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Luminescent properties of Pb-based (PbX) colloidal quantum dots (CQDs) in vacuum, on silicon and integrated… Foell III, Charles Alden 2016

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Luminescent properties of Pb-based (PbX)colloidal quantum dots (CQDs) in vacuum, onsilicon and integrated with a silicon-on-insulator(SOI) photonic integrated circuit (PIC)byCharles Alden Foell IIIM.Sc. Physics, University of Vermont, 2006B.Sc. Physics, University of Vermont, 2004a thesis submitted in partial fulfillmentof the requirements for the degree ofDoctor of Philosophyinthe faculty of graduate and postdoctoralstudies(Physics)The University Of British Columbia(Vancouver)May 2016c© Charles Alden Foell III, 2016AbstractIn the rapidly evolving field of experimental quantum information process-ing, one important sub-field pursues a potentially scalable implementationthat transports quantum information encoded in photons throughout “pho-tonic circuits” fabricated in a silicon wafer. A key component is an efficienton-demand source of these single photons, and this dissertation aimed to as-sess the feasibility of one proposed realization of such a source by integratingfew PbSe colloidal quantum dots (CQDs, demonstrated single photon emit-ters in nanoparticle form) into the mode volume of an optical microcavitydesigned to efficiently direct quantum dot emission into a silicon photoniccircuit. Although no direct evidence of single photon emission was observed,results prompted a number of follow-up experiments and considerable the-oretical modeling to understand this quantum dot, photonic circuit system.The methods of investigation included (1) temporally-, spectrally-, andspatially-resolved photoluminescence (PL) measurements of PbSe CQDs in-tegrated into SOI PICs and relatable environments (solution, thick film, thinfilm), (2) temperature-dependent, air-exposure studies of PbSe CQD thickfilm PL, (3) development and application of kinetic and quantum mechani-cal cavity-coupled modeling that admit complete accounting of the photonicdensity of states, depolarization effects, and non-radiative decay, and (4) aphoton coincidence test of single photon emission.The main findings of this work are: (1) while capture of cavity-enhancedPbSe CQD emission into a silicon photonic circuit was demonstrated, theoverall photon generate rate is inadequate for any useful implementation,(2) the measured coupling rate can be modeled and explained in terms ofiisystem parameters extracted from auxiliary experimental results obtainedwith the PbSe CQDs in isolation, or on isolated microcavities, and (3) con-sistent results could only be obtained after nontrivial depolarization factorsand non-radiative decay processes are properly accounted for. From thisit is clear that the performance of PbSe CQDs in this configuration of asingle photon source in silicon is currently limited by a long-lived trap statewith a several microsecond lifetime, and large depolarization effects that in-hibit emission. Although plausible future efforts may mitigate these effectssubstantially, performance may still be hindered by the intrinsic emissionstrength of PbSe CQDs.iiiPrefaceIdentification and large-scale design of the research program was primarilyset by my research supervisor and our group principal investigator, Jeff F.Young. My role was primarily implementation and development of the ex-perimental setups, measurements, modeling, and analysis used to implementthe research program.Three publications arising partially or entirely from the work within thisdissertation are as follows:• C. A. Foell, E. Schelew, H. Qiao, K. A. Abel, S. Hughes, F. C. J. M.van Veggel, and J. F. Young, Saturation behaviour of colloidal PbSequantum dot exciton emission coupled into silicon photonic circuits,Optics Express, Vol. 20, Issue 10, pp. 10453-10469 (2012) [73]• C. A. Foell, K. A. Abel, F. C. J. M. van Veggel, and J. F. Young, Ki-netic analysis of the temperature dependence of PbSe colloidal quan-tum dot photoluminescence: Effects of synthesis process and oxygenexposure, Phys. Rev. B 89, 045139 (2014) [74]• R. Quintero-Torres, C. A. Foell, J. Pichaandi, F. C. J. M. van Veg-gel and J. F. Young, Photoluminescence dynamics in solid formula-tions of colloidal PbSe quantum dots: Three-dimensional versus two-dimensional films, Appl. Phys. Lett. 101, 121904 (2012) [173]The experimental results of Foell et al. (2012) [73] are presented inChapter 2, and related modeling in Chapter 3. Much of the text of thispublication is directly incorporated into this dissertation. My role in thisivpublication was all modeling, including FDTD and quantum mechanical. Ialso contributed to the majority of the manuscript preparation and reviewof it. The stand-alone cavity was fabricated, sample prepared, and measure-ments performed by Haijun Qiao. Photonic circuits in that publication, andused in this dissertation in Chapter 4 were designed and characterized bySimon Dickreuter, Jacob Slack, Jeff F. Young, and Ellen Schelew. The quan-tum mechanical model used in modeling was proposed by Stephen Hughesand Jeff Young. CQDs were synthesized by Keith Alexander Abel.The experimental results of Foell et al. (2014) [74] are presented inChapter 2 and related modeling in Chapter 3. Much of the text of thispublication is also directly incorporated into this dissertation. My role inthis publication was all sample preparation, measurements and modeling. Ialso contributed to the majority of the manuscript preparation and reviewof it. The kinetic model used was proposed by Jeff F. Young. CQDs weresynthesized by Jothirmayanantham Pichaandi. The “dip-coating” apparatusand inert environment glove box were developed in large part by summerstudents Nancy Liu and Manveer Bains.The experimental results of Quintero-Torres et al. (2012) [173] are pre-sented in Chapter 2 and related FDTD dielectric modeling in Chapter 3.My role in this publication was all sample preparation and dielectric mod-eling. I also contributed to portions of the manuscript and review of it.Measurements were performed by Rafael Quintero-Torres and CQDs weresynthesized by Jothirmayanantham Pichaandi.Reproduction of content from these publications is with permission fromthe respective publishers.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . .xxvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Dissertation overview . . . . . . . . . . . . . . . . . . . . . . . 11.2 Quantum information processing (QIP) . . . . . . . . . . . . 51.2.1 QIP overview . . . . . . . . . . . . . . . . . . . . . . . 61.2.2 Bits and qubits . . . . . . . . . . . . . . . . . . . . . . 61.2.3 Classical and quantum logic gates . . . . . . . . . . . 81.2.4 Quantum teleportation: an example . . . . . . . . . . 111.2.5 Linear optical quantum information processing (LOQIP) 121.3 LOQIP in the SOI platform . . . . . . . . . . . . . . . . . . . 191.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 191.3.2 Linear optical components . . . . . . . . . . . . . . . . 201.3.3 Single photon detectors . . . . . . . . . . . . . . . . . 271.3.4 Single photon sources . . . . . . . . . . . . . . . . . . 30vi1.3.5 Hybrid approaches to SOI platform single photonsources . . . . . . . . . . . . . . . . . . . . . . . . . . 351.4 Lead-based (PbX) colloidal quantum dots (CQDs) for singlephoton sources in SOI LOQIP . . . . . . . . . . . . . . . . . . 361.4.1 Basic CQD photophysics . . . . . . . . . . . . . . . . . 361.4.2 Band structure context, CdX CQD comparison . . . . 391.4.3 Non-radiative recombination, defect/surface states,and CQD formulation . . . . . . . . . . . . . . . . . . 421.4.4 Impact of dielectric environment on CQD emission:depolarization and radiative density of states . . . . . 451.4.5 CQD emission on silicon and in SOI PICs . . . . . . . 461.5 Dissertation aim restatement, methodology, and organization 472 Experiment (non-PIC) . . . . . . . . . . . . . . . . . . . . . . 492.1 Substrates and photonic component fabrication . . . . . . . . 492.1.1 SOI and silicon substrates . . . . . . . . . . . . . . . . 492.1.2 Photonic crystal cavities . . . . . . . . . . . . . . . . . 502.2 PbX CQD formulations and integration methods . . . . . . . 512.2.1 PbX CQD formulations . . . . . . . . . . . . . . . . . 522.2.2 PbX CQD integration methods . . . . . . . . . . . . . 532.3 PL measurements overview and optical setups . . . . . . . . . 582.3.1 PL measurements overview . . . . . . . . . . . . . . . 582.3.2 Head-on continuous wave (CW) laser excitation . . . . 592.3.3 Pulsed excitation in back-scatter geometry . . . . . . 602.4 Power saturation of cavity-coupled CQD PL . . . . . . . . . . 622.5 Time-resolved decay of CQDs in various formulations . . . . . 652.6 Air exposure influence on CQD thick film temperature-dependent PL . . . . . . . . . . . . . . . . . . . . . . . . . . . 683 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.1 Overview of model . . . . . . . . . . . . . . . . . . . . . . . . 723.1.1 Exciton thermalization in the ground state manifold . 743.1.2 Depolarization, spontaneous emission rates . . . . . . 75vii3.1.3 Intrinsic dipole moment . . . . . . . . . . . . . . . . . 783.2 Power saturation of cavity-coupled CQD PL . . . . . . . . . . 793.2.1 Master equation model . . . . . . . . . . . . . . . . . . 803.2.2 Model dielectric environment . . . . . . . . . . . . . . 833.2.3 “Simple” model parameters . . . . . . . . . . . . . . . 833.2.4 Spontaneous emission rate γXG = γXG,ǫ(r) . . . . . . . 843.2.5 Cavity-QD coupling g . . . . . . . . . . . . . . . . . . 853.2.6 Laser-QD coupling Ω . . . . . . . . . . . . . . . . . . . 873.2.7 Fit parameter . . . . . . . . . . . . . . . . . . . . . . . 883.2.8 Saturation modeling results . . . . . . . . . . . . . . . 903.2.9 Saturation modeling conclusions . . . . . . . . . . . . 933.3 Modeling time-resolved decay of CQDs in various formulations 933.3.1 Dielectric model accounting of radiative decay . . . . 943.3.2 Radiative efficiency from time-resolved emission anddielectric modeling . . . . . . . . . . . . . . . . . . . . 953.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 963.4 Air exposure dependence of exciton kinetics . . . . . . . . . . 973.4.1 Fit methods and extracted parameters . . . . . . . . . 1033.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 1053.4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 1083.4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 1093.5 Modeling discussion . . . . . . . . . . . . . . . . . . . . . . . 1114 PbX CQDs in SOI PICs . . . . . . . . . . . . . . . . . . . . . 1144.1 Sample preparation (SOI PICs, CQD integration) . . . . . . . 1144.2 Measurement overview and optical setups . . . . . . . . . . . 1164.2.1 Optical setup . . . . . . . . . . . . . . . . . . . . . . . 1174.2.2 Microphotoluminescence . . . . . . . . . . . . . . . . . 1224.2.3 Photon coincidence . . . . . . . . . . . . . . . . . . . . 1264.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1344.3.1 Extrapolation of PIC-coupled photon rate . . . . . . . 1344.3.2 Estimated single CQD results . . . . . . . . . . . . . . 1364.3.3 Comparisons and potential use as a single photon source136viii5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1385.1 Conclusions, discussion and significance . . . . . . . . . . . . 1395.2 Limitations, strengths, and future work . . . . . . . . . . . . 140Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142A Dip coating procedural details . . . . . . . . . . . . . . . . . 171ixList of TablesTable 2.1 PbSe CQD thick film sample descriptions, for integratedPL traces plotted in Figure 2.10. . . . . . . . . . . . . . . 69Table 3.1 PbSe CQD thick film sample descriptions, for integratedPL traces plotted in Figure 3.8. Samples from our lab,already presented in Section 2.6, are reproduced here forconvenient comparison to samples from other labs. “Alkyl-” for studies mentioned here refer to alkylselenide [93]. . . 99xList of FiguresFigure 1.1 Bits and qubits. Bits take on one of two values, e.g. 1or 0. Qubits may be represented by a complex linear su-perposition of two orthogonal basis vectors. In the Blochsphere parametrization, a pure qubit state is representedby a vector of unit length and of angular direction (θ,φ),such that unitary operations upon the qubit rotate thevector to some other other direction. Bit measurement iscommonly deterministic, whereas qubit measurement isgenerally probabilistic. . . . . . . . . . . . . . . . . . . . 7Figure 1.2 Example classical logic circuit and logic gates NOT, AND,and XOR. Any algorithm may be encoded in a circuitconstructed of suitable arrangement of a universal (func-tionally complete) set of logic gates, e.g. of the gate setconsisting of the NOT gate and AND gate. . . . . . . . . 9Figure 1.3 Example universal set of quantum gates consisting ofthree single qubit rotation gates and one two-qubit CNOTgate, with circuit symbols, depictions, and representa-tions. Single qubit gates include rotations about eachof the Bloch sphere axes, generated by the Pauli matricesX, Y , and Z. The two qubit CNOT gate flips the targetqubit |qt〉 if and only if the control qubit |qc〉 is |1〉. Anymulti-qubit state may be constructed with these gates. . 10xiFigure 1.4 Quantum teleportation circuit. See Figure 1.3 for quan-tum gate definitions. Single lines are quantum channelsand double lines are classical channels. A quantum stateis transported from location A to location B using twoclassical information channels and one quantum channel. 11Figure 1.5 (A): General dual rail optical qubit basis states consistof single photon absence/presence in one of two opticalmodes. (B) and (C): Free-space polarization encodedphotonic qubits that exemplify dual rail qubits, and (D):mechanism to convert polarization encoded qubits to pathencoded qubits. . . . . . . . . . . . . . . . . . . . . . . . 14Figure 1.6 Universal LOQIP quantum gates, constructed from (A)phase shifters, (B) beam splitters, and photon detectors,for path encoded optical qubits. Rotation angles θ andφ map directly onto the Bloch sphere. (C): CNOT gatesuccess, i.e. |ψtarget,out〉 equaling |ψcontrol,in⊕ψtarget,in〉,coincides with photon detection in the output ancillarymodes |aancillary,out〉 and |bancillary,out〉. . . . . . . . . . . . 15Figure 1.7 Hong-Ou-Mandel (HOM) effect measurement setup, with“HOM dip” in photon detection event coincidences. Adip to zero coincidences (for zero path length differencefrom the beam splitter to each detector, controlled by avariable delay) is evidence of photon interference of thetwo photon sources and indication of the photon sourcesemitting photons indistinguishable from each other. . . . 17Figure 1.8 The SOI platform, for LOQIP. (A): Typical silicon-on-insulator (SOI) dimensions used for SOI-based photonicintegrated circuits and (B) example etching steps. Addi-tional functionality may be achieved by lithographic inte-gration of metal contacts, ion doping, and deposition ofother materials. (C): Example LOQIP circuit layout anddepicted embedment in an SOI wafer. . . . . . . . . . . . 21xiiFigure 1.9 (A): Total internal reflection at silicon-air and silicon-oxide interfaces. (B) and (C): Ridge waveguide thatutilizes total internal reflection to contain light withinthe waveguide. (C): Example electric field mode profile,showing non-zero field beyond the silicon. (D): Ridgewaveguide beam splitter, labeled with a characteristicbending radius (typically around 10 µm for these ma-terials) that limits the minimum size in accordance withthe total internal reflection angles described in (A). Beamsplitters admit Rαy single qubit rotations and, along withsingle photon detectors, may be used to realize a CNOTgate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 1.10 Example phase shifter, capable of producing single qubitrotations Rφz . A small current passing through a metallicstrip, connected to the control electronic microcircuitry,may locally heat and change the index of refraction, thusthe relative optical path length (note that the metallicstrip is not necessarily in contact with the waveguide, butmore likely embedded in a layer above or below it). . . . 23Figure 1.11 Photonic band gap confinement mechanism used in SOIphotonic circuits. (A): Slab hexagonal lattice photoniccrystal. (B): Definitions of TE and TM propagatingmodes. (C): Example photonic band structure for slabphotonic crystal similar to the one depicted in (A). . . . 25xiiiFigure 1.12 Photonic crystal structures. (A): Photonic crystal waveg-uide, consisting of a line defect in a slab photonic crystal,joined with a ridge waveguide. (B): Photonic crystal cav-ity, consisting of a point defect in a slab photonic crystal,accompanied by a sketch of the local photonic density ofstates (ρDOS) as a function of embedded emitter frequencyω at the cavity center. Slab photonic crystals may con-sist of a regular pattern of air holes which, for the casesof photonic crystal waveguides and cavities, are omitted(i.e. not made) along a line or localized region duringpatterning of the remainder of the structure. . . . . . . . 26Figure 1.13 (A): Waveguides terminating in a diffraction grating, thelatter for free-space/on-chip light conversion. (B): Par-tial band structure diagram for the photonic crystal withphotonic crystal waveguide bands (green). Guided (slab-like) modes in red and blue. Modes within the light coneare not confined to the device silicon. A bound state suchas a photonic crystal cavity (not shown in this diagram)would also lie within the TE band gap. The in-slab am-plitude of propagating waveguide modes (below the lightline) decays exponentially in the grating region (i.e. isnon-propagating and above the light line) as the field isdiffracted out of the device slab. . . . . . . . . . . . . . . 28Figure 1.14 Example integrated detectors, in which photodetectivematerial is placed atop waveguide within waveguide mode.(A): perspective view of detecting material atop waveg-uide, with connected electrical wires. (B): head-on view,overlayed with waveguide profile. Size of photodetectivematerial in (A) and (B) is slightly exaggerated for draw-ing purposes. (C): Realized integrated, superconductingsingle photon detector from the Young lab [9]. . . . . . . 29xivFigure 1.15 (A): Single photon emission from an incoherently pumped(via state |P 〉) two level system (|G〉,|X〉). (B): Inte-grated single photon source geometry, consisting of a ra-diative two level system embedded in a dielectric envi-ronment that efficiently channels photon emission into aridge waveguide. . . . . . . . . . . . . . . . . . . . . . . . 31Figure 1.16 Integrated emitter geometries for realization of a singlephoton source. (A): Emitter directly atop a ridge waveg-uide. (B): Emitter atop a photonic crystal waveguide.(C): Emitter in a waveguide-coupled photonic crystal cav-ity. Geometry (C) offers the best into-circuit emittercollection efficiency of these three geometries owing tothe largest collection efficiency by the cavity, followed byavailability of highly efficient transfer of cavity photons tothe ridge waveguide through the photonic crystal waveg-uide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 1.17 Illustrations of semiconductor quantum dots (QDs),(A) epitaxial and (B) colloidal/nanocrystal. QDs arenanometer-scaled semiconductor crystals that quantumconfine the otherwise bulk excitonic spectrum, resultingin synthetic two level systems and demonstrated singlephoton emission. . . . . . . . . . . . . . . . . . . . . . . 35xvFigure 1.18 Confinement of excitons in CQDs, exemplified for PbSesemiconductor. (A): Wannier exciton in bulk PbSe. (B):Colloidal PbSe quantum dot, capped with organic lig-ands. CQDs generally possess multiple crystallographicfacets, not drawn here. Ligands for CQDs measured inthis dissertation are oleic acid, a fatty acid roughly 2nm long (end to end, including a typical molecular bend)composed primarily of a hydrocarbon chain, which hasan orientation with respect to the CQD dependent uponthe orientation of crystallographic facet to which it is at-tached. (C): General effect of quantum confinement onthe electronic density of states ρ(ǫ). . . . . . . . . . . . . 37Figure 1.19 Example photophysical properties of PbX CQDs with C-band exciton emission. (A): Example absorption andemission spectra of PbSe CQDs in a colloidal suspension.(B): Collection of theoretical and experimental values offirst absorption peak energy versus CQD size for PbSCQD, reprinted with permission from [142] (Copyright2009 American Chemical Society). Unit conversion: 1 eV↔ 1240 nm, 1550 nm ↔ 0.8 eV. . . . . . . . . . . . . . . 38Figure 1.20 Comparison of band and state structures of PbSe andCdSe bulk crystals and quantum-confined nanocrystals.(A) and (B): Bulk band diagrams for PbSe and CdSe, re-spectively, adapted with permission from [236]. (C) and(D): (left) bulk and quantum confined (right) band edgeenergy levels, including electronic and spin degrees of free-dom. Bulk energy levels do not include splitting due tocrystal field or spin orbit coupling, but quantum confinedlevels do, along with splittings due to other interactions. 40xviFigure 2.1 (A): Schematic and scanning electron micrograph of an“L3” microcavity. (B): Fundamental in-gap cavity modeelectric field intensity at the silicon-air interface, withetched holes outlined. Axes originate at the L3 slab cen-troid, and zˆ is perpendicular to xˆ and yˆ. Yellow scale barsare 500 nm in length. Figure adapted from [164]. . . . . 51Figure 2.2 Dip-coating for thin film formulations, in an inert-gasglove box. (A): The glove box and dipping setup usedfor monolayer, sub-monolayer, and generally dip-coatingformulations. (B): Example scanning electron micrographof a sub-monolayer of CQDs on a silicon surface using thesetup in (A) and described in-text, published in [173]. . . 55Figure 2.3 Site-selective binding technique, as published in [164],used to integrated PbX CQDs to primarily within themain antinode of the the fundamental cavity mode ofa standalone L3 photonic crystal cavity, for the samplestudied in this chapter. Prior to the AFM site-selectivesurface oxidation depicted in (A), the silicon is coatedwith dodecyl molecules. In (B), application of a voltagefrom the AFM locally removes the dodecyl molecules andoxidizes the silicon surface. Immersion in a buffered oxideetch removes the oxidized silicon but leaves the dodecylcoated silicon intact. The sample is finally dipped in asuspension of CQDs (C), which adhere preferentially tothe hydrogen-terminated silicon (relative to the dodecylcoated silicon). (D) and (E) are atomic force micrographsof the sample surface, with (E) corresponding to the re-gion within the white rectangle in (D). (F): resulting mi-crophotoluminescence (µPL) collected directly from thecavity region. Yellow scale bar is 500 nm in (D) and 50nm in (E). Unit conversion: 1 eV ↔ 1240 nm, 0.8625 eV↔ 1500 nm. . . . . . . . . . . . . . . . . . . . . . . . . . 57xviiFigure 2.4 Head-on continuous wave (CW) HeNe excitation setupused for power saturation measurements of PbX CQDemission coupled to a standalone L3 cavity and stead-state integrated PL of PbSe CQD thick films. Mirrorpair MT1,T2 diverts collected light down (−xˆ) and then inthe direction of the Bruker FTIR; details are available inthe insets of Figure 4.4F. . . . . . . . . . . . . . . . . . . 60Figure 2.5 Back-scattering geometry with pulsed laser excitationsetup used for time-resolved studies in [173] and presentedin Section 2.5. . . . . . . . . . . . . . . . . . . . . . . . . 61Figure 2.6 Comparison of power dependence of PbSe CQDs in thinformulations in different dielectric environments. (A): Ex-ample low and high excitation power PL spectra of CQDson the surface of a SOI L3 optical microcavity, integratedby dip-coating, and labels indicating cavity-coupled andbackground contributions at a cavity mode wavelength.(B): Example low and high excitation power PL spectraof a thin film of PbSe CQDs on a bare silicon surface, alsodeposited by dip-coating, for the same excitation setupused for data in (A). (C): Power dependence compari-son for cavity-coupled PL of (A) and monolayer PL of(B), for the same excitation conditions, showing how thepower dependent PL of the monolayer is nearly linearbut strongly saturated for the cavity-coupled PL. (D):Power dependence comparison for samples with Nd:YAGexcitation and identical excitation/collection geometries,again exemplifying the difference in saturation powers.(E): Same as in (D), but the monolayer data scaled alongthe power axis by the excitation enhancement factor cal-culated in section 3.2 (a factor of 9) and scaled verticallyto best match the cavity-coupled data fit. Note the goodoverlap, which can be interpreted with Chapter 3 model-ing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63xviiiFigure 2.7 Experimental setup and resulting data modeled in thisarticle. (A): Schematic of excitation/collection geometry:excitation (at 633 nm) and collection performed with acommon 100X microscope objective. Red-filled circle in-dicates 1/e excitation spot intensity. Shaded square indi-cates span of grafted PbSe CQDs. (B): Example PL spec-trum with cavity-coupled emission indicated, and cavity-coupled PL versus pump power. . . . . . . . . . . . . . . 64Figure 2.8 Time-dependent PL at 300 K for PbSe CQDs dispersedin hexanes (black dots); drop-cast film (blue circles);and sub-monolayer (red squares). The inset shows thesteady state PL spectra from drop-cast (top, blue), solu-tion (middle, black), and sub-monolayer dispersions (bot-tom, red) of the same batch of CQDs. The monolayerwas excited with 3000 times more average power than thedrop-cast film. . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 2.9 Histograms of the shortest time constants, τ1 (left, (A)and (C)), and the average time constants A1τ1+A2τ2A1+A2 (right,(B) and (D)) components of the measured lifetimes ex-tracted from two-exponential fits to decay curves takenfrom various locations on the drop-cast samples (bottom,(C) and (D)), and the dip-coated samples (top, (A) and(B)). The mean values are (A) 90 ns, (B) 135 ns, (C)190 ns, (D) 200 ns. (E): Tabular summary of known andunknown radiative and non-radiative decay parameters,after measurements indicated in this section but beforemodeling of the photonic density of states performed inChapter 3. . . . . . . . . . . . . . . . . . . . . . . . . . . 67xixFigure 2.10 Integrated PL data sets (black squares), normalized totheir maximum values, along with best-fit model yieldcurves (calculated below) in solid red and correspondingmodel PL contributions from each of two possible emissivestates or clusters of emissive states in dotted and dashedlines, respectively. Modeling is described in Chapter 3.Table 2.1 contains descriptions of the samples. . . . . . . 70Figure 3.1 Overview of general considerations for modeling PbXCQD emission in nanophotonic environments. (A): Exci-tonic states are numerous and the distribution of transi-tion dipole moment magnitudes is varied across a num-ber of computational studies. (B): Simplified excitonicstate structure, for which rapid decay from higher-lyingstate(s) |P 〉 to a ground state excitonic manifold is under-stood |X〉, but the decay from the ground state excitonicmanifold |X〉 to the CQD ground state |G〉 is generally en-vironment dependent. (C): Example depolarization effecton the electric field for a dielectric sphere, one environ-mental contribution to exciton decay dynamics. . . . . . 73Figure 3.2 Minimal Hilbert space necessary to accommodate ob-served saturation behavior: four states (including trapstate) for the CQD subspace and two for the cavity sub-space. Significant decay paths indicated by solid bluearrows, of which squiggly lines are radiative and the re-mainder non-radiative. Laser field of Rabi coupling fre-quency Ω “pumps” the |P 〉 state. The cavity is “fed” bycoupling to the |X〉 ↔ |G〉 transition with electric-dipolecoupling strength g. . . . . . . . . . . . . . . . . . . . . . 81xxFigure 3.3 Model dielectric environment ǫ(r,ω) = ǫL3(r,ω) +ǫCQDs(r,ω). Nanocrystal array ǫCQDs(r,ω) on left,centered on the L3 cavity surface. The computationalvolume for FDTD calculations (see text) is restrictedto the 3 µm cube centered about the centroidal CQD.The intrinsic “test” dipole is located at the center ofcentroidal CQD, position rCQD. The device silicon slabis surrounded by vacuum above and below, with backingsilicon 1.2 µm below. . . . . . . . . . . . . . . . . . . . . 84Figure 3.4 Spontaneous emission rate of a point dipole source of fre-quency ωcav+ δω, for positions along the zˆ-axis of the L3cavity, excluding the cavity mode and CQD array, for elec-tric dipole orientations along axes xˆ, yˆ, or zˆ (see text andorientation definitions in Figure 2.1). All values normal-ized to the free-space spontaneous emission rate γXG,0. . 86Figure 3.5 Intensity profiles of HeNe excitation field, as modulatedby the L3 cavity ǫL3(r). Gaussian laser field was injectedalong the zˆ axis towards increasingly negative z, indi-cated by black arrow. Air-silicon interfaces lined in black.(left) Profile several nanometers above the slab surface,the plane containing the PbSe CQDs. (right) Profile inthe x= 0 plane. . . . . . . . . . . . . . . . . . . . . . . . 89Figure 3.6 Best (minimum χ2) fits to cavity-enhanced photolumines-cence for only three electronic levels (left), i.e. without anon-radiative state, and for four electronic levels (right),i.e. including a non-radiative “trap” state. . . . . . . . . 90xxiFigure 3.7 Trap state lifetime τtrap = γ−1Y G required to fit the data.Parametrization of τtrap is in terms of the “effective de-polarization”, DPF , which is defined in-text (see Equa-tion 3.24) and is equal to the laser field inside the CQDin the full model dielectric environment relative to thelaser field inside the same CQD in vacuum. Variationof τtrap with DPF is dominated by uncertainties in pa-rameters specific to our dielectric environment (photoniccrystal cavity, CQD array), whereas variation of τtrap for aparticular DPF is dominated by parameter uncertaintynot specific to our dielectric environment (e.g. solventpermittivity from solvent-based CQD properties). Pointsare sampled from the model parameter space. . . . . . . 92Figure 3.8 Integrated PL data sets (black squares), normalized totheir maximum values, along with best-fit model yieldcurves (calculated below) in solid red and correspondingmodel PL contributions from each of two possible emissivestates or clusters of emissive states in dotted and dashedlines, respectively. Samples series A and B are from workpublished in references [43, 93], and sample series C andD were already described in Section 2.6 but reproducedhere for convenient comparison. Table 3.1 contains de-scriptions of these samples. . . . . . . . . . . . . . . . . . 98Figure 3.9 Modeled energy level arrangement. Levels A and B are inthermal quasi-equilibrium and populated by pumping ofhigher-lying levels at a rate gex. They respectively consistof NA and NB states of average radiative decay rates γAand γB. The general non-radiative decay Γ, the nature ofwhich is described in detail in-text, is not specific to levelA or B for the purposes of this kinetic modeling, and isindicated by the dashed arrow. . . . . . . . . . . . . . . . 101xxiiFigure 3.10 Subscript j indexes the non-radiative decay pathways, e.g.as indexed in Equation 3.32. Bars represent the rangesof parameter values that, upon substitution into Equa-tion 3.29, using Equation 3.27, generate or nearly generatethe model curves in Figure 2.10. Rates are normalized asdescribed in-text (leading up to Equation 3.32), and ener-gies are in meV. Sample labeling is as in Figure 2.10 andTable 2.1. Parameter ∆ǫBA is restricted from above to80 meV for reasons described in-text. Rates sufficientlysmall to render their corresponding energies meaninglessare omitted, along with those energies. . . . . . . . . . . 104Figure 4.1 (A): Full photonic integrated circuit (PIC) designed andcharacterized in-lab [189] and used in this dissertation asa PIC in which PbSe CQDs were integrated and theirluminescence was measured. (B): PIC transmission mea-surement schematic. (C): Transmission spectrum of thePIC, prior to CQD integration. (D): PL of PbSe CQDsin solution, prior to their integration into the PIC. . . . . 115Figure 4.2 Optical setup used for characterizing PbX CQD emis-sion in and near the photonic integrated circuits, includ-ing (a) steady-state, Nd:YAG excited microphotolumines-cence (µPL) spectroscopy, (b) spectrally-integrated, time-resolved µPL emission using a 660 nm pulsed laser, and(c) photon coincidence (correlation) measurements. . . . 118Figure 4.3 Simple overlay of excitation and collection regions rela-tive to the PIC components. Collection area and positionwas controlled with the far apertures FAL,C,R. Positionof the excitation spot was controlled by adjusting the po-sition of the excitation lens assembly ELA and mirrorspreceding it. The 1/e2 minimum power diameters were20 µm and 3.5 µm for the Nd:YAG and 660 nm pulsedlaser excitation sources, respectively. . . . . . . . . . . . 119xxiiiFigure 4.4 Detailed illustrations of excitation and collection geome-tries, an elaboration upon the larger scale diagrams de-picted in Figures 4.2 and 4.3. . . . . . . . . . . . . . . . 120Figure 4.5 Example steady-state µPL for excitation with several mWof Nd:YAG laser focused onto the cavity region with a1/e2 power waist of 20 µm. (A): PL collected over thecavity region. (B): PL collected over the grating region.(C): Apertured (both near and far) spectrum collectedover part of the grating region, with a transmission plot(red) of the PIC, measured prior to CQD integration. (D):Power-saturation of the circuit-coupled, cavity-enhancedCQD PL, collected from the grating using the aperturesper (C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Figure 4.6 Example spectra (200 FTIR scans, 1 nm resolution) andtime-resolved decay (with superimposed single exponen-tial decay fits) of PL collected, for excitation with the660 nm Sepia pulsed laser source with 1/e2 power waistof 3.5 µm, 10 MHz repetition rate (1 MHz for collectionfrom the cavity region), and ≈ 0.05 mW average incidentpower. Background PL spectra with the Sepia laser exci-tation differ from background PL spectra with the 1064nm Nd:YAG excitation, which is not unexpected given dif-ferences in excitation spot size, intensity, and wavelength.The single exponential 1/e decay times for PL collectedfrom the gratings are 30 ns, but don’t capture the fasterdecay at short time scales. Decay from the cavity regionis characterized by a 1/e decay time of 60 ns. . . . . . . 124xxivFigure 4.7 (A): Idealized stream of regularly emitted on-demandphotons (red) compared to a stream of photons exhibit-ing photon bunching. (B): Histogram of photons within afixed time interval for a Poissonian source (striped yellow,purple) and an ideal stream of regularly emitted photonsfrom an on-demand source. (C): Basic photon coincidencesetup to test if a source emits only a single photon at atime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Figure 4.8 (A) and (B): PL spectra collected from diffraction grat-ings connected to the same cavity, for the cavity excitedwith pulsed 660 nm Sepia light, as used for coincidencemeasurements described later in this chapter, and beforeany spectral filtering was performed. See Figure 4.9 forspectral filtering performed. Insets are the same spectra,plotted over a smaller wavelength range around the cav-ity wavelength, with Lorentzian fits and indicated ratio ofpeak PL to background PL at the cavity wavelength (af-ter proper baseline subtraction). Spectra are noisier thanthose presented previously in this section due to a higherspectral resolution relative to a number of FTIR scans.Each cavity to background ratio for this sample is smallerthan for the samples in previous sections, but this sam-ple was the only, at the time of measurements, from whichcavity coupled PL collected from both gratings dominatedthe total PL signal at the cavity wavelength. . . . . . . . 128xxvFigure 4.9 Spectral filtering used for coincidence measurements. (A):The band pass free-space filter (FSF) from Edmundsblocks (with OD4) all but the wavelength range 1550 nmto 1600 nm. (B): The tunable narrow band pass fiber fil-ter (FF) from Koshin Kogaku possesses an approximatelyLorentzian lineshape with 1.2 nm FWHM and can betuned to the cavity wavelength. (C): Schematic of thefree-space to fiber coupler assembly and in-line fiber filter(FF), with pre- and post- filtering locations, as plotted in(D) through (F), circled. (D): Example measured spec-trum (from Figure 4.8B) before spectral filtering. (E):Extrapolated PL after propagating the spectrum throughthe free space filter and into the fiber, using the measuredpre-filter spectrum S(λ) and free space filter transmissionspectrum TFSF (λ), as well as the measured free-space tofiber coupling efficiency. (F): Extrapolated PL, after boththe free space and fiber filters, using the filter transmis-sion spectra TFF (λ;λ0) and TFSF (λ), and exemplified forthe tunable filter both tuned to the cavity wavelength andslightly detuned from it. . . . . . . . . . . . . . . . . . . 132Figure 4.10 Example coincidence plots for total count rate (darkcounts plus signal), dark counts only, and the differenceof the two. No evidence of antibunching was found fordetection and excitation settings considered. . . . . . . . 