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Electronic Transport Properties of Semiconductor Nanostructures

ProQuest Dissertations and Theses, 2011
Dissertation
Author: Yan Zhang
Abstract:
With reduced size and dimensions, semiconductor nanostructures have dramatic difference in electrical properties than their bulk counterparts. These differences have raised many interesting topics, such as quantum Hall effects and bandgap engineering. By utilizing these properties of nanostructures, numerous electrical devices have been proposed and created to improve human life quality and production efficiency. Graphene, carbon atoms formed in only one-atomic-layer, has been discovered in lab in 2004 and raised a lot of attentions. It has unique electronic band structure and promising applications. Many fundamental physics questions and practical limitations on device functions need to be addressed. We have investigated the low-frequency 1/f noise, which poses a limit on the signal-to-noise ratio in broad band electrical circuit, in both suspended and on-substrate graphene field-effect transistors, from T = 30 to 300K. We have found that, compared to on-substrate devices, in general suspended graphene devices show lower 1/f noise, as a result of their higher mobility. We explain the observed noise dependence on gate voltage using the Hooge's empirical relation with a variable Hooge parameter. We have also studied metal-insulator transition in monolayer graphene, and a phase diagram of metal and insulator phases from reported and our own results was proposed. Anomalous quantum Hall effect in ABC-stacked trilayer graphene was also studied, and we found chiral fermions with Berry's phase 3π and unusual Landau level quantization with 12-fold and 4-fold degeneracy in the n =0 and n >0 Landau levels, respectively. With the help of spacially resolved scanning photocurrent, we have studied charge transport in graphene in quantum Hall regime. And we found that the net photocurrent is determined by hot carriers transported to the device edges, where quantum Hall edge states provide efficient channels for their extraction to contacts. Moreover, optical bandgap and electrical properties of (GaN)1- x (ZnO)x solid solution nanowire have been studied to explore the possibility of using this material as a photovoltaic catalyst in water splitting for generating renewable energy. The nanowires with composition x [approximate] 0.12 were found with an optical bandgap ∼2.7eV. And the nanowire FETs were n-type conduction, with background carrier density ∼10 19 /cm3 and electron mobility ∼1 cm2 / V · s .

Contents List of Figures x List of Tables xvi Acknowledgements xvii 1 Introduction 1 1.1 Semiconductor nanostructures..........................1 1.2 What is graphene?................................3 1.3 Topics we want to study on graphene......................5 1.4 Photovoltaic effect in semiconductors and its application in water splitting.8 1.5 Organization of the dissertation.........................10 2 Synthesis and Electronic Properties of Graphene 11 2.1 Crystal structure of graphite...........................11 2.2 Band structure of graphene...........................12 2.2.1 Energy dispersion in monolayer graphene................12 2.2.2 Energy dispersion in few-layer graphene................16 2.3 Minimum conductivity in graphene.......................16 vi

2.4 Suspended graphene...............................17 2.5 Quantum Hall effect (QHE) in graphene....................18 2.5.1 Quantum Hall effect in monolayer graphene..............19 2.5.2 Quantum Hall effect in bilayer graphene................21 2.6 Device fabrication.................................23 2.6.1 Graphene exfoliation...........................25 2.6.2 E-beam lithography and metal deposition...............27 2.6.3 Suspended graphene device fabrication.................28 3 Low-Frequency Noise in Graphene 30 3.1 Introduction....................................30 3.2 Instrument setup.................................32 3.3 Results of resistivity and noise measurements.................33 3.4 Noise model from Hooge’s relation with a variable Hooge parameter.....41 3.5 Conclusion.....................................48 4 Magnetotransport Study of Graphene 50 4.1 Metal to insulator transition on the n=0 Landau level in graphene......50 4.1.1 Introduction................................50 4.1.2 Experimental...............................53 4.1.3 Results and discussion..........................53 4.1.4 Conclusion.................................59 4.2 Quantum Hall effect in trilayer graphene....................61 4.2.1 Introduction................................61 4.2.2 Device preparation and identification of stacking order........62 4.2.3 Transport measurements.........................64 vii

