<%BANNER%>

Magnetotransport and Tunneling Study of the Semimetals Bismuth and Graphite


PAGE 1

MAGNETOTRANSPORT AND TUNNELING STUDY OF THE SEMIMETALS BISMUTH AND GRAPHITE By XU DU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2004

PAGE 2

Copyright 2004 by Xu Du

PAGE 3

To my parents

PAGE 4

iv ACKNOWLEDGMENTS I would like to express my sincere gratitude to the many individuals who contributed to success of my wo rk. First of all I would like to thank my research advisor, Professor Arthur Hebard. Through his positive and open-minded attitude, and his enthusiasm and optimism toward physics resear ch, he created the legacy of the free, vivid, intelligent, friendly and communicative re search atmosphere in the lab. I feel really lucky to be able to work in such envir onment. His experience, knowledge, and guidance have been invaluable throughout my graduate career. I would also like to than k Professor Dmitrii Maslov for his theoretic support. Without the many useful discussions with him, and his constructive criticism, much of my work would have gone nowhere. I would al so like to express my deep appreciation to Professor Andrew Rinzler. I truly benefited fr om his valuable opinions his help with lab facilities, and collaborati on of some on his interesting and fr uitful projects. I also want to thank Professor Peter Hirschfeld, who gave me a better understanding of solid state physics through his teaching; a nd Professor David Norton, for being on of my committee members. I am dearly thankful to current and former members of our group (Josh Kelly, Jeremy Nesbitt, Partha Mitra, Ryan Ra irigh, Sinan Selcuk, Guneeta Singh, Kevin McCarthy, Quentin Hudspeth, Stephen Arnason, Nikoleta Theodoropoulou, and Stephanie Getty), who provide d a joyful working environm ent and great help. I would especially like to thank Sinan Selcuk for hi s help on E-beam lithography. I also want to

PAGE 5

v thank Jamal Derakhshan (who worked as an REU student in the lab), for his help with the bulk bismuth study. My gratitude also goes to Professor Gray Ihas, and to Professor Amlan Biswas and his students (Tara Dhakal, Jacob Tosado, a nd Sung-Hee Yun), who provided me great help in using their facilitie s. I thank Zhuangchun Wu, Jennife r Sippel, and Amol Patil for their kind help with my experiments. I also would like to thank Ronojoy Saha, for useful discussions on high magnetic field transpor t. Many thanks go to the machine shop personnel for their excellent work, which allowed my research work to move on smoothly. I would like to express my gr eat appreciation and deep love to my parents for their unconditional love and support. And finally, I would like to thank my dear wife, Zhihong Chen, who was a graduate st udent in Professor Andrew Rinzlers group. Her knowledge and intelligence have been of great help. She has shared my happiness and burden all these years. Her love changes my lif e and makes me a better individual.

PAGE 6

vi TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES...........................................................................................................viii LIST OF FIGURES...........................................................................................................ix ABSTRACT......................................................................................................................x ii CHAPTER 1 GENERAL INTRODUCTION.......................................................................................1 2 MAGNETOTRANSPORT IN GRAPHITE...................................................................4 2.1 Overview of Classical Magnetotransport in Semimetals.........................................5 2.2 Multi-Band Model...................................................................................................7 2.3 Sample Preparation and Characterizations..............................................................9 2.3.1 Sample Preparation........................................................................................9 2.3.2 Characterizations: Dingle Te mperature and Landau Levels.......................11 2.4 Transport in the Classical Region..........................................................................17 3 MAGNETOTRANSPORT OF GRAPHITE IN THE ULTRA-QUANTUM FIELD..24 3.1 Transport Data in th e Ultra-Quantum Field...........................................................24 3.2 In-Band Transport Behavior in the Ultra-Quantum Regime.................................27 3.3 Possible Models in the Ultra-Quantum Regime....................................................37 4 TUNNELING INTO BULK BISMUTH IN THE ULTRA-QUANTUM FIELD........41 4.1 Motivation..............................................................................................................41 4.2 Experimental..........................................................................................................43 4.3 Results and Discussion..........................................................................................47 5 ACHIEVING LARGE MAGNETORESISTANCE IN BISMUTH THIN FILMS....50 5.1 Introduction...........................................................................................................50 5.2 Experimental .........................................................................................................54 5.3 Results and Discussion.........................................................................................55

PAGE 7

vii 6 METALLIC SURFACE STATES IN THE ULTRA-THIN BISMUTH FILMS........63 6.1 Introduction: Physics of the Ultra-Thin Bismuth Films.......................................63 6.2 Transport Properties of the Ultra-Thin Bismuth Films.........................................66 6.2.1 Experimental...............................................................................................66 6.2.2 Metallic Surface States...............................................................................67 6.3 Control of the Surface States................................................................................74 7 SURFACE SUPERCONDUCTI VITY IN ULTRA-THIN BISMUTH FILMS.........80 7.1 Transport Evidence...............................................................................................80 7.2 Tunneling Evidence..............................................................................................84 7.3 Possible Picture.....................................................................................................89 8 FUTURE WORK.........................................................................................................91 LIST OF REFERENCES...................................................................................................97 BIOGRAPHICAL SKETCH...........................................................................................101

PAGE 8

viii LIST OF TABLES Table page 1-1. Basic parameters of bismuth and graphite..................................................................1 5-1. Summary of results for differe nt bismuth film growth conditions...........................61 6-1. Parameters for the simulating the effect of thickness and temperature on the magnetic field dependence of the Hall re sistivity in ultrathin Bi films..................72 6-2. Parameters for the simulating the e ffect of Ge coating on the magnetic field dependence of the Hall resistivit y in ultra-thin Bi films..........................................79

PAGE 9

ix LIST OF FIGURES Figure page 2-1. Configuration of leads on graphite transport sample................................................10 2-2. Shubnikov-de Haas oscillations in graphite at indicated temperatures....................11 2-3. The Landau level indices as a function of the inverse of magnetic field at different low temperatures......................................................................................................12 2-4. The amplitude of the ShdH oscillati ons as a function of th e inverse of magnetic field at 2K.................................................................................................................14 2-5. Scaled ShdH oscillations amplitude as a function of the inverse of magnetic field in different temperatures..............................................................................................15 2-6. Linear fit to the slopes of the scaled ShdH oscillation as f unction of temperature..15 2-7. Temperature dependence of the resistivity xx for a graphite crystal in different magnetic fields.........................................................................................................17 2-8. xx and xy versus applied magnetic field at the different temperatures...................20 2-9. Temperature dependence of mobility, relaxation time; and carrier density for the bands indicated in the le gends of each panel...........................................................21 3-1. The magnetic field dependence of the longitudinal and Hall re sistance of HOPG at different temperatures..............................................................................................25 3-2. The temperature dependence of the l ongitudinal resistance of HOPG in different magnetic fields.........................................................................................................26 3-3. The ratio of the measured Hall resist ance and longitudinal resistance as a function of magnetic field at 2K.............................................................................................29 3-4. The Landau band dispersion relation of gr aphite in 12 Tesla fi eld, calculated using the SWMcC model...................................................................................................32 3-5. Estimation of carrier un-compensati on in different magnetic fields at 2K..............33 3-6. Shape of the in-band re sistivity as a function of ma gnetic field at the indicated temperatures.............................................................................................................34