134xxviAcknowledgmentsFor Chapter 3, I gratefully acknowledge the insight regarding band structuremodels in this system provided by Pawel Hawrylak and Oleksandr Voznyy. Ialso acknowledge the financial support of the Natural Sciences and Engineer-ing Research Council, and the Canadian Institute for Advanced Research.For Chapter 4, I acknowledge the funding support of the Natural Sciencesand Engineering Research Council, the Canadian Institute for Advanced Re-search, CMC microsystems, and the Natural Resources and Applied Sciences(NRAS) Research Team Program of the Government of British Columbia. Ialso acknowledge Jacob Slack and Simon Dickreuter for their contributionsto the SOI devices, Lumerical Solutions, Inc. for their FDTD software andsoftware support, and Westgrid [2] for computing time on their cluster.I also acknowledge Haijun Qiao, Keith Abel, Ellen Schelew, JothirMayanantham Pichaandi, Jonathan Massey-Allard, Hamed Mirsadeghi,Hailong Ning, Mario Beaudoin, Georg Rieger, and Mohsen Akhlaghi foruseful discussions about research pertaining to this topic. This dissertationis built upon the knowledge of many people before me and alongside me,and I am thankful for that.xxviiChapter 1Introduction1.1 Dissertation overviewThis dissertation describes a combination of materials and process synthe-sis, optical spectroscopy, and numerical modeling results obtained while at-tempting to develop a non-classical, single photon light source in a silicon-based, planar photonic circuit platform. Such a source is one of the keyelements required to potentially realize scalable quantum information pro-cessing based on photons. This chapter motivates the work, and providesessential background information regarding relevant materials, concepts, andprior state of knowledge.A variety of natural and man-made sources of electromagnetic radiation(photons) with wavelengths in the range of a few hundred to a few thousandnanometers are familiar; starlight, burning embers, lightning, incandescentfilaments, fluorescent tubes, light emitting diodes, lasers etc. The nature ofthese sources differs qualitatively and quantitatively, but all are considered“classical light sources” owing to the statistical distribution of photons theyemit (e.g. variance in photon emission times). Illumination and display arethe obvious applications for many of these classical light sources, but they arealso indispensable for manufacturing (laser cutting), metrology (measuringthe flatness of surfaces, laser radar (LIDAR)), information processing (opti-cal storage disks, fiber-optic transmission links that drive the Internet), and1scientific exploration (e.g. formation of Bose-Einstein condensates).The technical definition of “classical light”, as worked out by Glauberover half a century ago [78], is an electromagnetic state that can be de-scribed by a proper, positive probability density function P (α) over Pois-sonian superpositions of quantum mechanical photon number states knownas coherent states |α〉 (e.g. with density operator ρ= ∫ dαP (α)|α〉〈α|). Thedistribution of states describing the emission from thermal sources is Gaus-sian, whereas it is typically Poissonian in the case of light emitted by lasers.An ideal on-demand single photon source [36, 47, 64, 131, 184] emitsa single, indistinguishable photon, upon triggering, into a specific opticalmode, with unity efficiency, no temporal jitter, narrow bandwidth, at a highrepetition rate (on order GHz). Such a stream of individual photons is non-classical in that its formal quantum mechanical state cannot be expressedin terms of a proper probabilistic distribution of coherent states.Interest in developing high quality single photon sources has been largelydriven by the rapid growth of quantum information science and technology.Quantum information research aims to understand and exploit the funda-mental quantum mechanical properties of physical systems as they pertainto the acquisition and processing of information in ways that are impossi-ble using classical tools. Three of the most compelling examples include“noise-free” measurement; the ability to overcome the fundamental statis-tical noise inherent in measurements based on classical probes of physicalproperties, quantum computation; quantum mechanically-based algorithmsexist for factoring large numbers, or searching vast databases that couldnever be accomplished using classical information algorithms, and quan-tum communications; the pursuit of encoding, transmitting, and decodingquantum state information. In order to realize the predictions of quantuminformation science, it is necessary to develop the technology to control andengineer the quantum mechanical state of discrete physical entities. Whilethe field is vast, a significant fraction of it is focused on demonstrating thiscontrol over photons. “Perfectly secure” quantum optical communicationchannels have already been demonstrated, and designs for an all-opticalquantum computer have been available for over a decade [110].2Until recently, the best - but far from ideal - single photon sources con-sisted of bulk optical nonlinear crystals that, when pumped by relativelypowerful laser beams, stochastically emit entangled photon pairs to real-ize “heralded” single photon sources, in which measurement of one photonguarantees the presence of another photon in the absence of losses. Powerfullaser-pumped bulk optical crystals are unlikely to form the basis of a manu-facturable quantum information technology. After approximately a decadeof effort, single photon sources based on nanometer-scale photonic compo-nents have started to compete with these bulk optical sources in terms ofraw performance, but interest in such sources derives as much from their po-tential high quality, as the potential they offer as a scalable, manufacturablequantum technology platform.Interestingly, the past decade and a half has seen the parallel devel-opment of new platforms for processing classical information using classicallaser light in “photonic circuits”, motivated by the need to make more manu-facturable the increasingly complex interfaces between microelectronic com-puter chips, and the optical fiber network that interconnects them. Startingin the 1990’s, much effort has gone into the development of photonic inte-grated circuits (PICs) that consist of miniaturized photon sources, detectors,and passive optical components to guide and manipulate light, all embeddedon a centimeter scale chip to overcome bulk component limitations. Whilecommercial implementations of PICs exist in a variety of material platforms,the most desirable is arguably silicon-on-insulator (SOI), for which majorbenefits include mature electronic integrated circuitry, and widely availableelectronic and photonic integrated circuit foundries [111, 122].All of the above strongly motivates the investigation of silicon-on-insulator based photonic circuit chips as a platform for realizing a manu-facturable photon-based quantum information processor. The linear-opticalquantum information processing (LOQIP) architecture alluded to above re-quires “only” high-quality single photon sources, single photon detectors,and linear optical components (such as beam splitters and phase shifters)[110, 114, 115]. High-quality, miniature linear optical components and singlephoton detectors have been demonstrated in the SOI material system; and3while further improvements in these components are still required, the mainchallenge at the moment is the realization of a high-quality single photonsource that is compatible with the SOI platform that typically functions bestat C-band telecommunication wavelengths around 1.55 µm [9, 198, 199].The development of single photon sources compatible with SOI signifi-cantly lags that of state-of-the-art sources realized in III-V semiconductorPICs [36, 208]. These successful sources in III-V platforms are based onpost-processing epitaxially-grown wafers in which high-quality single photonemitters composed of a relatively small direct band gap III-V semiconductor(e.g. InAs) “quantum dot” naturally grown in well-defined atomic planesof a distinct host III-V semiconductor (e.g. GaAs) [36] with a relativelylarge band gap. While silicon-germanium quantum dots can be epitaxiallygrown in a similar manner in chemical beam epitaxy (CBE) growth systems,their optical emission properties have yet to meet the standard attained bytheir III-V counterparts, at least in part due to the indirect band gap ofsilicon-germanium.The realization of integrated, on-demand single photon sources in theSOI platform with performance comparable to those realized in III-V PICstherefore currently relies on a fundamentally different strategy. First, ahigh-quality single photon emitter near 1.55µm must be synthesized inde-pendently of the SOI wafer production, and then a process must be devel-oped to controllably and judiciously position a single such emitter upon aphotonic circuit fabricated in the SOI, so as to efficiently couple the sin-gle photon emission into a low-loss waveguide to allow photon transport toother places on the photonic chip. Importantly, the process for selectivelylocating the single photon emitter in the silicon photonic circuit using thishybrid approach must preserve the high optical quality of the emitter.As explained below, some progress in this regard had been made bothwithin the Young group and elsewhere prior to the research described in thisthesis. The new experimental and modeling results obtained by the authorand described in this dissertation demonstrated for the first time that excitonemission from incoherently-excited colloidal PbSe nanocrystals with diame-ters ∼ 5 nm can be coupled to single mode silicon waveguides in commercial4SOI wafers. However, the efficiency of this process is currently so low thatit has not been possible to experimentally demonstrate single-photon emis-sion behavior. The remainder of the dissertation describes research doneto understand what physical phenomena are limiting the current couplingefficiency. This work serves to inform a final assessment as to the futureprospects for using this approach to realize single photon sources in a siliconplatform.The remainder of this chapter is intended to (i) motivate the desireto develop tools required to manipulate the quantum state of photons forquantum information processing purposes (Section 1.2), (ii) explain the ba-sic principles behind the approach adopted in this dissertation for hybridlyintegrating PbSe nanocrystals with planar photonic crystal microcavitiesand waveguides in silicon-on-insulator wafers, to act as a single photonsource (Section 1.3), and (iii) provide background information regarding theelectronic structure of PbSe nanocrystals and the electrodynamic principlesupon which the photonic crystal microcavities are designed (Section 1.4).The presentation presumes the reader is knowledgeable in general graduate-level physics. Following this introductory material is a more concise state-ment of the dissertation aim, and organization (Section 1.5). Sections andsubsections especially relevant to understanding the methodology includeSingle photon sources for LOQIP in the SOI platform 1.3.4, Hybrid ap-proaches to SOI platform single photon sources 1.3.5, and Lead-Based (PbX)Colloidal Quantum Dots (CQDs) for Single Photon Sources in SOI LOQIP1.4.1.2 Quantum information processing (QIP)This section reviews some basic elements of general quantum informationprocessing (QIP), and the linear optical approach to QIP (LOQIP) in orderto motivate the need to integrate single photon sources (and in particularon-demand single photon sources) in the silicon-on-insulator (SOI) platform.51.2.1 QIP overviewQuantum technologies refer to those that fundamentally rely on controllingthe quantum state of a physical system. The performance of certain classesof devices that do not make explicit use of quantum physics have alreadybeen surpassed by the performance of devices that do, e.g. SQUID-basedmagnetometers [98] or squeezed-state interferometers [5, 42]. Informationprocessing technologies, such as numerical simulation, computation, andcommunication, have an enormous impact on society, and in the early tomid 1980’s the idea of making explicit use of quantum physics to enhanceinformation processing was put forth by Feynman and others [60, 71, 136].Quantum information processing (QIP) involves initializing the state ofa collection of quantum mechanical objects and then manipulating the quan-tum mechanical properties of those objects to communicate or extract infor-mation, or to solve computational problems. Benefits of existing and pro-posed QIP applications include increased communication security [22, 65],improved metrology precision [114], increased simulation speed of many-body quantum systems [4, 71, 129], and increased computational speed [60]for important and difficult mathematical problems (e.g. integer factoring[196], database searching [83], and expectation values [88]).1.2.2 Bits and qubitsInformation processing protocols generally encode information in a collectionof bins. In the vast majority of digital classical information processors eachbin contains one bit, of information, that can take on one of two distinct(Boolean) values (e.g. 1 and 0). In contrast, information in QIP is typicallyencoded into quantum mechanical entities denoted qubits, which are thequantum states of a two-dimensional Hilbert space, as depicted in Figure 1.1.Correspondingly, any two level system (TLS) maps onto a qubit. Qubitsmay be represented by a complex linear superposition of two orthogonalbasis vectors. In the Bloch sphere parametrization, a pure qubit state isrepresented by a vector of unit length that can point in any angular direction(θ,φ).6Figure 1.1: Bits and qubits. Bits take on one of two values, e.g. 1or 0. Qubits may be represented by a complex linear super-position of two orthogonal basis vectors. In the Bloch sphereparametrization, a pure qubit state is represented by a vectorof unit length and of angular direction (θ,φ), such that unitaryoperations upon the qubit rotate the vector to some other otherdirection. Bit measurement is commonly deterministic, whereasqubit measurement is generally probabilistic.The state of any N -bit system may be represented by a simple tensorproduct of bit values, e.g. expressed as a string of integers: b1b2b3...bN .The simplest state for an N -qubit system, often the initial state for a QIPprocedure, is similar, and consists of a tensor product of qubit states, i.e.|q1〉|q2〉|q3〉...|qN 〉, where each state is some superposition of an eigenstatebasis, |qn〉 = an|0n〉+ bn|1n〉. QIP functionality however requires entangle-ment of at least some qubits [19, 60], e.g. as found in the two-qubit entangled7state |01〉|02〉+ |11〉|12〉, which cannot be factored into a simple tensor prod-uct |q1〉|q2〉 of the two individual qubits. A general form for the state of aN -qubit system may be written as the sum over all tensor products of qubiteigenstates:|Ψ〉=∑{j1,...jN}i∈{b1,...bN}α{j1,...jN}i |j1〉|j2〉...|jN 〉 (1.1)where {b1, ...bN} represents all length-N sequences of binary numbers bn.1.2.3 Classical and quantum logic gatesUniversal classical information processing requires (a) bit value initializa-tion, (b) bit value manipulation and comparison, and (c) resultant bit valuereadout. These components and operations may be arranged in a circuit,as exemplified in Figure 1.2. Bit state information is physically transportedalong classical channels (typically wires) and manipulation and comparisonis done by application of bit logic gates that typically change the output bitstate given a stable set of input bit states, when triggered by a clock pulse.The new output state typically becomes (one of) the stable input states fora downline gate that operates on it upon the arrival of the subsequent clockpulse. A set of logic gates which any algorithm may be built up from isdeemed universal and may, for example, consist of NOT and AND gates,also shown in Figure 1.2.Analogously, universal QIP requires (a) qubit state initialization, (b)qubit state manipulation and comparison, and (c) resultant qubit state(s)measurement. In the quantum circuit model of QIP, clock pulses still initiategate operations on stable input qubit states, however the physical “flow”of state information can take a variety of forms, as elaborated on below.Quantum logic gates perform unitary operations upon quantum states. Auniversal set of quantum logic gates for information processing withN qubitsmust be capable of implementing an arbitrary unitary operator defined overthe state space of all N qubits. A particularly simple-to-understand set ofuniversal gates consists of a subset that can arbitrarily rotate each individual8Figure 1.2: Example classical logic circuit and logic gates NOT, AND,and XOR. Any algorithm may be encoded in a circuit con-structed of suitable arrangement of a universal (functionallycomplete) set of logic gates, e.g. of the gate set consisting ofthe NOT gate and AND gate.qubit on its Bloch sphere, along with a collection of CNOT gates that canentangle any pair of qubit states, as exemplified in Figure 1.3.It is important to note the difference between quantum and classicalcircuit diagrams. In classical circuit diagrams as in Figure 1.2, the linestypically represent physical wires, the voltage of which represents the bitstate at the input or output of the gates. Cascaded gates are physicallycascaded as shown, and the information effectively flows, or is processedfrom left to right by one gate “length” during each clock pulse. Hence thehorizontal axis also corresponds in some sense to time.Quantum circuit diagrams can represent quite distinct physical situa-9Figure 1.3: Example universal set of quantum gates consisting ofthree single qubit rotation gates and one two-qubit CNOT gate,with circuit symbols, depictions, and representations. Singlequbit gates include rotations about each of the Bloch sphereaxes, generated by the Pauli matrices X, Y , and Z. The twoqubit CNOT gate flips the target qubit |qt〉 if and only if the con-trol qubit |qc〉 is |1〉. Any multi-qubit state may be constructedwith these gates.tions, depending on the implementation. For instance, if the qubits arediscrete two level systems, e.g. based on states of nuclear spin, electronspin or number, atomic spin, or Josephson junctions at two distinct physi-cal locations, then the horizontal axis of the gate circuits in Figure 1.3 canreally only be interpreted as time, as the input and output lines representthe same physical qubit [61, 121, 126, 149]. Such an implementation couldbe based entirely on these so called “stationary qubits”. As explained below,when individual photons are instead used to encode the qubit state, thereis usually propagation involved, in which case they are referred to as “flyingqubits”, and then the circuit diagrams can, at least in some cases, be inter-preted more like classical circuit diagrams, with the input and output lines10to gates representing distinct optical channels (optical fiber, waveguides, orlocations in free-space) [107].Common challenges for both stationary and flying qubits include (a)preservation of qubit coherence during transport or gate operations, (b)achieving sufficient qubit interaction in multi-qubit gates, and (c) achiev-ing adequate state preparation and measurement efficiencies. Scaling up tomany-qubit systems is a major challenge that motivates implementationswithin which components may be fabricated scalably. We now provide aconcrete example of a useful quantum information process, quantum tele-portation, to help tie together these theoretical foundations and practicalchallenges, and thus to motivate the integrated photonic circuit approach.1.2.4 Quantum teleportation: an exampleConsider how a qubit state |ψ1〉 initialized at location A, can be transferredto a second qubit at a remote location B, using four single gate operationsand two CNOT gate operations, along with two classical measurements.This is an essential process used in, for example, quantum cryptographicapplications.Figure 1.4: Quantum teleportation circuit. See Figure 1.3 for quan-tum gate definitions. Single lines are quantum channels anddouble lines are classical channels. A quantum state is trans-ported from location A to location B using two classical infor-mation channels and one quantum channel.11Shown in Figure 1.4, the state |ψ1〉 is first entangled with a maximallyentangled Bell State (e.g. (|1〉|1〉+ |0〉|0〉)/√2) and two measurements (pro-jections) are made on the resulting entangled state and the Hadamard-transformed (Rπ/2y Rπ/2z , see Figure 1.3 for symbol definitions) initial state|ψ1〉, all at location A. The maximally entangled Bell State is produced atlocation A using two identically prepared qubits |ψ2〉 and |ψ3〉, as inputs to aHadamard/CNOT gate sequence. The results of the measurements are thentransported classically, along with the Hadamard (Rπ/2y Rπ/2z ) transform of(|ψ3〉) to location B, where a rotation of the received qubit is performed,conditional on the classical results of the measurements done at location A.Ideally this results in |ψ4〉= |ψ1〉; teleportation.This teleportation scheme can in principle be realized using a variety ofstationary implementations of the initial and final qubit states, but in orderto operate between remote locations A and B, at least the rotated version of|ψ3〉 must be encoded in a flying qubit, as only photons thus far have beenproven capable of carrying quantum information over long (e.g. exceeding100 m) distances. The entire system may be based on flying qubits, too.1.2.5 Linear optical quantum information processing(LOQIP)The teleportation application is one of many QIP functions that may bene-fit from the unique qualities of photonic-based qubits, e.g. exemplary long-distance qubit transport, or making use of scalable, photonic integratedcircuits (PICs) [134, 155, 168, 212]. A persistent challenge however is thatvirtually all of these more general applications require a deterministic pho-tonic entanglement gate, commonly a deterministic photonic CNOT gate,true realization of which has seen many theoretical proposals [147, 149], butnot yet been experimentally realized. This is largely due to the requirementthat single photons must be able to nonlinearly interact via some materialmedium, which in turn requires very strong light-matter coupling.Although much experimental progress is being made in this direction[216], most of the experimental optical QIP community has focused insteadon demonstrating probabilistic CNOT gate operation, which can be achieved12using only linear optical components [35, 40, 95, 110, 114, 115, 170]. Thisline of research followed a seminal paper by Knill, Laflamme, and Milburnscheme [110] which theoretically demonstrated that universal QIP can inprinciple be achieved using only single photon sources, single photon detec-tors, linear optical components (phase shifters such as waveplates, and beamsplitters), and classical electronics.1The remainder of this subsection reviews the basics of LOQIP, with anemphasis on realization of an ideal on-demand single photon source, as perthe dissertation aim.Quantum gatesThe single photon detectors, beam splitters, and waveplates called for inLOQIP are readily available in high quality in the visible portion of thespectrum, so most of the experimental work on LOQIP has been done withbulk optical components in the visible. The following briefly explains howthe single qubit operations and probabilistic CNOT gate can be implementedusing path-encoded qubits generated by single photon sources, together withbeam splitters and single photon detectors.In bulk optical setups, flying qubits have commonly been encoded into abasis set consisting of orthogonal polarization states of photons, e.g. “hori-zontal” and “vertical”, as depicted in Figure 1.5B, and a single polarizationqubit may propagate along a single optical path. Qubit basis states neednot only be polarization encoded, but may also correspond to absence/pres-ence of photons within a pair of mutually exclusive optical paths, i.e. thedual rail path encoding, as depicted in Figure 1.5A. Transformation to apath encoding from a polarization encoding may be achieved with a polar-ization beam splitter, as shown in Figure 1.5D, and admits integration ofoptical components in ways not available to photons propagating along asingle optical path. Further, path encoding is particularly useful for inte-1Linear optical QIP in computational contexts is often referred to as linear optical quan-tum computing (LOQC), and in this dissertation we use the term linear optical quantuminformation processing (LOQIP) to include LOQC and other QIP tasks executable usinglinear optical methods.13Figure 1.5: (A): General dual rail optical qubit basis states consistof single photon absence/presence in one of two optical modes.(B) and (C): Free-space polarization encoded photonic qubitsthat exemplify dual rail qubits, and (D): mechanism to convertpolarization encoded qubits to path encoded qubits.grated optical environments for which polarization control and manipulationis challenging.The phase shifter and beam splitter components in Figure 1.6 illustratehow the two required single qubit rotation gates have been implementedin the case of the path encoding of the photonic qubits. The full SU(2)symmetry group may be generated by beam splitters alone [39], and Fig-ure 1.6 illustrates a configuration of beam splitters that transforms the input14path-encoded qubit proportional to Rαy . The rotation angle relates to theclassical electric field intensity reflectivity η by cos(θ/2)2 = η. Phase shiftersare proportional to Rαz . These two operations are sufficient to generate allsingle qubit states (Rαx =Rπ/2z R(−α)y R(−π/2)z may be formed from them).Figure 1.6: Universal LOQIP quantum gates, constructed from (A)phase shifters, (B) beam splitters, and photon detectors, forpath encoded optical qubits. Rotation angles θ and φ mapdirectly onto the Bloch sphere. (C): CNOT gate success, i.e.|ψtarget,out〉 equaling |ψcontrol,in⊕ψtarget,in〉, coincides with pho-ton detection in the output ancillary modes |aancillary,out〉 and|bancillary,out〉.The final gate in Figure 1.6 exemplifies how a probabilistic CNOT gatecan be implemented using a collection of beam splitters and single photonstate inputs [177]. Beam splitters are asymmetric and induce a sign changeupon reflection off the top for the top two beam splitters (BS2, BS3) and15upon the bottom for the bottom four beam splitters (BS1, BS3, BS4, BS5).Consider special case operations: first, where the upper path of the inputcontrol qubit is occupied by a photon (and the lower control path is not)the target qubit passes through a symmetric combination of beam splittersand exits as it enters (|Ψtarget,in〉= |Ψtarget,out〉) for the cases where an inputtarget photon does not exit the target qubit transmits into either the lowercontrol target path or lower ancillary path, and the input control photonexits via the top ancillary path 1/3 of the time. If instead the lower pathof the control qubit is occupied by a photon, this photon interferes withthe target state and it can be shown that the target qubit is flipped, i.e. aphoton in the upper input target path exits the lower exit target path andvice versa, assuming the target photon does not exit to the lower ancillarypath. Thus, the CNOT operation is performed in cases where control ortarget photons do not exit the target and control paths. In cases where aphoton is measured in both a target exit path and control exit path, the gateis successful (behaves according to standard CNOT gate operation) and thishappens 1/9 of the time.The operation described above assumes that at some moment when theCNOT operation is assumed to take place, four distinct single photon states(here, dual rail encoded) are present at the input. The reliance on inter-ference at the beam splitters within the CNOT gate requires precise timingof the input states and that the input photons are indistinguishable. Akey experiment that quantifies the ability of the photon sources to interfere,and thus quantum photonic gates to be realized, is the Hong-Ou-Mandel(HOM) effect [92], which measures the extent to which emitted photons candestructively interfere upon recombination at a beam splitter.A basic HOM setup is illustrated in Figure 1.7, wherein the coincidencesof photons transmitted through the two beam splitter outputs are moni-tored as a function of relative optical path length between the beam splitterand the detectors. How low the detected coincidence rate can be - i.e. seenby a “dip” in the coincidence curve for zero path length difference - indi-cates how well photons from the two paths can interfere. Photons that aretruly indistinguishable will destructively interfere perfectly at an ideal beam16Figure 1.7: Hong-Ou-Mandel (HOM) effect measurement setup, with“HOM dip” in photon detection event coincidences. A dip tozero coincidences (for zero path length difference from the beamsplitter to each detector, controlled by a variable delay) is evi-dence of photon interference of the two photon sources and indi-cation of the photon sources emitting photons indistinguishablefrom each other.splitter when simultaneously incident upon the beam splitter, such that themeasured coincidence rate can dip to zero (e.g both photons have to exitthe beam splitter together, with equal probability in ether direction).Adequate photon interference places demands on the single photonsources, now discussed.Photon sourcesBulk optical QIP demonstrations have typically relied on either (i) stronglyattenuated laser beams [64, 80], (ii) entangled photon pairs generated at fre-quencies ω1 and ω2 via parametric down-conversion of photons at frequencyω3 = ω1+ω2 in nonlinear optical crystals possessing large second order non-linear coefficients χ(2) [64, 80, 120, 148], or (iii) trapped ions, molecules, oratoms [50, 108, 119].None of these sources are ideal. Trapped atom and ion sources typicallyrequire large, complicated setups that have not yet yielded competitive singlephoton sources given the relative ease of implementing laser or down con-17version sources. Nonetheless, they have remained an important source ofvery high quality, indistinguishable photons for which state-of-the-art quan-tum optical experiments have been performed for decades. For both lasersand parametric down-conversion sources, suppression of unwanted photoncoincidences to levels low enough for QIP demonstrations comes at the ex-pense of suppressing the desired photon generation rate. These low ratesresult in impractically long experimental integration times, especially whencompounded with probabilistic gates (such as the CNOT gate above).Entangled photon pair sources based on parametric down-conversion seewidest use of these aforementioned source types, offering the highest singlephoton generation rates for adequately low accidental coincidences, the lat-ter property enabled by gated operation in the heralded scheme in whicharrival of one of the photons, say at ω1, is “heralded” by the detection ofits partner at ω2. Although the source rate of these entangled photon pairsources has improved to the MHz range [36, 148, 169] and exceeds the ratesof attenuated laser sources for equivalent accidental coincidence rates, theprobabilistic nature of the photon arrival time from such sources severelylimits the overall throughput of any quantum logic operation, such as theCNOT gate.For example, successful operation of teleportation and CNOT gates withheralded sources requires waiting for the output of multiple identical photonsources to coincide temporally at the CNOT gate or teleportation circuit in-puts, which degrades both the latency and throughput of QIP algorithmimplementations [36, 64], and practically prohibits - via long experimentalintegration times - algorithm implementation for even a handful of indepen-dent photon input states. For example, state-of-the art LOQIP experimentsusing heralded sources report 4-mode photonic state generation at a rate of20 Hz for a photon coincidence rate of each heralded source equal to 160KHz [139].Thus, despite the current popularity of heralded photon sources, scalingup QIP algorithms to significantly more qubits - as is needed for manyproposed QIP benefits - requires overcoming the indeterministic timing oftheir photon output by replacing them with on-demand photon sources in18which photon output is fixed relative to trigger pulses; in particular, anideal on-demand single photon source will emit exactly one photon a certainamount of time (no jitter) for each and every trigger pulse applied, and doso with high emission rate. A variety of systems have been actively pursuedto produce high-quality, truly on-demand single photon sources, includingsemiconductor quantum dots embedded in a variety of micro cavities ornano-pillar dielectric environments, and crystal defects (e.g. NV centers indiamond) that are efficiently coupled into optical fibers. Indistinguishabilityas high as 60% for independent on-demand photon sources has been observed[163], suggesting promise for high quality beyond already established highemission rates in the GHz range.Availability of single photon source quality is one major factor consid-ered in implementation of a LOQIP experiment, but not the only one. Wenow review LOQIP in the silicon-on-insulator (SOI) platform, for which sin-gle photon source development is the major challenge but the platform ispursued for otherwise providing major LOQIP benefits.1.3 LOQIP in the SOI platformThis section describes many of the components and processes involved inrealizing LOQIP in the silicon-on-insulator (SOI) platform, and as suchprovides important context and background information specific to the aimsof this dissertation.1.3.1 OverviewOne of the most significant drivers for photonic-based QIP is its potentialscalability (e.g. to incorporate multiple teleportation channels on a singletransceiver chip). The beam splitters and phase shifters and single photondetectors required for LOQIP, as reviewed above, can all be miniaturizedand integrated in planar lightwave circuits fabricated using well-establishedlithographic patterning and chemical etching techniques. Host waveguidematerials include silicon on insulator (SOI) [24], silica-on-silicon [40, 167],III-V semiconductors (e.g. gallium-based) [70, 218], diamond [8, 82, 89],19lithium niobate [15, 99, 202], silicon nitride [225], and silicon carbide [28, 38].The silicon-on-insulator (SOI) platform is pursued in this dissertation,because mature circuits that integrate both passive photonic and electroniccircuitry [109, 204, 208, 237] have already been commercialized in this plat-form after considerable industrial development. This investment in classi-cal integrated photonic circuitry is being leveraged to demonstrate scalableQIP-grade operations [27, 59, 87, 198] operating in the C-band (around 1.55µm wavelengths), which takes advantage of the massive telecommunicationsinfrastructure [104, 117, 232] in place worldwide. The following describesthe principles and techniques used in this thesis towards integrating an on-demand single photon source in the SOI platform, starting with an overviewof SOI-based photonic circuitry.1.3.2 Linear optical componentsPlatform and circuit overviewOptical modes in the SOI platform suitable for scalable transport, manip-ulation, and interaction of photons, may be constructed through a CMOS-compatible lithographic process, and reside primarily within a few-hundrednm silicon device layer, depicted in Figure 1.8A. Due to strong total internalreflection at the silicon-air, and silicon-oxide interfaces (i.e. only light propa-gating almost normal to the interface can escape the thin silicon layer), lightcoupled into the top silicon “device layer” is robustly confined to propagatelong distances within the plane of the wafer; this confinement mechanism isdepicted in Figure 1.9A. The light can be further routed and manipulatedby defining patterns that are etched into, typically completely through, thesilicon device layer. The method for patterning these in-plane waveguidesand waveguide devices is illustrated in Figure 1.8B. An example LOQIP PIClayout, as would be fabricated on a SOI wafer, is depicted in Figure 1.8C.20Figure 1.8: The SOI platform, for LOQIP. (A): Typical silicon-on-insulator (SOI) dimensions used for SOI-based photonic inte-grated circuits and (B) example etching steps. Additional func-tionality may be achieved by lithographic integration of metalcontacts, ion doping, and deposition of other materials. (C):Example LOQIP circuit layout and depicted embedment in anSOI wafer.Integrated waveguides, beam splitters, and phase shiftersWaveguides, e.g. ridge waveguides depicted in Figure 1.9B through D, fulfillthe role of quantum channels. As is the case for guidance of light in the de-vice slab, light is confined to within a ridge waveguide by internal reflection.Figure 1.9B depicts a silicon ridge waveguide superimposed a silicon-oxidelayer and surrounded by air (or vacuum), and Figure 1.9C exemplifies a crosssection with mode profile, for ridge waveguides small enough to support just21the fundamental waveguide mode (i.e. single antinode near the center of thewaveguide), of dimensions in the vicinity of 500 nm in height and width. Apair of parallel waveguides constitutes a dual rail qubit.Figure 1.9: (A): Total internal reflection at silicon-air and silicon-oxide interfaces. (B) and (C): Ridge waveguide that utilizestotal internal reflection to contain light within the waveguide.(C): Example electric field mode profile, showing non-zero fieldbeyond the silicon. (D): Ridge waveguide beam splitter, labeledwith a characteristic bending radius (typically around 10 µmfor these materials) that limits the minimum size in accordancewith the total internal reflection angles described in (A). Beamsplitters admit Rαy single qubit rotations and, along with singlephoton detectors, may be used to realize a CNOT gate.The evanescent portion of the field profile extending beyond the higher22index core of the waveguide admits waveguide-waveguide coupling, exem-plary of frustrated internal reflection. This coupling constitutes the under-lying mechanism of beam splitters, illustrated in Figure 1.9D. Because thephoton amplitude distribution over the two waveguides may be altered byphoton transfer between the waveguides, a beam splitter effectively rotatesa dual rail photonic qubit with the Bloch rotation angle θ tied to waveguide-waveguide distance, abutting length, and shape.Figure 1.10: Example phase shifter, capable of producing single qubitrotations Rφz . A small current passing through a metallic strip,connected to the control electronic microcircuitry, may locallyheat and change the index of refraction, thus the relative opti-cal path length (note that the metallic strip is not necessarilyin contact with the waveguide, but more likely embedded in alayer above or below it).Beyond quantum channels and beam splitters, a phase shifter for a dualrail qubit may be realized when one ridge waveguide out of a pair possessesa different optical path length - e.g. via index of refraction - than the otherwaveguide. One low loss way to do this is thermally [87], e.g. by applicationof an electrical current, as shown schematically in Figure 1.10. The differencein optical path length for photons traveling along different paths in the phaseshifter results in differing amounts of accumulated phase, without changingthe relative amplitude of the photon in either path, effectively rotating aqubit state about an eigenstate axis by some angle φ. Beam splitters andphase shifters have both been realized, often in tandem, in the SOI platform[26, 27, 198, 199]. These linear optical components may be combined with23single photon detectors to realize conditional qubit gates, e.g. the LOQIPCNOT gate in Figure 1.6C.Photonic band gaps: tighter confinement and improvedfunctionalityAlthough total internal reflection in this high index contrast environmentenables on-chip optical components much smaller than bulk counterparts,a second photon confinement mechanism, based on “photonic band gap”materials, allows for even further miniaturization, and importantly enableskey functionalities not feasible using only ridge waveguides. As elaboratedon below, efficient generation and detection of single photons in silicon pho-tonic circuits depends on their effective interaction strength with electronsin quantum emitters or superconducting wires that are placed in proximityto the silicon device layer where the photons propagate. This effective inter-action strength can be enhanced by engineering the dielectric environmentso that the photons are tightly localized in the vicinity of the emitter/ab-sorber, and localized for many optical cycles. Photonic crystals offer thebest means of achieving these objectives.In 1987, Yablonovich and John independently described a means of arti-ficially creating a band of frequencies within which there are no propagatingsolutions to the Maxwell equations [100, 228]. Even in non-absorbing ma-terial, if a 3-dimensional (3D) periodic texture with appropriate symmetryis imposed with sufficiently high refractive index contrast, it is possible toprevent photon propagation within a continuous range of frequencies, in anydirection, with any polarization, analogous to the periodic electronic poten-tial in an electronic crystal giving rise to electronic band gaps. The resulting“photonic band gap” is centered at a wavelength on the order of the pitch ofthe texture (taking account of the average refractive index of the medium).Figure 1.11A through C, illustrates how a 2-dimensional (2D) photonicband gap material can be realized in the SOI slab waveguide geometry toeffect a quasi photonic band gap for slab modes propagating in the devicesilicon layer. The dielectric contrast is sufficiently high (∼ 3.4 to 1) whenetching holes through the silicon layer, to create relatively large (∼ 10%24Figure 1.11: Photonic band gap confinement mechanism used in SOIphotonic circuits. (A): Slab hexagonal lattice photonic crystal.(B): Definitions of TE and TM propagating modes. (C): Ex-ample photonic band structure for slab photonic crystal similarto the one depicted in (A).to 15% of the center frequency) ranges of frequency where 2D waveguidemodes of TE polarization cannot propagate. Although technically there isno complete photonic band gap in this frequency range, because TM (seeTM and TE definitions in Figure 1.11B) polarized slab modes and near-normally incident waves that aren’t localized to the silicon device layer canstill propagate in it at these frequencies, by limiting operation to the TE25polarization, these 2D photonic crystals are very effective at reflecting slabmodes propagating in any in-plane direction.Figure 1.12: Photonic crystal structures. (A): Photonic crystalwaveguide, consisting of a line defect in a slab photonic crystal,joined with a ridge waveguide. (B): Photonic crystal cavity,consisting of a point defect in a slab photonic crystal, accompa-nied by a sketch of the local photonic density of states (ρDOS)as a function of embedded emitter frequency ω at the cavitycenter. Slab photonic crystals may consist of a regular patternof air holes which, for the cases of photonic crystal waveguidesand cavities, are omitted (i.e. not made) along a line or local-ized region during patterning of the remainder of the structure.Thus instead of using TIR to guide light in 1-dimensional (1D) ridgewaveguides, it is possible to use photonic crystal (PhC) regions to confinelight to propagate in a 1D channel, as depicted in Figure 1.12A. Right anglebends in such waveguides can be designed to be almost lossless, yieldingan effective bending radius of less than 1 µm. The photonic crystal defectfeature can in turn be used to localize light in 3D to volumes of a fractionof a cubic vacuum wavelength by simply leaving out one or more holes inthe photonic crystal, as shown in Figure 1.12B. These 3D photonic crystalmicrocavities can have quality factors (roughly how many optical cyclestrapped light remains in the cavity) easily in the range of 105 [159, 203]. Thisoffers a means of dramatically increasing the effective interaction strength26of light and electronic media that might be placed in the microcavity.As shown in Figure 1.11C, there is a range of the folded-zone bandstructure diagram where the continuum of radiation modes overlaps withthe confined mode dispersion (i.e. above the light cone in the surroundingmedium (air or SiO2). The bound modes associated with the 1D waveguidesand 3D microcavities discussed above are all formed from states lying belowthe light cone, which do not couple out of the plane. However in applicationsrequiring long-distance transport of photons, e.g. through free space or inoptical fibers over meter to kilometer distances much larger than the SOIchip, photons from in a ridge or photonic crystal waveguide need to bedirected off-chip. This can be accomplished by utilizing modes near thecenter of the Brillouin zone that do intrinsically couple to radiation modes(they diffract out of the device layer as they propagate).An example configuration enabling this is depicted in Figure 1.13, inwhich a photonic crystal waveguide couples to a ridge waveguide, then aparabolic tapered waveguide terminating in a diffraction grating. Photoniccrystal pitch, hole size, ridge waveguide width, and grating coupler pitch areall quantities that must be engineered in unison for efficient transmission oflight; see, for example, work from our lab in references [17, 188, 189]. Alens may collect light from the grating (as will be seen in Chapter 4) or anoptical fiber may be bonded to or near it.Single photon detectors and single photon sources for LOQIP in SOIPICs are now reviewed, exemplifying the important role of photonic bandgap confinement in these contexts.1.3.3 Single photon detectorsIdeal single photon detectors possess unity efficiency (one detection pulseout per one input photon), zero dark counts (no spurious detection pulses),and zero recovery time (ready for photon detection immediately after detect-ing a photon) [84]. As silicon is non-absorbing in the C-band, other typesof materials need to be integrated on the chips to realize efficient photondetection. Germanium (Ge), or a silicon-germanium compound (SixGe1−x)27Figure 1.13: (A): Waveguides terminating in a diffraction grating,the latter for free-space/on-chip light conversion. (B): Partialband structure diagram for the photonic crystal with photoniccrystal waveguide bands (green). Guided (slab-like) modes inred and blue. Modes within the light cone are not confined tothe device silicon. A bound state such as a photonic crystalcavity (not shown in this diagram) would also lie within theTE band gap. The in-slab amplitude of propagating waveguidemodes (below the light line) decays exponentially in the grat-ing region (i.e. is non-propagating and above the light line) asthe field is diffracted out of the device slab.can be epitaxially incorporated in the device silicon layer, and are com-patible with CMOS foundries. While conventional photodiodes for classicaltelecommunications have been successfully developed using this material,attempts to fabricate high quality avalanche photodiodes capable of single-photon detection have been plagued by excess noise.Arguably the most successful stand-alone infrared single photon detec-tors are based on superconducting nanowires, exemplified in Figure 1.14.Recently the Young lab has successfully integrated a short NbTiN nanowireon 1-dimensional photonic crystal microcavity etched in an otherwise siliconridge waveguide and demonstrated near unity quantum efficiency for con-verting a single waveguide-bound incident photon into an electronic “click”28Figure 1.14: Example integrated detectors, in which photodetectivematerial is placed atop waveguide within waveguide mode.