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The excess of dephasing rate in the gas annealed CVD graphene Shin, Hyungki 2018

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The excess of dephasing rate in thegas annealed CVD graphenebyHyungki ShinB.Sc., Yonsei University, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2018c© Hyungki Shin 2018The following individuals certify that they have read, and recommendto the Faculty of Graduate and Postdoctoral Studies for acceptance, a the-sis/dissertation entitled:The excess of dephasing rate in the gas annealed CVD graphenesubmitted by Hyungki Shin in partial fulfillment of the requirements forthe degree of Master of Sciencein PhysicsExamining Committee:Joshua Folk, PhysicsSupervisorKe Zou, PhysicsAdditional ExamineriiAbstractGraphene was expected to prove useful in the field of spintronics becausea long spin relaxation time (few micro second) was theoretically expected.However, experimental results using exfoliated graphene have shown thatthe spin relaxation time is a few orders of magnitude less than the theoreti-cal prediction. It was discovered that the reason for this unexpected shorterspin relaxation time is the presence of magnetic moments on graphene andmagnetic moments exist on most forms of graphene. Many theoretical ar-ticles expected these magnetic moments to arise due to graphene defects.However, it is not experimentally clear where and how they arise.To answer where and how, we investigates it with dephasing rate (phaserelaxation rate) monitored via weak localization on graphene, grown bychemical vapour deposition (CVD graphene). The experiments are per-formed on field-effect devices made from CVD graphene on various sub-strates under perpendicularly applied magnetic fields at 4.2 K. The samplesare thermally annealed under various conditions, which is a commonplacetechnique used to clean the surface of graphene.Only the gas annealing induces the additional source of dephasing rate onCVD graphene. However, this could not be seen in before-annealed samplesand vacuum annealed samples. Additional experiment confirms that thisadditional source on gas annealed sample has the magnetic property. Theresult on this thesis can help answer the origin of magnetic moments ongraphene.iiiLay summaryVarious distinctive properties in graphene, consisting of a single layer ofcarbon, has been theoretically predicted and verified experimentally. Thereare also active studies on various applications utilizing these characteristics.Among them, spintronics, which is expected to replace the conventionalsemiconductor technology, attracted considerable interest early in the dis-covery of graphene. However, the relaxation time of spin in graphene, whichis the core of spintronics, is measured in a short time in actual experiments,compared to theoretical expectation. Hence, graphene is difficult to use itas spintronics.The finding in this thesis could help explain the short spin relaxation timein graphene. In this thesis, we show that annealing under gases, which isthe conventional way to clean the surface of graphene, induces an additionalinteraction source on graphene grown by Chemical vapor deposition method(CVD). Experiments were carried out with resistance measurements in aperpendicularly applied magnetic field at 4.2 K, before and after annealingunder various condition.ivPrefaceChapter 4 is based on work conducted in Quantum devices group in Uni-versity of British Columbia by me and my supervisor, Dr. Joshua Folk,research associate Dr. Silvia Lu¨scher Folk, and our collaborators at theUniversity of British Columbia, Dr. Ali Khademi, and Dr. Rui Yang. I con-ducted all experiments and data analysis and developed the interpretationand conclusion of the experiment under the supervision of Dr. Joshua Folk.All of the sample fabrication processes, such as exfoliation and electronbeam lithography, were done by the author. Dr. Ali Khademi provided atest sample made from CVD graphene on SiO2 substrate. The additionalexperiment with in-plane magnetic fields on Appendix F was conducted byDr. Silvia Lu¨scher Folk. Dr. Silvia Lu¨scher Folk has the authorship of theresults of these additional experiments.Result of this thesis is soon to besubmitted for publication.The following figures were taken and from each corresponding article andmodified:Figure 2.1: Neto AC, Guinea F, Peres NM. Drawing conclusions fromgraphene. Physics World. 2006 Nov;19(11):33. [1]Figure 2.2: Neto AC, Guinea F, Peres NM, Novoselov KS, Geim AK.The electronic properties of graphene. Reviews of modern physics. 2009Jan 14;81(1):109. [2]Figure 2.3 (a): Novoselov KS, Geim AK, Morozov SV, Jiang DA, ZhangY, Dubonos SV, Grigorieva IV, Firsov AA. Electric field effect in atomicallythin carbon films. science. 2004 Oct 22;306(5696):666-9. [3]Figure 2.3 (b): Novoselov KS, Geim AK, Morozov S, Jiang D, KatsnelsonM, Grigorieva I, Dubonos S, Firsov AA. Two-dimensional gas of masslessDirac fermions in graphene. nature. 2005 Nov;438(7065):197. [4]Figure 2.3 (c): Morozov SV, Novoselov KS, Katsnelson MI, Schedin F,Ponomarenko LA, Jiang D, Geim AK. Strong suppression of weak localiza-tion in graphene. Physical review letters. 2006 Jul 5;97(1):016801. [5]Figure 3.5: Geim AK, Novoselov KS. The rise of graphene. InNanoscienceand Technology: A Collection of Reviews from Nature Journals 2010 (pp.11-19). [6]vPrefaceFigure 5.1: Chen JJ, Wu HC, Yu DP, Liao ZM. Magnetic moments ingraphene with vacancies. Nanoscale. 2014;6(15):8814-21. [7]viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Theoretical background . . . . . . . . . . . . . . . . . . . . . . 42.1 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.1 Honeycomb structure in real space and k-space . . . . 42.1.2 Tight binding model - Energy dispersion in Graphene 62.1.3 Transport properties of graphene . . . . . . . . . . . 72.2 Weak localization . . . . . . . . . . . . . . . . . . . . . . . . 92.2.1 Weak localization in graphene . . . . . . . . . . . . . 102.3 Various source of the dephasing . . . . . . . . . . . . . . . . 123 Experimental setup and background . . . . . . . . . . . . . . 153.1 Sample preparations . . . . . . . . . . . . . . . . . . . . . . . 163.1.1 CVD graphene on various substrates . . . . . . . . . 183.1.2 Exfoliated graphene on SiO2 . . . . . . . . . . . . . . 193.1.3 Lithography process . . . . . . . . . . . . . . . . . . . 193.2 Rapid thermal annealing system . . . . . . . . . . . . . . . . 203.3 Measurement system at 4.2K - Dunker . . . . . . . . . . . . 213.4 4 probes measurement with magnetic fields . . . . . . . . . . 23viiTable of Contents4 Experimental result . . . . . . . . . . . . . . . . . . . . . . . . 264.1 Measurement process . . . . . . . . . . . . . . . . . . . . . . 264.1.1 Weak localization fitting . . . . . . . . . . . . . . . . 284.2 CVD graphene on Silicon Oxide . . . . . . . . . . . . . . . . 284.2.1 Before-annealed CVD graphene . . . . . . . . . . . . 294.2.2 Ar gas annealed CVD graphene . . . . . . . . . . . . 314.2.3 Vacuum annealed CVD graphene . . . . . . . . . . . 334.3 CVD graphene on Hafnium Oxide (HfO2) substrate . . . . 354.4 Air exposure on CVD graphene on Silicon Oxide . . . . . . . 384.5 Comparison experiments to hBN and exfoliated graphene . 404.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.6.1 The excess of dephasing rate in CVD graphene . . . . 414.6.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 415 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47AppendicesA Details of sample fabrication . . . . . . . . . . . . . . . . . . . 54A.1 Exfoliation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54A.2 CVD graphene Transferring . . . . . . . . . . . . . . . . . . . 55B Weak localization fitting function . . . . . . . . . . . . . . . . 56C Surface temperature on RTA . . . . . . . . . . . . . . . . . . 58D Error bar in fitting process . . . . . . . . . . . . . . . . . . . . 60D.1 Temperature fluctuation . . . . . . . . . . . . . . . . . . . . 60D.2 Conductivity depending on magnetic fields . . . . . . . . . . 60D.3 Fitting parameters . . . . . . . . . . . . . . . . . . . . . . . . 61E Additional experimental data . . . . . . . . . . . . . . . . . . 62E.0.1 CVD graphene on hexagonal Boron Nitride (hBN) . . 62E.0.2 Exfoliated graphene . . . . . . . . . . . . . . . . . . . 63F Additional experiment with in-plane magnetic fields . . . 66viiiList of Tables3.1 Various types of graphene on various substrates samples. . . . 16C.1 Surface temperature in RTA . . . . . . . . . . . . . . . . . . . 59ixList of Figures2.1 Carbon allotrope and graphene structure . . . . . . . . . . . . 52.2 Electronic dispersion of graphene . . . . . . . . . . . . . . . . 72.3 Transport properties in Graphene . . . . . . . . . . . . . . . . 82.4 Weak localization from the loop . . . . . . . . . . . . . . . . . 92.5 Weak localization in graphene . . . . . . . . . . . . . . . . . . 113.1 Various of graphene samples . . . . . . . . . . . . . . . . . . . 173.2 Device chip carrier . . . . . . . . . . . . . . . . . . . . . . . . 183.3 Rapid Thermal Annealing system . . . . . . . . . . . . . . . . 203.4 Measurement system . . . . . . . . . . . . . . . . . . . . . . . 223.5 Electric field effect in graphene and the schematic samplegeometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.1 Example of experiment result . . . . . . . . . . . . . . . . . . 274.2 Before-annealed graphene result . . . . . . . . . . . . . . . . . 304.3 Ar annealed CVD graphene result . . . . . . . . . . . . . . . 324.4 Vacuum annealed CVD graphene result . . . . . . . . . . . . 344.5 CVD graphene on HfO2 substrate . . . . . . . . . . . . . . . 354.6 Hafnium Oxide sample result . . . . . . . . . . . . . . . . . . 374.7 Air and moisture exposure result . . . . . . . . . . . . . . . . 394.8 The excess of dephasing result . . . . . . . . . . . . . . . . . . 425.1 Induced magnetism from the vacancy on graphene . . . . . . 45A.1 sample fabrication process . . . . . . . . . . . . . . . . . . . . 54A.2 CVD graphene transfer process . . . . . . . . . . . . . . . . . 55C.1 RTA for surface temperature test . . . . . . . . . . . . . . . . 58E.1 Graphene on hBN result: conductivity changes . . . . . . . . 62E.2 Graphene on hBN result: the dephasing rate VS e-e interac-tion rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63E.3 Exfoliated graphene result: before and after annealing . . . . 64xList of FiguresF.1 In-plane magnetic fields data . . . . . . . . . . . . . . . . . . 66xiAcknowledgementsI would like to appreciate the current and former members in Quantumdevices group in University of British Columbia for their scientific and emo-tional supports. Especially, I would like to thank my supervisor, Dr. JoshuaFolk, for his kind guidance and patience during this Master program. I alsowish to thank Dr. Lu¨scher Folk, Dr. Nik Hartman, Dr. Andrey Blednov,Dr. Ali Khademi, Dr. Rui Yang, Ebrahim Sajadi, Christian Olsen, andAnnabelle Jiang. Their help and the support enabled me to successfullyfinish my experiments and to broaden my knowledge of physics and exper-imental skills. Having the discussion about the experimental results withthem also helped me a lot understand the results of my data and physics onit.Finally, I would like to thank my family and friends in both South Koreaand Canada for their emotional support and encouragement. With theirhelp, I was able to adapt and live well with my research life in UBC, Canada.Especially, I want to express my gratitude to Jeong-min, who is my oldfriend, strong supporter, and my fiance.xiiChapter 1IntroductionGraphene was expected to prove useful in the field of spintronics because along spin relaxation time was theoretically expected [8]. However, experi-mental results using exfoliated graphene have shown that the spin relaxationtime is a few orders of magnitude less than the theoretical prediction [9–12].It was discovered that this shorter spin relaxation is due to magnetic mo-ments on graphene [13]. It has further been discovered that these magneticmoments are one of the dominant causes of the suppression of quantum me-chanical coherent effects among conduction electrons. This suppression ofcoherent effect is called dephasing (phase relaxation) [14]. Magnetic mo-ments exist on most forms of graphene, such as exfoliated, epitaxial, andchemical vapour deposited (CVD) graphene [14, 15]. Many theoretical ar-ticles expected these magnetic moments to arise due to graphene defects[16–19]. However, experimentally, it has not been made clear where theycome from and how they arise. The result of experiments in this thesis canhelp to answer those questions with respect to CVD graphene.The work described in this thesis started as an extension of a previousexperiment by Dr. M. Lundeberg [14] from the Quantum Devices groupat the University of British Columbia (UBC). His work showed, via chargetransport measurements, that magnetic moments on exfoliated grapheneare a significant source of dephasing. After this publication, the QuantumDevices group compared those exfoliated graphene results to analogous be-haviours observed in CVD graphene. It is interesting to compare these twoforms of graphene because exfoliated graphene (which is peeled off usingadhesive tape) and CVD graphene have many different extrinsic physicalproperties, such as charge mobility and contamination level, yet in otherways are very similar. Surprisingly, the group found (anecdotally) that thethe dephasing rate in CVD graphene was very different before and after an-nealing. Before annealing, CVD graphene and exfoliated graphene showedthe same dephasing rates. After gas annealing, however, CVD grapheneshowed a drastic change