PAGE 10

x 3-8. Logarithmic plot of the shape of the in-band conductivity as function of temperature in different strong magnetic fields.......................................................36 3-9. Model of the field induced Lutti nger liquid with dressed impurity scattering........38 3-10. Scaled in-band conductivity as a functi on of temperature in magnetic fields above the UQL....................................................................................................................39 4-1. Procedure for making tunnel junctions on bulk semimetal using photolithography technique..................................................................................................................44 4-2. Mica mask method for making tunnel junctions on bulk semimetal........................46 4-3. Microscopic picture of a Bi(bulk)-AlOx-Pb tunnel junction....................................46 4-4. Differential conductance as a function of bias voltage in indicated strong magnetic fields at 300mk.........................................................................................................48 4-5. Differential conductance at low bias voltage in the magne tic fields indicated in the legend.......................................................................................................................48 5-1. Fermi surface and Brillouin zone of rombohedral bismuth......................................50 5-2. Magnetotransport behavior of bulk single crystal bismuth......................................51 5-3. Magnetotransport behavior of a bismuth thin film...................................................52 5-4. X-ray diffraction pattern for a 4-um-thick Bi/Au film.............................................56 5-5. Resistivity vs. temperature at 0 and 5T for two category-I Bi films........................57 5-6. Resistivity vs. temperature at 0 and 5T for three category-II Bi films.....................58 5-7. Resistivity vs. temperature at 0 and 5T for two category-III Bi films......................60 6-1. Illustration of semimeta l-to-semicinductor transition..............................................64 6-2. Resistivity vs. temperature for Bi film with indi cated thicknesses..........................67 6-3. Magnetoresistance at 5K for two different thicknesses Bi films..............................69 6-4. Hall Resistivity vs. magnetic fiel d for (a) 180 and (b) 400 Bi films..................70 6-5. Simulated Hall Resistivity vs. ma gnetic field for Bi(180) and Bi(400).............73 6-6. Temperature dependence of resi stivity for Bi(100) and Bi(100)/Ge..................75 6-7. Hall Resistivity vs. magnetic fiel d for (a) Bi(100) and (b) Bi(100)/Ge .............77

PAGE 11

xi 6-8. Simulated Hall Resistivity vs. magne tic field for Bi(100) and Bi(100)/Ge........78 7-1. Resistance vs. temperature in zero magnetic field for a 15nm bismuth film...........80 7-2. Example of resistance in creases during the transition..............................................81 7-3. Sharp feature of resi stance change observed in Hall resistivity measurements.......82 7-4. Film thickness dependence of th e critical magnetic field at 4.5K............................83 7-5. Differential conductance as a function of bias voltage in the superconducting gap region for a Pb-AlOx-Bi( 150) tunnel junction......................................................84 7-6. Differential conductance as a function of bias voltage in the superconducting gap region at 300mk for a Pb-AlO x-Bi(1000) tunnel junction....................................86 7-7. Differential conductance vs. bias voltage at 300mK in indicated low magnetic fields perpendicular and parallel to the junction plane......................................................87 7-8. Differential conductance vs. bias volta ge at 300mK in indi cated strong magnetic fields perpendicular and para llel to the junction plane.............................................88 7-9. A possible picture of surface superc onductivity in ultra-thin bismuth films...........90 8-1. Some examples of the s ub-micron sized bismuth patterns.......................................93 8-2. Magnetic field dependence of the resistivity for a re servoir pattern........................94 8-3. Measurements of a nano-cavity with a single grain-boundary in it.........................95

PAGE 12

xii Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MAGNETOTRANSPORT AND TUNNELING STUDY OF THE SEMIMETALS BISMUTH AND GRAPHITE By Xu Du December 2004 Chair: Arthur F. Hebard Major Department: Physics Magnetotransport and tunneli ng studies on bulk crystals, thin films and patterned nanostructures of semimetals reveal a surpri sing range of interesti ng behaviors. In our study of ultrathin bismuth films, we found that the transport behavior is greatly affected by the presence of metallic surface states, whic h become evident in th e thinnest films and are presumed to be responsible for a surf ace superconducting state s een in tunneling and transport anomalies. We also studied bulk samples of both of these semimetals in magnetic fields high enough to place all the ca rriers in the lowest Landau level. In this ultraquantum regime, the apparent re-ent rance in graphite from insulating to metallic/superconducting behavior at low temperatures corresponds to the in-band insulating behavior of carriers within a se miclassical 2-band model framework. This analysis brings into question recently propos ed explanations of a field-induced metalinsulating transition and magnetic-field-induced superconducting fluctuations in graphite.

PAGE 13

1 CHAPTER 1 GENERAL INTRODUCTION A semimetal is a semiconductor with a small conduction band-valence band overlap (instead of a gap). Semimetals have low Fermi energy. In contrast to semiconductors, which are insula tors at zero temperature ( T = 0 ) where the carrier concentration n = 0 semimetals have a finite conductivity at T = 0 where n is finite because of the nonzero overlap of the conduc tion and valence bands. Semimetals are metallic, with both electrons and holes contri buting to electric conduction. Graphite and bismuth are typical semimetals, with low Ferm i energies and low carrier concentrations. Table 1-1. Basic parameters of bismuth and graphite Ef (meV) Carrier concentration (m-3) (ne=np) Bismuth ~30 ~2310 Graphite ~22 ~2410 Semimetals have been of interest for many years, in many different aspects. A major aspect of semimetal study is magnetotran sport. Because of their small values of carrier concentration, semimetals can be driv en into the ultra-quantum regime, when only the lowest Landau level remains occupied, with a magnetic field of ~10 Tesla. In addition, light cyclotron masses cm in certain orientations of semimetals result in higher cyclotron frequencies (cm eB/) ensuring that quantum ma gneto-oscillations can be observed in moderate magnetic fields and at moderate temperatures. High purity allows the oscillations to survive th e effects of disorder. Magnetotr ansport study of semimetals in strong magnetic field allowed the Fermi surface to be mapped by quantum oscillations

PAGE 14

2 in semimetals. In applications, the extremely large magnetoresistance of semimetals makes them promising candidates for magnetic field sensors. Another major aspect of semimetal study originated from the long Fermi wavelength. By making bismuth thin films with thicknesses comparable to a Fermi wavelength, one could study the energy band quantization because of quantum confinement. Also, since the band mass is bigge r for electrons than holes, as the size of the bismuth structure decreases, the speed at which the conduction band shifts up will be faster than that of the valence band. At a certain point, a gap opens up, and the semimetal-semiconductor transition should happ en. Existence of the transition has been studied for many years, and is still not conclu sive; mainly because of the existence of the surface states, that smear out any sharp features of the transition. Evidence of metallic surface states were found in films of su perconducting bismuth clusters, which indicates surface superconducti vity because of the strongly increased surface density of states. Further evidence of metallic surface states was found by angle resolved photoemission sp ectroscopy (ARPES). Our study of semimetals focused on two major aspects: 1) magnetotransport and tunneling study of bulk single-crystal bismuth a nd graphite; and 2) the effect of bismuth surface states on transport and bismuth surface superconductivity. In the following chapters, we will show the motivation and our work on each aspect of our study. Chapter 2 first of all desc ribes the theoretic b ackground of transport behavior in semimetals. Then it explains the experimental details, sample characterization and low field transport behavior analysis of graphite. Chapter 3 explains the high magnetic field transport behavi or of graphite, and proposes possible theoretic models.

