45].1.3.2 Form and Phases of C60C60 is a truncated icosahedron (an Archimedian solid with 32 faces composedof two or more types of regular polygon) consisting of 12 pentagons and 20hexagons, with a total of 90 covalent bonds (60 single bonds and 30 doublebonds). Each C atom is part of 2 hexagons and 1 pentagon and has 2 singlebonds and 1 double bond to satisfy carbon’s valence of 4. The atomic bondingin C60 can be approximated as having sp2 character, with carbon atomsforming 3 σ bonds and a p-orbital each and π bonds delocalized around themolecule [46–48]. Figure 1.4 provides an illustration of the molecule.101.3. Introduction to BuckminsterfullerenesAt temperatures above 260 K, C60 forms an fcc8 bulk crystal with alattice constant of 14.2 A˚ which when sliced in the 111 direction (i.e. thebody diagonal oriented vertically) results in a hexagonal Bravais latticeon the exposed surface [52]. C60 molecules have a diameter of 7.1 A˚ andthe distance between neighbouring molecules (center-to-center) is 10 A˚[53]. In this phase, the C60 buckyballs are orientationally disordered anduncorrelated with the neighbouring molecules [53] (the molecules “spin,”with a rotational correlation time9 of 9 to 12 ps [54, 55] and activationenergies around 60 meV [51]). The four molecules that comprise the fcc unitcell are thus indistinguishable. However, C60 undergoes a phase transitionat 260 K at which point the molecules become orientationally ordered,resulting in a simple cubic lattice with a 4 molecule basis (this transition hasbeen independently experimentally confirmed through X-ray diffraction andcalorimetry) [46, 47, 51, 53, 56]. The orientational ordering can be explainedby C60 crystals being held together through weak intermolecular interactions(van der Waals) as well as the molecules’ anisotropic electronic distribution:the 6:6 bonds (double bonds connecting two hexagons) are short and containa significant π-electron density, while the pentagons (consisting of long bonds)are relatively electron-poor. The electrostatic repulsive interactions can thusbe optimized by having the 6:6 bonds sit over a pentagon and having nocarbon atom situated above a carbon atom of a neighbouring unit. Due tothe icosahedral symmetry of the molecule, interactions between all 12 nearest-neighbours may be simultaneously optimized [47]. The inequivalence of the4 sites could come from a distortion of the lattice (where the lattice siteshave moved relative to one another – like a Peierls distortion), a distortionof the molecule (if the molecule became the shape of a football insteadof a soccer ball), or a relative orientational order of the molecules. The8Kra¨tschmer et al. [50] reported the first measurements on crystalline C60, and, usingX-ray powder diffraction data, identified the lattice structure at room temperature as hcp.However, it is now generally accepted that room temperature bulk C60 has an fcc structure.There are several possible reasons for this discrepancy, as outlined in Ref. [51]. Two ofthese reasons are paraphrased as follows: (1) The hcp and fcc lattices share many of thesame Bragg peaks, thus a subset of these peaks can be indexed as either. (2) Residualsolvent in the powder can alter the structure of C60, including by nucleating an hcp phase.9the average amount of time it takes a molecule to rotate 1 radian111.3. Introduction to Buckminsterfullereneslast is what fits best with both theory and experiment [53].10 Figure 1.5illustrates the transition from fcc to sc in C60; the transition is accompaniedby a lattice constant contraction from 14.2 A˚ to 14.05 A˚ (∼ 1%) [47, 59].Lattice parameters for C60 in its relevant phases are collected in Table 1.1,for convenient reference.Table 1.1: Lattice Parameters of C60 [53, 59–61]C60 Temperature Lattice Type Diameter or Lattice ConstantMolecule n/a n/a 7.1 A˚Bulk RT fcc 14.2 A˚Bulk (< 260 K) sc 14.05 A˚Thin film RT fcc(111) 10.05 A˚Thin film (< 260 K) 4 basis sc(111) 9.94 A˚At temperatures greater than 260 K, C60 molecules experience freerotation or rotational diffusion (i.e. they spin). Below 260 K, C60 films containjump rotational diffusion between two symmetry-equivalent but energetically-distinct orientations of the buckyballs [54]. A second phase transition occursat ∼ 85 K, below which the molecules are largely orientationally ordered,with a minority of the crystal structure occupying the less energeticallyfavourable of the two symmetry-equivalent orientations in the crystal from85 - 260 K.To summarize, solid C60 exists in 3 phases: [57]• T > 260 K, where C60 molecules are “spinning” in place (experienceisotropic reorientational diffusion) [54, 58],• 85 < T < 260 K, where the C60 molecules become orientationallyordered, thus lowering the symmetry of the crystal and transitioningfrom an fcc to an sc lattice with a 4 molecule basis (accompanied byan abrupt, albeit small, lattice contraction); hopping or flipping occurs10Note that NMR can be used to determine bond lengths in molecules by measuring theinternuclear distances in orientationally disordered materials [57, 58].121.3. Introduction to BuckminsterfullerenesFigure 1.5: Model of phase transition from fcc to sc lattice. (a) An fcc latticewith a 1 unit basis; face-centered atoms (or in this case, C60 molecules)are delineated with a dashed black outline, corner sites have a solid blackoutline, and all sites are equivalent. (b) sc lattice with a 4 unit basis, wherea corner site and 3 of the face-centered sites are inequivalent (indicatedwith grey, purple, orange, and pink). (c) Extension of lattice to illustratehow each basis forms its own sc lattice (example shown for orange basis).Color (shade) gradient goes from left (darker) to right (lighter) and servesas a visualization aid. (d) Top-down view of the sc C60 lattice, with the 4inequivalent orientations of C60 shown and circled in the corresponding color.Image (d) is adapted from David et al.’s 1991 Letter to Nature [47].131.3. Introduction to Buckminsterfullerenesbetween two energetically distinct orientational configurations (6:6 nextto pentagon, 6:6 next to hexagon) [46, 59],• and T < 85 K, where C60 molecules are largely orientationally ordered,though not completely locked in place – a minority (5:1 ratio) of thecrystal structure will take the slightly less energetically favourableorientation of the 2 orientations in phase II [46, 57, 62].In order to probe the electronic band structure of these C60-based ma-terials, high purity films with long-range order and consistent thicknessesexceeding a bilayer are required [32]. However, molecular films – includingC60 – often exhibit a high degree of disorder due to the soft potentials, multi-ple crystal structures, and weak epitaxy with typical substrates, compared totheir inorganic counterparts. As such, successful film growth requires carefulconsideration of both substrate and growth protocols.1.3.3 Excitons in C60Like many organic semiconductors, C60 contains a cascade of excited states,as illustrated in Fig. 1.6. By experimentally determining the binding energies,decay rates, and momentum dispersion of these excitons (and subsequentlycomparing them with theoretical calculations and models), we can betterunderstand the dynamics and (de-)localization of excitonic states in C60. Forexample, in the case of a direct gap semiconductor with an optically allowedtransition, an exciton may be resonantly excited at the gap. In the case of anindirect gap semiconductor, recent literature [9] indicates that the ARPESspectra of excitons11 appears below the conduction band (LUMO) minima,with the distance equivalent to the exciton binding energy (as depicted inFig. 1.1).The dispersion in momentum of the exciton’s spectra comprises Boltzmann-weighted contributions of different (broad or narrow) distributions of excitons.A narrow distribution results in a spectra that resembles the valence band(HOMO); the broader the distribution of excitons, the more conduction band11Excitons in indirect gap semiconductors can be indirectly formed via intervalleyscattering [66].141.3. Introduction to BuckminsterfullerenesFigure 1.6: Cascade of exciton states in C60 [63–65]. HOMO refers to thehighest occupied molecular orbital, and CT refers to the charge transferstates. Center energies and bandwidths are based on data discussed in thisthesis.character appears [9]. Although C60 has a direct gap at the X point, thetransition is optically forbidden [68, 69]; moreover, the delocalization in realspace of the higher order CT excitons remains an open question. Figure 1.7shows one possibility for the configurations of the CT1 and CT2 excitons,12but these states may be delocalized across more than two neighbouringmolecules. Thus, acquiring momentum-resolved spectral signatures of these12The majority of the existing literature refers to these excitonic states as CT1 and CT2;however, very recent results [67] suggest that these states are of singlet character, and arereferred to as S2 and S3, respectively. For the purposes of this thesis, I will use CT1 andCT2, unless otherwise noted.151.3. Introduction to BuckminsterfullerenesFigure 1.7: An illustration of the possible localization of the S1, CT1, andCT2 excitons in C60. Here the S1 (Frenkel) exciton has LUMO characterand is located on a single C60 molecule. The charge-transfer (CT) excitonsare of LUMO (CT1) and LUMO+1 (CT2) character, and are distributedacross neighbouring C60 molecules. The extent of the delocalization in theCT excitons remains an open question in the field, and a very recent paper[67] claims that the CT1 and CT2 are singlets and refers to them as the S2and S3, respectively.161.3. Introduction to Buckminsterfullerenesexcitons has potential to provide valuable insight into the location and spatialdistribution of these excited states. By understanding the dynamics andlocalization of excitonic states first in neat C60 – and later in more complexfilms containing donor molecules – we will be able to describe the processesthrough which exciton dissociation and free charge generation occurs inOPVs.In order to understand exciton dissociation in C60, we must build amap of its electronic structure that depicts both the ground state and theevolution of the excited state. A technique called angle-resolved photoemis-sion spectroscopy (ARPES) and its time-resolved counterpart (TR-ARPES)enables us to experimentally map the basic electronic structure and exci-tation landscape of C60; however, it requires C60 thin films with ordered,large-scale domains. Conducting these measurements (and thereby mappingC60’s excited states) requires several key experimental techniques, describedin further detail in Chapter 2:1. Molecular beam epitaxy (MBE, Section 2.1) is a sample growth tech-nique, where ordered, pure thin films are grown to a specific molecularthickness in ultra-high vacuum. In our case, we have developed growthrecipes for monolayer to (at least) 10-layer C60 films on Au(111) andthin film C60 on Cu-intercalated graphene/SiC. While MBE is not nec-essary to grow materials for OPV devices, it is how we chose to growsamples with high enough purity and large enough ordered domainsto facilitate the experiments we use to map the electronic structure ofC60.2. Low energy electron diffraction (LEED, Section 2.2) is a sample char-acterization technique that probes the first few layers of a sample usingelectron diffraction. The elastically-scattered electrons are collectedwith a phosphor screen. The location, sharpness, and number of LEEDspots provide information about the sample character and quality. Weuse LEED to ensure that we successfully grew a high quality film inour MBE, prior to ARPES measurement.171.3. Introduction to Buckminsterfullerenes3. Angle-resolved photoemission spectroscopy (ARPES, Section 2.3) pro-vides information on the electronic structure of materials by photo-exciting a material and capturing the energy and momentum infor-mation of the photoemitted photoelectrons. ARPES enables us toexperimentally map the basic electronic structure of C60, but it re-quires a sample that is ordered on the scale of the area probed (at least).ARPES is conducted in a UHV environment and probes the surface ofa material, thus the sample must also be clean and UHV-compatible.4. Time- and angle-resolved photoemission spectroscopy (TR-ARPES,Section 2.4) measures the energy and momentum of electrons as functionof time following excitation. It adds a pump beam of photons thatexcites electrons in the sample material from unexcited states to excitedstates. The probe beam then photoemits the excited electrons at aknown delay time from the pump, which are subsequently collectedby the ARPES detector. This process enables the measurement of theexcited states of a material: thus, this provides information on theexcitation landscape and dynamics of C60. TR-ARPES has similarsample requirements to those of static ARPES.5. Scanning tunneling microscopy (STM), though beyond the scope ofthis thesis, will provides important complementary data for this projectthrough its measurement of the local density of states in an unexcitedmaterial. STM also requires samples to be clean and UHV-compatible.Minimal STM data illustrating long-range sample order is includedin Chapter 4 of this thesis, and possibilities for relevant future STMmeasurements are discussed in Chapter 7.This thesis investigates charge-transfer dynamics in OPV materials bymapping the occupied electronic structure and probing the excited statesin C60 thin films. It marks the first results from our collaborative researchproject and our new MBE system, and presents the body of work that took usfrom film growth to successful TR-ARPES experiments. Chapter 4 discussesa novel growth recipe developed for C60 thin films on Au(111) that produces181.3. Introduction to Buckminsterfullerenesconsistent long-range order of single domains in films up to 10 monolayers(ML) thick. Chapter 5 presents equilibrium ARPES data on films of varyingthicknesses, and Chapter 6 contains TR-ARPES data of the excited statesin C60. Chapter 3 provides an overview of some experimental developmentsthat may be useful to future graduate students involved with this project.19Chapter 2Experimental and AnalysisTechniquesAs specified in Chapter 1, to gain a dynamical view of the excited statesof a material, we used the following techniques: MBE, LEED, ARPES,and TR-ARPES. This chapter provides detail on the these experimentaltechniques.Figure 2.1: Image of lab system set up, including our MBE, LEED chamber,and ARPES chamber. This set up facilitates in-situ sample growth, char-acterization, and analysis, while maintaining an ultra-high vacuum (UHV)environment. Our ARPES experiments can be performed at temperaturesas low as 4 K.202.1. Molecular Beam Epitaxy (MBE)2.1 Molecular Beam Epitaxy (MBE)Successful ARPES analysis of OPV materials requires high-quality, pure,samples, with long-range orientational order on the scale of the probe (lampor laser) size. Such samples are frequently epitaxially grown via MolecularBeam Epitaxy (MBE). Additionally, the fragility of organic thin films restrictsus to an ultra-high vacuum (UHV) environment. From 2017 to 2019, wecommissioned an OMBE system and connected it to our ARPES system,and now can grow, characterize, and analyze our films while maintaining aUHV environment at all times. Figure 2.1 shows the complete lab setup, andFig. 2.2 provides a labeled schematic of the MBE system. For an extensivedescription of our OMBE system, please see my MSc thesis [70]. Elementsmost pertinent to the work described in this thesis are included below.Developed in the late 1960s [71], MBE has been integral to semiconductortechnology, due to its ability to produce thin films with atomically flat,ordered layers of extreme purity that simulate the material’s bulk structure.Today, MBE can be used to grow complex films with multi-layered growthcomprised of multiple materials. In our case, we use MBE to grow pure,ordered C60 films, controlling for the number of layers and attempting tominimize grain boundaries and orientational disorder. The same approachcan be used to grow multilayer or doped films. The detailed growth procedureis described in Chapter 4.Molecular beam epitaxy is a growth technique that incorporates colli-mated, collision-free, molecular beams directed towards a substrate in a UHVenvironment, facilitating epitaxial growth of a sample [72]. MBE combineslow-growth rate, temperature control of the substrate, and in-situ characteri-zation techniques in a UHV environment to grow films of a specific atomicthickness and high purity. To paraphrase a simile from John Arthur,13 MBEcan, at its simplest, be understood as the ability to spray paint your deposi-tion molecules onto a substrate, controlling each atomic layer’s compositionand impurity level as you go [73]. There are six principal components to an13One of the pioneers of molecular beam epitaxy through his work with Alfred Cho atBell Laboratories on the epitaxial growth of GaAs in the late 1960s.212.1. Molecular Beam Epitaxy (MBE)Figure 2.2: Schematic of Scienta Omicron customized Lab10 MBE system.Does not include our home-built characterization chamber. Figure frommy MSc thesis [70] and adapted from the Scienta Omicron Lab10 systemmanual.222.1. Molecular Beam Epitaxy (MBE)MBE that enable this process:• temperature controlled and stabilized effusion cells for material evapo-ration• UHV• shutters• growth thickness measurement (quartz crystal monitors – QCMs)• sample holder with controlled temperature• characterization technique(s) (in our case, post-growth LEED) to assessfilm quality and often thicknessThe effusion cells hold crucibles which are typically made of quartz orPBN, depending on the temperatures required to sublime the depositionmaterial. The crucible stores the material of interest (often in powder form)and is heated to the desired temperature for sample deposition. Note thatthe sublimation temperature affects the deposition rate, which affects thefilm growth. Specifically, the flux impinging on the substrate surface isproportional to the equilibrium vapour pressure of the deposition materialin the Knudsen cell P (T ), the area a of the cell aperture, the mass of thedeposition material m, and the distance to the substrate L [74].F =P (T )aπL2√2πmkBT1s · cm2 (2.1)The effusion cells emit directional beams of molecules which must travelon a nearly collision-free path to the substrate. If the pressure of the chamberis too high (and thus the beam path is replete with collisions), the beamas it reaches the substrate will not be regular. Additionally, too high ofa pressure indicates the presence of extraneous atoms or molecules in thechamber that will contaminate your sample. In order to grow pure films,MBE’s must be kept at ultra-high vacuum levels; our system has a basepressure of < 1.0× 10−10 mbar, sufficient for most organic films.232.2. Low Energy Electron Diffraction (LEED)sample plate + heatersample substratecrucible shutterscruciblesQCMs(growth monitors) sample shutterretractabletungsten heating filamentswater coolingFigure 2.3: Depiction of a basic MBE set up, including crucibles for sampledeposition, QCM growth monitors, a retractable shutter to precisely controldeposition time, and the sample plate and heater. Image taken from myMSc thesis [70].2.2 Low Energy Electron Diffraction (LEED)In order to ensure our samples are clean, well-ordered, and of the expectedsymmetry and rotation, we perform low energy electron diffraction (LEED).Developed by Davisson and Germer at Bell Laboratories in 1927 [75, 76],LEED is a surface characterization technique that utilizes the wave mechanicsof electrons to probe the periodicity of crystalline materials. AlthoughLouis de Broglie had already proposed the possibility of electron diffractionas a consequence of wave mechanics in 1923 [77], Davisson and Germer’sexperiment definitively showed that electrons diffract off of crystalline surfacesand can thus be treated as both particles and waves.14 Though LEED was14The experimental discovery of electron diffraction actually resulted from a luckymistake: Davisson and Germer were conducting scattering experiments in 1925, when theglass vacuum tube enclosing their set-up cracked. The resulting leak had led their nickelsample to badly oxidize. In order to clean the sample, they subjected it to prolongedheating in vacuum (i.e. they annealed it). When they resumed their experiment, Davissonand Germer saw unprecedented intensity peaks. After observing the sample with the helpof a microscopist, they discovered that the polycrystalline nickel surface had reformed to242.2. Low Energy Electron Diffraction (LEED)developed in 1927, it was not until the 1970s – with the advent of the requisiteexperimental and theoretical techniques15 – that LEED became the powerfuland nearly ubiquitous tool it is today [80, 81].Put simply, LEED involves firing a low energy (10 – 300 eV [20]) beamof electrons normal to a crystalline surface. If the sample surface is cleanand ordered, it will behave like an optical diffraction grating: the incidentbeam is diffracted by the crystal structure into a discrete set of constructiveinterference beams. The diffracted beams are visualized using a phosphorscreen, and the resulting pattern provides information on the size and shapeof the unit cell, as well as the presence (if any) of multiple domains [82, 83].A depiction of a LEED set up is shown in Fig. 2.4. This schematic showsthe relative configuration of several important components. Including theelectron gun, sample, grids, microchannel plate(s), detection screen, andthe camera. After diffraction, the inelastically-scattered electrons (whichcontribute to overall background intensity in LEED images) are filtered outwith a series of concentric hemispherical grids. The first grid is connected toground in order to provide an essentially field-free region between it and thesample, thereby minimizing the electrostatic deflection of diffracted electrons.The second and third grids have different negative potentials, creating aseries of fields that retard the inelastically scattered electrons and onlyallow a desired (and small) energy-range of electrons to pass through. Thefourth grid is once again grounded to protect against field penetration of theinterim grids due to the large positive voltage that is applied to the phosphordetection screen (in order to accelerate the electrons) [84, 85]. Next, theremaining electrons are multiplied using a microchannel plate (MCP). MCPsare thin (∼ 2 mm) plates of highly resistive material (often lead glass) thatfunction as an electron multiplier while maintaining positional information.They are typically included in experimental setups where a research focusbecome a series of 10 distinct crystal facets. Davisson and Germer thus surmised that itwas not the structure of the atoms themselves that caused the intensity peaks, but ratherthe atomic arrangement within the crystal that did so. Therefore, in their subsequent andground-breaking experiment, they chose to use a single crystal nickel sample. Davisson wasa recipient of the 1937 Nobel Prize for his work on electron diffraction by crystals [78, 79].15Specifically, UHV technology and models for multiple scattering theory.252.2. Low Energy Electron Diffraction (LEED)will be molecular (or other sensitive) films that may be damaged from highenergy electron bombardment. MCPs amplify the diffracted beam by a factorof up to 107; because the diffracted beam is approximately 10−2 – 10−4 thecurrent of the primary beam, the amplification of the MCP enables visibleLEED patterns (measurable in real-time by a camera) with a primary beamcurrent on the order of nA rather than µA [84]. Finally, the electrons aredetected by a phosphor screen, providing an image of the diffraction pattern.An example of this pattern for a sample of single-layer C60 (with hexagonalsymmetry) can be seen in Fig. 2.5.LEED detection screenelectron gunmicrochannel plates (MCP)samplephoton-V1-V2grids x4(retarding field)vacuum+Vcamerae–Figure 2.4: Schematic of OMBE’s LEED configuration. Figure adapted frommy MSc thesis [70].The crystal structure of the sample can be related to the LEED spot262.2. Low Energy Electron Diffraction (LEED)Figure 2.5: LEED image of ordered monolayer C60 on Au(111), taken withan electron beam energy of 77 eV. Example diffraction spots are indicatedas nth order (green) and (n+1)th order (blue).positions by using Bragg’s Law [86]nλ = d sin θ, (2.2)the de Broglie equationλ =hmv(2.3)(where m is electron mass and v is its velocity), and the kinetic energyof the electronE =12mv2. (2.4)With these equations, an understanding of the experimental set upof LEED optics (see Fig. 2.6), and basic algebra, we find the followingexpression for the atomic row spacing (d) as a function of the diffractionorder of the spots (n), the kinetic energy of the diffracted electrons (E), and272.2. Low Energy Electron Diffraction (LEED)the configuration of the experimental set up (where x and R are distancesdefined by the sample’s position relative to the screen, as illustrated in Fig.2.6):16d =nRhx√2mEA˚. (2.5)LEED detection screenelectron gun samplecameraxRϴFigure 2.6: Illustration of how the observed LEED pattern depends on theconfiguration of the LEED optics. Figure obtained from my MSc thesis andadapted from Arthur T. Hubbard’s The Handbook of Surface Imaging andVisualization, p. 291 [70, 86].In addition to providing important information on the crystal structure ofthe sample, LEED spots demonstrate the presence of surface reconstructions,multiple domains, and provide information on the order of the film. Thesharpness of the diffraction spots implies long-range order; general disordertypically manifests as an overall weakening of the intensity of the diffractedbeams along with an increase in the background intensity [85]. Both surfacereconstructions and disorder due to multiple rotational domains may resultin extra LEED spots [85, 87], but multiple rotational domains are identifiableby replicas of the single-domained LEED pattern rotated relative to one16m is the electron mass and h is Plank’s constant282.3. Angle-Resolved Photoemission Spectroscopy (ARPES)another. The relative intensity of the LEED spots gives an indication ofthe prominence of any dominant domain [85]. Further discussion of surfacereconstructions and rotational domains, as well as LEED images of theAu(111) herringbone surface reconstruction and a C60 sample containingmultiple domains, can be found in Chapter 4, Figs. 4.1 and 4.4.For complete derivations, a thorough explanation of our experimentalLEED set up, Ewald spheres, a calculation of the penetration depth of LEEDanalysis (approximately 5 A˚), as well as a discussion of how to quantitativelycalculate scatted wave fields in the Born approximation using kinematictheory, I refer the reader to Chapter 3.2 of my MSc thesis [70].2.3 Angle-Resolved Photoemission Spectroscopy(ARPES)Angle-resolved photoemission spectroscopy, or ARPES, is a technique used tomap out the electronic structure of materials by photoexciting the electronsof a material above the vacuum level and capturing the angular distribution(and therefore energy) and momentum data of the emitted photoelectrons.Photoemission or photoelectron spectroscopy (PES) is a more general termthat refers to any measurement technique that utilizes the photoelectriceffect to measure the energies of the material’s electronic states. Althoughthe basic principal of PES has remained unchanged [88] since Hertz’s andHallwachs’ initial experiments in 1887 [89, 90] and Einstein’s subsequentintroduction of the photoelectric equation in 1905 [91], the evolution of therequisite experimental infrastructure (e.g. UHV systems, laser technology)as well as progress in crystal growth and MBE systems continues to enablenovel experimentation in this field. Today, PES has matured into severaldistinct measurement techniques including x-ray photoemission spectroscopy(XPS), 2-photon photoemission spectroscopy (2PPE), and angle-resolvedphotoemission spectroscopy (ARPES).The description of photoemission contained in this section is informed byand benefits from Damascelli’s Probing the Low-Energy Electronic Structure292.3. Angle-Resolved Photoemission Spectroscopy (ARPES)of Complex Systems by ARPES [92]. For additional in-depth study, I alsorefer the reader to Hu¨fner’s works on photoelectron spectroscopy [93].In ARPES, a monochromatic light source is directed at a sample materiallocated in a UHV environment, where it excites electrons from the sample.If the energy provided by the light source is sufficient to overcome the workfunction of the material, these photoelectrons then travel to the surface ofthe sample and escape through the surface potential barrier. After travellingthrough the vacuum between the sample surface and the detector, thephotoelectrons pass through a hemispherical analyzer (where a potentialdifference is applied between the two concentric hemispheres) before hittingthe detector (a schematic of the experimental setup is shown in Fig. 2.7).By measuring the kinetic energy of these photoelectrons for a givenemission angle, and by taking advantage of total energy and momentumconservation laws,Efinal − Einitial = hν (2.6)kfinal − kinitial = khν , (2.7)as well as the photoelectric effect, one can relate the kinetic energy (Ek)and momentum (K) of the photoelectron in vacuum to the binding energy(EB) and crystal momentum (k) inside the solid [92]. First, we find thatEk = hν − Φ− |EB|, (2.8)where Ek is the measured kinetic energy of the photoelectron, hν is thephoton energy, Φ is the work function of the material of interest, and |EB| isthe binding energy of the electronic state inside the solid. This relation isperhaps most intuitively understood pictorially, as illustrated in Fig. 2.8.In vacuum, the wavevector momentum of the photoelectron can be derivedfrom their kinetic energies and emission angles (as defined in Fig. 2.9):302.3. Angle-Resolved Photoemission Spectroscopy (ARPES)Figure 2.7: Geometry of an ARPES experiment; in our system, the θ motorcan be varied from -40◦ to 40◦ (as long as the He lamp is retracted), andthe ϕ motor from -40◦ to 10◦. The θ slit accepts photoelectrons from 30◦of emission angle (-15◦ to +15◦). In this figure, the black arrow representsincoming photons, and the blue beam represents the electrons emitted fromthe sample. This figure provides a 2D top view schematic (left), which showsthe ability to move the sample in theta (with example θ motor positions of0◦ and 20◦), and a 3D side view schematic (right), which shows the