of dephasing rate compared to exfoliated graphene.The main goals of this thesis were to understand why the dephasing ratein CVD graphene depends so strongly on annealing, and to investigate the1Chapter 1. Introductionproperties of this enhanced dephasing. To this end, experiments on field-effect devices made from CVD graphene were performed, before and afterthermal annealing processes. The dephasing rate was monitored via weaklocalization and magnetoresistance measurements at 4.2 K. Also, whetherthe source of the increased dephasing rate has magnetic properties was es-tablished through the application of in-plane magnetic fields as an additionalexperiment.A crucial part of this work was the extraction of a dephasing rate forgraphene via a fitting function of weak localization theory. Weak localizationtheory is a quantum mechanical conductivity correction, and it is affectedby various interactions in graphene, such as inter- or intra-valley scatteringsand dephasing [20]. Therefore, scattering rates and the dephasing rate canbe extracted using weak localization theory. From this extracted dephasingrate, various interactions can be investigated as sources of dephasing bycomparing the behavior as a function of temperature or comparing withinteraction rate models [21, 22].The samples were annealed under various conditions. Annealing is theconventional method used to remove water and chemical residues from grapheneand other 2D materials, for example to make better ohmic contact to thesample [23]. Annealing can also improve mobility and other electronic prop-erties [24–26]. However, this annealing could induce some unintentionalresults [27]. For example, it can cause carbon to be dissolved from grapheneto the metal contacts [23] and graphene to be excessively adsorbed into thesubstrate [24]. Likewise, thermal annealing could in principle induce unin-tentional effects in CVD graphene, which could activate or create magneticmoments.By comparing various annealing processes and analyzing based on weaklocalization theory, the conditions of unusual enhancement of the dephasingrate and its specific properties for CVD graphene were investigated. Specif-ically, CVD graphene on several different substrates were annealed undervarious gas conditions, and the dephasing rate was extracted via weak lo-calization fitting. Finally, the unknown source of the increased dephasingrate was investigated through additional experiments involving the applica-tion of in-plane magnetic fields, which can confirm the presence of magneticmoments.As a result, it was demonstrated that thermal annealing in an inert gasdramatically increases the CVD graphene’s dephasing rate at a temperatureof 4.2 K. This increased dephasing rate shows several distinctive properties,such as a minimum rate at zero gate voltage and the increase as a functionof the charge carrier density.2Chapter 1. IntroductionThis thesis consists of four main chapters; In Chapter 2, theoreticalbackgrounds for graphene, the dephasing mechanism, and weak localizationare briefly given. Weak localization theory in graphene is also explainedin connection with dephasing. In Chapter 3, graphene sample preparationand fabrication are outlined, as are associated experimental setups, such asthe annealing and sample measurement systems. Experimental results forvarious graphene samples annealed under different atmospheric conditionsare shown in Chapter 4. Lastly, Chapter 5 concludes the annealed CVDgraphene experiments and discusses possible mechanisms which can createor activate magnetic moments on CVD graphene. In the Appendix, furtherdetails of sample fabrications and the fitting functions for use with weaklocalization theory are explained. Also, the details and results of samplesurface temperature measurements in the annealing system are shown. Ap-pendix also contains the results of exfoliated graphene, CVD graphene onhBN , and the additional experiments using in-plane magnetic fields, whichcan give information on any magnetic moments on annealed CVD graphene.3Chapter 2Theoretical backgroundThis chapter gives brief theoretical backgrounds for graphene, weak localiza-tion and source mechanisms of dephasing. Specifically, the following topicsare described in each section.• Graphene (Section 2.1)• Weak localization (Section 2.2)• Various source of dephasing (Section 2.3)2.1 GrapheneCarbon, which has atomic number 6 with 6 electrons per atom, has manydifferent allotropes as shown in Figure 2.1 (a). Graphene is one of theseallotropes, which has a two-dimensional (2D) structure. Specifically, it hasa single atomic layer of carbon with 1.1 A˚ thickness and these carbon atomsform a honeycomb or benzene ring structure. Graphene has many interestingphysical properties because of this honeycomb structure. For example, it haslinear energy dispersion with Dirac point, and shows distinctive propertiesin transport measurements [3, 28]. These physical properties make graphenedistinct compared to conventional 2D materials. In the following sections,a theoretical background of graphene and details of its physical propertiesare given.2.1.1 Honeycomb structure in real space and k-spaceIn a primitive cell of graphene, two carbon atoms are covalently bonded ata distance of 1.42 A˚ as shown in Figure 2.1 (b) and (c). These two carbonatoms are named A (filled circle) and B (empty circle). It can be seen thatthe structure is honeycomb in real and momentum space. Based on thishexagonal structure, the lattice vectors of graphene in real space can be42.1. GrapheneFigure 2.1: Carbon allotrope: graphene, graphite, carbon nanotube, andfullerene (C60) from top left to bottom right (Taken from Ref. [1]) Graphenelattice structure in (b) real space and (c) momentum space. Carbon atomssite on circles A and B with 1.42A˚. The dashed line of rhombus indicatesunit cell of graphene and solid arrows indicate lattice vectors.written asa1 =√32axˆ+32ayˆ, a2 = −√32axˆ+32ayˆ, (2.1)where a ≈ 1.42 A˚.These vectors form a rhombus shaped unit cell [Figure 2.1 (b)]. Thereciprocal-lattice vectors can be written in a similar way, as shown in Figure2.1 (c). For a honeycomb structure in momentum space, there are twospecial points K and K ′ at the corner of the Brillouin zone. The followingsection will show why these points are special for graphene. Although asingle carbon atom has 4 out of the 6 electrons filling the 2s and 2p orbitalstates, the outer orbitals 2s, 2p3 of the lattice are hybridized into 2sp2 and2pz orbitals between carbon atoms and form a trigonal planar structure ingraphene. These hybridized orbitals also form pi (conduction band), σ, andpi∗ (valence band) bonds where the pi bond has only one electron due to thePauli exclusion principle. Since this pi state is half-filled and protrudes outof the 2D-plane, most of the electrical transport properties are determinedby this half-filled state. Such lattice vectors and hybridized orbitals enablegraphene to have distinctive properties from other 2D materials [29, 30].This can be easier demonstrated in momentum space than real space.52.1. Graphene2.1.2 Tight binding model - Energy dispersion in GrapheneIn this subsection, distinctive energy dispersion in graphene will be ex-plained. The Hamiltonian for graphene in real space with a hopping term(t ≈ 3 eV), between the nearest neighbor orbitals [A→B or B→A in Figure2.1 (a)] which is the half-filled state, is given following Equation 2.2 by [31].H0 = E0 − t∑r|r,A〉 [〈r,B|+ 〈r − a1, B|+ 〈r − a2, B|+ h.c] (2.2)where a1 and a2 are lattice vectors in Equation 2.1 and r indicates theposition in the real space. E0 is the potential energy which is influenced bythe orbital binding energy and electrostatic potentials from external fields.Because the physical properties of graphene are represented better by thedispersion relation in momentum space, the energy dispersion relation inmomentum space is calculated from the real space Hamiltonian in Equation2.2:E(k) = E0 ± t√√√√1 + 4cos2(√32kxa)+ 4cos(√32kxa)cos(32kya)(2.3)where a is 1.42 A˚, t is the hopping energy, and kx and ky are coordinates ofmomentum space.At K and K ′, Equation 2.3 becomes zero when E0 = 0. Moreover, when weuse the low energy approximation around K and K ′, we can find a specialenergy dispersion relation [30]. That is,±E(q) = ±vF q (2.4)where vF is Fermi velocity and q is the momentum measured from the K orK ′. Since the energy is zero at q = 0, the so-called Dirac point as shown inFigure 2.2, graphene is classified as a zero bandgap semiconductor or semi-metallic [6, 31]. This zero-energy point symmetrically forms the valley atK and K ′ [Figure 2.2 zoom-in]. In these valleys, intravalley and interval-ley scatterings occur and contribute to diverse distinctive properties, suchas various interaction sources in weak localization [3, 20, 32]. The detailsof these interaction scatterings with weak localization will be discussed inSection 2.2.1. Moreover, when spin components including isospin from thesublattice (A and B), pseudospin from the valley (K and K ′), and real spinare included in the Hamiltonian of Equation 2.2, graphene has more degreesof freedom and the chirality between sublattice and momentum [29].62.1. GrapheneFigure 2.2: Electronic dispersion in the honeycomb graphene lattice. Zoomin of the energy bands close to one of the Dirac points: this shows two valleysabove and below the Dirac point. (Taken from Ref. [2])2.1.3 Transport properties of grapheneThe motion of electrons in graphene is governed not only by intrinsic proper-ties involving linear energy dispersion described above but also by extrinsicproperties. One of the extrinsic properties in graphene is disorder due toimpurities, structural defects, and other various reasons [33]. The combinedeffects of intrinsic properties and extrinsic disorders in graphene can be ob-served via transport experiments. Thus, the study of transport properties isa powerful tool to study graphene while encompassing intrinsic and extrinsicproperties. Various physical properties can be monitored via transport mea-surements, and here three examples are given: the Dirac point, the quantumHall effect, and low field magneto-transport property.When one changes the gate voltage on the graphene device inducingthe electric field on graphene, it can also change the charge carrier densityand Fermi level of graphene as shown in Figure 2.3 (a). When observingresistance versus applied gate voltage, the resistance gradually increases andreaches a peak and then gradually decreases again. This is because the typeof charge carrier is changed from hole to electron due to the applied electricfields. The maximum resistance peak between the transition of two typeof charge carriers represents the Dirac point shown in Figure 2.3 (a). Thismeans from the transport measurement with applied electric fields one can72.1. GrapheneFigure 2.3: . Various transport properties of graphene. (a) Dirac point inresistance measurement, (b) quantum Hall effect, and (c) weak localization.(These figures are taken from [3], [4], [5] and modified to show the purposeclearly).confirm the Dirac point as the form of a peak in the resistance measurementdata.When strong magnetic fields are perpendicularly applied to graphene andresistance is measured, peaks and steps of plateaus can be observed in ρxxand σxy respectively as shown in Figure 2.3 (b). This is because electrons areconfined in a 2D system (in the case of graphene), and the energy spectrumsplits into discrete energy levels, the so-called Landau levels. This Landaulevel is shifted as magnetic fields increases, and as a result, it shows theplateaus on σxy and the peaks on ρxx. This quantized magneto-transportproperty is called the quantum Hall effect [34].If weak magnetic fields are applied to graphene, different phenomenacan be observed in magneto-transport measurements as shown in Figure 2.3(c). As magnetic fields are applied, the resistance is decreased or increasedfrom a peak value at zero magnetic fields. This phenomenon is becausethe quantum conductivity correction by the various interactions with anelectron in the diffusive region can be suppressed by the magnetic fields.This phenomenon under weak magnetic fields is called weak localizationor weak anti-localization. Among the various physical properties studiedthrough transport measurements, weak localization is mainly focused on inthis thesis to investigate the behavior of dephasing on CVD graphene, beforeand after the annealing.82.2. Weak localization2.2 Weak localizationWhen an electron is moving diffusively, it experiences a series of randomscattering events [35]. Because of these random scattering events, the elec-tron propagates randomly and one example of these random propagationsis a loop in the clockwise or counter-clockwise direction as shown in Figure2.5. These loops are said to be paths which are time reversed with re-spect to one another, and they can interfere constructively or destructively[36]. This interference changes the backscattering probability which affectsthe electron transport resulting in a conductivity correction. This conduc-tivity correction is called weak localization (increasing the backscatteringprobability and decreasing conductivity). In other words, this conductiv-ity correction originates from the quantum mechanical interference betweenpairs of time-reversed paths with self-crossing trajectory.Figure 2.4: The randomly scattered paths of electron in (a) counter clock-wise and (b) clockwise loop. The colored circles represent impurities.If an electron in a diffusive region collides with other particles inelas-tically, such as with other electrons, phonons, and impurities during therandom scattering events, phase coherence between the loops is randomizedwith the rate τ−1φ . τ−1φ is called the dephasing rate (phase relaxation rate)and details the rate at which phase loss events occur [35, 37].If the phase coherence in these loops is broken for various reasons, theconductivity correction from this phase coherence can be suppressed. Forexample, when the magnetic fields are applied perpendicularly to the sys-tem, the Aharonov-Bohm effect changes the phase difference between theself-crossing paths and suppresses the conductivity correction [36]. Thismeans that applied magnetic fields can suppress the conductivity correctioninduced by weak localization. Hence, weak localization is most robust atzero magnetic fields, and it becomes suppressed when out of plane magneticfields are increased.92.2. Weak localizationFrom the Hikami-Larkin-Nagaoka equation [38], the theoretically mod-eled quantitative result of weak localization for 2D samples can be seen.Here, only the case for intermediate and low magnetic fields (limit of B h¯/(eDτtr), τtr is the momentum relaxation rate) is used because such lowmagnetic fields are enough to suppress the weak localization in our grapheneexperiments [39].