4.2.4 Conclusions................................74 5 Scanning Photocurrent Study of Graphene 75 5.1 Introduction....................................75 5.2 Experimental...................................76 5.2.1 Device fabrication.............................76 5.2.2 Photocurrent measurement setup....................77 5.3 Results and discussions..............................78 5.4 Summary and future work............................88 6 Electronic and Optoelectronic Study of (GaN) 1−x (ZnO) x Solid Solution Nanowires 90 6.1 Introduction....................................90 6.2 Experimental...................................92 6.2.1 Synthesis of (GaN) 1−x (ZnO) x solid solution nanowires.........92 6.2.2 Microstructural characterization.....................92 6.2.3 Preparation and electrical characterization of nanowire FET devices.93 6.3 Structure and composition analysis.......................93 6.4 Electrical properties of (Ga 0.88 Zn 0.12 )(N 0.88 O 0.12 ) FET.............97 6.5 Light decay and optical bandgap in (Ga 0.88 Zn 0.12 ) (N 0.88 O 0.12 ) nanowires..101 6.6 Summary.....................................106 7 Summary 107 Bibliography 109 A Hydrostatic Pressure Study of AlGaN/GaN High Electron Mobility Tran- viii

sistors (HEMT) 120 A.1 Crystal and Electronic structures of GaN....................120 A.2 Structures of AlGaN/GaN HEMT........................121 A.3 Measurement setup................................123 A.4 Results of hydrostatic pressure study and stress study.............125 ix

List of Figures 2.1 Stacking orders of graphene layers........................12 2.2 (a) Hexagonal crystal lattice in graphene,a 1 and a 2 are lattice vectors.(b) The first Brillouin zone in the reciprocal lattice.................13 2.3 Electronic band structure of graphene from tight-binding calculation.....14 2.4 (a) In-plane σ bonds.(b) Out-of-plane π bonds.................15 2.5 Cartoon of top-view and side-view of suspended graphene device and SEM image of a real suspended graphene device...................18 2.6 Integer quantum Hall effect in standard 2DEG,monolayer graphene and bi- layer graphene...................................20 2.7 Quantized magnetoresistance R xx and Hall resistance R xy in a monolayer graphene......................................22 2.8 Electronic band structure of bilayer graphene.................23 2.9 Quantum Hall effect in bilayer graphene....................24 2.10 Procedures of graphene exfoliation.......................25 2.11 Methods to measure number of graphene layers................26 2.12 Diagram of device fabrication procedure.....................27 2.13 Diagram and images of suspended graphene device fabrication procedure..29 x

3.1 Diagram of DC voltage and noise measurement setup..............33 3.2 Normalized noise spectra for NSG5 at different drain current I d ,with V g =0V. The solid line indicates the slope of 1/f dependence...............34 3.3 Normalized noise spectra for NSG5 at gate voltage of 0,10,20V,with I d =1µA. The solid line indicates the slope of 1/f dependence...............35 3.4 Resistivity and noise amplitude measurements in single-layer NSG5 device at room temperature.Inset shows typical optical image and the scale bar is 1 µm.........................................36 3.5 Resistivity and noise amplitude measurements in single-layer SG5 device at room temperature.Inset shows a typical SEM image and the scale bar is 2 µm.36 3.6 Temperature dependent resistivity measurements of NSG1 in temperature range of 30-300K..................................37 3.7 Noise amplitude dependence on gate voltage of NSG1 in temperature range of 30-300K.....................................38 3.8 Normalized noise vs.frequency for NSG1 at temperatures from 30 to 300K, with V g =-10V.The solid line indicates the slope of 1/f.............38 3.9 Temperature dependent resistivity measurements of SG5 in temperature range of 30-300K.....................................39 3.10 Noise amplitude dependence on gate voltage of SG5 in temperature range of 30-300K.......................................40 3.11 Dependence of Hooge parameter on carrier mobility at room temperature..42 3.12 Hooge parameter α H dependence on carrier mobility µ in SG5 at temperatures from 30 to 300K..................................44 xi