sample’smovement in ϕ as well as gives a sense of the structure of the chamber. Theimage of the DA30 hemispherical analyzer (inset) is reproduced from theScientaOmicron website.312.3. Angle-Resolved Photoemission Spectroscopy (ARPES)Figure 2.8: Illustration of the photoemission process, where EV is the vacuumenergy, EF is the Fermi energy, Φ is the work function of the material, E0 isthe bottom of the valence band relative to EF , V0 is the inner potential, andEK is the maximum kinetic energy of electrons that will be photoemittedwith a given photon energy hν. Figure adapted from Damascelli’s Probingthe Low-Energy Electronic Structure of Complex Systems by ARPES [92].322.3. Angle-Resolved Photoemission Spectroscopy (ARPES)Figure 2.9: Illustration of photoemission geometry as described by thederivations in this section. Figure adapted from Damascelli’s Probing theLow-Energy Electronic Structure of Complex Systems by ARPES [92].K∥ =p∥ℏ= Kx +Ky =√2meEkℏsin(θ)[cos(ϕ)xˆ+ sin(ϕ)yˆ] (2.9)K⊥ = Kz =√2meEkℏcos(θ)zˆ. (2.10)Conservation of momentum (equation 2.7) enables us to relate the mo-mentum of the photoelectron in vacuum to the crystal momentum. In typicalARPES experiment with photon energies of < 100 eV, the photon momen-tum can be neglected [92]. Due to the assumed translational symmetryin the sample’s surface-plane (defined as the x-y plane in Fig. 2.9), theparallel-component of crystal momentum is conserved during photoemission,and|k∥| = |K∥| =√2meEkℏsin(θ). (2.11)Less straightforward to recover is k⊥: since out-of-plane translationalsymmetry is broken at the sample-vacuum interface, and thus the perpen-dicular component of momentum is not conserved. By making an a prioriassumption regarding the final state of the photoelectron, however, one can332.3. Angle-Resolved Photoemission Spectroscopy (ARPES)determine k⊥. If one assumes a nearly-free electron model for the final state,then the energy of that final state electron Ef (k) is given byEf (k) =ℏ2k22me− |E0| (2.12)where E0 is the bottom of the valence band relative to EF (see Fig. 2.8).Recalling Eqs. 2.6 and 2.8, we can writeEf = hν − |EB| = Ek +Φ. (2.13)Equating Eq. 2.12 and Eq. 2.13, we getℏ2k22me= Ek +Φ+ |E0| = Ek + V0. (2.14)Recalling that k2 = k∥2 + k⊥2 and substituting in Eq. 2.11, givesk⊥ =√2meℏ2[Ekcos2(θ) + V0]. (2.15)V0 is referred to as the inner potential, and it is defined as the differencein energy between the bottom of the valence band and the vacuum level(see Fig. 2.8). Practically speaking, V0 is typically determined throughcomparison to theory or conducting ARPES experiments with a variety ofphoton energies, observing the periodicity over multiple BZs for each k⊥constant energy contour (CEC), and fitting the expected periodicity (basedon the crystal structure) with Eq. 2.15 [92].It is important to note that the above angle-to-k conversion equations aregiven in the reference frame of the sample. In the lab-reference frame that isoften used during ARPES experiments, the detector remains stationary: ϕand θ are determined by a combination of sample motion and experimentalparameters (such as the acceptor slit and modes of the analyzer). Given Eqs.2.11 and 2.8, we can see that our accessible range of k-space is limited by thephoton energy of our light source as well as the θ and ϕ angular range of ourexperimental set up. The ARPES spectra in this thesis was taken primarilywith photon energies of 6.2 eV and 22.8 eV; this results in two distinct but342.3. Angle-Resolved Photoemission Spectroscopy (ARPES)Figure 2.10: Shown at motor values of θ = ϕ = 0 with our finite θslit of ±15◦(left) and at maximum θ (for our experimental setup) of ±55◦ (θmax slit +θmax motor = 55◦). Taking into account the experimental restrictions of ϕwill result in further limiting of these accessible regions. Note that even atextreme θ values, the 6.2 eV laser cannot reach the edges of the Au(111) BZ.overlapping theoretically accessible k-space regions, given by Eq. 2.11 anddepicted in Fig. 2.10 relative to the size of the C60 and Au(111) Brillouinzones. The Brillouin zones are included to illustrate how advantageous ahigher photon energy can be in mapping out the band structure for the entireBZ, particularly on samples with a small unit cell.While some lab-specific experimental limits on θ were taken into accountin Fig. 2.10, the images depicted are intended primarily to be a usefulreference when considering the ability of light sources with different photonenergies to map out the BZ of a material, and they are by no means com-prehensive in their inclusion of experimental constraints. Indeed, angle-to-kconversion in the lab frame is a nuanced problem dependent on the specificsof a lab’s experimental setup. For the purposes of angle-to-k conversionconducted for data included in this thesis, the Damascelli lab’s angle-to-kconversion code was used.17 For a more thorough review of angle-to-k conver-17There exists an internal document detailing this conversion entitled “Angular-to-352.3. Angle-Resolved Photoemission Spectroscopy (ARPES)sion, including setup-specific considerations, I refer the reader to Ishida andShin’s Functions to map photoelectron distributions in a variety of setups inangle-resolved photoemission spectroscopy [94].In order to further understand photoemission, one may consider a moreformal definition of photoemission process in which one calculates the transi-tion probability of an optical excitation. If the light-matter interaction istreated as a perturbation given by Hint, the transition probability can beapproximated by Fermi’s golden rule:wf,i =2πℏ| ⟨ΨNf |Hint |ΨNi ⟩ |2δ(ENf − ENi − hν). (2.16)Here, ΨNi is the N-electron ground state and ΨNf is one of the possiblefinal states. The term δ(ENf − ENi − hν) takes energy conservation intoaccount, where ENi and ENf are the initial and final-state energies of theN-particle system. To understand Hint, one can begin with the classicalHamiltonian for a particle in an electromagnetic field:Hint =12m(p− qcA)2 + qΦ, (2.17)where A is the electromagnetic vector potential and p is the momentumoperator.Choosing the Coulomb gauge, such that Φ = 0, and dropping thequadratic term in A (it is considered negligible in the linear optical regime),we see thatHint =12m(p2 − qcp ·A− qcA · p). (2.18)Recalling thatH0 =p22m+ V (2.19)is the unperturbed Hamiltonian of the semi-infinite crystal, we can writemomenta conversion documentation” by Sean Kung (2021), based largely on an under-standing gained from Ref. [94].362.3. Angle-Resolved Photoemission Spectroscopy (ARPES)Hint = − q2mc(p ·A+A · p). (2.20)Making use of the commutator relation[p,A] = p ·A−A · p = −iℏ∇ ·A, (2.21)we getHint = − q2mc(2A · p− iℏ∇ ·A). (2.22)If we use the dipole approximation, where A is held constant over atomicdimensions, then ∇ ·A = 0 (this is valid for the ultraviolet, however it is notnecessarily true at the surface of a material, since electromagnetic fields mayhave strong spatial dependence). Finally, we haveHint = − qmc(A · p). (2.23)Although Eqs. 2.16 and 2.23 can be solved using a rigorous one-stepmodel approach (where photon absorption, electron removal, and electrondetection are all treated as a single process) [95, 96], this approach requiresthat the Hamiltonian include information about the sample surface [92]. Thephotoemission process is more typically described by the three-step model:1. optical excitation of the electron in the bulk,2. travel of the excited electron to the surface,3. and escape of the photoelectron into vacuum.By taking these steps to be independent and sequential, one can calculatethe total photoemission intensity with the product of the probabilities ofeach step.Step 1 is described by the transition probability, wf,i. Within the suddenapproximation (where we assume that the electron is instantaneously removedfrom the system), the wavefunction can be written as a Slater determinant,which can be written as a product of the wavefunctions for the initial/final372.3. Angle-Resolved Photoemission Spectroscopy (ARPES)state one-electron orbital (ϕk) and the other (N − 1)-electron system (alongwith an antisymmetric operator, A, that ensures the Pauli principle issatisfied):ΨNf,i = Aϕkf,iΨ(N−1)f,i . (2.24)Using Eq. 2.24, the matrix element from Eq. 2.16 can be written as⟨ΨNf |Hint |ΨNi ⟩ = ⟨ϕkf |Hint |ϕki ⟩ ⟨Ψ(N−1)m |Ψ(N−1)i ⟩ . (2.25)Here,⟨ϕkf |Hint |ϕki ⟩ ≡Mkf,i (2.26)is the one-electron dipole matrix element. This term is often referredto as the photoemission matrix element, and it is a function of electronmomentum, photon energy, and photon polarization.⟨Ψ(N−1)m |Ψ(N−1)i ⟩ ≡ cm,i (2.27)is the (N-1)-electron overlap integral (|cm,i|2 is the probability that re-moving an electron from initial state i will leave the (N-1)-particle system infinal state m). It is worth noting that the final-state wavefunction Ψ(N−1)fis an eigenstate of the (N-1)-particle system and can be expressed as anexcited state with eigenfunction Ψ(N−1)m and energy E(N−1)m (where the totaltransition probability is summed over all possible excited states m). Theinitial-state wavefuction Ψ(N−1)i , on the other hand, is not an eigenstate ofthe (N-1)-particle Hamiltonian: it is merely what is left of the N-particlewavefunction after having factored out one electron (ϕkf ).Using Eqs. 2.26 and 2.27 and summing over all possible excited states(m), we can now write Eq. 2.16 as follows:wf,i =2πℏ|Mkf,i|2∑m|cm,i|2δ(Ek + E(N−1)m − ENi − hν). (2.28)382.3. Angle-Resolved Photoemission Spectroscopy (ARPES)Thus, the photoemission intensity for a given Ek and k, is given byI(k, Ek) =∑f,iwf,i. (2.29)Step 2 involves the scattering probability (i.e. the mean free path) of thetravelling electron. As the photoelectron travels, subsequent scattering events(representing inelastic scattering processes in the material or in the analyzer)invalidate the photoemission conservation equations introduced at the begin-ning of this section and result in “secondary” photoelectrons that show upas background in our ARPES images. Thus, ARPES spectra will representthe electronic bandstructure of a material based on photoelectrons that didnot scatter within the solid: given the mean free path of photoelectrons insolids and typical ARPES photon energies of 10 - 100 eV, this correspondsto a penetration depth of 5 - 20 A˚. ARPES is, therefore, predominantly asurface-sensitive technique. It is worth noting that this surface-sensitivity cangive rise to photoemission spectra that represent surface-specific phenomena,such as periodic scattering with a surface superstructure (discussed furtherin Section 5.2.2).In Step 3, the photoelectron overcomes the work function (Φ) of thematerial and is transmitted into the final state in vacuum (a free-electronstate). Because, as previously discussed, we typically consider ARPES data inthe context of the sudden approximation, this implies that the photoelectronleaves the sample prior to the relaxation of the photo-hole [97]. Therefore, theemitted photoelectron has no interaction with the electronic structure fromwhich it came, allowing us to interpret ARPES data as directly proportionalto the single-particle spectral function:A(k, ω) = − 1πΣ′(k, ω)[ω − ϵk − Σ′(k, ω)]2 + [Σ′′(k, ω)]2. (2.30)Here, ϵk is the electronic dispersion of the sample without any interactions,and Σ(k, ω) is the self-energy of the particle which describes how the particlesare dressed by their interactions with the rest of the system. The self-energyis complex: the real part provides the shift in the particle’s binding energy392.3. Angle-Resolved Photoemission Spectroscopy (ARPES)due to the interaction between the particle and the system, and the imaginarypart pertains to the lifetime of the particle’s state [98].18Using the one-particle removal spectral function (A(k, ω)), the squaredone-electron matrix element (|Mkf,i|2, recall Eq. 2.28), and the Fermi function(f(ω))19 (which accounts for the fact that static photoemission only probesoccupied states), we can describe the total photoemission intensity (asmeasured in ARPES) as follows:I(k, ω) = I0(k, ω,A)A(k, ω)f(ω) ∝ |Mkf,i|2A(k, ω)f(ω). (2.31)Recall that k is the in-plane momentum (k∥), ω is the energy of theelectron relative to the Fermi energy (in the context of E−EF , ω is negative),and A is the electromagnetic vector potential included in the HamiltonianHint (recall Eqs. 2.23 and 2.26). Note that the matrix element |Mkf,i| alsoincorporates the energy and polarization of the photon.The beginning of this section established that the principal goal of ARPESis to determine the binding energy of electronic states within a solid as afunction of crystal momentum (EB(k)). This goal is realized by collectinga series of images which record the kinetic energies and emission angles ofphotoelectrons. A typical ARPES spectra consists of one of two types ofimages: a plot of the dispersion of kinetic energy as a function of kx or ky(Fig. 2.11), or a constant energy cut showing the dispersion of energy throughboth kx and ky (Fig. 2.12). The former illustrates the band structure ofthe material, akin to a calculation-based spaghetti plot, and often describedusing high symmetry points rather than values of kx,y; for a description ofthese high symmetry points for an fcc crystal projected in the (111) direction,see Fig. 2.13. The latter – a constant energy cut – is called a Fermi Surfacewhen taken at the Fermi energy. These two images are different slices of thesame data cube, with axes kx, ky, and energy, and where each data point isan intensity.How is this data cube generated? The hemispherical analyzer is essentially18It is also through the self energy that one can model excitonic signatures in ARPES,by coupling Bethe-Salpeter equation to the single-particle Green’s function [9, 99].19f(ω) = (eω/kBT + 1)−1402.3. Angle-Resolved Photoemission Spectroscopy (ARPES)Figure 2.11: ARPES data of bilayer C60 on Au(111) depicting the dispersionof kinetic energy as a function of kx. Distinct, sharp bands are Au(111)bands; C60 HOMO (between -1 and -2 eV) and HOMO-1 (between -2.5 and-3.5 eV) are fuzzy and broad. Γ and K points of the C60 Brillouin zone areindicated (for an explanation of these high symmetry points, see Fig. 2.13).Taking a constant energy cut of our data cube immediately below EF resultsin the image shown in Fig. 2.12.412.3. Angle-Resolved Photoemission Spectroscopy (ARPES)Figure 2.12: A constant energy cut showing the dispersion of energy throughboth kx and ky at E−EF = −0.2 eV, integrated over 0.1 eV. The ky = 0 lineis indicated in purple; taking a slice through the data cube holding ky = 0results in the image shown in Fig. 2.11.422.3. Angle-Resolved Photoemission Spectroscopy (ARPES)Figure 2.13: Depiction of the Brillouin zone of the bulk fcc crystal (highsymmetry points depicted in blue but labelled in black) projected in the (111)direction, resulting in the surface Brillouin zone for fcc(111) (high symmetrypoints depicted and labelled in blue). Image adapted from Refs. [100] and[101].432.4. Time- and Angle-Resolved Photoemission Spectroscopy (TR-ARPES)a capacitor: as the photoelectrons travel through the uniform electric fieldbetween the two hemispheres, their paths will be determined by their kineticenergies, allowing us to assign a kinetic energy to each electron that strikesthe detector. In order to enter into the analyzer, the photoelectrons mustfirst pass through the entrance slit20 that limits the angle of trajectoriesaccepted (called the acceptance angle θ); θ is the measured angular rangeof a given scan. The detector records the kinetic energies and angles (θ) ofthe photoelectrons; assuming we know the work function of the material andthe energy of our light source, this provides us with sufficient informationto plot the spectral function along a particular slice of reciprocal space (SeeFig. 2.11: intensity as a function of kinetic energy and kx, where angle θ hasbeen converted to kx).The equilibrium ARPES data presented in this thesis was taken usingone of two light sources (He lamp and XUV laser), the specifications forwhich are summarized in Table 2.1.212.4 Time- and Angle-Resolved PhotoemissionSpectroscopy (TR-ARPES)Time-Resolved ARPES (TR-ARPES) is an extension of ARPES, wherebythe light source emits a series of pulses which can be categorized into pumpand probe pulses. The pump pulse provides enough energy to perturb thesample – e.g. to excite electrons – but not enough to photoemit them. Theprobe pulse provides the energy to photoemit those excited electrons. Bycontrolling the time interval between the pump and the probe pulse, we canascertain the electronic structure of typically unoccupied states as well aspost-excitation dynamics and lifetimes of excited states in solids.To better understand the relationship between the pump and probepulse, as well as the significance of TR-ARPES as a technique that augmentsequilibrium ARPES, it is helpful to elaborate on the controllable time interval20The tunable entrance slit is determined by the potential difference between the twoconcentric hemispheres of the detector.21The 6 eV laser was used for TR-ARPES, as described in Section 2.4.442.4. Time- and Angle-Resolved Photoemission Spectroscopy (TR-ARPES)between the pump and the probe. In an archetypal TR-ARPES set-up, thereare two pulsed photon sources that arrive at the sample surface. These pulsesare (usually) of different photon energies (typically the lower energy pulse isthe pump and the higher energy pulse is the probe), and their bandwidth andpulse duration are the principal factors that determine the energy and timeresolution (respectively) of the experiment. The path length travelled bythe two pulses determines at what point, relative to one another, the pulseshit the sample. The difference in time between when the pump and probepulses hit the sample is called the delay. By modifying the path lengthsof the pulses relative to each other, we can control the delay. If the probepulse has a shorter path length than the pump pulse, and thus arrives at thesample before the pump pulse, the photoelectrons collected by the detectorwill have been directly photoemitted from the unexcited state (before thepump pulse even reached the sample). This scenario is called negative delay,and results in data that is comparable to equilibrium ARPES assuming thatthe repetition rate is low enough for the system to return to the ground statebetween pump pulses. Negative delay is a useful tool for determining if theexperimental parameters are as expected (aberrant signals might indicatethe presence of a pre-pulse, for example). If the path length of pump andprobe pulses is the same, then both pulses reach the sample at the sametime and we have pump-probe overlap on the sample. This scenario is calledzero delay or time zero, and provides information on the excited electronicstates that are directly accessed by the pump pulse (or nearly immediatelyoccupied through decay channels). If the probe has a longer path lengththan the pump, and thus arrives at the sample after the pump pulse, thephotoelectrons collected by the detector will have been photoemitted fromthe states occupied after excitation (either directly populated by the pump orsubsequently populated through relaxation). This scenario is called positivedelay. By varying the positive delay, we can record the lifetimes of excitedstates in our material of interest. These three scenarios are illustrated in Fig.2.14.In the context of the project described in this thesis, TR-ARPES playsan integral role due to our core questions regarding exciton dynamics, local-452.4. Time- and Angle-Resolved Photoemission Spectroscopy (TR-ARPES)Figure 2.14: Negative delay (probe before pump): the probe photoemitselectrons from their ground state (akin to equilibrium ARPES). Zero delay(probe and pump overlap): the probe photoemits electrons the directlyaccessible (or nearly immediately occupied through decay channels) electronicstates. Positive delay (probe after pump): first the pump photoexcites theelectrons and then the probe subsequently photoemits the electrons fromthe excited states. By varying the delay time (including multiple positivedelays), we can discern the lifetimes of the excited states.462.5. Denoising Convolutional Neural Network (CNN)ization, and carrier generation in C60 films. By enabling us to probe both thetime dynamics and the angular dispersion of excitonic states, TR-ARPESprovides us with the experimental data to help answer these questions.The TR-ARPES data presented in this thesis was taken using our lab’s 6eV Ti:sapphire laser with a 1.55 eV (∼ 800 nm) fundamental; its specificationsare summarized in Table 2.1.Table 2.1: Photon Sources in the Damascelli LabProperties He lamp XUV laser 6 eV laserhν (probe) 22 eV 8 - 35 eV 6.2 eVhν (pump) n/a 2.4 eV 1.55/3.1 eVPolarization unpolarized p s/p∆ E 5 meV 25 - 40 meV 20 meV∆ t n/a 100 fs 225 - 500 fsFluence n/a ≪ 10 µJ/cm2 150 - 300 µJ/cm2Spot size 1 mm 100 µm 10 - 100 µmRep. rate n/a 60 MHz 250 kHz2.5 Denoising Convolutional Neural Network(CNN)In ARPES, the acquisition time required to achieve a sufficient signal tonoise ratio is not trivial when compared to an experiment lifetime (takinginto account sample degradation, light source stability, temperature stability,etc.). For example, most of the data presented in this thesis (specifically, thedata cubes described in Section 2.3) took a minimum of 12 hours acquisitiontime. Our data on excited states (the subject of Ch. 6) took closer to 20hours per data cube. The requisite acquisition time for a single datasetcan easily become multiple days, depending on what sort of source fluenceand power the sample can tolerate (see Sections 6.1.4 and 6.3.1 for furtherinformation); these long acquisition times are in direct competition with thefact that samples can age and degrade, sometimes over similar timescales472.5. Denoising Convolutional Neural Network (CNN)(see Section A.2 for our sample-specific example). In machine learning(ML), image denoising is a vibrant and fundamental topic [102]. In recentyears, various scientific groups have begun experimenting with applyingML denoising techniques to spectroscopic data, creating models to assistwith feature extraction and noise reduction in ARPES’ energy-momentumdispersion maps [103].These machine learning models are predominantly based on convolutionalneural networks (CNNs). Although an in-depth study of machine learningprinciples is beyond the scope of this thesis, a brief explanation of CNNsmay be helpful to the reader. CNNs are part of an area of deep learningthat specializes in pattern recognition: practical applications include theoptical character recognition (OCR) in your smartphone, facial recognitionsoftware, and automatic tumor detection in medical imagery [104–106]. Theycomprise multiple layers, each of which can be associated with multiplefilters. Filters are where the parameters for pattern recognition get defined,and they are convolved with the original image in their given layer. Theresult of this convolution is a numerical array that describes the extent towhich the various pixels of the original image match the filter(s) in that layer.These numerical arrays can subsequently be combined in a process knownas ‘pooling,’ resulting in a (new) output image for that layer of the CNN.A few common methods of pooling are max pooling, average pooling, andmixed pooling. In max pooling, the maximum value for a given index of thenumerical arrays is kept; in average pooling, the average of the values foreach index is kept; in mixed pooling, a linear combination of the maximumand the average value is kept. As one progresses through the layers of theCNN, the filters can become more abstract and the pattern matching morecomplex [107]. A basic explanatory schematic of a CNN is shown in Fig.2.15.The application of CNN models to ARPES spectra can be traced toDong et al.’s 2016 paper [108] that proposed applying a convolutional neuralnetwork (CNN) method to single image super-resolution (SR). Single imageSR takes a single, low-resolution image as an input, and attempts to recover482.5. Denoising Convolutional Neural Network (CNN)Figure 2.15: CNNs are a type of deep learning that specializes in patternrecognition. Practical applications include the optical character recognition(OCR) in your smartphone, facial recognition software, and automatic tumordetection in medical imagery. A denoising CNN takes a noisy input imageand produces a denoised output image. It does this through a procedurewhich combines a series of layers and filters. The CNN contains a number oflayers. Each layer can be associated with multiple filters. Filters are wherethe parameters for pattern recognition get defined. Each filter is convolvedwith the original image in their given layer. The result of this convolutionis a numerical array that describes the extent to which the various pixelsof the original image match the filter(s) in that layer. These numericalarrays are then combined in a process known as ‘pooling.’ Once pooled, the(new) numerical array is the output image for that layer of the CNN. A fewcommon methods of pooling (shown in this figure) are max pooling, averagepooling, and mixed pooling. In max pooling, the maximum value for a givenindex of the numerical arrays is kept; in average pooling, the average of thevalues for each index is kept; in mixed pooling, a linear combination of themaximum and the average value is kept.492.5. Denoising Convolutional Neural Network (CNN)a high-resolution image from it.22 Dong et al.’s proposed super-resolutionCNN (or SRCNN) uses a CNN to learn the SR pipeline, directly mappingbetween low- and high-resolution images [108]. In 2020, Peng et al. [109]published a CNN method modified from Dong et al.’s SRCNN and used itfor feature extraction in 2D ARPES images. Here, they used a similar modelarchitecture but formulated as a classification problem (whether or not agiven energy band exists).23 They utilized a modified SRCNN to find a mapfrom experimental band structure dispersion data (that is broadened due to,for example, correlation effects, experimental energy resolution limitations,etc.) to theoretical energy-momentum dispersions. In essence, they canlocate, sharpen, and reveal ARPES features. Their results demonstratethat feature extraction in 2D ARPES images can be treated as an imagerestoration problem and tackled using a CNN [109].In 2021, Kim et al. [110] published a CNN method that discriminatesbetween noise and intrinsic signals and that they had successfully trained todenoise ARPES band dispersion maps. In juxtaposition with Dong et al’smodified SRCNN, Kim et al.’s method does not sharpen peaks for featureextraction but rather minimizes noise while maintaining the “true” bandintensity profiles. As Kim et al. discuss, conventional Gaussian smoothingcan be used to reduce noise in spectroscopic data [111, 112]; however, itinevitably blurs data and results in information loss, as can be seen in Fig.2.16 (and subsequent figures in this chapter). A denoising CNN, however,can take advantage of the fact that ARPES band structure features andtheir dispersion are typically larger than a data pixel: this implies thatthe most statistically probably real value for the pixel can be inferred fromthe adjacent pixel values [110]. Kim et al’s technique’s faithfulness to theunderlying data is extremely valuable to ARPES analysis because it preservesaccess to quantitative values with physical implications such as bandwidths22Because each low-resolution pixel could result in any number or configuration ofhigher-resolution pixels, this is a problem with no unique solution. Typically, strongprior information can be used to constrain the solution space, thereby mitigating theunderdetermined nature of the problem.23In this case, a sigmoid activation function is applied to the final layer of the networkin order to obtain a measure of confidence of the existence of the energy band.502.5. Denoising Convolutional Neural Network (CNN)and band gaps. Structurally, this deep neural network of 20 convolutionallayers is based on that of Jiwon Kim et al. [111]. The CNN was trained onpairs of original and generated ARPES spectra on a variety of materials (e.g.Au(111)), where the generated data is based on the original.24 The generateddata is a low-count25 sample of the (high-statistics) original data, assuming aPoisson distribution for the count probability.26 The arbitrary sampling usedto generate the low-count data helps ensure a randomness to the noise of theinput data, which prevents the CNN from learning to produce noise and thusenables a noise-free CNN output. The performance of the model is assessedusing a loss function equivalent to the weighted sum of the mean absoluteerror (MAE) and the multiscale structural similarity (MS-SSIM).27 A modeltrained using this loss function outperforms a model trained using the moreconventional mean squared error (MSE) loss function.28 The attributes ofand appropriate use cases for this combined loss function are described indetail in Ref. [113].I applied Kim et al.’s [110] denoising neural network to several of myown ARPES datasets and compared the results (Fig. 2.16 (d)) with theraw data (Fig 2.16 (a)), a contrast enhanced image (Fig. 2.16 (b)), and theimage after the application of a Gaussian filter (Fig. 2.16 (c)). Through thiscomparison, we can see that all four images show the same spectral features,but the denoising CNN produces the cleanest and crispest image of the four.The enhanced image was modified by increasing the contrast by a factor of2, using the pillow (PIL) ImageEnhance.Contrast function.29 This resultsin more weight on the spectral lines and can be helpful as a sanity check24Training was performed on 50 different original datasets and 2500 different generateddatasets; 50 datasets were randomly generated per original dataset, hence the larger numberof generated datasets. Generated datasets were augmented through rotation, flipping, andbrightness adjustment.25The number of counts varies to ensure the CNN can denoise data with a wide range ofstatistics.26At the limit of (the total count) N →∞, the count at a particular pixel divided by Nconverges to the Poisson distribution probability.27L = 0.3 ∗ LMSE + 0.7 ∗ LMS−SSIM28MAE imposes a higher penalty than MSE for small differences on a pixel-wise scale,and MS-SSIM is better able to assess similarity over a larger range of data.29https://pillow.readthedocs.io/en/stable/reference/ImageEnhance.html512.5. Denoising Convolutional Neural Network (CNN)when one is attempting to find low-level signals. However, purely enhancingthe contrast does not mitigate noise. The filtered image was filtered usingscipy.ndimage.gaussian_filter with σ = 2. This function applies asequence of 1D convolution filters with a Gaussian shape (and a standarddeviation of σ = 2 for the kernel size) across each input data axis.30 Thisprocedure does produce an output dataset that can be further manipulatedor analyzed, but, as is visible in Fig. 2.16 (c), Gaussian filters smear outor blur features. This can result in greater uncertainty of the location of aspectral feature (such as a band crossing) in momentum or energy space, andeven the concealing of real features that may get covered due to the blurring.It also precludes any quantitative analysis that is dependent on the width offeatures (e.g. decay constants in TR-ARPES, discussed in Section 6.1.3).The denoising CNN, on the other hand, results in an output dataset thatappears to match the other datasets in terms of feature position and relativeweight, but excels in terms of the sharpness of these features.In another example, consider the cone-like feature visible when one takesa constant ky slice (at ky = −0.36) in the raw data from Fig. 2.17. While thecones are clearly visible in all four images, the denoising CNN produces thesharpest image of these features. In addition to producing sharper images offeatures clearly visible in the raw data, the denoising CNN is also useful inillustrating features that may be to faint to see in the raw data. Fig. 2.18shows Fermi surface data of the same sample as in Fig. 2.16, but acquiredwith the He lamp.When one takes a slice of constant ky slice (at ky = −0.72) in the rawXUV data, cone-like features are clearly visible (see Fig. 2.19 panels a and b).Of course, the denoising CNN leads to the features being even more distinct(see Fig. 2.19 c). However, the comparable constant ky slice in the raw lampdata results in barely visible cone-like features (see Fig. 2.19 panels d and e).However, in this case, the denoising CNN still renders the features distinct,providing a substantial advantage when it comes to visually understandingone’s data. In fact, when considering the results of the denoising CNN in30https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.gaussian_filter.html522.5. Denoising Convolutional Neural Network (CNN)Figure 2.16: (a) Raw ARPES FS data, taken with our XUV source. (b)ARPES data enhanced by increasing the contrast by a factor of 2. (c) ARPESdata with a Gaussian filter applied. (d) Denoised ARPES data, using Kimet al.’s neural network [110].532.5. Denoising Convolutional Neural Network (CNN)Figure 2.17: (a) Raw ARPES high symmetry slice data, taken with our XUVsource. (b) ARPES data enhanced by increasing the contrast by a factor of2. (c) ARPES data with a Gaussian filter applied. (d) Denoised ARPESdata, using Kim et al.’s neural network [110].542.5. Denoising Convolutional Neural Network (CNN)Figure 2.18: (a) Raw ARPES FS data, taken with our He lamp source.