(A): perspective view of detecting material atop waveguide,with connected electrical wires. (B): head-on view, overlayedwith waveguide profile. Size of photodetective material in (A)and (B) is slightly exaggerated for drawing purposes. (C): Re-alized integrated, superconducting single photon detector fromthe Young lab [9].triggered by the resistance change across the superconducting wire when theenergy absorbed from the photon causes it to go normal. The device wasmade ultra-compact, as illustrated in [9], by routing the 8 nm by 35 nmarea superconducting nanowire through the center of a 1D photonic crystal-defined microcavity, shown in Figure 1.14C. This compactness admitted thesmall microcavity mode volume required for enhanced interaction betweena microcavity photon and the detecting nanowire, in turn admitting highphoton detection probability. The back PhC mirror is essentially 100% re-flecting, and the front PhC mirror’s reflectivity is designed to exactly matchthe absorption rate of a cavity photon by the nanowire, which maximizes29the absorption rate of waveguide-bound photons. The near unity quantumefficiency and sub Hz intrinsic dark count rate of these detectors when op-erated at 2 K means that high fidelity quantum optical experiments canalready be carried out with them [9, 146, 165, 205].1.3.4 Single photon sourcesThis subsection describes the key concepts that underpin the approach andmethodologies used in this dissertation to develop an on-demand single pho-ton source in the SOI platform. The main topics include the microcavityand waveguide photonic elements, the colloidal PbSe quantum dot emitters,with an emphasis on how they optically couple.Basic approachSince both high-quality linear optical components and single photon detec-tors have been demonstrated in the SOI platform, the outstanding imped-iment to SOI LOQIP is the lack of good on-demand single photon sources[72, 144, 208]. The essential elements of an ideal on-demand, fully integratedsource are (i) a bright, efficient quantum emitter that emits one and onlyone photon from a well-defined transition every time it is externally excited,as in Figure 1.15A, and (ii) a dielectric environment surrounding the quan-tum emitter that ensures the photon from the emitter is eventually routedinto a specific silicon ridge waveguide channel with unity efficiency, as inFigure 1.15B. The relevant quantum emitter characteristics are discussed indetail below in Section 1.4.The following subsection concentrates on the dielectric environment re-quired to efficiently couple the excited quantum emitter transition to a quasi-normal mode of the silicon circuit wherein all power is transported away fromthe quantum emitter through a single mode silicon ridge waveguide.Dielectric environment geometriesConsider what might happen if a quantum emitter at frequency ω0 is locatedon top of an isolated silicon ridge waveguide, as shown schematically in30Figure 1.15: (A): Single photon emission from an incoherentlypumped (via state |P 〉) two level system (|G〉,|X〉). (B): Inte-grated single photon source geometry, consisting of a radiativetwo level system embedded in a dielectric environment thatefficiently channels photon emission into a ridge waveguide.Figure 1.16A.The excited state can in general decay into any electromagnetic modethat has non-zero field amplitude and a polarization not perpendicular tothe transition dipole matrix element ~µ of the emitter, at the location of theemitter. The total radiative decay rate is simply related via Fermi’s GoldenRule, i.e. proportional to the amplitude of the transition dipole moment|~µ| and linear in the local density of photonic states ρ: R ∝ |~µ|2ρ. There isalways a continuum of radiation modes (intuitively thought of as plane wavestraveling in various directions at ω0, slightly renormalized in the vicinity ofthe waveguide due to scattering) and, depending on the waveguide geometry,there can also be a continuum of 1D guided modes, traveling in the forwardand backward directions, evanescently penetrating the surrounding cladding31Figure 1.16: Integrated emitter geometries for realization of a singlephoton source. (A): Emitter directly atop a ridge waveguide.(B): Emitter atop a photonic crystal waveguide. (C): Emitterin a waveguide-coupled photonic crystal cavity. Geometry (C)offers the best into-circuit emitter collection efficiency of thesethree geometries owing to the largest collection efficiency bythe cavity, followed by availability of highly efficient transferof cavity photons to the ridge waveguide through the photoniccrystal waveguide.regions. It is relatively easy to design the waveguides in SOI to support onlyone TE and one TM polarized continuum waveguide mode in the C-band,for a waveguide of dimensions around 200 nm tall by 500 nm wide. If thereceiving LOQIP circuit were situated to the right of the emitter, ideally theexcited state of the coupled emitter would decay directly into the rightwardTE polarized 1D bound mode with an overwhelmingly larger probability32than any of the other modes. Sometimes the ratio of coupling strength intothe desired mode, versus all other modes, is denoted by β.It is perhaps not surprising that the β calculated for the simple geometryshown in Figure 1.16A is much less than unity. However, by replacing theridge waveguide by a PC waveguide, terminated at one end, as shown inFigure 1.16B, it is theoretically possible to achieve quite large β factors forcoupling into a TE polarized PC waveguide channel [124, 135]. The expla-nation for this is most easily cast in terms of the various contributions to thetotal local density of states (LDOS) for photon modes at the location of theemitter, which is directly proportional to the imaginary part of the photonGreen’s function characteristic of the dielectric environment (i.e. charac-terizing the impulse electromagnetic response). While there will always besome non-zero contribution from 3D radiation modes (except inside a perfect3D photonic crystal’s band gap), if properly engineered, the combination ofthe 2D photonic crystal and the waveguide channel can concentrate a signif-icant fraction of the free-space radiation modes into the waveguided modeat frequencies near the cutoff of the 1D channel. This is illustrated in theband structure diagram of Figure 1.13B, where owing to the flatness of thedispersion near the Brillouin zone boundary, the LDOS associated with thenear-band edge 1D bound modes can be dramatically enhanced comparedto the contribution from residual radiation modes. Theoretical and exper-imental results in GaAs, using embedded epitaxially-grown InAs quantumdots as quantum emitters, show that this approach can yield β values inexcess of 0.85 [124, 135].Another way to engineer the LDOS is shown schematically in Fig-ure 1.16C, where the emitter is now located at the antinode of a 3D microcav-ity formed by introducing a localized defect (e.g. three missing holes) into auniform PC. The LDOS can be made very large at the cavity mode resonantfrequency, almost ensuring that the excited state emits into the cavity mode[23, 67, 157, 183]. If the cavity mode can in turn be efficiently coupled to asingle mode silicon ridge waveguide with a βwg close to unity (with the sameintent of efficient transfer of a photonic crystal cavity photon to a photoniccrystal waveguide [68, 69, 105, 132, 152, 193, 217]), then the overall system33will constitute a good single photon source [17, 68, 130, 189, 192, 230, 231].The latter system where the emitter is coupled to a cavity, and the cavityis coupled to single mode silicon ridge waveguides, is the approach taken inthis thesis work.Single photon emittersIII-V semiconductor photonic circuit platforms can have similar dielectricprofiles as SOI (refractive index of GaAs or InP and alloys are roughly thesame as silicon in the C-band), and in many regards there have been moreproof-of-principle demonstrations of useful LOQIP functionality in the III-V system than in SOI to date. The main drawback is the relative costand lack of substantial industrial infrastructure for large-scale integrationof both photonic and microelectronic circuits in the III-V platform. Thehuge advantage of the III-V platform is that high-quality quantum emitterscan be relatively easily grown directly in the middle of the device waveguidelayer via the Stranksy-Strazanov strained layer epitaxy technique, resultingin isolated, nanometer scale 3D islands of relatively low electronic band gapmaterial like InAs, surrounded by higher electronic band gap material likeGaAs, wherein the interface between the two is essentially free of electronicdefects. The direct band gap nature of the III-V alloys, together with thisnear ideal interface between the 3D island and the surrounding claddinglayer, means that the quantum yield of the excitonic transition associatedwith these quantum dots can be very high at cryogenic temperatures, andthe associated dipole transition moment is large. By far the best performingon-demand single photon sources to date (coupled to optical fibers, not as yetto integrated circuits) are based on these III-V epitaxial quantum emitters[23, 101, 178, 183, 192, 219], orders of magnitude faster than the commonlyimplemented heralded single photon sources [53, 59, 96, 190].Although it is possible to epitaxially grow SixGe1−x quantum dots insilicon, the dimensions are typically much larger than the III-V islands, anddue to the indirect band gap, the dipole transition moments of the associatedexcitons are relatively weak [127, 128, 224, 226, 227, 233, 234]. Coupling of34single SiGe QDs to high quality photonic crystal cavities has been recentlyreported [233], although the radiative efficiency is still very low comparedto III-V QDs on III-V substrates. The large size of the islands also makesit relatively difficult to isolate a single transition.1.3.5 Hybrid approaches to SOI platform single photonsourcesWhile it is possible to wafer bond III-V substrates containing epitaxial quan-tum dots to SOI, there has been limited success efficiently coupling them towaveguide modes in the silicon. There have also been reports of epitaxiallygrowing III-V materials directly on silicon substrates. The quality of pla-nar III-V material grown in this way is poor, but growth of nanowires fromnanoscale seeds can produce relatively high-quality material. Although thisroute has considerable potential, there are a number of challenges that haveto be overcome in order to site-selectively locate the III-V emitter in a waythat allows efficient coupling to the thin device layer of the SOI.Figure 1.17: Illustrations of semiconductor quantum dots (QDs), (A)epitaxial and (B) colloidal/nanocrystal. QDs are nanometer-scaled semiconductor crystals that quantum confine the other-wise bulk excitonic spectrum, resulting in synthetic two levelsystems and demonstrated single photon emission.An alternative approach, and the one adopted in this thesis work isto develop ways to incorporate colloidal quantum dot (CQD) emitters (seeFigure 1.17B) in SOI-based photonic circuits [31, 73, 164]. These CQDs,described in more detail below, are synthesized in solution [145], and someare demonstrated single photon emitters in the C-band [55]. This disserta-35tion addresses various aspects associated with attempts to incorporate PbX,where X represents either Se or S, CQDs as the single photon emitters inSOI-circuit-based single photon sources. Relevant background informationon PbX CQDs is presented in the following section.1.4 Lead-based (PbX) colloidal quantum dots(CQDs) for single photon sources in SOILOQIPThis section contains crucial background information about PbX CQD pho-tophysics required for interpreting the results of this dissertation work. Abrief overview of basic CQD photophysics is presented, followed by a moredetailed picture of the electronic structure, particularly as it relates to theirintegration into SOI photonic environments.1.4.1 Basic CQD photophysicsGenerally, quantum dots are synthetic structures in which a quantum quasiparticle is confined in three dimensions owing to a 3D local minimum inthe potential energy. Prevalent are colloidal semiconductor quantum dots(CQDs), in which bulk crystalline Wannier excitons, illustrated in Fig-ure 1.18A, are confined to nanocrystals smaller than the excitonic Bohrradius, as in Figure 1.18B. As is well understood, quantum confinementmay tend a near continuum of states - e.g. bulk Wannier exciton states- towards a discrete spectrum, as depicted in Figure 1.18C. The extent ofconfinement is related to the size of the object, and to the strength of theconfining potential, with the latter determined by the bulk material host,and the former being controlled during colloidal synthesis [145].The absorption edge and photoluminescent emission energy are typicallydominated by a ground state excitonic state manifold (more details below),so by controlling the size of the CQD, their optical properties can be var-ied over a wide range of energies, limited by the confining potential. Therelatively large confining potential and the ability to control the size onthe single nanometer scale has led to extensive use of CQDs as biomarkers36Figure 1.18: Confinement of excitons in CQDs, exemplified for PbSesemiconductor. (A): Wannier exciton in bulk PbSe. (B): Col-loidal PbSe quantum dot, capped with organic ligands. CQDsgenerally possess multiple crystallographic facets, not drawnhere. Ligands for CQDs measured in this dissertation are oleicacid, a fatty acid roughly 2 nm long (end to end, including atypical molecular bend) composed primarily of a hydrocarbonchain, which has an orientation with respect to the CQD de-pendent upon the orientation of crystallographic facet to whichit is attached. (C): General effect of quantum confinement onthe electronic density of states ρ(ǫ).[140], in emulsions (also known as CQD solids or thick films) as solar cells[153, 154], in fiber and waveguides as gain media [14, 44], as photodetectors[51, 171], and as emitters for consumer displays and lighting [41, 195]. Mostrelevant to this thesis, if the quantum confinement and confining potentialare substantial compared to the operating temperature, the decay from asingly-occupied ground state manifold of exciton states can be used as thebasis of a single photon source.Figure 1.19A shows a typical absorption and emission spectrum of a so-37Figure 1.19: Example photophysical properties of PbX CQDs withC-band exciton emission. (A): Example absorption and emis-sion spectra of PbSe CQDs in a colloidal suspension. (B):Collection of theoretical and experimental values of first ab-sorption peak energy versus CQD size for PbS CQD, reprintedwith permission from [142] (Copyright 2009 American Chem-ical Society). Unit conversion: 1 eV ↔ 1240 nm, 1550 nm ↔0.8 eV.lution of hexanes containing a concentration of PbSe CQDs with a nominaldiameter of 5 nm. The single peak in absorption, and the lowest peak inemission are usually attributed to the exciton transitions with significantoscillator strength within the ground state manifold. The second peak inthe absorption spectrum (around 1.2 µm), is usually attributed to tran-sitions associated with a second quantized manifold of excitons made upprimarily of conduction band states from the second quantized manifold,and valence band states from the same combination of the first and secondquantized manifolds of valence band states, with recent comparisons of abinitio, anisotropic k ·p band modeling, and comparison to 2-photon absorp-tion spectra suggesting dominance from the second quantized manifold ofvalence band states for PbSe CQDs emitting in the C-band [75, 150]. Therelatively large separation in energy from the ground state manifold (muchlarger than kBT even at room temperature) is characteristic of CQDs, withtheir relatively large confining potential compared to III-V epitaxial QDs:sharp excitonic emission peaks are only observed at cryogenic temperatures38in most III-V epitaxial QD samples.The threshold absorption peak energy follows an inverse relationshipwith CQD size as reliably documented for a variety of semiconductor com-positions, and exemplified for PbS CQDs in Figure 1.19E. Numerically, leadsulfide (PbS) and lead selenide (PbSe) CQDs of diameters around 4-6 nmexhibit emission and first absorption peaks in the C-band of around 0.8eV (compared to bulk band gaps of 0.3 eV for PbSe and 0.4 for PbS [52]),the target emission energy range for SOI photonics (0.8 eV = 1.55 µm)[48, 63, 220, 221].These basic absorption and emission characteristics are sufficient to un-derstand why and how CQDs are deployed in many sensing applications, andto qualitatively understand why CQDs are candidate single-photon emitterscompatible with silicon. A more in-depth consideration of the CQD elec-tronic properties, as provided below, is required to appreciate the more sub-tle processes that turn out to impact in particular the PbSe exciton emissionrate when placed in vacuum, on a silicon surface.1.4.2 Band structure context, CdX CQD comparisonThis subsection describes how discrete excitonic states can be thought of asa superposition of the continuum bulk crystalline electronic states. Corre-spondence between the two sets of states has been best understood in CdXCQDs (where X may be Se, S, Te), for which the vast majority of the exten-sive applications of CQDs referred to above have been based. This is largelybecause the bulk band gap of the corresponding binary semiconductors is inthe range of 1.5 to 2.4 eV, so that CQDs with sizes in the range of a few nmcan have emission/absorption energies tunable through the visible part ofthe spectrum (∼ 1.6 to 3.1 eV). All of the applications have driven a contin-uous improvement in Cd-based CQD radiative efficiency, price, and ease ofsynthesis on the one hand, and a corresponding amount of scientific studyaimed at quantitatively understanding the optical properties of excitons inthese materials. In this subsection, we compare PbX CQDs frequently toCdX CQDs to emphasize where PbX CQD understanding is lacking.39Figure 1.20: Comparison of band and state structures of PbSe andCdSe bulk crystals and quantum-confined nanocrystals. (A)and (B): Bulk band diagrams for PbSe and CdSe, respectively,adapted with permission from [236]. (C) and (D): (left) bulkand quantum confined (right) band edge energy levels, includ-ing electronic and spin degrees of freedom. Bulk energy levelsdo not include splitting due to crystal field or spin orbit cou-pling, but quantum confined levels do, along with splittingsdue to other interactions.40Compare the bulk band structures of CdSe (wurtzite crystal) and PbSe(rock salt crystal), shown in Figure 1.20A and B. Both are direct band gapsemiconductors but the band edge states occur at different locations in theBrillouin zone. At the zone center, CdSe conduction band edge states aretwo-fold degenerate in spin and the valence band edge states are four-folddegenerate (two spin, two electronic), for a total number of 8 excitonic states,while for PbSe there is both a twofold spin degeneracy, and a fourfold valleydegeneracy associated with the 4 equivalent valleys at the L point of theBrillouin zone for each of the conduction and valence edges, resulting in atotal of 64 possible excitonic states. These degeneracies are broken in facetedCQDs when quantum confinement shifts the bulk states up (conduction)and down (valence) in energy. When exchange terms are also included, thendepending on the faceting, the lowest lying conduction and valence bandstates qualitatively shift with respect to their bulk counterparts as shownschematically in Figure 1.20C and D.The spectral width of the absorption and emission peaks is thus con-stituted by a combination of (i) the distribution of CQD sizes in the solu-tion under study (inhomogeneous broadening) (ii) the distribution of groundstate manifold states with significant oscillator strengths, and (iii) the puredephasing (homogeneous broadening) [172] of each of those radiative states.Inhomogeneous line widths for size distributions with several percent of themean diameter are typically on the order of tens of meV over a wide rangeof CQD compositions, and so these typically dominate solution spectra.The spread of ground state manifold states with significant oscillatorstrengths is thought to be 25 meV (i.e. the crystal field) in CdS and CdSe,but as discussed in Chapter 3 below, there is no real agreement for thisdistribution in PbSe or PbS CQDs. Similarly, homogeneous line widthshave been fairly convincingly measured in some CdX CQDs, but there islittle consistency in the relatively few attempts to determine this parameterin PbX materials. The band edge transitions of single CdX CQDs exhibithomogeneous line widths as low as 100 µeV, typical of most epitaxial III-VQDs but not as good as the best-observed, nearly radiative lifetime-limitedline widths of QDs observed at low temperatures (around 1 µeV). Estimates41of the homogeneous line width in PbX CQDs vary from tens of meV [172]to as low as 5 meV [137]. Measurements of homogeneous line widths areoften difficult to interpret, especially when there is a large degeneracy ofstates in the underlying bulk material, so it is probably true that there hasbeen no reliable measurement of the homogeneous line width in PbSe or PbSCQDs: it is probably more likely that some combination of the distributionof ground state manifold states with significant oscillator strength, and theirhomogeneous line widths, are on the order of a few meV.When illuminated by high energy photons well above the renormalizedband gap energy, electrons from a variety of occupied valence band statescan be promoted to empty conduction band states shifted by the incidentphoton energy. The relatively high energy electron and hole states so ex-cited relax rapidly down into the ground state manifold via phonon emissionwithin typically a few picoseconds. Each of these single exciton states in theground state manifold will have a certain oscillator strength (dipole transi-tion moment). Depending upon the sample temperature, the exciton willoccupy some range of states with some Boltzmann-like probability, and thenet probability for its decay will be a statistically weighted average of thedecay rates from each of the available states. In the absence of non-radiativedecay processes, the net radiative decay rate at any given temperature willbe the statistically weighted radiative decay rate determined by the distri-bution of oscillator strengths within the ground state manifold.1.4.3 Non-radiative recombination, defect/surface states,and CQD formulationExcitons in the ground state manifolds discussed in the previous sectioncan decay, or recombine, either radiatively, via the emission of a photon(the desired decay mechanism), or non-radiatively via phonon emission andintermediate “defect states” (parasitic mechanisms). Non-radiative recom-bination processes turn out to play a critical role in interpreting our variousexperimental data. It is challenging to accurately calculate and experimen-tally confirm the energy and oscillator strength distribution of the “intrinsic”ground state manifold of excitonic states, let alone the “defect states”. This42is true even in the relatively well understood CdSe CQDs, and it is sig-nificantly more challenging for PbSe CQDs. The relatively good extent ofagreement between theory and experiment for CdSe CQDs is exemplifiedin reference [200], in which experimental observation of the number of op-tically active transitions, their magnetic field dependence, and nanocrystalanisotropy dependence corroborated long-developed theory of this groundstate excitonic manifold. This agreement between the predicted behavior of“intrinsic” exciton states, and the observed behavior in CdX CQDs is con-sistent with the relatively weak non-radiative decay in these highly-evolvedCQDs. In stark contrast, non-radiative recombination processes are foundto dominate the exciton decay in PbX CQDs integrated into an SOI environ-ment and quantifying this behavior formed a major part of this dissertation.An important contribution to non-radiative processes are surface statesthat bear significantly on CQD emission [10, 16, 21, 97], which is well-established for Cd-based CQDs emissive at visible wavelengths, and be-lieved to carry over in some way to PbX CQDs. These surface states lieenergetically within the band gap and admit additional exciton recombi-nation pathways, including “trap states” that may suppress CQD emissionintermittently (e.g. “blinking”). Whether entirely non-radiative or result-ing in emission of lower energy photons, surface states are deleterious tosingle photon source applications that call for a high efficiency, narrow bandemitter. Alleviation of sensitivity arising from these surface states is largelyachieved by passivating the CQDs with organic ligands such as oleic acid,or with a shell of relatively high band gap inorganics [10, 56, 106]. For PbXCQDs, the role of surface states has been inconsistent, ranging from earlyarguments that they should have little or no bearing on emission [11, 63, 220]to having substantial nanocrystal size and shape dependencies [46, 81].Estimates of in-solution radiative efficiency range from several tens ofpercent to 85% at room temperature [63, 194, 220], with upper estimatescomparable to high quality epitaxial QDs and CdX CQDs. The CQD for-mulation, in this case referring to in solution vs in thick film (as commonlystudied) or in thin film (as closer to a device setting) may affect ligandavailability and thus bear on non-radiative recombination. A lack of lig-43and availability CQDs integrated sparsely into an SOI PIC is suspected tostrongly degrade radiative efficiency relative to CQDs in solution, and thispossible contribution is clarified in the studies in this dissertation.A better known aspect of CQD non-radiative recombination is that (withfew exceptions [43, 93]) integrated photoluminescence at lower temperaturesis larger than at room temperature, indicating thermal activation of thesenon-radiative pathways [7, 172]. Studying the temperature dependent PLcan thus provide an understanding of non-radiative recombination beyondstudies only at one temperature. For example, work in our group prior tothe dissertation work reported here focused on quantitatively explaining thetemperature dependent emission spectra from relatively thick films of PbSeCQDs on silicon substrates [172].When trying to understand and improve on these properties, one ofthe biggest challenges has been in reproducing consistent results, withina research group, from batch to batch, and across research groups. Afterseveral years of effort, the PbX synthesis group who collaborated on thisdissertation work were able to provide quite reproducible batches of PbSeCQDs, which motivated an attempt to comprehensively study their opticalproperties with an emphasis on performance out of solution. Thick film PL(including temperature dependent spectra) provided the most reproducibleout-of-solution data, and it was somewhat reassuring that to the extentpossible with published data, these samples appeared to behave similarly toat least a subset of those reported by other groups [103, 180, 213].Despite excellent agreement between modeling and measurements inour thick film studies, results reported by another group [43, 93] exhib-ited markedly different behavior of thick film temperature-dependent PLand that work highlighted the large impact of air exposure on their results.Although earlier work from our lab characterized air effects at room tem-perature [207], it did not consider air dependent kinetics. To unify thedisparate thick film behavior, with the particular intent to understand thepossible influence of air exposure on our specific CQDs, this dissertationincludes temperature-dependent thick film PL studies of CQDs from thesame source (our collaborators, the van Veggel group at the University of44Victoria) and varied extents of air exposure, along with development andapplication of a general and useful PL kinetics framework in order to un-derstand temperature-dependent non-radiative recombination. As a note ofclarification, studies (e.g. [207]) support oxygen being the dominant influ-ence of air exposure on PbSe CQDs, and correspondingly air and oxygenare often used interchangeably in such literature.1.4.4 Impact of dielectric environment on CQD emission:depolarization and radiative density of statesThe non-radiative recombination, absolute and relative to radiative recom-bination, is tied not just to intrinsic photophysics, but also to the dielec-tric environment. For example, the radiative lifetimes of excitons in bothCdX (of order 10 ns) and PbX (of order 1 µs) CQDs are relatively long,in comparison to their III-V epitaxially-grown counterparts (often 100 psto 1 ns range), attributable in part due to the strong depolarization fieldthat reduces the amplitude of vacuum fluctuations inside the high dielectricconstant CQDs, which are typically surrounded by solvent or vacuum, asopposed to being buried within a high-dielectric bulk III-V host. Slow ex-citon recombination directly impedes photon emission rate and thus singlephoton source performance. This depolarization effect also influences theability to excite CQDs.Beyond depolarization at the CQD-environment interface, determinedby the host dielectric environment, the dielectric environments also bearssignificantly on the photonic modes available for the CQD to radiate into,which in turn affects radiative recombination rates relative to non-radiativerecombination, and thus the radiative efficiency. The choice of cavity pluswaveguide geometry in 1.3.4 represents one aspect of optimizing the dielec-tric environment for improved photon collection efficiency and guidance intoa PIC. Proper accounting of the influence of depolarization and the photonicdensity of states is essential in understanding CQD emission in SOI PICs,and a major portion of this dissertation is dedicated to doing so (specificallyChapter 3).451.4.5 CQD emission on silicon and in SOI PICsAs indicated above, researchers have made considerable progress in under-standing and improving the optical properties of CdX CQDs in particular,and to a lesser degree CQDs based on PbX materials. Much of this progresshas been achieved in solvent environments where the CQDs are synthe-sized, and where their organic passivation layers can thrive. To be usefulas quantum emitters in SOI circuits, the PbX CQDs must function out ofsolution, on or near a silicon surface, in vacuum, or encapsulated with someprotective solid film. Accounting for the influence of environment on CQDemission is a major part of the understanding developed in this dissertation,constituting the majority of the experiment and modeling in Chapters 2and 3, respectively. With many of the key photophysical processes of PbXCQDs reviewed earlier in this section, consider now PbX CQD photophysicsspecifically in SOI PICs and related environments.Prior to PbX CQD integration into SOI photonic circuit components,CQD emission enhancement by a microcavity (Cd-based CQDs at visiblewavelengths) in 2003 [166] and PbS CQD emission enhancement by photoniccrystal microcavities (at 900 nanometers for AlGaAs-host cavities) in 2005[76] were demonstrated. Proposed realization of a C-band single photonsource via integration of PbX CQDs in SOI-host photonic crystal cavities in2005 [30] was followed by C-band PbX CQD emission enhancement by SOIphotonic components primarily photonic crystal cavities) [31, 33, 34, 62, 90,133, 138, 164, 175, 176, 223, 229].A particular concern raised in these studies [175, 223] was potentiallylow radiative efficiency of sub- to few-layer PbX CQDs on substrates, re-ported to be as low as around 1% [125, 185, 206], much less than reportedin solution. A low radiative efficiency, when combined with already slowemission lifetimes and low detection efficiencies in the near infrared (NIR),also increases the challenge to measure CQD emission, impeding studies oftheir properties out of solution [175, 223]. A proposed mechanism for lowradiative efficiency on substrates was poor passivation due to ligand un-availability, and subsequent trapping of exciton population in non-radiative46surface states [185, 206], supported in part by sub-linear power scaling ofCQD emission [175].Prior work in Young’s group [164] advanced previous research by oth-ers [125, 133, 175, 223] on improving understanding of PbX on-substrateradiative efficiency and emission rates into SOI photonic circuits. Noted inthese earlier works was the lack of a consistent relationship between mea-sured CQD PL cavity enhancement (as quantified by the Purcell factor) andthe cavity quality factor [133], a relationship already understood for singleepitaxial QDs in III-V photonic systems [67, 179, 191, 215]. The lack ofconsistency could be attributed to most works indiscriminately coating thesilicon cavities with an ensemble of CQDs, causing indeterminacy in theCQD-cavity coupling. The work from our lab in Reference [164] establishedsite-selectively binding of PbSe nanocrystals to within the main antinode ofan SOI photonic crystal microcavity which solved this problem, but at thetime that work was published, the data was not fully analyzed. A majorportion of this dissertation involved modeling the power saturation of thiscavity-coupled emission in an effort to overcome assumptions holding backinterpretation of other studies, including proper accounting of the dielectricenvironment and allowing for sufficiently general non-radiative recombina-tion as a free parameter.1.5 Dissertation aim restatement, methodology,and organizationThe aim of this thesis work was to assess the feasibility of using PbSe CQDsas the source of single photons that could be efficiently coupled into sin-gle mode silicon waveguides in conventional SOI photonic circuits operat-ing near 1.55 µm wavelengths. The author carried out a number of novelexperiments that involved CQD sample preparation and their integrationwith previously fabricated SOI photonic circuits, and quantitative opticalemission measurements at temperatures ranging from 4 K to 300 K. A con-siderable fraction of the research involved developing models and solvingthem numerically in order to quantitatively interpret various measurements47that in one way or another elucidated the radiative and non-radiative decayrates of ground-state-manifold excitons in PbSe CQDs in various dielectricenvironments.Chapter 2 explains the experimental methodologies used for samplepreparation and all of the optical experiments done with the PbSe CQDseither in solution, or in thin or thick film formulations on silicon surfaces, orsite-selectively attached to isolated photonic crystal microcavities (specifi-cally excluding all of the photonic circuit coupling work, which is describedin Chapter 4). With the exception of the temperature-dependent photo-luminescent yield data obtained as a function of air exposure, all of theexperimental optical data in Chapter 2 was gathered by other members ofthe Young group; it is presented because all of the modeling of that data,done entirely by the author, as described in Chapter 3, is based on thisdata. Chapter 4 is self-contained, and describes all of the experimental andmodeling work done by the author, characterizing the coupling of PbSe ex-citon emission into single mode silicon waveguides. Chapter 4 also draws onresults from Chapter 3, for interpreting the photonic circuit data. Chapter 5summarizes the knowledge gained from this body of work by first summa-rizing the key factors that limited the circuit-based performance obtained inthis research, and then speculating on the feasibility for improving on theseresults through future efforts.48Chapter 2Experiment (non-PIC)This chapter describes the experimental setups and methodologies used toobtain PbSe photoluminescence spectra directly from the photo-excited re-gion of various textured and untextured substrates. Corresponding modelingis contained in Chapter 3. Studies of the PbSe CQD PL coupled into singlemode silicon waveguide circuits is dealt with in Chapter 4.2.1 Substrates and photonic componentfabrication2.1.1 SOI and silicon substratesMuch of the work in this thesis involved taking PbSe CQDs out of theirnative solvent environment and placing them on either bare silicon, or onthe device layer of patterned or unpatterned SOI. The band gap of silicon,corresponding to its linear absorption edge, is at 1.1 eV (≈ 1100 nm freespace wavelength) at room temperature. In the high resistivity samples usedfor photonic applications, the residual absorption associated with band tailstates and phonon absorption bands at longer wavelengths result in a broadlocal minimum in absorption that spectrally includes the important 1.55micrometer wavelength near-infrared (NIR) absorption minimum of long-haul silica fiber.49At those wavelengths, silicon has a high index of refraction of ≈ 3.4which allows for tight confinement of light. This high refractive index isexploited to form low-loss planar waveguides in silicon-on-insulator (SOI)wafers that consist of a thin, typically ≈ 200 nm high quality, high-resistivitysilicon device layer atop an electrically insulating, low-index of refractionsilicon dioxide layer on the order of 1 µm thick, all of which is supportedon a thicker (upwards of 1 mm) silicon backing wafer. In some instances,the silicon dioxide layer underneath the photonic crystal is etched away byimmersing the sample in aqueous HF for 10 to 20 minutes, thereby increasingthe refractive index contrast further.SOI wafers with a silicon device layer thickness of 198+4−4 nm, oxide layerthickness of 1193+10−10 nm from Galian Photonics were used for e-beam litho-graphic fabrication of the standalone photonic crystal cavity used in thischapter, where super- and sub-scripts denote uncertainty deviations fromin-line numerical value. Bare and SOI silicon surfaces were cleaned beforeintegration of PbSe CQDs, as described in the section below.2.1.2 Photonic crystal cavitiesAs discussed in Chapter 1, integrated single-photon source schemes based onluminescent CQDs as emitters often invoke a microcavity to efficiently collectthe CQD excitonic emission, in a microcavity mode at a rate that exceedsthe emission rate into other electromagnetic modes. The enhancement ofthe radiative decay rate of the exciton into any given cavity mode, relativeto the free space decay rate, is quantified by that mode’s Purcell factorF . The Purcell factor of any mode is proportional to its quality factor Q(as used generally for resonances) divided by its mode volume V , the latterquantifying how tightly the mode is distributed spatially. In formulae:F =34π2(λn)3 QV(2.1)V =∫drǫ(r) |Ecav(r)|2ǫ(r0) |Ecav(r0)|2(2.2)50where r0 is the location at which ǫ(r) |Ecav(r)| is maximum, where the cavitymode field is Ecav(r) and the cavity structure is defined by the dielectricfunction ǫ(r).Large Purcell factors are crucial for efficient photon collection and manycavity designs have been explored to achieve this. A cavity design for whichlarge quality factor and small mode volumes, and thus potentially efficientphoton collection, has been realized in the SOI platform is the “L3” configu-ration, shown in Figure 2.1, along with an intensity profile of its fundamen-tal in-gap cavity mode. Such cavities can be coupled efficiently to photoniccrystal waveguides that are impedance matched to low-loss, sub-µm scalesilicon channel waveguides [17]. Other in-gap (localized) modes are alsosupported by L3 cavities, but the fundamental mode typically exhibits thehighest quality and Purcell factors.Figure 2.1: (A): Schematic and scanning electron micrograph of an“L3” microcavity. (B): Fundamental in-gap cavity mode elec-tric field intensity at the silicon-air interface, with etched holesoutlined. Axes originate at the L3 slab centroid, and zˆ is per-pendicular to xˆ and yˆ. Yellow scale bars are 500 nm in length.Figure adapted from [164].2.2 PbX CQD formulations and integrationmethodsThis section describes CQD formulations (solvent, thin film, thick film) andmethods of integrating PbX CQDs onto and near silicon substrates as used51in this dissertation.2.2.1 PbX CQD formulationsSolvent: Colloidal quantum dots are synthesized, stable, most commonlymeasured, and exhibit their highest observed quantum efficiency with reli-ably measured radiative lifetime, in solution. Each other formulation (de-scribed below) either derives from or utilizes the solution formulation. Thus,in-solution measurements represent a useful reference for all other CQD ex-periments. For our experiments, CQDs are synthesized according to [207]by collaborators at the University of Victoria. To avoid inter-CQD effects,solution measurements are performed for CQD concentrations below whichthe spectral profile is unchanged if the concentration is further reduced,typically well below ≈ 5 mg/mL CQD weight by volume in solution.The photostability of these PbX CQDs was thoroughly characterizedbefore the work in this dissertation, results of which are largely containedin reference [207]. Exposure to air and light tended to shift and degradein-solution PbX CQD PL spectra over days to months time scales, whichcan be prevented by storing PbX CQDs in sealed vials filled with Argon (toprevent air from entering the vial) in the dark (e.g. wrapped in aluminumfoil and stored in a dark cabinet), and also be helped by refined synthesismethods. These early photostability studies included effects of air exposureon the room temperature integrated photoluminescence of PbSe thick films,noting long-term photostability under vacuum, degradation when exposedto air, and recovery once placed back under vacuum. These studies informedthe integration methods described below.Thin film: Many device settings, particularly single photon sources, callfor few (ideally one) CQD in the vicinity of a substrate in vacuum or atmo-sphere, not in solution. This formulation falls within what will be referredto herein as the “thin film” formulation. The composition of such films istypically inhomogeneous across the surface, consisting of regions containingisolated CQDs, close-packed monolayers of CQDs, with the possible inclu-sion of two or three layer thick islands. The exact morphology depends52critically on the thin film formation process, as discussed below.Thick film: A relatively simple means of obtaining homogeneous formu-lations of CQDs out of solution is by means of drop-casting dense solutionsof CQDs on substrates. Depending on the method of depositing the solution(spin-coating or from a pipette), these “thick films” are typically tens of µmthick. There are many studies of CQD emission from thick film emulsionsreported in the literature. The Young group had previously published de-tailed results of the temperature dependence of the luminescence lineshapefrom thick film PbSe emulsions [172]. In this and the following chapters,the temperature dependence of the photoluminescence yield is studied, withparticular attention paid to the impact of air exposure.2.2.2 PbX CQD integration methodsUse of inert gas environments and vacuums: In between experiments,CQDs are stored in glass vials that are sealed with parafilm under Nitrogenor Argon gas flow, and wrapped in light-blocking aluminum film, to helpprevent air and/or light mediated changes to the CQD emission and ab-sorption properties. Vials of CQDs in solution were checked regularly (overtime scale of months) to make sure solvent had not evaporated, and in theexceptional situations when solvent did evaporate, addition of solvent (tothe original solvent level) followed by re-sealing under inert gas flow wasperformed. Some other formulation steps, e.g. when drop-casting or dip-coating, were performed either under low nitrogen gas flow, or in a glove boxfilled with nitrogen gas (described further below). After CQD integrationonto a substrate, samples are placed under vacuum to preserve the CQDsand allow for low-temperature measurements (also described further below).If held under vacuum, the optical properties of these films remained almostunchanged for at least several months.Solvent transfers: CQDs are received from our collaborators in a sus-pension in toluene, an organic solvent for which photophysical properties ofPbX CQDs were found to be largely preserved when stored long-term in thedark [6] (tetrachloroethylene (TCE) also works well for long-term storage).53Suspension of CQDs in other solvents, notably hexanes, were found betterfor CQD integration processes, so a solvent transfer from toluene to hexaneswas performed prior to immersion of a silicon or SOI sample in a CQD so-lution. Solvent transfer therefore involves evaporation of solvent under drynitrogen gas flow for upwards of a few hours, followed by reconstitution withthe target solvent. In a variety of experiments, it was useful to quantify theCQD concentration, and this may conveniently be done during the solventtransfer process as follows: (a) Before solvent transfer, weigh the destina-tion vial. (b) Fill the destination vial with the toluene (or TCE)-dispersedCQDs, then evaporate under dry nitrogen flow for upwards of several hours.