PAGE 15

3 Chapter 4 describes the magneto-tunneling measurements on bulk bismuth tunnel junctions. Chapter 5 explains our work on achieving large magnetoresistance in Bi-Au thin films. Chapter 6 describes the effect of the metallic surface states on the transport properties of ultra-thin bismuth films. Ch apter 7 describes the surface superconductivity behavior we observed in the ultra-thin bism uth films. Chapter 8 discusses some possible interesting future works on bismuth, includ ing nano-meter sized bi smuth structures and spintronics applications.

PAGE 16

4 CHAPTER 2 MAGNETOTRANSPORT IN GRAPHITE Graphite is a typical semimetal, with a low Fermi energy (~22 meV) and low carrier concentration (~3 2410 3 m ). The zero-temperature conductivity in graphite results from the small overlap between th e conduction band and the valence band. The Fermi level lies in the middle of the overlap, which makes graphite a typical compensated 2-band material. Transport properties of graphite had been studied intensively since 1950s. Recently, interest in magnetotransport in graphite was renewed because of the observation of an effect that looks lik e a magnetic-field-induced metal-insulator transition: the metallic temperature-dependence of the in-plane resistivity in zero field turns into an insulating-like one when a magnetic field of a few tens of mTesla is applied perpendicular to the basal (ab) plane. Increa sing the field to about 1 Tesla produces a reentrance of the metallic behavior. It has been proposed that the low-field effect is caused by a magnetic-field-induced ex citonic insulator transition of Dirac fermions,1, 2 whereas the high-field behavior is a manifest ation of field-induced superconductivity.3, 4 It has also been suggested that the a pparent metal-insulator transition in graphite is similar to that in 2D heterostructures (although the latter is driven by a field parallel to the conducting plane). To elucidate these issues, we performed detailed measurements of magnetoresistance in graphite and found da ta quite similar to data reported in 1-4 over comparable temperature and field ranges. Ho wever, our interpretation is significantly different from theirs.

PAGE 17

5 2.1 Overview of Classical Magnetotransport in Semimetals A combination of some unique features specific to semimetals [i.e., low carrier density, high purity, small effective mass and equal number of electrons and holes (compensation)] led to an unusual temperatur e dependence of the magnetoresistance even in classically strong fields, defined by the condition T kB c / (2-1) where is a scattering time of the carriers. He re we qualitatively compare a semimetal with a conventional, high-den sity, uncompensated metal. To begin with, if the Fermi surface is isotropic, a metal does not e xhibit magnetoresistance because of the cancellation between the longitudinal and Hall components of the electric field.5 In real, anisotropic metals, this cancellation is broken, and as a result, magnetoresistance is finite and proportional to 2 c in weak magnetic fields (1c ). In stronger fields (1c ), classical magnetoresistance saturates .6 In contrast (Equation 2-14), magnetoresistance of a compensated semimetal grows as 2 B in both weakand strongfield regions. In addition to the saturation effect descri bed above, another f actor that makes the magnetoresistance much smaller in conventional metals than in semimetals is the higher scattering rates and hence the smaller values of c. The impurity scattering rate in semimetals is smaller than in conventional metals simply because semimetals are typically much cleaner materials. The lower carrier density of semimetals also reduces the rates of electronphonon scattering compared to that of conventional metals. For temperatures above the transport Debye temperature, which sepa rates the regions of the

PAGE 18

6 T and 5Tlaws in the resistivity, / D FBksk where kF is the Fermi wave vector and s is the speed of sound (both properly averaged over the Fermi surface), one can estimate the electronphonon scattering rate7 as / ) / )( (0 0 1T k m m a kB F (2-2) where 0a is the atomic lattice constant, and m* and m0 are respectively the effective mass and the bare electron mass. In a conventional metal,1 ~0a kF and 0* m m In this case, D is of the order of the thermodynamic Debye temperature 0/Bska ~few 100 K and 11/BkT Barring numerical factors, T kB / cannot be satisfied in a typical metal. This means that as soon as it en ters the classically strong field region, magnetoresistance saturates and quantum magneto-oscillations start to show up. In a low-carrier-density material (01Fka ), D is much smaller (for Bi and graphite ~D few K) and also 11/BkT which ensures that the inequality (2-1) can be satisfied. Therefore, in a low-carrier-density compensated semimetal a wide interval of temperatures and magnetic fields exists in which a) the scattering time is linear in T, in accordance with Equation 2-2, b) we ar e in the regime of classically strong magnetoresistance with essentially no signa tures of quantum magneto-oscillations, as specified by the inequality (2-1), and c) the magnetoresistance is large. An additional feature that is crucial for in terpreting the experimental data is that the Fermi energies of graphite ( EF = 22 meV)8 and bismuth ( EF = 30 meV [holes])9 are relatively low; and the temperat ure dependence of the resistivity is therefore a function of Inequality (1) can be satisfied in a typical metal for D T when the (transport) time 51trTT /. For an uncompensated metal, however, magnetoresistance saturates in this regime.

PAGE 19

7 two temperature-dependent quantities, n(T) and (T) That materials are pure helps to ensure that electron-phonon scattering is a dominant mechanism for resistance (in a doped semiconductor, impurity scattering dominates). 2.2 Multi-Band Model In the semiclassical theory of conduction in metals, DC electrical conductivity in a multi-band system (in absence of a magnetic field) is described by n n) ( (2-3) ) ( 3 2 ) () )( ( ) ( )) ( ( 4 k n n n n nnf k v k v k dk e (2-4) wherefis the Fermi function, and k k k vn n ) ( 1 ) (. Since 0 f except when is within T kB of F filled bands have no contribution to the conductivity. Only those partly filled bands that are close to the Fermi level contribute to the conductivity. In the presence of a classi cally strong magnetic field z B B (the Landau energy level quantization is negligible), for an isotr opic system in which all the occupied orbits are closed, there will be no magnetoresist ance because of the can cellation of Lorentz force by the Hall components of the electric field. If an external electric field x E Ex is applied, the induced current density will bex E jx0 where 0 is the in-plane zero magnetic field conductivity. The Hall component of the electric field will be generated: x c yE E ) ( Then the definition: E j hence

PAGE 20

8 0 ) ( 0 00 x c x xE E E (2-5) will yield ) 0 ( 0 0 0 ) ( 1 ) ( 1 0 ) ( 1 ) ( 12 0 2 0 2 0 2 0 zz c c c c c c (2-6) This, in terms of resistivity, which is experimentally measured, is simply 0 0 0 10 0 0 0 ) ( ) (ZRB RB B B (2-7) where ne R 1 is the Hall coefficient. Note that the longitudinal composnents of the resistivity have no field dependence. Now consider such a system with more th an one band. Each band contributes to the conductivity of the system in para llel with the other bands. Then the total resistivity is in terms of the resistivity of each band: ii zi i i i i iB R B R1 0 0 0 1 10 0 0 0 (2-8) Even without calculating the resistivity above in detail, we can readily see that the magnetic field dependence (which belongs to the off-diagonal components in the resistivity tensor of each single band) may ente r into the diagonal components of the total

PAGE 21

9 resistivity. Thus the multiband system can have magnetoresistance even though none of its band has magnetoresistance by itself. For the simple (and most useful) case of a 2-band system, the resulting longitudinal resistivity and Hall resistivity are: 2 2 2 1 2 2 1 2 1 2 2 2 2 1 2 1 2 1) ( ) ( ) ( ) ( B R R B R Rxx (2-9a) 2 2 2 1 2 2 1 1 2 2 2 2 1 3 2 1 2 1) ( ) ( ) ( ) ( B R R B R R B R R R Rxy (2-9b) For a system of more than 2 bands, it is convenient to describe the contribution of each band in terms of conductivity. In a simple Drude model, i i i i xxB en2) ( 1 (2-10a) i i i i xyB B en2 2) ( 1 (2-10b) where, in and i are carrier density and mobility of the ith band. From the conductivity tensor, we can then calculate the measured values of resistivy and Hall constant: ) ( ) ( ) ( ) (2 2B B B Bxy xx xx and ) ( ) ( / ) ( ) (2 2B B B B B Rxy xx xy H 2.3 Sample Preparation and Characterizations 2.3.1 Sample Preparation The sample used in the study, a recta ngular shaped highly oriented pyrolytic graphite, with dimensions 2.4 mm wide by 8 mm long by 0.5 mm thick, was cut from a bulk piece of highly oriented pyrolytic graphite (HOPG) using wire saw.