∆σ(B) = σ(B)− σ(0) ≈ −2e2pihF(τ−1Bτ−1φ)(2.5)τ−1B =4eh¯DB (2.6)τ−1φ =4eh¯DBφ (2.7)where F (z) = lnz + ψ(0.5+z−1), and ψ(x) is the digamma function. τ−1B isthe interaction rate scale of applied magnetic field, τ−1φ and Bφ are dephasingrate and its field scale respectively. D is diffusion coefficient. This equationin low field limit assumes that the dominant interaction in weak localizationis dephasing compared to other interactions.Using this weak localization Equation 2.7, one can make the fitting func-tion and can extract the dephasing rate (τ−1φ ) from magneto-conductivitymeasurements. Because dephasing rate is comprised of various interactions,such as electron-electron interaction and electron-phonon interaction, onecan investigate the presence of specific interaction or magnitude of interac-tion rates from this extracted dephasing rate. The details of weak localiza-tion for graphene case and dephasing rate details will be discussed in thefollowing Sections.2.2.1 Weak localization in grapheneAs mentioned in previous section, weak localization in 2D materials andmetallic materials is mostly dominated by dephasing interaction, τ−1φ . How-ever, other materials like graphene have several other dominant interactionterms in weak localization. In graphene, there are additional elastic scatter-ing terms due to the intervalley and intravalley scatterings at the valleys, Kand K ′ in Figure 2.2 and Figure 2.5 [20, 22, 32]. Hence, the manifestation102.2. Weak localizationFigure 2.5: The intravalley scattering (τ−1∗ ) and intervalley scattering(τ−1i ) in momentum space of graphene. The dashed line represents theBrillouin zone of graphene. The solid line trigonal shapes at K and K ′represent the Fermi surface at a finite energy in the vicinity of two non-equivalent valleys.of weak localization in graphene is mainly determined by the following inter-play of inelastic and elastic scattering mechanisms; the intravalley scatteringrate τ−1∗ , the intervalley scattering rate τ−1i , and the dephasing rate τ−1φ [20].Weak localization or anti-weak localization in graphene are determined bythe relative speeds of these interactions.Through these particular interaction mechanisms and due to the weakspin-orbit interaction in graphene, the general theory of weak localization inEquation 2.5 can be transformed into an equation for graphene with severalmodifications as following equation shows [20, 29, 40].∆σ(B) = σ(B)− σ(0) (2.8)≈ e2pih[F(τ−1Bτ−1φ)− F(τ−1Bτ−1φ + 2τ−1i)− 2F(τ−1Bτ−1φ + τ−1∗)]where F (z) = lnz + ψ(0.5 + z−1), and ψ(x) is the digamma function. Com-pared to the general weak localization theory of Equation 2.5, two additionalterms added; intervalley scattering (τ−1i ) and intravalley scattering (τ−1∗ ).Also, in graphene’s case, a diffusion coefficient can be defined in Equation2.7 asD =σpih¯vf2e2√pins, vf = 106m/s. (2.9)112.3. Various source of the dephasingwhere σ is conductivity, ns is charge carrier density, and vf is the Fermivelocity of graphene.This weak localization of Equation 2.8 is modified into a fitting functionto extract the respective interaction rates from the measured data [41]. Forinstance, the linearity term of the measured data and the maximum resis-tance term are added into the weak localization fitting function. The detailsof the weak localization fitting function are in given in Appendix B.From this weak localization fitting function, interaction rates can beextracted and the magnitude of each rate as a function of other externalchanges, such as a function of charge carrier density and the condition ofannealing, can be compared. Particularly, among the interaction rates, thedephasing rate is focused on since the dephasing rate can be caused byvarious interactions and the behavior of the dephasing rate can allow variousinteractions such as electron-electron interaction [22] or electron-magneticimpurity interaction [42] to be characterized [35, 37]. The following sectionwill discuss more details of dephasing.2.3 Various source of the dephasingDephasing (phase-relaxation) is the term for when coherent effects betweenthe electrons of various paths is suppressed for any reason [37]. In otherwords, any events inducing a random phase difference between the electronpaths is a dephasing process. Here are the main sources of dephasing:• Electron-phonon interactions: τ−1e−h• Electron-electron interactions: τ−1e−e• Impurities with internal degrees of freedom: τ−1e−iDephasing is the result of these various interactions and the dephasing rateτ−1φ is the approximate sum of these interaction rates as given in the follow-ing equation:τ−1φ ≈ τ−1e−p + τ−1e−e + τ−1e−i. (2.10)The first two interactions, electron-phonon and electron-electron inter-actions, are the intrinsic causes of the dephasing and include a temperaturedependence. Additionally, impurities with internal degrees of freedom is theexternal factors which contribute to the dephasing rate.122.3. Various source of the dephasingWhen an electron interacts with a phonon, an electron-phonon inter-action, the phonon changes the phase of the electron randomly with time,and it results in a non-stationary interference pattern [35]. Hence, electron-phonon interactions suppress the coherent effect. However, since it is rel-atively weak at low temperature due to the reduction of the number ofphonon, the effect of electron-phonon interactions on the dephasing can benegligible in experiments performed at 4.2 K [21, 43].In graphene case, electron-electron interactions are more dominant indephasing because phonon has smaller relaxation rate than electron’s at lowtemperature [21, 22, 44, 45]. This electron-electron interaction does notchange the net momentum but changes the phase coherence between theelectrons, and this change induces the dephasing. The electron-electron in-teraction rate in two dimensions can be described by the following equation:τ−1e−e =kBTh¯(ln(G2)G), G =σAl(2.11)where σ is conductivity, G is conductance, A is the area of the cross section ofthe sample, and l is its length [21]. This equation tells us that an electron-electron interaction can be represented as a function of conductance andlinearly depends on the temperature. More importantly, this equation isnot related with dephasing rate or weak localization. Thus, the magnitudeof electron-electron interaction rate can be extracted from the conductivitymeasurement with this equation, regardless of magnitude of dephasing rateor weak localization. If one compares the electron-electron interaction ratefrom Equation 2.11 with the dephasing rate from Equation 2.8 and Equation2.7, one can determine how much electron-electron interaction influences thedephasing process.Impurities which have internal degrees of freedom can also cause dephas-ing [35]. This is because impurities can change the electron’s phase stateupon interaction [46]. For example, when the electron interacts with localmagnetic moments which have an internal spin fluctuating with time, thephase in the electron varies randomly with time as well. The effect of theseimpurities can be reduced by changing the external environment, such as thetemperature and applying low magnetic fields. For example, when in-planemagnetic fields are applied to the magnetic moments, the spin directions ofthe magnetic moments are aligned with the direction of the applied fieldsand these magnetic moments behave like a rigid impurity. Thus, in-planeapplied magnetic fields weaken the dephasing mechanism by suppressing the132.3. Various source of the dephasingdegrees of freedom in impurities. However, if this in-plane field is parallel tothe direction of electron’s motion, it does not affect the electron transport.Additionally, when magnetic fields are applied to the system, the phasecoherence among the electrons in different paths is changed due to theAharonov-Bohm effect. Hence, this applied magnetic field can affect co-herent effects, such as weak localization as mentioned in previous Section2.2. The dephasing rate induced by the various sources described above canaffect many physical properties seen in various transport measurements.Conversely, the dephasing rate can be extracted from experimental resultsof transport measurements [47]. We extract the dephasing rate from themagneto-conductivity data using weak localization.With this extracted dephasing rate via weak localization and its fitting,the source of the dephasing can be verified in various ways, such as by appliedin-plane magnetic fields, compared with theoretical models such as Equation2.11, and observation of the change of the dephasing rate as a function ofexternal parameters. In this thesis, the dephasing rate is compared beforeand after thermal annealing processes to investigate the effect of annealing.Also, the dephasing rate is compared with the electron-electron interactionrate, which is investigated via the change of conductivity and Equation 2.11,to verify the dominant source and additional sources of dephasing in CVDgraphene.14Chapter 3Experimental setup andbackgroundThe goals of the experiments in this thesis were to determine under whatconditions the increase of the dephasing rate happens and how it changeswhen the gate voltage or charge carrier density changes for CVD graphenesamples. These goals were founded on the previous experimental resultthat CVD graphene and exfoliated graphene show similar behavior in de-phasing rate before annealing, and CVD graphene shows drastic increase ofdephasing rate beyond electron-electron interaction rate after annealing. Toconduct these experiments, we mainly prepared CVD graphene samples onseveral substrates, and additionally exfoliated graphene samples. Becauseof their different manufacturing methods, their properties, such as mobility,the position of the Dirac point, and the level of surface contamination differ[48]. Also, to investigate the effect of the substrate we used several differ-ent substrate materials; silicon oxide (SiO2) and hafnium oxide (HfO2).Thereafter, these graphene samples were processed into the standard Hallbar geometry to measure the conductivity and charge carrier density throughcharge transport measurements. After sample fabrication, the charge trans-port properties of the samples were measured under perpendicularly appliedmagnetic fields at 4.2 K, before and after annealing in a custom-made rapidthermal annealer (RTA). Thermal annealing was performed under variousatmospheres, from vacuum to N2 gas, to investigate any resulting effects.This chapter has sections, detailing sample fabrication and the experi-mental measurement setups. Section 3.1 shows the preparation of variousgraphene samples built on several different substrates. Section 3.2 and Sec-tion 3.3 show the custom-made, rapid thermal annealing (RTA) system andthe 4.2 K measurement experimental setups respectively. Lastly, Section3.4 explains the four probes charge transport measurement under appliedmagnetic fields.153.1. Sample preparations3.1 Sample preparationsCVD graphene was mainly prepared on SiO2 and HfO2, whereas exfoliatedgraphene was prepared on SiO2 as shown in Table 3.1 and Figure 3.1. CVDgraphene and exfoliated graphene both have a carbon-based mono-layeredstructure and should have the same physical properties as described in Sec-tion 2.1. However, several of their properties will differ as they are fabricatedin different ways [48, 49].Table 3.1: Various types of graphene on various substrates samples.GraphenetypeSubstrateLength(µm)Width(µm)AnnealingtypeTemp.