(c) Weigh the destination vial plus dried CQDs, and subtract from this theweight of the empty destination vial. The resulting weight is of the CQDsplus ligands, and reconstitution with a known volume of solvent permitsknowledge of the mass of CQDs (plus ligands) per volume of solvent.Drop-casting: After as-received CQDs are transferred to a solutionof hexanes, much of the hexanes solvent is evaporated under Nitrogen gasflow, until the concentration of CQD mass per volume is on the order of ≈ 50mg/mL, a process that typically takes several hours. During evaporation, asilicon or silicon on insulator wafer portion is removed of organic residuesby RCA-1 and RCA-2 cleaning procedures (see, for example, [102]). Thecleaned wafer portion is mounted in a cryostat and nitrogen gas is pumpedthrough the cryostat, such that a slight positive pressure of nitrogen gasinside the cryostat is maintained. The dense suspension of CQDs is thenpipetted onto wafer surface (temporarily lifting the cryostat window for eachdeposition), resulting in approximately a few square mm of coverage andsub-mm thickness. The influence of air on CQDs emission and absorptionrequires we study these properties for CQDs under vacuum, so the sampleis placed under vacuum after the CQD solid is drop-casted. A Janis Inc.ST-500 cryostat was the sole cryostat used in the work in this dissertation.The sample chamber was pumped down to 10−4 millibar with a turbo pumpcapable of reaching low 10−6 millibar vacuums, then pumped for another30 minutes. Shortly prior to measurements, the cryostat chamber would bere-pumped until the vacuum reached the 10−6 millibar range, typically ∼ 1054to 15 minutes.Figure 2.2: Dip-coating for thin film formulations, in an inert-gasglove box. (A): The glove box and dipping setup used for mono-layer, sub-monolayer, and generally dip-coating formulations.(B): Example scanning electron micrograph of a sub-monolayerof CQDs on a silicon surface using the setup in (A) and de-scribed in-text, published in [173].Dip-coating: Samples for which a monolayer or submonolayer thicknessof CQDs on a silicon surface are prepared as follows, with additional detailsfound in Appendix A. For reference, the procedure is often called “dip-coating” and is depicted, with example results, in Figure 2.2. Firstly, siliconor silicon-on-insulator substrates are cleaned of organic residues by RCA-1and RCA-2 cleaning. Following this cleaning, the silicon surface is preparedto improve adhesion of the CQDs to it. As also described in [164], the oleate(ligand)-capped PbSe CQDs used in our laboratory adhere preferentially(by a few orders of magnitude) to hydrogen-terminated silicon relative tooxidized silicon (a ∼ 1 nm layer on the silicon surface), the latter formingrapidly and commonly upon exposure of a silicon surface to air. Hydrogen-terminated silicon is achieved by thoroughly cleaning a silicon surface of55organic residues (in our case, with RCA-1 and RCA-2 procedures), followedby gentle hand-held agitation of the silicon sample in 2% aqueous HF for 10to 20 minutes. The aqueous HF treatment etches away any exposed oxidizedsilicon and produces the hydrogen-terminated surface. Oleate-capped PbSeCQDs also adhere relatively poorly to dodecyl-coated silicon [164], as usedin AFM-assisted site-selective binding (described below).CQDs are dispersed in hexanes to a concentration of ≈ 5 mg/mL CQDweight by volume in solution (see solvent transfer information above for howthis concentration is measured). The CQD solution, sample, and cryostatare then placed in an inert nitrogen gas glove box. In the nitrogen environ-ment, the sample substrate is mounted on tweezers with its plane vertical.Directly below the sample is a mechanically controlled stage upon which anopen vial of the solution is placed. The stage can move up or down at aspecified speed by LabView control of an attached stepper motor. Groupmember Stephanie Flynn studied the effect of dipping speeds monolayerspectra, and found insensitivity to the speed at which the sample substrateis introduced into the CQD solution, but high sensitivity to the speed atwhich the substrate is removed from solution. For PbSe CQDs similar tothose used in this dissertation, withdrawal speeds of 0.8 mm/s to 1.0 mm/sprovided larger and more consistent spectra than 1.2 mm/s, and a speed of0.8 mm/s was used for samples in this dissertation. Upon removal of thesample from solution, the sample is placed in the cryostat and subsequentlyunder vacuum, as done for drop-cast samples.AFM-assisted site-selective binding: This procedure is publishedin reference [164], and used for integration of the CQDs into the standalonecavity used in power saturation measurements in this chapter. Figure 2.3summarizes these steps. Preferential binding of PbSe CQDs via hydrogen-termination of the silicon surface is also utilized in this integration method bylocally oxidizing areas of desired CQD binding with application of a voltagebetween a positioned conducting AFM tip and subsequently immersing thesample in aqueous HF. All other areas, i.e. in which CQDs are not desired,are chemically coated with dodecyl, a molecule that (a) is destroyed duringlocal oxidation by the application of the AFM voltage, (b) protects the56Figure 2.3: Site-selective binding technique, as published in [164],used to integrated PbX CQDs to primarily within the mainantinode of the the fundamental cavity mode of a standaloneL3 photonic crystal cavity, for the sample studied in this chap-ter. Prior to the AFM site-selective surface oxidation depictedin (A), the silicon is coated with dodecyl molecules. In (B),application of a voltage from the AFM locally removes the do-decyl molecules and oxidizes the silicon surface. Immersion in abuffered oxide etch removes the oxidized silicon but leaves thedodecyl coated silicon intact. The sample is finally dipped ina suspension of CQDs (C), which adhere preferentially to thehydrogen-terminated silicon (relative to the dodecyl coated sil-icon). (D) and (E) are atomic force micrographs of the samplesurface, with (E) corresponding to the region within the whiterectangle in (D). (F): resulting microphotoluminescence (µPL)collected directly from the cavity region. Yellow scale bar is 500nm in (D) and 50 nm in (E). Unit conversion: 1 eV↔ 1240 nm,0.8625 eV ↔ 1500 nm.non-oxidized silicon surface from hydrogen termination when the sampleis immersed in aqueous HF, and (c) preferentially (relative to hydrogenterminated silicon) rejects adhesion of oleate-capped PbSe CQDs. A typical57site oxidized by the AFM tip was roughly circular and ∼ 50 nm in diameter,with CQD areal density of ∼ 3× 103 nanocrystals per square µm (withineach site), compared to ∼ 10 nanocrystals per square µm on portions of thesample protected with the dodecyl layer [164].2.3 PL measurements overview and opticalsetupsThis section describes the experimental setups and alignment proceduresused for the three non-circuit-based PbX luminescence measurements, andthe three following sections describe the results of these measurements. Thesetup for two of these measurements - temperature and air exposure depen-dence of steady-state PbSe CQD thick film PL (Section 2.6), and power-dependence of cavity-coupled PbSe CQD PL (Section 2.4) - are nearly iden-tical and presented in Subsection 2.3.2. The setup for the third measurement- time-resolved PbSe CQD emission in various formulations (Section 2.5) -contains similar elements and is summarized in Subsection PL measurements overviewThe three sets of PL measurements contained in this section are as follows.The first set of measurements, performed by Haijun Qiao formerly of ourgroup, is the power dependence of cavity-coupled PbSe CQD PL, for PbSeCQDs site-selectively integrated into the main antinode of an “L3” photoniccrystal cavity. This power dependence, found to saturate at low excitationpowers for which in-solution, sub-monolayer, and thick film PL are eitherlinear or only slightly sub-linear, can provide insight into PbSe exciton dy-namics when combined with the modeling efforts in Chapter 3. The secondstudy involved systematic, time-resolved photoluminescence decay measure-ments of PbSe CQDs in solution, thick films, and sub-monolayer films, forthe same PbSe CQDs used elsewhere in this dissertation, the results of whichwere later combined with dielectric modeling in Chapter 3 to improve un-derstanding of the environmental dependence of non-radiative decay. Thethird set of measurements studied the impact of air exposure on the temper-58ature dependence of PbSe CQD thick films, which extends the air exposuredependence studies of [207] that were only performed at room temperature,and can be compared to the thorough temperature-dependent thick filmstudies of [172]. These studies provide new insight into the non-radiativedecay kinetics.2.3.2 Head-on continuous wave (CW) laser excitationBoth the µPL of CQDs in silicon microcavities and thick CQD film PL weremeasured using the setup shown in Figure 2.4. Components not shown aretemperature controller equipment and cryogen used to adjust the temper-ature of the thick CQD films. The white light source was not used in thethick film measurements, but was used in the µPL measurements to imagethe sample for translation to the appropriate location. In both experimentsthe sample is prepared as described in the previous section, and is locatedin the cryostat.A continuous wave Helium-Neon (HeNe) laser is collimated, passedthrough a neutral density filter wheel, diverted by a visible wavelength beamsplitter that’s transparent around 1.55 µm wavelengths, and focused ontothe sample surface using a 100X long working distance microscope objectiveto a 1/e2 power spot diameter of 2.0 µm. The same objective collects PLand diverts it to a Bruker Fourier transform infrared (FTIR) spectrometer,utilizing a liquid nitrogen cooled Germanium (Ge) detector. In µPL exper-iments the spot is focused onto the cavity center, using the scattered HeNelight as an indicator of the spot position. In the thick CQD film measure-ments, the excitation spot position is adjusted to optimize integrated signalinto the detector.In thick CQD film experiments, the excitation intensity was adjustedsuch that both the integrated PL was proportional to the excitation intensityand the PL spectrum profile was unchanged, on the order of tens of µW.In µPL/microcavity power saturation measurements, the PL was clearlybrought out of this linear regime up to sub-linear, saturated regime (startingaround several µW and measured up through 70 µW).59Figure 2.4: Head-on continuous wave (CW) HeNe excitation setupused for power saturation measurements of PbX CQD emissioncoupled to a standalone L3 cavity and stead-state integrated PLof PbSe CQD thick films. Mirror pair MT1,T2 diverts collectedlight down (−xˆ) and then in the direction of the Bruker FTIR;details are available in the insets of Figure 4.4F.2.3.3 Pulsed excitation in back-scatter geometryExcitation and collection equipment was similar for time-resolved PL mea-surements as it was for continuous wave (CW) PL measurements, but theCW laser was replaced by a 660 nm pulsed Sepia II diode laser with rep-etition rate of 1 MHz and pulse duration of 500 ps, and the additionalfunctionality of gated single photon detection with a model ID210 photoncounter from ID Quantique (detection range 900 nm to 1700 nm), plus Pi-coHarp 300 time correlator, were added, as seen in Figure 2.5. Results werecorroborated with a pulsed Ti:Sapphire laser with a 1.2 ps pulse durationand emission wavelength of 800 nm. The oscillator used for laser pulseswas used to gate photon detection in the photon counter, and used for sync60pulses for the time correlator. Toggling between gated photon counting andPL spectral measurements was done by addition of a kinetic mirror. PLdiverted by the kinetic mirror was focused into a multimode fiber by a lens,a fiber that carried the PL to the single photon counter.Figure 2.5: Back-scattering geometry with pulsed laser excitationsetup used for time-resolved studies in [173] and presented inSection 2.5.Pulse duration was ≈ 500 ps and the repetition rate and average powerwere kept low enough for spectra and time-resolved PL curve shapes to beinsensitive to both repetition rate and excitation power. The correspondingaverage peak laser intensities were less than 300, 300, and 3000 Watts persquare centimeter for solution, drop-cast, and dip-coated samples, respec-tively, and the corresponding repetition rate was 1 MHz. The excitationspot was ≈ 3 µm in diameter. Spectra were also obtained with the BrukerFTIR. CQD formulations on substrates were measured while in the cryostat,whereas the CQDs in solution were measured while in a vial.612.4 Power saturation of cavity-coupled CQD PLPower saturation measurements of CQD PL can provide insight into theirexcitonic population dynamics, particularly when the excitation field at theCQD location is known. For example, PL from a CQD with no non-radiativedecay will only saturate when the excitation rate is comparable to the ra-diative relaxation rate, but saturation can occur at much lower powers forCQDs with a long-lived, non-radiative “trap state”. The emission rate in thepower saturated regime is directly related to the maximum rate at which theCQD may emit photons. Both non-radiative recombination and maximumradiative emission rate are key figures of merit for single photon sources.Our aim here is to understand the saturation behavior of cavity-coupledPbSe CQD emission into a SOI PIC, as it would affect the performanceof an integrated single photon source. This power saturation behavior ispresented in Chapter 4, and in this section and Chapter 3, the saturationbehavior of a PbSe CQD emission coupled to a standalone SOI microcavityis presented and analyzed. The motivation to study the standalone cavitysystem is that it is significantly less complicated (relative to the full PIC)to account for the full dielectric environment in simulations, and there is nocompelling reason to believe the core cause of power cavity-coupled PL inthe two systems (full PIC vs standalone cavity) is different.The motivation to study power saturation of cavity-coupled CQD PL isdriven further by intriguing differences in the power dependence of cavity-coupled PbSe CQD emission relative to PbSe CQDs in a thin film formula-tion on bare silicon or SOI, wherein all factors (including dip-coating inte-gration of CQDs and excitation with a HeNe laser) aside from the photonicenvironment are identical. What is observed, as exemplified in Figure 2.6,is that under these conditions the cavity-coupled PbSe CQD PL saturatesfaster than the uncoupled PL, and over the same power range the thin filmCQD PL is unsaturated. Further, for thick film and solution CQD formula-tions, emission is linear over the same power range. En route to understand-ing the saturation of cavity-coupled PbSe CQD PL, may we self-consistentlyexplain the saturation power differences?62Figure 2.6: Comparison of power dependence of PbSe CQDs in thinformulations in different dielectric environments. (A): Examplelow and high excitation power PL spectra of CQDs on the sur-face of a SOI L3 optical microcavity, integrated by dip-coating,and labels indicating cavity-coupled and background contribu-tions at a cavity mode wavelength. (B): Example low and highexcitation power PL spectra of a thin film of PbSe CQDs on abare silicon surface, also deposited by dip-coating, for the sameexcitation setup used for data in (A). (C): Power dependencecomparison for cavity-coupled PL of (A) and monolayer PL of(B), for the same excitation conditions, showing how the powerdependent PL of the monolayer is nearly linear but strongly sat-urated for the cavity-coupled PL. (D): Power dependence com-parison for samples with Nd:YAG excitation and identical exci-tation/collection geometries, again exemplifying the differencein saturation powers. (E): Same as in (D), but the monolayerdata scaled along the power axis by the excitation enhancementfactor calculated in section 3.2 (a factor of 9) and scaled verti-cally to best match the cavity-coupled data fit. Note the goodoverlap, which can be interpreted with Chapter 3 modeling.63To improve understanding of the CQD PL power dependence, it is usefulto reduce variation of as many system variables as possible. In order to dothis, instead of indiscriminate integration of CQDs by dip-coating (as donein Figure 2.6), which results in an indeterminate coupling strength of CQDsto the cavity mode, we may site-selectively graft CQDs, using the AFM-assisted binding technique (Figure 2.3, reference [164]) to within just themain antinode of the L3 fundamental cavity mode, indicated by the 200 nmsquare patch in Figure 2.7A. Site-selective grafting of the CQDs to only the200 nm square patch also reduces variation of the excitation laser field overthe CQD region, relative to indiscriminate integration of CQDs.Figure 2.7: Experimental setup and resulting data modeled in thisarticle. (A): Schematic of excitation/collection geometry: ex-citation (at 633 nm) and collection performed with a common100X microscope objective. Red-filled circle indicates 1/e exci-tation spot intensity. Shaded square indicates span of graftedPbSe CQDs. (B): Example PL spectrum with cavity-coupledemission indicated, and cavity-coupled PL versus pump power.Sample fabrication, AFM-assisted binding of the CQDs, and measure-64ments of the power-dependent PL of this sample was performed by HaijunQiao, and the modeling thereof by the author of this dissertation in Sec-tion 3.2 of Chapter 3. Power dependent studies of silicon cavity-coupledPbX CQD PL have been performed before (e.g. [33, 175], but modelingis crucial for understanding the behavior, as it involves balance of severalkey factors, such as depolarization at the CQD surface, non-trivial photonicdensity of states available to the CQD, and an unknown contribution ofnon-radiative decay, the last of these not considered a free parameter in anymodeling prior to the work in this dissertation.The center of the stand-alone cavities was excited at normal incidencewith continuous wave 633 nm HeNe laser light polarized in the yˆ-direction,using a 100X microscope objective that also collected light scattered normalto the sample surface. The 1/e2 intensity diameter was 2.0 µm on the cavitysurface, and the excitation power was varied by attenuation with variousneutral density filters. Measurements were performed with the sample invacuum, in the Janis ST-500 cryostat. An example spectrum, along with aplot of the power-dependent cavity-coupled PL that is modeled in detail inthe following chapter, are shown in Figure 2.7B.2.5 Time-resolved decay of CQDs in variousformulationsIn modeling the power saturation (measurements described in the previoussection), information about non-radiative recombination was treated as afree parameter and extracted by consideration of the balance between ex-citation and relaxation as required to reproduce the observed saturationpower. Alternatively, information about the non-radiative recombinationmay be obtained by combining the total PL decay time with knowledge ofthe radiative decay rate alone. This section describes measurements of thetotal PL decay times for CQDs in various formulations, which are combinedwith model simulation results of the corresponding radiative decay rates todetermine relative radiative and non-radiative contributions for thin andthick film formulations.65Samples in each of solution, thin film and thick film formulations wereprepared by the author of this dissertation, and the time-resolved decaycurves were measured by Rafael Quintero-Torres (as published in [173]).The experimental setup consisted of the head-on pulsed laser excitationsetup described in Subsection 2.3.3, and the resultant curves (normalized atzero time delay) are shown in Figure 2.8. Insets show corresponding spectra,normalized and vertically offset.Figure 2.8: Time-dependent PL at 300 K for PbSe CQDs dispersedin hexanes (black dots); drop-cast film (blue circles); and sub-monolayer (red squares). The inset shows the steady state PLspectra from drop-cast (top, blue), solution (middle, black), andsub-monolayer dispersions (bottom, red) of the same batch ofCQDs. The monolayer was excited with 3000 times more aver-age power than the drop-cast film.The steady-state, drop-casted integrated PL was 3000 times larger thansub-monolayer PL, and the solution PL in between those two. The red shiftof the peak PL wavelength for the drop-casted film, relative to the solutionand sub-monolayer spectra, arises from exciton diffusion from higher energyCQDs to lower energy CQDs; no such exciton diffusion exists for the lattertwo. Thorough measurements and modeling of exciton diffusion, mediated66by Fo¨rster energy transfer, of the drop-casted films were studied in ourlaboratory separately from the work contained in this dissertation [174].While the decay of CQDs in solution can be well-described by a sin-gle decay constant, it is clear more than one decay constant is required toadequately fit the decay for thin and thick film formulations. Thus, forthose latter two formulations, two decay constants (one short, one long)were extracted for each curve by fitting the time-resolved intensity to theI(t) =A1 exp(−t/τ1)+A2 exp(−t/τ2). These fit curves are plotted with theraw data in Figure 2.8.Figure 2.9: Histograms of the shortest time constants, τ1 (left, (A)and (C)), and the average time constants A1τ1+A2τ2A1+A2 (right, (B)and (D)) components of the measured lifetimes extracted fromtwo-exponential fits to decay curves taken from various loca-tions on the drop-cast samples (bottom, (C) and (D)), and thedip-coated samples (top, (A) and (B)). The mean values are(A) 90 ns, (B) 135 ns, (C) 190 ns, (D) 200 ns. (E): Tabularsummary of known and unknown radiative and non-radiativedecay parameters, after measurements indicated in this sectionbut before modeling of the photonic density of states performedin Chapter 3.Histograms of the shortest time constant extracted for each of the thinand thick films, τ1, are presented on the left hand side ((A) and (C)) Fig-ure 2.9. A weighted average of the two extracted time constants (betterrepresentative of the overall PL decay time than either of the two time con-67stants extracted) for these formulations is presented on the right hand side(subfigures (B) and (D)). Clearly the thin film formulation decays fastest,and solution formulation slowest. The ∼ 135 ns decay time of the thin filmformulation is similar to some previous values reported for thin films (e.g.[32]).The absolute quantum efficiency (QE) of the CQDs in solution formula-tion was reported by our collaborators to be 30%. With this absolute quan-tum efficiency and the measured total PL decay time, the radiative contribu-tion to the total decay time was extracted and found to be 1/τrad = 3×105Hz. How much non-radiative recombination and radiative recombinationeach contribute to the total decay time for thin and thick films is deter-mined by modeling, as described in the following chapter, the change in rateof radiative recombination going from solution formulation to the thin andthick film formulations.2.6 Air exposure influence on CQD thick filmtemperature-dependent PLEarly photostability studies in reference [207] showed the integrated PLof PbSe CQDs thick films at room temperature can recover from air expo-sure, once returned to a vacuum environment. The temperature-dependenceof PbSe CQD thick film PL in reference [172] from our group provided aconvincing quantitative understanding of exciton diffusion and kinetics inthis formulation, and consistent with the literature, namely a monotonic,Arrhenius-like decay of the integrated PL with increasing temperature from5 K to 295 K, described by a single non-radiative pathway with activationenergy of ∼ 20 meV.Not addressed by those studies, but a natural extension of them, is theair exposure dependence of the temperature-dependent PbSe CQD thickfilm PL, which could provide further insight into exciton dynamics. Forexample, if air exposure at lower temperatures is also recoverable, and whatnon-radiative pathways (if any) are introduced by exposure to air. The aimto pursue this understanding was further motivated by the work in refer-68Key Description (air exposure extent and originating publication)C1 No air exposure as drop-cast, some during CQD synthesis, Qiao et al. [172]C2 No air exposure as drop-cast, some during CQD synthesis, Qiao et al.[172] Distinctdrop-cast from C1.D1 No air exposure as drop-cast, some during CQD synthesis. Same CQD drop-castsample as traces D2 and D3.D2 30 minutes exposure as drop-cast, some during CQD synthesis, measured after 2hours in vacuumD3 2 hours exposure as drop-cast, some during CQD synthesis, measured after 48hours in vacuumTable 2.1: PbSe CQD thick film sample descriptions, for integratedPL traces plotted in Figure 2.10.ence [43, 93], in which air exposure dependence was carefully controlled atboth CQD synthesis and post-formulation stages of temperature-dependentPbSe CQD thick film PL. In those studies the thick film PL took on behav-ior markedly different than previous studies, i.e. exhibiting non-monotonictemperature dependence.Temperature control was achieved by cooling the cryostat cold fingerto liquid helium temperatures then locally heating the cold finger using afeedback-enabled temperature controller. Finite time to achieve temper-ature stability of the cold finger and sample (as indicated by stability ofmeasured temperature and observed PL spectrum) restricted temperatureramping to ∼ 1 K per per minute, or ∼ 300 minutes (5 hours). Theseresults were consistent with using this 1 K per minute ramp at low temper-atures, where temperature dependence of the PL is greatest, combined witha slightly faster (several K per minute) ramp at higher temperatures. Cool-ing down directly to liquid helium temperatures could be performed muchfaster, on the order of 10 minutes. Prior to starting each measurement, thesample was pumped down for at least 30 minutes with an aforementionedturbo pump, to the 10−6 millibar range.Table 2.1 summarizes the temperature-dependent, integrated PL forsamples from our group (e.g. as partially published in [172] and from thenew temperature-dependent integrated PL curves for different air exposures,69measured for this dissertation. Thick films were formulated as described inSection 2.2. Figure 2.10 contains plots of this data. The markedly differ-ent integrated PL behavior reported in [43] and [93] are presented in thecorresponding modeling and discussion sections in Chapter 3.Figure 2.10: Integrated PL data sets (black squares), normalized totheir maximum values, along with best-fit model yield curves(calculated below) in solid red and corresponding model PLcontributions from each of two possible emissive states or clus-ters of emissive states in dotted and dashed lines, respectively.Modeling is described in Chapter 3. Table 2.1 contains de-scriptions of the samples.Air exposure effect measurements presented in traces D1 through D3were collected as follows: after measuring trace D1, the sample was exposedto air for a duration of 2 hours, in the dark. After this time, the sam-ple chamber was pumped down again with the turbo pump for about 30minutes, followed by quick cooling down to liquid helium temperatures andsubsequent measurement of trace D2. After measurement of trace D2, thesample was exposed to air, in the dark, for 48 hours. After those 48 hours,the sample chamber was again put under vacuum, the sample cooled, and70then trace D3 was measured. Section 3.4 contains the results of applying aphysically-based kinetic model that captures the essential behavior of inte-grated PL data from all samples listed in Table 2.1 and the samples fromreferences [43] and [93].71Chapter 3ModelingExperimental results of Chapter 2 are modeled in this chapter, in the sameorder as presented there.3.1 Overview of modelSeveral key issues pervade modeling the emission of photoexcited PbSeCQDs: (a) upon excitation, a PbX CQD will quickly (on the order of pi-coseconds) relax to the lowest energy excitonic state, (b) this lowest energyexcitonic state is really a manifold of multiple (many for PbX) electron-holestates with various associated transition dipole moments, (c) as supportedby previous modeling of temperature dependent luminescence spectra fromPbSe, the excitons in the ground state manifold are assumed to thermalizewithin their relatively long lifetimes, and (d) evidence points to significantnon-radiative exciton recombination for CQDs in some environments, par-ticularly out of solution. A sketch of these basic PbX CQD model elementsis shown in Figure 3.1.The aim of self-consistently modeling the data of Chapter 2 across CQDformulations and synthesis methods is to elucidate the exciton dynamicsand radiative coupling in diverse environments. This chapter describes akinetic model used to quantitatively determine radiative and non-radiativedecay rates of primarily PbSe excitons in various CQD formulations. To72Figure 3.1: Overview of general considerations for modeling PbXCQD emission in nanophotonic environments. (A): Excitonicstates are numerous and the distribution of transition dipolemoment magnitudes is varied across a number of computationalstudies. (B): Simplified excitonic state structure, for whichrapid decay from higher-lying state(s) |P 〉 to a ground stateexcitonic manifold is understood |X〉, but the decay from theground state excitonic manifold |X〉 to the CQD ground state|G〉 is generally environment dependent. (C): Example depo-larization effect on the electric field for a dielectric sphere, oneenvironmental contribution to exciton decay dynamics.augment this kinetic modeling, it was necessary to also develop a method fortaking into account the significant effects of depolarization, or local fields, onthe radiative coupling of the excitons in these high-dielectric host materialsembedded in relatively low dielectric solvents or vacuum.The order of modeling efforts in this chapter are chronological, reflectingthe fact that the successful first modeling of the cavity-coupled PL satura-tion underscored the importance of better understanding the non-radiative73pathways in PbSe CQD emission. This actually motivated the additionalexperimental and modeling work described in Chapters 2 and Exciton thermalization in the ground state manifoldIndependent models [43, 93, 172] have been developed to quantify various as-pects of the published PbSe CQD exciton kinetics. However, we are unawareof any account of a systematic attempt to fit the entirety of this disparatePbSe nanocrystal temperature-dependent integrated PL data from 5K to300K using a single, physically-based model. Our model is as follows.Various band structure calculations suggest that the 64-fold degenerateexcitonic ground state of bulk PbSe is spread into a manifold of excitonicstates in small (3 to 5 nm diameter) CQDs, with total electron and holewavefunctions having predominantly S (spherical) symmetry [12]. Interval-ley coupling splits the states over an energy range of tens of meV, whileelectron-hole exchange splitting further lifts the degeneracies by a smalleramount, on order of a few meV [12]. Of these 64 states, only a few havesignificant oscillator strength. Assuming that the excitons thermalize to aFermi-Dirac distribution [181] within the ground state exciton manifold atall temperatures, the steady-state, spectrally integrated PL emission ratecan be expressed as:gr =∫ ǫmaxǫminγr(ǫ)f(ǫ)e(ǫ−µ)/kBT +1dǫ, (3.1)where f(ǫ) is a sum of 64 delta functions defining the energies of the exci-ton states within the ground state exciton manifold, spanned by ǫmin andǫmax, γr(ǫ) is the radiative decay rate distribution of the states within themanifold, and the remaining part of the integrand is the Fermi-Dirac oc-cupation factor. Assuming weak (linear), non-resonant optical excitationinto the high-lying quasi-continuum of the CQD absorption spectrum, andrapid decay to the ground state manifold at a rate gex, the steady-state74quasi-chemical potential µ of the excitons is determined by solving:gex =∫ ǫmaxǫmin[γr(ǫ)+Γnr(ǫ,T )]f(ǫ)e(ǫ−µ)/kBT +1dǫ (3.2)for µ at each T , assuming the other parameters are fixed. Here Γnr(ǫ,T )is the distribution of non-radiative recombination rates for different excitonstates in the ground state manifold, which can be temperature dependent.3.1.2 Depolarization, spontaneous emission ratesDepolarization effects typically do not play an important role in III-V basedquantum electrodynamic modeling of InAs QDs as there is negligible di-electric contrast between the InAs QDs and the surrounding host mate-rial. However, depolarization effects must be included in similar modelingof PbSe CQDs, as absorption and emission properties are typically mea-sured in dilute solutions or in vacuum, on the surface of bulk silicon or asilicon photonic crystal in our experiments, where the dielectric contrast ofthe CQD and surrounding environment is large.When a dipole is surrounded by a thin shell of high dielectric PbSe, theMaxwell equations dictate that the dipole field scatters from the interfacebetween the PbSe and the solvent, which significantly modifies the field atthe location of the dipole, and thus the radiated power. For very smallspheres much less than the wavelength, the reduction of the field at thedipole location is essentially given by the “static” result for the depolariza-tion of the field internal Ein to a small sphere compared to the external fieldEin = 3Eext/|2+ ǫPbSe/ǫsolvent|. Note that the dielectric constants that enterthis Lorentz depolarization factor expression are evaluated at the frequencyof the oscillating dipole.For the values ǫPbSe =23.0 and ǫsolvent =2.1 evaluated at the wavelengthof 1.55 µm, the depolarization factor is 0.23, and quantities quadratic inthe local electric field - such as radiated power, to be discussed more below- can be reduced to a factor of 0.232 = 0.05, exemplifying depolarizationinfluence of two orders of magnitude. The practical relevance and impor-75tance of including depolarization effects [20, 45, 186] when quantitativelycomparing various CQD optical properties has been nicely demonstratedin (1) relating PbSe CQD threshold absorption coefficients and oscillatorstrengths to radiative decay rates, in an analysis by Moreels et al. [142],and (2) in modeling short-wavelength, continuum PbSe CQDs absorptioncharacteristics, particularly accounting for absorption coefficient differencesof PbSe and PbSe/CdSe core/shell CQDs in terms of dielectric depolariza-tion effects alone, in an analysis by De Geyter et al. [77]. The Lorentzlocal field factor was also found adequate in local-field modeling of emissionlifetimes of CdSe/ZnS CQDs on various dielectric substrates [235].The approach we take to account for depolarization effects on the ra-diative decay rates in our target dielectric environments (e.g. thick film,thin film, L3 cavity with thin film) is based on the fact that the ratio of ra-diative spontaneous emission rates (γXG,0 and γXG,ǫ(r)) of a point-like twolevel system in two distinct dielectric environments is equal to the ratio ofpowers radiated (Prad,0 and Prad,ǫ(r)) by a classical point dipole driven at theresonant frequency of the two level system in those two distinct dielectric en-vironments (e.g. see references [20, 45, 151, 186, 201] for related derivationsand discussions):γXG,ǫ(r)γXG,0=Prad,ǫ(r)Prad,0(3.3)where the background dielectric environment is described by the (real) per-mittivity ǫ(r). In cases where the dipole emitter orientation is not fixed,three separate calculations are performed for dipole sources of orientationxˆ, yˆ, or zˆ, and then averaged appropriately. A major benefit of this ap-proach is that it can be used to relate firm results from simple dielectricenvironments (e.g. single CQD in uniform solvent) to complicated environ-ments - i.e. a CQD in a photonic crystal cavity - for which less data and noclosed-form theoretical results exist. This radiated power approach was usedin conjunction with finite difference time domain software from LumericalSolutions Inc., chosen because it can produce accurate field distributions (asverified by numerous benchmarks), for both simple CQD environments and76richer nanophotonic environments (e.g. photonic crystal cavities).To validate the use of the FDTD field solver to determine the powerradiated by point dipoles in nanoscale dielectric environments, consider twoscenarios: (a) the power radiated by a classical dipole at the center of a 5 nmdiameter sphere of PbSe of a dielectric constant of ǫPbSe, embedded in a back-ground solvent with dielectric constant ǫsolvent, and (b) the power radiatedby the same dipole in a uniform solvent without the PbSe casing. The powerradiated by a source of driving current density j is P = −∫ dr j(r)∗ ·E(r),where E(r) is the total electric field. For a point dipole source at loca-tion rd, of moment p, and driving at frequency ω (i.e. current densityj(r) =−iωpδ(r− rd)), the power radiated by the dipole is:〈P 〉 = ω2Im[p∗ ·E(rd)] (3.4)and for the dipole in a uniform dielectric ǫsolvent, the result is:〈P 〉 = ω4|p|23πǫsolventc3(3.5)Applying the Lorentz field factor result to Equation 3.3, the power radi-ated from the dipole within the 5 nm PbSe dielectric sphere is:〈P 〉 = ω4|p|23πǫsolventc3∣∣∣∣ 32+ ǫPbSe/ǫsolvent∣∣∣∣2(3.6)In FDTD simulations, the dipole source is defined as a “soft source”,meaning the electric field at the location of the source is a superposition of adriving, fixed electric field and a contribution from electric fields arising frominteraction of the driving field with the dielectric environment (i.e. the totalelectric field). The driving electric field consisted of a finite pulse of Gaussiantime envelope and known explicit time dependence. A “conformal” mesh,handled by the FDTD solver, was chosen for the majority of the simulationvolume, with a finer mesh (fractions of a nm) override in the vicinity of thedielectric sphere (tested down to 4 nm diameter).Absolute accuracy of better than 5% and convergence with simulation77settings to within 5% were achieved for both (1) the radiated power equa-tion and (2) Lorentz factor closed-form example equations above (note thatthe local electric field needed to be averaged over several grid points). Con-vergence of the radiated power and local electric field each to a single value(within the 5% state FDTD solver accuracy) with incrementation of the fol-lowing simulation parameters was achieved for both test and model dielec-tric environments: (a) computational simulation volume, (b) mesh step/dis-cretization, and (c) location of power monitors. Values of these simulationparameters found adequate to achieve the converged powers