(b) ARPES data enhanced by increasing the contrast by a factor of 2. (c)ARPES data with a Gaussian filter applied. (d) Denoised ARPES data,using Kim et al.’s neural network [110].552.5. Denoising Convolutional Neural Network (CNN)juxtaposition with the results of the contrast enhancement and the Gaussianfilter as applied to this barely-visible feature, as shown in Fig. 2.19, thedenoising CNN does a substantially better job of qualitatively enhancingvisibility of features in the data. A more quantitative application of this toolas it pertains to fitting procedures, as well as further analysis of denoiseddata, follows in Chapter 5 of this thesis.Figure 2.19: A comparison of the constant ky high symmetry slices of theangular data taken with our XUV (a) and He lamp (d) sources on 1 MLfilms. The resulting raw data is depicted in panels (b) and (e). Note thatthe sharp, linearly-dispersing features visible in (b) are barely visible in(e). However, once the denoising CNN has been applied, the right cone-likefeature becomes obvious in the lamp data (f) as well as the XUV data (c).Due to the rapidly ongoing development of this field and its nascency inbeing applied to ARPES data, caution is warranted when utilizing the tools562.5. Denoising Convolutional Neural Network (CNN)described in this section. The reliability and the extent of the applicabilityof these techniques is not yet fully understood, in part because the tools arestill in the process of being created. Nevertheless, denoising neural networksin their current state are already useful for feature-identification, and theirpotential to enable cleaner ARPES spectra from less measurement time, ifrealized, will greatly benefit the field of ARPES.57Chapter 3Experimental Background:Technical DetailsThis chapter provides an overview of some of the experimental developmentsthat were required to enable the results presented in this thesis, and it isprimarily intended as a helpful guide for future work. In particular, thetemperature calibration plot included in Section 3.3 is likely to be referencedfrequently in future projects.3.1 Sample Mounting ProcedureThe experiments described in this thesis required custom sample-mountingsolutions. This is due to the fundamental incompatibility of the sample holderdesigns intrinsic to the MBE and the ARPES systems, as illustrated in Fig.3.1. The MBE uses a flag-style sample plate, typical of ScientaOmicron’sSTM systems, and the custom Scienta ARPES chamber is configured fora bullet-and-post sample holder. In order to facilitate in situ transfer ofsamples from the MBE to the ARPES chamber, we developed a hybrid styleof sample holder that we call the “double-decker” sample holder (describedfurther in Section 3.2). Using this double-decker holder (and conductingARPES experiments on our sample) required mounting our substrate crystalto a post.The Au(111) tophat crystal is held to the post by epoxy (copper paste),to facilitate good electrical contact, and a mechanical brace of Tantalumwire. Epoxy alone is insufficient to hold our (heavy) crystal, particularlygiven that our sample is frequently suspended upside-down. The cage-likeclamp of tantalum wires, as can be seen in Figs. 3.3 and 3.4, has proved to583.2. Updated Sample Holder Designa. b.B2UNLESS OTHERWISE SPECIFIED:CHECKEDSIZETITLE:INTERPRET GEOMETRICTOLERANCING PER:Q.A.DWG NODATEDIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH BENDTWO PLACE DECIMALTHREE PLACE DECIMALMATERIALNAMEENG APPR.COMMENTS:DRAWNMFG APPR.1<COMPANY NAME>UNLESS OTHERWISE SPECIFIED:CHECKEDSIZEAPPLICATIONTITLE:INTERPRET GEOMETRICTOLERANCING PER:Q.A.FINISHDWG.DATEUSED ON ADIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH BENDTWO PLACE DECIMALTHREE PLACE DECIMALNEXT SSYMATERIALNAMEDO NOT SCALE DRAWING SCALE: 1:1AD PTEENG APPR.YOLECOMMENTS:DRAWNMFG APPR.2 112<COSample Location18 mmTop HatMount36 mm2.5 mma.b.B2UNLESS OTHERWISE SPECIFIED:CHECKEDSIZETITLE:INTERPRET GEOMETRICTOLERANCING PER:Q.A.DWGNODATEDIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACHBENDTWO PLACE DECIMALTHREE PLACE DECIMALMATERIALNAMEENG APPR.COMMENTS:DRAWNMFG APPR.1<COMPANY NAME>UNLESS OTHERWISE SPECIFIED:CHECKEDSIZEAPPLICATIONTITLE:INTERPRET GEOMETRICTOLERANCING PER:Q.A.FINISHDWG.DATEUSED ONADIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACHBENDTWO PLACE DECIMALTHREE PLACE DECIMALNEXT SSYMATERIALNAMEDO NOT SCALE DRAWINGSCALE: 1:1ADPTEENG APPR.YOLECOMMENTS:DRAWNMFG APPR.211 2<COSample Location18 mmTop HatMount36 mm 2.5 mm) )M lybdenumpostCopper bulletSamplelocation2.5 m 36Figure 3.1: Standard sample plate/holder mechanisms for (a) ScientaOmicronsystems (including our MBE) and (b) the custom Scienta ARPES system. (a)The sample is either clamped or epoxied to the surface of the flag-style sampleplate. (b) The sample is typically epoxied to the top of the molybdenumpost. The bullet and post can be made from a variety of UHV-safe materials;Copper and Molybdenum are used in this figure because those are thematerials used for the experiments described in this thesis. This figure isadapted from my MSc thesis [70].be successful in holding our crystal even in the case of epoxy failure. Ourattempts to cut a brace from Molybdenum foil (according to the designillustrated in Fig. 3.2) were less fruitful: although we were able to waterjetthe foil cleanly by clamping it between sheets of stiffer metal, the result wastoo bulky and brittle to achieve a secure assembly.3.2 Updated Sample Holder DesignAlthough the sample mounting procedure described above ensured reasonablygood contact between the Au tophat crystal and the post (and it gave ussecurity that the crystal could not fall), our initial crystal + post + double-decker sample plate system had a significant flaw: low thermal conductivitymeant that our crystal could not reach appropriate annealing temperatures.This issue was diagnosed by placing the sample plate (with the crystal) on ahot-plate and observing the temperature gradient between the hot-plate and593.2. Updated Sample Holder Design 3.50 A AB BC CD DE EF F44332211DRAWNCHK'DAPPV'DMFGQ.AUNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES: LINEAR: ANGULAR:FINISH: DEBURR AND BREAK SHARP EDGESNAME SIGNATURE DATEMATERIAL:DO NOT SCALE DRAWING REVISIONTITLE:DWG NO.SCALE:5:1 SHEET 1 OF 1A4WEIGHT: ClampingFoilSOLIDWORKS Educational Product. For Instructional Use OnlyFigure 3.2: This design is a foil clamp, made of 0.125 mm thick molybdenum.It is intended to be placed over the crystal (with the crystal surface insidethe 3.5 mm hole), and then have the prongs folded around the crystal andpost, thereby mechanically securing the crystal to the post. In practice, themolybdenum foil was too brittle to allow for tight clamping of such smallcomponents.Figure 3.3: Side view of sample in sample holder. Au(111) crystal is mountedto the molybdenum post using tantalum wires. Note the copper blockinstalled in the double-decker sample holder: the block facilitates adequatethermal conductivity to the sample as discussed in Section 3.2.603.3. Temperature Calibration ExperimentFigure 3.4: Top-down view of the Au(111) crystal, mounted on a molybdenumpost, fastened in the double-decker sample holder. Tantalum wires can beseen using the “brim” of the tophat crystal to secure the crystal to the post.the crystal, and it was solved by inserting a copper block into the double-decker sample plate as illustrated in Fig. 3.3.31 As discussed in my M.Sc.thesis, our system uses a double-decker sample holder to hold our sample ina manner than is compatible with both the OMBE and the ARPES system(albeit via an extremely tricky transfer – see Ch. 4 of my M.Sc. thesisfor details) [70]. This double-decker sample holder was designed and builtin-house.3.3 Temperature Calibration ExperimentThe modification of the sample holder design discussed above enables us toachieve our desired temperatures at the surface of the sample. However, thereis a non-zero difference between the manipulator temperature and the tem-perature of the sample. The plot shown in Fig. 3.5 can be used to calibrate.This data was acquire by the following means: First, a dummy sample postwas placed in the double-decker sample holder. Fine thermocouple wires wereattached to the dummy sample post using copper paste. The double-decker31It’s worth noting that the insufficient thermal conductivity we confirmed in air wouldpresent an even bigger problem in vacuum!613.3. Temperature Calibration ExperimentFigure 3.5: Plot shows temperature of the manipulator vs temperature ofthe sample.sample holder with the dummy post and and the thermocouple wires werecarefully inserted into the main chamber, after removing one of the sideflanges, and inserted into the manipulator. Ceramic beads were carefullystrung onto the thermocouple wires, in order to insulate them from eachother. Finally, the side flange on the OMBE’s main chamber was replacedwith a flange containing a thermocouple feed-through. The manipulator washeated and the temperatures at the sample location were collected usingthermocouple readings with the system under vacuum.62Chapter 4C60/Au(111): SystemDescription and GrowthTechniquesAs an organic semiconductor and a prototypical acceptor molecule in organicphotovoltaics, C60 has broad relevance to the world of organic thin filmelectronics. Although a high degree of order in C60 thin films is necessary toconduct spectroscopic analysis of the electronic structure, reported C60 filmsshow relatively low quality beyond a monolayer – a phenomenon commonto molecular materials. Here, we have developed a generalizable growthtechnique that consistently results in large-scale single-domain C60 filmsof controllable thicknesses, using Au(111) as an epitaxially well-matchedsubstrate. We have characterized grown films using low energy electrondiffraction, scanning tunneling microscopy, and angle-resolved photoemissionspectroscopy. We report successful epitaxial film growth of C60/Au(111) of1 monolayer (ML), 5 ML, and 10 ML films of sufficient quality to performARPES measurements using a two-stage growth technique. This workprovides general guidance for the growth of C60-based and other vacuumdeposited molecular/organic thin films. The growth method and structuralcharacterization is described here, and the ARPES data enabled by the highquality films grown is reported in Ch. 5.634.1. Introduction4.1 IntroductionOrganic semiconductors provide an alternative to silicon and other inorganicsemiconductors, serving as the foundation of a broad range of devices, in-cluding organic thin film transistors (OTFTs), organic light emitting diodes(OLEDs), and organic solar cells (OSCs) [114–116]. OSCs have been heraldedas revolutionary technology in the renewable energy sector [1] due to theirflexible and light-weight nature and their low production cost [117–119].As an excellent acceptor material, C60 serves a fundamental role in thestudy of exciton dynamics and free charge generation in a broad class ofOPV devices. In order to probe the electronic band structure of C60-basedmaterials, high purity films with long-range order and atomically-consistentthicknesses exceeding a bilayer are required [32]. However, molecular filmsoften exhibit a high degree of disorder due to the soft potentials, multiplecrystal structures, and weak epitaxy with typical substrates, compared totheir inorganic counterparts.Molecular beam epitaxy (MBE) is the technique of choice for achievinghigh quality films with atomic-layer control [73] and is widely used to grow C60films and related small-molecule semiconductors. Despite widespread use ofMBE for film growth, reported C60 films – grown using a typical single-stagegrowth technique – show insufficient orientational order32 for angle-resolvedspectroscopic measurements beyond a monolayer; such disorder also poses aproblem for device efficiency due to the role of interfaces in disrupting chargetransport [123].Here, we describe a two-stage growth recipe, combining heteroepitaxialand homoepitaxial growth processes at different temperatures, that enablesconsistent growth of high purity C60 films on Au(111), with long range orderand thicknesses up to 10 ML (see Fig. 4.1 for an introduction to the epitaxialorientation of our film):• Stage 1 (Heteroepitaxial Growth33): Deposit > 1 nm of C60 at a rateof 0.01 nm/min, maintaining a substrate temperature of 300◦ C.32indicated by multiple domains or no pattern visible in LEED [120–122]33i.e. C60/Au(111)644.1. IntroductionFigure 4.1: Introduction to the 2√3 x 2√3 R30◦ superstructure ofC60/Au(111). (a) Schematic of one of C60’s preferential epitaxial growthson Au(111) (the 2√3 x 2√3 R30◦ superstructure) in real space. Unit cellsare delineated with dashed lines, and example lattice vectors are illustrated.(b) Schematic of epitaxial relationship between C60 Brillouin zone (BZ) andAu(111) BZ in momentum space. (c) LEED image of Au(111) substrateprepared for growth. Inset shows LEED image of herringbone structure ofclean Au(111) [124]. (d) LEED image of ML C60 on Au(111), grown withstage 1 process. Note that the sample orientation was maintained, showingthe 30◦ rotation relative to the gold structure in (c) (between grey hexagonand gold hexagon, respectively).654.2. Motivation for Growth Recipe50 0 50 100 150 200 250 3007LPH PLQ 01002003007HPS & Figure 4.2: Depiction of our multi-stage film growth procedure, beginningwith a clean substrate, followed by growth of the first ML, and finally growthof the desired number of additional layers. Note that the first ML is grownat 300◦ C, and the subsequent layers are grown at 155◦ C.• Stage 2 (Homoepitaxial Growth34): Deposit C60 at a rate of 0.01nm/min, maintaining a substrate temperature of 155◦ C, until desiredfilm thickness has been achieved (up to 10 ML).Our two-stage growth method consists of high temperature over-depositionof 1 ML followed by a lower temperature homo-epitaxial growth of subse-quent layers (Fig. 4.2) (growth rates and film thicknesses confirmed byQCMs). We characterize these films using low energy electron diffraction(LEED), scanning tunneling microscopy (STM), and angle-resolved photoe-mission spectroscopy (ARPES), demonstrating the long-range order neededfor area-integrated electronic structure measurements.4.2 Motivation for Growth RecipeOur two-stage growth relies on a difference in interaction strength betweenC60-Au and C60-C60. As shown in this chapter, the relative strength of theC60-Au interaction can be utilized to split our film growth process into aheteroepitaxial growth stage and a homoepitaxial growth stage. In stage 1,the higher temperature overcomes the C60-C60 van der Waals interaction34i.e. C60/C60664.2. Motivation for Growth Recipeand any molecules not bound to the Au are desorbed; this distillation growthprocedure produces uniform high-quality ML films [125, 126] – in this case apristine C60 ML in a 2√3 x 2√3 R30◦ superstructure (see Fig. 4.1). In stage2, the lower temperature allows for homoepitaxial growth of C60 layers on theC60 ML, preserving order and facilitating large single domains when growingthicker films. Our two-stage growth recipe demonstrably exceeds the resultsof attempts to grow C60 films thicker than 1 ML using a single stage growthrecipe with the substrate held at a constant temperature [120–122]. Withthis growth recipe, we consistently generate uniform, flat, and well-orderedfilms up to 10 ML in thickness.There are several types of domains to consider, when determining whethera film is well-ordered: translational, rotational, mirrored, and combinationsthereof. We are predominantly concerned with the presence of multiplerotational domains, as rotational domains (if present in the sample area beingprobed) will contribute to independent spectroscopic signals thereby creatingreplica bands. In LEED (our primary means of determining whether our filmis well enough ordered for more intensive and time-consuming spectroscopicmeasurements), rotational domains present as multiple rotations of ourexpected hexagonal symmetry single-domain LEED spots, as illustrated inSection 4.5. In order for domains to be visible in LEED, they must belarge compared to the lateral coherence length of the incident electron beam(determined by the instrumental response function, and typically on theorder of a few hundred A˚ngstrom). Smaller domains manifest as weakened orbroadened spots and contribute to diffuse intensity. In the case of rotationaldomains, spot intensities are proportional to the fraction of the surface areathat contains the corresponding domain orientation [85].In general, the structure of a single ML film growth is determined bythe strength of the interactions between the material of interest and thesubstrate, lattice mismatch, and substrate corrugation and reconstructions,as well as kinetic parameters of the growth like deposition rate and substratetemperature. A substrate is chosen based on those qualities as well asvarious experimental considerations. In our case, a conductive substrate is35often of different thicknesses674.2. Motivation for Growth RecipeTable 4.1: Disorder in C60 Films [127]Type of Disorder Description Relevant Temperature RangeEpitaxial different epitaxial relation to the substrate growth recipe dependentOrientationalmultiple inequivalent rotational domainsof ordered C60 relative to the substrategrowth recipe dependentIslandingordered C60 grows in isolatedregions, forming islands35growth recipe dependentRotationalmolecules spin in their fcclattice location> 260 KFlippingjump rotational diffusion betweensymmetry-equivalent orientations(now sc lattice)85 - 260 Knecessary to us because it is suitable for both ARPES and STM measurements(insulating samples can charge in an ARPES system, thus modifying theelectronics of the system and corrupting the measurement). Au(111) wasan obvious initial choice of substrate because C60 on Au(111) can forma 2√3 x 2√3 R30◦ close-packed structure with a < 1% lattice mismatch[128, 129]. The 2√3 x 2√3 R30◦ adsorbate superstructure on clean Au(111),corresponds to one of several expected epitaxial domains, with minimal latticedistortion allowing every molecule to be equivalently bound [130, 131]. ForSTM studies illustrating this reconstruction, see Gardener’s work [132]. Sincethe lattice matching of the 2√3-type superstructure is much better than thein-phase superstructure, thermodynamics favour the former (see Fig. 4.3 foran illustration). However, the kinetics of the growth process (nucleation andgrowth of C60 domains at step edges) favour the in-phase structure [122],highlighting the importance of substrate preparation in the growth process.While C60 is often considered to be inert due to its chemical and structuralsimilarity to graphite, results of several studies have shown that C60 interactsstrongly with numerous substrates including GaAs(110), Si(111)(7x7), and –most relevant to us – Au(111) [133–135]. Multiple studies show the growthand structure/configuration of C60 films on Au(111) are strongly dependenton the adsorption site, with different configurations appearing at domainboundaries, island edges, and step edges [122]. Moreover, although Au is684.2. Motivation for Growth Recipe2√3 x 2√3 R30°38 x 38 in phaseC60/Au(111) (Å)Figure 4.3: Comparison of C60’s 2√3 x 2√3 R30◦ and in-phase epitaxialgrowths on Au(111). Unit cells are delineated with dashed lines, and ex-ample lattice vectors are illustrated with arrows. Note that in the 2√3superstructure, the C60 molecules occupy identical lattice sites relative tothe Au substrate. In juxtaposition, the in-phase superstructure results inmolecules sitting atop a variety of different Au lattice sites. This is illustratedin the schematic by the different configurations of Au atoms visible withinthe C60 molecules (circles) in the in-phase diagram (note that although someconfigurations appear similar, they are not identical). This figure is adaptedfrom Ref. [132].generally considered chemically inert, fullerenes bond strongly enough toan Au(111) substrate to lift the 23 x√3 herringbone reconstruction that ispresent at pure Au(111) surfaces [122, 131, 136, 137]. Additionally, epitaxialgrowth requires strong enough interaction between the film and the substratefor ordering to occur. Although this strong bonding may be unexpected, itis not entirely unexplained: studies of C60/Au(111) show that the bondingbetween fullerene and substrate should not be considered pure van der Waalsbonding but rather chemisorption, where charge transfer and LUMO-Au6sp-band hybridization explains the additional interaction strength [125, 135].694.3. MethodsOur two-stage growth recipe takes advantage of the unusually strongbond between C60 and Au, enabling us to deposit heteroepitaxially at ahigher temperature to favour the thermodynamically preferred 2√3 x 2√3R30◦ overlayer and template the lower temperature homoepitaxial layers.This recipe leads to highly crystalline films of varying thicknesses, providingan ideal sample for ARPES and other measurement techniques that benefitfrom long-range order.4.3 MethodsThe C60 films are grown in an MBE chamber with a base pressure of9 × 10−11 mbar. The C60 is evaporated using a water-cooled quad clustersource from MBE Komponenten with PBN crucibles, and the growth rateis calibrated using a water-cooled quartz crystal monitor. The growth rateis kept consistent throughout the deposition; our growth recipe is robustto deposition rates ranging from 0.01 to 0.1 nm/min. In order to ensureconsistent 2√3 superstructures, excellent substrate preparation and closely-controlled growth temperature and rate are paramount.The Au(111) single-crystal substrate is prepared by sputtering with Ar+with a SPECS’ IQE 11/35 ion source held at 1.3 keV for 40 minutes to 1 hour,followed by annealing the substrate at 440◦ C for 90 minutes. We repeatthis sputtering and annealing process if necessary, to ensure the substrate isclean and flat. We confirm the substrate is properly prepared using LEED.Although LEED images of the Au(111) indicate the presence of a herringbonereconstruction (see Fig. 4.1c), it is well-documented in the literature that C60thin-films lift the herringbone reconstruction in gold [122]. Once the substrateis prepared, we begin our two-stage growth process. The C60-Au bond canwithstand 500◦ C temperatures without the C60 molecules desorbing, whereasthe C60-C60 van der Waals bonds break down in temperatures above 300◦C [128]. Thus, in stage 1 (when our substrate is held at 300◦ C) despitedepositing nearly 3 nm of C60 onto the substrate to ensure complete coverage,C60 layers beyond the first ML are desorbed and we are left with a clean ML.Our LEED is a BDL600IR-MCP model from OCI Vacuum Microengi-704.4. Film Growth Procedureneering Inc., with a 7 - 750 eV beam energy and a spot size of approximately0.5 mm. The base chamber pressure is 2.0× 10−10 mbar.All STM and STS measurements were taken in a ScientaOmicron low-temperature scanning probe microscope with a base chamber pressure of3×10−11 mbar, using a cut platinum-iridium tip. Measurement temperatureswere 4.2 K. Sample transfer from OMBE to STM chamber took place undervacuum (≤ 1× 10−5 mbar).4.4 Film Growth ProcedureIn order to grow ordered C60 films, we adhere to the following steps:361. To ensure a clean substrate, we degass the Au(111) crystal by annealingto approximately 460◦ C for 60 - 120 min, sputter with Ar+ for 40minutes, and then anneal the substrate to 440◦ C for 90 minutes.2. We over-deposit the first monolayer of C60 by heating the crucible upto 365 - 370◦ C and maintaining a substrate temperature of 300◦ C.Our subsequent layers are deposited at the same crucible temperature,but with our substrate temperature decreased to 155◦ C. This facili-tates ordered growth of C60 layers, mitigating orientational disorder,islanding, and grain boundaries.3. Our growth recipe is robust to deposition rates ranging from at least0.01 to 0.1 nm/min, as measured by our in-situ quartz crystal monitors.4. Finally, we characterize and confirm the quality of our films usingour in-situ (and home-built) LEED chamber. Note that we allow thesample to cool to < 80◦ C prior to transferring it into the LEEDchamber.36Note that the values listed here are achieved by converting our system manipulatorheating temperature to the actual sample temperature using the results of a temperaturecalibration experiment we conducted. This step is required due to the modified configurationof our sample plate, which facilitates sample transfer between the OMBE and the ARPESsystem. See Section 3.3 for further details.714.5. LEED and LEEM5. Note that we can control additional sources of disorder (rotational andflipping in table 4.1) through sample temperature when conductingour experiment.4.5 LEED and LEEMUsing LEED, we are able to identify the orientation of our unit cell andvisualize the presence of multiple domains, if any, in our sample, with a spotsize similar to or greater than many lab-based ARPES photon sources.37Our two-stage growth recipe demonstrably exceeds the results of attemptsto grow C60 films thicker than 1 ML using a single stage growth recipewith the substrate held at a constant temperature, as shown in Fig. 4.4[120–122]. With this growth recipe, we consistently generate uniform, flat,and well-ordered films up to 10 ML in thickness. In LEED images, multiplerotational domains in the sample manifest as multiple single-domain LEEDpatterns rotated relative to one another. In the case of a C60 film, thehexagonal pattern is rotated forming a ring of spots (Fig. 4.4 (a)). Therelative intensity of the spots gives an indication of the prominence of adominant domain [85].To further investigate the origins of the multidomain growth of the single-stage recipe, we used low energy electron microscopy (LEEM)38 to visualizea 1.5 ML film grown at 190◦ C. Figure 4.5 shows the diffraction, bright-fieldand selected dark-field images for the resulting multidomain film. Whilethe 2√3 x 2√3 R30◦ domains (4.5 (c)) form the predominant structure atthis growth temperature, there is significant diffraction intensity from twoother domains corresponding to the in-phase (R0◦, 4.5 (e)) and 7 x 7 R14◦(R±14◦, 4.5 (d, f)) structure previously reported [132]. The dark-field imagescorresponding to these structures (4.5 (d - f)) show small nucleation centresthat appear to mostly be aligned along step edges (see arrows in Fig. 4.537Lab-based APRES photon sources typically range from 250 µm to 1 mm [83], or evenas small as 100 µm for some of the data presented in this thesis; our LEED spot size is 0.5mm.38LEEM measurements along with the associated film growth and LEED experimentswere performed by our collaborator Erik Ma˚rsell at MAX IV Laboratory.724.5. LEED and LEEMa)b) c)Single Stage Growth:5 ML C60 (Å-1)Two Stage Growth:5 ML C60 (Å-1)Two Stage Growth:10 ML C60 (Å-1)Figure 4.4: LEED data comparing the results of a typical one-stage growthrecipe (a) to films grown using our two-stage growth recipe (b) and (c).LEED images are taken with a beam energy of approximately 10 eV, to bestillustrate the presence or lack of domains (note that both penetration depthand beam area are a function of energy). (a) Film A was grown with thesubstrate held at 155◦ C for the entire duration. LEED images show thatthe single-stage growth film A contains significant multiple domains and is oflesser quality than films B and C. (b) Film B is of similar thickness to film A,but it was grown in two stages. The first ML was grown with the substrateheld at 300◦ C. The subsequent 4 layers were grown with the substrate heldat 155◦ C. Film B shows no signs of multiple domains. (c) Like film B, filmC (10 ML) was grown using a two-stage growth method and shows no signsof multiple