PAGE 22

10 The HOPG sample has a mosaic spread, de termined by X-rays, of 2 degrees. After the sample was cut, it was glued onto a glass substrate. Figure 2-1 shows the configuration of the measurement leads on th e sample. The 4-terminal measurement leads were connected to the sample applying silver paint. Because of the high in-plane/out-ofplane conductivity ratio in la yered graphite, we found it nece ssary to place the current leads uniformly in contact with the sides of the sample. Thin-foil indium was coated uniformly with silver paint, and was attached to the graphite end plates as current leads. Gold wires with tiny loops were silver pasted with ~2 mm separation to the edges of the sample as voltage leads. I+I-V+V-VHall Figure 2-1. Configuration of l eads on graphite transport sample Resistance measurements at 17 Hz were carried out us ing a Linear Research 700 resistance bridge. The sample was measured over the temperature range 2K~ 350K in fields as high as 17.5 Tesla. Low magnetic field measurements we re carried out in a Quantum Design Physical Property Measuremen t System (PPMS) with a 7 Tesla magnet. High magnetic field measurements were carrie d out in a He3 refrigerator with a 17.5 Tesla magnet in the National High Magnetic Fi eld Labs (NHFML). In all measurements,

PAGE 23

11 the magnetic fields were applied perpendicular to the graphite basal plane (i.e., parallel to the c-axis). 2.3.2 Characterizations: Dingle Temperature and Landau Levels In the presence of strong magnetic fields, the energy bands of graphite split up into Landau levels. With increasing magnetic fields, the interval between Landau levels increases: c cm eB / where c is the cyclotron frequency, and cm is the cyclotron mass When a Landau level moves acr oss the Fermi surface, sharp features of conductivity change appear. This caused the oscillatory beha vior of resistivity in the magnetic field sweep (Shubnikov-de Haas oscillations). Figure 2-2. Shubnikov-de Haas os cillations in graphite at indicated temperatures. The oscillations are obtaine d by subtracting the background magnetoresistance from the resistance vs. magnetic field curves. The inset shows the resistance as a function of magnetic field at 2K. 0.00.51.0 -0.15 -0.10 -0.05 0.00 2K 5K 10K 15KRosc()1/B(Tesla-1) -1012345678 0.0 0.2 0.4 0.6 0.8 R ()B (Tesla)

PAGE 24

12 Given the Fermi energy Ef, the number of Landau levels below the Fermi energy can be estimated as c fm eB E N / 1 Hence the period at which the one Landau level moves across the Fermi surface goes like 1/ B As the magnetic field increases, every time one Landau level shifts across the Fermi level, the resistivity will decrease because of the high density of states at the bottom of the Landau band. And a valley will show up in the resistivty vs. magnetic field pl ot. By plotting the valley positi ons of the ShdH oscillations vs. 1/ B one gets evenly spaced points. By labeling these points one can count the number of Landau levels lying below or across the Fermi surface. Since the band structure does not change with temperature, the valley positions measured at different temperatures should overlap well. Figure 2-3 below shows th e Landau level indices as a function of the inverse of magnetic fields at different low temperatures. Figure 2-3. The Landau level i ndices as a function of the i nverse of magnetic field at different low temperatures 0.20.40.60.81.01.21.41.6 2 3 4 5 6 7 8 Number of Landau Levels 1/B (Tesla-1) 2K 5K 10K

PAGE 25

13 Figure 2-2 shows that the ShdH oscillat ions are most pronounced at very low temperatures (c BT k ). At higher temperatures, the oscillations are smeared by phonon scattering. The relation between the am plitude of the ShdH oscillations and temperature T at magnetic fiel d B is shown in Equation 2-11.10 B T T B Ad osc) ( exp ~2 / 5 (2-11) Here Td, the Dingle temperature, describes th e temperature-inde pendent scattering from impurities and dislocations. Dingle temperature is a useful parameter in characterizing the quality of the graphite sa mple. The lower the Dingle temperature, the less imperfection the sample has. Dingle temperature can be measured from conductance-field sweep at different temperatures. First, the background of the conduc tance vs. field curves is subtracted out, and the oscillatory part is pl otted vs. 1/B. Then the osci llation amplitudes are obtained by subtracting the envelope curves of the oscillations valleys fr om the envelope curves for the peaks (Figure 2-4). Since only the shapes of those curves are important, we used arbitrary smooth functions to fit the envelope curves. This method of interpolation give much more precise oscillation amplitude values than simply subt racting the resistance values at the valleys from those at the adjacent peaks (which do not correspond to the same field). After we get the amplitudes of the oscillations Aosc, we plot 2 / 5B Aoscvs. B / 1, and obtain straight lines in 2 / 5B Aoscvs. B / 1 plots ((Figure 2-5)). The slopes of the straight lines, according to Equa tion 2-11, simply correspond to ) (dT T

PAGE 26

14 Figure 2-4. The amplitude of the ShdH osc illations as a functi on of the inverse of magnetic field at 2K, obtained by subt racting the bottom envelope curves from the top envelope curve of the osci llations, as indicated in the inset. We then plot the values of the slope s vs. their corresponding temperatures, and perform a linear equation fitting to the curve. The fitted straight line then intersects with the negative side of the temperature axis, w ith the offset being the Dingle temperature Td. For the graphite used in our study, the Dingle temperature we got from the analysis described above is about 4.5K. This result suggests that the sm earing of the ShdH oscillations by the imperfections in the HOPG corresponds to the thermal smearing of 4.5K. 0.40.60.81.01.21.41.6 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Amp. osc1/B 0.00.51.01.52.0 -0.5 0.0 0.5 Conductance_osc (-1)1/B (Tesla-1)

PAGE 27

15 Figure 2-5. Scaled ShdH os cillations amplitude: Ln(2 / 5B Aosc), as function of the inverse of magnetic field in di fferent temperatures. 0246810121416 -1x105-8x104-6x104-4x104 Td4.51111 0.99368a*(T+Td)T ( K ) Figure 2-6. Linear fit to th e slopes of the scaled ShdH oscillation as function of temperature. 0.40.60.81.01.21.41.6 -4 -3 -2 -1 0 1 2K 5K 10K 15Kln(amp.*B^(5/2))1/B (Tesla-1) K Td1 5 4