3.13 Qualitative noise amplitude dependence on gate voltage for the Coulomb, short range,and mixed scattering.The dotted lines near charge neutrality indicate the gate voltage dependence of noise amplitude when considering charge carrier inhomogeneity...........................45 4.1 Experimental phase diagram of the Quantum Hall Metal-Insulator transition in graphene....................................52 4.2 QHE data as a function of the gate voltage V g ,for B = 18 T at T = 0.25 K.54 4.3 Contour map of the longitudinal resistivity,conductivity and derivative of Hall conductivity.................................56 4.4 Temperature dependence of the longitudinal resistivity,and longitudinal and Hall conductivities at B=18T..........................57 4.5 Semi-log plot of ρ xx versus temperature at B = 18 T for 12 filling factors ν.60 4.6 Band structure of ABC-stacked trilayer graphene...............62 4.7 The image of the etched Hall bar trilayer graphene (TLG) device used in our experiments and schematics of the measurement setup.The black scale bar is 10 µm.......................................63 4.8 Raman spectrum of 2D band in trilayer graphene with different stacking orders 64 4.9 The spatial map of FWHM and center peaks of the 2D band.The figures illustrate that graphene device has uniform domain of stacking order.The scale bar is 5 µm..................................65 4.10 Mobility and conductance of trilayer graphene as a function of V g at temper- ature T=0.35K..................................66 4.11 Longitudinal resistivity ρ xx and Hall conductivity σ xy of the trilayer graphene device as a function of V g (carrier concentration n) at B = 18 T and T = 0.35 K 67 xii

4.12 Longitudinal resistivity ρ xx and Hall resistivity ρ xy measured in the device of Fig.4.7 for V g =70 V at T = 0.35 K.......................68 4.13 SdHOs as a function of magnetic field at different carrier concentrations...70 4.14 Fan diagram of SdHOs at different Vg.....................71 4.15 Dependence of B F on V g ,the error bars show standard deviation of the fitting. The dashed line is the linear fit of B F (V g )....................72 4.16 The phase shift of magneto-oscillations,β,as a function of V g .........72 4.17 Schematic illustration of the Landau level density of states (DOS) in ABC- stacked trilayer graphene.............................73 5.1 Optical image of the device.Dashed outlines mark the channel and the two connected electrodes.The four side electrodes are not in contact with the device........................................77 5.2 Schematic diagram of the photocurrent measurement..............78 5.3 (a)Conventional two-terminal conductivity in quantum Hall regime.(b) Pho- tocurrent measured with laser spot at the center of the graphene channel (cross in Fig.5.1) for B = 9 T...........................79 5.4 Spatial photocurrent maps for different gate voltages from -45V to 45V,at B = 9 T.......................................81 5.5 Photocurrent as a function of V G along the arrow shown in Fig.5.1,extracted from 240 individual scans across the graphene channel for V G from -45 V to +45 V (B = 9 T).................................82 5.6 Landau levels in graphene............................83 5.7 Illustration of photocurrent generation and collection,assuming a partially occupied n = 2 Landau level...........................86 xiii

5.8 Carrier relaxation and photocurrent collection in graphene devices in the QHE regime.......................................87 6.1 SEM images of the solid solution nanowires...................94 6.2 High-resolution TEM image and fast-Fourier-transform electron diffraction pattern of the nanowires.............................95 6.3 EDS spectrum taken from a large region of the nanowire............95 6.4 EELS spectrum taken from the same part of the nanowire as in Fig.6.3....96 6.5 Scanning electron microscope image of a typical (Ga 1−x Zn x )(N 1−x O x ) nanowire FET,and a corresponding schematic diagram of its lateral profile.The scale bar is 1 µm....................................97 6.6 Gate-dependent I D −V D characteristics of a ∼70 nm diameter nanowire for several gate voltages,from +20 V to -15 V.Inset:plot of the conductance versus gate voltage................................98 6.7 I D − V G curves recorded for V D from 0.4 V to 2.0 V and the inset shows transconductance dI D /dV G versus V D ......................99 6.8 Photocurrent response (I Light /I Dark ) versus time t of a nanowire FET under V G = 0 V and V D = 2 V.............................102 6.9 Photocurrent response under various incident light wavelengths ranging from 390 nm to 470 nm.Light was turned on at t = 20 s...............103 6.10 Photocurrent on-off ratio normalized by the incident light’s power density plotted against wavelength............................105 A.1 Crystal structures of GaN............................121 A.2 Energy band structure of wurtzite GaN.....................122 A.3 Cross-sectional and planar view of AlGaN/GaN HEMT............122 xiv