(◦C)Vacuum 200-350N2/H2 300Ar/H2 300N2 300CVD graphenefrom GrapheneaSiO2 120-300 40-100Ar 300Vacuum 200-350HfO2 120 30 Ar 300Vacuum 200-350CVD graphenefrom ACShBN 120 30Ar 300Vacuum 200-350ExfoliatedgrapheneSiO2 60-40 20-15 Ar/H2 200-350CVD graphene is grown via CH4 gas deposition on copper or nickel foiland then transferred to other substrates such as SiO2 [50]. During the vapordeposition process on the metal substrate, graphene can have unintendedcarbon vacancies and multiple domains. Also, during the transfer process,graphene is chemically contaminated because CVD grown graphene needsto be covered by polymers to protect the surface. Thus, CVD graphenetypically has structural defects and chemical contaminations. However, Thishas the advantage of being unlimited in size.On the other hand, since exfoliated graphene is made from bulk graphiteby exfoliation, sample size will be smaller than CVD graphene but also lesscontaminated. Because of less chemical contamination, exfoliated grapheneshows a lower doping effect and has a higher mobility than CVD graphene.Due to these differences, both types of graphene samples were prepared inthe experiments of this thesis to compare the results. However, the resultof exfoliated graphene is not compared in the main thesis part but in theappendix because exfoliated graphene cases show fitting problems. The163.1. Sample preparationsFigure 3.1: CVD graphene (a) on HfO2 substrate and (b) on hBN . Greenarea under yellow indicates the hBN flake. (c) Exfoliated graphene on SiO2substrate. Yellow colors indicate Ar/Cr electrodes and dashed lines indicatethe standard Hall bar geometry of graphene.173.1. Sample preparationsdetails of exfoliated graphene and CVD graphene on hBN will be discussedin Appendix E.Samples were processed into the standard Hall bar geometry via a con-ventional electron beam lithography process using Au (80 nm thickness) andCr (5 nm thickness) electrodes in all samples. Photographic and schematicpictures of the sample geometry are shown in Figure 3.1 and 3.5 (b) re-spectively. After this fabrication step, the sample was placed on the chipcarrier as shown in Figure 3.2. More fabrication details are summarized inthe following section and Appendix A.Figure 3.2: Chip carrier with the graphene sample on the center. The sample(black color) is wire bonded to the chip carrier (yellow color) by gold wires.3.1.1 CVD graphene on various substratesIn these experiments, three different types of substrates are used with CVDgraphene: 295 nm SiO2, 30 nm HfO2 to investigate the effect of the sub-strates [Figure 3.1]. These substrates were chosen for the following reasons:1. SiO2 is the common substrate used for all types of graphene. 2. As HfO2is grown by atomic layer deposition (ALD), this substrate is single crystalstructure and one can compare the effect of substrate type. AdditionallyhBN was used as a substrate for CVD graphene because hBN is known asa better substrate than SiO2 and because it shows high mobility [51, 52].In Appendix E the result of CVD graphene on hBN is shown.Commercial CVD graphene on SiO2 from Graphenea [53] was used forSiO2 substrate experiments. In the case of HfO2 and hBN , CVD grapheneon filtered paper manufactured by ACS materials was used and transferredonto these substrates [54]. CVD graphene transfer process details are ex-183.1. Sample preparationsplained in Appendix A.3.1.2 Exfoliated graphene on SiO2The exfoliated graphene is exfoliated from bulk graphite on a SiO2 substratein a similar way to the hBN exfoliation [Figure 3.1 (c)]. Further details ofthe exfoliation process are given in Appendix A. Only exfoliated graphenewas used on SiO2 unlike in the CVD graphene case. This is because wealready discerned that the increase of dephasing occurs in CVD graphene onSiO2 hence it was only necessary to confirm whether this increase occurs inexfoliated graphene. If the same result is observed in both graphene samples,then this increase is a common phenomenon in both CVD and exfoliatedgraphene. If it is not, then this effect should be specially activated only inCVD graphene because of the specific characteristics of CVD graphene.3.1.3 Lithography processIn order to pattern the Hall bar geometry on the samples, electron beamlithography process was carried out in five (CVD graphene sample cases) orfour (exfoliated graphene cases) steps. CVD graphene sample cases need anextra step to remove some part of graphene covered area on the substrateto make the bonding pads at the beginning. During each step, the 650nmthickness of double layered PMMA (C4 and A2) was used as electron beamresists. 5 nm thickness of Cr and 80 nm thickness of Au were thermallyevaporated and deposited on the substrate and graphene as wire-bondingpads and electrodes. Cr was deposited before Au deposition on the substratebecause Au does not stick well to SiO2.The first step was making wire-bonding pads (100 µm by 100 µm) andalignment marks, 500-1000 µm away from the graphene flake. The secondstep was making the leads from wire-bonding pads to near the grapheneflake. The third step was connecting the graphene flake and the lead. Thelast step was making the rectangular Hall bar geometry with oxygen plasmaetching as shown in Figure 3.1.After this electron beam lithography process, the sample was attachedon the chip carrier by silver paste as shown in Figure 3.2. Au wire-bondingpads on the graphene sample were wire bonded to a chip carrier.193.2. Rapid thermal annealing system3.2 Rapid thermal annealing systemAnnealing is important in the experiments of this thesis to investigate thesource the increasing of the dephasing rate. A custom-made rapid thermalannealer (RTA) was used (as shown in Figure 3.3) to anneal the sampleunder a vacuum and various gases (Ar, N2, and H2/N2 mixture). It isknown that annealing in different atmospheres has different effects on thesamples. For example, annealing in Ar is better for removing contaminationsthan annealing in a vacuum [26, 55, 56]. Hence, the effect of annealingunder different gases was studied by comparing the magneto-conductivitymeasured data and the change of dephasing.Figure 3.3: Custom-made Rapid Thermal Annealer (RTA) in (a) the realpicture and (b) schematic figure of RTA. (c) Schematic map of RTA andpumping system. Setup in dashed line is only for high vacuum annealing.This custom-made RTA contains a halogen light bulb covered with acopper sheath, a gas line for releasing various gases, and a quartz glass coverto isolate the RTA from the external environment. Moreover, this RTA wasconnected to vacuum pumps to remove other unwanted gases which mightaffect the sample. Only a dry scroll pump was used in gas annealing cases,and dry scroll pump and turbo pump were used in high vacuum annealingcases as shown in Figure 3.3.In the gas annealing case, the RTA was degassed for 15 minutes using203.3. Measurement system at 4.2K - Dunkera dry scroll pump and the annealing system was purged with the relevantgas at least five times. The purging process removes unwanted gases fromthe RTA through a connected gas cylinder. After this process, the gaswas released following a specific recipe to make an equal gas flow rate inevery gas annealing case. A stable pressure level (200 mmHg) was observedduring the gas annealing process after 1 hour and after 5 hours of annealing.This means that other unwanted gases barely trespassed into the RTA andaffected the sample during the gas annealing process so any effect from otherunwanted gases including oxygen could be ruled out for the experimentalresults. After the gas purging and releasing process, the RTA was turnedon and the sample annealed under various temperature conditions from 200◦C to 350 ◦C.In vacuum annealing cases, firstly degassing was performed for periodsof 1 hour to 5 hours using the dry scroll pump and the turbo pump as shownin Figure 3.3 (c). The vacuum level of the RTA was kept below 5 × 10−3mbar, which is the minimum pressure level Pirani gauge can read. Afterthis degassing procedure, the RTA was turned on and the sample annealedunder various temperature conditions, from 200 ◦C to 350 ◦C.In addition to these annealing processes under vacuum and gas, furtherexperiments were conducted to compare the surface temperature of eachannealing condition. The results show similar surface temperatures for thegas and vacuum annealing cases. This fact confirms that the experimentalresults in this thesis do not result from a temperature difference. Detailsof the sample-surface temperature comparison experiment under gas andvacuum are shown in Appendix C.3.3 Measurement system at 4.2K - DunkerAfter these annealing processes, the RTA was cooled to room temperatureand the sample was immediately moved to the 4.2 K dunker measurementsystem [Figure 3.4 (b) and (c)], less than one minute with minimal air ex-posure. The minimal air exposure is important in this experiment becausemoisture and gases in the atmosphere may have an effect on the annealing orcreate unintended effects on the graphene, such as inducing a doping effect.The 4.2 K dunker has a chip carrier holder at the end [Figure 3.4 (b)]and copper wires are connected from this chip carrier holder to the breakoutbox and the lock-in amplifier measurement system, which allows us to applyvoltage source and to measure the nano scale current. After the sample isplaced on the dunker and covered by the stainless steal tube as shown in213.3. Measurement system at 4.2K - DunkerFigure 3.4: (a) Measurement system - dunker in liquid Helium dewar. Themagnet in the dewar (orange color) induces perpendicular magnetic fieldson the device. (b) Zoom-in figure shows the chip carrier (left - schematicpicture, right - real picture) at the end of dunker covered by stainless steel.(c) chip carrier holder in dunker without (left) and with the device (right).223.4. 4 probes measurement with magnetic fieldsFigure 3.4 (c), this measurement system was degassed for 20 minutes usingthe turbo pump, and helium gas was added to the dunker to facilitate heatexchange between the liquid helium and the sample. Liquid helium keepsthe temperature close to 4.2 K in the dunker.After degassing and the helium gas adding process were finished, thedunker was placed into the liquid helium dewar as shown in Figure 3.4 (a)and then all the experiment setups are ready to be measured. The liquidhelium dewar has a magnet at the bottom as shown with orange color inFigure 3.4 (a). This magnet can induce perpendicular magnetic fields onthe sample and is variable to allow sweeping of the magnetic fields froma strength of zero up to a few Tesla. The dunker was placed where themagnetic field is at its maximum strength in order to conduct more accurateexperiments and to avoid different magnitude between real magnetic fieldsand reading fields. If the dunker is placed on wrong position, the magnitudebetween the applied magnetic field and read magnetic field is different andit could lead experimental error and weak localization fitting error.3.4 4 probes measurement with magnetic fieldsIn transport experiments, many physical properties can be investigated bymeasuring the current or voltage changes with applied electric or magneticfields as mentioned in Chapter 2.3. Figure 3.5 (a) shows the resistancechange as a function of gate voltage (main image) and the change of Fermilevel (inset images) in graphene. As shown in this figure, one can investigatethe physical properties below the Dirac point (hole charge carrier region) andabove the Dirac point (electron charge carrier region) by applying transverseelectric fields [29].To do this transport measurement in different charge carrier densityregions of graphene, the standard hall bar geometry was made with a backgate underneath of the substrate as shown in Figure 3.5 (b). From thisgeometry, the conductivity σXX =g∗IVXX(ρxx=VXXg∗I ) can be extracted, whereI is the applied current and g is geometric ratio of width to length betweenVXX (longitudinal voltage change) and VXY (transverse voltage change).Additionally, the charge carrier density can be calculated from a VXYmeasurement with applied magnetic fields. To extract the charge carrierdensity, the low magnetic field approximation can be used and it gives ns =I/edVXY /dB[35]. Through this charge carrier density ns and resistivity ρxxfrom the above, the mobility µ = 1|e|nsρxx and the diffusion coefficient D =σpih¯vf2e2√pins(vf=Fermi velocity) can also be obtained [35, 57].233.4. 4 probes measurement with magnetic fieldsFigure 3.5: (a) Resistivity as a function of applied gate voltage at 4 K.The dashed line indicates the Dirac point, and the small side peak on theright side is the experimental noise. (b) Simplified device geometry andmeasurement setup of CVD graphene on HfO2 substrate. Blue indicatesCVD graphene and yellow indicates Au (80nm)/Cr (5nm) electrodes, I in-dicates applied current, and B indicates perpendicularly applied magneticfields. (c) Real picture of CVD graphene on HfO2 substrate. Dashed lineindicates Hall bar geometry of graphene.In addition, when the gate voltage (VG) is applied through the back gateon the sample, electric fields can be applied onto the substrate, inducing acapacitor effect on graphene and changing the Fermi level as shown in Figure3.5 and the charge carrier density also. Moreover, weak localization can beconfirmed by applying perpendicular magnetic fields [indicated as B in Fig-ure 3.5 (b)] and observing the change in conductivity, as the magnetic fieldssuppress the conductivity correction. The confirmation of weak localizationin graphene will be described in Section 4.1Ideally, graphene is at its Fermi level under zero gate voltage as shownin Figure 2.3 (a) [6], which means that the Dirac point can be seen at zerogate voltage and graphene shows zero conductivity at zero gate voltage.However, in real experimental graphene samples, one can rarely see thelowest conductivity or highest resistance, which are the signal of Dirac point,243.4. 