PAGE 28

16 ShdH oscillations also provide informa tion about the Fermi surface. By measuring ShdH oscillations in different magnetic fiel d orientations, one can map out the extremal of the Fermi surface. For graphite, by measur ing ShdH oscillations and calculating the volume of the Fermi pockets, we can then calculate the carrier concentration. Here we simplify the problem by treating the Fermi surface of graphite as ellipsoids with anisotropy ratio By measuring the ShdH oscillations with magnetic field parallel to the c-axis of graphite, we get the pe riod of the quantum oscillations to be c fm E e B ) (1 (2-12) where cm is the cyclotron mass for magnetic fiel d along the c-axis. This provides the information about the area of the extremal cr oss section of the Fermi surface with a plane perpendicular to the magnetic field: c f extrm E S 2 (in momentum space). Given the anisotropy ratio we can then calculate the volume of the ellipsoid and hence the carrier concentration: 2 / 3 1 2 / 3) ( 4 3 1 B N h e n (2-13) where 6 N is the number of ellipsoids in the Brillouin zone. Taking ~ 12-17, the carrier concentration calc ulated from the measured oscillations period is 3 2410 3 2 ~ m n This number corresponds to the zero temperature carrier concentration in graphite. At low enough te mperatures, one can separate the ShdH oscillations periods from elect rons and holes, and calculate the carrier concentration for the two different carriers. Also, for each carrier group, there will be two sets of oscillations because of the spins. At 2K how ever, we are not yet able to distinguish the

PAGE 29

17 different periods result from the small eff ective mass difference between electrons and holes, and from the spin splitting. 2.4 Transport in the Classical Region In this section, we pres ent a detailed study of low field magnetotransport in graphite and show that the unusual behavi or of the temperatur e and field-dependent resistance, such as shown in Figure 2-7, can be described in a st raightforward way by a simple multi-band model that takes into accoun t contributions to the conductivity from the electron and hole carriers associated with the overlapping valence and conduction bands. 050100150200 1E-8 1E-7 1E-6 0 mT 20 mT 40 mT 60 mT 80 mT 100 mT 200 mT 050100150200 0.0 0.5 1.0 1.5 IB (Tesla)T (K)II III xx ( m)T (K) Figure 2-7. Temperature depe ndence of the resistivity xx for a graphite crystal plotted on a logarithmic axis at the magnetic fiel ds indicated in the legend. The solid lines are the fits to the data using th e six parameters derived from the three bands described in the text. The shadow ed region on the inset and its mapping onto the data in the main panel are described in the text.

PAGE 30

18 We use the qualifier unusual in describing the data of Figure 2-7, since on lowering the temperature the resistance increas es as it does in an insulator but then saturates at lower temperatures. The nontrivial explanations of Kopelevich et.al 3,4 rely heavily on such features as the Dirac spectrum of fermions and almost two-dimensional transport, which are unique for graphite but not for Bi. That Bi and graphite behave similarly suggests that these features are not responsible for the observed phenomena. Our explanation for the insulating-like behavior in a magnetic field does not require more exotic explanations of a magnetic-field-indu ced opening of an excitonic gap in the spectrum of interact ing quasiparticles.11 Instead, we propose that the uniqueness of the low magnetic field transport be havior of semimetals lies in the existence of a wide interval of temperatures and magnetic fields defined by the inequalities of Equation 2-1. Our analysis of the experimental data confirms the inequalities Both xx and xy (see Figure 2-8) were measured in magnetic fields up to 0.2 Tesla at different temperatures A small field-symmetric component caused by slightly misaligned electrodes was subtracted from the xy(B) data. To fit the data, we adopt a standard multi-band model.5 Each band has two parameters: resistivity i xx and Hall coefficient i i in q R 1 where e qi is the charge of the carrier. In agreement with earlier studies, we fix the number of bands to three.1 Two of the bands are the majority electron and hole bands, and the third one is the minority hole band. Although the presence of the third band is not essential for a qualitative understandi ng of the data, it is necessary for explaining fine features in xy. Our fitting routine incorporates both xx(B) and xy(B) simultaneously by adjusting the six unknown parameters independently, until the differences between the fitting curves and the experimental data are minimized.

PAGE 31

19 Because the majority carriers in graphite derive from Fermi surfaces that have sixfold rotational symmetry about the c -axis, we only need to deal with the 2x2 magnetoconductivity tensor with elements xx and xy. Here, we define the conductivity 2 2 2 2) ( ; ) ( B R B R B Ri i i i xy i i i i xx and the resistivity *2/iiiimne for the ith band. The total conductivity is simply a sum of the contributions from all the bands: 13..i i The observable resistivity tensor is obtained by inverting : 1 Qualitatively, the unusual temperature dependence of xx displayed in Figure 2-7 can be understood for a simple case of a two-band semimetals, where xx reduces to 2 2 2 2 2 2B R R B R Rh e h e e h h e h e h e xx (2-14) Here ) (h e and ) (h eR Rare resistivity and Hall coefficien t for the electron (hole) band, respectively. Assuming thata h eT with 0 a, we find that for perfect compensation (i.e., h en n where en and hnare carrier density for the el ectron band and the hole band respectively), R R Rh e and the 2-band resistivity described by Equation 2-14 can be decomposed into two contri butions: a field-independent terma T and a fielddependent term aT B T R/ ) (2 2. At high T, the first term dominates and metallic behavior ensues. At low T, ) ( / 1 ) (T n T R saturates and the seco nd term dominates, giving insulating behavior.

PAGE 32

20 Figure 2-8. xx and xy versus applied magnetic field at the temperatures indicated in the legend. The solid lines are determined by a fitting procedure described in the text. The inset in the xy plot magnifies the lowfield region where the contribution from the minority band is important. 0.000.050.100.150.20 10-810-710-6 40K 70K 100K 100K 200K 5K 10K 15K 20K 25Kxx ( m)B (T)0.000.050.100.150.20 0.0 5.0x10-81.0x10-71.5x10-72.0x10-72.5x10-73.0x10-7 40K 70K 100K 150K 200K 5K 10K 15K 20K 25Kxy (m)B (T)0.000.010.020.03 -2.0x10-90.0 2.0x10-94.0x10-96.0x10-98.0x10-91.0x10-81.2x10-81.4x10-8 xy (m)B (T)

PAGE 33

21 0501001502000.0 2.0 4.0 6.0 8.0 10E24 band 1 band 2 band 3Temperaturecarrier density (m-3)0.0 0.3 0.6 0.9 1.2 1.5 1.8E12 band 1 band 2 band 3 (sec-1)0 50 100 150 200 250 300 350 band 1 band 2 band 3mobility (m2V-1s-1) Figure 2-9. Temperature dependence of the fitting parameters: A) mobility; B) relaxation time; and C) carrier density, for the bands indicated in the legends of each panel. The actual situation is somewhat more complicated because of the T-dependence of the carrier concentration, the presence of the third band, and an imperfect compensation A B C

PAGE 34

22 between the majority bands. Results for the temperature-dependent fitting parameters are shown in Figure 2-9, where band 1 corresponds to majority holes, band 2 to majority electrons and band 3 to minority holes. The insu lating-like behavior of the carrier density with a tendency towards saturation at low temperatures is well reproduced. For the majority bands, 1 and 2, the carrier concentrations are approximately equal and similar in magnitude to literature values.12 The slope of the linear-in-T part of /exp 1T kB with ) 3 ( 065 0exp (dashed line in Figure 2-9, panel A) is consistent with the electronphonon mechanism of scattering. To see this, we adopt a simple model in which carriers occupying the ellipsoidal Fermi surface with parameters mab (equal to 0.055m0 and 0.04 m0 for electrons and majority holes, correspondingly), mc (equal to 3m0 and 6m0, correspondingly) interact with longitudinal phonons via a deformation potential, characterized by the coupling constant D (equal to 27.9 eV). In this model, the slope in the linear-in-T dependence of is given by7 3 2 0 2 3/ *) ( ) / 2 ( ab F theors D E m (2-15) where 0 3 / 1 221 0 ) ( m m m mc ab both for electrons and holes, 3 0/ 27 2 cm g is the mass density of graphite, and s cm Sab/ 10 26 is the speed of s ound in the ab-plane. (The numerical values of all parameters ar e taken from standard reference on graphite12) With the above choice of parameters, 052 0 theor for both types of carriers. This value is within 20% of the value found experimentally. Given the simplicity of the model and uncertainty in many material parameters, especially the value of D such an agreement between the theory and experi ment is quite satisfactory.