domains. The self-contained, ordered growth described in thischapter results in films up to 10 ML thick with long-range ordered domains.734.6. STM(d)). This is consistent with the observations of Altman et al. [122] thatfound nucleation and growth of the in-phase structure from the step edgesis kinetically favoured, despite the thermodynamically favoured 2√3 x 2√3R30◦.4.6 STMSTM enables us to resolve the molecular structure of our films and providesinformation on the local density of states. The sample was grown in ourMBE using our stage 1 growth recipe, then transferred under vacuum intothe scanning probe microscope chamber. Using STM, we have confirmedour stage 1 growth is a single ML film with a lattice constant of 10.05 A˚.Our film predominantly consists of a single, ordered domain, as illustratedin Fig. 4.6, with additional domains nucleating near step edges. Less than5% of scans contained a different domain. Negligible vacancies or defects arevisible, though we see evidence of some surface contamination, likely incurredduring the sample transfer. No signs of the gold herringbone reconstructionare visible, which is in agreement with other reports that the C60 lifts thereconstruction on Au(111) [122, 131].4.7 ConclusionHere we have demonstrated a two-stage recipe that exploits both homoepi-taxial and heteroepitaxial growth, resulting in highly ordered films confirmedby LEED and STM compared to those grown using a more traditional, single-stage recipe. Such films enable techniques such as ARPES, that require longrange orientational order, bringing the insights into the electronic structureof organic photovoltaic materials and other applications of C60. In additionto generating ordered C60-based thin films, this approach exploiting a strongmolecule-substrate interaction may be generalizable to other organic films.This would facilitate further research into the electronic structures of organicthin films, with potentially broad implications for OLEDs, OTFTs, and otherorganic semiconductor-based technologies.744.7. ConclusionBright fieldR30 R+14R-14R0LEEDR30R+14R0R-14(a) (b)(c) (d)(e) (f)Figure 4.5: LEEM results of 1.5 ML C60 single-stage growth showing multido-main diffraction (a) typical of single stage growth recipes, bright-field LEEMimage showing contrast between first and second layer (b), and dark-fieldLEEM images corresponding to R30◦ (c), +14◦ (d), in-phase (e), -14◦ (f)domains relative to the Au(111) lattice. Examples of locations where grainsappear to be nucleated at step edges are indicated by arrows in (d), includinga 60◦ bend at the right-most arrow indicative of the underlying Au(111)surface.754.7. Conclusion10nma)3nmb)c)Figure 4.6: Data from STM experiment on 1 ML C60/Au(111) using thefirst stage of our growth recipe. Film grown in OMBE and transferred toSTM chamber under vacuum (≤ 1× 10−5 mbar). (a) STM image of 1 MLfilm. The step edge through the center of the image is a step in the Ausubstrate (∼ 0.24 nm). The C60 overlayer ‘blankets’ the step edge with nochange in the rotational or translational domain. The dark spot is a pitin the Au substrate confirmed by its height. Single bright spot indicatessurface contamination, likely incurred during the transfer. (b) Fine electronicstructure of fullerene molecules (taken on a different sample than in (a)). C60is oriented in two configurations: hexagon down (“dogbones”) or C-C bonddown (“cheerios”). This data is consistent with the preferential orientation ofC60 on Au(111) described in literature [127, 138]. (c) FFT of (a), confirminga single rotational domain.76Chapter 5ARPES on C60/Au(111)The development of a novel growth recipe that consistently resulted inthin films with long-range order facilitated angle-resolved photoemissionspectroscopy measurements on C60 thin films; these measurements enabledus to map the occupied electronic structure of 1 ML, 5 ML, and 10 ML films.This chapter also includes ARPES data on a pristine Au(111) substrate asa reference for the spectra of C60 overlayers. The quite comprehensive setof ARPES spectra acquired on 5 ML C60/Au(111) is, to the best of ourknowledge, the first of its kind.39 The experiments detailed in this chapterwere conducted using a Scienta DA30 hemispherical electron analyzer andmultiple lab-based light sources, the parameters of which are summarized inCh. 2 Table 2.1. The base chamber pressure is 6.6× 10−11 mbar.5.1 Au(111)The ARPES data collected on our Au(111) substrate crystal provides both asecondary means of characterizing our substrate (in addition to LEED, asdescribed in Ch. 4) as well as a useful comparison to our thin film C60/Au(111)data. Figure 5.1 shows ARPES spectra of our Au(111) substrate, after beingcleaned by sputtering with Ar+ ions and annealing to 440◦ C using theprocedure that is conducted prior to a thin film growth (see Section 4.3).The LEED data taken on this crystal prior to our ARPES measurement isequivalent to that presented in Fig. 4.1.Figure 5.1 includes a Fermi surface of the Au(111) crystal, depictingthe circular surface state around Γ as well as the hexagonal sp band thatis closer to the edges of the Brillouin zone. This data was taken with our39The first ARPES data on C60 films thicker than 1 ML, grown on an Au substrate.775.1. Au(111)Figure 5.1: ARPES spectra of clean Au(111) taken with He lamp (hν =22.1 eV, T = 10.5 K). (Left) Fermi surface of Au(111) substrate after beingprepared for growth. Area enclosed by grey dotted line is original data;outside data is generated by symmetrizing (rotating) original data [85].(Right) High symmetry cut at ky = 0 (gold dashed line in (a)), showingRashba splitting of the Au(111) surface state. Quality of data indicates clean,flat single-crystal Au(111).He lamp source (hν = 22.1 eV) at T = 10.5 K; although a photon energyof 22.1 eV does theoretically reach the edges of the Au(111) BZ (see Fig.2.10), the motor angle limitations of our experimental set up further limitour data acquisition. In this case, the area enclosed by the grey dotted lineis the original data; the full BZ is reconstructed by symmetrization (rotatingthe original data), taking advantage of fcc(111)’s three-fold symmetry [85].Figure 5.1 also shows a high symmetry cut taken at ky = 0 (representedby the gold dashed line in the Fermi surface). The high symmetry cutdepicts the Au(111) parabolic surface state. Rashba (spin-orbit coupling-induced) splitting of the noble metal surface state is visible [139–141], which –particularly given the spot size of our photon source (∼ 1 mm) speaks to thequality of our crystal and substrate preparation (the spin-splitting becomesless obvious even as the sample ages over the span of 48 hours in UHV).Figures 5.2 and 5.3 show the Au(111) band structure extending deeper in785.1. Au(111)Figure 5.2: ARPES spectra of clean Au(111) taken with the p-polarizedXUV source (hν = 22.8 eV, T = 20 K), EB = (−10, EF ).binding energy. The differences in polarization40 between the two sources (atsimilar photon energies) likely explain the discrepancies in intensity betweenthe two images: for example, Fig. 5.2 has prominent spectral weight on theband near E − EF = −4 eV as the band goes negative in kx. That regionof that band, though still visible in Fig. 5.3, is much less obvious. It isworth noting that the inset in Fig. 5.3 containing the parabolic surface statedepicts the same data as the larger image, but with enhanced contrast inthe enclosed region to better visualize the surface state.40He lamp and unpolarized and XUV is, in this case, p-polarized.795.1. Au(111)Figure 5.3: ARPES spectra of clean Au(111) taken with the unpolarized Helamp source (hν = 22.1 eV, T = 20 K), EB = (−6, EF ). Note that surfacestate contrast has been enhanced for visualization purposes.805.2. 1 ML C60/Au(111)5.2 1 ML C60/Au(111)Although the principal goal of this project is to probe the bulk-like (occupiedand unoccupied) electronic band structure of C60, and thus one mightconclude that the thicker our film the better (as as to better simulate theOPV-relevant bulk material), a single ML film is the easiest to grow in anordered and pure manner. We wanted to ensure that our film quality wassufficient for us to acquire good ARPES data before progressing to a thickerfilm.5.2.1 ARPES DataFigures 5.4 and 5.5 show spectra from a 1 ML C60/Au(111) thin film, takenwith our XUV source (hν = 22.8 eV, T = 12 K) and He lamp source (hν =22.1 eV, T = 9 K) respectively. In both figures, Au substrate bands and C60bands are visible. The C60 HOMO and HOMO-1 as well as some prominentAu(111) bands are labelled. The location of the HOMO relative to EF isdetermined by a Gaussian fit to the EDC; the fit, peak center, and FWHMare all reported in the lower plot in figures 5.4 and 5.5.Upon closer inspection of the data, however, we noticed bands thatwere not ascribable to either the pure Au(111) 5.2 or the C60: Figure 5.6demonstrates that a minor adjustment of source photon-energy (affecting thephotoemission matrix elements) reveals a linearly-dispersing band, extendingthrough the C60 HOMO and all the way to EF (pink boxed data with a lightpink dashed line serving as a guide to the eye). The spectral feature thatwould exist in this energy region due purely to our Au(111) substrate is thenoble metal surface state. ARPES data on Au(111) in the relevant regionof k-space is presented boxed in gold, and can be directly compared to thedata boxed in pink.These linearly-dispersing features do not disperse in kz, as can be seenin Fig. 5.7’s photon-energy dependent data comparison. The lack of kzdispersion indicates that these features are 2-dimensional and therefore notbulk Au bands; however, the fact that these features extend several eV belowEF implies that neither are they associated with the surface state.815.2. 1 ML C60/Au(111)Figure 5.4: ARPES spectra (ky = 0) and EDC of 1 ML C60/Au(111) takenwith our XUV source (hν = 22.8 eV, T = 12 K). (Top) C60 HOMO andHOMO-1 as well as some prominent Au(111) bands are labelled. (Bottom)EDC plot including the fit, with peak center and FWHM values. The locationof the HOMO relative to EF is determined by a Gaussian fit to the EDC.825.2. 1 ML C60/Au(111)Figure 5.5: ARPES spectra (ky = 0) and EDC of 1 ML C60/Au(111) takenwith our He lamp source (hν = 22.1 eV, T = 9 K). (Top) C60 HOMO andHOMO-1 as well as some prominent Au(111) bands are labelled. (Bottom)EDC plot including the fit, with peak center and FWHM values. The locationof the HOMO relative to EF is determined by a Gaussian fit to the EDC.835.2. 1 ML C60/Au(111)Figure 5.6: Unexpected bands not obviously attributable to Au(111). Al-though the ARPES spectra on ML C60/Au(111) does not obviously showbands above the C60 HOMO, by adjusting the XUV source photon-energyfrom hν = 22.8 eV to hν = 25 eV, we are able to discern a linearly-dispersingband that extends through the C60 HOMO and all the way to EF (pink boxeddata; light pink dashed line serves as a guide to the eye). This dispersion isclearly different from the surface state that is apparent in this energy rangeon pure Au(111) (gold boxed data). Note that all data is normalized withinits respective plot.845.2. 1 ML C60/Au(111)hv = 32.2 eV hv = 34.6 eV hv = 37 eVhv = 25 eVhv = 22.7 eV hv = 22.7 eVhv = 27.4 eV hv = 29.8 eVPhoton Energy Dependence of Unexpected Bandsa)Figure 5.7: High symmetry cuts taken at ky = 0 show a linearly-dispersingfeature extending through the C60 HOMO and band gap to EF . (a) (left)Region above HOMO shows no obvious features, but (right) normalized datain that isolated region shows multiple linearly-dispersing features. (b) Anexample linearly-dispersing feature extends several eV below EF but doesnot disperse in kz, indicating that it is a surface-resonant bulk band. (Pinkdashed lines serve as a guide to the eye.) Data taken at T = 9 K.855.2. 1 ML C60/Au(111)Constant energy cuts of the 1 ML C60/Au(111) thin films, taken withboth the XUV and He lamp sources, also depict structure near EF thatcannot be attributed to pure C60 or Au(111). Figure 5.8 presents a subsetof CECs, taken with both sources at equivalent binding energies; Figure5.9 compares a CEC taken at 0.2 eV below EF with a DFT 5-layer slabcalculation of the Au Fermi Surface. (A Fermi Surface contour of an Au(111)surface measured with a momentum microscope is included as an additionalpoint of comparison [142]). The spectral features overlaid by the light greenhighlights could be attributed to the surface state and the sp band of theAu(111); the dispersion that is visible in the region between the light greenoverlay is clearly inconsistent with the spectral features expected from anAu(111) FS, and thus cannot be attributed solely to the Au(111) substrate.Because C60 is a semiconductor, we would not expect to see any C60band structure at the Fermi energy (EF ) of C60/Au(111) (this energy regionlies in the band gap of C60). However, the constant energy cuts near EFof our 1 ML C60/Au(111) show complex features that are reminiscent ofthe hexagonal structure of the C60 BZ. In fact, the C60 BZ overlaid onthese CECs indicates close agreement with some of the prominent spectralintensity, as can be seen in Fig. 5.10. High symmetry slices of this datareveal sharp and distinct linearly-dispersing features that extend several eVbelow EF that are reminiscent of Dirac cones at each K point of the C60 BZ(Fig. 5.11).This more complex spectral intensity, visible in the C60 band gap butnot attributable to the Au surface state or sp band, is well reproduced byreplicas of the surface-resonance Au sp band, due to the epitaxial supercellformed by C60 on Au(111), and has been the subject of multiple recentpapers [143, 144].865.2. 1 ML C60/Au(111)0.0 --0.4 --0.8 --1.2 -0.0 --0.4 --0.8 --1.2 -0.0 --0.4 --0.8 --1.2 -–0.3-–0.6-0.0-0.3-k y(Å-1)EF–0.2 eV–0.4 eV0.0 -–0.4 -–0.8 -–1.2 -0.0 -–0.4 -–0.8 -–1.2 -–0.3-–0.6-0.0-0.3-k y(Å-1)0.0 -–0.4 -–0.8 -–1.2 -kx (Å-1)EF–0.2 eV–0.4 eVXUV He LampFigure 5.8: Comparison of constant energy cuts of 1 ML C60/Au(111), takenwith XUV (left) vs He lamp (right) light sources. CECs are taken near EFat equivalent binding energies (EB). Photon energies were approximately22.8 eV (XUV) and 22.1 eV (He lamp). Data taken at T = 9 K.875.2. 1 ML C60/Au(111)Figure 5.9: Comparison of a CEC taken at 0.2 eV below EF on 1 MLC60/Au(111) with DFT and experimental data on pristine Au(111). (a) DFT5-layer slab calculation of the Au Fermi Surface. (b) A Fermi Surface contourof an Au(111) surface measured with a momentum microscope is included asan additional point of comparison (image adapted from Tusche et al. [142]).(c) CEC of 1 ML film at E−EF = −0.2 eV with XUV source (hν = 22.8 eV).The relevant (experimentally accessible) region of the calculation is indicatedby the blue rectangle. The light green circle and rounded hexagon highlightthe Au surface state and the sp band. The light green highlights are overlaidon only half of the data, to avoid obscuring all of the data. The spectralfeatures overlaid by the light green highlights could be attributed to thesurface state and the sp band of the Au; the dispersion that is visible in theregion between the light green overlay is clearly inconsistent with the spectralfeatures expected from an Au(111) FS, and thus cannot be attributed solelyto the Au(111) substrate.885.2. 1 ML C60/Au(111)Figure 5.10: Constant energy cut of 1 ML C60 on Au(111), taken at E−EF =−0.2 eV (XUV, hν = 22.8 eV). Grey dashed hexagons demarcate the C60Brillouin zone. Note that these hexagons are located approximately 1 eVcloser to EF than the top of the C60 HOMO (Fig. 5.4).5.2.2 Band Folding ModelIn order to understand how replicas of the surface-resonance Au sp bandcan result a pattern like we see in our data, it is helpful to consider theconcept of band folding. Band folding occurs due to a new periodicityimposed at a surface, for example at a metal-molecule interface. The metal-molecule interface plays a critical role in devices as the semiconductor-electrode interface [145]. Not only can the hybridization of metallic andmolecular orbitals at the metal-molecule interface result in qualitatively newelectronic states [146], but the superstructure unit cells that arise at themetal-molecule interface create the possibility of distinct interface states aswell [147]. Band folding occurs when a superstructure in real-space leadsto a new periodicity and a new (smaller) BZ in reciprocal-space; becauseof the new periodic potential, the original bands get “folded” into this newBZ (see Fig. 5.12) to preserve translational symmetry across BZs. In ourcase, C60 forms a 2√3-type superstructure on the Au(111)); a model of thissuperstructure in k-space along with relevant Au sp band and surface state895.2. 1 ML C60/Au(111)Figure 5.11: ARPES spectra of linearly-dispersing features found at K pointsof C60 BZ. (Left) Constant energy cut at E−EF = −0.2 eV shows diffractedreplica of the surface resonance Au sp band, with the C60 BZ overlaid indashed grey lines; these replicas are due to the epitaxial C60 supercell andare only visible on a highly ordered sample. Purple and red dashed linesindicate the constant ky slices that are taken to produce the images to theright. (Right) linearly-dispersing features, formed by the crossing of replicabands at the K and K’ points of the C60 BZ (see circular inset at top left).Note that here prime denotes the second BZ.905.2. 1 ML C60/Au(111)Figure 5.12: A comparison of the C60/Au(111) system in real space (left)and reciprocal space (right). A superstructure in real-space leads to a newperiodicity and new (smaller) Brillouin zone in reciprocal-space; because ofthe new periodic potential, the original bands get folded into this new BZ.are depicted in Fig. 5.13. This scale model will enable one to visualize howband folding can explain the complex patterns present in our data (Fig. 5.8).In Fig. 5.14, the Au sp band is folded across all 6 edges of the C601st BZ. However, the resulting pattern (Fig. 5.14 (b), right panel) is nottranslationally symmetric across all C60 Brillouin zones. This can be clearlyseen because the C60 1st BZ is empty, while the 2nd BZs contain foldedbands. This implies that additional band folding is required to preservetranslational symmetry. In our case, a second fold, depicted in Fig. 5.15, issufficient.Now that we have a complete model of the expected bands due to oursuperstructure-induced band folding, the question becomes whether ourmodel matches our data. Figure 5.16 compares the band folding model resultwith our CEC data, and finds visual agreement between the two. In thedata shown in Fig. 5.16, 10/12 bands in our model (Fig. 5.15) are visible.This is unsurprising, as ARPES spectra intensity fluctuates as a function ofphotoemission selection rules. For clarity in comparison, we remove these2 bands (see Fig. 5.17) and keep the relevant 10. Rest assured, the other915.2. 1 ML C60/Au(111)Figure 5.13: A model of how the C60 2√3-type superstructure’s Brillouinzones tile to fill the Au(111) BZ at the Fermi surface (the Au sp bandand surface state are delineated in green). Four times the Γ− M C60 cutis equivalent to the Γ− K cut for Au. Three times the Γ− K C60 cut isequivalent to the Γ− M cut for Au.925.2. 1 ML C60/Au(111)Figure 5.14: Illustration of first fold of the Au sp band given the C60superstructure. (a) Au BZ (yellow) and sp band at the Fermi Surface (green)are folded across the edge (dashed purple) of the C60 BZ (dashed black)resulting in a new band (purple). (b) Folding of the Au sp band into theC60 BZ, taking into account the system’s 6-fold symmetry.935.2. 1 ML C60/Au(111)Figure 5.15: Illustration of second fold of the Au sp band given the C60superstructure. (a) Au BZ (yellow) and sp band at the Fermi Surface (green)are folded across the 2 edges (dashed purple and dashed blue) of the C60 BZ(dashed black) resulting in new bands (purple and blue). (b) Folding of theAu sp band fully into the C60 BZ, taking into account the system’s 6-foldsymmetry.945.2. 1 ML C60/Au(111)Figure 5.16: Constant energy cut of 1 ML C60/Au(111), taken at E − EF =−0.2 eV, with band folding model overlaid. Bands not seen due to matrixelement effects not shown in this model.2 bands are visible in data collected with an alternate photon source (Fig.5.18). A quantitative comparison of the slope of our replica with the Ausp band, shown in Fig. 5.19, also suggests a match between our model anddata.The agreement between the band folding model result and our datasupports the conclusion that these replicas are of the surface-resonance Au spband due either to band folding or to diffraction of the band through the C60ML. Band folding of the surface-resonant bulk state of the Au(111) sp bandat the Au-C60 interface, due to the potential imposed by C60’s 2√3-typesuperstructure, would result in the density of electrons being confined to ahexagonal lattice the size of the C60 BZ directly below the Fermi Energy,with Dirac cone-like features at each K point (Fig. 5.11); this phenomenon isdescribed as artificial graphene by Yue et. al. [148], in their study of C60 onvarious noble metal substrates. On the other hand, Krivenkov et al. claimsthat because C60 molecules are bonded to Au(111) covalently but relativelyweakly, it is unlikely that a weak molecular superpotential would result in a955.2. 1 ML C60/Au(111)Figure 5.17: This series of images shows our complete band folding model,comprising 12 bands (left), the 2 bands that are removed (middle), and theremaining 10 bands that we use for comparison to our XUV (p-polarized,hν = 22.8 eV) data. Because ARPES spectra intensity fluctuates as afunction of photoemission selection rules, in is unsurprising that we do notsee all 12 bands in our data. For clarity in comparison, we remove these 2bands and keep the relevant 10. Rest assured, the other 2 bands are visiblein data collected with an alternate photon source (Fig. 5.18).strong superlattice effect on a deep subsurface-localized resonance. Instead,they find a more probable scenario to be the diffraction of photoelectronsthrough the molecular grid overlayer [143]. Although determining whetherthis phenomenon is band folding or diffraction lies outside the scope of thisthesis, one would be able to differentiate using the following information:• Diffraction should occur for all bands, including bulk bands, whereasband folding is an interface effect.• Band folding should lead to hybridization and gaps opening up in thelinearly-dispersing cone-like features. Krivenkov et al. did not findevidence of gaps [143], but we do not have the experimental resolutionto confirm their findings.41As a final note, it is worth considering that both diffraction and bandfolding could occur in this system simultaneously.41Though our data could, in principle, provide an upper limit for the size of a gap.965.2. 1 ML C60/Au(111)Figure 5.18: Comparison of Fermi Surface spectra taken on monolayer C60with unpolarized 22.1 eV He lamp light source (left) vs. p-polarized 22.8 eVXUV light source (right). ARPES spectra intensity fluctuates as a functionof photoemission selection rules; relevant parameters include light sourcepolarization and photon energy. In this case, 10/12 bands from our modelfit the XUV data on the right, and the other 2 bands are visible in the Helamp data on the left.975.2. 1 ML C60/Au(111)kx (Å-1)E-EF(eV)−0.400 0.5−0.5 0 0.5−0.5 −0.5−11 ML C60 (DCNN) 1 ML C60 Au(111)ky = −0.36 Å-1 ky = −0.36 Å-1 ky = −0.72 Å-1Figure 5.19: Comparison of slope of replica band with Au sp band. (Left)High symmetry cut at ky = −0.36 A˚−1 on 1 ML C60/Au(111) showing replicabands (taken with XUV, hν = 25 eV, T = 9 K). Data was passed through thedenoising convolutional neural network described in Section 2.5. Lorentzianpeaks were fit to the right side of the left cone-like feature using a rolling fit(see Fig. 5.22 for further information); centers of fit results are indicated byturquoise dots. A linear fit to the centers of those peaks results in the purpledashed line. This line has a slope of -7.9 ± 0.2 and matches our replicaband data well. (Middle) Fit is plotted on, and agrees with, our raw data.(Right) High symmetry cut at ky = −0.72 A˚−1 on pristine Au(111) showingsp band (taken with He lamp, hν = 22.1 eV, T = 10.5 K). This value of kycontains the portion of the sp band equivalent to the section that results inthe relevant replica band, assuming band folding has occurred. The purpledashed line has the same slope as the fit result from the replica band with aconstant offset chosen to allow the line to overlay the sp band. The fit resultfrom our replica band data matches the slope of the sp band in pristineAu(111), further supporting agreement between our model and data.985.2. 1 ML C60/Au(111)5.2.3 Denoised Data AnalysisAlthough we do not have the experimental resolution to confirm Krivenkovet al.’s conclusion that the linearly-dispersing cone-like features lack theavoided crossing gaps found in ground state replicas (band folding) [143],the analysis of these features provides an excellent opportunity to illustratethe advantages the convolutional neural network denoising process [110]described in Ch. 2.Figure 5.20 shows the linearly-dispersing features that lie at the K pointsof the 1st BZ (ky = −0.36) with linear fits on both the (a) raw and (b)denoised XUV data, along with (c) a comparison of the 2 fits overlaid on topof both the raw and denoised data. This comparison conveys the advantageof denoised data as it produces a visually better fit. The denoised dataproduces even more impressive results on our He lamp data, as shown inFig. 5.21. Here, the linearly-dispersing feature is barely visible in the rawdata, and numerous data points must be excluded in order to generate anarguably acceptable fit (a). The denoised data can not only be fit to withless data selection, but also produces an image in which the cone-like featurecan be readily discerned. In case the reader is interested, Fig. 5.22 explainsthe fitting procedure used in this section. Nevertheless, one can see from thefits that the presence of a hybridization gap cannot be either confirmed orexcluded based on this data.995.2. 1 ML C60/Au(111)Figure 5.20: Linearly-dispersing features that lie at the K points of the 1stBZ (ky = −0.36) with linear fits on both the (a) raw and (b) denoised XUVdata, along with (c) a comparison of the 2 fits overlaid on top of both theraw and denoised data.1005.2. 1 ML C60/Au(111)Figure 5.21: Comparison of raw and denoised data of linearly-dispersingfeature with fits. a) Raw data with fits: (i) raw data, (ii) initial fit, (iii)datapoints to be discarded marked in blue (for the purposes of generatinga better fit), (iv) final fit on raw data, excluding some data points. (b)Denoised with fits using the same initial parameters as in a (ii) and a (iv) (forb (ii) and b (iii), respectively). (c) (i) Denoised data with the raw data fit inpurple (a (ii)) and the denoised fit in turquoise (b (ii)). Note that not onlyis the fit from the denoised data better when compared to the underlyingdata in (i), but the fits cannot easily be visibly compared to the raw data,because the feature is so faint (ii).1015.2. 1 ML C60/Au(111)Figure 5.22: Fitting Procedure: Lorentzian peaks are fit in three discretesections (bottom, middle, and top of “cone”); the number of peaks expectedis specified per section (2, 2, and 1, respectively). For each section, data issliced in y and a “rolling fit” is applied. For example: We fit the (a) top ofour cone (pink) with (b) a y range of 0.1 eV (black bracket), a window of+/- 0.02 eV (green dotted lines), and 20 steps. These parameters mean thateach y center value is 0.1 / 20 = 0.005 eV apart. For each y center value (reddashed line), we get an average y slice (where, for every x value, the y center+/- 0.02 eV values are averaged, and thus a line plot of eV vs intensity canbe made). (c) We then fit a single Lorentzian peak to that line data. (d)Finally, we add the (x=Lorentzian peak center, y=y center value) (circledwith black arrow pointing to it) to our list of coordinates, which we use tofind our best fit lines.1025.3. 5 ML C60/Au(111)5.2.4 Summary of Section 5.2Although these replica features visible in 1 ML C60/Au(111) were not part ofour initial rational for this experiment, they provide a useful characterizationand present a potentially exciting opportunity. If the phenomenon is dueto diffraction, it means we have grown an excellent ML film [143]. If it isband folding, it implies that we can modify the electronic structure at theinterface. An examination of any new features created by the C60/Au(111)interface would provide a foundational result for studies of C60 or C60-basedheterojunction materials (including OPV materials), while also illustratingan opportunity to use organic materials to impose superstructures on metallicsubstrates to generate new interfacial electronic structure features. In thelarger context of our experiment, as previously discussed, we are attemptingto grow thin films in a manner that simulates bulk C60 (due to the relevanceto OPVs) and we want to avoid any influence of the substrate. Therefore,pragmatically, these results meant that we needed to grow high qualitythicker films in order to clearly see the electronic states of C60 without anyinterference from this phenomenon, regardless of its attribution.5.3 5 ML C60/Au(111)5.3.1 ARPES DataAfter determining that we needed to grow films thicker than 1 ML to avoidthe confounding interfacial phenomenon described in the previous section, wesuccessfully grew and collected ARPES data on ordered 5 ML films. Figures5.23 and 5.24 show ARPES data from a 5 ML C60/Au(111) film, taken withour XUV source (hν = 22.8 eV, T = 10 K) and our He lamp source (hν =22.1 eV, T = 27 K), respectively. In both datasets, the HOMO is located at∼ -2.05 eV below EF and has a FWHM of ∼ 560 meV, and the HOMO-1is located at ∼ -3.4 eV below EF and has a FWHM of ∼ 800 meV. Thesevalues for the HOMO are consistent with the calculations and experimentalresults of other groups [64, 120, 149], the HOMO-1 is slightly broader thanexpected but still reasonable.1035.3. 5 ML C60/Au(111)Figure 5.23: ARPES spectra and EDC of 5 ML C60/Au(111) taken with ourXUV source (hν = 22.8 eV, T = 10 K). The location of the HOMO andHOMO-1 relative to EF is determined by two Gaussians fit to the EDC. The(bottom) EDC plot includes the fit, reporting the peak center and FWHMvalues.1045.3. 5 ML C60/Au(111)Figure 5.24: ARPES spectra and EDC of 5 ML C60/Au(111) taken with ourHe lamp source (hν = 22.1 eV, T = 27 K). The location of the HOMO andHOMO-1 relative to EF is determined by two Gaussians fit to the EDC. The(bottom) EDC plot includes the fit, reporting the peak center and FWHMvalues.1055.3. 