A.4 Experimental setup for I D −V DS and I D −V G measurements.........123 A.5 Diagram of pressure cell with cables for electrical measurements.......124 A.6 I D −V DS with V G from -3V to +1V at 1V interval...............125 A.7 I D −V DS with V G = +1V in hydrostatic pressure from1bar to 10kbar at 1kbar interval.......................................126 A.8 Time dependent I D when the device goes through stress and recovery stage.127 A.9 Stress test for 84 consecutive hours in hydrostatic pressure 1atm,3.5kbar, 7kbar,10.5kbar,7kbar,3.5kbar and 1atm with 12 hours in each pressure..128 xv

List of Tables 3.1 Description of samples used in noise measurements...............49 xvi

Acknowledgements Graduate school has taught me to be not only an independent researcher but also a team player,and the years in Stony Brook were such an enjoyable adventure in my life. I would like to thank my advisor,Prof.Emilio Mendez,for his instructions and support during my PhD study.He impressed me so many times with his unbelievable memory and straightforward logic thinking.He led me through the ups and downs with his passion in research and his constant encouragements. I amvery lucky to get the opportunities to work together with many prestigious scientists from Stony Brook University (SBU) and Brookhaven National Laboratory (BNL).It was a pleasure to work together with Prof.Xu Du for a project on graphene,I learned a lot of knowledge and experimental skills about graphene from him.His passion in science and fruitful ideas inspired me.I would also like to thank Prof.Liyuan Zhang,who used to be a postdoc in BNL.He taught me how to make graphene FETs.And I enjoyed the days and nights that we worked together fabricating devices in the cleanroom and running magnet in the lab.Prof.George Nazin,who also used to be a postdoc in BNL,we worked together on a joint project on photocurrent study in graphene.His hard working ethic and in-depth knowledge in physics has been a major source to deliver the nice results.Moreover,I would like to thank Dr.Weiqiang Han from Center for Functional Nanomaterials (CFN) at BNL, who gave me the opportunities to work on first-hand photovoltaic nanomaterials.

Now I would like thank my colleagues who led me into the laboratories.Bent Nielsen, A.K.M.Newaz and Megumi Kinoshita were the ones who taught me first-hand knowledge and experiences in the labs.Without them,I would be begging Emilio all the time to come to the lab and teaching me the equipments that I’ve never seen in my life before.Moreover, Fernando Camino,Chang-Yong Nam,Ming Lu,Aaron Stein and Don Elliott were the ones who helped me to get used to the instruments in CFN.I would also like to thank Paul DiMatteo,Mark Jablonski,Jeffrey Slechta,Jeffrey Thomas and Walter Schmeling from the machine shop.They offered me with their expertise in machining,and I enjoyed the days I spent in the student machine shop to make fancy pieces for my research.Eugene Shafto and Chuck Pancake from the electronics shop have been the ones who helped me with expertise and knowledge in electronic circuits. Finally,I want to thank my family and friends.My parents are always supportive to my decisions,and they have taught me to be an honest and hard working person with their own examples.I would also love to express my appreciation to my fianc´ee.She brought so much joy and courage to me that I can survive the jungle of graduate school.I would like to thank all my friends who have made my life in Stony Brook a superb experience,and I will list them in my heart instead of occupying pages of the dissertation here.