4 probes measurement with magnetic fieldsat the zero gate voltage because of various factors. Especially on CVDgraphene as described in Section 3.1, chemical contaminations from the CVDgrowth process or the lithography fabrication process induce the dopingeffect on graphene. As a result, the Dirac point in most experiments is notat the zero gate voltage as shown in Figure 3.5 (a). As the CVD graphenesamples of this work show the hole doped effect (voltage of the Dirac point,VDP , is above zero.), the hole doped region (E < EF and VG < VDP ) ismostly focused on.Also, since most of the before-annealed samples and air exposed sampleshave very high Dirac points (VDP > 80 V ) and extremely high gate voltagescannot be applied on the samples, the Dirac point is estimated by usinga linear relation between the charge carrier density (ns) and applied gatevoltage (VG); ns = α(VG − VDP ) with α = substrate/(edsubstrate) which isa capacitance and experimentally extracted. From the fact that theoreticalvalue of ns at the VDP is zero, the Dirac point can be estimated [2].25Chapter 4Experimental resultWith graphene samples before and after the annealing process, transportmeasurement experiments were conducted at 4.2 K under application ofperpendicular magnetic fields and application of back gate voltage. Phys-ical properties including various interaction rates were extracted from themeasured data via weak localization fitting. The effect of annealing at differ-ent temperatures and different atmospheres was investigated by comparingthe change of conductivity as a function of the applied gate voltage or asa function of the applied magnetic fields. The dephasing rate extractedusing Equation 2.8 and the electron-electron interaction rate from Equa-tion 2.11 are also compared. From the comparison of experimental resultswith various samples, the creation or activation condition and the propertiesresponsible for increasing the dephasing rate were investigated.Section 4.1 shows the steps to measure the conductivity as a functionof the applied gate voltage and details the extraction of the interactionrate. Section 4.2 shows the results of the CVD graphene sample on SiO2substrate annealing under various atmospheres. Section 4.3 shows the resultsof CVD graphene on HfO2 substrate annealing under the same conditions.Based on these two substrates experiments, Section 4.4 shows the additionalexperimental results focusing on air and moisture exposure. Section 4.5briefly describes the reason why the results of exfoliated graphene and CVDgraphene on hBN are not compared with CVD graphene on SiO2 and HfO2results. Lastly, Section 4.6 summarizes the experimental results.4.1 Measurement processAfter the sample preparation described in Chapter 3, the measurement inthe dunker at 4.2 K is performed before and after annealing process underapplication of perpendicular magnetic fields and the back gate voltage.First, back gate voltages are applied to the sample through the substrateover wide range as shown in Figure 4.1 (a) to investigate the change ofconductivity as a function of the applied gate voltage and to find the positionof Dirac point.264.1. Measurement processFigure 4.1: The example of experimental procedures in this thesis. (a)Measurement of conductivity change as function of applied gate voltage.This is the case of Ar annealed CVD graphene with VG = from -80 V to 30V, and VG = 18 V. Magneto conductivity data measured at 4.2 K in (b) longrange magnetic fields (± 100 mT) and (c) shot range magnetic fields (± 10mT) and its weak localization fitting. These two field ranges are measuredseparately.Second, perpendicular magnetic fields are swept over ranges of ± 100 mTand ± 10 mT ranges [Figure 4.1 (b) and (c)] at each gate voltage with a stepbased on the variation of charge carrier density. Because each field rangehas a different dominant interaction mechanism based on its interaction rate,the measurements with different magnetic field ranges allow one to extractmore accurate fitting parameters. For example of CVD graphene case, in 100mT range, intravalley scattering rate dominantly affects weak localizationfitting, and in 10 mT range, dephasing rate dominantly affects the fitting.Additionally, these magneto-transport measurements begin 20-15 V belowfrom the Dirac point VDP , which is the hole charge carrier region. This isbecause one can reduce the effect of electron-hole puddles [22, 32].With this measured magneto-conductivity data, the dephasing rate isextracted using the weak localization fitting function from Equation 2.8,and the electron-electron interaction rate is calculated via conductivity and274.2. CVD graphene on Silicon OxideEquation 2.11. This fitting function is briefly described in the followingsection, and further details are given in Appendix B. Next, these extractedrates are compared as a function of charge carrier density and applied gatevoltage. If the dephasing rate and electron-electron interaction rate areequal, this means that the main source of the dephasing in graphene isthe electron-electron interaction as mentioned in Section 2.3. If not, otherinteractions can be expected to be additional sources of the dephasing aswell as the electron-electron interaction.4.1.1 Weak localization fittingThe weak localization theory for graphene in Equation 2.8 is modified to beused as a fitting function in the following equation and the fitting resultsare shown in Figure 4.1 (b) and (c).f(B) = L ∗ (B −B0) +R0 −R20(e2pih[F (z1)− F (z2)− 2F (z3)])∗ g (4.1)F (z) = ln(z) + ψ(0.5 +1z)(4.2)z1 =|B −B0|Bφ, z2 =|B −B0|Bφ + 2Bi, z3 =|B −B0|Bφ +B∗(4.3)In this fitting function, the followings are the fitting parameter: L is linearityof measured data, B is the perpendicularly applied magnetic fields, R0 isthe maximum resistance, B0 is magnetic field where R is the maximum, gis geometric ratio (width/length), and ψ is digamma function. Bφ,i,∗ arethe magnetic field scale of each interaction rates. More details of this fittingfunction are given in Appendix BThis fitting function is used to extract interaction rates in terms of mag-netic field scale from the magneto-conductivity data at each charge carrierdensity with ± 100 mT and ± 10 mT magnetic fields ranges. Then, one cancalculate interaction rates; τ−1φ,i,∗ =4eh¯ DBφ,i,∗ as desribed in Section 2.2.1.Because this weak localization fitting process cannot perfectly fit on themeasured data and extract interaction rates due to the various reasons, weused the error bar on the extracted rates to compensate this imperfection offitting process. The details of this error bar are described in Appendix D.4.2 CVD graphene on Silicon OxideThe first experiment was conducted with CVD graphene on SiO2 substrate.For these samples, commercial CVD graphene from Graphenea [53] is used284.2. CVD graphene on Silicon Oxideafter fabrication steps described in previous Chapter 3. These samples wereannealed at temperatures from 200 ◦C to 350 ◦C in vacuum or under pres-ence of Ar, N2, or a N2&H2 mixture. Since a significant change of dephasingrate in the 200 ◦C and 250 ◦C annealed samples could not be seen, only the300 ◦C annealed samples are compared in this chapter.4.2.1 Before-annealed CVD grapheneFirst, CVD graphene samples, after lithography process and before any an-nealing process, are measured. Because applying extremely high voltagecould damage the device, we only applied up to 60 V and estimated theDirac point based on a linear relation as described in 3.4. The Dirac pointsfor these samples are located between 88 V to 114 V. The case of VDP= 88V is described in this Section and the results are shown in Figure 4.2.Figure 4.2 (a) shows the change of charge carrier density as a function ofapplied gate voltage. The linear fit in this figure (a) indicates the positionof Dirac point at 88 V. The conductivity in Figure 4.2 (b) increases linearlywith dσdV = -0.46 e2/hV as the applied gate voltage changes from 60 V to-40 V. This slope (which is related to field-effect mobility, µ ∝ σVG ) andcurvature of σ(VG) near the Dirac point can tell inhomogeneity and thelevel of charged impurity [58, 59]. This result will be compared with Arannealed and vacuum annealed cases.Figure 4.2 (c) compares the magneto-conductivity in ± 10 mT rangeresults at each charge carrier density. ∆σ in ± 10 mT does not satu-rate, but continuously increases as the charge carrier density increases from2×1012/cm2 to 9×1012/cm2 (red to black color). This means that the con-ductance correction due to the weak localization is larger as charge carrierdensity increases. This also shows that the dephasing rate is getting sloweras carrier density increases [22].The dephasing rate, which is extracted from weak localization Equation2.8, and electron-electron interaction rate, which is calculated via conduc-tivity and Equation 2.11, are quantitatively compared in Figure 4.2 (d).Even these two rates are extracted from two different sources with eachequation, these rates are equally decreased within the error as a functionof charge carrier density. Therefore, before annealing, it can be confirmedthat the main mechanism of the dephasing in CVD graphene at 4.2 K is theelectron-electron interaction.Furthermore, intervalley scattering rates (τ−1i ) are higher than 300 /ns,and intravalley scattering rates (τ−1∗ ) are higher than 10 /ps for all chargecarrier density ranges. This result made less fitting error in dephasing rate294.2. CVD graphene on Silicon OxideFigure 4.2: Before-annealed CVD graphene (a) Hall bar measured holecharge carrier density as a function of applied gate voltages. Dashed linesrepresents the linear line fit as a extension of measured data from -40 V to60 V. (b) change of σ as a function of applied gate voltages from -40 V to60 V. Solid line represents the σxx measurement, swept gate voltage from0 V to 60 V. Markers represents the. (c) ∆σ in magnetic field. Dashedline represents the measured data and the solid line represents the weaklocalization fitting. (d) extracted rates as function of charge carrier den-sity (dashed line: τ−1φ (dephasing rate), solid line: τ−1ee (electron-electroninteraction rate)). Each color represents each charge carrier density from2× 1012/cm2 to 9× 1012/cm2.304.2. CVD graphene on Silicon Oxidebecause variation of one parameter did not affect others during the fittingprocess.4.2.2 Ar gas annealed CVD grapheneAfter before-annealed samples were measured, those samples were annealedunder various type of gases to investigate the effect of gas annealing ondephasing. The Dirac points in gas annealed CVD graphene on SiO2 casesare located between 18 to 40 V. This Section and Figure 4.3 show the resultof Ar annealed CVD graphene sample, which was used in previous Section4.2.1. This sample was annealed for 1 hour at 300 ◦C under 99.999 % purityAr gas and it has the Dirac point at 18 V.When the conductivities before-annealed sample in Figure 4.2 (b) and Arannealed sample in 4.3 (b) are compared, conductivity change as a functionof the applied gate voltage is only shifted close to zero voltage without asignificant change. Also, dσdV is -0.43 e2/hV (green dashed line) in the gatevoltage range from 0 V to -90 V, which is close to the before-annealed case(-0.46, blue dashed line) except near the Dirac point. The slope and thesharp curvature of σ(VG) near the Dirac peak indicate less impurity andinhomogeneity in Ar annealed CVD graphene sample compared to before-annealed sample.Figure 4.3 (c) compares the magneto-conductivity data measured ateach carrier density. One of the most significant changes is that ∆σ indifferent charge carrier densities fold on top of each other when the chargecarrier density is larger than 3 × 1012/cm2, although σ keeps increasing asshown in (b). This fact is distinct from the before-annealed case shown inFigure 4.2 (c), which the curvature of ∆σ keeps changing. This shows thatthe conductivity correction due to weak localization is maintained even thecharge carrier density increases.When the dephasing rate from WL fitting and electron-electron inter-action rate from conductivity are quantitatively compared in Figure 4.3(d), these two rates are no longer the same. The difference between thesetwo rates becomes larger as the charge carrier density increases. To be spe-cific, although the electron-electron interaction rate decreases, the dephasingrate is maintained indicating the effects from additional sources of dephas-ing would increase as the charge density increases. Interestingly, this phe-nomenon also occurs even when annealing under different gases, i.e. underN2 and under a H2/N2 mixture, and this fact indicates that gas annealinginduces additional source of dephasing on CVD graphene.314.2. CVD graphene on Silicon OxideFigure 4.3: Ar-annealed CVD graphene (a) Hall bar measured hole chargecarrier density as a function of applied gate voltages. Dashed line (red) rep-resents the linear fit. (b) change of σ as a function of applied gate voltagesfrom -80 V to 30 V. Two dashed lines represents the linear line fits frombefore-annealed one from Figure 4.2 (blue color) and Ar annealed one data(green color). Before-annealed case is shifted by 70 V, which is VDP differ-ence. (c) ∆σ in magnetic field and (d) extracted rates as function of chargecarrier density (dashed line: τ−1φ , solid line: τ−1ee ) Each color represents eachcarrier densities.324.2. CVD graphene on Silicon Oxide4.2.3 Vacuum annealed CVD grapheneTo confirm whether annealing under any condition could induce the addi-tional source of dephasing on CVD graphene, the similar experiments wereconducted with vacuum annealed CVD graphene sample. Before experi-ments were conducted, similar result was expected as was seen with the Arannealed sample experimental result, because Ar with 99.999% purity is aninert gas, close to vacuum.First, the fresh CVD graphene on SiO2 sample was measured beforeannealing and it showed similar behavior of conductivity and dephasingrate as was observed in before-annealed sample, Figure 4.2. The dephasingrate and electron-electron rate were the same in error range as shown forthe before-annealing case in Figure 4.2 (d). After this measurement, thisCVD graphene sample was annealed for 1 hour at 300 ◦C under a vacuumcondition below 5 × 10−3 mbar. These vacuum annealed cases shows theDirac point between 42 to 114 V. Figure 4.4 shows the result of VDP = 114 Vcase.In this vacuum annealed case, the Dirac point was estimated from