5 ML C60/Au(111)M M'ΓK Γ'k|| (Å-1)E-EF(eV)MC60KC60KAuMAuC60/Au(111)kxky5 ML C60/Au(111) 5 ML C60/Bi2Se3 (Latzke et al.)5 ML C60/Bi2Se3 CurvatureM M'Γ K K'Γ' M M'Γ KΓ'a) b)c)d)–1.5 -- - - - -–2 -–2.5 -–3 -–3.5 -–4 -DFT: 1ML C60/Bi2Se3E-EF(eV)Figure 5.25: Comparison of our 5 ML C60 band structure data with pub-lished experimental data and calculations. (a) Bandstructure of our 5 MLC60/Au(111) film (XUV, hν = 22.8 eV, T = 10 K). (b) Latzke and Ojeda-Aristizabal et al.’s published work of 5 ML C60/Bi2Se3 [149]. (c) Adaptationof Latzke and Ojeda-Aristizabal et al.’s figure in [149] depicting (left) thecurvature of their experimental data and (right) their calculated results forsingle layer C60/Bi2Se3 band structure. The lines from the calculation thatbest fit the curvature data are highlighted in red (right) and plotted overthe data (left). (d) Schematics of the C60 BZ and the relevant HS cuts for(left) our data and (right) Latzke and Ojeda-Aristizabal’s data.1065.3. 5 ML C60/Au(111)Figure 5.25 compares a high symmetry cut taken from our (streak cor-rected – see Appendix D) data with Latzke and Ojeda-Aristizabal et al.’s[149] published work of C60 on Bi2Se3 (both data and calculations). Althoughtaken with different sources – a lab-based XUV source with hν = 22.8 eV(T = 10 K) vs a synchrotron with hν = 45 eV (T = 20 K) – and on differentsubstrates, the data comparison can be useful. Specifically, the curvatures,bandwidths, and relative location of the HOMO to the HOMO-1 appearconsistent. Further analysis of our high symmetry cut reveals that the peaklocation and bandwidths of the HOMO and HOMO-1 remain quite consistentacross high symmetry points K, Γ, M, Γ′, and M′ (see Fig. 5.26).Because we are interested in simulating the OPV-relevant bulk material,it is also relevant to see if our data approximates bulk calculations. Figure5.27 compares our band structure data to theoretical calculations for bulkC60 in the fcc phase (DFT by Jalali-Asadabadi et al. [65]) and in the sc phase(tight-binding by Laouini et al. [150]). Recall that C60 undergoes a phasetransition at ∼ 260 K at which point it transitions from its fcc bulk structure(> 260 K) to a simple cubic structure with a 4 unit basis (< 260 K) – seeSection 1.3.2 for further details. We see general agreement between the dataand calcualtions regarding the band locations and bandwidths. A prominentdiscrepancy is the dispersion in the HOMO at the Γ point, where we seean oval pocket in the data, but more of a parabola in Jalali-Asadabadi’scalculation; the data better agrees with Laouini’s calculated dispersion at Γ,which is unsurprising given that our data was taken at T = 10 K and theC60 is expected to be in the sc phase.Figures 5.28 and 5.29 show ARPES spectra of our 5 ML films takenwith our XUV source (hν = 22.8 eV, T = 10 K) and our He lamp source(hν = 22.1 eV, T = 27 K), respectively, and depict CECs taken at energiesapproximating the top, middle, and bottom of the HOMO and HOMO-1.High symmetry slices taken across the BZs are included and illustrated withpink and purple dashed lines. These CECs show comparable intensity toLatzke and Ojeda-Aristizabal et al.’s work on C60/Bi2Se3 published in Ref.[149].42 In particular, CECs through the HOMO should show a hexagon of42Bi2Se3 was chosen for its small lattice mismatch of 3.4% [151].1075.3. 5 ML C60/Au(111)Figure 5.26: Comparison of the HOMO and HOMO-1 peak positions andwidths at high symmetry points in a 5 ML C60 sample. (Top) High symmetrycut of C60 band structure including HOMO and HOMO-1. Integrationwindows are indicated around each high symmetry point. (Bottom) EDCswith Gaussian fits reveal that the peak location and bandwidths of theHOMO and HOMO-1 remain quite consistent across high symmetry pointsK, Γ, M, Γ′, and M′.1085.3. 5 ML C60/Au(111)Intensity(arb. u)C60 (fcc)(Jalali-Asadabadi et al.)W WL Γ KXM M'ΓK Γ'k|| (Å-1)E-EF(eV)C60 (sc)(Laouini et al.)MΓ ΓX R M5 ML C60/Au(111)a) b)c)-3.40 eV0.87 eV-2.08 eV0.57 eV–1.5 -–2 -–2.5 -–3 -–3.5 -–4 -–1.5 -–2 -–1.5 -–2 -–2.5 -–3 -–3.5 -–4 -- - - - - - - -Figure 5.27: Comparison of high symmetry cut data of a 5 ML C60/Au(111)film to band structure calculations. (a) HS data of our film, taken with theXUV source (hν = 22.8 eV), including center energies and fwhm. (b) Bandstructure calculation for fcc C60 (applicable to bulk C60 at room temperature)from Jalali-Asadabadi et al. (Ref. [65]). Black dashed line indicates top ofHOMO in (b), which is considered EF in Ref. [65]. For easier comparisonwith our data, an offset was applied to (b)’s y-axis such that the center ofthe calculated HOMO at Γ is aligned with our data at -2.08 eV (grey dottedline). (c) Band structure calculation for C60 with 4 distinct orientations(applicable to our low-temperature sc phase with a 4 unit basis) from Laouiniet al. (Ref. [150]). Note that the dispersion in the HOMO at the Γ pointthe data better agrees with Laouini’s (Ref. [150]) calculated dispersion at Γthan Jalali-Asadabadi’s (Ref. [65]) calculation. This is unsurprising giventhat our data was taken at T = 10 K and the C60 is expected to be in the scphase.1095.3. 5 ML C60/Au(111)intensity along the Brillouin zone boundary that slowly transitions to a sixpointed star as one moves lower in binding energy (towards the bottom ofthe HOMO), as is depicted in Ref. [149]. A honeycomb pattern is featuredin the middle of the HOMO-1.Figure 5.28: ARPES spectra of 5 ML C60/Au(111) taken with XUV (hν =22.8 eV, T = 10 K). (a) Constant energy cuts of C60 at energies approximatingthe top, middle, and bottom of the HOMO and HOMO-1. (b) The highsymmetry points and relative Brillouin zones of C60 and Au(111). (c) Verticalslice taken at kx = Γ (depicted by the dashed purple lines) illustrating thedispersion of the C60 band manifolds; the top (green), middle (dark red),and bottom (brown) energies of the HOMO and HOMO-1 are shown withminor ticks and labels.1105.3. 5 ML C60/Au(111)Figure 5.29: ARPES spectra of 5 ML C60/Au(111) taken with He lamp(hν = 22.1 eV, T = 27 K). (a) Constant energy cuts of C60 at energiesapproximating the top, middle, and bottom of the HOMO and HOMO-1. (b)The high symmetry points and relative Brillouin zones of C60 and Au(111).(c) Vertical slice taken at kx = Γ (depicted by the dashed purple lines)illustrating the dispersion of the C60 band manifolds; the top (green), middle(dark red), and bottom (brown) energies of the HOMO and HOMO-1 areshown with minor ticks and labels.5.3.2 Denoised Data AnalysisWe can again take advantage of the convolutional neural network denoisingprocess [110], described in Ch. 2, to generate denoised images of our bandstructure. Figure 5.30 illustrates the difference between taking the curvature1115.4. 10 ML C60/Au(111)(data is smoothed first, by applying a Gaussian filter) of the raw data versusthe denoised data. This comparison also illustrates the benefit of caution inapplying this denoising filter: although the curvature of the denoised datacrisply depicts the most prominent features, it appears to wash out some ofthe structure visible in the curvature of the raw data.M M'Γ Γ'k|| (Å-1)–1.5–2–2.5–3–3.5–1.5–2–2.5–3–3.5–1.5–2–2.5–3–3.5–1.5–2–2.5–3–3.5M M'Γ Γ'k|| (Å-1)E-EF(eV)E-EF(eV)E-EF(eV)E-EF(eV)Raw Data and Curvature Denoised Data and CurvatureFigure 5.30: Comparison of raw and denoised data of the C60 band structure(taken with the XUV source). Top plots illustrate raw (left) and denoised(right) data, while bottom plots present the curvature of each. Data issmoothed using a Gaussian filter before taking the curvature (the 2nd deriva-tive along the y-axis). Although the curvature of the denoised data crisplydepicts the prominent doubled structure at the top of each band, it appearsto wash out some of the lower structure visible in the curvature of the rawdata.5.4 10 ML C60/Au(111)Although the bulk of our static ARPES data was acquired on 1 ML and 5ML C60/Au(111) films, we also successfully grew ordered 10 ML films. Our10 ML films were primarily grown for the purposes of conducting TR-ARPES1125.4. 10 ML C60/Au(111)Figure 5.31: ARPES spectra (ky = 0) of 10 ML C60/Au(111) taken with ourHe lamp source (hν = 22.1 eV, T = 10.5 K).experiments, however we did acquire limited ARPES data on these filmsas well, for characterization purposes and consistency checks. Figure 5.31presents an ARPES spectra of the band structure taken with the He lampsource (hν = 22.1 eV, T = 10.5 K), and Fig. 5.32 provides an EDC thatincludes the HOMO and HOMO-1. The peak locations and widths aresimilar to those found for a 5 ML film. For a complete list of the thicknessdependence of peak positions for C60’s HOMO and HOMO-1, see Table 5.1.1135.5. Summary of Static ARPES ResultsFigure 5.32: EDC of 10 ML C60/Au(111) band structure, including theHOMO and HOMO-1. The location of the peaks relative to EF is determinedby a fit with 2 Gaussian peaks.5.5 Summary of Static ARPES ResultsThis section provides a summary of the C60 HOMO and HOMO-1 peakpositions (integrated over all kx) as a function of film thickness and photonsource (see Table 5.1). It also compares band structure data taken with theXUV source on pristine Au(111), a 1 ML film, and a 5 ML film. Figure5.33 shows the three datasets over the same energy and kx, and it alsoincludes a direct comparison of the region between the HOMO and EFwhich emphasises the distinct spectral features visible only in the 1 MLC60/Au(111) (described further in Section 5.2.2) in juxtaposition with theAu ss and the 5 ML C60 band gap.1145.5. Summary of Static ARPES ResultsTable 5.1: Thickness Dependence of C60 Band PositionsFilm Thickness hν Source HOMO HOMO-11 ML He lamp −1.64 eV too much Au signalto fit with confidence1 ML XUV −1.7 eV too much Au signalto fit with confidence5 ML He lamp −2.05 eV −3.41 eV5 ML XUV −2.03 eV −3.37 eV10 ML He lamp −2.06 eV −3.42 eVb)−1−2−3−4−0.4 −0.2 0 0.2 0.4 −0.4 −0.2 0 0.2 0.4 −0.4 −0.2 0 0.2 0.4a)Au(111) 1 ML C60 5 ML C60E-EF(eV)E-EF(eV)−1−0.4 −0.2 0 0.2 0.4−0.4 −0.2 0 0.2 0.4−0.4 −0.2 0 0.2 0.4kx (Å-1) kx (Å-1) kx (Å-1)kx (Å-1) kx (Å-1) kx (Å-1)Figure 5.33: Summary of band structure data taken with XUV source onpristine Au(111) (gold, hν = 25 eV), 1 ML C60 (green, hν = 22.65 eV), and5 ML C60 (grey, hν = 22.8 eV). (a) Data covers EB = (−4.4, EF ). Eachdata set is normalized. (b) Same data as in (a) but EB = (−1.2, EF ). Thisillustrates the distinct spectral features visible only in the 1 ML C60/Au(111)(described further in Section 5.2.2), in juxtaposition with the Au ss and the 5ML C60 band gap. Each newly-limited data set is normalized and maximumintensity is set to 0.8 for the sake of feature visibility.115Chapter 6TR-ARPES on C60/Au(111)As previously stated, the overarching goal of the research described in thisthesis is to use TR-ARPES to help understand charge transfer in OPVs; thisrelies on the successful acquisition of TR-ARPES data on the excited statesof C60. Because the HOMO-LUMO transition in C60 is optically forbidden[68, 69] and therefore absorption is weak, there is limited optical data on C60-based samples. However, some transient absorption data has been publishedon both neat C60 and C60-based heterojunction films [152, 153]. Such workhas investigated the photoexcitation dynamics of C60 films, elucidatingfeatures such as triplet yield, exciton diffusion rates, and recombinationdynamics. While experimental differences such as substrate, film thickness,and the level of disorder in the sample may effect results, this previous researchindicates the presence of both CT and Frenkel excitons and speaks to thelifetimes of some of these states, providing valuable background informationand context for our TR-ARPES measurements (addressed further in Section6.1.4). In turn, the TR-ARPES data included in the following chapterestablishes a complementary next step to these prior works.Although the HOMO-LUMO transition in C60 is dipole-forbidden, litera-ture indicates that we can populate a manifold of excited states with a 3.1eV pump pulse [32, 63, 67]. For the purpose of this thesis, I will refer to thethree accessible excited states as the CT2, CT1, and S1; this nomenclature ischosen for ease of comparison with preexisting work [63]. However, recentresults suggest that these states are all of singlet character and are thusreferred to, in Ref. [67], as the S3, S2, and S1, respectively. As discussed inSection 1.3.3 (and illustrated in Fig. 1.7), the extent of the delocalization ofthese states – to what degree they are of charge-transfer nature – remainsan open question [32, 63, 67].116Chapter 6. TR-ARPES on C60/Au(111)Figure 6.1: Artistic rendering of TR-ARPES experiment on C60/Au(111),using ScientaOmicron’s DA30 hemispherical analyzer and conducted withUBC’s 3.1/6.2 eV pump-probe set up. Image shows a 1.55 eV seed pulsepassing through a barium borate nonlinear optic crystal (BBO) used forfrequency doubling. Data displayed in the analyzer is from the measurementsdescribed in this chapter. This image is an adaptation of a figure from Ref.[154].The data in this chapter was collected over the course of multiple mea-surements and with different experimental setups. The TR-ARPES spectraof the excited states presented in this chapter were acquired with the 3.1 eVpump and 6.2 eV probe (referred to after this as the 3.1/6.2 eV pump-probe)set up, illustratively depicted in Fig. 6.1. Additional data is shown forcomparison in Appendix A. Table 6.1 provides, for the reader’s reference, asummary of the data, experiment configuration, and the relevant section(s)of this chapter.1176.1. DynamicsTable 6.1: Summary of TR-ARPES ExperimentsDate Sample Thickness hν (pump/probe) Polarization Time Res. Section(s)April 2022 5 ML 2.4/22.8 eV p/p n/a 6.3.1February 2023 10 ML 3.1/6.2 eV s/(n/a) 500 fs 6.1 & 6.2May 2023 10 ML 3.1/6.2 eV p/s 440 fs Appendix A.1June 2023 10 ML 3.1/6.2 eV p/p 225 fs 6.1 & 6.26.1 Dynamics6.1.1 Pump Effect & Identifying Excitonic StatesUsing a 3.1/6.2 eV pump-probe set up, we were able to visualize the pumpeffect and excitonic states in our C60 thin film. Figure 6.2 presents a time-resolved and angle-integrated scan of the dynamics of our 10 ML C60/Au(111)film, taken at 10.6 K. The log intensity heatmap shows visible pumped signalbeginning at zero delay of the CT2 and CT1 states. The dark, oversaturatedsignal intensity that extends up to ∼ 2.05 eV above the HOMO is signal fromthe Au(111) substrate (the Fermi energy of Au(111) is 2.05 eV above theC60 HOMO). The S1 state is discernible in the raw data but is not visible inFig. 6.2 because it lies within the oversaturated region of the image. The S1state is visible in the raw data, while the CT1 is discernible, and the CT2 isnot visible with this contrast, as seen in Fig. 6.3. An inset image illustratesall three excited states with different saturation levels. Both Figures 6.2and 6.3 note regions of negative delay, zero delay (“t0”) and positive delay(“pumped”); integrating over these delays provides the data featured in theEDC (energy distribution curves) plots in Fig. 6.4.Taking EDCs integrated over various delays enables us to determinewhere our states lie in energy, as well as providing information regardingthe decay rates of these states. The pump effect populating the S1 state ismore clear in the EDCs. In Fig. 6.4 (top, linear plot), we can see that theS1 state is least prominent at negative delay (-1 to -0.5 ps), more prominentat zero delay (-0.5 to 0.5 ps),43 and most prominent at positive delay (0.543The range that constitutes zero delay is determined by the experiment’s time resolution.1186.1. DynamicsFigure 6.2: Time-resolved and angle-integrated scan of the dynamics of our10 ML C60/Au(111) film, taken with our 6 eV source in Feb. 2023 (T = 10.6K). This plot illustrates the pump effect (dark is signal intensity), where weexpect pumped signal only at or after zero delay. In our case, the CT1 (red)and CT2 (yellow) are visible beginning at a delay of up to -0.5 ps, due toour having a time resolution of ∼ 500 fs. The pump effect of the S1 is notvisible in this plot due to the oversaturated signal up to the Au(111) Fermienergy. Visibility of the CT2 signal is achieved by taking a log plot of theheatmap data (colorbar inset) and is necessary because the excitonic signalsare very weak; this is also why the signal below EF appears oversaturated.1196.1. DynamicsFigure 6.3: Time-resolved and angle-integrated scan of the dynamics of our10 ML C60/Au(111) film, taken with our 6 eV source in Feb. 2023 (T = 10.6K). This plot illustrates the pump effect, where we expect signal above EFonly at or after zero delay. This plot has not been oversaturated, therefore theCT2 (yellow) is close to invisible (in comparison to the discernible intensityin the 2.4 - 3.0 eV region of Fig. 6.2). We can, however, detect some increasein pumped signal in the S1. It is perhaps slightly more obvious in the insetimage, which illustrates all three states with different saturation levels (the 3excitonic states are indicated by a yellow, red, and grey bar on the left axis).Note how the S1 state gets brighter at positive delay.1206.1. DynamicsFigure 6.4: Energy distribution curves (EDCs) of the S1, CT1 and CT2 statesintegrated over negative delay (-1 to -0.5 ps, blue), zero delay (-0.5 to 0.5 ps,orange), and positive delay (0.5 to 1 ps, green). (Top) Linear plot shows theS1 state is least prominent at negative delay, more prominent at zero delay(-0.5 to 0.5 ps), and most prominent at positive delay. (Bottom) Log plothighlights the dynamics of the CT states, with the CT1 displaying the samedynamics pattern as the S1, in contrast to the CT2 that is almost uniquelypopulated at time zero. These dynamics agree with literature that suggestsdirect population of the CT2 and subsequent decay into the longer-lived CT1and S1 states [63].1216.1. Dynamicsto 1 ps). This indicates that the S1 state is not directly populated by thepump pulse, but rather is occupied via shorter-lived states decaying into it.Upon examining the dynamics of the higher order CT1 and CT2 (bottom,log plot), we see a similar pattern in the dynamics of the CT1, but theCT2 is clearly almost uniquely populated at time zero. This agrees withliterature that suggests direct population of the CT2 and subsequent decayinto the longer-lived CT1 and S1 states [63]. The decay rate of the CT2 couldbe compared with the population rates of the lower states to confirm thiscascading effect using rate equations in future analysis.6.1.2 States in EnergyTo determine where these excited states lie in energy, we fit Gaussians44 tothe peaks present in the relevant EDC. This section describes a multitude offits for each excited state, manifesting as a dense discussion of fit comparisonsand peak values; a summary (Tables 6.2 and 6.3) is included at the end of thissection for the benefit of the reader. Figure 6.5 shows the time-resolved andangle-integrated heatmap of the CT2 at Γ along with the EDC at zero delay(from our February experiment). Both plots indicate at least three peaksassociated with the CT2: 2.57 eV, 2.76 eV, and 2.96 eV. The peak positionsand FWHMs are reported in the figure. Figure 6.6 shows the time-resolvedand angle-integrated heatmap of the CT2 along the Γ - K cut, as well as theEDC at zero delay (from our June experiment). Fitting three peaks to thisEDC finds states at 2.58 eV, 2.78 eV, and 3.04 eV. The location of the peaksare largely consistent with the results from February’s measurement (givenour measurement resolution of 18 meV), with the highest peak deviating themost (by 80 meV). The FWHMs of the peaks show the same trend acrossmeasurements, with the 2.57/2.58 eV peak found to be the broadest, the2.76/2.78 eV peak the narrowest, and the 2.96/3.04 eV peak of a breadthbetween the two others. Some differences in the fitted peak values couldbe attributed to the raw data having been acquired over overlapping butdifferent ranges in energy.44allowing for a constant offset1226.1. DynamicsFigure 6.5: TR-ARPES spectra and EDC of the CT2 at Γ taken in February2023. Data integrated in θ approximating kx = (-0.13, 0.13) A˚−1 as illustratedin the inset image of hexagonal BZ: purple line represents available data, pinkline indicates integration window. (Top) Time-resolved and angle-integratedheatmap of the CT2. (Bottom) EDC at zero delay (integrated from -0.5 to0.5 ps). Three peaks are visible in both images; the EDC is fit with threeGaussians, allowing for a constant offset. Peaks are found to be at 2.57 eV,2.76 eV, and 2.96 eV.1236.1. DynamicsFigure 6.6: TR-ARPES spectra and EDC of the CT2 along Γ - K takenin June 2023. Data integrated in θ approximating kx = (0.02, 0.27) A˚−1as illustrated in the inset image of hexagonal BZ: purple line representsavailable data, pink line indicates integration window. (Top) Time-resolvedand angle-integrated heatmap of the CT2. (Bottom) EDC at zero delay(integrated from -0.5 to 0.5 ps). Three peaks are visible in both images; theEDC is fit with three Gaussians, allowing for a constant offset. Peaks arefound to be at 2.58 eV, 2.78 eV, and 3.04 eV.1246.1. DynamicsFigures 6.7 and 6.8 show the time-resolved and angle-integrated heatmapof the CT2 along the M - K cut, as well as the EDC at zero delay (fromour June experiment). The datasets of these two figures were acquired overdifferent delays; Fig. 6.7 contains data from a delay of -1 to 1 ps (the samedelay window as Fig. 6.5), and Fig. 6.8 contains data from a delay of -0.5to 0.5 ps (the same delay window as Fig. 6.6). Note that all of the EDCsshown in these four figures are integrated over the same region, from -0.5to 0.5 ps. As expected, fits to the data in Figures 6.7 and 6.8 report verysimilar values. Peaks values are found to be 2.69/2.7 eV, 2.76/2.77 eV, and2.98/3.0 eV (as shown in the middle panel and top EDC plot of the twofigures). The FWHMs of the top states were quite narrow, and the lowerpeak location did not necessarily appear to provide the best fit (especially inFig. 6.8). An alternative fit is show in the bottom panel (lower EDC) of thetwo figures, in which the lowest peak has been fixed at 2.57 eV. All otherparameters of the fit were allowed to vary. The two higher peak values remainnearly unchanged, but the relative FWHMs of the three peaks become moreconsistent with the fits at Γ and Γ - K. Of course, the energies of the excitonicstates and the bandwidths may change depending on the location in the BZ;therefore, we cannot assume that the second fits in Figures 6.7 and 6.8 arenecessarily correct. Both fits are worth keeping in mind for future reference,as we continue to build a more complete picture of these excitonic states.1256.1. DynamicsFigure 6.7: TR-ARPES spectra and EDC of the CT2 along M - K takenin June 2023, with data spanning -1 to 1 ps delay. Data integrated inθ approximating kx = (0.02, 0.27) A˚−1 as illustrated in the inset imageof hexagonal BZ: purple line represents available data, pink line indicatesintegration window. (Top) Time-resolved and angle-integrated heatmap ofthe CT2. (Middle) EDC at zero delay (integrated from -0.5 to 0.5 ps) withfit where peak values and FWHMs are allowed to vary. (Bottom) EDC atzero delay (-0.5 to 0.5 ps) with fit where lowest peak value is fixed at 2.57eV. All other parameters are allowed to vary.1266.1. DynamicsFigure 6.8: TR-ARPES spectra and EDC of the CT2 along M - K takenin June 2023, with data spanning -0.5 to 0.5 ps delay. Data integrated inθ approximating kx = (0.02, 0.27) A˚−1 as illustrated in the inset imageof hexagonal BZ: purple line represents available data, pink line indicatesintegration window. (Top) Time-resolved and angle-integrated heatmap ofthe CT2. (Middle) EDC at zero delay (integrated from -0.5 to 0.5 ps) withfit where peak values and FWHMs are allowed to vary. (Bottom) EDC atzero delay (-0.5 to 0.5 ps) with fit where lowest peak value is fixed at 2.57eV. All other parameters are allowed to vary.1276.1. DynamicsFitting over our entire acquired energy range (as presented in Figures6.2 and 6.3) enables us to find the location in energy of our CT1 and S1states as well our CT2. Figure 6.9 shows the EDC over our largest energyregion (and integrated from 0.25 to 0.5 ps), along with its best fit whichincludes seven Gaussian peaks. As shown in the figure, the three peaks inthe CT2 are found to be fairly consistent with the those fit to the isolatedCT2 (Fig. 6.5), although the 2.5/2.57 eV peak (in particular) is narrower.This is reasonable because the seven-peak fit includes the lower states, thetails of which contribute to the intensity found at 2.5 eV. This phenomenonis perhaps more intuitively understood by observing the fit components plotin Fig. 6.9. The seven peaks are found to be at the following locations,and shown in log scale with labels of the relevant states in Fig. 6.10: (S1)1.63 eV, 1.8 eV, (CT1) 1.98 eV, 2.12 eV, (CT2) 2.5 eV, 2.75 eV, 2.96 eV.It is worth noting that we are not confident that these peaks represent thecomplete manifold of excited states expected in this energy region, howeverthat is the minimum number of states which enable a reasonably accurate fit(no substantial anisotropy in the residuals, for example).Although we do not have data from our June measurement that covers asimilar range in energy with comparable signal-to-noise as the data presentedin Figures 6.9 and 6.10, we are able to show some consistency in peak valuesof the lower states across measurements as well. Figures 6.11 and 6.12 showtime-resolved and angle-integrated heatmaps centered on the CT1 taken atΓ - K and M - K, respectively. EDCs of the heatmaps, integrated from 0to 1 ps and fit with three Gaussian peaks as well as a Fermi-Dirac function(and allowing for a constant offset), indicate peaks at (inferred S1 peak belowdata minimum) 1.87/1.68 eV, (CT1) 2.12/2.21 eV, and (bottom of CT2)2.48/2.52 eV. Over the same energy region, February data indicated peaks at(S1) 1.63 eV, 1.8 eV, (CT1) 1.98 eV, 2.12 eV, and (CT3) 2.5 eV (Fig. 6.9).1286.1. DynamicsFigure 6.9: EDC of the full energy range acquired at Γ in February 2023showing our best fit and the fit components. (Initial angular integration inθ approximating kx = (-0.13, 0.13) A˚−1.) (Top) EDC of all three excitedstates, taken at Γ and integrated from 0.25 to 0.5 ps. The best fit of thisdata includes seven Gaussian peaks, a Fermi-Dirac (which takes into accountthe Au(111) signal), and allows for a constant offset. This represents theminimum number of contributions that enable an accurate fit. (Bottom)Plot of the fit components along with peak energies and FWHMs. The sevenpeaks are found to be at the following locations: (S1) 1.63 eV, 1.8 eV, (CT1)1.98 eV, 2.12 eV, (CT2) 2.5 eV, 2.75 eV, 2.96 eV.1296.1. DynamicsFigure 6.10: Log plot of the EDC and fit from Fig. 6.9 including labels ofthe relevant states and residuals of the fit, showing no obvious anisotropy orstructure.1306.1. DynamicsFigure 6.11: TR-ARPES spectra and EDC centered on the CT1 along Γ- K taken in June 2023. Data integrated in θ approximating kx = (0.02,0.27) A˚−1 as illustrated in the inset image of hexagonal BZ: purple linerepresents available data, pink line indicates integration window. (Top)Time-resolved and angle-integrated heatmap centered on the CT1. (Bottom)EDC integrated from 0 to 1 ps and fit with 3 Gaussian peaks as well as aFermi-Dirac function (and allowing for a constant offset). Peaks are found at(inferred S1 peak below data minimum) 1.87 eV, (CT1) 2.12 eV, and (bottomof CT2) 2.48 eV.1316.1. DynamicsFigure 6.12: TR-ARPES spectra and EDC centered on the CT1 along M- K taken in June 2023. Data integrated in θ approximating kx = (0.02,0.27) A˚−1 as illustrated in the inset image of hexagonal BZ: purple linerepresents available data, pink line indicates integration window. (Top)Time-resolved and angle-integrated heatmap centered on the CT1. (Bottom)EDC integrated from 0 to 1 ps and fit with three Gaussian peaks as wellas a Fermi-Dirac function (and allowing for a constant offset). Peaks arefound at (inferred S1 peak below data minimum) 1.68 eV, (CT1) 2.21 eV,and (bottom of CT2) 2.52 eV.1326.1. DynamicsA summary of the peak values across our multitude of datasets delineatedthroughout this chapter is included in Tables 6.2 and 6.3. Additionally, forthe purposes of comparing our states with those reported in literature, threepeaks have been fit to the full energy range of data from our February data,giving the following values: (S1) 1.70 eV, (CT1) 2.11 eV, and (CT2) 2.68eV. A comparison of our results with those from literature as well as furtherdiscussion of the excitonic states is included in Section 6.1.4. For more detailson the fits in this chapter see Section A.3.Table 6.2: Summary of Peak Values for CT2 across Fits45Γ Γ - K M - K 46 M - K 47 Γ - K M - K 1 peak CT22.96 3.04 2.99 / 2.98 3.0 / 2.97 n/a n/aPeaks (eV) 2.76 2.78 2.76 / 2.79 2.77 / 2.77 n/a n/a 2.682.57 2.58 2.69 / 2.57 2.70 / 2.57 2.48 eV 2.52Int. (ps) -1 to 1 -0.5 to 0.5 -1 to 1 -0.5 to 0.5 0 to 1 0 to 1 0.25 to 0.5Figure 6.5 6.6 6.7 6.8 6.11 6.11 A.5Table 6.3: Summary of Peak Values for S1 and CT1 across FitsΓ Γ - K M - K 1 peak each: CT1, S12.212.12 2.12 2.11Peaks (eV) 1.98 1.871.801.63 1.68 1.7Integration (ps) 0.25 to 0.5 0 to 1 0 to 1 0.25 to 0.5Relevant Fig. 6.5 6.11 6.11 A.545We advise caution in directly comparing the results reported in the middle two columns(in between the doubled vertical lines) to the results of the first four columns. The dataused for those two fits spans a very different energy range from the data behind the firstfour columns. See the relevant figures and surrounding text for further information.46Green values are fit with lowest peak fixed at 2.57 eV.47Ibid1336.1. Dynamics6.1.3 Exciton DecaysIn this section, we further probe the dynamics of the excited states. Figures6.13, 6.14, and 6.15 provide estimates of the decay constant for the CT2at Γ - K, M - K, and Γ, respectively. Decay constants are calculated byfitting a Gaussian convolved with an exponential to the (angle-integratedand energy-integrated) temporal distribution curve (TDC).48 Our June data(with a time-resolution of ∼ 225 fs) produces a decay constant of 119 fs (Γ- K) and 124 fs (M - K). Our February data (with a time-resolution of ∼500 fs) produces a decay constant of 204 fs (Γ); when each of the three CT2excited state peaks are fit independently, the given decay constants are 204fs, 181 fs, and 232 fs (see Fig. 6.16). It is important to note that while theseresults do not agree with the 40 fs decay constant found in Ref. [32], thediscrepancy is unsurprising given our time-resolution. With a time-resolutionthat is four to twelve times the expected decay constant, we do not anticipatebeing able to accurately resolve the CT2 decay constant by direct fitting ofthe decay. A discussion of the pulse duration’s possible effect on the decayrate of the CT2 can be found in Section 6.3.4.48The term TDC is not particularly widespread. However, EDCs and MDCs are commonparlance, and TDC makes sense for the comparable time-resolved plot.1346.1. DynamicsFigure 6.13: TR-ARPES spectra and TDC with (decay constant) fit of theCT2 along Γ - K taken in June 2023. Data integrated in θ approximatingkx = (0.02, 0.27) A˚−1 (see inset hexagon). (Top) Time-resolved and angle-integrated heatmap of the CT2 with a source time resolution of 225 fs.