and electricfields were (a) a 3 µm cube centered upon the test dipole, (b) 0.25 nm inthe vicinity of the test dipole, and (c) along the surfaces of a one µm cubecentered around the test dipole.This approach was then used in the more complex dielectric environ-ments encountered in the different experimental conditions described inChapter 2, as summarized below.3.1.3 Intrinsic dipole momentThe fact the emission rate modification of both a quantum transition dipolemoment (between two states |G〉 and |X〉 separated by energy h¯ω) and aclassical dipole emitter radiating at frequency ω may be accounted for withthe same classical electromagnetic computation, for arbitrary dielectric en-vironments, motivated our definition and extraction of an “intrinsic,” free-space dipole transition moment for the emissive exciton transition, |µXG,0|,independent of the variety of environments considered in this dissertation.In taking this approach, we firstly calculated the intrinsic dipole using thewell-established in-solution emission data and basic application of the radi-ated power method and (as justified above) Lorentz field factor. We thenconsidered this intrinsic dipole to be located within model dielectric environ-ments (e.g. thick film, thin film, etc.), and the FDTD simulations were usedto evaluate the electric field at the dipole, which included all depolarizationfactors with computational exactitude.The intrinsic, free-space dipole moment |µXG,0| of the |X〉 ↔ |G〉 tran-78sition was extracted with reference to the reliably-measured and modeledspontaneous emission rates of a dilute solution of ∼ 5 nm diameter PbXCQDs in solvent. In this environment, the radiative lifetime was taken tobe γ−1XG,CQD+sol = 3+1−1 µs, consistent with many photoluminescence lifetimeand quantum efficiency reports of approximately 1 to 2 µs and several tomany tens of percent, respectively. Relating this to |µXG,0| was achievedby firstly relating |µXG,0| to the free-space spontaneous emission rate γXG,0via Fermi’s Golden Rule, then relating γXG,CQD+sol to γXG,0 with aid of theLorentz field factor. In this approach, we obtained:γXG,CQD+sol =√ǫsol∣∣∣∣ 32+ ǫCQD,nr(ωXG)/ǫsol∣∣∣∣2γXG,0 (3.7)=√ǫsol∣∣∣∣ 32+ ǫCQD,nr(ωXG)/ǫsol∣∣∣∣2 ω3XG|µXG,0|23πǫ0h¯c3(3.8)where ǫCQD,nr(ωXG) = (25.0+2.5−2.5)+ (1+1−1)i is the non-resonant CQD permit-tivity at ωXG (i.e. excludes contribution from the |X〉 ↔ |G〉 transition),which is based on calculations in [143], and ǫsol = 2.1+0.2−0.2 is typical for arange of solvents in which PbSe CQDs are commonly dispersed.The resulting values are |µXG,0|= 7+3−2 Debye and γXG,0 = 5+6−2×106 Hz.The corresponding in-bulk PbSe spontaneous emission rate, for nbulk ≈ 5and ǫCQD,nr(ωXG) comparable to bulk PbSe permittivity at ωXG [209], isγXG,bulk ≈ nbulkγXG,0 = 2+3−1×107 Hz, which is 10 to 200 times slower thanthe typically 0.5 to 2 GHz spontaneous emission rates of epitaxial InAs QDsin bulk semiconductor hosts [54, 116, 161]. The “intrinsic” dipole transitionmoments of the PbSe excitons are therefore on order 3 to 7 times smallerthan those of typical InAs QD excitons [29, 66, 197, 222].3.2 Power saturation of cavity-coupled CQD PLThis section describes the full model used to analyze the saturation behaviorof the PL from PbSe CQDs located at the antinode of an L3 photonic crystalmicrocavity, as described in Section 2.4. It includes a thorough treatmentof the electromagnetic environment (including excitation source scattering,79local radiative density of states at PbSe CQD locations, and depolarizationfactors), and exciton dynamics within the CQD.When comparing to related experiments using epitaxial InAs quantumdots in III-V host microcavities (e.g. [67, 68]), it is important to note (i) that,as discussed above, depolarization issues are not a factor in the III-V case,and (ii) the electronic/exciton dynamics at cryogenic temperatures in the III-Vs are much richer. In particular, for the epitaxial QD system, quantitativeexplanations of experimentally-measured emission spectra as a function ofcavity-exciton detuning, and excitation power, require explicit treatmentof acoustic phonon-scattering, rather than treating it phenomenologically,and do not require consideration of non-radiative recombination processes(e.g., see references [37, 91, 94, 123, 160, 182, 214, 231]). In contrast, roomtemperature experiments reported here involve solid-state formulations ofcolloidal PbSe CQDs with dephasing rates of tens of meV [85, 172], in excessof the cavity detuning, and quantum yields much less than unity [7, 63, 172,207]. We find it necessary to explicitly include non-radiative decay processesto explain the saturation behavior, and a phenomenological treatment ofphonon interactions is sufficient.3.2.1 Master equation modelA simplified Hilbert space shown schematically in Figure 3.2 was used tomodel the observed saturation behavior. A single exciton state, |X〉, repre-sents the low-energy, “brightest” component of the ground state manifold ofexcitonic states that is split by many factors in PbSe CQDs. This is the stateresponsible for exciting the cavity mode. Inclusion of more than 2 cavitymode Fock states did not change the calculated cavity photon population.A single higher-lying state, |P 〉, resonantly absorbs energy from the HeNeexcitation source and rapidly transfers it to the |X〉 state. In order to fit theobserved saturation behavior, and to be consistent with the small quantumyield of exciton emission from monolayers of PbSe CQDs on silicon surfaces,a non-radiative decay channel via state |Y 〉 was also included.The model system Hamiltonian consists of the bare Hamiltonian, H0,80Figure 3.2: Minimal Hilbert space necessary to accommodate ob-served saturation behavior: four states (including trap state)for the CQD subspace and two for the cavity subspace. Sig-nificant decay paths indicated by solid blue arrows, of whichsquiggly lines are radiative and the remainder non-radiative.Laser field of Rabi coupling frequency Ω “pumps” the |P 〉 state.The cavity is “fed” by coupling to the |X〉↔ |G〉 transition withelectric-dipole coupling strength g.electric dipole coupling of the excitonic transition to the cavity field, Hcav,and a continuous wave laser field resonantly coupled to the higher energyelectronic transition, Hpump:81H0 =∑ℓh¯ωℓ|ℓ〉〈ℓ|+ h¯ωcava†a (3.9)Hpump = h¯Ω( |P 〉〈G|+ |G〉〈P | )cos(ωpumpt) (3.10)Hcav = h¯g( |X〉〈G|+ |G〉〈X| ) (a†+a) (3.11)HS = H0+Hpump+Hcav (3.12)where ℓ indexes the CQD subspace, h¯ωℓ are CQD state energies, and a† isthe creation operator in the cavity subspace. Products with subspace unitoperators are implicit.We calculated the steady state density matrix ρ with the Lindblad-formmaster equation, which allows explicit inclusion of the population decay(γjk) and pure dephasing (γ′j) rates:dρdt=ih¯[ρ,HS ]+∑jk[DjkρD†jk−12(D†jkDjkρ+ρD†jkDjk)]+γcav[aρa†− 12(a†aρ+ρa†a)], (3.13)Djk =√γjk |k〉〈j| quantum dot population decay, |j〉 → |k〉(3.14)Djj =√γ′j |j〉〈j| quantum dot pure dephasing (3.15)To solve for the steady-state behavior, we first transformed these equa-tions to a picture with no explicit time dependence in the rotating waveapproximations for ωcav ≈ ωX −ωG = ωXG and ωpump ≈ ωP −ωG. The col-lection of steady state density matrix element equations dρ/dt= 0 was thencast into superoperator form, Lρv = 0, in which the steady state densitymatrix elements are components of the eigenvector of the zero eigenvalue ofthe superoperator L, and calculated via the inverse power method. Fromthe steady state density matrix we calculated the cavity population 〈a†a〉,82which is proportional to the observed cavity intensity emission.3.2.2 Model dielectric environmentThe model dielectric environment of the CQDs in the saturation experi-ment is shown in Figure 3.3. The total permittivity, ǫ(r,ω) = ǫL3(r,ω)+ǫCQDs(r,ω), consists of the silicon-host L3 photonic crystal cavity ǫL3(r,ω)(with backing silicon) and a close-packed hexagonal array of 45 CQDs on thecavity surface ǫCQDs(r,ω) with pitch varied from 6 nm to 8 nm. The CQDarrangement is based on electron microscope images of CQDs on silicon sur-faces that exhibit short-range hexagonal order, packed with a pitch withinthe range adopted in our model. The intrinsic dipole was then considered tobe located at the center of the centroidal CQD, at position rCQD. The L3cavity slab has a thickness of 198+4−4 nm, pitch of 420+4−4 nm, air hole radiusof 122+10−10 nm, and the two holes on the xˆ-axis are shifted away from thecavity centroid by 10+4−4 nm. The distance between the L3 cavity slab andbacking silicon is 1193+10−10 nm.3.2.3 “Simple” model parametersBefore calculation of the intrinsic dipole moment and other depolarization-sensitive quantities, let us establish the many “simple” model parametersthat are known already and are unaffected by depolarization specific to ourdielectric environment.The cavity mode frequency ωcav was taken directly from the PL spectra,and for data fitting we set the exciton transition energy h¯ωXG = h¯(ωX −ωG) = h¯ωcav. The pumped transition energy h¯(ωP − ωG) was set to theHeNe excitation photon energy, h¯ωpump = hc/633.0nm, where h is Planck’sconstant and c is speed of light in vacuum.The measured cavity Q of 3×103, along with ωcav, sets γcav=7×1010 Hz.CQD inclusion had negligible effect on the decay rate. The population decaytime γ−1PX from |P 〉 to |X〉 was taken to be 5 picoseconds, based on a varietyof measured and calculated values [13, 18, 25, 86, 156]. Other significantdecay parameters are described in the “fit parameter” subsection, below.83Figure 3.3: Model dielectric environment ǫ(r,ω) = ǫL3(r,ω) +ǫCQDs(r,ω). Nanocrystal array ǫCQDs(r,ω) on left, centered onthe L3 cavity surface. The computational volume for FDTDcalculations (see text) is restricted to the 3 µm cube centeredabout the centroidal CQD. The intrinsic “test” dipole is locatedat the center of centroidal CQD, position rCQD. The devicesilicon slab is surrounded by vacuum above and below, withbacking silicon 1.2 µm below.A pure dephasing rate of γ′X = 4.8×1013 Hz was taken from an analysisof PbSe thick film PL spectra [172]. The |Y 〉 state pure dephasing was takento be γ′Y = γ′X , but the exact value is neither known or consequential for ouranalysis. The ground state pure dephasing γ′G was assumed negligible. Forcompleteness (see “Laser-QD coupling Ω” subsection), a value of γ′P = 1014Hz was used in the simulations reported here, although our modeling resultsare independent of γ′P for a large range of γ′P , owing to its large value.3.2.4 Spontaneous emission rate γXG = γXG,ǫ(r)The spontaneous emission rate of an exciton associated with a CQD locatedwithin a hexagonally-packed array of CQDs on the L3 cavity surface (ourǫ(r) environment), into all electromagnetic modes except the cavity mode,γXG,ǫ(r), was calculated with the methods outlined in the previous section.84In doing so, we also (1) averaged γXG,ǫ(r) over all three dipole orientations,and (2) excluded the cavity mode contribution to γXG,ǫ(r), which is alreadyaccounted for in g, by considering only the power radiated at several cavitymode line widths above the cavity mode frequency (i.e. at ωcav+ δω). Theresult is essentially independent of δω, and equalsγXG = γXG,ǫ(r) (3.16)=〈Prad,ǫ(r)(ωcav+ δω)〉orientationPrad,0(ωcav+ δω)γXG,0 (3.17)= 4+5−2×105 Hz (3.18)Thus the spontaneous emission rate of excitons in this complex dielectricenvironment coincidentally turns out to be very similar to isolated CQDs insolution (γXG,CQD+sol). A decomposition of influences on the spontaneousemission rate is as follows: taking the CQDs out of solution and into airincreases the dielectric contrast, resulting in a smaller spontaneous emissionrate by a factor of 4 to 7 (depending on the originating solvent). In con-trast, despite the presence of the photonic band gap, the L3 cavity - evenexcluding the cavity mode - increases an otherwise free-space spontaneousemission rate by a factor of ∼ 4, when averaged over three orthogonal dipoleorientations. The spontaneous emission rate enhancement due to the L3slab, excluding the cavity mode and CQD array, is presented in more de-tail in Figure 3.4. Such behavior at the surface of a uniform, hexagonal,silicon-host photonic crystal has been previously reported [112].3.2.5 Cavity-QD coupling gGiven the intrinsic dipole transition moment, calculation of the cavity-QDcoupling g = µXG,0 ·Evaccav(rCQD)/h¯ was reduced to calculation of the cavitymode vacuum electric field at the CQD position, Evaccav(rCQD). This too wascalculated using FDTD Solutions, here by exciting the cavity mode in thefull ǫ(r) dielectric environment, letting all electric fields except the cavity85Figure 3.4: Spontaneous emission rate of a point dipole source of fre-quency ωcav+δω, for positions along the zˆ-axis of the L3 cavity,excluding the cavity mode and CQD array, for electric dipoleorientations along axes xˆ, yˆ, or zˆ (see text and orientation def-initions in Figure 2.1). All values normalized to the free-spacespontaneous emission rate γXG,0.mode field Ecav(r) decay entirely, then evaluating:|Evaccav(rCQD)|=√√√√√h¯ωcav2ǫ0∫dr ǫ(r)(|Ecav(r)||Ecav(rCQD)|)2 = 3+1−1×104 V/m, (3.19)This expression is simply an application of the amplitude of the electricfield operator for a photon, E= (h¯ω/2ǫV )1/2. Integration was over the entirecomputational volume, and the value is consistent with the value from acorrected formula for non-Hermitian modes [118]. CQD inclusion has an86insignificant effect on the cavity mode volume. The cavity-CQD couplingstrength is g = 6+4−2× 109 Hz. The scattering rate into the cavity mode isRcav = g2/γ′X = 8+13−4 ×105 Hz.3.2.6 Laser-QD coupling ΩDirect calculation of Ω = µGP,0 ·Epump,ǫ(r)(rCQD)/h¯ is impossible, as weknow of no way to directly determine the laser-pumped dipole transitionmoment µGP,0 from experimental data. However, the saturation behaviorof interest depends not on Ω alone, but instead on the absorption rate R ofthe CQD, related to Ω and the electric field intensity inside the CQD byR≈ Ω2γ′P=|µGP,0|2h¯2γ′P|Epump(rCQD)|2 (3.20)Thus, as can be seen through this closed-form expression and as con-firmed for our simulations, neither a specific value of Ω or γ′p was necessaryfor simulating the saturation behavior. Instead, knowledge of the absorp-tion rate R, particularly for a calculable laser field amplitude at the intrinsicdipole location, is adequate.The in-solution absorption rate per CQD per incident electric field in-tensity at our pump wavelength of 633 nm was obtained from Moreels et al.[141] by way of their reported absorbance at 400 nm, A400nm = 1.246 cm−1,of a known concentration CQ−PbSe = 0.32 µM of PbSe CQDs, and an ab-sorption spectrum showing that the absorbance at 633 nm relative to theabsorbance at 400 nm is A633nm/A400nm ≈ 0.2. In terms of the laser fieldamplitude inside the CQD, |Epump(rCQD)|, this absorption rate per CQD isR=A400nmCQ−PbSeA633nmA400nmh¯ωpump√ǫsol2η0∣∣∣∣2+ ǫCQD(ωpump)/ǫsol3∣∣∣∣2|Epump(rCQD)|2 (3.21)where η0 is the electromagnetic wave impedance in free space (equal to in-airvalue within our uncertainties), and ǫCQD(ωpump) = (1+ i)(25.0+2.5−2.5) is theCQD permittivity evaluated at the pump HeNe wavelength.To finalize application of these equations to our system, we needed to87relate the laser field amplitude inside the CQD for our full ǫ(r) dielectricenvironment, |Epump,ǫ(r)(rCQD)|, to the measured power, P0, of our HeNeexcitation source. This was accomplished by (1) FDTD simulations fromwhich we extracted |Epump,ǫ(r)(rCQD)|/|Epump,0|, where |Epump,0| is the in-cident laser field amplitude, and (2) relating |Epump,0| to P0 via the Gaussianbeam profile and our measured minimum 1/e2 beam radius W0 = 1.0 µm,|Epump,0|2/2η0 = 2P0/πW 20 . Combining, we obtained:Ω =√γ′PR (3.22)=√√√√2√ǫsol A400nmCQ−PbSe A633nmA400nm γ′PP0h¯ωpumpπW 20∣∣∣∣2+ ǫCQD(ωpump)/ǫsol3∣∣∣∣ |Epump,ǫ(r)(rCQD)||Epump,0|= 3+1−1×105√γ′PP0 (3.23)for P0 in Watts and γ′P and Ω in Hz. The complex dielectric environmentresults in a highly structured HeNe scattered wave distribution, seen inFigure 3.5, necessitating computation. Within the estimated environmentuncertainties, this wave distribution and the laser coupling Ω is insensitiveto the photonic crystal air hole radius and the distance between the L3slab and the backing silicon. Environment parameters bearing directly andsignificantly on the laser coupling g include the L3 slab thickness, photoniccrystal pitch, and CQD array pitch, which account for approximately ≈±20%, ≈±5%, and ≈±15% uncertainties in Ω, respectively.3.2.7 Fit parameterIn previous subsections, we established the pump rate and rates for the tworadiative decay paths, i.e. |X〉 → |G〉 and through the cavity. Of all themodel parameters, the two not addressed in previous subsections are bothassociated with the non-radiative decay path, i.e. γXY and γY G. Neither ofthese are known for our particular CQDs beyond the modeling efforts here.However, the limit of γXY ≫ γXG+Rcav enables a unique determination ofthe non-radiative decay time τnon−rad = γ−1Y G+γ−1XY for a particular dielectricenvironment, and we chose this to be our sole fit parameter to characterize88Figure 3.5: Intensity profiles of HeNe excitation field, as modulatedby the L3 cavity ǫL3(r). Gaussian laser field was injected alongthe zˆ axis towards increasingly negative z, indicated by blackarrow. Air-silicon interfaces lined in black. (left) Profile severalnanometers above the slab surface, the plane containing thePbSe CQDs. (right) Profile in the x= 0 plane.the non-radiative decay path (results next section). Drawing from γXG =4+5−2×105 Hz and Rcav = 8+13−4 ×105 Hz as presented in previous subsections,the limit in which we extract τnon−rad equates to γXY ≫ 1.2+1.8−0.6×106 Hz.This enabling limit is motivated by (1) measurements indicating lowquantum yields of exciton emission from monolayers of PbSe CQDs on un-patterned SOI wafers, and (2) FDTD simulations indicating Rcav + γXGcalculated for our textured dielectric environment is not significantly largerthan the spontaneous emission rate of CQDs in a monolayer on unpatternedSOI. These measurements consist of (1) published [172] thick-film integratedPL versus temperature in which the room-temperature PL is observed tobe a factor of 10 lower than the low-temperature PL, thus establishing amaximum 10% quantum efficiency at room temperature, and (2) the PLlifetime measurements and modeling of non-radiative relaxation in monolay-ers of PbSe CQDs on unpatterned SOI wafers presented in this dissertation,shown to be several times faster than in thick films.893.2.8 Saturation modeling resultsAttempts to exclude the non-radiative decay path were unsuccessful in ac-commodating the observed cavity-coupled saturation behavior, as seen inFigure 3.6, in which the best (minimum χ2) 3-state fits are inadequate. Thebest 3-state fits are presented for the smallest and largest saturation powersconsistent with the model parameters. The smallest 3-state fit saturationpower is still 5 times larger than the observed saturation power. The fourthstate |Y 〉 can, however, accommodate the lower observed saturation powerif it possesses a sufficiently long lifetime, i.e. if it serves as a non-radiative“population-trapping” state, as seen in Figure 3.6, for which the 4-state fit isadequate. Consequently, minimally four CQD states are necessary to modelour system.Figure 3.6: Best (minimum χ2) fits to cavity-enhanced photolumi-nescence for only three electronic levels (left), i.e. without anon-radiative state, and for four electronic levels (right), i.e.including a non-radiative “trap” state.Over our model parameter space, including all estimated uncertainties,we find the τnon−rad values required for a 4-state fit are τnon−rad ≈ 3+3−2 µs.Further, because τnon−rad = γ−1Y G+γ−1XY and γXY ≫ 1.2+1.8−0.6×106 Hz, as es-tablished in the previous section, our fit parameter approximately coincides90with the trap state lifetime, τtrap ≡ γ−1Y G. Thus the trap state lifetime con-sistent with our model parameters is τtrap ≈ 3+3−2 µs.The span of τtrap is dominated physically by (1) uncertainty in the CQDpacking density, (2) uncertainty in the L3 slab thickness, and (3) stateduncertainty in the solvent permittivities. The first two of these three have adirect and significant bearing on the pump field inside the CQD, so for thepurpose of graphically representing the influence of these factors on the trapstate lifetime, it is convenient to define a plot parameter directly relatedto the pump field inside the CQD. We defined an effective depolarizationparameter, DPF , that is equal to the pump field inside the CQD (for ourfull dielectric environment), normalized to the pump field in the CQD foran otherwise isolated CQD in free space, for a fixed pump power:DPF =|Epump,ǫ(r)(rCQD)||Epump,QD(rCQD)| =|Epump,ǫ(r)(rCQD)||Epump,0|∣∣∣∣ 32+ ǫCQD(ωpump)∣∣∣∣−1(3.24)Figure 3.7 contains the plot of τtrap versus DPF . Variation of τtrap withDPF is primarily due to uncertainty specific to our dielectric environment,e.g. relating to the photonic crystal cavity or CQD array, whereas variationof τtrap for a fixed value of DPF is attributable primarily to the assumed un-certainty in the solvent permittivity that entered into our model through theestimated absorption rate R, and radiative lifetime γ−1XG,CQD+sol = 3+1−1 µs,of the CQDs in solution.The fact that the effective depolarization parameter is near unity reflectsthe fact that, despite the multitude of significant depolarization mechanisms(e.g. CQD array, SOI platform, L3 cavity), the laser field inside the CQDis comparable to the laser field inside the same CQD isolated in vacuum forthe same pump intensity. This is a coincidence of this particular dielectricenvironment, and the contributing factors can be decomposed as follows:the SOI platform alone results in a decrease of the pump field in the CQDby a factor of ≈ 5 (relative to a free-space pump field), the L3 cavity textureincreases the pump field by a factor of ≈ 3 (relative to a bare SOI substrate),and the surrounding CQD array increases the pump field inside the CQDby another factor of ≈ 1.4; compounding these results in a value of ≈ 0.8 for91Figure 3.7: Trap state lifetime τtrap = γ−1Y G required to fit the data.Parametrization of τtrap is in terms of the “effective depolariza-tion”, DPF , which is defined in-text (see Equation 3.24) and isequal to the laser field inside the CQD in the full model dielec-tric environment relative to the laser field inside the same CQDin vacuum. Variation of τtrap with DPF is dominated by un-certainties in parameters specific to our dielectric environment(photonic crystal cavity, CQD array), whereas variation of τtrapfor a particular DPF is dominated by parameter uncertaintynot specific to our dielectric environment (e.g. solvent permit-tivity from solvent-based CQD properties). Points are sampledfrom the model parameter space.the central set of parameters. Note that non-inclusion of any of these factorswould result in a pump field amplitude outside our estimated uncertainties.These modeling results are consistent with the power dependence datapresented in Figure 2.6E, in which it was found that suitable excitationpower scaling resulted in identically shaped saturation behavior of the92cavity-coupled and bare SOI PL. Although not presented in this disser-tation, other in-lab data suggests this scaling holds for HeNe excitation too.This highlights the accuracy and necessity of including scattering effectsat both the excitation and emission wavelengths in order to quantitativelydescribe the PbSe behavior in diverse dielectric environments.3.2.9 Saturation modeling conclusionsExtensive quantitative modeling of the cavity-coupled emission saturationhighlights the importance of dealing with large depolarization factors, orlocal field corrections, in this system, as compared to the more commonlystudied InAs epitaxial CQD systems. The conclusion drawn from the mod-eling is that non-radiative trap states retain excited excitons, and preventthem from returning to the ground state with a time constant on the orderof ∼ 3 µs. This occurs when the rate γXY at which excitons decay to thisnon-radiative state far exceeds their total radiative decay rate to both thecavity and radiation modes, i.e. γXY ≫ 1× 106 Hz. These conclusions areconsistent with low quantum yields observed for exciton emission from PbSeCQDs on silicon surfaces, in vacuum.3.3 Modeling time-resolved decay of CQDs invarious formulationsThe time-resolved results presented in Section 2.5 clearly indicate excitondecay is faster for sub-monolayers than for drop-casts, and faster for drop-casts than for in-solution. However, without modeling of the influence ofthe dielectric environment on the radiative lifetime, or relatively challengingabsolute quantum efficiency measurements, it is not clear from these resultsalone whether the large differences in exciton decay rates is due to changesin radiative rates, non-radiative rates, or some combination thereof. In thissection, we use the depolarization modeling methods described earlier in thischapter to calculate the influence of each CQD formulation on the radiativedecay rate of embedded (“intrinsic”) dipole emitters, then combine themwith the time-resolved results to make inferences about both non-radiative93and radiative decay in each formulation.Direct measurements of the relative radiative τrad and non-radiativeτnon−rad contributions to the total PL decay time τPL, related by 1/τPL =1/τrad + 1/τnon−rad, are challenging to measure in film formulations, butare available for the CQDs used in this dissertation when dispersed in sol-vent. This total decay time in solution, τPL = 1.0 µs, is similar to solution-based decay times reported by others. Direct measurements of the quan-tum yield from similarly prepared PbSe quantum dots using an integratingsphere, and our own measurements with an integrating sphere, suggest thequantum yield in solution is 30+5−5%. The measured net lifetime and thisquantum yield therefore suggest that the radiative lifetime in solution isτrad = 3.3+0.3−0.3 µs, and the corresponding non-radiative recombination timeis τnon−rad = 1.4+0.2−0.2 µs.3.3.1 Dielectric model accounting of radiative decayThe radiative decay time of CQDs in a densely packed, three-dimensional(3D) array should be considerably different than that of isolated CQDs ina low-index solvent, due to depolarization effects associated with the large(Re(ǫ) ≈ 23) dielectric constant of the CQD. CQDs in solvent and in thinfilms on silicon (and SOI) were modeled as described in the previous section(sans photonic crystal). The drop-cast film was modeled in FDTD simula-tions by a sub-micron cube of hexagonally close-packed (7 nm pitch) spher-ical nanoparticles of 5 nm diameter in an oleic acid interstitial of refractiveindex noa ≈ 1.45, with the remainder of the film modeled by a homogeneousmedium of permittivity equal the average permittivity of the nanoparti-cle/interstitial region, all adjacent to a silicon substrate. The power radiatedby test dipoles located at the center of various CQDs in the close-packedarray is approximately three times that for isolated CQD in hexanes, whenaveraged equally over three orientations, one perpendicular to the substrateand two parallel to the substrate.The same numerical estimate (test dipole, radiated power, three orien-tation average) for the radiative decay rate of a test dipole located (a) on94an isolated silicon surface or (b) in a 2D close-packed arrays of CQDs on asilicon surface suggests that for these on-silicon environments, the radiativedecay rate is only increased over the solvent value by at most ≈ 50%. The2D close-packed array led to an at most ≈ 20% increase on the radiativedecay rate of any particular CQD in the array relative to the bare siliconsubstrate. For comparison, radiative decay rates of an isolated CQD on anyof bare silicon, bare SOI, or at the center of the L3 cavity surface (away fromthe cavity resonance, as discussed in the previous section) were all similar.Similarly, the decay rates of a CQD in a close-packed array on any of thesethree substrates were all similar.3.3.2 Radiative efficiency from time-resolved emission anddielectric modelingFrom these simulation results, we deduce that the quantum yield QY =(1/τPL)/(1/τrad+1/τnon−rad) in the drop-cast sample is ≈ 20%, with a cor-responding non-radiative decay time of ≈ 250 ns. This follows from therelationship between the total PL decay time measured τPL = 190 to 200 nsas presented in Figure 2.9, and the contributions from radiative and non-radiative decay described earlier in this section, for which the FDTD resultsindicated the radiative decay rate contribution increased by a factor of ≈ 3compared to in-solution. The non-radiative decay rate is thus ≈ 6 timeslarger than in-solution.We also conclude that the PL from the dip-coated samples, characterizedby the both the measured time constants of ≈ 90 ns and ≈ 135 ns presentedin Figure 2.9, is completely dominated by non-radiative decay processes.The average quantum yield for the dip-coated samples is thus ≈ 4% to 10%.The non-radiative decay rate is thus a factor of ≈ 1.2 to 2.8 larger for CQDsisolated on a silicon surface relative to in a thick film (or ≈ 7 to 16 relativeto solution).To develop an appreciation for these quantities, note that this dip-coatedquantum yield, when compared with the ≈ 20% estimated quantum yieldsin the thick 3D film, is consistent with the ≈ 3000 times reduction in overallsignal strength from the two sample types: the number of CQDs excited by95the 658 nm laser in the random close-packed (fill fraction ≈ 63%) emulsivefilm is estimated to be about 500 times larger than for the 2D film (estimatedto have ≈ 7% average coverage), assuming an absorption depth in the thickfilm at 658 nm of ≈ 250 nm. The remaining difference in signal strength isthen, within uncertainty, the ratio of quantum yields.Additional notes include (a) we find that solvent rinsing of the dip-coated samples using hexanes or TCE, before placing them in the cryostat,dramatically reduces the quantum yield of the sub-monolayer samples, and(b) the non-radiative decay time for CQDs in the thin film formulation,using the 1.4+0.2−0.2 µs value in solution and ≈ 7 to 16 increase in non-radiativedecay, is ≈ 80 to 200 ns.Also, recall the simplifying assumption made in Subsection 3.2.7 in re-gard to the non-radiative decay time calculation in the saturation modeling,namely that the decay rate from the exciton state to the trap state, de-scribed by the rate γXY , was much faster than the total radiative decayrate, γXG+Rcav = 4+5−2× 105 Hz+8+13−4 × 105 Hz = 1.2+1.8−0.6× 106 Hz. Thisassertion is directly supported by the results in this section, in which - bycombining time-resolved PL data and FDTD modeling of a thin-film CQDformulation - we see that the non-radiative decay rate of 1/(80 to 200 ns) = 5to 13 MHz is at least several times faster, and as high as 20 times faster,than the 1.2+1.8−0.6 MHz total radiative decay rate of CQDs in the L3 cavitystudied in the saturation modeling.3.3.3 DiscussionFrom these results we deduce that the non-radiative decay rate of the CQDin the close-packed 3D emulsive films is increased by a factor of ≈ 6 com-pared to in-solution and further by a factor of ≈ 1.2 to 2.8 when the CQDsare more isolated, on a silicon surface. We attribute this increase in non-radiative decay rate to a degradation in surface passivation when there areno mobile ligands available to mend defects. An alternative interpretationwould attribute the degradation to increased oxidation of the solid statedispersions. While this is a possible contributing factor, we note that for96both solid formulations, samples are stable for months when held in vacuumenvironments of < 10−3 Torr. If oxidation is a factor, it would have to occur,for the thick films, during the brief (< 20 min) casting under nitrogen flowor, for the thin films, during the likewise brief (< 3 min) presence in theglove box of low but potentially non-negligible air content. However, as wedo not observe significant changes in PL yields for various sample durationsin the glove box, we suspect that ligand damage is the main source of theincreased non-radiative decay rate in the 2D films. This is also consistentwith the deleterious effects of solvent rinsing the sub-monolayer samples.Various methods for better protecting the excitons may help to reduce thedegradation in quantum yield on silicon surfaces.3.4 Air exposure dependence of exciton kineticsThe most prominent example of PbX CQD chemical sensitivity is exposureto air, believed to be dominated by the influence of oxygen in the air [207].Prior to the work in this dissertation, it was known that emission of PbXCQDs in solution, in ambient (air) conditions, will diminish and blueshift,with the blueshift and x-ray diffraction results consistent with oxidation ofthe CQD surfaces [43, 57, 93, 207, 210, 211]. Enormous efforts have been putforth to decrease deleterious sensitivity of CQDs to air exposure, includinguse of alternative ligands, inorganic shells, post-formulation treatments, andsynthesis modifications [16, 43, 46, 57, 58, 93, 113, 162, 187, 210].Understanding the effect of air at a microscopic level has been con-founded by a wide variety of results. One report in 2007 found that steady-stated integrated photoluminescence at room temperature, for CQD emul-sions (also referred to as quantum dot solids, or drop-cast films) in vacuum,recovers from temporary exposure to air [207]. Studies from 2011 [43] and2012 [93] revealed markedly different photoluminescence than seen in theprior decade on PbX CQDs, for PbX CQDs synthesized in the absence ofair, as opposed to synthesis in air. This behavior included (a) clear evidenceof two emission peaks, one thermally activated around 100 K to 200 K, asopposed to the single or nearly single peak observed in nearly all other stud-97ies, and (b) insensitivity to air exposure when an alkyl-based (alkylselenide;not the typical oleic acid) ligand was used. In these studies, air exposureof the common oleic-capped CQDs tended the temperature-dependent PLqualitatively towards more commonly obtained results, but found effects ofair exposure on these samples to be irreversible, as opposed to the previ-ously reported reversibility of air exposure of oleic-capped PbX CQDs atroom temperature [207].Figure 3.8: Integrated PL data sets (black squares), normalized totheir maximum values, along with best-fit model yield curves(calculated below) in solid red and corresponding model PLcontributions from each of two possible emissive states or clus-ters of emissive states in dotted and dashed lines, respectively.Samples series A and B are from work published in references[43, 93], and sample series C and D were already described inSection 2.6 but reproduced here for convenient comparison. Ta-ble 3.1 contains descriptions of these samples.These results prompted us to carry out further temperature dependentstudies of CQD PL from thick films as a function of air exposure, as reportedin Chapter 2. This data was presented in Section 2.6 and is reproduced alongwith the data from [43] and [93] in Figure 3.8 and described in Table 3.198for convenient comparison. This section compares our measurements oftemperature dependent integrated PL strength under various air-exposureconditions with those reported by Chappell et al. and Hughes et al. Thekinetic model used to analyze all of this combined data is then described,and the results of that analysis are used to infer similarities and differencesbetween the two formulations of nominally very similar PbSe CQDs.Key Description (air exposure extent and originating publication)A1 No air exposure during CQD synthesis or as drop-cast, oleic- ligands, Hughes et al. [93]A2 No air exposure during CQD synthesis or as drop-cast, alkyl- ligands, Hughes et al. [93]Distinct drop-cast from A1.B1 No air exposure during CQD synthesis or as drop-cast, Chappell et al.[43] Same CQD drop-cast sample as traces B2 through B5.B2 1 minute of air exposure as drop-cast, none during CQD synthesis, Chappell et al. [43]B3 30 minutes of air as drop-cast, none during CQD synthesis, Chappell et al. [43]B4 2 hours of air exposure as drop-cast, none during CQD synthesis, Chappell et al. [43]B5 12 hours of exposure as drop-cast, none during CQD synthesis, Chappell et al. [43]B5 12 hours of exposure as drop-cast, none during QD synthesis, Chappell et al. [43]C1 No air exposure as drop-cast, some during CQD synthesis, Qiao et al. [172]C2 No air exposure as drop-cast, some during CQD synthesis, Qiao et al.