List of Publications • Mobility Dependent Low Frequency Noise in Graphene Transistors Y.Zhang,E.E.Mendez,and X.Du.To be submitted. • The Experimental Observation of Quantum Hall Effect of l = 3 Chiral Quasiparticles in Trilayer Graphene L.Zhang,Y.Zhang,J.Camacho,M.Khodas,and I.A.Zaliznyak.To be submitted. • Visualization of Charge Transport through Landau Levels in Graphene G.Nazin,Y.Zhang,L.Zhang,E.Sutter,and P.Sutter.Nature Physics 6,870-874 (2010) • Metal to Insulator Transition on the N=0 Landau Level in Graphene L.Zhang,Y.Zhang,M.Khodas,T.Valla,and I.A.Zaliznyak.Physical Review Letters 105,046804 (2010) • Growth and Electronic Properties of GaN/ZnO Solid Solution Nanowires W.Han,Y.Zhang,C.Nam,C.T.Black,and E.E.Mendez.Applied Physics Letters 97,083108 (2010) • Magn´eli Phases Ti n O 2n−1 Nanowires:Formation,Optical,and Transport Properties W.Han,and Y.Zhang.Applied Physics Letters 92,203117 (2008)

Chapter 1 Introduction 1.1 Semiconductor nanostructures Semiconductors,which are materials with a fundamental energy band gap between that of a metal and an insulator,are the backbone of modern electronics because of their great flexibility in terms of allowing the control of electronic and optical properties.In computers, telecommunications,health,and transportation,they are almost everywhere in our daily life.The demand for smaller,faster and more energy efficient semiconductor devices has been driving the multibillion business for years,and it continues that way.Following the International Technology Roadmap for Semiconductors,transistor dimensions have been reduced from 10µm in 1971 to 32nm in 2010,and the electronic properties of material have changed dramatically due to the size reduction. Generally,a nanostructure can be defined as a structure with size smaller than one hundred nanometer in at least one of the three dimensions,with a variety from two to zero dimension confinements,i.e.quantum well,quantum wire and quantum dot for 2-,1-,0- dimensions nanostructures,respectively.The electronic properties of structures depend on 1

the dimensionality and the geometric details of the materials. About forty years ago,Dr.Gordon E.Moore,Intel’s co-founder,described the trend of progress in electronics with an empirical observation:the number of transistors that can be placed in an integrated circuit with respect to the minimum component cost doubles ap- proximately every two years,which is now known as Moore’s law.So far the semiconductor industry is still on track with the prediction,with the help of mature silicon technology, which enjoys the advantages of ultra low defect density,thin and stable dielectric SiO 2 ,and extraordinary low cost.However,fundamental limits pose obstacles for better electronics, such as electron mobility poses a limit on transistor operational frequency.Thus the scien- tific and technology world have been looking for alternative materials for years,which can give rise to cheaper and faster devices.So far,numerous materials have been developed,but none of them can replace silicon in terms of cost and overall performance. People have put in a lot of effort on carbon,which is easy to access;numerous ground- breaking discoveries have been made during the past twenty years.Carbon nanotubes (CNT) raised a lot of interest,due to its high mobility and potential as a ballistic transistor.How- ever,the difficulties in sorting nanotubes (metallic or semiconducting,diameter,and chiral- ity) make it hard to utilize CNTs in industrial scale electrical circuits.In 2004,graphene, carbon atoms formed in a single atomic layer,was discovered in the laboratory.The unique electronic structure,high electrical mobility and potential to be engineered with existing Si technology has brought huge interest in graphene from both the academic and industrial worlds.Thus studying the electrical properties of graphene has become an interesting work to do. Besides making smaller and faster devices,finding energies to power up these devices is also important.The majority of energy supporting human activities is from coal,oil and natural gas,which took hundreds of millions of years to form.These energy sources 2