(Middle) TDC integrated across full energy range and fit with a Gaussianconvolved with an exponential (and allowing for a constant offset), resultingin a decay constant of 119 fs. (Bottom) Residuals of the fit.1356.1. DynamicsFigure 6.14: TR-ARPES spectra and TDC with (decay constant) fit of theCT2 along Γ - M taken in June 2023. Data integrated in θ approximatingkx = (0.02, 0.27) A˚−1 (see inset hexagon). (Top) Time-resolved and angle-integrated heatmap of the CT2 with a source time resolution of 225 fs.(Middle) TDC integrated across full energy range and fit with a Gaussianconvolved with an exponential (and allowing for a constant offset), resultingin a decay constant of 124 fs. (Bottom) Residuals of the fit.1366.1. DynamicsFigure 6.15: TR-ARPES spectra and TDC with (decay constant) fit of theCT2 at Γ taken in February 2023. Data integrated in θ approximating kx= (-0.13, 0.13) A˚−1 (see inset hexagon). (Top) Time-resolved and angle-integrated heatmap of the CT2 with a source time resolution of 500 fs.(Bottom) TDC integrated across full energy range and fit with a Gaussianconvolved with an exponential (and allowing for a constant offset), resultingin a decay constant of 204 fs. (Bottom) Residuals of the fit.1376.1. DynamicsFigure 6.16: Comparison of the CT2 decay constant for each energy peak.(Top) Time-resolved and angle-integrated heatmap of the CT2 taken at Γ inFebruary 2023 (time resolution: 500 fs), divided into three energy regionscontaining the top (green), middle (orange), and bottom (blue) CT2 peaks.(Middle) TDCs integrated across the three distinct energy ranges and each fitwith a Gaussian convolved with an exponential (and allowing for a constantoffset). The resultant decay constants are 204 fs, 181 fs, and 232 fs. (Bottom)Table reporting the relevant energy regions and results of fits where τ is thedecay constant, t0 is the location relative to time zero of the peak, and ∆t isthe time-resolution in the fit (the FWHM of the Gaussian component).1386.1. DynamicsDelay (ps)E-EHOMO(eV)−0.10.102.221.80 20 40 60 80 100Difference Map of S1 and CT1Figure 6.17: Difference map of the time-resolved and angle-integrated scanof the dynamics of our 10 ML C60/Au(111) film, taken at Γ (February2023). Data integrated in θ approximating kx = (-0.13, 0.13) A˚−1. The firstfour columns of the data were averaged and then subtracted from the rest;pumped signal is shown in red, unpumped signal is white, and depletionis blue. Horizontal red streaks indicate multi-peak structure in the S1 andCT1. The approximate energy regions of the excited states are indicated bythe grey (S1) and red (CT1) vertical bars to the left of the plot. This plothas been oversaturated (by capping the intensities) to better illustrate thisstructure. It is worth noting that the depletion visible below EF at laterdelays (blue) may be attributable to the pre-pulse at -20 ps present in ourFebruary measurement.Although Figures 6.2 and 6.3 illustrate the relative dynamics of the CT2,CT1, and S1 – and they indicate that the lower two states are most prominentfrom 0.5 ps onwards – further data suggests that the CT1 and S1 statesare also substantially longer-lived than the CT2. As is illustrated in Fig.6.17, pumped signal from the CT1 and S1 is present at least on the orderof tens of picoseconds and possibly much longer. Data from our June 2023measurement is consistent with a CT1 decay constant on the order of tensof picoseconds, as can be seen in difference maps of this data, displayed inFigures 6.18 and 6.19. This data also supports the possibility of multi-peakstructure within the CT1, most clearly visible in Fig. 6.19.1396.1. DynamicsFigure 6.18: Difference map of the time-resolved and angle-integrated scanof the dynamics of the CT1 and CT2. Scan taken along Γ - K on a 10 MLC60/Au(111) film, taken with our 6 eV source in June 2023 (T = 10.6 K).Data integrated in θ approximating kx = (0.02, 0.27) A˚−1 as illustratednext to the title: purple line represents available data, pink line indicatesintegration window. The first four columns of the data were averaged andthen subtracted from the rest; pumped signal is shown in red, unpumpedsignal is white, and depletion is blue (see Fig. 6.17 for scale bar). There maybe some multi-peak structure in the CT1, but higher statistics are needed toconfirm.1406.1. DynamicsFigure 6.19: Pump effect and dynamics of the CT1 and CT2 along M - Kon a 10 ML C60/Au(111) film, taken with our 6 eV source in June 2023 (T= 10.6 K). Data integrated in θ approximating kx = (0.02, 0.27) A˚−1 asillustrated next to the title: purple line represents available data, pink lineindicates integration window. (Upper) Difference map of the time-resolvedand angle-integrated scan of the dynamics. The first four columns of thedata were averaged and then subtracted from the rest; pumped signal isshown in red, unpumped signal is white, and depletion is blue. (Lower) EDCof the raw data, integrated from -1 to 0 ps delay (blue), from 0 to 1 ps delay(gold), and from 1 to 5 ps delay (green). Although the heatmap suggestsmultiple peaks in the CT1 (similar to Fig. 6.17), the lack of discernible peakstructure in the EDC plot integrated from 1 to 5 ps (green line) implies aneed for better statistics to facilitating fitting to these peaks.1416.1. DynamicsTo further illustrate and quantitatively probe the decay rate of theselower order states, Figures 6.20 and 6.21 show EDCs waterfall plots of thestates taken at various delays. Figure 6.20 presents EDCs integrated over5 ps, 10 ps, and 20 ps windows, which illustrates that integrating over 20ps helps minimize noise while preserving the peak dynamics visible in thesmaller integration windows. Figure 6.21 displays the result of fits to the20 ps EDC waterfall plot, including plots of the peak centers, FWHMs, andheights for the CT1 and S1 states over time. Comparable data from our Junemeasurement covers a higher energy range, but can also be used to probethe decay constant of the CT1, as illustrated in Figures 6.22 and 6.23.Our observed decay rate of tens of picoseconds or longer for the S1 agreeswith literature-reported values [32, 155]; however, according to Ref. [32],the decay rate for the CT1 is not expected to exceed 1.5 ps. Although wecannot confidently state the cause of our longer-lived state at this point,one possibility is that it is due to a bottleneck effect: any pre-populationof our lower states could result in an artificially-lengthened lifetime of anupper state. Something like a pre-pulse (which was present at -20 ps in ourFebruary data, but not present in our June data; see Section 6.3.3) or evena long enough pulse width (as discussed relative to the CT2 in Section 6.3.4)could cause this. Given either of those effects, we would expect the decayconstant for CT1 to be shorter in our June data than in our February data;this is loosely substantiated by our data as illustrated in Fig. 6.24. However,Figures 6.25 and 6.26 show that decay constants from the June data arecomparable to February, not shorter, giving preliminary evidence that atleast the CT1 exhibits these long lifetimes, possibly due to the high filmquality.1426.1. DynamicsIntensity (arb. u)E-EHOMO(eV)5 ps10 ps20 ps0.5 1 1.5 2 2.52.42.221.82.42.221.82.42.221.8EDCs of S1 and CT1Figure 6.20: EDCs of the CT1 and S1 states integrated over 5 ps, 10 ps, and20 ps rolling integration windows. Data is from our February measurement,taken at Γ (integrated in θ approximating kx = (-0.13, 0.13) A˚−1). Note thatthe 20 ps plot shows less noise while preserving the peak dynamics visible inthe smaller integration windows.1436.1. DynamicsFigure 6.21: EDCs of the CT1 and S1 states integrated over 20 ps with a fitoverlaid. Bottom panels display the fit results, including the peak centers,FWHMs, and heights for the CT1 (orange) and S1 (blue) states over time.1446.1. DynamicsFigure 6.22: EDCs of the CT1 and CT2 states integrated over 10 ps witha fit overlaid. Bottom panels display fit results for the peak centers, andheights for the CT1 (orange) and CT2 (green) states over time. Data fromour June measurement, taken along Γ - K (integrated in θ approximating kx= (0.02, 0.27) A˚−1).1456.1. DynamicsFigure 6.23: EDCs of the CT1 and CT2 states integrated over 10 ps witha fit overlaid. Bottom panels display fit results for the peak centers, andheights for the CT1 (orange) and CT2 (green) states over time. Data fromour June measurement, taken along M - K (integrated in θ approximatingkx = (0.02, 0.27) A˚−1).1466.1. DynamicsDecay: 9.89 +/- 0.44 psDecay: 4.82 +/- 0.22 psDecay: 5.75 +/- 0.14 ps010.80.60.40.205 10Γ (500 fs)Γ - K (225 fs)M - K (225 fs)15 20 25 30Delay (ps)Intensity(arb.u)CT1 Lifetime ComparisonFigure 6.24: Comparison of TDCs of the CT1 (integrated from E - EHOMO= 2.0 - 2.3 eV) from normalized data collected with 500 fs and 225 fs time-resolution. The resolution of the data (particularly at later delays in the 225fs data) is insufficient to support a conclusive comparison of decay constants.However, the data loosely substantiates a shorter decay constant for the225 fs data. Additionally, all three plots show the CT1 state populated forlonger than the 1 - 1.5 ps previously reported [32]. The decays in this plotare generated by fitting an exponential to the normalized data at delays >0. Note that a more accurate fitting technique for decay constants involvesfitting for peaks and then subsequently fitting for the amplitudes over time;this exponential fit is helpful for getting a better sense of the data.Figure 6.24 compares normalized TDCs of the CT1 from data collectedwith 500 fs and 225 fs time-resolution, each fit with an exponential at delays> 0. Figure 6.25 was generated by first taking EDCs of the CT1 with a rollingintegration window of 10 ps and then fitting the heights of those peaks (as afunction of delay) with a Gaussian convolved with an exponential. Futureanalysis could better model the dynamics of this state by incorporatingpopulation dynamics (the excitons are decaying from CT2 into CT1, so thedecay rate of the higher state should be related to the population of the1476.1. Dynamics500 fs (Γ): < 30 psFeb. Decay:5.79 +/- 1.10 ps225 fs (Γ - K)Decay Constants for CT1225 fs (M - K)June Decay:4.57 +/- 1.20 ps0.22heightdelay (ps)0.180.140.10.1height 0.080.060.040.240.20.160.120.080 5 10 15 20 250 5 10 15 20 25 30delay (ps)delay (ps)0 5 10 15 20 25June Decay:5.04 +/- 1.58 psdatafitFigure 6.25: Comparison of decay constants for the CT1 from data collectedwith 500 fs and 225 fs time-resolution. These fits are the results of takingEDCs of the CT1 with a rolling integration window of 10 ps and then fittingthe heights of those peaks (as a function of delay) with a Gaussian convolvedwith an exponential. The February data was limited to a range of delayssimilar to the data acquired in June. The decay constants are comparableacross measurements.1486.1. Dynamicslower state).A preliminary version of this analysis has been conducted for the CT1decaying into the S1. Figure 6.26 shows the pumped signal due to boththe CT1 and S1 (it is integrated across the energy range that contains CT1and S1: 1.7 to 2.3 eV). Here, the upper state is modeled with a simpleexponential (upper state model = Aue−(x−t0)/τu) while the lower state’smodel incorporates a rise time that is fixed to the decay constant of theupper state (lower state model = Ale−(x−t0)/τl(1− e−(x−t0)/τu)). Note thatτu is allowed to vary during the fit. The full model (upper state model +lower state model) is fit to the data resulting in decay constants of 5.28 ±0.90 ps for the CT1 and 38.06 ± 4.95 ps for the S1.49 As previously stated,this analysis is preliminary, and it would be worth comparing the results tofits over narrower energy ranges in the future – especially on data without theeffects of a pre-pulse, which may enable us to subtract the Au backgroundsignal. Even these initial results, however, correspond reasonably well to thedirect decay constant fitting of the CT1 (as shown in Fig. 6.25 and consistentwith no blockade effect) and reported lifetimes for the S1 [155].Ideally, future experiments on the dynamics of the excited states in C60would be conducted using a photon source with better time-resolution;50this would help mitigate any possible bottleneck effect as well as enable usto better resolve the decay rates of the CT states. Reported decay rates forthese three excited states in a variety of thicknesses of film and on multiplesubstrates as well as results from our data can be found summarized in tablesin Section 6.1.4.49Note that incorporating the time resolution of the experiment into this analysis, byconvolving both the upper state and lower state models with the appropriate Gaussian,will likely result in slightly shorter decay constants.50< 150 fs1496.1. DynamicsIntensity(arb.u)Intensity(arb.u)Delay (ps)0 20 40 60 80 100Decay Constant Analysis of CT1 and S1S1 & CT1: (1.7, 2.3) eV-1 0 11000.20.40.60.8100.20.40.60.81DataDecay CT1: 5.28 +/- 0.90 psDecay S1: 38.06 +/- 4.95 psFit of combined model (CT1 + S1)Figure 6.26: Analysis of decay constants assuming a decay from the CT1into the S1. The top image shows the pumped signal due to both the CT1and S1 (integrated from 1.7 to 2.3 eV). Data is shown for delays from -1 psto 100 ps, with -1 to 1 ps shown in the inset. The bottom image illustrates afit using a model that assumes a decay from the CT1 into the S1. Here, theupper state (CT1) is modeled with a simple exponential (upper state model= Aue−(x−t0)/τu) while the lower state (S1)’s model incorporates a rise timethat is fixed to the decay constant of the upper state (lower state model =Ale−(x−t0)/τl(1− e−(x−t0)/τu)). Note that τu is allowed to vary during the fit.The full model (upper state model + lower state model) is fit to the dataresulting in the green line and decay constants of 5.28 ± 0.90 ps for the CT1and 38.06 ± 4.95 ps for the S1.1506.1. Dynamics6.1.4 Summary of DynamicsThe excited states in C60 are a source of valuable information for address-ing photoexcited charge dissociation but remain enigmatic, with time- andangle-resolved photoemission spectroscopy only recently achieving the timeand energy resolutions necessary to probe these states [156, 157]. As such,many questions remain regarding the characteristics of excitons and theirdissociation. Techniques such as photoluminescence measurements [69] andtime-resolved two-photon photoemission [155], as well as theoretical calcula-tions [158], have provided insight into the excited state electronic structurewhich we can use to inform our measurements and analysis. The lower-lyingS1 state is particularly well-documented: it is commonly considered to belocalized to a single buckyball as a Frenkel exciton [158, 159] with a longlifetime (33 ps to 1.5 ns [155]) due to a forbidden singlet dipole transition[33, 160]. Instead of decaying directly into the HOMO, the singlet likelyrelaxes by spin-orbit interaction (via intersystem crossing) into a triplet state[155, 161],51 though it may reside in a localized self-trapped state (a Frenkelexciton trapped by a lattice deformation) in which strong electron-vibrationcoupling can weaken selection rules resulting in radiative recombination [69].The higher-energy CT excitons, however, remain less understood. Forexample, whether the CT2 is of LUMO or LUMO+1 character and theextent to which the CT excitons are (de)localized across multiple molecularsites52 is the subject of ongoing research [32, 67]. Our data suggests that theCT2 may be of LUMO+1 character, although confirmation of the locationand bandwidth of the LUMO in our system is required to be sure (this canbe achieved through STS measurements). The experiments referenced andsummarized below (Refs. [32, 63, 67]) represent the majority of the relevantexperimental work on these states by TR-(AR)PES.Table 6.4 compiles the specifications of the photon sources used for thedata summarized in this section, including polarizations of pump and probe,the relevance of which is addressed further in Section 6.3.2. In all cases,51In isolated molecules at ultracold temperatures, the spin-symmetric triplet lifetimehas been measured in the hundreds of µs [155].52See Fig. 1.7 for an illustration.1516.1. Dynamicspump fluence was limited to ensure the experiment remained in the linearregime, where the timescales of the exciton dynamics do not depend on theapplied fluence; this implies no significant formation of biexcitons or trions[63].Table 6.4: Photon Source ComparisonSample hν (pump/probe) Time Res. Energy Res. Spot Size Rep. Rate Fluence Refs.5, 15 ML C60/Ag(111) 3.2/22.2 eV 30 fs 150 meV 250 µm 10 kHz 50 - 100 uJ/cm2 [162]> 1 ML C60/Cu(111)53 2.9/26.5 eV 100 fs 200 meV 12 µm 500 kHz 90 uJ/cm2 [157]10 ML C60/Au(111) 3.1/6.2 eV 225, 500 fs 18 meV 100 µm 250 kHz 90 - 225 uJ/cm2 [163]5 ML C60/Au(111) 2.4/22.8 eV ∼ 150 fs 50 meV 100 µm 60 MHz ≪ 10 uJ/cm2 [156]Tables 6.5 – 6.8 and Figures 6.27 & 6.27 summarize the experimentalresults probing excitonic states in C60 with TR-(AR)PES, including ourresults (Table 6.8) as well as those reported in literature on samples ofdiffering thickness and substrate [32, 63, 67]. We see agreement in theenergies of the S1, CT1, and CT2 across experiments (minimal variation isexpected due to the differing substrates). The decay constants of the S1are also consistent. The decay constants of the CT states on Ag(111) arelonger in 15 ML films than in 5 ML films, indicating that dynamics in a 5ML film are affected by the substrate (this effect is particularly pronouncedin the longer-lived CT1). No decay constants are reported on multilayerC60/Cu(111).The very long decay times we observed for the CT exciton states inC60/Au(111), relative to the other results discussed here, are at least inpart attributable to details of our experiment that render any basic rateanalysis of minimal use.54 While the dominant factor affecting the lifetimeof the CT states is likely a bottleneck effect due to the pre-pulse55 or thequality of our film, accurate modeling of these states requires complexanalysis incorporating both the pre-population (due to the pre-pulse) andthe extended population (due to a long pump pulse56) of states. Additional53“Multilayer” – film thickness is not specified.54It is also possible that a higher quality film with fewer defects and grain boundariescould result in longer exciton lifetimes.55Recall that a -20 ps pre-pulse was present in our February data.56Our time resolution approximated 500 fs.1526.1. DynamicsTable 6.5: Exciton States in 15 ML C60/Ag(111) [32, 63]State E - EHOMO Decay TimeCT2 2.8 eV 38 ± 10 fsCT1 2.2 eV 1.5 ± 0.3 psS1 1.9 eV several hundred psTable 6.6: Exciton States in 5 ML C60/Ag(111) [32, 63]State E - EHOMO Decay TimeCT2 2.8 eV 45 ± 10 fsCT1 2.2 eV 0.8 ± 0.3 psS1 1.9 eV several hundred psTable 6.7: Exciton States in Multilayer C60/Cu(111) [67]State E - EHOMO Decay Time(S4) 3.6 eV n/aCT2 (S3) 2.8 eV n/aCT1 (S2) 2.0 eV n/aS1 1.7 eV n/aTable 6.8: Excitonic States in 10 ML C60/Au(111) (this work)State E - EHOMO Decay TimeCT2 2.68 eV 150 - 225 fsCT1 2.11 eV > 5 psS1 1.70 eV > 20 ps1536.1. DynamicsCT1S1CT2Excitonenergy(eV)Film thickness (ML)Ag(111)Cu(111) - film thickness not statedAu(111)Figure 6.27: Summary of exciton energies for different C60 film thicknessesand different substrates. Ag(111) results are from Refs. [32, 63], Cu(111)results are from Ref. [67], and Au(111) are our results (reported in thisthesis).data acquired with a shorter pulse duration would enable us to confirm oroverride our derived decay constants. Further discussion of the effects of along pump pulse on our data can be found in Section 6.3.4.While this chapter presents some of the first TR-ARPES data on theexcited states of C60, transient absorption measurements provide valuablebackground information on both Frenkel and CT states by selectively excitingthe film with a given pump excitation pulse (2 eV or 2.75 eV in the caseof Ref. [152]). At 2 eV (where Frenkel excitons dominate), the transientabsorption spectra does not significantly change over the first 5 ps, and therelaxed Frenkel excitons have a decay constant of 150 ps, consistent withS1 decay constants observed by TR-ARPES. Data acquired with a 2.75 eV1546.1. DynamicsFilm thickness (ML)CT1S1CT2Excitondecayconstant(ps)Ag(111)Au(111)Figure 6.28: Summary of exciton decay constants for different C60 filmthicknesses and different substrates. Ag(111) results are from Refs. [32, 63],and Au(111) are our results (reported in this thesis). Arrows indicate a decayconstant of at least the value of the marker.1556.1. Dynamicspump (where both Frenkel and CT excitons are generated) shows a strongdecay feature at 0.18 ps, attributed to the CT excitons. Interestingly, aweaker decay feature occurs at 5 ps (with both the 2 eV and 2.75 eV pulse);Ref. [152] suggests that this could be in part due to CT state dynamics, butthat it likely involves the relaxation of Frenkel excitons (potentially at grainboundaries). While Ref. [152] does not directly specify which CT exciton isresponsible for each decay feature, the CT exciton with a decay constant of0.18 ps is only visible with the 2.75 eV pulse, suggesting it is comparableto our CT2 exciton. The decay feature at 5 ps is visible with both 2.75eV and 2 eV pulse, indicating that it is likely our CT1 exciton. Althoughexcitation dynamics may depend on many factors including substrate, filmthickness, and the degree of disorder in a sample, the decay constants foundthrough transient absorption measurements provide useful context for ourTR-ARPES experiments. Moreover, they are notably similar to the decayconstants reported in this thesis: 150 - 225 fs, ∼ 5 ps, and > 20 ps.It is also worth noting that calculations suggest numerous CT excitonslocated in the CT2 energy region [164]: in fact, three distinct band manifoldsare indicated. Our visible three-peak CT2 structure is reminiscent of (andnot inconsistent with) this calculation (see Table 6.9). Our results may bethe first TR-ARPES data to reveal these multiple manifolds, due in part tothe higher energy resolution of our experiment compared to others (18 meV,see Table 6.4); angular-resolved data of these manifolds is included in theupcoming Section 6.2. While dynamics are particularly helpful in identifyingthese excitonic states, it is through our angular-resolved data that we hopeto eventually address these questions of (de)localization.1566.1. DynamicsTable 6.9: Excitonic States up to 3.0 eV: fit vs calculated57Fit58 Calculated59 State602.96 eV2.76 eV 2.73 eV CT2.65 eV CT2.62 eV CT2.57 eV 2.58 eV CT2.55 eV CT2.12 eV 2.33 eV CT1.98 eV1.80 eV 1.80 eV S1.72 eV S1.63 eV 1.58 eV S57Both data and calculated values are at Γ for C60 in its low-temperature phase.58See fit at Γ in Tables 6.2 and 6.3.59A three-dimensional analog of the Merrifield model using the nearest-neighbor approx-imation; see Ref. [164]. Calculation of the band structure of the singlet excitons using amodel Hamiltonian (though 2.33 eV is a CT exciton); see Ref. [158].60Charge-transfer or singlet, according to calculation.1576.2. Angular Dispersion6.2 Angular Dispersion6.2.1 Constant Energy CutsIn addition to the dynamics described in Section 6.1, this thesis presentswhat is, to our knowledge, the first angular-resolved data within the firstBrillouin zone of the excited states of C60. Figure 6.29 shows CECs atmultiple energies associated with the CT1. The intensity is mostly localizedto the edges of the BZ; however there is a clear progression from wedges ofintensity that reach towards the intensity-free center (at lower energies), toa more consistent ring of intensity at the edge of the BZ with one point ofintensity at Γ (at higher energies). The point of intensity at Γ correspondsto the bottom of a parabolic band of intensity that we see in HS cuts ofour CT2 (see Section 6.2.2 for further details). Based on the data shown inFig. 6.29 as well as subsequent, confirmatory measurements, the dispersionthroughout the BZ for the CT1 appears to be 6-fold symmetric.Figure 6.30 shows CECs throughout the CT2, again with the 1st BZ fullyreconstructed. Here, the intensity is visible in multiple locations around theedge of the BZ, including the K points, at lower energies. However, as wemove up in energy, the intensity becomes more localized at alternating Mpoints (this is especially visible at 2.96 eV). Interestingly, our May experimentresulted in the same asymmetry but rotated 60 degrees (see Appendix A.1).This intensity variation may be due to matrix element effects associatedwith a different probe polarization, or it may represent the real symmetryof the CT2. This phenomenon is the subject of ongoing analysis and futureexperiments.1586.2. Angular DispersionFigure 6.29: CECs throughout the CT1, with a red box around the plottaken at the CT1 fitted peak value (the relevant EDC plot is included forreference at the top of the figure). Raw data is enclosed by the gray dashedline and used to reconstruct the full first BZ (yellow dashed line). Scans weretaken at a positive delay of 600 fs. Heatmap data is linear and normalized.1596.2. Angular DispersionFigure 6.30: CECs throughout the CT2, with orange boxes around the plottaken at the CT2 fitted peak values (the relevant EDC plot is included forreference at the top of the figure). Raw data is enclosed by the gray dashedline and used to reconstruct the full first BZ (yellow dashed line). Scanswere taken at zero delay. Heatmap data is linear and normalized.1606.2. Angular Dispersion6.2.2 High Symmetry CutsTo determine the dispersion of our excited states, we can take slices alongthe HS cuts of the Brillouin zone at the excited state energies. This providesk|| vs. energy plots akin to spaghetti plots, just like those shown in Ch. 5.(and introduced in Section 2.3). Figure 6.31 shows a series of images, takenin June 2023, that depict the band structure at HS points of interest atzero delay. Further analysis of this data (including comparison with theory)may enable us to answer questions regarding symmetry of the system andthe initial population of excited states. Based on recent literature [9], weexpect the dispersion to predominantly match the dispersion of the valenceband (located, in k||, at the minimum of the conduction band); however, abroad exciton distribution with excitons of different COM momentum areBoltzmann weighted to get the complete spectra, resulting in a dispersionwith both valence band and conduction band similarities (see Fig. 5 in Ref.[9]). As such, the somewhat blobby dispersion in our data is not unexpected,given the pocketed and flat structure of C60’s occupied bands. Some ofthe clearest dispersion visible is near the Γ point. Figure 6.32 shows thisdispersion throughout the CT1 and CT2 from both our February and Junemeasurements. One can see a faint parabolic feature extending through theCT2 in both datasets, with three flat bands at energies of 2.53/2.51 eV, 2.8eV, and 2.99 eV. As discussed in Section 6.1.4 and illustrated in Fig. 6.33,the three flat bands are reminiscent of the expected manifold of CT bands inthis region (see Table 6.9 for a quantitative comparison of fit and calculatedenergies) [164].1616.2. Angular DispersionDispersion at various HS pointsE-EHOMO(ev)E-EHOMO(ev)E-EHOMO(ev)kx (Å-1)Γ KK0.240.160.180.140.080.080.08MMMK K32.82.62.42.42.22.22.42.20-0.2 0.20-0.2 0.20-0.1 0.1Figure 6.31: Dispersion at various HS points throughout the BZ, taken atzero delay. Top image shows dispersion across the K - Γ - K cut, includingdispersion in the CT2 energy range at Γ. Middle image shows the slice takenacross opposing M points. Bottom image shows slice taken at the bottomof the BZ. Inset images display relevant slices. HS points have not beenlabelled because the k-correction of this data is still being finalized. Recall:Γ - K ∼ 0.42 A˚−1 and Γ - M ∼ 0.36 A˚−1.1626.2. Angular DispersionCT1 & CT2 at Γ (June)CT1 & CT2 at Γ (Feb.)2.992.80 2.802.53 2.512.11 2.16datafit CT2fit CT1E-EHOMO(eV)kx (Å-1)Intensity(arb. u.)EDCEDCIntensity(arb. u.)kx (Å-1)0-0.1 0.10-0.1 0.132.82.62.42.232.82.62.42.2Figure 6.32: Comparison of angular dispersion at Γ of both the CT2 and CT1from our February (left) and June (right) experiments. Both images show aparabolic feature that extends through the CT2, with 3 flat bands at energiesof 2.53/2.51 eV, 2.8 eV, and 2.99 eV. The highest peak is too faint to be fitin the June data presented here; however, the three flat bands correspondto the peaks visible in Figures 6.5 to 6.8, which includes three-peak fits tothe June data. The CT1 is present in both images at very similar energies:2.11 eV and 2.16 eV. An M-like dispersion is visible in the CT1 in February,but not obviously in June. The side branches of the M may have broadenedinto the two large regions of intensity (in the CT1 and symmetric aroundΓ) visible in June. There is a region of intensity right at Γ in February(the point of the M) that coincides with a lack of signal in June; possibleexplanations for this include the unintentional change in the polarizationof the probe between experiments or a slight difference in offset angle (inky). The discontinuities in both datasets (obvious in February image, lessapparent but at 2.5 eV in June image) occurs where datasets are stitched. InFebruary data, the CT2 taken at zero delay with the CT1 at 0.6 ps positivedelay. In June, all data was acquired at zero delay.1636.2. Angular DispersionThe highest peak is too faint to be fit in the June data presented in Fig.6.32, but these three flat bands correspond to the peaks visible in Figures6.5 to 6.8, which includes three-peak fits to other June data. The CT1 ispresent at 2.11/2.16 eV in both datasets. An M-like dispersion is visible inthe CT1 in February, though it is not obvious in June. It is possible that theside branches of the M have broadened into the two large regions of intensity(in the CT1 and symmetric around Γ) visible in June. It does appear thatthere is a region of intensity right at Γ in February (the point of the M) thatcoincides with a lack of signal in June, however. One possible explanation forthis is a change in the polarization of the probe. Additionally, the Februaryimage stitches together data for the CT2 taken at zero delay with the CT1at 0.6 ps positive delay, while the June image shows data all taken at zerodelay.6161The delay was chosen by finding the peak intensity of the pump effect for the givenstate.1646.2. Angular DispersionCT2 at Γ (Feb.)KΓ X M R Γ MΓ X M R Γ MEDCCT excitons(low T: sc)CT excitons(high T: fcc)Intensity(arb. u)kx (Å-1)E-EHOMO(eV)KK2.992.802.530-0.1 0.10.1 Å-10.1 Å-132.82.62.52.92.7Figure 6.33: Comparison of the pumped angular dispersion centered at Γ(Γ - K orientation) with a tight-binding-style calculated CT excitonic bandstructure of the low-temperature simple cubic C60 and the high-temperaturefcc structure, as published by Pac et al. [164]. Data has been oversaturated(by capping the intensities) to better illustrate the band structure, andincludes an EDC with a three-peak fit, where peaks are likely attributableto the manifold of excitonic states. Red dashed lines illustrate location ofcalculated exciton bands at Γ on our data. Energy axes are comparableacross images; however, our data (and peak values) may be overestimatedby as much as 0.3 eV relative to the calculations. This is because our datais plotted relative to the middle of the HOMO and calculations are oftenplotted relative to the top of the valence band (though not specified in Ref.