thelinear relation between charge carrier density and applied gate voltage asdescribed in Section 3.4 and it is shown in Figure 4.4 (a). dσdV is -0.4 e2/hVand the conductivity changed similarly to the above two measurements asshown in Figure 4.4 (b). Although we could not compare near the Diracpoint, the slope shows that annealing under vacuum or gas does not affect thechanging of the conductivity significantly. When the charge carrier densityincreases, ∆σ continues to increase without any overlap as shown in Figure4.4 (c). This is similar to the case of the before-annealed experiment.Figure 4.4 (d) shows that the dephasing rate and electron-electron in-teraction rate decrease with a similar slope as a function of charge carrierdensity. However, there is a maintained difference (∼ 4 /ns) between thedephasing rate and electron-electron interaction rate. In other words, unlikewith gas annealing, the main source of the dephasing in vacuum annealedCVD graphene is still the electron-electron interaction. However, since thetwo interaction rates do not have the same value and the difference is main-tained for all charge carrier densities, the creation or activation of additionalinteractions for the dephasing is also expected in the vacuum annealed case.Otherwise, these differences can be simply a systematic error because theseare within the error range.In addition to this 1 hour vacuum annealing experiment, there was stillno overlap of ∆σ even with the 5 hours vacuum annealing case. However,the maintained difference between the dephasing rate and electron-electron334.2. CVD graphene on Silicon OxideFigure 4.4: Vacuum-annealed CVD graphene (a) Hall bar measured holecharge carrier density as a function of applied gate voltages. Dashed lines(red) represents the linear line fit. (b) change of σ as a function of appliedgate voltages from -20 V to 60 V. Dashed line (black) represents the changeof conductivity in before- annealed case from Figure 4.2 with the offset alongVG. (c) ∆σ in magnetic fields and (d) extracted rates as a function of chargecarrier density (dashed line: τ−1φ , solid line: τ−1ee ). Each color represents eachcarrier density from 3.5× 1012/cm2 to 8.6× 1012/cm2.344.3. CVD graphene on Hafnium Oxide (HfO2) substrateinteraction rate is slightly larger (∼ 8.5 /ns) than the 1 hour vacuum an-nealing case (∼ 4 /ns). From the fact that this increase in 5 hours annealingis beyond the error range, one can confirm that vacuum annealing inducesadditional source of dephasing, which is maintained in all charge carrierdensities unlike the case of Ar annealing.4.3 CVD graphene on Hafnium Oxide (HfO2)substrateAs the change of dephasing rate in gas annealed CVD graphene on SiO2substrate is confirmed in previous chapter, one can suspect gas annealing orthe SiO2 substrate as the cause of dephasing change. For this reason, hereCVD graphene on HfO2 substrate samples were used. We also measuredthree different types of annealing cases: before-annealed, vacuum annealedand gas annealed. The Dirac points in these cases were located near 0 V un-like the cases of CVD graphene on SiO2. Nonetheless, those CVD grapheneon HfO2 experiments show the similar results in change of interaction ratesas CVD graphene on SiO2 shows above.Figure 4.5: Ar-annealed CVD graphene on HfO2 substrate. (a) Hall barmeasured hole charge carrier density as a function of applied gate voltages.(b) change of σ as a function of applied gate voltages from -100 V to 20V. Dashed line indicates Ar annealed CVD graphene on SiO2 substratewith offset along VG. (c) ∆σ as a function of magnetic fields. Each colorrepresents each carrier density.Figure 4.5 shows the result of Ar annealed CVD graphene on HfO2.Compared to Ar annealed on SiO2 substrate case, graphene on HfO2 showstwo significant differences; charge carrier density and conductivity slowly354.3. CVD graphene on Hafnium Oxide (HfO2) substratechange as a function of applied gate voltage with dσdV = −0.25e2/hV , andthe position of Dirac points are close to zero gate voltage. This is becauseHfO2 has higher dielectric constant than SiO2, κ = 25 (κ for SiO2 =3.9), and much thinner than SiO2 (60 nm in HfO2 and 285 nm in SiO2).However, ∆σ as a function of magnetic fields in Figure 4.5 (c) shows thesimilar overlap at higher charge carrier density region as Ar annealed SiO2substrate shows. The overlap of ∆σ in both substrates cases indicates thatthe sample on HfO2 also has the additional source of dephasing after gasannealed.For the detailed quantitative comparison of dephasing rate and electron-electron interaction rate, Figure 4.6 shows the change of dephasing rateand electron-electron interaction rate as a function of charge carrier densitybefore, and after annealing in vacuum or under gas, in case of HfO2 andSiO2 substrates. In case of before-annealing shown in Figure 4.6 (a), thedephasing rate and the electron-electron interaction rate are almost equallydecreased for all charge carrier density ranges. The slight difference betweenthe dephasing rate and electron-electron rate at the lowest carrier densitycan arise from the electron-hole puddle [58]. After the annealing in vacuumshown in Figure 4.6 (b), the interaction rates are of a similar range tothe before-annealed case, and the difference between the dephasing rate andelectron-electron interaction rate is maintained as ∼4.5 /ns for all chargecarrier densities.After new sample was annealed under Ar gas, as shown in Figure 4.6 (c),both interaction rates are increased compared to the before-annealed case,to around 15 /ns for the electron-electron interaction rate and 20 /ns forthe dephasing rate. The difference between the dephasing rate and electron-electron interaction rate continues to increase as a function of charge carrierdensity.When HfO2 cases in Figure 4.6 (a), (b), (c) are compared with SiO2cases in (d), (e), (f), it is confirmed that there is no significant differencein the change of the dephasing rate between CVD graphene on SiO2 andHfO2 substrates. Only noticeable difference between these two cases is atthe low carrier density region. HfO2 cases show the significant discrepancyin dephasing rate and electron-electron interaction at low density region.For this reason, electron-hole puddle can be suspected.Furthermore, as the unusual increase of the dephasing rate due to theadditional sources after gas annealing occurs in both CVD graphene sampleson oxide substrates, these results can be interpreted so: the induction ofadditional source of dephasing could be an effect from the oxide substrate,or not affected by the type of substrate.364.3. CVD graphene on Hafnium Oxide (HfO2) substrateFigure 4.6: The results of CVD graphene on HfO2 substrate in three an-nealing cases. Extracted rates as function of charge carrier density are in(a) before-annealed, (b) vacuum annealed, and (c) Ar annealed sample.To make comparison with SiO2 substrate, the figures from the experimentabove with SiO2 are used; (d) before-annealing, (e) vacuum annealing, (f)Ar gas annealing. Both substrate cases show the similar behavior in dephas-ing rate (τ−1φ ) and electron-electron interaction rate (τ−1ee ) at each annealingprocess.374.4. Air exposure on CVD graphene on Silicon Oxide4.4 Air exposure on CVD graphene on SiliconOxideAlong with the above experiments, another experiment was conducted tosee how the position of Dirac point and the air exposure affect the changeof dephasing rate. The reason for this experiment was there are significantdifferences in the position of Dirac point VDP between before-annealed, gasannealed, and vacuum annealed samples. This position difference could in-duce the difference in the additional source of dephasing. This experimentwas also to verify whether the dephasing rate returns to the electron-electroninteraction rate which can indicate the unknown interaction effect for de-phasing disappears.As the increase of dephasing and the difference between the dephasingrate and electron-electron interaction rate was observed for all oxide sub-strates cases, these experiments were conducted only with the samples, CVDgraphene on SiO2.First, the new CVD graphene sample was annealed under H2/N2 andmeasured [Figure 4.7, 1 ]. Then, this sample was intentionally exposed toair [Figure 4.7, 2 - 4 ]. The effect of this intentional exposure to air is tointroduce a hole-doping effect on graphene [60]. Specifically, each numberindicates the step of treatments on the sample; 1 : 1 hour annealing inH2/N2 mixture, 2 - 4 : air exposure, 5 : additional 1 hour annealing ingas. Accordingly, after these air exposures, the Dirac points in 2 − 4 areshifted to a higher positive voltage (∆VDP > 0). The results of the followingtreatments on the same graphene sample are summarized in Figure 4.7.When the Dirac point of the gas annealed sample [ 1 in Figure 4.7] isshifted away due to the air exposure [ 2 − 4 in Figure 4.7], the overalldephasing rate decreases in the low carrier density region and then increasesagain in the higher charge carrier density region. However, the electron-electron interaction rates only decrease without other significant changes.This sample is further annealed under gas at 300 ◦C for 1 hour, and theDirac point is shifted back to 70 V [ 5 ]. In this case, the Dirac point and thedephasing rate are larger than the initial annealing case 1 (VDP = 60 V ).However, the electron-electron interaction rates are within the same rangesimilar to the case of 1 , which indicates that there is no relation betweenthe magnitude of the dephasing rate and the position of the Dirac point.To thoroughly compare the quantitative changes between the dephas-ing rate and the electron-electron interaction rate, Figure 4.7 (b) showsthe excess of the dephasing rate, which is subtracting the electron-electron384.4. Air exposure on CVD graphene on Silicon OxideFigure 4.7: (a) Dephasing rate (solid lines) and electron-electron interactionrate (dashed lines), and (b) the excess of the dephasing rate (τ−1φ − τ−1e−e)as a function of charge carrier density. Arrow denotes the minimum value.(VDP : 1=60 V, 2=92 V, 3=109 V, 4=140 V, 5=70 V)interaction rate from dephasing rate (τ−1φ − τ−1e−e ) and only indicates theadditional source, as a function of charge carrier density. After only 1 hourof gas annealing cases [ 1 - 4 ], although the Dirac point has shifted awaysignificantly, the excess of the dephasing rates in these cases are maintainedbetween 10 /ns and 30 /ns in a shape consistent with a minimum. This sug-gests that the effect from gas annealing is preserved even after the sampleis exposed to air for a long time, while it is shifted to higher carrier densityregion. Also, considering the remarkable increase of the excess of dephasingof in the extra annealed case 5 , it is expected that additional annealingunder gas conditions would induce more additional source of the dephasingand further increase the excess of dephasing. This means that the anneal-ing under gas would keep creating or amplifying the unknown source of the394.5. Comparison experiments to hBN and exfoliated graphenedephasing.Another interesting feature in Figure 4.7 (b) is that every case of the ex-cess of dephasing rate has the minimum excess rate (marked with arrows),when the applied gate voltage is zero. This fact suggests that the applyinggate voltage on the sample could play a significant role in switching on theeffect of the additional source on dephasing rate. However, how the gatevoltage affects the dephasing rate could not be clearly answered. Theoret-ical model by [61] could help to answer this, which suggests applied gatevoltage could affect the orbital of graphene. Another explanation can begiven as follows: because the minimum excess rate in gas annealed casesis not negligible compared to the before-annealed cases, the mechanism ofincreasing the excess rate can be divided into two types. One can cause thefixed extra increment of the dephasing rate regardless of the applied gatevoltage as observed in vacuum annealed cases. The other type can cause theproportional increment as a function of the applied gate voltage as observedin gas annealed cases only.4.5 Comparison experiments to hBN andexfoliated grapheneExperiments with CVD graphene on hBN and exfoliated graphene on SiO2were also conducted. However, experimental results of these samples are notcompared with the above experimental results. This section briefly describeswhy these results are not compared with CVD graphene on oxide substrateresults. The details of experimental result and the reason shows in AppendixE.In case of CVD graphene on hBN , electron-electron interaction rates arehigher than dephasing rates in all annealed cases and we could not observeany significant effect of annealing in vacuum and under gases. In exfoliatedgraphene on SiO2 samples, intravalley scattering rate and intervalley scat-tering rate and dephasing rate are comparable, which are close to 50/ns.These similar magnitudes made significant error during the weak localiza-tion fitting process. Also, it has no drastic difference between gas annealingand vacuum annealing for the dephasing rate.Due to these reasons, we decided that the experiments conducted withhBN and exfoliated graphene does not give the meaningful data and results.More details of these experiments are explained in Appendix E.404.6. Summary4.6 Summary4.6.1 The excess of dephasing rate in CVD grapheneWhen the values excluding the electron-electron interaction rate from thedephasing rate (τ−φ 1 − τ−ee1), which is the excess of dephasing rate as afunction of charge carrier density and as a function of applied gate voltageare compared, very interesting results are observed as shown in Figure 4.8.In