will be used up eventually.Thus saving energy and exploring new energy sources become an important issue for society.Solar energy,which used to be stored in coal,oil and natural gas, is among one of the promising renewable energy sources.One effective way to use solar energy is through solar cells,which collect solar light and transform it to electricity.On the other hand,photocatalysis is also a promising direction,in which one uses solar energy to split a water molecule into oxygen and hydrogen,and the produced hydrogen can be stored and used as a fuel that could be burned whenever it is needed.Thus finding a suitable photocatalyst with high catalysis efficiency is a crucial step towards obtaining H 2 fuel.Nanostructuring photocatalysts is one of the ways to find highly efficient photocatalysts,due to its large surface to volume ratio which is crucial in surface reactions in the photocatalytic process. In the following two sections,background of graphene and photocatalyst is covered sep- arately. 1.2 What is graphene? Graphene,a flat monolayer of carbon atoms formed in a 2D honeycomb lattice 1 ,has been studied by theoriticians for over sixty years and is widely used to describe properties of carbon-based materials.It can be stacked into 3D graphite,rolled into 1D carbon nan- otube or wrapped up into 0D fullerene.It was believed not to exist stably and freely as its curved counterparts – nanotube and fullerene.However,in 2004,Andre Geim and Kon- stantin Novoselov at Manchester University in England demonstrated its existence in the laboratory[1],and their work was awarded the Nobel prize in physics in 2010.The experi- ment was as simple as drawing on a piece of paper with a pencil.Basically,the researchers 1 Although strictly speaking,graphene consists of a monolayer of carbon atoms,we often speak of bilayer or trilayer graphene which refer to two or three atomic layers of carbon atoms,respectively. 3

used scotch tape to peel bulk graphite to very thin layers and stuck them onto a SiO 2 /Si wafer.After removing the adhesive tapes,an atomic thin graphite layer was magically found on the wafer under an optical microscope.The thickness of SiO 2 appeared to be critical for successful observations of monolayer graphene on wafers.It was found that 90nm and 300nm thick SiO 2 have good contrast between graphene and wafer. Since the discovery in 2004,research on graphene has exploded.Graphene has exceptional mechanical,electronic and optical properties.It is the thinnest however strongest material ever measured,with Young’s modulus ∼1.0TPa [2].The charge carriers in graphene have huge intrinsic mobility and zero effective mass,and they can travel for micrometers without scattering at room temperature.Graphene has been demonstrated as a sensor to detect pH in solution[3] and detect single gas molecule[4].Additionally,graphene has very high optical transparency,with ∼ 98% in monolayer graphene and ∼ 95% in bilayer graphene[5],which together with its high electrical conductivity makes it a very good candidate as a transparent conductor for LCD and solar cells. In order to produce graphene in industrial scale,a mass production method is needed, since the scotch tape exfoliation method would be too slow and costly.So far graphene has been successfully grown on SiC [6,7],and a few different metals,such as Ru,Ni,Cu [8–10].However,there hasn’t been a good way to transfer graphene from its initial substrate onto a dielectric substrate to make field effect transistors (FET).People have tried coating as-grown graphene with resist and etching away the substrate,and then placing the graphene- attached resist onto the target wafer and dissolving the resist to make successful transfer. The transferred graphene flakes appear to have lots of wrinkles and cracks,which degrade the electronic properties dramatically.These engineering issues need to be solved,in order to improve the quality of devices made from grown graphene. The exceptional electronic and optical properties of graphene make it a good candidate 4

for many applications.However,several fundamental electronic transport properties need to be addressed to predict and control the electronic behavior of graphene devices. 1.3 Topics we want to study on graphene Noise in electrical systems refers to the electrical signal fluctuations in excess of the target signal,posing a limit on signal to noise ratio,which is important in electrical systems. The fluctuations are not always undesirable,and the nature of them usually depend on the underlying physical process.By measuring noise,information not available from time- averaged measurements,can be retrieved.Usually electrical measurements in a conductor, such as voltage,current and resistance,are time-averaged values.These measurements do not contain any information about the fluctuations.In order to measure fluctuations,time resolved methods are needed. There are three types of electrical noise,thermal noise,shot noise,and low-frequency or 1/f noise.Thermal noise is due to thermal fluctuations of charge carriers in a conductor, and is frequency-independent.Shot noise is due to the particle nature of charge carriers, and also is frequency-independent (becoming frequency-dependent in very high frequency). When average current I passes through a potential barrier randomly and independently,its spectral density of current noise is given by S I = 2e I.The shot noise may deviate from this value when the motions of charge carriers passing through the potential barrier are not independent. Low-frequency noise arises from mobility fluctuations of charge carriers or from number fluctuations,caused by charge trapping and detrapping.Low-frequency noise is frequency- dependent,with a spectral density in the resistance that typically follows S R ∝ 1/f.This type of noise is important in broadband and low-frequency circuits. 5