[164]). See Table 6.9 for a quantitative comparison of fit and calculatedenergies.The faint parabolic band that extends throughout this energy region issteeper and more dispersive than we expect for our CT states (illustrated inFig. 6.33) [164]. One possible explanation is to attribute it to the LUMO.Although the HOMO-LUMO transition is dipole-forbidden due to parity(both are ungerade) [68], Herzberg-Teller active vibrational modes can leadto weak absorption [165], or the LUMO could be rapidly populated via theCT2. The calculated band structure for the LUMO of the 4-basis simplecubic C60 does include some parabolic structure around Γ, as shown in Fig.6.34. However, different computational methods place the LUMO at a range1656.2. Angular DispersionCT2 at Γ (Feb.)Γ X M R Γ M Γ X W L Γ XEDCIntensity(arb. u)kx (Å-1)E-EHOMO(eV)LUMO(low T: sc)LUMO(high T: fcc)KK2.992.802.530-0.1 0.10.1 Å-1 0.1 Å-132.82.62.52.92.7Figure 6.34: Comparison of the pumped angular dispersion centered at Γ (Γ -K orientation) with the calculated (using tight-binding) band structure for theLUMO of the low-temperature simple cubic C60 and the high-temperature fccstructure, as published by Laouini et al. [150]. Data has been oversaturated(by capping the intensities) to better illustrate the band structure, andincludes an EDC with a three-peak fit, where peaks are likely attributableto the manifold of excitonic states depicted in Fig. 6.33. Note that the sccalculation does indicate the presence of some parabolic bands centered at Γ,although they are depicted in the Γ - M and Γ - R bulk HS cuts, makingdirect comparison difficult. As a reminder, K points would be expected atapproximately 0.42 A˚−1 in our data.1666.3. Considerations for Future Measurementsof energies that depend on system-specific parameters such as film thicknessand substrate material; the precise location and bandwidth of the LUMO inour system requires experimental verification.6.3 Considerations for Future MeasurementsThe data in this chapter is the subject of our current analysis, and we hopethat – in conjunction with theoretical work by our collaborators, includingDr. Mona Berciu and Dr. Alexander Kemper – this work will contribute toanswering open questions regarding the (de)localization of excitonic states inC60. The following few subsections may prove useful for future experiments.6.3.1 Damage ThresholdsGiven the two TR-ARPES sources described in Ch. 2, it is reasonable towonder why the data presented in this chapter was taken with the 6 eVsource. After all, the 6 eV source probes a smaller area of k-space (smallerthat the C60 BZ) and it cannot probe the occupied bands of C60.62 Due tothese limitations, the XUV source was our first choice for this experiment.However, using the XUV set up it is difficult to achieve the required pumpfluence without damaging the sample (recall that the repetition rate of theXUV is 60 MHz). Although we have thus far been unable to see clearexcitonic states using the XUV, we have established a film damage thresholdof 500 - 800 mW of pump power. We measured a 5 ML film with 225 mW ofpump power and saw no obvious signs of degradation; after measuring with500 mW we saw an increase in the background; after measuring for only afew minutes with 840 mW of pump power, we saw the background countsincrease and the HOMO broaden dramatically. Figure 6.35 shows a CECtaken near the Fermi energy after we damaged our film. Note the similaritiesto the replica structure in single ML C60/Au(111) films described in Ch. 5.622.05 eV (HOMO) + 4.65 eV (work function) > 6.2 eV (probe)1676.3. Considerations for Future MeasurementsFigure 6.35: CEC of a damaged film at a binding energy of 0.7 eV belowEF . The original film was 5 ML C60/Au(111) film. After applying the XUVsource (2.4 eV) pump at various powers up to 840 mW, the band structureof the resulting film (shown here) resembles the replica structure in singleML C60/Au(111) films described in Ch. 5. Signs of sample damage, such asan increase in background counts, began after applying 500 mW of pumppower to the sample.The damage to the sample was global. Based on our current information, wewould advise not exceeding 500 mW pump power in future measurements;ideally, we would remain below 225 mW.6.3.2 Polarization EffectsThe polarization of both pump and probe is important: recall Ch. 2’sdiscussion of matrix element effects, where we see that the probe polarizationaffects the photoemission spectral weights and photoemission yields (anexample of this can be seen in our data described in Section 5.2.2). Asmentioned in Section 6.2.2, a change in probe polarization may be responsible1686.3. Considerations for Future Measurementsfor differences in spectral weight at Γ in our CT1 excited state. Additionally,Ref. [32] found that pump polarization will affect the exciton generationefficiency in C60, with an approximate 30% reduction in efficiency whenmoving from a p- to an s-polarized pump source; this experimental result iscomparable to a calculated estimate that is applicable to our system.Given the experimentally-determined index of refraction for a 28 nm C60film [166], we can estimate the complex index of refraction for our pumpphoton energy: n(3.1 eV) = n1(3.1 eV) + i ∗ n2(3.1 eV) = 2.5 + 1.25i. Then,we can use the Fresnel equations to solve for the transmitted fraction ofperpendicular-polarized and of parallel-polarized optical power through aninterface (with a complex index of refraction and taking into considerationthe angle of incidence of the light63). The ratio of those two values givesus the absorption of s-polarized light as a percentage of p-polarized lightin bulk C60. In our case, the expected absorption of s-polarized light isapproximately 73% that of p-polarized light. Calculations were performedwith the python package pypolar.fresnel.6.3.3 Pre-pulse EffectsThe presence of a pre-pulse at -20 ps in the February data has been alludedto throughout this chapter. As described previously, it may be partiallyresponsible for our longer (than previously reported) decay constants ofthe CT excitonic states, due to the > 20 ps lifetime of the S1. Althoughpredominantly a complicating factor to be avoided in future experiments,the pre-pulse may help us discern at what point in energy our excitonicstates have lifetimes < 20 ps. Figure 6.36 shows data that supports thepossibility that the S1 was already populated at zero delay in our Februarymeasurement.64 It also illustrates that signs of pre-population at zero delayvanish above 2.05 eV, indicating that excitonic states at and above thatenergy have lifetimes < 20 ps.63In our experimental set up: 45 degrees.64Note that while the data shown in this plot has been normalized, subtracting theaverage signal (for the appropriate energy range) from 95 to 100 ps without normalizing(essentially assuming that our system is in a state of equilibrium 95 ps after the pumppulse) results in a qualitatively comparable plot.1696.3. Considerations for Future MeasurementsCT1: (2.0, 2.3) eVS1: (1.7, 2.0) eVCT2: (2.3, 2.6) eVCT1: (2.05, 2.15) eVS1: (1.75, 1.85) eVS1: (1.85, 1.95) eVS1: (1.95, 2.05) eVIntensity(arb.u)Intensity(arb.u)Delay (ps)Delay (ps)a)b)0-1 0 1-1 0 120 40 60 8000.20.40.60.81 1010Population of Excitonic StatesFigure 6.36: Population of excitonic states illustrating pre-pulse effect atzero delay (data is from February 2023). (a) Plot of the population of theCT2 (integrated from 2.3 to 2.6 eV), CT1 (2.0 to 2.3 eV), and S1 (1.7 to2.0 eV) from -1 to 100 ps. Inset image shows same data from -1 to 1 ps(region to the left of the black dashed line in the principal image). The greyintensity at negative delay indicates (pre-)population of the S1, likely dueto the pre-pulse at -20 ps (note that the lifetime of the S1 is expected tobe > 20 ps. (b) Integrating over narrower ranges in energy allows us todetermine which energies show signs of pre-population. Above 2.05 eV, signsof pre-population abruptly vanish, indicating that excitonic states above 2.05eV have lifetimes < 20 ps.1706.3. Considerations for Future Measurements6.3.4 Pulse Width EffectsBottleneck EffectAs discussed in Section 6.1.3, we found a shorter decay constant for the CT2with our 225 fs pulse than with our 500 fs pulse.65 However, typically a muchlonger pulse cannot resolve the decay constant of a short-lived state andresults in a peak with little-to-no asymmetry that can be modelled with apure Gaussian. In fact, fitting a pure Gaussian peak to a much shorter-livedstate is how we determine the time resolution of our pump-probe overlap.In our case, the longer decay constant for the CT2 found with our 500 fspulse may be due to a bottleneck effect: given a long pulse width, excitonsfrom our highest and shortest-lived state could decay into a lower statewhile the upper state is still being pumped. Now these upper state excitonshave nowhere to decay to, resulting in an artificially extended lifetime.66Ideally, shorter pulse durations would be used, however more complex rateequations to account for this could also be applied to extract more physicallymeaningful values, as discussed in Section 6.1.4.Relative Intensity of the CT2As illustrated in Fig. 6.37, the relative intensity of the CT2 to the lower statesis larger in the June data than in the February data. A significant differencebetween the two measurements was the time resolution of the pump-probeexperiment: in June it was approximately 225 fs, and in February it wascloser to 500 fs. The change in pulse width is a possible explanation for thechange in relative intensity of the CT2.Consider two pulses with the same photon flux, so they both generateN carriers, but with different pulse widths. The longer pulse (with a largertime resolution) takes longer to populate our excited state. In that case,the number of carriers that are being put into the excited state at any65Of course, given that the expected lifetime of the CT2 is shorter than the time resolutionof both experiments [32], we can not accurately fit for the CT2 decay constant in eithermeasurement.66It is also possible that, just as discussed for the CT1, the observed longer-lifetime ofthe CT2 state is attributable to our film quality.1716.3. Considerations for Future Measurementsgiven time, N(t), will be lower than N(t) for a shorter pulse. Now let usconsider the fact that this excited state has a finite lifetime and an availablelower state to decay into. As the carriers decay into the lower state, N(t)decreases as a function of time. If the pulse duration is longer than thedecay constant, then effectively the state is decaying faster than it is beingpopulated. This corresponds to fewer carriers in the excited state availableto be photoemitted. The larger the discrepancy between pulse duration anddecay constant, the more pronounced this effect will be. In contrast, given apulse that is much shorter than the lifetime of the state, the state will be fullypopulated effectively instantaneously, and at that moment (prior to decaying)will all be available to be probed via photoemission. This could explain therelative lower intensity of the CT2 observed in February as opposed to June.1726.3. Considerations for Future MeasurementsΓ - K region (June)M - K region (June)Γ region (Feb.)E - EHOMO (eV)322 2.2(-1, -0.5) ps(-0.5, 0.5) ps(0.5, 1) ps2.4 2.62 2.2 2.4 2.62 2.2 2.4 2.61016128403020100Intensity(arb.u)Intensity(arb.u)Intensity(arb.u)Figure 6.37: EDCs integrated over negative (blue), zero (orange), and positive(green) delays along the Γ (February), Γ - K (June), and Γ - M (June) slices.Although the excited states (and Fermi edge) are visible in all 3 scans, notethe relative intensity of the CT2 to the CT1 in the February data as opposedto the June data. All angular integration windows were in θ approximatingkx = (-0.13, 0.13) and (0.02, 0.27) A˚−1 and are illustrated by the pink linerelative to the BZ, consistent with the rest of this chapter.173Chapter 7Concluding Remarks7.1 SummaryThis thesis contains the first results investigating charge-transfer dynamics inOPV materials by lab-based TR-ARPES. The scope of the work included inthis thesis is as follows: We have showcased a film growth technique appliedto C60/Au(111) that facilitates long-range order of single domains in films upto 10 ML thick. We probed the occupied band structure of 1, 5, and 10 MLfilms using angle-resolved photoemission spectroscopy and revealed the time-evolution and (previously unpublished) angular dispersion of several excitonicstates in C60 using time- and angle-resolved photoemission spectroscopy.Chapter 3 of this thesis provided an overview of some experimentaldevelopments that were required for the reported experiments. The technicalnature of the chapter is reflective of its potential as an experimental guide.In particular, the temperature calibration plot for the double-decker sampleplate (Fig 3.5) is likely to be referenced frequently in future projects.In Chapter 4, we described a novel growth recipe developed for C60 thinfilms on Au(111). Low energy electron diffraction and scanning tunnelingmicroscopy used to characterize films showed long-range order in a 2√3 x2√3 R30◦ superstructure. Long-range order and minimal defects on theorder of the probe spot size (∼ 100 µm) are a prerequisite to successful(TR-) ARPES experiments, and it is due in part to this growth recipe thatthe data from Chapters 5 and 6 were able to be acquired. Growth of C60films is revisited in Appendix B, where we provide a recipe for growth on aCu-intercalated graphene/SiC substrate.Through the work described in this thesis, we hope to contribute to anunderstanding of the electronic band structure and exciton (de)localization1747.1. Summaryin C60. The relevant photoemission data is presented in Chapters 5 and6. Equilibrium ARPES data on films of varying thicknesses is described inChapter 5. The intriguing ARPES spectral features that appear in 1 MLC60/Au(111) systems were well described by a “case-study”-type explanationof band folding, which occurs when a superstructure in real-space leads to anew periodicity and a new (smaller) BZ in reciprocal-space (because of thenew periodic potential, the original bands get “folded” into this new BZ topreserve translational symmetry across BZs – see Fig. 5.12 for a depictionof the process). The resulting pattern substantiated the possibility theseintriguing spectral features could be due to band folding (as described in Ref.[148]), but they could also be diffraction of the surface-resonant bulk state ofthe Au(111) sp band through the periodic C60 ML (as argued in Ref. [143]).Using photon-energy dependent measurements, DFT, and a reconstructionof the folded band pattern, we were able to confirm that the replicas are ofthe surface-resonant bulk state of the Au(111) sp band (agreeing with Ref.[143]). A confident attribution of the phenomenon to (only) band foldingor diffraction is beyond the scope of this thesis, however, and would requireadditional data.67 Chapter 5 also provided a thorough report of the occupiedband structure (HOMO and HOMO-1) of low-temperature C60 thin films,including high symmetry band structure plots and constant energy cuts ofthe entire C60 BZ, providing a basis for TR-ARPES experiments.Chapter 6 delved into the TR-ARPES data of the excited states, corre-sponding to the CT2, CT1, and S1 exciton states discussed in prior literature[32]. Here, we reported the results of multiple experiments: identifying thestates (in energy relative to the HOMO), probing the time-evolution of thestates, and mapping the angular dispersion of the states. These results wereconsistent across measurements, showing that these results are reproducible.As of the publication of this thesis, Ch. 6 presents, to our knowledge, thefirst angle-resolved data within the first Brillouin zone of the excited states67As described in Ch. 5, better statistics of the band crossing might enable to confirmor rule out the presence of hybridization gaps. Alternatively, we could attempt to gatherdata on the diffraction of Au bulk bands, however the location of the C60 HOMO-1 wouldcomplicate those efforts.1757.2. Advancements & Outlookof C60. Acquiring angle-resolved data in the 1st BZ facilitates analysis thatspeaks to the real-space character of these states [167]. The momentum-space dispersion of the excitonic bands can provide valuable information: bycomparing the k-space structure with the result of theoretical calculations[67], we expect to be able to confirm the extent of delocalization of thesestates – information that has implications for charge-separation in devices.This chapter also provided notes on the damage threshold of the sample, theeffect of the polarization of the pump, and the potential implications of thetime-resolution of the experiment relative to exciton lifetimes. We hope thatthese notes may serve as a helpful resource for future measurements.7.2 Advancements & OutlookTo the best of our knowledge, this thesis presents the first comprehensiveset of both static and TR-ARPES results on a C60 thin film with a consis-tent substrate. The experimental challenge of these measurements meansthe acquisition of such data has only become possible in recent years [168].As discussed in Ch. 6, some optical data has been previously publishedon both neat C60 and C60-based heterojunction films [152, 153], providingvaluable context regarding the photoexcitation dynamics of C60 films. Whilepump-probe spectroscopy can speak to the lifetimes and energies of excitedstates [169], and techniques such as photoluminescence spectroscopy andspectroscopic ellipsometry can elucidate the role of vibrational energy levelsin radiative transitions [170], (TR-)ARPES experiments crucially providemomentum space-resolved data. By analyzing k-space dispersion and com-paring the data with models of these excitonic states, we can extract keyparameters such as delocalization and binding energy of a given excitonicstate. By combining TR-ARPES with STS and optical experiments, we havethe potential to build a complete picture of the excited state manifold.While others have published static ARPES data of (> 1 ML thick) C60on Bi2Se3 and Ag(111) [120, 149, 171], TR-PES data of C60/Ag(111) [32],and angle-resolved data of the excited states of C60/Cu(111) [67], this thesisshowcases static ARPES data, time-resolved excited state data, as well1767.2. Advancements & Outlookas angle-resolved data of the excited states (TR-ARPES) of C60/Au(111),including angular-resolved data of the 1st BZ of C60. It is worth noting thatour film growth recipe resulting in long-range well-ordered films over 5 layersthick enabled us to acquire this data with photon source spot sizes up to anorder of magnitude larger than what has been used elsewhere, enabling lab-based (as opposed to synchrotron-based) measurements [157]. Additionally,this thesis contains the first experimental data (to our knowledge) thatresolves what may be additional excitonic states68 in this energy region orband structure of the excited states.69Prior to acquiring the data in the thesis, we did not know to what extentit was possible to visualize the time dynamics and angle-resolved excitonicstates in the 1st BZ of C60. Nor did we know the experimental requirementsfor achieving such a measurement. This thesis provides a blueprint for futureexperimental spectroscopic data acquisition on these samples: speaking tothe importance of single-domained films, and discussing various possiblepump-probe configurations. The data presented in this thesis, in conjunctionwith future theoretical calculations, will enable a more complete picture ofexciton (de)localization, diffusion, and dissociation in C60-based OPV films –laying the foundation for future studies on heterojunction systems that mapmore closely to real-world devices.In addition to providing unprecedented insights into neat-C60, this re-search establishes the foundation for future work investigating exciton dy-namics in doped C60-based films. As discussed in Ch. 1, many OPVsrely on donor-acceptor heterojunction-type devices. 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Ganguly, “Analytical model for the optical functions of amorphoussemiconductors and its applications for thin film solar cells,” ThinSolid Films, vol. 455-456, pp. 388–392, 2004. The 3rd InternationalConference on Spectroscopic Ellipsometry.[184] H. Shahrokhabadi, A. Bananej, and M. Vaezzadeh, “Investigation ofCody–Lorentz and Tauc–Lorentz Models in Characterizing DielectricFunction of (HfO2)x(ZrO2)1−x Mixed Thin Film,” Journal of AppliedSpectroscopy, vol. 84, pp. 915–922, November 2017.199Appendix ASupplementary TR-ARPESData and AnalysisA.1 Comparison of TR-ARPES CECs acrossExperimentsFigure A.1 presents a compilation of constant energy cuts taken throughoutthe excited states of C60 from our different TR-ARPES experiment runs(February, May, and June 2023). Chapter 6 includes data taken from thesedifferent experiments and discusses the differences in the experimental setup. Table 6.4 provides a summary of the experiment parameters associatedwith each measurement.Although the CECs shown in Ch. 6 (Figures 6.29 and 6.30) and includedin the February column of Fig. A.1 appear fairly consistent with the Mayand June data, there are some differences. Figure A.2 demonstrates that theintensity in the CT2 from the June data appears rotated 60 degrees relativeto the February data. This may substantiate the possible 3-fold symmetryof this state. Figure A.3 compares the 2.2 eV CECs from February and Maywith the intensity capped at 0.6 to help visualize any fainter structure in theimage. The intensity in the February data appears at the edges of the BZ(yellow dashed line; distance from Γ to K = 0.42 A˚−1); the intensity in theMay data appears further inside the BZ. This may be a real effect, or it ispossible that there is an error in the k-correction of this data. Analysis isongoing.200A.1. Comparison of TR-ARPES CECs across ExperimentsMay 2023 June 2023E - EHOMO (eV)2.22.12.96 / 3.02.752.62.52.32.4February 2023Figure A.1: Compilation of CECs through excited states from differentexperiment runs (February, May, and June 2023). Energies associated withthe CT1 are boxed in red, energies associated with the CT2 are boxed inorange. Raw data is enclosed by the gray dashed line and used to reconstructthe full first BZ (yellow dashed line; distance from Γ to K = 0.42 A˚−1).Data is normalized, and the scale bar applies to all images. For experimentparameters associated with each measurement, see Table 6.4.201A.1. Comparison of TR-ARPES CECs across ExperimentsFebruary: 2.96 eV June: 3.0 eVFigure A.2: Comparison of CECs taken at 2.96/3.0 eV from February andJune data. The intensity in the two images appears rotated 60 degreesrelative to one another. Yellow hexagon delineates BZ edges; Red hexagonscale was chosen to align with intensity for the purpose of illustrating the 60degree rotation. Raw data is enclosed by the gray dashed line.February: 2.2 eV May: 2.2 eVFigure A.3: Comparison of CECs taken at 2.2 eV from February and Maydata. The intensity in the February data appears at the edges of the BZ(yellow dashed line; distance from Γ to K = 0.42 A˚−1); the intensity in theMay data appears further inside the BZ. This may be a real effect, or it ispossible that there is an error in the k-correction of this data. Analysis isongoing. Additionally, the February data shows a star-like pattern around Γ,while the May data does not. (See text for explanation.)202A.2. Mystery FeatureA.2 Mystery FeatureAn additional discrepancy between February and May’s data is as follows:the February data shows a star-like pattern around Γ, while the May datadoes not (see Fig. A.3). This is due to a feature that appears in our dataafter some amount of measurement time (typically 3 to 7 days, with thelatter timeline occurring in June, when we over-deposited the first ML of ourfilm). It is a cone-like feature that appears just above the Fermi energy ofAu(111), as illustrated in Fig. A.4. Once it appears, it remains present whenwe block the pump, and it appears to be a global feature (not limited to theregion we are measuring). This suggests a possible doping effect. Althoughwe would expect doping due to sample contamination to be a gradual effect(which this is not), it could be that some contaminant at the surface of theAu or even Au atoms themselves might be intercalating through the filmand migrating towards the surface (at which point an effect would be visiblein photoemission). Additional data is necessary for us to understand thisphenomenon. Future experiments could include depositing Au on a C60 filmthat does not yet show this cone-like feature to see if the feature is induced.Figure A.4: Cone-like feature that appears just above the Fermi energyof Au(111) after 3 to 7 days of TR-ARPES measurement with the 3.1/6.2eV pump-probe source. This image was taken in February with the pumpblocked.203A.3. Application of the Durban-Watson TestA.3 Application of the Durban-Watson TestThe Durban-Watson (DW) test is a method of assessing autocorrelationin the residuals of a regression analysis [176]. Typical fitting algorithmsaim to minimize the residuals, often through least-squares fitting. Such atechnique relies on the amplitude of the residuals, but does not distinguishbetween sequential residuals being positive or negative. An accurate modelfit to data results in uncorrelated residuals linked to random noise; however,an inaccurate model often produces correlated residuals with an apparentstructure. The DW test provides a score that ranges from 0 to 4 and helps toindicate model accuracy. In the case of uncorrelated residuals, the DW testgives a 2. This indicates that the model describes the data well. As the testresult deviates from 2, it signifies an increase in correlation of the residuals.It is commonly accepted that any result between 1.5 and 2.5 is consideredreasonable; results outside the [1, 3] interval are a definite red flag implyingthat the model does not adequately describe the data. Results that lie in theintervals [1, 1.5] and [3, 3.5] should prompt reconsideration of the model.When applied to our TR data, the DW test provides substantiation ofour multi-peak (per excitonic state) analysis and indicates the potential thatthere are additional features in our data that we have yet to uncover. FigureA.5 depicts a comparison of two different fits to an EDC from our Februarydata70 that includes all three excitonic states (S1, CT1, and CT2). The firstfit includes three Gaussians – one for each state – as well as a Fermi-Diracto account for the Au(111) signal and allows for a constant offset. Theresiduals show substantial anisotropy and structure, indicating an inadequatefit. Of course, this is apparent to the eye; however, the DW test provides aquantifiable assessment. The three-peak fit, unsurprisingly, resulted in anred-flag DW score of 0.670. In comparison, the seven-peak fit (also depictedin Fig. A.5) shows less structure in the residuals (although notably not nonebelow EF ) and achieves a DW score of 1.097. This demonstrates markedimprovement in the fit, but indicates that there may be additional featuresin the data that are not described by the current model. A similar analysis70All data in this section is from the February 2023 experiment.204A.3. Application of the Durban-Watson TestDurban-Watson: 1.097Durban-Watson: 0.670Fit of S1, CT1, and CT2: 7 peaksFit of S1, CT1, and CT2: 3 peaksFigure A.5: Comparison of two different fits to an EDC (integrated from 0.25to 0.5 ps) that includes all three excitonic states (S1, CT1, and CT2). Bothfits include a fixed number of Gaussians as well as a Fermi-Dirac to accountfor the Au(111) signal, and they allow for a constant offset. The first fit (left)includes three peaks, one for each excitonic state. The fitted peak locationsare 1.7, 2.11, and 2.68 eV. The residuals (plotted below) show substantialstructure, and the DW score is 0.670. The second fit (right) includes sevenpeaks. The fitted peak locations are 1.63, 1.8, 1.98, 2.12, 2.5, 2.75, and 2.96eV. The residuals (plotted below) show much less structure, and the DWscore is 1.097, indicating improved model accuracy. Data is from February2023.is performed on the isolated S1 and CT1 energy region (Fig. A.6) and theisolated CT2 energy region (Fig. A.7), to assess the quality of those fitsindependently.71 The result of the fit comparison in both energy regionssupports our assessment that multiple peaks per state better describes thedata, but it also suggests that our model accuracy could be improved.We also used the DW test to assess the fit of our TDC of the CT2 (a fitwhich provides the decay constant of the state). Figure A.8 compares two71The CT2 is energetically more distinct in our data, whereas it is more difficult todistinguish between the CT1 and the S1 given their proximity and their spanning the AuFermi energy.205A.3. Application of the Durban-Watson TestFit of S1 and CT1: 2 peaksDurban-Watson: 0.343 Durban-Watson: 0.671Fit of S1 and CT1: 4 peaksFigure A.6: Comparison of two different fits to an EDC (integrated from0.25 to 0.5 ps) that includes the lower two excitonic states (S1, CT1). Bothfits