this figure, all the gas annealed cases are annealed at 300 ◦C for 1 hourand the vacuum annealed samples are annealed for 1 hour and 5 hours.First, when the applied gate voltage is zero, all the gas annealed caseshave the minimum excess of the dephasing rate except in theHfO2 substratecase. A possible reason that HfO2 has an exception at VG = 0 is because itsDirac point is close to zero volts so weak localization in this sample might beaffected by electron-hole puddles. Also, all gas annealed cases have a similarexcess of the dephasing rate at similar charge carrier densities. These areincreased with a similar slope,(τ−1φ −τ−1eens), in a similar rate range.In contrast to the cases with gas annealing, vacuum annealing cases havea near-zero increment of the dephasing rate (∼ 4 /ns for 1-hour annealingand ∼ 8.5 /ns for 5 hours annealing). These increases are maintained irre-spective of the charge carrier densities and the applied gate voltages. Fromthese results, one can expand the possible explanation of the two differ-ent mechanisms responsible for increasing the dephasing rate, as describedin Section 4.4. The mechanism causing the fixed extra increment in thedephasing rate regardless of the applied gate voltage might occur in bothgas annealing and vacuum annealing, but the effect in vacuum annealingis weaker than in gas annealing. Also, the source causing the proportionalincrement as a function of the applied gate voltage (charge carrier density)is only created or activated by the gas annealing. The details for the errorbar in Figure 4.8 are described in Appendix D.4.6.2 SummaryFrom the results of the experiments with CVD graphene on oxide substrates,the following statements can be concluded.First, the excess of the dephasing rate is arisen in both vacuum annealingand gas annealing cases [Figure 4.4 and 4.3]. However, in the case of vac-uum annealing [Figure 4.4], the excess rate is very small (4 /ns) comparedto gas annealing cases and is maintained irrespective of the charge carrierdensities and the applied gate voltages. On the other hand, in the case414.6. SummaryFigure 4.8: The excess of dephasing rate (τ−1φ − τ−1e−e) as function of appliedgate voltage (a) and of charge carrier density (b) on various annealing con-ditions. The cases of CVD graphene on HfO2 before annealing and vacuumannealed are excluded due to the similarity to CVD graphene on SiO2 cases.(before-annealed: VDP= 90 V, Vacuum in 1 hour VDP= 115 V, in 5 hours30 V, Ar: VDP= 18 V, N2: VDP= 31 V, H2&N2: VDP= 60 V, HfO2 onAr: VDP= 5 V)424.6. Summaryof gas annealing, the excess of the dephasing rate keeps increasing as thecharge carrier density increases with the minimum rate at zero gate voltage.Therefore, the excess of the dephasing rate produced by these two annealingprocesses should come from the two different mechanisms or sources. Oneinduces the maintained increment of dephasing rate regardless of appliedgate voltage. The other induces the increment of the dephasing rate whichincreases as a function of applied gate voltage. Vacuum annealing only in-duces the first mechanism due to the constant increment of extra dephasingrate in all applied gate voltages. Whereas gas annealing induces both mech-anisms due to the shape of the minimum excess of dephasing rate at zerogate voltage.Moreover, since both annealing cases show a similar surface temperature[Appendix C], the temperature difference of the sample surface as the causeof the dephasing rate increase can be ruled out. Because the pressure level ismaintained at 200 mmHg during gas annealing, we could rule out the effectfrom unwanted gases such as oxygen or moisture.Second, the additional experimental result in Appendix F that the ex-cessive dephasing rate caused by gas annealing is reduced by the in-planemagnetic fields [Figure F.1] can suggest the following statements; magneticmoments are induced or activated by the gas annealing, and it causes the ad-ditional dephasing source for graphene. The effect of this additional dephas-ing source disappears when in-plane magnetic fields “freeze” the magneticmoments. Moreover, since all the gas annealed cases have a minimum of theexcess of dephasing rate at 0 V and this excess of dephasing rate keeps in-creasing with the applied gate voltage, the applied gate voltage could triggerthe magnetic moments, and the additional dephasing source.In addition, since SiO2 and HfO2 show similar trends of the incrementof the dephasing rate after annealing under different gases, this effect canbe caused by the interaction between graphene and the oxide substrate. Toclearly confirm whether this effect is from the oxide substrate, similar ex-periments with CVD graphene on other substrates, such as SiC and Al2O3,are necessary under the same annealing and experimental conditions.43Chapter 5ConclusionThe goals this thesis were to understand why the dephasing rate in CVDgraphene shows certain unexpected behaviors and how the increase of de-phasing rate happens, and to investigate the properties of the increaseddephasing. Another supplementary goal was to verify whether this sourcehas magnetic properties. To achieve these research goals, weak localizationtheory for graphene and thermal annealing experiments under various con-ditions were used. CVD graphene on different oxide substrates samples weremeasured at 4.2 K using perpendicularly applied magnetic fields.As a result, it was found that the excess of the dephasing rate, where theelectron-electron interaction rate is excluded from the dephasing rate, hasseveral interesting findings. When the CVD graphene sample was annealedunder gas, the dephasing excess had a turning point shape with the minimumrate at zero gate voltage and it increases as a function of applied gate voltage.Also, all the gas annealed CVD graphene on oxide substrates had a similarexcess of dephasing rates at similar charge carrier density regions. When theCVD graphene sample was annealed under a vacuum, the dephasing excessis maintained in all charge carrier densities at 4 /ns for 1 hour vacuumannealing and 8.5 /ns for 5 hours vacuum annealing. Both maintained ratesin the 1 hour and 5 hours vacuum annealing cases are smaller than theminimum rate in the gas annealing cases.From these findings, it can be concluded that there are two mechanismsfor the dephasing excess. One causes the constant increment of the de-phasing rate regardless of the applied gate voltage. The other causes thedifference in the dephasing rate which increases as a function of the appliedgate voltage. Vacuum annealing only induces the afore-mentioned mech-anism as there is a constant increment for all applied gate voltages. Gasannealing induces both mechanisms as there is a turning point shape withthe minimum at zero gate voltage.In the additional experiment, when the in-plane magnetic fields are ap-plied to the gas annealed CVD graphene on SiO2, the dephasing rate is de-creased from 66 /ns to 23 /ns. This result indicates that in-plane magneticfields “freeze” the additional source of dephasing. Thus, the gas annealing44Chapter 5. Conclusionshould cause or activate the magnetic moments on CVD graphene on oxidesubstrates.From the dephasing rate derived by combining weak localization theoryand the experimental results with CVD graphene, the conditions for creatingor activating the magnetic moments as a source of the dephasing rate aregiven as: Annealing CVD graphene on SiO2 or HfO2 substrates undergases, such as Ar, N2, and H2/N2 mixture, at temperature above 300◦C.The properties of this enhanced dephasing are:• It has the minimum at zero gate voltage.• It has the similar excess of dephasing rate at the similar charge carrierdensity.• It decreases when in-plane magnetic fields are applied on the sample.Figure 5.1: Theory simulations of local magnetic moments in graphene withvacancies. Optimized atomic structure and charge distribution for spin upand spin down states (a) with one vacancy and (b) with two A sublatticevacancies and one B sublattice vacancy, where green balls and red balls indi-cate the A sublattice atoms and B sublattice atoms, respectively. (Adaptedfrom Ref. [7])Here, an additional possible explanation for how magnetic moments are45Chapter 5. Conclusioncreated or activated via gas annealing is proposed: firstly, because it is re-ported that the vacancies, defects, and impurities in graphene can createmagnetic moments [Figure 5.1] [7, 16, 62–64], gas annealing might createthe vacancies or impurities on graphene as the source of magnetic moments.Otherwise, as gas annealing could remove the impurities that were placedin the carbon vacancies, magnetic moments could be activated due to therestored carbon vacancies. It also may induce magnetic moments under-neath graphene because annealing in gas could break the dangling bond ofthe oxide substrate [65, 66]. Adatoms, such as hydrogen or oxygen fromthe annealing process, could be the possible reason for magnetic momentson CVD graphene, because it is theoretically and experimentally proventhat hydrogenated graphene has magnetic properties [67–71]. Also, the factthat oxidation on graphene has the magnetic property is theoretically shown[72]. However, since hydrogenation on graphene needs much different condi-tion than our annealing, such as using hydrogen plasma reactor or few GPapressure on the graphene, hydrogenation is unlikely.Also, orbital hybridization induced by applied gate voltage on graphenevacancy could induce the local magnetic moments. 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Partial hydrogenation induced interaction in agraphene–sio 2 interface: irreversible modulation of device characteris-tics. Nanoscale, 9(4):1662–1669, 2017.[67] J Zhou, Q Wang, Q Sun, XS Chen, Y Kawazoe, and P Jena. Ferromag-netism in semihydrogenated graphene sheet. Nano letters, 9(11):3867–3870, 2009.[68] David Soriano, Dinh Van Tuan, Simon MM Dubois, Martin Gmitra,Aron W Cummings, Denis Kochan, Frank Ortmann, Jean-ChristopheCharlier, Jaroslav Fabian, and Stephan Roche. Spin transport in hy-drogenated graphene. 2D Materials, 2(2):022002, 2015.[69] Jayakumar Balakrishnan, Gavin Kok Wai Koon, Manu Jaiswal,AH Castro Neto, and Barbaros O¨zyilmaz. Colossal enhancement ofspin–orbit coupling in weakly hydrogenated graphene. Nature Physics,9(5):284, 2013.[70] Bernard R Matis, Felipe A Bulat, Adam L Friedman, Brian H Hous-ton, and Jeffrey W Baldwin. Giant negative magnetoresistance and atransition from strong to weak localization in hydrogenated graphene.Physical Review B, 85(19):195437, 2012.[71] Susumu Okada, Kenji Shiraishi, and Atsushi Oshiyama. Magnetic or-dering of dangling bond networks on hydrogen-deposited si (111) sur-faces. Physical review letters, 90(2):026803, 2003.[72] Thaneshwor P Kaloni, YC Cheng, R Faccio, and Udo Schwingenschlo¨gl.Oxidation of monovacancies in graphene by oxygen molecules. Journalof Materials Chemistry, 21(45):18284–18288, 2011.[73] Yuan Huang, Eli Sutter, Norman N Shi, Jiabao Zheng, Tianzhong Yang,Dirk Englund, Hong-Jun Gao, and Peter Sutter. Reliable exfoliationof large-area high-quality flakes of graphene and other two-dimensionalmaterials. ACS nano, 9(11):10612–10620, 2015.53Appendix ADetails of sample fabricationA.1 ExfoliationFigure A.1: Mechanical exfoliation process. Cleaning the SiO2 substrate(a) in the 60 ◦C Acetone and (b) in the Oxygen plasma for 20 minutes. (c)Exfoliated graphite flakes on the blue tape. (d) The tape with flakes on thecleaned SiO2. (e) Baking process at 100◦C hot plate.We follow the steps in Reference [73] to exfoliate graphene and hBN.First, we prepare the clean SiO2 substrates. We cut the bulk substrate into3 cm × 3 cm size and submerge this in Acetone, then we put this into theultrasonic cleaner for 3 minutes and the hot plate for 15 minutes at 60◦C[Figure A.1 (a)]. These processes remove all the organic contaminationsand dust on the surface. We conduct next procedures in the clean roomto prevent the contaminations from air. We conduct the oxygen plasma onsilicon oxide for 20 minutes to remove the remained contamination and make54A.2. CVD graphene Transferringthe surface flat [Figure A.1 (b)]. For the exfoliation, we use the nitro tapebecause this nitro tape makes less residue on the substrate when we testedmany tapes. We put the bulk hexagonal boron nitride (hBN) or graphite onthe tape, and exfoliate several times [Figure A.1 (c)]. Then, we place thistape on oxygen plasma conducted SiO2 and bake this substrate at 100◦Cfor 1 minute, and remove this tape from the substrate [Figure A.1 (d) and(e)].After finding the proper size and thickness of hBN or graphene throughthe microscope, we cleave the substrate into 5 mm × 5 mm to put thissubstrate onto the chip carrier [Figure 3.2]. Also, we make the standard Hallbar geometry pattern by the conventional electron beam lithography processand evaporate the Cr(5 nm)/Au(80 nm) on the sample as the electrodes[Figure 3.5 (b) and 3.1]. After connected Au wires between electrodes andchip carrier, exfoliated sample is prepared to be measured.A.2 CVD graphene TransferringFigure A.2: CVD graphene on center of the filtered paper. Deionized waterdrops are on four corners of filtered paper to wet the paper. After this wetprocess, this graphene is transferred on hBN or HfO2 substrates.We use commercial CVD graphene manufactured by ACS company fortransferring process [54]. Based on their technical data sheet, this CVDgraphene is produced by conventional chemical vapor deposition processon the copper foil substrate and transferred onto the filtered paper [FigureA.2]. We follow the procedure that ACS provides and transfer this grapheneonto the hBN or HfO2 substrates. After this transfer process, we removethe chemical