[172] Distinct drop-castfrom C1.D1 No air exposure as drop-cast, some during CQD synthesis. Same CQD drop-cast sample astraces D2 and D3.D2 30 minutes exposure as drop-cast, some during CQD synthesis, measured after 2 hours invacuumD3 2 hours exposure as drop-cast, some during CQD synthesis, measured after 48 hours in vacuumTable 3.1: PbSe CQD thick film sample descriptions, for integratedPL traces plotted in Figure 3.8. Samples from our lab, alreadypresented in Section 2.6, are reproduced here for convenient com-parison to samples from other labs. “Alkyl-” for studies men-tioned here refer to alkylselenide [93].The integrated CQD PL reported in Chappell et al. and Hughes et al.,corresponding to series A and B in Figure 3.8 and described in Table 3.1,is marked by either strong non-monotonicity and/or explicit increases withincreasing temperature. This is in spite of nominally similar CQD synthesesfor samples A1 and B1 through B5 and no air exposure for samples A1,99A2, and B1. Non-monotonic PL yield persists even after their samples areexposed to a controlled air environment from minutes to hours. This behav-ior is attributed to PL contributions from two distinct radiative states atdifferent energies in these CQD samples, consistent with spectral line shapeanalysis, at least in dilute glass-encased samples, that reveals two peaksseparated by several tens of meV, over a range of temperatures.In order to limit the free parameters in the kinetic model presented earlierin this chapter, but be general enough to accommodate all kinetics we’vementioned, we make two assumptions: (i) there are at most two states, ormore generally two clusters of closely spaced states, that have significantoscillator strengths, and (ii) the net non-radiative decay rate from the entiremanifold can be fit using a temperature-dependent function that does notinclude any level-specific parameters.These assumptions are schematically summarized in the energy leveldiagram of Figure 3.9. Non-radiative decay in our model is generally fromthe collective manifold of excitonic states instead of pathways specific tostates within the manifold. Assumption (i) is chosen to be consistent withto-date observations of thick film PbSe PL, but can be relaxed if futureworks reveal otherwise. Assumption (ii) does not preclude a more state-specific interpretation of whatever temperature dependent function is fit tothe non-radiative decay rate.With reference to Figure 3.9, and to Equation 3.1 the two clusters ofemissive states, A and B, have radiative decay rates {γA} and {γB} re-spectively, and the average or centroid energy of the B state cluster ǫB lies∆ǫBA above the average or centroid energy ǫA of the A state. The radiativeemission rate is thus approximated as:gr =NAγAe(ǫA−µ)/kBT +1+NBγBe(ǫB−µ)/kBT +1(3.25)= nAγA+nBγB , (3.26)where the overline denotes the net or average value of the correspondingquantity associated with the A or B cluster of emissive states.100Figure 3.9: Modeled energy level arrangement. Levels A and B are inthermal quasi-equilibrium and populated by pumping of higher-lying levels at a rate gex. They respectively consist of NA andNB states of average radiative decay rates γA and γB . Thegeneral non-radiative decay Γ, the nature of which is describedin detail in-text, is not specific to level A or B for the purposesof this kinetic modeling, and is indicated by the dashed arrow.The non-radiative contribution in Equation 3.2, denoted by gnr, isgnr =∫ ǫmaxǫminΓnr(ǫ,T )f(ǫ)e(ǫ−µ)/kBT +1dǫ. (3.27)Thus the net PL yield, YPL, which is also proportional to the observed PL,is of the form:YPL = gr/gex (3.28)=1+ NBγBNAγA e−∆ǫBA/kBT1+ NBγBNAγA e−∆ǫBA/kBT + gnrNAγAe−(ǫA−µ)/kBT, (3.29)where we have taken the Maxwell-Boltzmann limit of the Fermi-Dirac distri-101bution function. The model was solved more generally, but the experimentalexcitation conditions and model results are all consistent with this Maxwell-Boltzmann limit.Using Equation 3.27 in the Maxwell-Boltzmann limit, the last term inthe denominator of Equation 3.29 can be re-expressed as a normalized netnon-radiative decay rate,g′nr =gnrNAγAe−(ǫA−µ)/kBT(3.30)=1NAγA∫ ǫmaxǫminΓnr(ǫ,T )f(ǫ)e−(ǫ−ǫA)/kBTdǫ. (3.31)Excellent fits of the functional form ηYPL, for temperature-independent con-stant η, to all data sets were found for g′nr set equal to the sum of N Arrhe-nius terms, i.e.:g′nr =N∑j=1Γ′je−∆Ej/kBT , (3.32)for N , ∆Ej, and Γ′j dependent upon sample type, but in all cases only 1 or2 non-radiative pathways are needed.By modeling the manifold’s net non-radiative decay using Equation 3.32,the only influential state energy for the purposes of our fitting methodol-ogy is that of the B state cluster, relative to that of the A state cluster,i.e. ∆ǫBA; energies ǫA and ǫmin become irrelevant. Individual terms inEquation 3.32 have no specific association with the exciton states in themanifold: any one term could in principle represent some combination of athermal occupancy factor for a particular state (bright or dark) and an as-sociated non-radiative decay rate, with the implication that there are threeclusters of states through which most of the non-radiative recombination oc-curs. However, there are no such attributions implied by this more generalfunctional fit.1023.4.1 Fit methods and extracted parametersExtracted parameter values are plotted in Figure 3.10. In those plots, avertical bar for a particular parameter and particular sample represents therange of that parameter value for which there exists a complimentary set ofparameters such that the model fit satisfies χ2−min(χ2) ≤ 4, where χ2 =Σ(observed−model)2/σ2, “observed” is the observed PL, “model” is themodel PL in the Maxwell-Boltzmann limit (ηYPL for YPL of Equation 3.29),σ= 0.02 max(IPL), and min(χ2) is evaluated at the global best fit, obtainedaccording to the procedures described below. The number of non-radiativepathways used to fit to any particular curve was chosen such that min(χ2),normalized to the number of data points for that curve, was less than 3. Thisthreshold was found to admit best fits that captured qualitative behavior ofall the sample curves, especially relating to the effects of air exposure.The sole constraint imposed upon the parameters is an upper limit of 80meV for ∆ǫBA, based on the spectral range over which the PL was integrated,and allowing for possible differences in the Stokes shifts associated with thetwo radiative levels in sample series A and B. Otherwise, the parametersearch domains correspond to the plotting ranges in Figure 3.10.The first segment of our best fit algorithm involves (1) sampling a set ofparameters logarithmically from the parameter search domain, (2) applyingthe Levenberg-Marquardt algorithm with this set of parameters as an ini-tial condition to determine the local best-fit parameters, (3) repeating (1)and (2) a total of 103 times, and (4) associating the best fit of these localbest fits with the global best fit. This global best fit was corroborated viaapplication of local minimization to a parameter search domain grid (thelatter contrasted with random sampling of the parameter search domain).The logarithm of the likelihood function was found to be quadratic in mostparameters near the best fit points.Red lines in Figure 2.10 are the model curves corresponding to the bestfit parameters found by this procedure. Dotted and dashed lines are plotsof the individual model A state and B state contributions from each statefor the same best-fit parameters.103NBγBNAγA100101102103104∆ǫBA0255075100Γj ’10010210410610310210110−110−2∆EjA 1 A 2 B 1 B 2 B 3 B 4 B 5 C 1 C 2 D 1 D 2 D 3 Figure 3.10: Subscript j indexes the non-radiative decay pathways,e.g. as indexed in Equation 3.32. Bars represent the ranges ofparameter values that, upon substitution into Equation 3.29,using Equation 3.27, generate or nearly generate the modelcurves in Figure 2.10. Rates are normalized as described in-text (leading up to Equation 3.32), and energies are in meV.Sample labeling is as in Figure 2.10 and Table 2.1. Parameter∆ǫBA is restricted from above to 80 meV for reasons describedin-text. Rates sufficiently small to render their correspondingenergies meaningless are omitted, along with those energies.104The second segment of our fit routine - generation of the vertical pa-rameter bars in Figure 3.10 - consisted of (5) dividing up each parametersearch domain into a set of many narrow subdomains, (6) restricting, pa-rameter by parameter of a particular sample, that parameter value to one ofthose narrow subdomains, (7) sampling a complimentary set of parameterslogarithmically from the large parameter search domain, (8) applying theLevenberg-Marquardt algorithm to determine a local best fit, (9) repeating(7) and (8) at total of 102 times, (10) identifying the best fit of those localbest fits, (11) checking to see if χ2−min(χ2) ≤ 4 is satisfied for the bestof those local best fits, and (12) repeating steps (6) through (12) for everyother narrow subdomain. The vertical bars in Figure 3.10 are lines thatextend from the minimum to maximum parameter values with which someχ2−min(χ2)≤ 4 exists, as found in steps (5) through (12).Figure 2.10 indicates that good quality fits to the data are obtainedusing the Maxwell-Boltzmann limit of the model. This limit should applyonly when gex/NAγA≪ 1, in which case the results are independent of gex.We estimated gex for both our data sets and those of Chappell et al. usingmeasured laser powers and spot sizes, along with absorption coefficients fromthe literature [141]. The spontaneous emission rate of the lower emissivestate was estimated from lifetime measurements of our drop cast films anddielectric modeling we previously employed [73]. For both our samples andthose of Chappell et al., we estimate gex/NAγA ≪ 10−1. Furthermore, ifgex is increased to the point where the Maxwell-Boltzmann approximationbreaks down, it becomes very difficult to fit any data set (impossible in thestrongly degenerate limit).3.4.2 ResultsWith reference to the parameter summary in Figure 3.10, the most signifi-cant difference between the various samples is that high-quality fits requiredNBγB/NAγA ≫ 1 for all Chappell et al. and Hughes et al. samples, andNBγB/NAγA ≪ 1 for all of our samples. This is consistent, in the formercase, with the prominent mid-temperature increase in PL and double-peaked105mid-temperature spectra, and in the latter case, with our observation of onlya single emission peak within the few-meV resolution of previously reportedspectra [172]. Also, although a trend in NBγB/NAγA with air exposureis admissible, any such trend does not follow necessarily from our kineticanalysis, and it is further clear that increasing air exposure does not trendNBγB/NAγA in their samples towards the value for our samples.Fits require the A-B energy separation for series A and B samples tobe ∆ǫBA ≈ 55 meV to 80 meV. It should be noted that the ∆ǫBA valueobtained from fits to the no-exposure data agrees reasonably well with theseparation of the emission lines in the solution spectra, but not in the dropcast samples. This is to be expected since thermalization of the excitonpopulations is known [172] to have a strong influence on the temperaturedependent Stokes shift of the peak PL emission energy, while there shouldbe minimal effects of thermalization on the spectra obtained in a dilutesolution, where the Fo¨rster interaction strength is negligible.For all samples that were not intentionally exposed to air, the integratedPL can be fit assuming only a single non-radiative pathway. The associatedparameters of this non-radiative pathway (an activation energy around a fewtens of meV and normalized prefactor on the order of several to a few tens)are quite similar for the unexposed sample from Chappell et al. (B1) andour unexposed samples (C series and D series excluding D2). Non-radiativedecay in series A samples is consistent with a single non-radiative pathwaywith a considerably lower activation energy. Without information regardingthe absolute quantum yield in the case of series A samples, it is not possiblefrom the fitting procedure to separate small differences in assumed activationenergy and the corresponding prefactor for this single non-radiative decayprocess (hence the unbounded arrows for series A samples). Introductionof a second sub-10 meV non-radiative pathway increases fit quality for theChappell et al. unexposed sample (B1), but the difference in fit quality issmall. The slight increase in integrated PL at low temperatures in the A2sample is not captured with our model, but a third, relatively dark level,just slightly below the A level in energy, could be introduced to capture thisbehavior.106Samples intentionally exposed to air (B2 through B5 and D2) absolutelyrequire the inclusion of two non-radiative pathways for adequate fits. Oneof these new pathways has a low (sub-10 meV) activation energy, with acorresponding prefactor in the range of 1 to 10, indicated by the red bars inFigure 3.10. In our air exposed sample (D2), the parameters associated withthe second non-radiative pathway are not dramatically different than beforeair exposure, whereas in the case of samples B2 through B5, the secondpathway has a very high activation energy (> 100 meV), and high normalizedprefactor (100’s of thousands). There is no indication of the need for a highenergy pathway in any of the unexposed, or our air exposed samples. Wenote that while the low-energy non-radiative pathway is common amongstall air exposed samples, Chappell et al. report irreversibility of this airexposure effect for their samples, in stark contrast to the reversibility of theimpact of our air exposure (see sample D3 compared to D1 and D2). Finally,we note that inclusion of a third non-radiative pathway with an activationenergy several tens of meV increases the quality of fit for the B2 through B5samples, but again, the improvement is minor.Regarding phonon-mediation of non-radiative decay, Chappell et al. andHughes et al. assumed a Nph-phonon absorption functional form for theirlow-energy, non-radiative pathway, [43, 93] and they reported fits suggestedNph = 4+2−2. In cases where present, if we replace the several to ten meVnon-radiative Arrhenius pathway (Γ′e−∆E/kBT ) with a one-phonon emissionfunctional form Γ′ph (1− exp(−Eph/kBT ))−1, similar quality fits to thoseshown in Figure 2.10 can be obtained for a phonon energy of ≈ 5 to 10meV. From this analysis, there is no preference for the single phonon versuslow-activation energy Arrhenius process, but it is nevertheless unambiguousthat a non-radiative decay channel with a low (< 10 meV) activation energyis required to fit all of their and our air-exposed samples. The lack of pref-erence between these two functional forms can be attributed to substantialparameter covariance.1073.4.3 DiscussionThe behavior of the lower energy A state for samples from series B is verysimilar to that of the only radiative state that manifests itself in our samples(series C and D). With no intentional air exposure, the integrated PL fromthe A transition in sample B1 is almost identical to that observed in allseries C and D samples save for the the one exposed to air (D2). In thecase of all air–exposed samples from series B and D, the change in behaviorof the A state contribution is very similar to the change in behavior of oursingle emissive state in sample D2, up to temperatures above approximately125 K, beyond which point the A state contribution in air-exposed B seriessamples decays more rapidly than in sample D2. It would appear that airintroduces a new, low-activation energy non-radiative decay path for state A,and our single emissive state, that causes more rapid (than in the absenceof air exposure) falloff of the emission as temperature is increased fromapproximately 5 K. The difference in behavior at higher temperatures forthe A state contribution from samples in series B, is apparently due to anadditional, high activation energy non-radiative pathway that air exposurecauses in those samples. It seems plausible that this high activation energynon-radiative channel is somehow tied to the B state that is apparent in allseries A and B samples, but absent in our series C and D samples.One explanation for the absence of radiative and non-radiative evidenceof the B state in our samples is that the next highest lying state with sig-nificant oscillator strength in our samples has a ∆ǫBA much larger than ≈80 meV. An alternate explanation for the lack of radiative evidence of the Bstate in our samples, is the possible impact of nanoparticle shape/symmetryon the oscillator strengths [79] of the states within the ground state excitonmanifold. Positing explanations for these conjectures raises the issue of thenature of both the A and B states; are either or both “intrinsic” excitonicstates constructed from the one electron and one hole single particle statestypically calculated for these CQDs, or are either or both associated withdefects, either bulk-like or surface-like? Based on most published band struc-ture calculations for these systems, it is hard to identify an “intrinsic state108that could be associated with the A state in this analysis, since almost all ofthese calculations conclude that the ground states of the intrinsic manifoldare “dark”, with the first “bright” states located on the order of 10 meV to20 meV above the intrinsic ground state. Since, with the exception of theHughes et al. sample A2, and possibly other Hughes et al. samples similarto the A series, there is no experimental evidence of increasing PL emissionfrom temperatures of 5 K, the A state must be close to the energeticallylowest available excitonic state in the CQDs, whatever its nature. In thecase of the Hughes et al. sample A2, the weak rise in integrated PL atlow temperature does suggest that the A state in those samples lies slightlyabove the ground state, but not by the amount suggested by most publishedband structure calculations. Thus, to the extent that current band struc-ture calculations accurately capture the intrinsic properties of these CQDs,this suggests the A state in series B samples, and the only emissive state inour CQDs, is a defect state with non-negligible oscillator strength, or thatsome detail of the nanoparticle structure influences the theoretical oscillatorstrengths in such a way that low-energy exchange-split states have large os-cillator strengths. If the impact of symmetry is sufficient to impact the lowenergy A state, it may not be so surprising that the higher energy B state’soscillator strength could be quite sensitive to sample synthesis details.Further experiments, and theoretical calculations that include defectsand particles of various symmetries are required to explain the nature of theoptically active states in PbSe CQDs, and the reversibility of the influenceof air in some samples, and its irreversible nature in other samples.3.4.4 ConclusionsA kinetic model that allows for luminescent emission from up to two brightclusters of states, and non-radiative decay from any of the excitonic statesin the lowest manifold of PbSe CQD thin-films can accurately reproduce adiverse range of measured temperature-dependent integrated PL emissiondata from 5 to 300 K. A thorough statistical analysis of the best-fit param-eters (at most 6, and in some cases as few as 2), including their covariance,109reveals the commonalities and differences in the optical emission proper-ties of nominally similar PbSe CQD samples grown in different laboratories,including their response to oxyge and air exposure.One set of samples (labeled C and D) effectively emit from only a singlecluster of bright states that have energies at or very close to the lowest ofthe accessible excitonic states. In the absence of intentional air exposure,the non-radiative decay from these samples is well described by a singleArrhenius process with an activation energy on order of 20 meV. The othersets of samples (labeled A and B) exhibit significant emission from primarilytwo clusters of states separated by ≈ 75 meV, with the lower energy statevery close to the bottom of the manifold of accessible states. In the absenceof intentional air exposure, samples A and B either exhibit the same ∼ 20meV activated non-radiative decay behavior of samples C and D, or a non-radiative decay with negligible activation energy, depending on the organiccapping layer.Air exposure of samples B, C and D changes their behavior in a waythat can be described by introducing a second, distinct Arrhenius-like non-radiative decay channel with a relatively low activation energy. The biggestdifference between samples B and samples C and D in this regard, is thatthe effects of air exposure on samples B is irreversible, while it is reversiblefor samples C and D.This analysis and sample comparison suggests that the lower energytransition in samples A and B shares many attributes of the single emissivestate in samples C and D. The fact that the energy of this bright state isvery close to the bottom of the ground manifold of accessible exciton statesis difficult to reconcile with existing calculations of the oscillator strengthdistribution within the “intrinsic” ground state manifold of PbSe CQDs.This, together with the apparently fickle nature of the higher energy emissivestate evident in one set of samples but absent in the other, suggests thateither (i) the low energy emissive state is associated with defects, and/or(ii) that current calculations of band structure and oscillator strengths failto capture important details, perhaps associated with morphological detailsthat have yet to be experimentally determined.1103.5 Modeling discussionAs exemplified by the studies in Chapters 2 and 3, there are numerousand significant challenges towards development of an integrated, NIR singlephoton source based on PbX colloidal quantum dots. The efficiency of sucha source may suffer from low internal quantum efficiency when improperlypassivated, particularly in combination with air exposure. Additionally, theradiative emission rate may be lowered by large depolarization effects.The work in these chapters however provides a solid, self-consistent pic-ture that addresses each of these influences, improving prospects to developand interpret experiments much closer to a realized single photon sourceenvironment, i.e. studies of PbX CQDs integrated into photonic integratedcircuits, the subject of the following Chapter 4. In this section, we sum-marize the picture of PbX CQD emission developed in this chapter and theprevious, as a basis for interpretation of Chapter 4 results. Further, thevalue of this picture towards development of a single photon source is bol-stered by the fact that the CQD synthesis method was held constant over allexperiments in this dissertation, eliminating common inconsistent behaviorarising from synthesis variations from group to group.Consider firstly radiative efficiency estimates for thick films: theroom temperature integrated PL and low-temperature integrated PL ra-tio (PL(300K)/PL(4K) = 0.1 to 0.3 in Figure 2.10 of Section 2.6) supportsa radiative efficiency of 10% to 30% at room temperature. This is consis-tent with the independent time-resolved plus FDTD modeling results thatindicated a radiative efficiency of around 20% at room temperature (Sec-tion 3.3).FDTD modeling, combined with PL decay measurements, resulted in aradiative efficiency of 4% to 10% for PbSe CQD thin films on silicon. Themodeling resulted in similar radiative decay rates for CQDs in the mainantinode of an L3 cavity, calculated for the power saturation spectroscopyof cavity-coupled PL. Although no absolute radiative efficiency was deter-mined in the power saturation study, the need for a significant non-radiativepathway (i.e. need for the four state model, including the trap state) to ac-111commodate the strong saturation was established and is consistent withlow-on chip radiative efficiency of PbSe CQD thin films. The trap-state life-time was obtained from the saturation modeling by presuming that decayfrom the excitonic state to the trap state is much faster than radiative decay.The time-resolved study of PbSe CQDs in a thin film, when combined withFDTD modeling, provided quantitative support of this assertion.Modeling PbSe CQD emission involved accounting for numerous depo-larization factors, yet with the time-resolved data provided self-consistentunderstanding of emission dependence on pump intensity: (a) the lack ofsaturation for CQDs on bare SOI or silicon, relative to the CQD PL coupledto a L3 cavity, is due to an enhancement of the excitation field arising fromthe L3 cavity texture. (b) the lack of saturation for thick films, relativeto CQDs in the L3 cavity, is not tied to local field differences, but can beunderstood by studies from our lab external to this dissertation contents,i.e. by exciton diffusion [172, 174].The saturation behavior is arguably the biggest problem for SPS ap-plications. In principle, if the enhanced coupling of the CQD exciton tothe cavity mode was sufficiently large, this problem could be mitigated tosome extent, however from the simulations, the net rate of coupling to thecavity mode versus other radiative decay routes when the CQD is at theantinode on top of the L3 cavity was only 2 times. If the PbSe were in factembedded within the silicon at the true antinode position, the better modeoverlap (increased by a factor of ∼ 9), along with reduced coupling to otherradiative states (decreased by a factor of ∼ 7 from Figure 3.4), and reduceddepolarization effect (improved by a factor of ∼ 10, square of Lorentz fieldfactor in solution vs in silicon), would all combine to increase this factor to∼ 1000. Note that recent absorption measurements of PbX CQD depositedmonolayer by monolayer on silicon waveguides [158] would offer useful datato further test our depolarization models.The influence of air on CQD emission was studied in thick film formu-lations, and experimental conditions required to minimize its effect weredeveloped (e.g. adequately rejecting air exposure influence by performingspecific experimental steps in inert gas environments) and can be readily112adhered to in future studies. Air exposure introduces a low-energy (< 10meV), non-radiative pathway beyond the most common (∼ 20 meV) non-radiative pathway, and recovery from air exposure in thick film formulationsis possible. A picture of ligand immobility, in thin film formulations, be-ing the dominant culprit for non-radiative decay is supported. Throughthese three sets of measurements, which form the basis of Chapters 2 and3, non-statistical photophysics of the ground state exciton of PbSe CQDs isself-consistently understood, paving the way for solid interpretation of PbSeCQDs in SOI PICs, the subject of the next chapter, as a next step towardsevaluating this approach to realization of an SOI-integrated single photonsource.113Chapter 4PbX CQDs in SOI PICsThis chapter describes the study of CQDs integrated into a full silicon pho-tonic circuit, starting with a description of the experimental setup, followedby characterization of the setup, experimental results, and finally modelingof the results.4.1 Sample preparation (SOI PICs, CQDintegration)While microcavities are excellent for collecting emission from luminescentCQDs, an integrated quantum optical system requires us to carry that col-lected photon efficiently to other places on the photonic chip. The cavityis thus coupled to a low-loss single-mode ridge waveguide. SOI PICs withthe circuit layouts employed in this dissertation were characterized in [189].They are are shown in Figure 4.1 and consist of an L3 cavity symmetricallycoupled to two photonic crystal waveguides. The photonic crystal waveg-uides are in-turn coupled to channel waveguides, and for the sake of easyand efficient free-space collection of cavity-waveguide-coupled photolumi-nescence, each channel waveguide is coupled to a large multi-mode taperedwaveguide, terminated with a diffraction grating-coupler.The inclusion of two sets of waveguides plus gratings symmetrically cou-pled to the same cavity facilitated measurement of transmission spectra of114Figure 4.1: (A): Full photonic integrated circuit (PIC) designed andcharacterized in-lab [189] and used in this dissertation as a PICin which PbSe CQDs were integrated and their luminescencewas measured. (B): PIC transmission measurement schematic.(C): Transmission spectrum of the PIC, prior to CQD integra-tion. (D): PL of PbSe CQDs in solution, prior to their integra-tion into the PIC.the PIC, and it also facilitated photon correlation measurements directly,without the need for an external beam splitter. This circuit design is anoptimized version of an earlier realization in which our group measured ef-ficient cavity-waveguide coupling in the absence of CQDs [17]. Fabricationwas through ePIXfab [3] and IMEC [1].As-received SOI photonic chips were spin-coated with 2 µm of AZ P4110photoresist to ensure the cavity-wavelength emission would emanate fromthe grating coupler at a convenient collection angle θ. Photoresist over thephotonic crystals (including photonic crystal cavities and waveguides) wasremoved by exposure to ultraviolet light and subsequent chemical develop-ment (using AZ P4110 specific developer, with deionized water at ratio of1:4), while leaving resist over the tapered waveguides and grating couplers.Photonic crystals (again including photonic crystal cavities and waveguides)115and channel waveguides were undercut by dipping the sample in a bufferedoxide etch solution for 20 minutes. The etch was arrested by rinsing thesample in deionized water, and then dried under nitrogen flow and stored inambient conditions in a dark cabinet.The PIC transmission spectrum, measured approximately 1 month priorto integration of the PbSe CQDs and about 1 year after the initial HFundercutting (removal of oxide underneath the PhC region), is shown inFigure 4.1C. The in-solution PL spectrum of the PbSe CQDs that werethen integrated into the PIC is shown in Figure 4.1D. Integration of thesePbSe CQDs was performed as follows: the sample was dipped for 10 secondsin a 0.5 mg/mL hexanes solution of PbSe CQDs and subsequently put undervacuum in accordance with the dip coating procedure outlined in Chapter 2and detailed in Appendix A.4.2 Measurement overview and optical setupsThree sets of measurements were performed on the luminescence of thePbSe CQDs integrated into the PIC: (a) steady-state microphotolumines-cence (µPL) spectroscopy using continuous wave (CW) Nd:YAG 1064 nmlaser excitation applied at various locations across the sample surface, andmonitoring the PL emission from various other locations, using differentcollection geometries. The main points of this work were to verify the sat-uration behavior observed from the stand-alone cavities, and to optimizethe collection of waveguide-coupled exciton emission while minimizing thecontribution from background luminescence. (b) time-resolved µPL charac-terization, and corresponding µPL spectra, using 660 nm pulsed excitation.This work helped to further refine the spectral filtering strategy required forphoton correlation measurements, and it also provided lifetime data thatcould be compared to the thin film studies on uniform substrates as re-ported in Chapters 2 and 3. (c) photon correlation measurements of thecircuit-coupled PL, using the same 660 nm pulsed excitation.In pursuit of understanding the PIC-coupled, cavity-enhanced CQD PL,a persistent challenge was isolation of this signal from the relatively broad116emission from CQDs not located directly at the cavity antinode. This iso-lation was pursued in two ways: (a) spectral filtering, i.e. rejection of col-lected CQD µPL not at the cavity wavelength, and (b) improvement ofcavity-enhanced contrast, i.e. reducing non-cavity-coupled µPL at the cav-ity wavelength relative to the cavity-coupled PL. Improvement of cavity-coupled PL contrast relative to non-cavity-coupled PL was achieved usingtwo sets of apertures: (a) one in the far field to select light emitted onlywithin a well-defined solid angle from the sample, in accordance with theangle at which cavity-coupled is diffracted from the PIC diffraction gratings,and (b) a separate set of apertures in an image plane to preferentially collectonly the PL emitted from a specific location on the sample surface (typicallyjust near the edge of one of the output grating couplers).4.2.1 Optical setupThe general setup used for all luminescence measurements performed on theSOI PIC samples is shown in Figure 4.2. The excitation source, followingthe excitations paths drawn in green, was one of (a) a variable output powerNd:YAG 1064 laser and (b) the 660 nm pulsed Sepia laser used in Section 2.5.The Nd:YAG source was used instead of the HeNe source of Chapter 2 be-cause excitation intensities required to achieve cavity-coupled power satu-ration could be achieved with it, but not with the HeNe source, given thePIC excitation geometry constraints (in particular the longer working dis-tance and correspondingly larger spot size). Collected light was ultimatelydetected by one of (a) the Bruker FTIR or (b) the ID210 single photondetectors, each of which were also described in Chapter 2. The collectionpaths (blue lines) consisted of a 15X reflecting microscope objective (OBJ),sometimes preceded by an aperture plate (AP), passage through a yˆ-orientedlinear polarizer (P), deflection towards the detectors by use of a mirror pairMT1,T2, passage through a far aperture (one of FAL,C,R), diversion to eitherthe Bruker FTIR by a combination of mirrors, or to the free-space to fibercouplers (FFCL,R), and in the latter case passage through a free-space filter(F), focusing lens, and in-line narrow band spectral filter (FFL,R). Many of117the mirrors after the far apertures were kinetically mounted (KM), meaningthey could be placed in and out of the optical setup with ease to change thecollection paths. Details of the optical setup are as follows.Figure 4.2: Optical setup used for characterizing PbX CQD emis-sion in and near the photonic integrated circuits, including (a)steady-state, Nd:YAG excited microphotoluminescence (µPL)spectroscopy, (b) spectrally-integrated, time-resolved µPL emis-sion using a 660 nm pulsed laser, and (c) photon coincidence(correlation) measurements.Figure 4.3 contains a simple overlay of exemplary excitation and collec-tion areas relative to the PIC components. Measurement of the position118and extent of the excitation and collection areas was done in part with theaid of a white light imaging system, which allows simultaneous broad-band,scattered white light imaging of the sample surface and scattered excitationlight, thus a knowledge of both the collection and excitation area relative tothe sample at any desired time. White light was directed towards the samplesurface via a visible wavelength 50/50 beam splitter (VBS) located behindthe 15X reflecting objective (OBJ) used for imaging and light collection fromthe sample (note that the beam splitter transmits all incident C-band light).Control of the collection area and position was done by adjusting the posi-tion and aperture diameter diris of the far apertures FAL,C,R. The centralfar aperture FAC was aligned early on to coincide with the optical axes ofthe collecting objective and Bruker FTIR spectrometer. Details of the faraperture system are contained in Figure 4.4D through F.Figure 4.3: Simple overlay of excitation and collection regions relativeto the PIC components. Collection area and position was con-trolled with the far apertures FAL,C,R. Position of the excitationspot was controlled by adjusting the position of the excitationlens assembly ELA and mirrors preceding it. The 1/e2 mini-mum power diameters were 20 µm and 3.5 µm for the Nd:YAGand 660 nm pulsed laser excitation sources, respectively.119Figure 4.4: Detailed illustrations of excitation and collection geome-tries, an elaboration upon the larger scale diagrams depicted inFigures 4.2 and 4.3.Excitation light was expanded, collimated, then focused using asphericallenses to obtain the smallest excitation spot size possible given space andreasonable budget constraints, shown broadly in the lower right corner ofFigure 4.2. For the Nd:YAG laser, the 1/e2 power waist was 20 µm and forthe Sepia 660 nm pulsed source it was 3.5 µm. The spatial constraint wasset in part by the focal length (2.8 cm) of the reflecting objective used forcollecting luminescence and white-light imaging the sample surface. Justenough space was available for a several-mm wide, square mirror in betweenthe objective and cryostat window to divert excitation light onto the samplesurface. The mirror was located to pass as much luminescence as possiblefrom the chip to the collection objective while minimizing the spot size ofthe focused excitation laser on the sample surface. A major benefit of usingthe reflecting objective is that its focusing properties are largely wavelength120independent from VIS through NIR, meaning a good white light image ofa specific PIC location obtained with the objective corresponds to near-or in-focus collection of NIR PL emitted from that location (which wasverified for PbX CQD luminescence from various locations on the PIC).Refer to Figures 4.4A through C for detailed diagrams of the region nearthe collection objective, sample, and excitation turning mirror, as well asthe apertured plate, now discussed.A large number of similar circuits were available from the IMEC chip,each with slightly different cavity resonant frequency and grating couplingproperties, as characterized in our lab [189]. For the present experimentsdevices were chosen so that photons at the cavity wavelength would bediffracted out of the grating couplers (when coated with photoresist), atangles within the 5 degree to 20 degree collection (relative to the opticalaxis) of the reflecting objective, such that all cavity light coupled to thewaveguides and diffracted from the gratings could be collected. For thesamples studied in this dissertation, ∼ 90% of a given wavelength incidenton the grating coupler (e.g. at the cavity emission wavelength), emanatedwithin a 5 degree spread, ∆θ, of the nominal out-coupled direction θ. Forthe various samples studied, θ varied from 14 to 17 degrees. Generally,spurious CQD PL emission from the sample was across a much larger spreadin solid angle, which permitted increasing the ratio of cavity-coupled PLdiffracted from the gratings, relative to all other PL, by collecting lightonly from the small solid angle at which cavity-coupled PL diffracted. Thiswas achieved by placing a re-positionable aperture plate (AP) between thecollecting objective and the sample, about 1 mm away from the objective,as shown in Figure 4.4B.Free space to fiber coupler assemblies (FFCL,R), used in the photon co-incidence measurements and detailed in Figure 4.8, consisted of precision3-dimensional translation stages upon which a spectral filter (F), single fo-cusing lens, and fiber tip were secured, and the position of the lens relativeto the fiber tip could be finely adjusted in all three directions and done soindependently of the position of the assembly relative to the far apertures.The 50 µm core diameter, 125 µm cladding diameter multimode fibers were121chosen to be compatible with coupling both to the ID210 detectors, andthe Koskin Kogaku narrow band (1.2 nm FWHM) tunable, fiber band passfilters. The overall peak transmission efficiency from just before the freespace to fiber coupler to the final output of the fiber (which attaches to thefiber input connector of the ID210 detector), as measured using laser lightat the cavity wavelength and scattered off the sample surface, was 30%, atthe peak transmission of the in-line filter.4.2.2 MicrophotoluminescenceConsider the steady-state µPL spectra collected directly from cavity (e.g. asimilar geometry to that described in the isolated cavity results in Chapters 2and 3) compared to that collected from the grating couplers, for Nd:YAG(1064 nm) excitation shown in Figures 4.5A through C.The narrow resonance near 1564 nm in each corresponds to the cavity-enhanced CQD PL, which excites only TE-polarized (zˆ ·E = 0) channelwaveguide modes that in turn couple out of the grating couplers with yˆ-polarization. Unpolarized PL collected directly from the cavity, not shown(instead, all spectra in Figure 4.5 are for yˆ polarization), is similar to thestandalone cavity µPL of Chapter 2, i.e. a broad PL background similar tothe CQD solution PL, with cavity mode enhancements superimposed.Isolation of the cavity-out-coupled signal of interest was improved byuse of the apertured plate (AP) placed between the sample and collectingobjective, and far apertures (FAL,C,R). Figure 4.5 illustrates the utility ofnear and far apertures in greatly improving the ratio of on-cavity-wavelengthPL to off-cavity wavelength PL. No spectral filtering was performed for anyof the spectra shown in Figure 4.5.The PIC-coupled, cavity-enhanced CQD PL also exhibits strong powersaturation, plotted in Figure 4.5D. It is useful to compare the excitationsource and saturation power to the standalone cavity power saturation ofChapter 2: in Chapter 2, the 1/e2 beam power waist was 2.0 µm, saturationpower was several µW, and the absorption coefficient of CQDs at the HeNewavelength used was 2/cm. Here, the saturation was observed for a beam122Figure 4.5: Example steady-state µPL for excitation with several mWof Nd:YAG laser focused onto the cavity region with a 1/e2power waist of 20 µm. (A): PL collected over the cavity region.(B): PL collected over the grating region. (C): Apertured (bothnear and far) spectrum collected over part of the grating region,with a transmission plot (red) of the PIC, measured prior toCQD integration. (D): Power-saturation of the circuit-coupled,cavity-enhanced CQD PL, collected from the grating using theapertures per (C).waist of 20 µm, saturation power on the order of a mW, and the CQDabsorption coefficient at 1064 nm excitation is 5/cm, thus the differences inbeam waist and absorption coefficient compensate for the ∼ 103 differencein saturation powers between the two scenarios.Figure 4.6 contains both time-averaged PL spectra and time-resolved,spectrally averaged decay plots obtained using the pulsed Sepia II 660 nm123Figure 4.6: Example spectra (200 FTIR scans, 1 nm resolution) andtime-resolved decay (with superimposed single exponential de-cay fits) of PL collected, for excitation with the 660 nm Sepiapulsed laser source with 1/e2 power waist of 3.5 µm, 10 MHzrepetition rate (1 MHz for collection from the cavity region),and ≈ 0.05 mW average incident power. Background PL spec-tra with the Sepia laser excitation differ from background PLspectra with the 1064 nm Nd:YAG excitation, which is not un-expected given differences in excitation spot size, intensity, andwavelength. The single exponential 1/e decay times for PL col-lected from the gratings are 30 ns, but don’t capture the fasterdecay at short time scales. Decay from the cavity region ischaracterized by a 1/e decay time of 60 ns.laser. The excitation source had a 1/e2 power waist of 3.5 µm, 10 MHzrepetition rate (1 MHz for collection over cavity region), and ≈ 0.05 mWincident power. Gated detection was performed with 5.00 ns gate width, 10%internal detector quantum efficiency (best available for gated operation),124and 100 ns dead time. The gate width is an effective width defined inthe ID210 manual, not a strict rectangular apodization, so the temporalresolution appears better than the quoted 5 ns gate width. The time delaywas controlled by sending the sync out of the Sepia power unit to a HPfunction generator controlled by a Matlab script that incremented the delayevery 2 seconds. This script was started manually at the same time a scriptwas run on the ID210, in which the ID210 integrated counts for 2 seconds,stored the result, then repeated. The width of the rising edge in the time-resolved PL curves is equal to this 2 to 3 ns value. No spectral filtering(free space or in-line) was performed for the results in Figure 4.6. Spectraobtained with the pulsed Sepia excitation are similar to those observed withNd:YAG excitation, with some differences in the background spectral shape,which was not unexpected given the differences in excitation wavelengths.The PL decay times of ≈ 30 ns for PL collected from the grating regionare significantly lower than observed for the thin or thick films of CQDs onbare silicon or SOI substrates. Since the microcavity PL only contributesa small portion to the total PL in these PL curves, the signal contributingto this decay is dominated by non-cavity coupled background PL and theshort lifetime must be representative of another lifetime shortening process.Collection of PL from the cavity region, exhibiting a decay time of 60 ns,slightly less than the short decay time of 90 ns obtained for CQDs in a thinfilm formulation in Section 2.5. These results are discussed further at theend of this chapter.Attempts to narrow down the dominant locations of the µPL were made,including excitation upon areas other than the cavity region and collectionfrom small areas other than centered on the cavity or grating. No PL wasdetectable when collecting and exciting over a coincident location on ornear the gratings or tapered waveguides, and instead the background PLwas coming from somewhere around the cavity region but possibly as faraway as from stray CQDs on the PhC waveguides or single mode ridgewaveguides. This is not unexpected since, even with the small excitationbeam waist, excitation light is easily scattered off the highly textured PhCstructures.1254.2.3 Photon coincidenceBasic principlePhoton coincidence measurements are the de facto method for determiningwhether a photon source emits only one photon at a time. The experimentalsetup for such measurements, illustrated in Figure 4.7, typically consists ofa Hanbury, Brown and Twiss (HBT) configuration in which emission fromthe source of interest is sent to a beam splitter, the two outputs of whichare sent to two single photon detectors, the outputs of which are then sentto a time correlator that keeps track of photon coincidence events.Figure 4.7: (A): Idealized stream of regularly emitted on-demandphotons (red) compared to a stream of photons exhibiting pho-ton bunching. (B): Histogram of photons within a fixed timeinterval for a Poissonian source (striped yellow, purple) and anideal stream of regularly emitted photons from an on-demandsource. (C): Basic photon coincidence setup to test if a sourceemits only a single photon at a time.126Coincidences in the HBT setup correspond to the number of times anevent is measured on one counter then another within the same time bin,as a function of time delay between photon arrivals. Because an ideal singlephoton source does not emit more than one photon at a time, for zero pathlength difference between the source and the two detectors the coincidencerate theoretically drops to zero. The dip arising is a form of antibunching,corresponding to less “bunching” (more photons than average observed in atime interval) seen in Poissonian or thermal processes. Testing for this dip,or evidence of antibunching, is a key test of a single photon source.Ideal versions of our PIC samples would send cavity-collected emissionequally to each of the diffraction gratings, as a 50/50 beam splitter in a HBTsetup. Thus by imaging the emission from the two grating couplers to twodistinct single photon counters, the HBT experiment can be done without anexternal beam splitter. Ideally, the PIC would emit light from both gratingsthat only arrived at the grating coupler via the cavity and waveguide. Thespectra from the grating regions would then consist of only a narrow peakat the cavity wavelength, and the signals could be sent directly to two singlephoton counters. In lieu of these idealized spectra, a good candidate PICwould exhibit large ratios of cavity-coupled PL to background PL at thecavity wavelength for PL collected from either grating. The PIC that bestfit these criteria exhibited grating-collected spectra plotted in Figure 4.8.The ratio of PL at the cavity wavelength relative to slightly detuned fromthe cavity