Since low-frequency noise carries information about the number and mobility fluctuations in a conductor,studying its behavior in graphene helps elucidate the influence of charge traps and different scattering mechanisms on the electrical conduction process. Besides electrical noise,the fundamental electronic structure is interesting to a larger sci- entific community because it determines the macroscopic uniqueness of graphene.Graphene has a linear energy dispersion,which is similar to photon,and it is quite different from quadratic dispersion in standard semiconductors.The charge carriers in graphene can be explained by relativistic Dirac equation.It is a zero band gap semiconductor or semimetal, and the charge polarity can be easily switched fromhole to electron by changing gate voltage from negative to positive values,which is impossible in traditional semiconductors. The electronic transport of graphene in magnetic field is also very interesting.It has four-fold degeneracy in the quantum Hall effect (QHE),which is due to spin and valley degeneracy[11].Numerous theoretical and experimental work have been done on graphene in the quantum Hall regime.However,the nature of the electronic states at n = 0 Landau level are still unclear.Some theories predict unusual metallic transport via gapless edge states[12, 13] and other suggest a gap opened up at high magnetic fields,resulting in an insulating state near the charge-neutrality point[14,15].There have been several experimental studies on this topic and so far there has not been an agreement.We explored the electronic states at n = 0 Landau level and tried to gave more evidence and well founded explanations. Besides studying the electronic states at n = 0 Landau level,we are also interested in how the charge transport takes place in the quantum Hall regime.Similar to QHE in standard semiconductors,band bending creates pathways for charge carrier transport.Due to the fact that graphene is exposed to external environment,its electronic properties are affected dramatically by external charged impurities and substrate roughness.Thus,besides band bending,charge transport should be also affected by potential fluctuations caused by the 6

external imperfections,which will create an uneven local electric field across the device.If we direct a laser on graphene,the generated electron-hole pairs could be separated by the local electric field at the laser spot and transported across the device to reach the electrodes. Thus by measuring the photovoltage on the electrodes while scanning the position of the laser spot,we can gather information about local potential distribution.With this method, we explored the effect of external surface doping in graphene on charge transport through Landau levels in the quantum Hall regime. In contrast to monolayer graphene,with its linear energy dispersion and zero band gap, bilayer graphene has a quadratic dispersion relation and also zero band gap,which has already been studied extensively[15,16].It is natural to think about what happens in trilayer graphene.With only one additional layer,it is actually much more complicated than bilayer graphene.Trilayer graphene has two different stacking orders (ABA and ABC), which will be explained in the next chapter,with two different electronic band structures. The electronic band structure of ABA-stacked trilayer graphene consists of superimposed monolayer and bilayer band structures[17,18],which are linear and quadratic,respectively. And it has been already studied in experiments[19,20].On the other hand,the electronic band structure in ABC-stacked graphene has been predicted in theory to be a unique cubic dispersion which is different from both monolayer and bilayer graphene[18,21–23].To our best knowledge,there has not been any experimental study done on ABC-stacked graphene and we explored it in detail.Twelve- and four-fold degeneracy in n = 0 and n > 0 Landau levels,respectively,has been observed in our experiments. 7

1.4 Photovoltaic effect in semiconductors and its ap- plication in water splitting Photovoltaic effect is the direct conversion of light into electricity at the atomic level. Some materials exhibit a property to absorb photons of light and generate electron-hole pairs. When these electron-hole pairs are well separated and collected before their recombination, in an open-circuit configuration,an electric voltage can be generated on the charge collection electrodes.If a resistive load is connected between the electrodes,a photocurrent is expected. The photoelectric effect was first noted by a French physicist,Alexandre Edmond Bec- querel,in 1839,who found that certain materials would produce small amounts of electric current when exposed to light[24,25].In 1905,Albert Einstein described the nature of light and the photoelectric effect on which photovoltaic technology is based,for which he won a Nobel prize in physics in 1921. To generate the photovoltaic effect in a semiconductor,the photon energy needs to be greater than the energy band gap of the material,so that electrons can be excited from the valence band to the conduction band and then possibly collected by electrodes.This effect has a few applications.The first well known application is solar cell,which converts solar energy to electricity,and the first photovoltaic module was built by Bell Lab in 1954. Another interesting application is found in a photocatalytic reaction,which happens when electron-hole pairs,created by incident light,generate free radicals able to undergo secondary reactions,such as splitting water molecule to hydrogen and oxygen.The minimum energy needed into separate H 2 O molecule to H 2 and O 2 is 1.23 eV.A photocatalyst needs to have its conduction band edge well above the hydrogen reduction level and the valence band edge well below the water oxidation level for an efficient production of hydrogen and oxygen from water.This is because the electrons and holes will migrate to the surface of the 8