PAGE 35

23 The solid lines through the data points in Figure 27 are calculated from the temperature-dependent fitting parameters de rived from our three-band analysis and plotted in Figure 2-8. The shaded region (II) de picted in the inset of Figure 2-7 represents those temperatures and fields that satisfy the inequalities of Equation 2-1. In region (I) ShdH oscillations can be seen at sufficientl y low T (our sample has a Dingle temperature of 5K), and in region(II) th e magnetoresistance is low. The boundary between (I) and (II) reflects the rightmost of the inequality 2-1 and is determined by the relation / m eB T where 5 has been chosen to represent the ratio c BT k /. A larger value of would decrease the slope of this boundary and diminish the area of (II). The boundary between (II) and (III) refl ects the leftmost inequality of 2-1 and is determined by the relation ) ( / T e m B where ) ( / 1 T is obtained from e xperimental fitting parameters (Figure 2-9). In the main panel of Figure 2-7, we s uperimpose region (II), again as shaded area, on the ) ( B Txx data. Below the lower boundary 1 c, and the magnetoresistance is relatively small. The upper boundary is determin ed by the locus of (B,T) points satisfying the rightm ost inequality of 2-1 for 5 Clearly region (II), constrained by the inequality 2-1, overlaps we ll with the metal-insulating like behavior of graphite. We thus conclude that the semime tals graphite and, by implication, bismuth share the common features of high purity, lo w carrier density, small effective mass and near perfect compensation, and accordingly obe y the unique energy scal e constraints that allow pronounced metal-insulating beha vior accompanied by anomalously high magnetoresistance.

PAGE 36

24 CHAPTER 3 MAGNETOTRANSPORT OF GRAPHITE IN THE ULTRA-QUANTUM FIELD 3.1 Transport Data in the Ultra-Quantum Field The inequality discussed in chapter 2: T kB c /defines two limits that are satisfied within a wide temperature range in semimetals: c / (or ) 1 c gives rise to the large magnetoresistance in the semimetals; T kB c defines the classically strong magnetic field (weak fi eld), in which the number of Landau levels below the Fermi level is so large that the quantum oscillations are well smeared by temperature, hence the effect of quantization of the energy bands is negligible. In stronger magnetic fields, there are onl y few Landau levels below the Fermi level and T kB c is no longer satisfied. Eventually, when the magnetic field is so strong that all the conduction electrons are all in the lowest Landa u level, the so-called ultraquantum limit is reached. Above the ultra-quantum limit, th e energy of the electrons is fully quantized in the plane perpendicular to the field. The movement along the field lines is free; hence the electrons in the system a ssume movement with sp iral trajectories along the field lines. Ideally, in the absence of scatte ring and interaction, a system in the ultraquantum regime should have zero conductance in the plane perpendicu lar to the magnetic field, because the Lorentzian force confines the movement of the el ectron to the spiral trajectories. However, with interactions and s cattering, the electr on can move along the plane perpendicular to the fiel d lines in a diffusive manner.

PAGE 37

25 Figure 3-1 shows the strong magnetic field magneto-transport data taken from the same HOPG used in the low magnetic field study. 05101520 0 300 600 900 1200 1500 70K 40K 20K 15K 10K 7.5KRxx (m)B ( T ) 5K 05101520 0 20 40 70K 40K 20K 15K 10K 7.5K 5KRxy (m)B (T) Figure 3-1. The magnetic field dependence of the A) longitudinal; and B) Hall resistance of HOPG at different temperatures B A

PAGE 38

26 020406080100 0 500 1000 1500 2000 4TRab (m) T (K)17.5T 16T 14T 12T 10T 8T 6T 1T Figure 3-2. The temperature dependence of the longitudinal resi stance of HOPG in different magnetic fields From the magnetic field dependence of the longitudinal resistance data, we see that the resistance increases roughly linearly with magnetic field, a nd tends to saturate in very high magnetic field (>10 Tesla). For the curves taken at very low temperatures (T <15K), we see ShdH oscillations on top of the ma gnetoresistance. The Hall resistance has much smaller values than the longitudinal resistan ce in high magnetic fields, and has rather complicated field dependence. We are most interested in the temperature dependence of the resistance in different strong magnetic fields. Here we see that, the resistance increases with decreasing temperature for T >30K, similar to what is observed in the low (classical) magnetic fields. For T <30K, however, the resistance pl unges down with decreas ing temperature in strong magnetic fields.

PAGE 39

27 The metallic behavior observed in str ong magnetic fields and low temperatures can not be explained by semi-classical trans port theory. It was proposed that the highfield transport behavior is a manifestation of field-induced superconductivity4. However, we find a more conventional interpretation by co nsidering graphite as a multi-band system. Our strategy of analyzing the data re lies on obtaining in-band transport behavior from the experimentally measured data usi ng the multi-band model. Then we will try to understand the in-band transport, which repres ents the intrinsic phys ics of the graphite system. 3.2 In-band Transport Behavior in the Ultra-Quantum Regime In strong magnetic fields, the multi-band model still applies, except that we can no longer take the resistivity and Hall coefficient of each single band to be field-independent parameters, because of the strong quantum ef fect. Instead of curv e fitting with field independent parameters, we need to start by simplifying the multi-band model. Since the contribution of the minority band vanishes in high fields, we can a pply the simple 2-band model, in which: 2 2 2 1 2 2 1 2 2 1 2 2 2 1 2 1 2 1) ( ) ( ) ( ) ( B R R B R Rxx 2 2 2 1 2 2 1 2 1 2 2 2 1 3 2 1 2 1) ( ) ( ) ( ) ( B R R B R R B R R R Rxy Now we make the assumptions that, in hi gh magnetic fields, the system is nearly compensated, and the resistivitie s of each band are very close: 2 1 (3-1a) R R R 2 1 (3-1b)