wavelength was 5 for collection from either grating, as indicated inthe insets (raw spectral shown, but proper spectral background subtractionwas required for this calculation).Since there was significant background signal over a broad spectral rangeeven using the two sets of apertures, spectral filters were added. Tunablenarrow band pass (1.2 nm FWHM, Lorentzian lineshape TFF (λ;λ0)) fiberfilters (FF in Figure 4.2) from Koshin Kogaku were used to preferentiallypass the cavity-wavelength emission (of FWHM 1 nm). However, becausebackground PL was significant outside the designed operating wavelengthrange of the fiber filters, additional spectral filtering was required. Free spaceband pass filters (FSF in Figure 4.2) of 50 nm bandwidth centered at 1575127Figure 4.8: (A) and (B): PL spectra collected from diffraction grat-ings connected to the same cavity, for the cavity excited withpulsed 660 nm Sepia light, as used for coincidence measurementsdescribed later in this chapter, and before any spectral filteringwas performed. See Figure 4.9 for spectral filtering performed.Insets are the same spectra, plotted over a smaller wavelengthrange around the cavity wavelength, with Lorentzian fits andindicated ratio of peak PL to background PL at the cavity wave-length (after proper baseline subtraction). Spectra are noisierthan those presented previously in this section due to a higherspectral resolution relative to a number of FTIR scans. Eachcavity to background ratio for this sample is smaller than forthe samples in previous sections, but this sample was the only,at the time of measurements, from which cavity coupled PL col-lected from both gratings dominated the total PL signal at thecavity wavelength.128nm and OD4 (optical density 4) blocking outside the bandpass region fromEdmunds were added to the free space to fiber assemblies (FFA) to achievethis additional spectral filtering. To optimize the ratio of cavity-coupled PLsent to the ID210 detectors, a robust alignment procedure, described in thesubsection below along with spectral filtering results was required.Optical alignment and resultsSeveral alignment methods were attempted to optimize this ratio of cavity-coupled PL to background PL on the ID210 detectors. The most successfulmethod, in terms of (a) the best ID210 on-cavity-wavelength PL detec-tion rates, and (b) maximal ratios of on-cavity-wavelength PL to off-cavity-wavelength PL measured on the ID210, is as follows:1. Prior to the steps below, ensure the fiber filter cartridges are tuned tothe cavity wavelength by (a) performing a Bruker FTIR spectrum thatresolves the cavity-coupled light, (b) diverting attenuated laser lighttowards the Bruker FTIR to make sure the laser output spectrum peakcoincides with the cavity wavelength peak, (c) divert the tunable laserlight towards the fiber tip in the free-space located in the free-spaceto fiber, and ensure only laser light is entering the fiber, and (d) tunethe fiber filter cartridge to optimize ID210 count rate.2. Perform an optimization using Bruker FTIR spectra. Positions of theapertures FAL and FAR were adjusted such that the peak solid angulardensity (e.g. power propagated per solid angle) cavity-coupled lightpassed through the center of each aperture. The excitation optics werethen verified as positioned to optimize this cavity coupled PL collectedfrom the gratings, without any adjustment to the collection optics, forSepia pulsed laser excitation with 80 MHz rep rate. The far aperturediameter was chosen to be as large as possible without degrading thecavity-coupled to background PL ratio (at the cavity wavelength) bymore than 10%.3. Close down the far apertures very tightly, set the tunable laser output129to the cavity wavelength, send the laser light into the excitation lensassembly (Sepia pulsed laser off, excitation optics not moved relativeto step (1), and scatter this laser light off the sample surface. Then,put the already designed/optimized apertured plate (AP) in position,to ensure the scattered laser light collected is collected at the sameangle the cavity-coupled PL emanates from the grating (i.e. to mimicthe cavity PL as best as possible).4. Begin optimization of alignment on ID210 count rates (in free runningdetection mode). With no focusing lens of the free space to fiber as-semblies (FFA) in place, iteratively adjust the angle of the KMR andKML mirrors and position of the fiber tip such that (a) the peak solidangular density (e.g. power propagated per solid angle) is centeredon the fiber tip, as indicated by the count rate on the ID210 detec-tor, and (b) insertion of focusing lens does not displace the peak solidangular density off of the center of the fiber tip. This step ensurescavity-wavelength laser light, collected from the sample at the sameangle as cavity-wavelength light emanating from the diffraction grat-ing, is collected along a single collection path that is aligned with thefiber axis near the fiber entrance. Ideally this is done with cavity-wavelength PL collected from the diffraction grating, but the signal isnot strong enough to practically align the system (if at all, given thefinite mechanical drift).5. The focusing lens was then translated along the collection path, rela-tive to the fiber tip, to maximize ID210 count rate. It was then verifiedthat the focusing lens is still along the collection path established instep (3) by verifying that small displacements of each of the optical ele-ments perpendicular to the collection path established in (3) decreasesthe ID210 count rate. It was then verified that, for larger far aperturediameters, each of the optical elements are optimally (regarding ID210count rates) positioned (i.e. that small displacements of any of theseelements degrades ID210 count rates).1306. Now, turn the laser light off and Sepia pulsed laser back on (still at80 MHz). Set the far aperture diameter to value established earlier.Set the ID210 to gated mode, using the sync out of the Sepia system.The internal delay of the ID210 was adjusted to identify the delay atwhich the peak ID210 rate relative to minimum ID210 rate is largest(corresponding to the leading excitation pulse edge), and the otherID210 settings (gate width, dead time) were adjusted to maximize thePL rate on the ID210 detector. The internal delay was adjusted againto make sure PL detection rate is optimal.7. After optimizing the ID210 parameters in step (5), adjust the positionof the free-to-fiber focusing lens position, along the collection path, tooptimize the ID210 PL detection rate, then iterate (5) and (6) againto make sure ID210 detection settings and the collection path settingsare jointly optimized for peak PL detection rate on the ID210.After alignment, the on-cavity wavelength, off-cavity wavelength ratiowas tested by tuning the fiber filter through the cavity PL wavelength. Theratio obtained was 3 for collection from either grating under conditions wherethe spectra from the gratings were as in Figure 4.8. This value is less thevalue of 5 observed in the FTIR spectra in Figures 4.8, and is explained(and limited) by the finite band pass spectral width of the fiber filters, asillustrated in Figure 4.9, in which the observed grating-collected spectra S(λ)from Figures 4.8A and B are multiplied by the filter transmission spectraTFF (λ;λ0) and TFSF (λ). Symbolically:∫dλ S(λ)TFSF (λ)TFF (λ;λcav)∫dλ S(λ)TFSF (λ)TFF (λ;λcav+ δλ)≈ 3 (4.1)The 1/e lifetimes of PL measured for the fiber filter tuned to the cavitywavelength and slightly detuned from it were measured by monitoring thephoton detection rates while adjusting the internal photon detector delays.When the fiber filter was slightly detuned from the cavity wavelength, the131Figure 4.9: Spectral filtering used for coincidence measurements. (A):The band pass free-space filter (FSF) from Edmunds blocks(with OD4) all but the wavelength range 1550 nm to 1600 nm.(B): The tunable narrow band pass fiber filter (FF) from KoshinKogaku possesses an approximately Lorentzian lineshape with1.2 nm FWHM and can be tuned to the cavity wavelength.(C): Schematic of the free-space to fiber coupler assembly andin-line fiber filter (FF), with pre- and post- filtering locations,as plotted in (D) through (F), circled. (D): Example measuredspectrum (from Figure 4.8B) before spectral filtering. (E): Ex-trapolated PL after propagating the spectrum through the freespace filter and into the fiber, using the measured pre-filter spec-trum S(λ) and free space filter transmission spectrum TFSF (λ),as well as the measured free-space to fiber coupling efficiency.(F): Extrapolated PL, after both the free space and fiber filters,using the filter transmission spectra TFF (λ;λ0) and TFSF (λ),and exemplified for the tunable filter both tuned to the cavitywavelength and slightly detuned from it.1321/e decay time was ∼ 25 ns, comparable to the 30 ns measured for grating-collected PL in the previous subsection. When the fiber filter was tuned tothe cavity wavelength, the 1/e decay time was ∼ 10 ns, much smaller andlikely limited at least in part by the detection gate width (4.00 ns FWHM).These lifetimes are consistent with the cavity photon decaying on a sub-nanosecond timescale associated with the cavity Q, and the 1/e decay timeof signal at the cavity wavelength being a weight sum of this fast (likelydetector limited) decay and the slower background PL decay. With thespectral input of the ID210 detectors understood, coincidence events weremeasured to test for antibunching.Coincidence resultsSettings for photon coincidence measurements were as follows: excitation ata repetition rate available of 80 MHz with an average pump power of 0.4mW, detector settings of 4.00 ns effective gate width, gates triggered at the80 MHz sync signal output of the excitation laser, dead time of 0.1 µs, andinternal efficiency of 10% (largest available). Results presented below arefor these settings, but other detector and excitation settings were explored.ID210 dark count rates from the two gratings were 2.7 KHz and 3.7 KHzand detection rates were 0.4 KHz and 0.5 KHz in gated detection mode. Ineach case, the detection rate on each ID210 was maximized by adjusting theinternal ID210 detection gate temporal delay. The detection events on eachID210 were sent to the PicoHarp 300 time correlator, which kept track ofcoincidence events, i.e. detection events from one ID210 detector relative tothe other ID210, as a function of time of arrival between the detection events.The time correlator was operated in time-tagged mode, in which a timestamp was recorded for each photon detection event, and the coincidencerate calculated after data collection was complete. The time bins were 0.512ns in width (setting the timing resolution) and a total of ∼ 65,000 time binsrecorded. The longest integration time was 28000 seconds (8 hours).Example coincidence plots are presented in Figure 4.10, in which coin-cidences were binned at each excitation pulse. No evidence of antibunching133of luminescence at the cavity wavelength was observed over a wide range ofdetector and excitation settings.Figure 4.10: Example coincidence plots for total count rate (darkcounts plus signal), dark counts only, and the difference ofthe two. No evidence of antibunching was found for detectionand excitation settings considered.4.3 DiscussionThe total (combined) count rate from the single photon detectors underthe optimal contrast conditions was 900 counts per second, with ≈ 2/3 ofthese attributable to the cavity coupled photons, i.e. 600 counts per second.Even though it was not shown that the photons contributing to this signalwere characteristic of a single photon source, it is useful to work backwardto estimate the (more relevant) corresponding photon current in the siliconchannel waveguide in order to estimate potential performance as an inte-grated single photon source. We then estimate and compare results to theexpected waveguide photon current for a hypothetical single CQD in thePIC cavity, using results of previous chapters.4.3.1 Extrapolation of PIC-coupled photon rateA photon emitted into the cavity mode may decay into one of several chan-nels, e.g. directly into free space or into the adjacent photonic crystal waveg-134uides. A combination of modeling and characterization of PICs fabricated inthe same process at the same foundry, presented in references [189], reportsgrating to grating peak transmission of 2.6%, and 20% grating coupling ef-ficiencies, from which we can extract the probability a photon passing fromwaveguide to waveguide to be 0.026/0.22 =0.65 and the probability of a cav-ity photon ending up in a waveguide (either of them) to be ∼ 0.80, or 0.4 fora particular waveguide. The probability of a cavity photon to be diffractedout of a specific grating is then 0.4×0.2 = 0.08, and to be diffracted off-chip0.16.Between the grating and the detector are numerous collection opticscharacterized as follows (refer to Figure 4.2): reflecting objective (∼ 50%),polarizer (95%), mirrors MT1,T2 (97% each), mirror KML,R (97%), and freespace to fiber couplers plus fiber filter peak (30%, measured directly). Thefiber filter (1.2 nm FWHM, approximately Lorentzian lineshape) passes ≈60% of the cavity-coupled PL (1.0 nm FWHM, approximately Lorentzianlineshape). The resulting overall grating to detector efficiency is ≈ 8%.Once at the detector, the probability of detection is tied to the internalquantum efficiency (10% for gated operation) and gate time (4.00 ns) relativeto the cavity photon decay time (inversely proportional to the cavity Q).Since the latter is sub-nanosecond, there is no degrading of the efficiencydue to the finite gate width.Overall, the off-chip collection optics and detectors admit a 0.08×0.1 =0.008 probability of photon detection. Combining this with the on-chipprobability of 0.16, the probability of a cavity photon being detected is≈ 0.0013, or ≈ 0.0006 per detector when assuming the cavity photon hasequal probability of arriving at either detector.Using the 600 counts per second total PIC-coupled PL on the detec-tors, this corresponds to a cavity photon generation rate of ≈ 500 KHz andtotal waveguide photon generation rate of ≈ 400 KHz, or ≈ 200 KHz perwaveguide.1354.3.2 Estimated single CQD resultsWe now estimate what the theoretical waveguide flux of cavity-coupled pho-tons should be by making use of the the standalone cavity results fromChapters 2 and 3, in which the calculated cavity-CQD scattering rate was∼ 0.8 MHz, the radiative decay rate into other modes was ∼ 0.4 MHz, andthe extracted trap state lifetime was ∼ 3 µs.If we use the same values for a CQD in our PIC cavity and combine itwith the observed ∼ 60 ns PL decay time (or 16.7 MHz decay rate) for CQDsin the cavity region extracted in Figure 4.6A, the branching ratio of excitondecay into the cavity mode is (0.8 MHz)/(16.7 MHz) ≈ 0.05. Using also a∼ 3 µs trap state lifetime which on average (for the low radiative efficiency)restricts exciton decay to the ground state and thus exciton generation to arate of less than ∼ 1/(3 µs)∼ 0.3 MHz, the corresponding maximum cavityphoton generation rate is ∼ 0.05×3 MHz∼ 15 KHz. Using the ∼ 0.8 prob-ability of a cavity photon entering a waveguide, the estimated (maximum)rate of photons emitted by a single CQD within the PIC cavity is ∼ 10KHz. If we consider the range of trap state lifetimes extracted in Chapter 3,τtrap ≈ 3+3−2 µs, the rate of cavity photons generated spans to ≈ 8 to 50 KHz,and the rate into a specific waveguide is ≈ 3 to 20 KHz.Note that some model assumptions may bear on these estimates. Forexample, at least one research group reported photoluminescence from PbXCQDs integrated into a silicon photonic environment larger than could be ex-plained when accounting for depolarization, local photonic density of states,and collection optics [133]. If such an enhancement were to depend on thenumber of CQDs, e.g. mediated by interdot coupling, then extrapolation ofthe multiple CQD results to a single CQD would not necessarily hold.4.3.3 Comparisons and potential use as a single photonsourceComparing the estimated PIC-coupled photon rate in a single waveguide,for a single CQD in the PIC cavity of ≈ 3 to 20 KHz and the photon rate ina single waveguide extrapolated from measured count rates and measured136photon transmission and detection efficiencies of ≈ 200 KHz, it is estimatedthat there are on the order of at least 200/20 = 10 (but fewer than ∼ 102)CQDs significantly coupled to the PIC cavity mode. Using an estimated∼ 500 nm2 area in which the cavity mode profile is significant on the siliconsurface (e.g. see Figure 2.1), this corresponds to a CQD area density of∼ (10 to 100)/(5×100 nm2)∼ 200 to 2000 CQDs per square µm, or averageCQD spacing of ∼ 20 to 70 nm.For the coincidence measurement, we seek reduced photon coincidences(a dip) in the curve due to the unavailability of more than one photonemitting from the cavity within the duration of the time bin used. For asingle CQD in the PIC cavity, there are two time constants relevant to thisavailability factor, the net exciton lifetime (∼ 60 ns in the cavity region), andthe trap lifetime, estimated from the saturation behavior to be ∼ 3 µs. Adetailed model for the expected coincidence behavior for this 4 state system,including the relatively large contribution of background and dark counts,was not developed as part of this dissertation. All that can be concludedfrom the data in Figure 4.10 at this point is that there is no obvious signatureof antibunching on either of these timescales.Even if a low radiative efficiency CQD with a long trap lifetime could beshown to exhibit antibunching, the present estimated flux of maximum 50KHz is not ideal. This low rate could potentially be increased with bettercoupling to the cavity, and a method for minimizing depolarization effects,e.g. as considered in part of Section 3.5. This obviously would require majorredesign of the cavity and probably a modified hybrid integration strategy.137Chapter 5ConclusionsThe broad motivation of this dissertation was to develop on-demand sin-gle photon sources integrated into silicon-based photonic integrated circuits(PICs), which could be used to advance a variety of quantum informationprocessing experiments and applications. The approach involved the hybridintegration of PbSe CQDs on the surface of L3 photonic crystal microcav-ities coupled symmetrically to two single TE mode silicon channel waveg-uides, the ends of which were connected to grating couplers for diffractingwaveguide-bound light off chip.Excitonic emission for incoherently photoexcited PbSe CQDs was suc-cessfully captured as photons in the fundamental mode of an L3 cavity asevidenced by (a) their scattering directly into the top half space from the cav-ity, and (b) their coupling to the single mode waveguides, then off-chip. Thepower dependence of the cavity-coupled PL signal was thoroughly charac-terized in both cases, in conjunction with separate studies of the PbSe CQDemission on bare silicon or SOI surfaces. From all of these measurementsand modeling efforts, the following conclusions and outlook for future workemerged.1385.1 Conclusions, discussion and significanceIf the performance-limiting trap state could be eliminated, the best possiblerate of coupling single photons into the single channel waveguide by placingthe CQD on the surface of an L3 could be as high as ∼ 0.6 MHz (assuming ∼0.8 probability of cavity to waveguide transfer), limited then by depolariza-tion effects and the intrinsic dipole transition moment. Somehow embeddingthe CQD at the maximum field position of the L3 cavity fundamental modewould improve this by close to a factor of 9, bringing the emission rate upto ≈ 6 MHz (excluding improvements to depolarization effects).Several depolarization effects were identified and subtly combined tocoincidentally result in a depolarization effect for a CQD in the L3 cavitysimilar the depolarization effect in solution. These included the presenceof the silicon slab, L3 texture, nearby CQDs, and far-field permittivities(e.g. solvent, vacuum, silicon). Depolarization effects still greatly limitedpotential CQD performance; if, for example, the CQD were embedded insilicon, the CQD emission rate could be increased by a factor of ≈ 11 (beyondthe 9-fold improvement due to the mode overlap).Even if the trap state were eliminated and the CQD were embedded insilicon, the resulting emission rate of ∼ 6×11 MHz = 66 MHz falls short ofbest available GHz emission rates of III-V epitaxial CQDs, due to a smaller“intrinsic” dipole moment as discussed in Chapter 3.Separate studies of the PbSe itself revealed that the radiative efficiencydecreases monotonically from in-solvent (∼ 30%), to thick-film (∼ 20%)where the CQDs are presumably in a bath of oleic acid, and on-silicon (∼ 4%to 10%). Again, proper treatment of depolarization factors was essential forextracting these efficiencies.Temperature-dependent studies indicate that the quantum yield at leastin thick film form, increases by up to 3 to 10 times at cryogenic temper-atures, at least for our PbSe CQDs (3 to 5 for CQDs specifically used inthis dissertation). Reports from other groups (without quantum yield val-ues quoted), show less temperature dependence and in some cases larger PLat room temperature [93], which suggest possible changes in synthesis that139could improve room temperature performance.The self-consistency of the methodology (modeling and experiment) andresults of all the studies within this dissertation also provide a robust basisfor building upon these results in a variety of directions, described in thefollowing section. In sum, the work in this dissertation provides experimentalresults, general and extensible modeling, and demonstrations that advanceunderstanding of and use of PbX CQDs in SOI PICs in conditions relevantto realization of SOI PIC-integrated, on-demand single photon sources.5.2 Limitations, strengths, and future workViability of PbX CQDs as a single photon emitter in SOI PICs is contingentupon substantial synthesis strategy improvements capable of reducing thenon-radiative recombination rate on silicon. If this is shown possible, thenusing such CQDs with the site-selective binding technique in our lab toensure only one CQD at cavity antinode, could possibly produce an on-demand SPS compatible with SOI circuits, at roughly a rate of 600 KHz.If coincidence measurements on such a new sample yielded promising re-sults, this could motivate investigation of alternate cavities (e.g. slot waveg-uides) to improve CQD-cavity coupling. Similarly, a post-integration, en-capsulation process could be used to reduce depolarization effects in such acavity. Mitigation of depolarization effects could potentially raise the sourcerate by another order of magnitude and, along with improved CQD-cavitycoupling could be combined to improve the emission rate to tens of MHz inconceivable scenarios. These scenarios assume that the ground state man-ifold of excitons in these new formulations are not overly complex (a wideenergy distribution of high oscillator strength transitions), something thatexperiments would ultimately have to decide.Alternatively, the spherical PbSe CQDs used in this dissertation couldreadily be replaced with something similar to a III-V nanowire with QD in-wire [49], the intrinsic dipole moment of which should be superior, and forwhich epitaxial radial encapsulation might be expected to maximize quan-tum yield, at the cost of cryogenic operation. “Nanoplatelet” formulations140of PbSe CQDs may also offer improved oscillator strength and radiative effi-ciency, although it isn’t clear that they would be good candidates for singlephoton emission. The modeling and general processes and characterizationtechniques developed and described in this dissertation would be directlytransferable to that scenario.In all, the work in this dissertation both significantly advances knowledgeof PbX CQD emission, particularly as relevant to their use in on-demandsingle photon emitters in SOI PICs, and provides tools and readily relatableresults to advance these aims further, e.g. through emitter- or SOI photonic-specific improvements as pursued by our laboratory and others.141Bibliography[1] IMEC. URL http://www.imec.be/. Accessed January 14th, 2016. →pages 115[2] WestGrid. URL http://www.westgrid.ca/. Accessed January 14th,2016. → pages xxvii[3] ePIXfab. URL http://www.epixfab.eu/. Accessed January 14th, 2016.→ pages 115[4] S. Aaronson and A. Arkhipov. The computational complexity oflinear optics. In Proceedings of the Forty-third Annual ACMSymposium on Theory of Computing, STOC ’11, pages 333–342, NewYork, NY, USA, 2011. ACM. ISBN 978-1-4503-0691-1.doi:10.1145/1993636.1993682. → pages 6[5] J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R.Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari,C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron,D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, and M. C.Araya. Enhanced sensitivity of the LIGO gravitational wave detectorby using squeezed states of light. Nature Photonics, 7(8):613–619,Aug. 2013. ISSN 17494885. doi:10.1038/nphoton.2013.177. → pages 6[6] K. A. Abel. Synthesis and Characterization of Colloidal LeadChalcogenide Quantum Dots and Progress towards Single PhotonsOn-Demand. PhD thesis, University of Victoria, 2011. → pages 53[7] K. A. Abel, H. Qiao, J. F. Young, and F. C. J. M. van Veggel.Four-Fold enhancement of the activation energy for nonradiativedecay of excitons in PbSe/CdSe Core/Shell versus PbSe colloidalquantum dots. The Journal of Physical Chemistry Letters, 1(15):2334–2338, Aug. 2010. ISSN 1948-7185. doi:10.1021/jz1007565. →pages 44, 80142[8] I. Aharonovich, A. D. Greentree, and S. Prawer. Diamond photonics.Nature Photonics, 5(7):397–405, July 2011. ISSN 1749-4885.doi:10.1038/nphoton.2011.54. → pages 19[9] M. K. Akhlaghi, E. Schelew, and J. F. Young. Waveguide integratedsuperconducting single-photon detectors implemented as near-perfectabsorbers of coherent radiation. Nature Communications, 6(8233),Sept. 2015. doi:10.1038/ncomms9233. → pages xiv, 4, 29, 30[10] A. P. Alivisatos. Semiconductor clusters, nanocrystals, and quantumdots. Science, 271(5251):933–937, Feb. 1996.doi:10.1126/science.271.5251.933. → pages 43[11] G. Allan and C. Delerue. Confinement effects in PbSe quantum wellsand nanocrystals. Physical Review B, 70(24):245321, Dec. 2004.ISSN 1098-0121. doi:10.1103/PhysRevB.70.245321. → pages 43[12] J. M. An, A. Franceschetti, and A. Zunger. The excitonic exchangesplitting and radiative lifetime in PbSe quantum dots. Nano Letters,7(7):2129, July 2007. ISSN 1530-6984. doi:10.1021/nl071219f . →pages 74[13] J. M. An, M. Califano, A. Franceschetti, and A. Zunger.Excited-state relaxation in PbSe quantum dots. J. Chem. Phys., 128(16):164720, 2008. ISSN 00219606. doi:10.1063/1.2901022. → pages83[14] A. D. Andreev and A. A. Lipovskii. Effect of anisotropy of bandstructure on optical gain in spherical quantum dots based on PbSand PbSe. Semiconductors, 33(12):1304, Dec. 1999. ISSN 1063-7826.doi:10.1134/1.1187913. → pages 37[15] L. Arizmendi. Photonic applications of lithium niobate crystals.phys. stat. sol. (a), 201(2):253–283, Jan. 2004. ISSN 1521-396X.doi:10.1002/pssa.200303911. → pages 20[16] W. K. Bae, J. Joo, L. A. Padilha, J. Won, D. C. Lee, Q. Lin, W.-k.Koh, H. Luo, V. I. Klimov, and J. M. Pietryga. Highly effectivesurface passivation of PbSe quantum dots through reaction withmolecular chlorine. Journal of the American Chemical Society, 134(49):20160–20168, Dec. 2012. ISSN 0002-7863.doi:10.1021/ja309783v. → pages 43, 97143[17] M. G. Banaee, A. G. Pattantyus-Abraham, M. W. McCutcheon,G. W. Rieger, and J. F. Young. Efficient coupling of photonic crystalmicrocavity modes to a ridge waveguide. Applied Physics Letters, 90(19):193106, May 2007. doi:10.1063/1.2737369. → pages 27, 34, 51,115[18] H. Bao, B. F. Habenicht, O. V. Prezhdo, and X. Ruan. Temperaturedependence of hot-carrier relaxation in PbSe nanocrystals: An abinitio study. Physical Review B, 79(23):235306, June 2009.doi:10.1103/PhysRevB.79.235306. → pages 83[19] A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa. Conditionalquantum dynamics and logic gates. Physical Review Letters, 74:4083–4086, May 1995. doi:10.1103/PhysRevLett.74.4083. → pages 7[20] S. M. Barnett, B. Huttner, and R. Loudon. Spontaneous emission inabsorbing dielectric media. Physical Review Letters, 68(25):3698–3701, June 1992. doi:10.1103/PhysRevLett.68.3698. → pages 76[21] M. G. Bawendi, M. L. Steigerwald, and L. E. Brus. The quantummechanics of larger semiconductor clusters (“quantum dots”).Annual Review of Physical Chemistry, 41:477–496, Oct. 1990.doi:10.1146/annurev.pc.41.100190.002401. → pages 43[22] C. H. Bennet and G. Brassard. Quantum cryptography: Public keydistribution and coin tossing. In IEEE International Conference onComputers, Systems, and Signal Processing, Bangalore, page 175,1984. → pages 6[23] O. Benson, C. Santori, M. Pelton, and Y. Yamamoto. Regulated andentangled photons from a single quantum dot. Physical ReviewLetters, 84(11):2513–2516, Mar. 2000.doi:10.1103/PhysRevLett.84.2513. → pages 33, 34[24] W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon,J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets,V. Wiaux, and S. Beckx. Basic structures for photonic integratedcircuits in silicon-on-insulator. Optics Express, 12(8):1583–1591,2004. doi:10.1364/OPEX.12.001583. → pages 19[25] C. Bonati, A. Cannizzo, D. Tonti, A. Tortschanoff, F. van Mourik,and M. Chergui. Subpicosecond near-infrared fluorescenceupconversion study of relaxation processes in PbSe quantum dots.144Physical Review B, 76(3):033304, July 2007.doi:10.1103/PhysRevB.76.033304. → pages 83[26] D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka,M. Ezaki, C. Natarajan, M. Tanner, R. H. Hadfield, S. Dorenbos,V. Zwiller, J. O’Brien, and M. Thompson. Quantum interference insilicon waveguide circuits. In Group IV Photonics (GFP), 2011 8thIEEE International Conference on, pages 1–3, 2011. → pages 23[27] D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka,M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N.Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson. Quantuminterference and manipulation of entanglement in silicon wirewaveguide quantum circuits. New Journal of Physics, 14(4):045003,2012. doi:10.1088/1367-2630/14/4/045003. → pages 20, 23[28] A. Boretti. Optical materials: Silicon carbide’s quantum aspects.Nature Photonics, 8(2):88–90, Feb. 2014. ISSN 1749-4885.doi:10.1038/nphoton.2013.375. → pages 20[29] P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin,D. Ouyang, and D. Bimberg. Rabi oscillations in the excitonicground-state transition of InGaAs quantum dots. Physical Review B,66(8):081306, Aug. 2002. doi:10.1103/PhysRevB.66.081306. → pages79[30] R. Bose, D. V. Talapin, X. Yang, R. J. Harniman, P. T. Nguyen, andC. W. Wong. Interaction of infiltrated colloidal PbS nanocrystalswith high Q/V silicon photonic bandgap nanocavities fornear-infrared enhanced spontaneous emissions. In H. H. Du, editor,Photonic Crystals and Photonic Crystal Fibers for SensingApplications, volume 6005, page 600509. SPIE, Oct. 2005.doi:10.1117/12.632900. → pages 46[31] R. Bose, X. Yang, R. Chatterjee, J. Gao, and C. W. Wong. Weakcoupling interactions of colloidal lead sulphide nanocrystals withsilicon photonic crystal nanocavities near 1.55 µm at roomtemperature. Applied Physics Letters, 90(11):111117, Mar. 2007.doi:10.1063/1.2714097. → pages 35, 46[32] R. Bose, J. F. McMillan, J. Gao, K. M. Rickey, C. J. Chen, D. V.Talapin, C. B. Murray, and C. W. Wong. Temperature-tuning of145near-infrared monodisperse quantum dot solids at 1.5 µm forcontrollable Fo¨rster energy transfer. Nano Letters, 8(7):2006–2011,2008. doi:10.1021/nl8011243. PMID: 18512994. → pages 68[33] R. Bose, J. Gao, J. F. McMillan, A. D. Williams, and C. W. Wong.Cryogenic spectroscopy of ultra-low density colloidal leadchalcogenide quantum dots on chip-scale optical cavities towardssingle quantum dot near-infrared cavity QED. Optics Express, 17(25):22474–22483, Dec. 2009. doi:10.1364/OE.17.022474. → pages 46,65[34] R. Bose, J. F. McMillan, J. Gao, and C. W. Wong.Solution-processed cavity and slow-light quantum electrodynamics innear-infrared silicon photonic crystals. Applied Physics Letters, 95(13):131112, Sept. 2009. doi:10.1063/1.3238555. → pages 46[35] D. E. Browne and T. Rudolph. Resource-efficient linear opticalquantum computation. Physical Review Letters, 95(1):010501, June2005. doi:10.1103/PhysRevLett.95.010501. → pages 13[36] S. Buckley, K. Rivoire, and J. Vucˇkovic´. Engineered quantum dotsingle-photon sources. Reports on Progress in Physics, 75(12):126503,2012. doi:10.1088/0034-4885/75/12/126503. → pages 2, 4, 18[37] M. Calic, P. Gallo, M. Felici, K. A. Atlasov, B. Dwir, A. Rudra,G. Biasiol, L. Sorba, G. Tarel, V. Savona, and E. Kapon.Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitonsto photonic crystal cavities. Physical Review Letters, 106(22):227402,June 2011. doi:10.1103/PhysRevLett.106.227402. → pages 80[38] G. Calusine, A. Politi, and D. D. Awschalom. Silicon carbidephotonic crystal cavities with integrated color centers. AppliedPhysics Letters, 105(1):011123, 2014. doi:10.1063/1.4890083. →pages 20[39] R. A. Campos, B. E. A. Saleh, and M. C. Teich.Quantum-mechanical lossless beam splitter: SU(2) symmetry andphoton statistics. Physical Review A, 40:1371–1384, Aug 1989.doi:10.1103/PhysRevA.40.1371. → pages 14[40] J. Carolan, C. Harrold, C. Sparrow, E. Mart´ın-Lo´pez, N. J. Russell,J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh,G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto,146J. L. O’Brien, and A. Laing. Universal linear optics. Science, 349(6249), July 2015. doi:10.1126/science.aab3642. → pages 13, 19[41] J. M. Caruge, J. E. Halpert, V. Wood, V. Bulovic, and M. G.Bawendi. Colloidal quantum-dot light-emitting diodes withmetal-oxide charge transport layers. Nature Photonics, 2(4):247–250,Apr. 2008. ISSN 1749-4885. doi:10.1038/nphoton.2008.34. → pages37[42] C. M. Caves. Quantum-mechanical noise in an interferometer.Physical Review D, 23(8):1693–1708, Apr. 1981.doi:10.1103/PhysRevD.23.1693. → pages 6[43] H. E. Chappell, B. K. Hughes, M. C. Beard, A. J. Nozik, and J. C.Johnson. Emission quenching in PbSe quantum dot arrays byshort-term air exposure. The Journal of Physical Chemistry Letters,2(8):889–893, Apr. 2011. ISSN 1948-7185. doi:10.1021/jz2001979. →pages xxii, 44, 69, 70, 71, 74, 97, 98, 99, 107[44] C. Cheng. A multiquantum-dot-doped fiber amplifier withcharacteristics of broadband, flat gain, and low noise. Journal ofLightwave Technology, 26(11):1404–1410, 2008. URLhttp://jlt.osa.org/abstract.cfm?URI=jlt-26-11-1404. → pages 37[45] H. Chew. Radiation and lifetimes of atoms inside dielectric particles.Physical Review A, 38(7):3410, Oct. 1988. ISSN 0556-2791.doi:10.1103/PhysRevA.38.3410. → pages 76[46] H. Choi, J.-H. Ko, Y.-H. Kim, and S. Jeong. Steric-hindrance-drivenshape transition in PbS quantum dots: Understandingsize-dependent stability. Journal of the American Chemical Society,135(14):5278–5281, Apr. 2013. ISSN 0002-7863.doi:10.1021/ja400948t. → pages 43, 97[47] C. J. Chunnilall, I. P. Degiovanni, S. Ku¨ck, I. Mu¨ller, and A. G.Sinclair. Metrology of single-photon sources and detectors: a review.Optical Engineering, 53(8):081910, July 2014.doi:10.1117/1.OE.53.8.081910. → pages 2[48] S. W. Clark, J. M. Harbold, and F. W. Wise. Resonant energytransfer in PbS quantum dots. The Journal of Physical Chemistry C,111(20):7302–7305, May 2007. ISSN 1932-7447.doi:10.1021/jp0713561. → pages 39147[49] J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou,N. Gregersen, C. Sauvan, P. Lalanne, and J. Ge´rard. A highlyefficient single-photon source based on a quantum dot in a photonicnanowire. Nature Photonics, 4(3):174–177, Jan. 2010. ISSN1749-4885. doi:10.1038/nphoton.2009.287. → pages 140[50] J. F. Clauser. Experimental distinction between the quantum andclassical field-theoretic predictions for the photoelectric effect.Physical Review D, 9:853–860, Feb 1974.doi:10.1103/PhysRevD.9.853. → pages 17[51] J. P. Clifford, G. Konstantatos, K. W. Johnston, S. Hoogland,L. Levina, and E. H. Sargent. Fast, sensitive and spectrally tuneablecolloidal-quantum-dot photodetectors. Nat Nano, 4(1):40–44, Jan.2009. ISSN 1748-3387. doi:10.1038/nnano.2008.313. → pages 37[52] Collaboration: Authors and editors of the volumes III/17E-17F-41C.Lead selenide (PbSe) effective masses, Fermi level., volume 41C:Non-Tetrahedrally Bonded Elements and Binary Compounds I.SpringerMaterials - The Landolt-Bo¨rnstein Database.doi:10.1007/10681727 899. → pages 39[53] M. Collins, C. Xiong, I. Rey, T. Vo, J. He, S. Shahnia, C. Reardon,T. Krauss, M. Steel, A. Clark, and B. Eggleton. Integrated spatialmultiplexing of heralded single-photon sources. NatureCommunications, 4(2582), Oct. 2013. doi:10.1038/ncomms3582. →pages 34[54] M. Colocci, A. Vinattieri, L. Lippi, F. Bogani, M. Rosa-Clot,S. Taddei, A. Bosacchi, S. Franchi, and P. Frigeri. Controlled tuningof the radiative lifetime in InAs self-assembled quantum dots throughvertical ordering. Applied Physics Letters, 74(4):564–566, Jan. 1999.doi:10.1063/1.123146. → pages 79[55] R. E. Correa, E. A. Dauler, G. Nair, S. H. Pan, D. Rosenberg, A. J.Kerman, R. J. Molnar, X. Hu, F. Marsili, V. Anant, K. K. Berggren,and M. G. Bawendi. Single photon counting from individualnanocrystals in the infrared. Nano Letters, 12(6):2953–2958, June2012. ISSN 1530-6984. doi:10.1021/nl300642k. → pages 35[56] B. O. Dabbousi, J. Rodriguez-Viejo, F. V. Mikulec, J. R. Heine,H. Mattoussi, R. Ober, K. F. Jensen, and M. G. Bawendi.148(CdSe)ZnS core-shell quantum dots: Synthesis and characterizationof a size series of highly luminescent nanocrystallites. J. Phys. Chem.B, 101(46):9463–9475, Nov. 1997. ISSN 1520-6106.doi:10.1021/jp971091y. → pages 43[57] Q. Dai, Y. Wang, Y. Zhang, X. Li, R. Li, B. Zou, J. Seo, Y. Wang,M. Liu, and W. W. Yu. Stability study of PbSe semiconductornanocrystals over concentration, size, atmosphere, and lightexposure. Langmuir, 25(20):12320–12324, Oct. 2009. ISSN0743-7463. doi:10.1021/la9015614. → pages 97[58] Q. Dai, Y. Zhang, Y. Wang, Y. Wang, B. Zou, W. W. Yu, and M. Z.Hu. Ligand effects on synthesis and post-synthetic stability of PbSenanocrystals. The Journal of Physical Chemistry C, 114(39):16160–16167, Oct. 2010. ISSN 1932-7447. doi:10.1021/jp102660g. →pages 97[59] M. Davanc¸o, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa,F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan.Telecommunications-band heralded single photons from a siliconnanophotonic chip. Applied Physics Letters, 100(26):261104, 2012.doi:10.1063/1.4711253. → pages 20, 34[60] D. Deutsch. Quantum theory, the Church-Turing principle and theuniversal quantum computer. Proceedings of the Royal Society A,400(1818):97–117, July 1985. doi:10.1103/PhysRevB.90.035312. →pages 6, 7[61] I. Djordjevic. Quantum Information Processing and Quantum ErrorCorrection. Academic Press, 2012. → pages 10[62] D. F. Dorfner, T. Hu¨rlimann, G. Abstreiter, and J. J. Finley. Opticalcharacterization of silicon on insulator photonic crystal nanocavitiesinfiltrated with colloidal PbS quantum dots. Applied Physics Letters,91(23):233111, 2007. doi:10.1063/1.2822441. → pages 46[63] H. Du, C. Chen, R. Krishnan, T. D. Krauss, J. M. Harbold, F. W.Wise, M. G. Thomas, and J. Silcox. Optical properties of colloidalPbSe nanocrystals. Nano Letters, 2(11):1321, Nov. 2002. ISSN1530-6984. doi:10.1021/nl025785g. → pages 39, 43, 80[64] M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov. Invitedreview article: Single-photon sources and detectors. Review of149Scientific Instruments, 82(7):071101, 2011. ISSN 00346748.doi:10.1063/1.3610677. → pages 2, 17, 18[65] A. K. Ekert. Quantum cryptography based on Bell’s theorem.Physical Review Letters, 67:661–663, Aug 1991.doi:10.1103/PhysRevLett.67.661. → pages 6[66] P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy,and L. F. Lester. Transition dipole moment of InAs/InGaAsquantum dots from experiments on ultralow-threshold laser diodes.Applied Physics Letters, 77(2):262–264, 2000. doi:10.1063/1.126944.