residue polymers by Acetone and make the standard Hall bargeometry on this sample.55Appendix BWeak localization fittingfunctionTo extract τ−1φ and other interaction rates via magnetotransport measure-ment, we make the fitting function from weak localization theory for grapheneas described in Section 2.2.1∆σ(B) = σ(B)− σ(0) (B.1)=e2pih¯[F(τ−1Bτ−1φ)− F(τ−1Bτ−1φ + 2τ−1i)− 2F(τ−1Bτ−1φ + τ−1∗)]Our fitting function of weak localization is following.f(b) = L ∗ (b+ b0) +R0 −R20(e2pih(F1 − F2 − 2F3))∗ g (B.2)F1 = ln(z1) + ψ(0.5 +1z1), z1 =|B −B0|Bφ(B.3)F2 = ln(z2) + ψ(0.5 +1z2), z2 =|B −B0|Bφ + 2 ∗Bi (B.4)F3 = ln(Z3) + ψ(0.5 +1z3), z3 =|B −B0|Bφ +B∗(B.5)where L is linearity of measured data, b is the perpendicularly applied mag-netic fields, R0 is the maximum resistance, B0 is magnetic field where Ris the maximum, g is geometric ratio (Width/Length), and ψ is digammafunction ψ(x) = ddx ln(Γ(x)). In order to use this fitting function, we needto set the initial values. We set L and B0 as zero, and R0 as the maximumvalue of magneto conductivity data. Also, we fix the g = 1 because we al-ready consider the width and length ratio of samples when we process theraw data into conductivity or resistance.When |B−B0| is zero (B = B0), ln(z) and ψ(0.5+1/z) are not defined inthis fitting function. In Igor program we used, as these undefined parameters56Appendix B. Weak localization fitting functionshow zero, fitting function f(B = B0) has only R0 part, which indicates themaximum resistance when weak localization of graphene is not suppressed.With these fitting parameters we can extract Bφ,i∗ at each measured dataand calculate τ−1φ,i,∗ with using Equation 2.7 and 2.10.To be specific for the fitting process, R0 and B0 are fixed at the firststep because these values are clearly seen as a peak in measured data underapplied magnetic fields. After these parameters are fixed, weak localizationfitting function is applied to long range magnetic field scan (± 100 mT)because τ−1i,∗ are dominant in this long range and these rate can be extractedaccurately compared to τ−1φ . After this long range fitting process, shortrange fitting (± 10mT) is processed with fixing τ−1i,∗ extracted from longrange fitting, and this process enables to extract more accurate τ−1φ .57Appendix CSurface temperature on RTAFigure C.1: Test sample in RTA with k-type thermocouple on its surfaceWhen we confirmed the different behavior of dephasing rate between thegas annealed experiment and vacuum annealed experiment, we suspect thatthe increase of dephasing rate can occur if the temperature of the sample sur-faces differ between gas annealing and vacuum annealing processes. Hence,we conduct experiment with measuring the sample surface temperature byattaching the extra k-type thermocouples during thermal annealing processon RTA [Figure C.1]. Two thermocouples are mounted on the surface ofthe sample and copper sheath to measure the temperature on the bottomand surface of the sample. For the sample surface, we use the very thin58Appendix C. Surface temperature on RTAk-type thermocouple from Omega company (diameter: 0.002 inches) to pre-vent external heat being transferred to the sample. When we measure thetemperature at room temperature, copper sheath and the surface of sampleshow 1 ◦C difference. And then, we turn on the power on RTA to increasetemperature from 100 ◦C to 325 ◦C, and measure the temperature undereach atmosphere condition. As shown in the Table C, vacuum annealedand gas annealed show the similar temperature variation, which is 71 % oftemperature on the copper sheath, bottom of the sample.From this result, we confirm that there is no temperature difference onthe sample surface between vacuum annealing and gas annealing. Thus, sur-face temperature difference is not responsible for the increase of dephasingrate.Table C.1: Surface temperature in RTACopper T Vacuum surface T Copper T Gas surface T100 ◦C 75 ◦C 125 ◦C 85 ◦C300 ◦C 210 ◦C 175 ◦C 127 ◦C311 ◦C 220 ◦C 298 ◦C 218 ◦C325 ◦C 229 ◦C 300 ◦C 220 ◦CSurface T ≈ 71.4 % of copper T Surface T ≈ 71.8 % of copper T59Appendix DError bar in fitting processThere are several factors which can contribute the experimental error. In thisthesis, only the following experimental errors are mainly considered throughthe error bar. The details of these errors are explained in this Appendix D• Temperature fluctuation• Conductivity depending on magnetic fields• Fitting parametersD.1 Temperature fluctuationOur measurement system is dunked in liquid helium dewar [Figure 3.4],which is 4.2 K. Thus, the temperature of our system should be maintainedat 4.2 K. However, there might be the temperature fluctuation because mea-surement system cannot be totally isolated from room temperature atmo-sphere. Also, the heat from the outer system can be transferred to ourmeasurement system. If there is temperature fluctuation (T=4.2 K ±∆),electron-electron interaction rate in Equation 2.11 is also fluctuating. How-ever, in our experiments, since we assume that the temperature fluctuation∆ is negligible compared to the temperature 4.2 K in our measurement sys-tem and the effect of this fluctuation is negligible compared to other errorfactors, we do not consider this temperature fluctuation in error bar.D.2 Conductivity depending on magnetic fieldsWhen we apply and increase the perpendicular magnetic fields from 0 mTto 100 mT, conductivity keeps increasing until the weak localization effect istotally suppressed. Therefore, there are small differences in electron-electroninteraction rate, diffusion coefficient (D =σpih¯vf2e2√pins), and the dephasing rate(τ−1φ =4eh¯ DBφ), when we use the minimum conductivity at 0 mT or themaximum conductivity at 100 mT. However, as the maximum conductivity60D.3. Fitting parametersis up to 3 % higher than the minimum conductivity, the interaction ratesand diffusion coefficient in these extreme conductivities show negligible dif-ferences. Thus, the error from conductivity difference is negligible comparedto the fitting parameters error described in the following section.D.3 Fitting parametersWhen we use the weak localization fitting, we need to determine the geomet-ric ratio (width/length) as described in Appendix B. The geometric factorduring the fitting process should be fixed to 1 because we already divide thepure voltage measured data by the width and length ratio (1 - 1.5) of thesample in Figure 3.1 and the applied currents in the process of calculat-ing the conductivity. However, this process with geometric factor of 1 doesnot make the best fitting results in every cases, which means the χ2 is notalways the minimum when geometric factor is fixed to 1. For this reason,we need to adjust the geometric factor within the ± 5 % of χ2, which givesusually geometric factor placed between 0.9 - 1.1, and extract the dephasingrate during the adjustment processes. With these dephasing rates from theadjustment process, we define the experimental error bars.Also, we conduct the same adjustment process with changing intervalleyscattering rate τ−1i , and intravalley scattering rate τ−1∗ . However, when wechange these rates, the magnitude of error bar is negligible compared toerror bar from geometric factor except for the exfoliated graphene cases.61Appendix EAdditional experimental dataIn this appendix, the results of non compared experimental data from CVDgraphene on hBN substrate and exfoliated graphene on SiO2 are described.E.0.1 CVD graphene on hexagonal Boron Nitride (hBN)Figure E.1: CVD graphene on hBN substrate. change of RXX (top) andσ (bottom) as a function of applied gate voltages from -80 V to 20 V. TheDirac point is positioned at -5 V.We measure CVD graphene on hBN substrate before and after annealingunder the same atmosphere conditions as used in previous experiments.Unlike other CVD graphene on oxide substrates experiments, these sampleshave a very sharp Dirac point shown in Figure E.1 and this is similar toother graphene-hBN experimental results [51, 52]. However, when it goesaway from the Dirac point, it shows very flat conductivity changes, dσdV =62Appendix E. Additional experimental dataFigure E.2: CVD graphene on hBN. Change of the dephasing rate andelectron-electron interaction rate as a charge carrier density (a) before an-nealing, (b) vacuum annealing, and (c) gas annealing cases. All cases showthat electron-electron interaction is higher than the dephasing rate. Also,all cases have the similar dephasing rate between 70 /ns and 25 /ns.-0.1 e2/hV . Also, when the conductivity is compared between hBN andsilicon oxide substrates, it shows 34 e2/h at -80 V and 23 e2/h at -40 V inCVD graphene on hBN but it shows 54 e2/h at -80 V and 40 e2/h at -40 Vin CVD graphene on silicon oxide substrate.This hBN substrate sample shows unexpected results in before-annealed,vacuum annealed, and gas annealed cases, shown in Figure E.2. In all cases,electron-electron interaction rates are higher than the dephasing rates, whichis not observed in other CVD graphene sample experiments. Additionally,the dephasing rates in all cases have a similar value range even after gasannealing, i.e. an effect of annealing in CVD graphene on hBN sample isnot observed. More specifically, gas annealing does not induce the additionalsource of dephasing in hBN substrate samples. From the results of thiswork it is hard to define the main source of changing the dephasing ratein graphene on hBN samples. Due to these reasons, CVD graphene-hBNexperiments are not compared with other CVD graphene experiments.E.0.2 Exfoliated grapheneThe same annealing process and measurements were performed on the ex-foliated graphene on SiO2 samples. There are two significant experimen-tal differences between exfoliated graphene and CVD graphene on oxidesubstrates. The first is that the Dirac point of before-annealed exfoli-ated graphene is close to zero voltage when compared to the case of CVDgraphene. In other words, there are less chemical contaminations on the63Appendix E. Additional experimental dataFigure E.3: Exfoliated graphene result: (a) before annealing and (b) aftergas annealing.surface of exfoliated graphene than for CVD graphene and a lesser dopingeffect. This is because of the omission of a transfer process in contrast towith CVD graphene.The second significant difference is the magnitude of the intervalley andintravalley scattering rates. In the case of CVD graphene, the intravalleyscattering rate is much higher than the intervalley scattering rate and thedephasing rate. However, in the case of the exfoliated graphene, the threeinteraction rates are comparable. Due to the similar scattering rates, thereis no dominant interaction in the used range of magnetic fields. Hence, ifone interaction rate is modified during the weak localization fitting process,the other rates also vary significantly. This difference should come fromthe sample size difference between CVD graphene (length: 100 − 150 µm,width: 30 − 50 µm) and exfoliated graphene (length: 40 − 60 µm, width:13 − 20 µm) or the level of surface contamination. Specifically, when thedevice dimensions are comparable to the phase coherence length or the levelof contamination is different, other disorder can affect interaction rates andresults in different magnitudes of the interaction rate.Moreover, even if gas annealed exfoliated graphene shows a tendency ofan increase of the dephasing rate as shown in Figure E.3, it cannot be statedthat the main mechanism of dephasing is not electron-electron interactionbecause the increment in the excess of the dephasing rate is not so significantand not proportional to the charge carrier density (applied gate voltage)unlike with CVD graphene on oxide substrates samples.For these reasons, the experimental results for exfoliated graphene are64Appendix E. Additional experimental datanot compared with the results of CVD graphene on oxide substrates samples.65Appendix FAdditional experiment within-plane magnetic fieldsFigure F.1: Magnetoconductivity in B⊥ = ±10 mT with B‖ = 0 mT (red,triangle) and 700 mT (purple, circle), and its WL fitting (solid lines) at T=100 mK. After applied B‖ = 700 mT, the dephasing rate is decreased from66 /ns to 23 /ns (inset: differential of MC)Figure F.1 shows the results of additional experiments using a dilutionrefrigerator conducted by Dr. Silvia Lu¨scher Folk. The dilution refrigeratoris used to measure the sample below 4.2 K. The fresh CVD graphene sam-ples on SiO2 are annealed under the same gas conditions are used in theexperiment Section 3.4. The experiment is performed at 100 mK and theperpendicular magnetic fields are scanned within a ±10 mT range with thesame methods as described in Section 3.4. In this experiment, additional700 mT in-plane magnetic fields are applied to investigate the presence ofmagnetic moments which have an internal degree of freedom and can be the66Appendix F. Additional experiment with in-plane magnetic fieldssource the dephasing, as described in Section 3.4. The reason for the appli-cation of in-plane magnetic fields is that these in-plane magnetic fields can“freeze” the motion of magnetic moments on the CVD graphene samples.Thus, it is expected that the excess of the dephasing rate would decrease ifthere are magnetic moments and in-plane magnetic fields freeze those. Whenin-plane magnetic fields are applied at ns = 4.8 × 1012/cm2, the change of∆σ is increased and the dephasing rate decreases from 66 /ns (red) to 23/ns (purple) as shown in Figure F.1. This result indicates that the effectof increasing the dephasing rate is induced by the magnetic moments andthese magnetic moments are caused or activated by gas annealing.67

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