PAGE 40

28 We will see that these assumptions are vali d when applied to the experimental data in high magnetic fields. With th e simplification above, we have 2 2 2 2 2 24 2 B B Rxx (3-2a) 2 2 2 2 2 24 B B R Bxy (3-2b) where 2 1R R is the difference of the electron and hole Hall coefficients. The ratio of the two numerator terms and R Bin high magnetic fields gives rise to two different pictures of tr ansport properties in this regi on. In the first picture, we assume that the magnetoresistance shown in xx is mostly from the magnetoresistance of each single band. An extreme case of this picture is when: RB and hence: 2 / xx and 4 / Bxy In this case, the longitudinal resistivity of the 2-band system is essentially the same as that of each single band. Accordingly, we see that in this pict ure, we do need the nontrivial explanations for the nonsaturating MR in a system with closed orbits, i.e., field induced metal-insulator transition (MIT) a nd re-entrance to metallic behavior in quantizing magetic fields.1-4, 13 In the second picture, we assume that the MR shown in xx is mostly from the diagonal (Hall) resistivity, 2 2) ( RB (or 1 ) (2 c). Then the simplified forms of the high field limit resistivities are: 2 2 2 2 24 2 B B Rxx (3-3a)

PAGE 41

29 2 2 2 3 24 B B Rxy (3-3b) The ratio of the two measured parameters, 2 Bxx xy is plotted in the figure below: Figure 3-3. The ratio of the measured Hall resistance and longitudinal resistance as a function of magnetic field at 2K. It can be seen in the figure that, the ratio 1 B for field above the ultraquantum limit. This rules out the possibility of un-compensation (i.e., 0 ) as a mechanism for the re-entrant behavior in high magnetic fields and low temperatures, since the second term in the denominator of both xx and xy can be neglected. Now we have a even more simplified form of xx and xy : 22 2B Rxx (3-4a) 612 1E-3 0.01 0.1 xy/xxB (T)

PAGE 42

30 2 3 24 B Rxy (3-4b) It can be seen from these relations above that, the transport be havior in the second picture is drastically different from that in the first picture. The 2-band longitudinal resistivity is now proportional to the reciprocal of the resi stivity of each single band! Therefore the re-entrance to metallic behavi or of the 2-band system as measured by xx would really correspond to a cross over from metallic to insulating behavior for each band (as measured by 2 1 ) as the temperature drops. The criterion for the second pi cture to be valid is that: RB must be satisfied. In relatively low magnetic fields (say B ~ 0.1 Tesla), ta king the values of 810 ~and 610 ~R we see that this criteria is well satisf ied. Hence we are confident in ruling out any non-trivial MIT mechanism in explaini ng the MIT-like beha vior. Despite the complicated field-dependence of the major mechanism for MR is the Hall resistivity term RB In very strong magnetic field, RB is required for the result 22 2B Rxx to be valid. Hence we require that RBxx In the range of the magnetic field we are studying, the carrier concen tration increases slowly with increasing field12, hence the inband Hall coefficient R decreases with increasing fiel d. Taking the experimentally measured mxx 410 3 ~, and 1 610 mT R we can see that RBxx is satisfied for B ~ 10 Tesla. This indicates that our sec ond picture is self-consis tent according to the experimental data.

PAGE 43

31 From the analysis above, we see that RB is generally satisfied in the magnetic field range of our study. We also note that RB and 1 B implyR Hence our assumption that the system in strong ma gnetic field is nearly compensated is well consistent with the experimental results. Till now, we havent made any assumption on the expressions of the resistivities and the Hall coefficients of the two bands. Ideally, if we have the complete information on the band structure of graphi te in high magnetic field and the scattering mechanisms, we can exactly calculate the conductivity tensor using Kubo formula. Such a procedure, however, will be extremely complicated. In the ultra-quantum limit (UQL), the probl em may get simplified by the fact that all the carriers are in the lowest Landau level at sufficiently low temperatures: f c BE T k This can be understood by examining the Landau band structure of graphite in the ultra-quantum limit field. The energy band quantization due to the ma gnetic field can be calculated using the classical tight-binding SWMcC model.12 The dispersion relati on from the calculation shows that, in magnetic fields, each energy band separates into different Landau bands. With increasing magnetic field, all othe r conduction bands and valence band move further and further away from each other a nd from the Fermi level, while the lowest (zeroth) Landau bands remains field in-dep endent. For field above the ultra-quantum limit (~ 8 Telsa for graphite), the Fermi level runs across only the lowest (zeroth) conduction band and valence band, which are th e only Landau bands that contribute to the conduction. Figure 3-4 shows the Landau band structure of graphite in 12 Tesla field,

PAGE 44

32 obtained from the classical band structure calculation (SWMcC model). The field independence of the zeroth Landau bands was confirmed by the recent high magnetic field scan tunneling spectr oscopy measurements on HOPG.14 Figure 3-4. The Landau band disp ersion relation of graphite in 12 Tesla field, calculated using the SWMcC model. From the Landau band structure shown in Figure 3-4, we can see that in strong magnetic field, at suffici ently low temperature: f c BE T k the number of the thermally excited electrons (and holes) in the higher Landau levels is negligible hence we can make the approximation that he carrier concentra tion does not change significantly with temperature nor magnetic field. Since the high field limit of the Hall c0 v0 v1 v2 c1 c2 c3 e h h

PAGE 45

33 coefficient is simply: ne R 1 R will be roughly field and temperature independent in this region (compared with the f actor of two resistivity ch ange in this region). With the approximation above, we have enough information to separate out the inband resistivity using the 2-ba nd longitudinal resistivity. We can also estimate the uncompensation in this high B low T region, by calculating 2 2R Bxy xx Figure 3-5 below shows the values ca lculated from experimental data: Figure 3-5. 2 2R Bxy xx as function of magnetic fiel d at 2K, calculated from the experimental data. The saturation of 2 2R Bxy xx is seen in the Figure at field above 8 Tesla (UQL for graphite). The weak field dependence can be attributed to the combination of weak 24681012141618 101102103104105106 xx 2/(B*xy)B (Tesla)

PAGE 46

34 thermal excitation and field dependence of un-compensation, and the saturation of Using the value of R ~ 10-6 T / (from the band structure calc ulation), we can estimate that 1710 ~T / Hence our assumption of near co mpensation is well satisfied. From the self-consistent approximations above, we reach a very simple high magnetic field limit ( B > BUQL) result: the resistivity of each single band is proportional to the reciprocal of the 2-band resistivity in graphite: xxB R 2 2 Figure 3-6 shows xxB2 calculated from measured data. The high field part of the curve will represent the resistivity of a single band itself under our assumption that R is field-independent in high magnetic field. Figure 3-6. xxR B2 as a function of magnetic field at th e indicated temperatures, calculated from the experimental data. 110 0.1 5K 7.5K 10K 15K 20K 25K 40K 70KB2 / RxxB (Tesla)

PAGE 47

35 From Figure 3-6 above we can clearly see the tendency of scaling of curves in high magnetic fields and low temperatures (curve s become parallel to each other). This indicates that in this region, we only need to care about the cont ribution from the lowest Landau band, and neglect the thermally ex cited carriers in the higher index number Landau levels. Figure 3-6 also give s us a range of such regime: B >10 Tesla and T <20K. We note that this range satisfies the inequa lity for temperature and field independent carrier density: f c BE T k (at 10T, 20K: meV T kB9 0 ~, meV Ef c6 ~ ) With this simplification, we can direc tly analyze the temperature dependence of resistivity in high fields and low temperatures assuming that the carrier densities of the two bands are temperature independent, or R is T-independent. By treating R as a Tindependent and B-independent constant, we see that the in-band resistivity has a temperature dependence xxB /2 The in-band conductivity scaler, which contains the intrinsic physics about the interactions and scat tering of the system, is simply 2 2 0~ ) ( 1B RBxx xx Here since *2 0m ne and because of the week temperature and magnetic field dependence of n and m* in the ultra-quantum region, this implies that the relaxation time: 2~ B xx Figure 3-8 shows the shape of the in-band conductivity 0 vs. T using logarithmic axis. From Figure 3-8 we see that above the UQL field and for f c BE T k : 1) at fixed temperature, the in-band conductivity 0 decreases with increasing magnetic field; 2) at fixed magnetic field, the in-band conductivity 0 decreases with decreasing temperature.