→ pages 79[67] D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka,Y. Arakawa, Y. Yamamoto, and J. Vucˇkovic´. Controlling thespontaneous emission rate of single quantum dots in atwo-dimensional photonic crystal. Physical Review Letters, 95:013904, Jul 2005. doi:10.1103/PhysRevLett.95.013904. → pages 33,47, 80[68] D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucˇkovic´.Generation and transfer of single photons on a photonic crystal chip.Opt. Express, 15(9):5550–5558, 2007. doi:10.1364/OE.15.005550. →pages 33, 34, 80[69] A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vucˇkovic´.Efficient photonic crystal cavity-waveguide couplers. Applied PhysicsLetters, 90(7):073102, 2007. doi:10.1063/1.2472534. → pages 33[70] A. Faraon, A. Majumdar, D. Englund, E. Kim, M. Bajcsy, andJ. Vucˇkovic´. Integrated quantum optical networks based on quantumdots and photonic crystals. New Journal of Physics, 13(5):055025,2011. ISSN 1367-2630. doi:10.1088/1367-2630/13/5/055025. →pages 19[71] R. Feynman. Simulating physics with computers. InternationalJournal of Theoretical Physics, 21:467–488, 1982.doi:10.1007/BF02650179. → pages 6[72] H. Flayac, D. Gerace, and V. Savona. An all-silicon single-photonsource by unconventional photon blockade. Scientific Reports, 5:11223, June 2015. doi:10.1038/srep11223. → pages 30150[73] C. A. Foell, E. Schelew, H. Qiao, K. A. Abel, S. Hughes, F. C. J. M.van Veggel, and J. F. Young. Saturation behaviour of colloidal PbSequantum dot exciton emission coupled into silicon photonic circuits.Optics Express, 20(10):10453–10469, May 2012.doi:10.1364/OE.20.010453. → pages iv, 35, 105[74] C. A. Foell, K. A. Abel, F. C. J. M. van Veggel, and J. F. Young.Kinetic analysis of the temperature dependence of PbSe colloidalquantum dot photoluminescence: Effects of synthesis process andoxygen exposure. Physical Review B, 89:045139, Jan 2014.doi:10.1103/PhysRevB.89.045139. → pages iv, v[75] A. Franceschetti, J. Luo, J. An, and A. Zunger. Origin of one-photonand two-photon optical transitions in PbSe nanocrystals. PhysicalReview B, 79(24):241311(R), June 2009. ISSN 1098-0121.doi:10.1103/PhysRevB.79.241311. → pages 38[76] I. Fushman, D. Englund, and J. Vucˇkovic´. Coupling of PbS quantumdots to photonic crystal cavities at room temperature. AppliedPhysics Letters, 87(24):241102, Dec. 2005. ISSN 00036951.doi:10.1063/1.2138792. → pages 46[77] B. D. Geyter and Z. Hens. The absorption coefficient of PbSe/CdSecore/shell colloidal quantum dots. Applied Physics Letters, 97(16):161908, 2010. doi:10.1063/1.3499754. → pages 76[78] R. J. Glauber. Coherent and incoherent states of the radiation field.Physical Review, 131:2766–2788, Sep 1963.doi:10.1103/PhysRev.131.2766. → pages 2[79] S. V. Goupalov. Selection rules for optical transitions in PbSenanocrystal quantum dots: Drastic effect of structure inversionasymmetry. Physical Review B, 79(23):233305, June 2009. ISSN1098-0121. doi:10.1103/PhysRevB.79.233305. → pages 108[80] P. Grangier. Experiments with single photons. In T. Damour,O. Darrigol, B. Duplantier, and V. Rivasseau, editors, Progress inMathematical Physics, volume 47, pages 135–149. Birkha¨user Basel,2006. doi:10.1007/3-7643-7436-5 5. → pages 17[81] F. Grassi, M. Argeri, L. Marchese, and M. Cossi. First principlestudy of capping energies and electronic states in stoichiometric andnonstoichiometric PbSe nanoclusters. The Journal of Physical151Chemistry C, 117(49):26396–26404, Dec. 2013. ISSN 1932-7447.doi:10.1021/jp4102465. → pages 43[82] A. D. Greentree, B. A. Fairchild, F. M. Hossain, and S. Prawer.Diamond integrated quantum photonics. Materials Today, 11(9):22–31, Sept. 2008. ISSN 1369-7021.doi:10.1016/S1369-7021(08)70176-7. → pages 19[83] L. K. Grover. Quantum mechanics helps in searching for a needle ina haystack. Physical Review Letters, 79:325–328, Jul 1997.doi:10.1103/PhysRevLett.79.325. → pages 6[84] R. H. Hadfield. Single-photon detectors for optical quantuminformation applications. Nature Photonics, 3(12):696–705, Dec.2009. ISSN 1749-4885. doi:10.1038/nphoton.2009.230. → pages 27[85] J. M. Harbold and F. W. Wise. Photoluminescence spectroscopy ofPbSe nanocrystals. Physical Review B, 76(12):125304, Sept. 2007.doi:10.1103/PhysRevB.76.125304. → pages 80[86] J. M. Harbold, H. Du, T. D. Krauss, K. Cho, C. B. Murray, andF. W. Wise. Time-resolved intraband relaxation of strongly confinedelectrons and holes in colloidal PbSe nanocrystals. Physical ReviewB, 72(19):195312, Nov. 2005. doi:10.1103/PhysRevB.72.195312. →pages 83[87] N. C. Harris, Y. Ma, J. Mower, T. Baehr-Jones, D. Englund,M. Hochberg, and C. Galland. Efficient, compact and low lossthermo-optic phase shifter in silicon. Optics Express, 22(9):10487–10493, May 2014. doi:10.1364/OE.22.010487. → pages 20, 23[88] A. W. Harrow, A. Hassidim, and S. Lloyd. Quantum algorithm forlinear systems of equations. Physical Review Letters, 103:150502, Oct2009. doi:10.1103/PhysRevLett.103.150502. → pages 6[89] B. J. M. Hausmann, B. Shields, Q. Quan, P. Maletinsky,M. McCutcheon, J. T. Choy, T. M. Babinec, A. Kubanek, A. Yacoby,M. D. Lukin, and M. Loncˇar. Integrated diamond networks forquantum nanophotonics. Nano Letters, 12(3):1578–1582, Mar. 2012.ISSN 1530-6984. doi:10.1021/nl204449n. → pages 19[90] J. Heo, T. Zhu, C. Zhang, J. Xu, and P. Bhattacharya.Electroluminescence from silicon-based photonic crystal microcavities152with PbSe quantum dots. Optics Letters, 35(4):547–549, Feb. 2010.doi:10.1364/OL.35.000547. → pages 46[91] U. Hohenester, A. Laucht, M. Kaniber, N. Hauke, A. Neumann,A. Mohtashami, M. Seliger, M. Bichler, and J. J. Finley.Phonon-assisted transitions from quantum dot excitons to cavityphotons. Physical Review B, 80(20):201311, Nov. 2009.doi:10.1103/PhysRevB.80.201311. → pages 80[92] C. K. Hong, Z. Y. Ou, and L. Mandel. Measurement ofsubpicosecond time intervals between two photons by interference.Physical Review Letters, 59:2044–2046, Nov 1987.doi:10.1103/PhysRevLett.59.2044. → pages 16[93] B. K. Hughes, D. A. Ruddy, J. L. Blackburn, D. K. Smith, M. R.Bergren, A. J. Nozik, J. C. Johnson, and M. C. Beard. Control ofPbSe quantum dot surface chemistry and photophysics using analkylselenide ligand. ACS Nano, May 2012. ISSN 1936-0851.doi:10.1021/nn301405j. → pages x, xxii, 44, 69, 70, 71, 74, 97, 98, 99,107, 139[94] S. Hughes, P. Yao, F. Milde, A. Knorr, D. Dalacu, K. Mnaymneh,V. Sazonova, P. J. Poole, G. C. Aers, J. Lapointe, R. Cheriton, andR. L. Williams. Influence of electron-acoustic phonon scattering onoff-resonant cavity feeding within a strongly coupled quantum-dotcavity system. Physical Review B, 83(16):165313, Apr. 2011.doi:10.1103/PhysRevB.83.165313. → pages 80[95] P. C. Humphreys, B. J. Metcalf, J. B. Spring, M. Moore, X.-M. Jin,M. Barbieri, W. S. Kolthammer, and I. A. Walmsley. Linear opticalquantum computing in a single spatial mode. Physical ReviewLetters, 111(15):150501, Oct. 2013.doi:10.1103/PhysRevLett.111.150501. → pages 13[96] C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combri’e,G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton.Multi-photon absorption limits to heralded single photon sources.Scientific Reports, 3, Nov. 2013. doi:10.1038/srep03087. → pages 34[97] A. H. Ip, S. M. Thon, S. Hoogland, O. Voznyy, D. Zhitomirsky,R. Debnath, L. Levina, L. R. Rollny, G. H. Carey, A. Fischer, K. W.Kemp, I. J. Kramer, Z. Ning, A. J. Labelle, K. W. Chou,153A. Amassian, and E. H. Sargent. Hybrid passivated colloidalquantum dot solids. Nature Nanotechnology, 7(9):577–582, Sept.2012. ISSN 1748-3387. doi:10.1038/nnano.2012.127. → pages 43[98] A. B. J. Clarke. The SQUID handbook. Wiley-VCH, 2004. → pages 6[99] H. Jin, F.-M. Liu, P. Xu, J.-L. Xia, M.-L. Zhong, Y. Yuan, J.-W.Zhou, Y.-X. Gong, W. Wang, and S.-N. Zhu. On-chip generation andmanipulation of entangled photons based on reconfigurablelithium-niobate waveguide circuits. Physical Review Letters, 113(10):103601–, Sept. 2014. doi:10.1103/PhysRevLett.113.103601. → pages20[100] S. John. Strong localization of photons in certain disordereddielectric superlattices. Phys. Rev. Lett., 58:2486–2489, Jun 1987.doi:10.1103/PhysRevLett.58.2486. → pages 24[101] S. Kalliakos, Y. Brody, A. Schwagmann, A. J. Bennett, M. B. Ward,D. J. P. Ellis, J. Skiba-Szymanska, I. Farrer, J. P. Griffiths, G. A. C.Jones, D. A. Ritchie, and A. J. Shields. In-plane emission ofindistinguishable photons generated by an integrated quantumemitter. Applied Physics Letters, 104(22):221109, 2014.doi:10.1063/1.4881887. → pages 34[102] W. Kern. The evolution of silicon wafer cleaning technology. Journalof The Electrochemical Society, 137(6):1887–1892, 1990.doi:10.1149/1.2086825. → pages 54[103] A. Kigel, M. Brumer, G. I. Maikov, A. Sashchiuk, and E. Lifshitz.Thermally activated photoluminescence in lead selenide colloidalquantum dots. Small, 5(14):1675, July 2009. ISSN 16136810.doi:10.1002/smll.200801378. → pages 44[104] G. Kim, H. Park, J. Joo, K.-S. Jang, M.-J. Kwack, S. Kim,I. Gyoo Kim, J. Hyuk Oh, S. Ae Kim, J. Park, and S. Kim.Single-chip photonic transceiver based on bulk-silicon, as a chip-levelphotonic I/O platform for optical interconnects. Scientific Reports, 5(11329), June 2015. doi:10.1038/srep11329. → pages 20[105] G.-H. Kim, Y.-H. Lee, A. Shinya, and M. Notomi. Coupling of small,low-loss hexapole mode with photonic crystal slab waveguide mode.Optics Express, 12(26):6624–6631, 2004.doi:10.1364/OPEX.12.006624. → pages 33154[106] S. Kim, B. Fisher, H.-J. Eisler, and M. Bawendi. Type-II quantumdots: CdTe/CdSe (Core/Shell) and CdSe/ZnTe (Core/Shell)heterostructures. Journal of the American Chemical Society, 125(38):11466–11467, Sept. 2003. ISSN 0002-7863. doi:10.1021/ja0361749. →pages 43[107] H. J. Kimble. The quantum internet. Nature, 453(7198):1023–1030,June 2008. ISSN 0028-0836. doi:10.1038/nature07127. → pages 11[108] H. J. Kimble, M. Dagenais, and L. Mandel. Photon antibunching inresonance fluorescence. Physical Review Letters, 39:691–695, Sep1977. doi:10.1103/PhysRevLett.39.691. → pages 17[109] L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K.Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson,J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras,D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong.Electronic-photonic integrated circuits on the CMOS platform. InJ. A. Kubby and G. T. Reed, editors, Silicon Photonics, volume6125, 2006. doi:10.1117/12.654455. → pages 20[110] E. Knill, R. Laflamme, and G. J. Milburn. A scheme for efficientquantum computation with linear optics. Nature, 409(6816):46–52,Jan. 2001. ISSN 0028-0836. doi:10.1038/35051009. → pages 2, 3, 13[111] T. L. Koch and U. Koren. Photonic integrated circuits. AT&TTechnical Journal, 71(1):63–74, Jan. 1992. ISSN 1538-7305.doi:10.1002/j.1538-7305.1992.tb00148.x . → pages 3[112] A. F. Koenderink, M. Kafesaki, C. M. Soukoulis, and V. Sandoghdar.Spontaneous emission rates of dipoles in photonic crystalmembranes. Journal of the Optical Society of America B, 23(6):1196–1206, June 2006. doi:10.1364/JOSAB.23.001196. → pages 85[113] W.-k. Koh, A. Y. Koposov, J. T. Stewart, B. N. Pal, I. Robel, J. M.Pietryga, and V. I. Klimov. Heavily doped n-type PbSe and PbSnanocrystals using ground-state charge transfer from cobaltocene.Scientific Reports, 3:2004, June 2013. doi:10.1038/srep02004. →pages 97[114] P. Kok and B. W. Lovett. Introduction to Optical QuantumInformation Processing. Cambridge University Press, 2010. → pages3, 6, 13155[115] P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, andG. J. Milburn. Linear optical quantum computing with photonicqubits. Reviews of Modern Physics, 79:135–174, Jan 2007.doi:10.1103/RevModPhys.79.135. → pages 3, 13[116] L. Kong, Z. C. Feng, Z. Wu, and W. Lu. Temperature dependentand time-resolved photoluminescence studies of InAs self-assembledquantum dots with InGaAs strain reducing layer structure. Journalof Applied Physics, 106(1):013512, 2009. doi:10.1063/1.3159648. →pages 79[117] C. Kopp, S. Bernabe, B. Bakir, J.-M. Fedeli, R. Orobtchouk,F. Schrank, H. Porte, L. Zimmermann, and T. Tekin. Siliconphotonic circuits: On-CMOS integration, fiber optical coupling, andpackaging. Selected Topics in Quantum Electronics, IEEE Journalof, 17(3):498–509, 2011. ISSN 1077-260X. → pages 20[118] P. T. Kristensen, C. Van Vlack, and S. Hughes. Generalized effectivemode volume for leaky optical cavities. Optics Letters, 37(10):1649–1651, 2012. doi:10.1364/OL.37.001649. → pages 86[119] A. Kuhn, M. Hennrich, and G. Rempe. Deterministic single-photonsource for distributed quantum networking. Phys. Rev. Lett., 89:067901, Jul 2002. doi:10.1103/PhysRevLett.89.067901. → pages 17[120] P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko,and Y. Shih. New high-intensity source of polarization-entangledphoton pairs. Phys. Rev. Lett., 75:4337–4341, Dec 1995.doi:10.1103/PhysRevLett.75.4337. → pages 17[121] T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, andJ. L. O’Brien. Quantum computers. Nature, 464(7285):45–53, Mar.2010. ISSN 0028-0836. doi:10.1038/nature08812. → pages 10[122] M. L. M. Larry A. Coldren, Scott W. Corzine. Diode Lasers andPhotonic Integrated Circuits. Wiley, 2nd edition, 2012. → pages 3[123] A. Laucht, N. Hauke, J. M. Villas-Boˆas, F. Hofbauer, G. Bo¨hm,M. Kaniber, and J. J. Finley. Dephasing of exciton polaritons inphotoexcited InGaAs quantum dots in GaAs nanocavities. PhysicalReview Letters, 103:087405, 2009.doi:10.1103/PhysRevLett.103.087405. → pages 80156[124] A. Laucht, S. Pu¨tz, T. Gu¨nthner, N. Hauke, R. Saive, S. Fre´de´rick,M. Bichler, M.-C. Amann, A. W. Holleitner, M. Kaniber, and J. J.Finley. A waveguide-coupled on-chip single-photon source. PhysicalReview X, 2:011014, Mar 2012. doi:10.1103/PhysRevX.2.011014. →pages 33[125] M. Lee, W. J. Chung, S. K. Park, M. su Kim, H. S. Seo, and J. J. Ju.Structural and optical characterizations of multi-layered andmulti-stacked PbSe quantum dots. Nanotechnology, 16(8):1148–1152,Aug. 2005. ISSN 0957-4484. doi:10.1088/0957-4484/16/8/028. →pages 46, 47[126] G. Leuchs and T. Beth. Quantum Information Processing. Wiley,2005. → pages 10[127] C. B. Li, C. J. Huang, B. W. Cheng, Y. H. Zuo, R. W. Mao, L. P.Luo, J. Z. Yu, and Q. M. Wang. Cavity-enhanced photoluminescenceof SiGe/Si multiquantum wells grown on silicon-on-insulatorsubstrate. Journal of Applied Physics, 95(10):5914–5916, 2004.doi:10.1063/1.1707203. → pages 34[128] C. B. Li, B. W. Cheng, Y. H. Zuo, A. P. Morrison, J. Z. Yu, andQ. M. Wang. Influence of the cavity on the low-temperaturephotoluminescence of SiGe/Si multiquantum wells grown on asilicon-on-insulator substrate. Applied Physics Letters, 88(12):121901, 2006. doi:10.1063/1.2187433. → pages 34[129] S. Lloyd. Universal quantum simulators. Science, 273(5278):1073–1078, 1996. doi:10.1126/science.273.5278.1073. → pages 6[130] P. Lodahl, S. Mahmoodian, and S. Stobbe. Interfacing singlephotons and single quantum dots with photonic nanostructures.Reviews of Modern Physics, 87(2):347–400, May 2015.doi:10.1103/RevModPhys.87.347. → pages 34[131] B. Lounis and M. Orrit. Single-photon sources. Reports on Progressin Physics, 68(5):1129, 2005. doi:10.1088/0034-4885/68/5/R04. →pages 2[132] L. Lu, A. Mock, and J. O’Brien. Efficient coupling between aphotonic crystal nanocavity and a waveguide with directionalend-facet emission. Journal of Optics, 14(5):055502, 2012. ISSN2040-8986. doi:10.1088/2040-8978/14/5/055502. → pages 33157[133] T. S. Luk, S. Xiong, W. W. Chow, X. Miao, G. Subramania, P. J.Resnick, A. J. Fischer, and J. C. Brinker. Anomalous enhancedemission from PbS quantum dots on a photonic-crystal microcavity.Journal of the Optical Society of America B, 28(6):1365–1373, June2011. doi:10.1364/JOSAB.28.001365. → pages 46, 47, 136[134] X.-S. Ma. Integrated quantum photonics: On-chip teleportation. NatPhoton, 8(10):749–751, Oct. 2014. ISSN 1749-4885.doi:10.1038/nphoton.2014.223. → pages 12[135] V. S. C. Manga Rao and S. Hughes. Single quantum dot spontaneousemission in a finite-size photonic crystal waveguide: Proposal for anefficient “on chip” single photon gun. Physical Review Letters, 99(19):193901, Nov. 2007. doi:10.1103/PhysRevLett.99.193901. → pages 33[136] Y. I. Manin. Vychislimoe i nevychislimoe [computable andnoncomputable]. Sov. Radio., pages 13–15, 1980. → pages 6[137] F. Masia, W. Langbein, I. Moreels, Z. Hens, and P. Borri. Excitondephasing in lead sulfide quantum dots by x-point phonons. Phys.Rev. B, 83:201309, May 2011. doi:10.1103/PhysRevB.83.201309. →pages 42[138] J. McMillan, M. Yu, W.-k. Koh, C. Murray, D.-L. Kwong, and C. W.Wong. Purcell-enhanced spontaneous emission of colloidal PbSquantum dots in slow-light silicon photonic crystal waveguides at thenear-infrared. In Conference on Lasers andElectro-Optics/International Quantum Electronics Conference, pages1–2, 2009. doi:10.1364/IQEC.2009.IFA4. → pages 46[139] B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A.Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri,W. Steven Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford,P. G. Smith, and I. A. Walmsley. Multiphoton quantum interferencein a multiport integrated photonic device. Nature Communications,4:1356, Jan. 2013. doi:10.1038/ncomms2349. → pages 18[140] X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose,J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S. Weiss.Quantum dots for live cells, in vivo imaging, and diagnostics.Science, 307(5709):538–544, Jan. 2005. ISSN 1095-9203.doi:10.1126/science.1104274. → pages 37158[141] I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman,J. C. Martins, G. Allan, and Z. Hens. Composition andsize-dependent extinction coefficient of colloidal PbSe quantum dots.Chem. Mater., 19(25):6101–6106, Nov. 2007. ISSN 0897-4756.doi:10.1021/cm071410q. → pages 87, 105[142] I. Moreels, K. Lambert, D. Smeets, D. D. Muynck, T. Nollet, J. C.Martins, F. Vanhaecke, A. Vantomme, C. Delerue, G. Allan, andZ. Hens. Size-dependent optical properties of colloidal PbS quantumdots. ACS Nano, 3(10):3023–3030, Oct. 2009. ISSN 1936-0851.doi:10.1021/nn900863a. → pages xvi, 38, 76[143] I. Moreels, G. Allan, B. De Geyter, L. Wirtz, C. Delerue, andZ. Hens. Dielectric function of colloidal lead chalcogenide quantumdots obtained by a Kramers-Kro¨nig analysis of the absorbancespectrum. Physical Review B, 81(23):235319, June 2010.doi:10.1103/PhysRevB.81.235319. → pages 79[144] J. Mower and D. Englund. Efficient generation of single andentangled photons on a silicon photonic integrated chip. PhysicalReview A, 84:052326, Nov 2011. doi:10.1103/PhysRevA.84.052326. →pages 30[145] C. B. Murray, S. Sun, W. Gaschler, H. Doyle, T. A. Betley, andC. R. Kagan. Colloidal synthesis of nanocrystals and nanocrystalsuperlattices. IBM J. Res. Dev., 45:47–56, 2001.doi:10.1147/rd.451.0047. → pages 35, 36[146] F. Najafi, J. Mower, N. C. Harris, F. Bellei, A. Dane, C. Lee, X. Hu,P. Kharel, F. Marsili, S. Assefa, K. K. Berggren, and D. Englund.On-chip detection of non-classical light by scalable integration ofsingle-photon detectors. Nature Communications, 6, Jan. 2015.doi:10.1038/ncomms6873. → pages 30[147] K. Nemoto and W. J. Munro. Nearly deterministic linear opticalcontrolled-NOT gate. Phys. Rev. Lett., 93:250502, Dec 2004.doi:10.1103/PhysRevLett.93.250502. → pages 12[148] L. A. Ngah, O. Alibart, L. Labonte´, V. D’Auria, and S. Tanzilli.Ultra-fast heralded single photon source based on telecomtechnology. Laser & Photonics Reviews, 9(2):L1–L5, 2015. ISSN1863-8899. doi:10.1002/lpor.201400404. → pages 17, 18159[149] M. A. Nielsen and I. L. Chuang. Quantum Computation andQuantum Information. Cambridge University Press, 2000. → pages10, 12[150] G. Nootz, L. A. Padilha, P. D. Olszak, S. Webster, D. J. Hagan,E. W. V. Stryland, L. Levina, V. Sukhovatkin, L. Brzozowski, andE. H. Sargent. Role of symmetry breaking on the optical transitionsin lead-salt quantum dots. Nano Letters, 10(9):3577–3582, Sept.2010. ISSN 1530-6984. doi:10.1021/nl1018673. → pages 38[151] L. Novotny and B. Hecht. Principles of Nano-Optics. Cambridge,2006. → pages 76[152] K. Nozaki, H. Watanabe, and T. Baba. Photonic crystal nanolasermonolithically integrated with passive waveguide for effective lightextraction. Applied Physics Letters, 92(2):021108, 2008.doi:10.1063/1.2831916. → pages 33[153] A. J. Nozik. Quantum dot solar cells. Physica E, 14:115–120, 2002.→ pages 37[154] A. J. Nozik, M. C. Beard, J. M. Luther, M. Law, R. J. Ellingson, andJ. C. Johnson. Semiconductor quantum dots and quantum dotarrays and applications of multiple exciton generation tothird-generation photovoltaic solar cells. Chem. Rev., 110(11):6873–6890, 2010. doi:10.1021/cr900289f . → pages 37[155] J. O’Brien, B. Patton, M. Sasaki, and J. Vucˇkovic´. Focus onintegrated quantum optics. New Journal of Physics, 15(3):035016,2013. doi:10.1088/1367-2630/15/3/035016. → pages 12[156] T. Okuno, Y. Masumoto, M. Ikezawa, T. Ogawa, and A. A.Lipovskii. Size-dependent picosecond energy relaxation in PbSequantum dots. Applied Physics Letters, 77(4):504–506, July 2000.doi:10.1063/1.127025. → pages 83[157] S. Olivier, C. Smith, H. Benisty, C. Weisbuch, T. Krauss, R. Houdre,and U. Oesterle. Cascaded photonic crystal guides and cavities:spectral studies and their impact on integrated optics design.Quantum Electronics, IEEE Journal of, 38(7):816–824, 2002. ISSN0018-9197. doi:10.1109/JQE.2002.1017592. → pages 33160[158] A. Omari, P. Geiregat, D. Van Thourhout, and Z. Hens. Lightabsorption in hybrid silicon-on-insulator/quantum dot waveguides.Optics Express, 21(20):23272–23285, 2013.doi:10.1364/OE.21.023272. → pages 112[159] Y. Ooka, T. Tetsumoto, A. Fushimi, W. Yoshiki, and T. Tanabe.CMOS compatible high-Q photonic crystal nanocavity fabricatedwith photolithography on silicon photonic platform. ScientificReports, 5:11312, June 2015. doi:10.1038/srep11312. → pages 26[160] Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa. Impact ofelectron-phonon interactions on quantum-dot cavity quantumelectrodynamics. e-print: arXiv:0908.0788v1, 2009. URLhttp://arxiv.org/abs/0908.0788v1. → pages 80[161] M. Paillard, X. Marie, E. Vanelle, T. Amand, V. K. Kalevich, A. R.Kovsh, A. E. Zhukov, and V. M. Ustinov. Time-resolvedphotoluminescence in self-assembled InAs/GaAs quantum dots understrictly resonant excitation. Applied Physics Letters, 76(1):76–78,Jan. 2000. doi:10.1063/1.125661. → pages 79[162] Y. Pan, H. Bai, L. Pan, Y. Li, M. C. Tamargo, M. Sohel, and J. R.Lombardi. Size controlled synthesis of monodisperse PbTe quantumdots: using oleylamine as the capping ligand. Journal of MaterialsChemistry, 22(44):23593–23601, 2012. ISSN 0959-9428.doi:10.1039/C2JM15540K. → pages 97[163] R. B. Patel, A. J. Bennett, I. Farrer, C. A. Nicoll, D. A. Ritchie, andA. J. Shields. Two-photon interference of the emission fromelectrically tunable remote quantum dots. Nature Photonics, 4:632–635, 2010. doi:10.1038/nphoton.2010.161. → pages 19[164] A. G. Pattantyus-Abraham, H. Qiao, J. Shan, K. A. Abel, T.-S.Wang, F. C. J. M. van Veggel, and J. F. Young. Site-selective opticalcoupling of PbSe nanocrystals to Si-based photonic crystalmicrocavities. Nano Letters, 9(8):2849, Aug. 2009. ISSN 1530-6984.doi:10.1021/nl900961r. → pages xvii, 35, 46, 47, 51, 55, 56, 57, 58, 64[165] W. Pernice, C. Schuck, O. Minaeva, M. Li, G. Goltsman,A. Sergienko, and H. Tang. High-speed and high-efficiency travellingwave single-photon detectors embedded in nanophotonic circuits.Nature Communications, 3:1325, Dec. 2012.doi:10.1038/ncomms2307. → pages 30161[166] C. B. Poitras, M. Lipson, H. Du, M. A. Hahn, and T. D. Krauss.Photoluminescence enhancement of colloidal quantum dots embeddedin a monolithic microcavity. Applied Physics Letters, 82(23):4032,June 2003. ISSN 00036951. doi:10.1063/1.1581007. → pages 46[167] A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien.Silica-on-silicon waveguide quantum circuits. Science, 320(5876):646–649, 2008. doi:10.1126/science.1155441. → pages 19[168] A. Politi, J. Matthews, M. Thompson, and J. O’Brien. Integratedquantum photonics. Selected Topics in Quantum Electronics, IEEEJournal of, 15(6):1673–1684, 2009. ISSN 1077-260X.doi:10.1109/JSTQE.2009.2026060. → pages 12[169] E. Pomarico, B. Sanguinetti, C. I. Osorio, H. Herrmann, and R. T.Thew. Engineering integrated pure narrow-band photon sources.New Journal of Physics, 14(3):033008, 2012. ISSN 1367-2630.doi:10.1088/1367-2630/14/3/033008. → pages 18[170] R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek,T. Jennewein, and A. Zeilinger. High-speed linear optics quantumcomputing using active feed-forward. Nature, 445(7123):65–69, Jan.2007. ISSN 0028-0836. doi:10.1038/nature05346. → pages 13[171] D. Qi, M. Fischbein, M. Drndic´, and S. Sˇelmic´. Efficientpolymer-nanocrystal quantum-dot photodetectors. Applied PhysicsLetters, 86(9):093103, 2005. doi:10.1063/1.1872216. → pages 37[172] H. Qiao, K. A. Abel, F. C. J. M. van Veggel, and J. F. Young.Exciton thermalization and state broadening contributions to thephotoluminescence of colloidal PbSe quantum dot films from 295 to4.5 k. Physical Review B, 82(16):165435, Oct. 2010.doi:10.1103/PhysRevB.82.165435. → pages 41, 42, 44, 53, 59, 68, 69,74, 80, 84, 89, 99, 106, 112[173] R. Quintero-Torres, C. A. Foell, J. Pichaandi, F. C. J. M. van Veggel,and J. F. Young. Photoluminescence dynamics in solid formulationsof colloidal PbSe quantum dots: Three-dimensional versustwo-dimensional films. Applied Physics Letters, 101(12):121904, 2012.doi:10.1063/1.4752737. → pages iv, v, xvii, xviii, 55, 61, 66[174] R. Quintero-Torres, F. C. J. M. van Veggel, and J. F. Young.Temperature dependence of Fo¨rster thermalization and population162decay in PbSe nanocrystals. The Journal of Physical Chemistry C,118(2):1377–1385, Jan. 2014. ISSN 1932-7447.doi:10.1021/jp4109046. → pages 67, 112[175] M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan.Spectroscopy of 1.55 µm PbS quantum dots on Si photonic crystalcavities with a fiber taper waveguide. Applied Physics Letters, 96(16):161108, 2010. doi:10.1063/1.3396988. → pages 46, 47, 65[176] M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan. Fiber-basedcryogenic and time-resolved spectroscopy of PbS quantum dots.Optics Express, 19(3):1786–1793, Jan. 2011.doi:10.1364/OE.19.001786. → pages 46[177] T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White. Linearoptical controlled-NOT gate in the coincidence basis. Phys. Rev. A,65:062324, Jun 2002. doi:10.1103/PhysRevA.65.062324. → pages 15[178] G. Reithmaier, S. Lichtmannecker, T. Reichert, P. Hasch, K. Mu¨ller,M. Bichler, R. Gross, and J. J. Finley. On-chip time resolveddetection of quantum dot emission using integrated superconductingsingle photon detectors. Scientific Reports, 3:1901, May 2013.doi:10.1038/srep01901. → pages 34[179] J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn,S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke,and A. Forchel. Strong coupling in a single quantumdot-semiconductor microcavity system. Nature, 432(7014):197–200,Nov. 2004. ISSN 0028-0836. doi:10.1038/nature02969. → pages 47[180] V. Rinnerbauer, H. Egelhaaf, K. Hingerl, P. Zimmer, S. Werner,T. Warming, A. Hoffmann, M. Kovalenko, W. Heiss, G. Hesser, andF. Schaffler. Energy transfer in close-packed PbS nanocrystal films.Physical Review B, 77(8), Feb. 2008. ISSN 1098-0121.doi:10.1103/PhysRevB.77.085322. → pages 44[181] F. Rossi. Theory of Semiconductor Quantum Devices. Springer,2010. → pages 74[182] C. Roy and S. Hughes. Phonon-dressed Mollow triplet in the regimeof cavity quantum electrodynamics: Excitation-induced dephasingand nonperturbative cavity feeding effects. Physical Review Letters,163106(24):247403, June 2011. doi:10.1103/PhysRevLett.106.247403. →pages 80[183] C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto.Triggered single photons from a quantum dot. Physical ReviewLetters, 86:1502–1505, Feb 2001. doi:10.1103/PhysRevLett.86.1502.→ pages 33, 34[184] C. Santori, D. Fattal, and Y. Yamamoto. Single-photon Devices andApplications. Wiley, Nov. 2010. → pages 2[185] E. H. Sargent. Infrared quantum dots. Advanced Materials, 17(5):515–522, Mar. 2005. ISSN 0935-9648. doi:10.1002/adma.200401552.→ pages 46, 47[186] S. Scheel, L. Kno¨ll, D. Welsch, and S. M. Barnett. Quantumlocal-field corrections and spontaneous decay. Physical Review A, 60(2):1590–1597, Aug. 1999. doi:10.1103/PhysRevA.60.1590. → pages76[187] M. Scheele, J. H. Engel, V. E. Ferry, D. Hanifi, Y. Liu, and A. P.Alivisatos. Nonmonotonic size dependence in the hole mobility ofmethoxide-stabilized PbSe quantum dot solids. ACS Nano, 7(8):6774–6781, Aug. 2013. ISSN 1936-0851. doi:10.1021/nn401657n. →pages 97[188] E. Schelew. Characterization of photonic crystal basedsilicon-on-insulator optical circuits fabricated by a CMOS foundry.Master’s thesis, University of British Columbia, 2011. → pages 27[189] E. Schelew, G. Rieger, and J. Young. Characterization of integratedplanar photonic crystal circuits fabricated by a CMOS foundry.Journal of Lightwave Technology, 31(2):239–248, Jan. 2013. ISSN0733-8724. doi:10.1109/JLT.2012.2228466. → pages xxiii, 27, 34, 114,115, 121, 135[190] E. Schelew, M. K. Akhlaghi, and J. F. Young. Integrating singlephoton sources and high-efficiency, low dark count single photondetectors using photonic crystal microcavities in silicon-on-insulatorwaveguides. In Nonlinear Optics: Novel Phenomena, Materials andApplications, 2015. → pages 34164[191] A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C.Jones, D. A. Ritchie, and A. J. Shields. On-chip single photonemission from an integrated semiconductor quantum dot into aphotonic crystal waveguide. Applied Physics Letters, 99(26):261108,Dec. 2011. doi:10.1063/1.3672214. → pages 47[192] A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths,G. A. C. Jones, D. A. Ritchie, and A. J. Shields. In-planesingle-photon emission from a L3 cavity coupled to a photoniccrystal waveguide. Optics Express, 20(27):28614–28624, 2012.doi:10.1364/OE.20.028614. → pages 34[193] H. P. Seigneur, M. Weed, M. N. Leuenberger, , and W. V.Schoenfeld. Controlled on-chip single-photon transfer using photoniccrystal coupled-cavity waveguides. Advances in OptoElectronics,2011:893086, 2011. doi:10.1155/2011/893086. → pages 33[194] O. E. Semonin, J. C. Johnson, J. M. Luther, A. G. Midgett, A. J.Nozik, and M. C. Beard. Absolute photoluminescence quantumyields of IR-26 dye, PbS, and PbSe quantum dots. The Journal ofPhysical Chemistry Letters, 1(16):2445, 2010. doi:10.1021/jz100830r.→ pages 43[195] Y. Shirasaki, G. J. Supran, M. G. Bawendi, and V. Bulovic.Emergence of colloidal quantum-dot light-emitting technologies. NatPhoton, 7(1):13–23, Jan. 2013. ISSN 1749-4885.doi:10.1038/nphoton.2012.328. → pages 37[196] P. Shor. Polynomial-time algorithms for prime factorization anddiscrete logarithms on a quantum computer. SIAM Journal onComputing, 26(5):1484–1509, 1997. doi:10.1137/S0097539795293172.→ pages 6[197] K. L. Silverman, R. P. Mirin, S. T. Cundiff, and A. G. Norman.Direct measurement of polarization resolved transition dipolemoment in InGaAs/GaAs quantum dots. Applied Physics Letters, 82(25):4552–4554, 2003. doi:10.1063/1.1584514. → pages 79[198] J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida,N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield,V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G.Thompson. On-chip quantum interference between silicon165photon-pair sources. Nature Photonics, 8(2):104–108, Feb. 2014.ISSN 1749-4885. doi:10.1038/nphoton.2013.339. → pages 4, 20, 23[199] J. W. Silverstone, R. Santagati, D. Bonneau, M. J. Strain, M. Sorel,J. L. O’Brien, and M. G. Thompson. Qubit entanglement betweenring-resonator photon-pair sources on a silicon chip. NatureCommunications, 6, Aug. 2015. doi:10.1038/ncomms8948. → pages 4,23[200] C. Sinito, M. J. Ferne´e, S. V. Goupalov, P. Mulvaney, P. Tamarat,and B. Lounis. Tailoring the exciton fine structure of cadmiumselenide nanocrystals with shape anisotropy and magnetic field. ACSNano, 8(11):11651–11656, Nov. 2014. ISSN 1936-0851.doi:10.1021/nn5049409. → pages 43[201] J. E. Sipe and J. V. Kranendonk. Macroscopic electromagnetictheory of resonant dielectrics. Phys. Rev. A, 9:1806–1822, May 1974.doi:10.1103/PhysRevA.9.1806. → pages 76[202] W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme,H. Herrmann, D. Bu¨chter, S. Reza, W. Grundko¨tter, S. Orlov,H. Suche, R. Nouroozi, and Y. Min. Integrated optical devices inlithium niobate. Opt. Photon. News, 19(1):24–31, 2008.doi:10.1364/OPN.19.1.000024. → pages 20[203] B.-S. Song, S. Noda, T. Asano, and Y. Akahane. Ultra-high-Qphotonic double-heterostructure nanocavity. Nat Mater, 4(3):207–210, Mar. 2005. ISSN 1476-1122. doi:10.1038/nmat1320. →pages 26[204] R. Soref. The past, present, and future of silicon photonics. SelectedTopics in Quantum Electronics, IEEE Journal of, 12(6):1678–1687,2006. ISSN 1077-260X. doi:10.1109/JSTQE.2006.883151. → pages 20[205] J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci,F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Ho¨fling,R. Sanjines, and A. Fiore. Waveguide superconducting single-photondetectors for integrated quantum photonic circuits. Applied PhysicsLetters, 99(18):181110, 2011. doi:10.1063/1.3657518. → pages 30[206] J. Steckel, S. Coe-Sullivan, V. Bulovic´, and M. Bawendi. 1.3 µm to1.55 µm tunable electroluminescence from PbSe quantum dotsembedded within an organic device. Advanced Materials, 15(21):1661862–1866, Nov. 2003. ISSN 0935-9648.doi:10.1002/adma.200305449. → pages 46, 47[207] J. W. Stouwdam, J. Shan, F. C. J. M. van Veggel, A. G.Pattantyus-Abraham, J. F. Young, and M. Raudsepp. Photostabilityof colloidal PbSe and PbSe/PbS core/shell nanocrystals in solutionand in the solid state. The Journal of Physical Chemistry C, 111(3):1086, Dec. 2007. ISSN 1932-7447. doi:10.1021/jp0648083. → pages44, 45, 52, 59, 68, 80, 97, 98[208] M. Streshinsky, R. Ding, Y. Liu, A. Novack, C. Galland, A. E.-J.Lim, P. Guo-Qiang Lo, T. Baehr-Jones, and M. Hochberg. The roadto affordable, large-scale silicon photonics. Opt. Photon. News, 24(9):32–39, 2013. doi:10.1364/OPN.24.9.000032. → pages 4, 20, 30[209] N. Suzuki, K. Sawai, and S. Adachi. Optical properties of PbSe.Journal of Applied Physics, 77(3):1249–1255, Feb. 1995.doi:10.1063/1.358926. → pages 79[210] M. Sykora, A. Y. Koposov, J. A. McGuire, R. K. Schulze, O. Tretiak,J. M. Pietryga, and V. I. Klimov. Effect of air exposure on surfaceproperties, electronic structure, and carrier relaxation in PbSenanocrystals. ACS Nano, 4(4):2021–2034, Apr. 2010. ISSN1936-0851. doi:10.1021/nn100131w. → pages 97[211] D. V. Talapin and C. B. Murray. PbSe nanocrystal solids for n- andp-channel thin film field-effect transistors. Science, 310(5745):86–89,Oct. 2005. doi:10.1126/science.1116703. → pages 97[212] S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, andD. Ostrowsky. On the genesis and evolution of integrated quantumoptics. Laser & Photon. Rev., 6(1):115–143, Jan. 2012. ISSN1863-8899. doi:10.1002/lpor.201100010. → pages 12[213] L. Turyanska, A. Patane`, M. Henini, B. Hennequin, and N. R.Thomas. Temperature dependence of the photoluminescenceemission from thiol-capped PbS quantum dots. Applied PhysicsLetters, 90(10):101913, 2007. ISSN 00036951. doi:10.1063/1.2711529.→ pages 44[214] S. M. Ulrich, S. Ates, S. Reitzenstein, A. Lo¨ffler, A. Forchel, andP. Michler. Dephasing of triplet-sideband optical emission of aresonantly driven InAs/GaAs quantum dot inside a microcavity.167Physical Review Letters, 106(24):247402, June 2011.doi:10.1103/PhysRevLett.106.247402. → pages 80[215] K. J. Vahala. Optical microcavities. Nature, 424(6950):839–846,Aug. 2003. ISSN 0028-0836. doi:10.1038/nature01939. → pages 47[216] J. Volz, M. Scheucher, C. Junge, and A. Rauschenbeutel. Nonlinearπ phase shift for single fibre-guided photons interacting with a singleresonator-enhanced atom. Nat Photon, 8(12):965–970, Dec. 2014.ISSN 1749-4885. doi:10.1038/nphoton.2014.253. → pages 12[217] E. Waks and J. Vucˇkovic´. Coupled mode theory for photonic crystalcavity-waveguide interaction. Optics Express, 13(13):5064–5073,2005. doi:10.1364/OPEX.13.005064. → pages 33[218] J. Wang, A. Santamato, P. Jiang, D. Bonneau, E. Engin, J. W.Silverstone, M. Lermer, J. Beetz, M. Kamp, S. Ho¨fling, M. G.Tanner, C. M. Natarajan, R. H. Hadfield, S. N. Dorenbos, V. Zwiller,J. L. O’Brien, and M. G. Thompson. Gallium arsenide (GaAs)quantum photonic waveguide circuits. Optics Communications, 327:49–55, Sept. 2014. ISSN 0030-4018. doi:10.1364/JOSAB.13.001039.→ pages 19[219] N. A. Wasley. Nano-photonics in III-V Semiconductors forIntegrated Quantum Optical Circuits. Springer InternationalPublishing, 2014. doi:10.1007/978-3-319-01514-9. → pages 34[220] B. L. Wehrenberg, C. Wang, and P. Guyot-Sionnest. Interband andintraband optical studies of PbSe colloidal quantum dots. TheJournal of Physical Chemistry B, 106(41):10634–10640, Oct. 2002.ISSN 1520-6106. doi:10.1021/jp021187e. → pages 39, 43[221] F. W. Wise, J. Harbold, S. Clark, and B.-R. Hyun. Electronrelaxation in lead-salt quantum dots. volume 5929, pages59290S–59290S–9, 2005. doi:10.1117/12.617285. → pages 39[222] D. C. Wu, J. K. Kao, M. H. Mao, F. Y. Chang, and H. H. Lin.Determination of interband transition dipole moment ofInAs/InGaAs quantum dots from modal absorption spectra. In OSATechnical Digest Series (CD), page JTuA111. Optical Society ofAmerica, May 2007. → pages 79168[223] Z. Wu, Z. Mi, P. Bhattacharya, T. Zhu, and J. Xu. Enhancedspontaneous emission at 1.55 µm from colloidal PbSe quantum dotsin a Si photonic crystal microcavity. Applied Physics Letters, 90(17):171105, Apr. 2007. ISSN 00036951. doi:10.1063/1.2731657. → pages46, 47[224] J. S. Xia, K. Nemoto, Y. Ikegami, Y. Shiraki, and N. Usami.Silicon-based light emitters fabricated by embedding Geself-assembled quantum dots in microdisks. Applied Physics Letters,91(1):011104, 2007. doi:10.1063/1.2754356. → pages 34[225] C. Xiong, X. Zhang, A. Mahendra, J. He, D.-Y. Choi, C. J. Chae,D. Marpaung, A. Leinse, R. G. Heideman, M. Hoekman, C. G. H.Roeloffzen, R. M. Oldenbeuving, P. W. L. van Dijk, C. Taddei,P. H. W. Leong, and B. J. Eggleton. Compact and reconfigurablesilicon nitride time-bin entanglement circuit. Optica, 2(8):724–727,2015. doi:10.1364/OPTICA.2.000724. → pages 20[226] X. Xu, T. Tsuboi, T. Chiba, N. Usami, T. Maruizumi, andY. Shiraki. Silicon-based current-injected light emitting diodes withGe self-assembled quantum dots embedded in photonic crystalnanocavities. Opt. Express, 20(13):14714–14721, 2012.doi:10.1364/OE.20.014714. → pages 34[227] X. Xu, N. Usami, T. Maruizumi, and Y. Shiraki. Enhancement oflight emission from Ge quantum dots by photonic crystalnanocavities at room-temperature. Journal of Crystal Growth, 378:636–639, Sept. 2013. ISSN 0022-0248.doi:10.1016/j.jcrysgro.2012.11.002. → pages 34[228] E. Yablonovitch. Inhibited spontaneous emission in solid-statephysics and electronics. Phys. Rev. Lett., 58:2059–2062, May 1987.doi:10.1103/PhysRevLett.58.2059. → pages 24[229] J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic,and P. Bhattacharya. Enhanced photoluminescence from embeddedPbSe colloidal quantum dots in silicon-based random photoniccrystal microcavities. Applied Physics Letters, 92(26):261110, June2008. doi:10.1063/1.2954007. → pages 46[230] P. Yao and S. Hughes. Controlled cavity QED and single-photonemission using a photonic-crystal waveguide cavity system. Physical169Review B, 80:165128, Oct 2009. doi:10.1103/PhysRevB.80.165128. →pages 34[231] P. Yao, V. Manga Rao, and S. Hughes. On-chip single photonsources using planar photonic crystals and single quantum dots.Laser & Photon. Rev., 4(4):499–516, 2010. ISSN 1863-8899.doi:10.1002/lpor.200810081. → pages 34, 80[232] W. S. Zaoui, A. Kunze, W. Vogel, M. Berroth, J. Butschke,F. Letzkus, and J. Burghartz. Bridging the gap between opticalfibers and silicon photonic integrated circuits. Optics Express, 22(2):1277–1286, 2014. doi:10.1364/OE.22.001277. → pages 20[233] C. Zeng, Y. Ma, Y. Zhang, D. Li, Z. Huang, Y. Wang, Q. Huang,J. Li, Z. Zhong, J. Yu, Z. Jiang, and J. Xia. Single germaniumquantum dot embedded in photonic crystal nanocavity for lightemitter on silicon chip. Optics Express, 23(17):22250–22261, 2015.doi:10.1364/OE.23.022250. → pages 34, 35[234] Y. Zhang, C. Zeng, D. Li, X. Zhao, G. Gao, J. Yu, and J. Xia.Enhanced light emission from Ge quantum dots in photonic crystalring resonator. Opt. Express, 22(10):12248–12254, 2014.doi:10.1364/OE.22.012248. → pages 34[235] L. Zhu, S. Samudrala, N. Stelmakh, and M. Vasilyev. Spontaneousdecay of CdSe/ZnS core-shell quantum dots at the air-dielectricinterface. Opt. Express, 20(3):3144–3151, 2012.doi:10.1364/OE.20.003144. → pages 76[236] K. Zhuravlev. PbSe vs. CdSe: Thermodynamic properties andpressure dependence of the band gap. Physica B: Condensed Matter,394(1):1–7, May 2007. ISSN 0921-4526.doi:10.1016/j.physb.2007.01.030. → pages xvi, 40[237] H. Zimmermann. Silicon Optoelectronic Integrated Circuits.Springer, 2013. doi:10.1007/978-3-662-09904-9. → pages 20170Appendix ADip coating proceduraldetailsProcedural notes for QD monolayer preparation (or generally, dipping) withglove box/dipper setup1. Establish known weight/solvent volume of nanocrystalsa. Weigh empty 1 dram vial (usually ∼ 6 g)b. Fill with as-received CQD solution (e.g. CQDs in TCE), ∼ 4 mLc. Slowly evaporate solvent under N2 flow, ∼ 2-3 hoursd. Weigh the vial with CQDse. Determine the CQD weight by subtracting off empty vial weightf. Constitute CQDs with Hexanes to ∼ 5.0 mg/mLg. Mark solvent line, label vial, Teflon tape on threads, cap onh. Have CQD solution in glove box prior to BOE/HF treatment2. Prepare substratesa. Establish two (or more) ∼ 5 mm x 10 mm silicon or SOI waferpieces. Polished on at least one side, device sideb. RCA-1 clean them as best as possible (+pre-RCA solvent rinses)171c. Have on-hand, in H20, ready for BOE/HF treatment3. Prepare cryostata. Remove aluminum mount/backingb. Prepare in-cryostat sample stage for accepting two samples. Keepsamples near bottom of cryostat windowc. Keep filled with nitrogen gas before placing into glove boxd. Have N2 ready to fill cryostat with steady N2 flow for immediatelyafter cryostat removal from glove box (after samples in cryostat)e. Have cryostat on glove box transfer tray during dip-coating4. Dip-coatinga. Dip-coating is ready to occur when:i. Sample substrates are ready to be HF-treatedii. Dipping solution (in vial) is on the dipping stage in the glovebox, and positioned such that a sample held by the self-clamping tweezers is a few mm above the solution surfaceiii. Cryostat is on the sample glove box tray, filled with nitrogeniv. Glove box at positive pressure (for faster transfer chamberbackfill)v. Rough pumping on valve just before transfer chamber (butnot yet on transfer chamber ... just ready to)vi. N2 line on right of wet bench is ready to hook up to cryostatand flow N2 through cryostat immediately aftervii. Dipping stage is ready to be controlled (launch Step dir6 ondesktop, run file, and test that you can control stage move-ment up/down using switch/button controller located on topof desktop computer. Motor is powered by PS below monitor:turn on button on left, and press ‘out’ for power out)viii. Sample stage of cryostat is ready to accept dipped samples,particularly so region of interest is optically accessible near172bottom of cryostat window. [Recommended: fasten sampleto stage done under strong nitrogen flow outside glove box]ix. Turbo pump is not spinning, is at STP, and ready to quicklyattach to cryostat to pump it downb. HF-treat the samples and put on sample tray, if appropriatec. Put samples + tray + tweezers into glove box transfer chamberd. Evacuate glove box transfer chamber with roughing pumpe. Once evacuated, close valve from pump to transfer chamberf. Backfill transfer chamber with N2 from glove box, making sureto actively fill glove box with more N2g. When transfer chamber and glove box at same pressure, opendoor between transfer chamber and glove boxh. Transfer sample to self-clamping tweezersi. Dip-coat by raising/lowering dipping stagej. Once dip-coated, put samples into cryostat in desired locationk. Close glove box/transfer chamber door, open lab room/transferchamber doorl. Quickly move cryostat to right of wet bench, flow N2 through itm. Fasten samples to sample stage of cryostat (N2 flow persistent)n. When samples in place, detach N2 flow hardware (keep cryostatsample chamber valve open) and place cryostat on computer tablenear turbo pumpo. Pump down sample chamber with turbo pump, making sure vac-uum is quickly established. Pump for ∼ 30 minutes after pressurereaches 10−4 mbar.p. After pumped down, close sample chamber valve, then black valveon turbo pump, then turn off pump. Make sure each step suc-cessful along the way.173


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