semiconductor and need enough energy to reduce and oxidize the reactants adsorbed on the surface. Theoretically,semiconductors satisfy the energy band structure requirement can be used for photocatalytic hydrogen production,however,there are other factors influencing hydro- gen production efficiency.First,if the conduction-band electrons and valence-band holes recombine before they reach the surface,they will release energy in the form of unproductive heat or light and not participate in any catalytic reactions.Second,even if the hydrogen and oxygen are successfully generated,they can recombine quickly into water (backward reaction) and be unable to be collected separately.Third,generally the efficiency of cat- alytic reaction increases with increasing surface area of the catalyst,reaches a maximum and may stay constant or decrease with further increase in surface area,and the situation differs fromsystemto system[26].Additionally,the width of energy band gap is also a factor. Wide band-gap semiconductors,such as TiO 2 with a 3.2 eV band gap,can only absorb UV light for catalytic reaction.Since UV light only accounts for about 4% of the solar energy while the visible light contributes about 50%,reducing the band gap of photocatalyst can potentially capture larger portion of the solar energy. ZnO,another wide band-gap semiconductor,has been proposed as a water-splitting pho- tocatalyst,and it was found that by forming GaN/Zno solid solution,the band gap can be reduced to 2.2 eV[27],which is well in the visible light spectrum.However,the electronic properties of this material,such as charge carrier concentration and electrical mobility,are still not clear but are essential for understanding the catalytic behavior.We conducted elec- tronic and optoelectronic transport measurements in the GaN/ZnO solid solution nanowire devices trying to address some of these questions. 9

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Abstract: With reduced size and dimensions, semiconductor nanostructures have dramatic difference in electrical properties than their bulk counterparts. These differences have raised many interesting topics, such as quantum Hall effects and bandgap engineering. By utilizing these properties of nanostructures, numerous electrical devices have been proposed and created to improve human life quality and production efficiency. Graphene, carbon atoms formed in only one-atomic-layer, has been discovered in lab in 2004 and raised a lot of attentions. It has unique electronic band structure and promising applications. Many fundamental physics questions and practical limitations on device functions need to be addressed. We have investigated the low-frequency 1/f noise, which poses a limit on the signal-to-noise ratio in broad band electrical circuit, in both suspended and on-substrate graphene field-effect transistors, from T = 30 to 300K. We have found that, compared to on-substrate devices, in general suspended graphene devices show lower 1/f noise, as a result of their higher mobility. We explain the observed noise dependence on gate voltage using the Hooge's empirical relation with a variable Hooge parameter. We have also studied metal-insulator transition in monolayer graphene, and a phase diagram of metal and insulator phases from reported and our own results was proposed. Anomalous quantum Hall effect in ABC-stacked trilayer graphene was also studied, and we found chiral fermions with Berry's phase 3π and unusual Landau level quantization with 12-fold and 4-fold degeneracy in the n =0 and n >0 Landau levels, respectively. With the help of spacially resolved scanning photocurrent, we have studied charge transport in graphene in quantum Hall regime. And we found that the net photocurrent is determined by hot carriers transported to the device edges, where quantum Hall edge states provide efficient channels for their extraction to contacts. Moreover, optical bandgap and electrical properties of (GaN)1- x (ZnO)x solid solution nanowire have been studied to explore the possibility of using this material as a photovoltaic catalyst in water splitting for generating renewable energy. The nanowires with composition x [approximate] 0.12 were found with an optical bandgap ∼2.7eV. And the nanowire FETs were n-type conduction, with background carrier density ∼10 19 /cm3 and electron mobility ∼1 cm2 / V · s .