include a fixed number of Gaussians as well as a Fermi-Dirac to accountfor the Au(111) signal, and they allow for a constant offset. The first fit (left)includes two peaks, one for each excitonic state. The fitted peak locations are1.72, and 2.10 eV. The residuals (plotted below) show substantial structure,and the DW score is 0.343. The second fit (right) includes four peaks. Thefitted peak locations are 1.63, 1.8, 1.98, and 2.12 eV. These peak resultsmatch the lower four peaks found in the more accurate fit of Fig. A.5. Theresiduals (plotted below) show much less structure, and the DW score is0.671, indicating improved model accuracy. Data is from February 2023.206A.3. Application of the Durban-Watson TestDurban-Watson: 0.383Durban-Watson: 0.137Fit of CT2: 3 peaksFit of CT2: 1 peakFigure A.7: Comparison of two different fits to an EDC (integrated from-0.5 to 0.5 ps) that includes the upper excitonic state (CT2). Both fitsinclude a fixed number of Gaussians as well as a Fermi-Dirac to account forthe Au(111) signal, and they allow for a constant offset. The first fit (left)includes one single peak for the excitonic state. The fitted peak locationis 2.69 eV (with a FWHM of 3.33 eV). The residuals (plotted below) showsubstantial structure, and the DW score is 0.137. The second fit (right)includes three peaks. The fitted peak locations are 2.57, 2.76, and 2.96 eV.The residuals (plotted below) show much less structure, and the improvedDW score is 0.383. It is worth noting that this DW score, though improved,still indicates that our model may not fully describe our data. Data is fromFebruary 2023.207A.3. Application of the Durban-Watson Testfits; both models contain a Gaussian convolved with an exponential, but thefirst allows for a constant offset while the second allows for a linear offset.Allowing for a constant offset is a conservative and physically appropriatechoice in this case. Although it is not inconceivable that the model wouldrequire a linear offset to accurately describe some physical phenomenon, thephysical phenomenon in question is not readily apparent. However, allowingfor a linear offset visibly – and quantitatively – appears to better describe thedata: the DW test gives scores of 1.113 and 1.673, respectively. Interestingly,this result leads one to consider that there may be a physical reason for alinear offset (that should be ascertained), or perhaps the DW test resultsshould be relied on in a considered manner when operating within the [1, 3]result interval.As a final note in this section, Fig. A.9 uses the DW test to illustratethe importance of integration window choice when building a fit model(particularly in our TR data). Here we see that the three-peak fit of our 3excitonic states, with data integrated from -0.5 to 1 ps, gives a DW scoreof 0.334. The same fit with data integrated from 0.25 to 0.5 ps results ina DW score of 0.670. The discrepancy in scores (and fit accuracy) may beattributable to the prominence of the CT2 in the first EDC (which includeszero delay) relative to the second EDC (which excludes zero delay). TheCT2 intensity is fairly localized to zero delay and the state contains threevisible peaks that we are fitting with a single Gaussian in this model; thiswill result in anisotropy of the residuals and a corresponding worsening ofthe DW score.208A.3. Application of the Durban-Watson TestDurban-Watson: 1.673Durban-Watson: 1.113CT2: Γ regionPeak: -0.04 psFWHM: 0.454 psDecay: 204 fsConstant Offset Linear OffsetPeak: -0.04 psFWHM: 0.473 psDecay: 174 fsFigure A.8: Comparison of two different fits to an angle-integrated TDCof the CT2. The upper plot shows the time-resolved and angle-integratedheatmap of the state; the TDC data is generated by integrating over thefull energy range. Both fits are a Gaussian convolved with an exponential;the first fit (left) allows for a constant offset, and the second fit (right)allows for a linear offset. The DW test gives scores of 1.113 and 1.673,respectively, indicating that including a linear offset results in a model thatbetter describes the data. The physical justification of a linear offset is notcurrently known, but should be investigated. It is also worth consideringto what extent the DW test results should be relied upon within the [1, 3]result interval. Data is from February 2023.209A.3. Application of the Durban-Watson TestDurban-Watson: 0.334 Durban-Watson: 0.670Fit of S1, CT1, and CT2:0.25 to 0.5 psFit of S1, CT1, and CT2:-0.5 to 1 psFigure A.9: Comparison of two EDCs integrated over different delays ((-0.5,1) and (0.25, 0.5) ps) fit with the same three-peak model. The EDCs coverthe same energy range that includes all three excitonic states (S1, CT1, andCT2). The fit is a sum of three Gaussians as well as a Fermi-Dirac to accountfor the Au(111) signal and allows for a constant offset. The DW scores are0.334 and 0.670, respectively. The discrepancy in scores may be attributableto the prominence of the CT2 in the first EDC (which includes zero delay)relative to the second EDC (which excludes zero delay). The CT2 intensityis fairly localized to zero delay and the state contains three visible peaks thatwe are fitting with a single Gaussian in this model. This figure illustrates theimportance of the integration window when building a fit model, pariticularlynear zero delay in our TR data. Data is from February 2023.210Appendix BC60/GrapheneGraphene/SiC is an appealing substrate for C60 thin films due to excel-lent lattice matching facilitating epitaxial growth and the lack of substratebands around Γ [177]. This ensures that even if graphene bands are visiblethrough the C60 film, any dispersion visible around Γ will be represen-tative of C60 band structure. For this experiment, two substrates wereused: Cu-intercalated graphene/SiC (graphene/Cu/SiC) and H-intercalatedgraphene/SiC (graphene/H/SiC). This chapter contains the preliminaryresults for substrate preparation, film growth, and characterization usingLEED. For LEED images of graphene/H/SiC and graphene/Cu/SiC, seeFigures B.1 and B.2, respectively.Figure B.1: LEED image of graphene/H/SiC. Image taken at beam energyof 130 eV. Brightest spots are SiC, blurry spots are graphene. Graphene-SiCreconstruction not visible due to inadequate sample quality. Image takenafter 7 (cumulative) hours of annealing at 475◦ C. This graphene sample isinadequate and must be replaced.211Appendix B. C60/GrapheneThe LEED pattern of graphene/H/SiC provides an example of how LEEDcan be used to determine substrate quality. Figure B.1 shows that, despiteextensive annealing (a total of 27 hours), the graphene spots never becomeclear. Persistent blurry patterns in LEED may indicate a lack of long-rangeorder to the sample (either inherent or incurred) or an irregular surfacecontaminant not removed by annealing; in this case, it is likely that thesample sustained damage when broken off the parent sample with a razorblade. A sample in this condition will be an inadequate substrate for filmgrowth.Figure B.2: LEED image of graphene/Cu/SiC. Image taken at beam energyof 131 eV. Brightest spots in outer ring are graphene (blue arrow), surroundedby 6 spots that are due to the graphene-SiC reconstruction (green arrow).Additional spots surrounding those 6 are due to the Cu-intercalation, causinga 6√3 x 6√3 reconstruction (yellow arrow). SiC (1 x 1) shows up as faintspots between the more complex patterns (orange arrow). See Qu’s doctoralthesis [178] for further information about this sample.212Appendix B. C60/GrapheneThe LEED pattern of graphene/Cu/SiC (Fig. B.2) provides an exampleof a moderately complex LEED pattern: the brightest spots in outer ring aregraphene, surrounded by 6 satellite spots that are due to the graphene-SiCreconstruction. The additional spots surrounding those 6 are due to theCu-intercalation, producing a 6√3 x 6√3 reconstruction. SiC (1 x 1) showsup as faint spots between the more complex patterns.Although literature points to highly ordered C60 layers on graphene[179], the weak interaction between the two materials may result in multipledomains of C60, as seen in Fig. B.3. It is worth noting that while the lackof bands near Γ will help us isolate the C60 occupied bands in our ARPESspectra, STM measurements indicate a band gap of ∼ 3.5 eV (larger thanC60/Au(111)) which will impose new requirements on our pump source forTR-ARPES [179].Figure B.3: LEED image of C60 on graphene/Cu/SiC taken at beam energyof 24 eV. The 6 bright spots in each ring suggest a (reproducible) dominantdomain, however the rings illustrate the multi-domained nature of this sample.The 3 rings correspond to the first 3 orders of C60 spots. The dark oval inthis image – to the top-right of the electron gun – is an artifact of our LEEDset up and is not related to the sample.213Appendix B. C60/GrapheneTo prepare the substrate, we annealed at 480◦ C for 120 min. The filmshown in Fig. B.3 was grown by depositing C60 on clean graphene/Cu/SiCfor 30 min, with a growth rate of ∼ 0.1 nm/min and holding the substrate at150◦ C. After deposition, the sample was annealed at 160◦ C for 120 min, 165◦C for 140 min, and 175◦ C for 120 min. LEED images were similar after eachanneal; Fig. B.3 shows the LEED image taken after the final anneal. The 6bright spots in each ring suggest a dominant domain that we found to bereproducible, however the rings illustrate the multi-domained nature of thissample. However, literature suggests that this ratio of dominant-to-multipledomains can be sufficient for ARPES [180, 181]. Note that annealing at 190◦C for 60 min results in total evaporation of C60 film and a clean substrate.214Appendix CEllipsometry on C60While film thicknesses were measured using in-situ quartz crystal monitors(QCMs), with readings taken during film growth, films of varying thicknesseswere also characterized using ellipsometry to confirm the calibration of ourQCMs. Ellipsometry is an optical spectroscopic technique, whereby a beam ofcircularly polarized light is shone at a sample; the beam is either transmittedor (as in our case) reflected by the sample. The change in polarization ofthe measurement beam, due to this transmission through or reflection fromthe sample, can be characterized by the ellipsometric parameters Ψ and ∆,wheretanΨ · ei∆ = ρ = rprs, (C.1)with rp and rs representing the reflectivity of p-polarized light and s-polarized light, respectively. The ratio of these two values, ρ, is a complexnumber that can be represented in polar form, where tan(Ψ) is the magnitudeof the reflectivity ratio and ∆ is the phase. This expression can be derivedbeginning with the wave equation for an electric field in a uniform, isotropicmedium with complex permittivity ϵ:[∇2 − ϵ(ω)c2∂2∂t2]E⃗(r⃗, t) = 0. (C.2)The monochromatic plane wave propagating along the z-axis is a solutionto this equation:E⃗(z, t) =[Ex(t)Ey(t)]= Re{[Xei∆Y]}ei(kzz−ω(t−t0)) (C.3)By setting z = 0, we get the time-dependence of the vector E⃗(t) in the215Appendix C. Ellipsometry on C60x-y plane at z = 0; this expression describes the polarization ellipse depictedin Fig. C.1.Figure C.1: A polarization ellipse that illustrates the ellipsometric anglesΨ and ∆. In this image, the electromagnetic (elliptically polarized) wavepropagates out of the page towards the reader (along the positive z-axis).Elliptic polarization can be described by the phase shift ∆ (the relative phaseof the vibrations along the x and y directions) and the relative amplitudeX/Y , which can be expressed as tan(Ψ) = XY . If the beam is linearlypolarized, ∆ = 0 or π. In this case, the vibrations along x and y are eitherin-phase or have the opposite phase, and the ellipse will collapse into astraight line that connects opposite corners of the purple rectangle. If abeam is circularly polarized, Ψ = π4 and ∆ =π2 or −π2 . This implies thatthe x and y vibrations have the same amplitude, and the polarization ellipsebecomes a circle. This figure is adapted from the Handbook of Ellipsometry(Chapter 1, Figure 1.1) [182].The y-component of this vector is at its maximum at t = t0, and thex-component is at its maximum at t = ∆ω . Given the diagram in Fig. C.1,one can see that the amplitudes X and Y are defined by sinΨ and cosΨ,respectively. Thus, the Jones vector (which represents the amplitude and216Appendix C. Ellipsometry on C60Figure C.2: Example of ellipsometry data with fit overlaid. Data plotted aseV vs. Ψ (red) and eV vs. ∆ (green). Film thickness was determined to be4.29 ± 0.005 nm. Data analyzed on August 24, 2022.phase of the electric field in the x and y directions) is[sinΨei∆cosΨ]. (C.4)Because, in ellipsometric measurements, multiplying both X and Y by acommon constant results in a variation of the intensity, only the ratio of Xto Y (along with the phase) is required to define the state: tanΨ · ei∆.To summarize, ellipsometry measures the reflectivity of polarized light.We collect data on the change in polarization of the beam in the form of theellipsometric parameters Ψ and ∆, which represent the amplitude and phaseshift of the reflected light. Ψ and ∆ depend on the optical properties andthickness of the sample. We fit for those parameters using the Cody-Lorentzfunction [183].72 An example of the resulting plot (including the fit) isillustrated in Fig. C.2. The film thickness was determined to be 4.29 ±0.005 nm. For further information on this subject, I refer the reader to theHandbook of Ellipsometry [182].72The Cody-Lorentz function is an alternative to the Tauc-Lorentz model for relativepermittivity that allows for absorption of photons with hν < Ebandgap, often applicable formaterials with a larger band gap [184].217Appendix DC60 Band StructureStreak-CorrectionA portion of the raw (static) photoemission data taken with slit = 300 on5 ML C60/Au(111) contained regular vertical streaks. This phenomenonhas been seen in other measurements with slit = 300, and is likely due toparticulates that can accumulate on the entrance of the thinner slit during abake. This artifact has been dealt with using the following procedure (thesesteps are illustrated in Fig. D.1, albeit with the datacube integrated over allΦ in order to illustrate the streaks most prominently):• Take a slice of the datacube in Φ, then integrate over all EK , generatingan MDC. The streaks are visible as small oscillations in the MDC.• Fit a (in this case 4th order) polynomial to the MDC.• Generate a correction ratio array, by dividing the MDC fit by the MDCdata.• Multiply this correction ratio array by each row of data (EK).• Conduct this procedure for all slices in Φ.This procedure results in the bottom image in Fig. D.1, which clearly hasless pronounced streaks when compared with the top image. Applying thisprocedure to all slices in Φ of a datacube renders streak-corrected CECs aswell: Fig. D.2 shows CECs of the raw data compared to the streak-correcteddata, taken at energies throughout the HOMO and the HOMO-1.218Appendix D. C60 Band Structure Streak-CorrectionFigure D.1: Streak-correction of the HOMO of a 5 ML C60/Au(111) film,integrated over all Φ. Top image shows the streaked raw data with theMDC (integrated over all EK) overlayed. Middle image shows the MDCwith a 4th-order polynomial fit overlayed. The streak-correction ratio arrayis generated by dividing the fit by the data. Bottom image shows the HOMOdata after the streak-correction ratio array has been applied to each row ofthe data (in EK).219Appendix D. C60 Band Structure Streak-CorrectionFigure D.2: CECs of the raw data compared to the streak-corrected data forthe HOMO (left set of panels) and the HOMO-1 (right set of panels).220Appendix EExperiment TimelineFuture students may find the following timeline useful when searching yearsof lab books for old experiment details and previously encountered (hopefullysolved!) problems. This also conveys, in a limited fashion, the extent of thetechnical work required to build the foundational capabilities of this system.221Appendix E. Experiment Timeline222Appendix E. Experiment Timeline223Appendix E. Experiment TimelineFigure E.1: Timeline of my PhD including significant experimental issues,solutions, and successes.224Appendix FRelevant DFT Calculations: abrief how-toF.1 Introductory InformationLogin to LISA with putty.Useful commands• ls → list directories• cd → navigate• :wq → save• i → editWien2K lattice types• P – all primitive cells except hexagon• F – FCC• H – hexagonSuggested folder structure: Wien2K → AuBulk → HS → case→ filesF.2 Bulk High Symmetry Cut CalculationFiles needed for case folder: xxx.cif, case.cif (renamed duplicate of original),run lapw2, run wien2k1. move .cif file over to LISA using WinSCP225F.2. Bulk High Symmetry Cut Calculation2. copy run lapw2 and run wien2k files into case folder3. duplicate .cif file and rename copy case.cif4. convert .cif to structure file: cif2struct case.cif5. input command xcrysden then load case.struct file to make sure itlooks appropriate6. run init lapw (only uses case.struct ; spits out a whole bunch of files):(a) reduction % = 2 or 0, just make sure sum total < nn(b) new scheme(c) accept(d) nn bondlength = 2(e) continue (x3 usually)(f) non-magnetic (-nm) don’t forget the minus!(g) PBE (calculation type, best for solids)(h) core-valence separation energy: -6 for graphite, -8 for Au (justtype -8, not -8.0!!)(i) edit RKM value here: 7 for carbon, 8.5 to 9.5 for Au(j) kgen: ∼ 200− 400 (400 is 20 for Au in bulk calc)(k) continue(l) no spin-polarized(m) vi case.in1 edit RKM value (9.5 for gold if simple calculation, 8.5is good enough otherwise, 7 is fine for carbon)(n) vi case.klist shows density of points in k space, must do self-consistency calculation(o) sbatch run wien2k(p) squeue -u username(q) grep :ENE case.scf226F.3. Fermi Energy Corrections(r) save lapw –d RKM x kpts xxConvergence tests needed:• kpts• bases of wavefunctions• must test both of those for convergence to ensure calculation accurateto x meV (choice of x)Generate case.qtl file1. xcrysden → define k path2. save with odd number of k points (101)3. filename: case.klist band4. each red cross in spaghetti plot is a k point (n of k points per band isdefined earlier)5. back in command prompt case check: vi case.klist band6. sbatch run lapw27. squeue –u username8. vi case.qtl9. now on to EF corrections. . .F.3 Fermi Energy Corrections(Do this right before plotting, don’t need to do this for every convergencecalculation)• get EF: grep :FER *scf (use the last one, just copy to a sticky note)• replace EF in case.qtl file (lattice constant is here too, in Bohr)227F.4. Self-Consistency Check• x spaghetti –p (to generate new case.insp file)• replace EF in case.insp file (where x.xxxxx)• x spaghetti• go on to gnuplot. . .PlottingMake sure Xming is running on desktop. To plot directly in commandprompt:• gnuplot• gnuplot > p ′case.spaghetti ene′ u ($4 ∗ 1.89) : 5Otherwise/then download the following files (and rename) for matlabcode:• case.klist band → AuBulkGK.klist band• case.qtl → AuBulkGK.qtl• case.struct → AuBulk.struct• supportInfo.kpath → AuBulkGK info.kpath (NOTE: grab this immedi-ately off of LISA, it will be overwritten if you run another calculation)• write text file with calculation parameters and store in fileF.4 Self-Consistency CheckRelaxation calculation:Need to find convergence for basis functions, number of k points, andlattice parameter. Use kmesh + basis-set: see page 9 (section 3.6.1) ofKetty’s notes on using Wien2K. Need to update number of k points andbasis limits, can do so without fully re-running calculation.• self-consistency calculation: run wien2k228F.4. Self-Consistency Check• then: save lapw -d RKM 7 kpts 20• RKM is defined in case.in1 (generated during initialization step).• RKM (radius muffin tin * kmax): typical range is between 5 and10; depends on the atoms in your crystal; these k points are in thecase.klist file; to restore, restore lapw -f -d RKM 7 kpts 20 ; go into theRKM 7 kpts 20 directory then vi case.scf to find energy values thatwe grab through shortcuts grep :ENE case.scf ; gives total energy ofsystem in Rydbergs. We will be plotting this (last) value as a functionof kmesh and basis functions (separately – two plots).• Change RKM first, then kpts.• RKM values: 5.5 or more for Carbon (7 is fine), 8.5 for Au (go toWien2K RKmax FAQ for table of values)• redo calculation– for RKM:∗ vi case.in1∗ change RKM number– for kpts:∗ x kgen∗ specify number of kpts (the number you give will be reducedfrom whole cell to irreducible cell, so type 500 but get 32 asthe new actual kpts)• to calculate with new values: sbatch run wien2k• check status: squeue –u username• once calculation is done: save it (save lapw -d RKM x kpts xx ) → grep:ENE case.scf → take last energy data point → run all this againRKM process229F.4. Self-Consistency Check• Commands: sbatch run wien2k → squeue –u username → grep :ENEcase.scf → put last energy data point into excel doc → save lapw -dRKM x kpts xx → vi case.in1 → edit RKM• to restore: restore lapw -f -d RKM x kpts xxkpts process• Commands: x kgen → enter no of kpts (200-400) → sbatch run wien2k→ squeue –u username → grep :ENE case.scf → put last energy datapoint into excel doc → save lapw -d RKM x kpts xx → edit kpts with“x kgen”• can always check case.klist and case.in1lattice parameter process• create folders at same level of previous case folder names a NewLatticeParam(i.e. Wien2K → AuBulk → HS → a 7.88→ case)• copy case.struct file into case folder and edit to have proper latticeparams• copy run lapw2 and run wien2k files into case folder• editcase.struct to have new lattice params (keep all decimal places!!)• use init lapw on case folder• check vi case.klist and vi case.in1• sbatch run wien2k• squeue –u username• grep :ENE case.scf• put last energy dat point into excel doc230F.5. Au(111) Slab Calculation• save lapw –d RKM x kpts xx• consider including threshold energy someplace in filename or notesF.5 Au(111) Slab CalculationPreparation: Create case.struct File• create folder: Wien2K → AuSlab• copy case.cif (from x-ray experiment), run lapw2, and run wien2k intofolder• cif2struct case.cif• x symmetry• cp case.struct st bulk.struct• run octave• type s=loadstruct(“bulk.struct”)• s=makeconventional(s)• make transformation matrix (example for hex symmetry, slab of 4layers) (see Fig. F.1)• sout=makesupercell(s, T)• ensure Xming is active• look in xcrysden with showstruct(sout) (see Fig. F.2)• save with savestruct(sout, “supercell.struct”)• exit• back in case folder, type cp supercell.struct case.struct• supercell231F.5. Au(111) Slab CalculationFigure F.1: Transformation matrix for a slab of 4 layers with hexagonalsymmetry.• filename: supercell.struct• no of cells in x, y, z: 1 1 1• optional atomic shift: 0 0 0• add vacuum in z-direction: 38 bohr (= 20 Angstroms, standard “enoughfor wavefunction to decay substantially”)• Prompt: Repeat atoms at z=0 at the top (y/n) → this pertains to thedefinition of the unit cell, which we’ll deal with in the x sgroup step,so say “n”.• cp case super.struct case.struct• x sgroup• cp case.struct sgroup case.struct• check in xcrysden (file case.struct sgroup but must be renamed tocase.struct for xcrysden to work) (see Fig. F.3).• modify number of units drawn (e.g. x = 2, y = 2) and rotate• and we should have hexagons! (see Fig. F.4)DFT232F.5. Au(111) Slab CalculationFigure F.2: Slab of 4 layers with hexagonal symmetry shown in xcrysden.233F.5. Au(111) Slab CalculationFigure F.3: Example slab with vacuum layer added shown in xcrysden.Figure F.4: Example slab with extended number of unit cells drawn toillustrate hexagonal structure.234F.5. Au(111) Slab Calculation• run init lapw• 2% reduction in RMT• new scheme (N)• make sure sums value < nn-dist value, then accept• nn-bondlength fact = 2• non-magnetic: -nm• PBE• core-valence separation energy: -6 for graphite, -8 for Au (just type -8not -8.0 or you will break calc)• kgen: 400 gives 56 kpts for 8 layer slab (40 for 4 layer)• if you get the following warning: ”WARNING: 2D-BZ, better useTEMP and not TETRA in case.in2” you can go into case.in2 andchange TETRA to TEMP anytime before you run sbatch run wien2k,but not necessary!• not spin-polarized (typically)• save lapw –d k 22 cutoff n8 PBE (kgen 400 gave 22kpts, core-valencecutoff energy is -8, used PBE method)• in case.in2 optionally change TETRA to TEMP• vi case.in1 → edit RKM value (9.5 for gold if simple calcs, 8.5 is goodenough otherwise, 7 is fine for carbon)• vi case.klist → shows density of points in k space, must do self-consistency calculation• sbatch run wien2k• squeue –u username235F.5. Au(111) Slab Calculation• go to step 6q in the Bulk High Symmetry Cut Calculation section ofthese notes to complete EF adjustments and generate case.qtl. fileSpin Orbit Calculation• create folder: Au 5slab→ SOC• copy DFT folder from Au5slab/HS/DFT into SOC folder• init so• follow default prompts:– 0 0 1, “enter”, 5, None– ensure Xming is active, close pop-ups that appear– N to spinpolarized (symmetso)• modify your run wien2k file so it has run lapw -p -cc 0.0001 -ec 0.0001-i 80 -so (basically you add the -so flag)• rerun scf calculation (sbatch run wien2k)• modify your run lapw2 file so it reads– x lapw1 -p -band– x lapwso -p -band– x lapw2 -p -qtl -band –so• run band structure calculation (sbatch run lapw2 )• grep :ENE case.scf• save lapw –d RKM x kpts xx• Note that unless you change your case.klist band file, the case.qtl filethat’s generated for plotting will be the same HS cut or k-cut that youdefined in your last (slab, bulk, etc.) calculation. When you copy overthe whole DFT folder, that file is included!Fermi Energy Corrections - see section F.3 for procedure.236F.6. Fermi Surface CalculationF.6 Fermi Surface Calculation• create folder: Au 5slab→ FS• copy DFT folder from Au 5slab/HS/DFT into FS folder• copy python file into Au 5slab/FS/DFT/case folder• (You’re starting the calculation from the step after you have runrun wien2k in the HS calculation (i.e. band generation))• python write FS klist.py –n 51 –kz 0 –c caseThe python write FS klist.py command uses Berend Zwartsenberg’spython script ”write FS klist.py” to calculate a Fermi surface (by writ-ing a kmesh) at a particular kz. The format for this command is pythonwrite FS klist.py –n npoints –kz atkz –c casename. Note the following:• atkz is the integer kz at which the kmesh is made; atkz = 0 for a trueFermi Surface• npoints is the number of points in the BZ; suggestion = 51 for initialcalculation, 101 later• casename is whatever you use as your casename – in these examplenotes casename=case• check that case.klist band file exists and is not empty, and that it makessense• run sbatch run lapw2 to generate case.qtl file (just the normal version,not the SOC file)• Note: this will take a long time!• squeue –u username• vi case.qtl• now on to EF corrections. . .Fermi Energy Corrections - see subsection F.3 for procedure.237F.7. Adding a PotentialF.7 Adding a Potential• Copy slab calculations to a new folder.• Execute init lapw → when it asks for the cross correlation potential(XCPOT), instead of PBE use LDA (worse approximation, but allowsyou adjust potentials).• After completing init lapw, run ini orb lapw –orb (see p. 75 of DFTmanual). This generates required input files for the potentials, calledcase.inorb and case.indm.• Inside case.indm you’ll see a list: the first column is atom number(referenced to structure file – so atom 1 is the surface atom. The secondcolumn is the number of orbitals you want the calculation to consider.The last column is the identity of that orbital. For example: for bulkAu the default is 1 1 2→ atom1 (only 1 atom in the unit cell), 1 orbital,L=2 (d orbitals). You need to have this file, but unless you want tomodify the orbitals, you don’t necessarily need to change it.• Inside case.inorb you’ll see the same list, but after that there will beanother row that looks like: 0.000000000 0.0000000000 U J (Ry). Theseare the onsite Coulomb potential (U) and magnetic exchange potential(J). In our case, J=0 and we modify U how we want. For each atomin the unit cell, we must define this. They should all be listed at 0.00.0, so just find the one we need to modify. Note that units are inRydbergs.Figuring out the potential to put is the hard part. For example, we needto know how many slab unit cells the C60 molecule covers, and we will needto use x supercell to define that new structure (and make sure that it doesnot get reduced by init lapw because it will think we are defining a largerunit cell than we need). Then we have to figure out which surface atoms wewant to modify – which one is the C60 sitting on and what number is it inthe .struct file, then go find it in case.inorb and modify it.238F.7. Adding a Potential• Once all of the potentials are modified, we can run sbatch run wien2k,modified so that inside the file we have runsp c lapw -p -cc 0.00001 -ec0.00001 –orb (i.e. the same as usual but add the –orb flag).• After that, we can do bandstructure calculations: sbatch run lapw2but modified with the following commands:– x lapw1 -p -band -up -orb– x lapw1 -p -band -dn -orb– xlapw2 -p -qtl -band -up -orb– xlapw2 -p -qtl -band -dn –orb• For spin-orbit coupling, you use init so, then when running sbatchrun lapw2 you use this script:– x lapw1 -p -band -up -orb– x lapwso -p -band -up– x lapw1 -p -band -dn -orb– x lapw2 -p -qtl -band -up -orb -so– x lapw2 -p -qtl -band -dn -orb -soSo basically, we need to get the identities of the (surface) atoms from the.struct file, plot them on a mesh with a label (figure out where they actuallyexist in a lattice), overlay the C60 potential on top (which we are modellingas a sphere with an onsite potential, a certain distance away from the planeof Au atoms – undergrad E&M problem). Code should then spit out a listof atom number, locations, and onsite potentials for all of the Au atoms wewant to modify. Then it should write out / modify the (generate a second)case.inorb. Note that only atom number and potential will be used to modifythe case.inorb file, but location might be useful at another time.Python scripts to write:• get the identities of the (surface) atoms from the .struct file239F.7. Adding a Potential• write code to generate PDF based on sphere with specific potential U,radius R, distance d from plane• plot them on a mesh with a label (figure out where they actually existin a lattice), overlay the C60 potential on top → returns list of atomnumber, location, and onsite potentials for base atoms (Au)• modify case.inorb file with new data240
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From growth to TR-ARPES of C₆₀ : a prototypical OPV system
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