PAGE 48

36 Figure 3-8. Logarithmic plot of the shape of the in-band conductivity (~ 2 B xx) as function of temperature in different strong magnetic fields, calculated from the experimental data. Using 0 we can also calculate th e in-band conductivity tensor: xx c c xxB 1 ~ 1 ~ ) ( ) ( 12 2 0 2 0 (3-5a) Bc c c xy1 ~ ) ( 10 2 0 (3-5b) Since in fixed magnetic fi eld, the relaxation time decreases with decreasing temperature, 1 ~xx will increase with decreasing temperature. The In-band Hall conductivity is independent of the relaxation time. 110100 5 10 15 20 25 17.5T 16T 14T 12T 10T 8T 6Txx/B2T (K)4T

PAGE 49

37 3.3 Possible Models in the Ultra-Quantum Regime: At this step, we have disc overed the transport behavior directly resulting from the physics of interactions in the graphite system in UQL field. Now we will try to understand the physics that causes this tran sport behavior: 1) the relaxation time decreases with decreasing temperature; 2) 1 ~xx increases with decreasing temperature. In this section, we will consider two possible models that give this kind of transport behavior: the magnetic field induced Luttinger liquid with impurity scattering, and phonon delocalization (dephasing). In the model of magnetic field induced Luttinger liquid with impurity scattering, the scattering mechanism considered is the elastic scattering of the impurities dressed with the Friedel potential,15 as illustrated in Figure 3-9. At zero temperature, the electrons are localized by dressed impurities along the di rection of the field lines. The potential of the dressed impurities is considered as a tunnel barrier. With increasing temperature, because of the increasing energy of the electr ons, the effective scattering cross section of the impurities will decrease, and the probabi lity for the electrons to tunnel trough the dressed impurity potential will increase. Th ese will lead to an increasing relaxation time (hence 0 ) with increasing temperature. The temperature dependence of conductivity along the field direction, LL zz, coincides with that of 0 With increasing conductivity along the field direct ion with increasing temperat ure, the con ductivity along the plane perpendicular to the field will decrease with increasing temperature: 1 ~LL xx. Since there is also classical magnetoresist ance in the x-y plane, the field induced

PAGE 50

38 Luttinger liquid behavior is a secondary correction to the semi-classical magnetotransport behavior: LL xx xx xx ) 0 (. Figure 3-9. Model of the field induced Luttinge r liquid with dressed impurity scattering. The model of the field induced Luttinger liquid with impurity scattering predicts that the correction of the conductance has power law temperature dependence, with magnetic field dependent powers: 15 ) (~ ~B LL zzzzT (along the field direction), (3-6a) ) (~ / 1 ~B LL xxxxT ( perpendicular to the field). (3-6b) A most important prediction from the model is the field dependent power factor. To check the field dependence of the experimental data, we plot scaled in-band conductivity c pz Friedel oscillations impurity

PAGE 51

39 o as function of temperature in different high magnetic field above the UQL. The conductivities are normalized at the lowest temperature point: Figure 3-10. Scaled in-band c onductivity as a function of te mperature in magnetic fields above the UQL indicated in the legend. It can be seen from the Figure 3-10 that for field well above the UQL, the scaled conductivities overlap perfectly. This indica tes that the magnetic field dependence and the temperature dependence of the conductivity can be separated: ) ( ) (0T G B F This is obviously contrary to the prediction from the magnetic field induced Luttinger liquid theory, in which the power factor of th e power law temperature dependence itself depends on the magnetic field. Another possible model is the phonon deloca lization (dephasing) model. In this model, the electrons are delocalized by phonon scattering. Hence with increasing

PAGE 52

40 temperature, the conductivity along the magne tic field increases, while the conductivity perpendicular to the magnetic field decr eases. The phonon delocalization mechanism predicts the same trend of the temp erature dependence of the conductance:16 zzTDP zz ~ ~ (along the field direction), (3-7a) xxTDP xx ~ / 1 ~ (perpendicular to the field). (3-7b) The phonon delocalization mechanism differs from the field induced Luttinger liquid by an exponent which is now independent of the ma gnetic field. So the phonon delocalization mechanism agrees better with the experimental data. However, as far as we know, there is no complete theory for phonon de localization, and ther e is no theoretical prediction of the values of the power factors. Further wo rk needs to be done to quantitatively understand the transport beha vior of graphite in the UQL region.

PAGE 53

41 CHAPTER 4 TUNNELING INTO BULK BISMUTH IN THE ULTRA-QUANTUM FIELD 4.1 Motivation In the previous chapters, we have disc ussed the magneto-trans port properties of semimetal graphite. Graphite is a relatively simple system for transport study in a sense that, in its hexagonal Brillouin zone, the Fermi surface comprises six cigar shaped pockets with their long axis parallel to the c axis. Transport in gr aphite is roughly 2-D due to the weak coupling between the graphene layers and large rati o of out-of-plane and in-plane effect mass. All these factors simplif y the transport study of graphite so that it can be treated as an isotropic 2-D system, in which only two major groups of carriers electrons and holes (each has one single mobility), need to be considered. Bismuth, on the other hand, is much more complicated. In the Brillouin zone of bismuth, there are 3 electron pockets and 1 hole pocket (see Figure 5-1 in chapter 5). None of the pockets is parallel to any of the others, hence Bismuth is 3-D in all orientations. And in most of the orientations, every pocke t contributes carriers with different mobility. Hence in bismuth, one need s to consider up to 4 majority bands, each with different effective mass and different mobility. This makes the magneto-transport study of bismuth very complicated. Rather than studying transport, we studi ed the magneto-tunneling properties of bismuth in strong magnetic fields. The origin al intent of our work was to study the possible high magnetic field induced 1-D (Luttinger Li quid) behavior. The tunnel junctions used in the study comp rise metal-insulator-semimetal trilayer structure. In zero

PAGE 54

42 field, we are simply tunneli ng from a 3-D metal into a 3D semimetal. Tunneling theory predicts that the measured differential conductance has a very weak dependence on the density of states of any of the electrodes and depends mainly on the properties of the tunnel barrier. When a strong magnetic field is applied, the energy levels in the semimetal separate into different Landa u bands. When the magnetic field is strong enough so that all the electrons in the semimetal are in the lo west Landau level, the semimetal enters the ultra-quantum regime, and the tunneling is between a 3-D Fermi liquid in the normal metal and Landau tubes in the semimetal. In this regime, the semimetal has an essentially 1D character with 1D Landau tubes aligned along the magnetic field and perpendicular to the tunnel junction area. For 1-D systems, one can no-longer desc ribe the physics using the Fermi liquid theory, because of the strong perturbation of Coulomb interaction due to the lack of screening and phase space for scattering. Inst ead the 1-D system will be described by the Luttinger liquid theory. The tunneling experime nt provides an opportunity to discover the enhanced density of states predic ted by the Luttinger liquid theory. When tunneling into a 1-D system, the tunneli ng theory predicts that the measured differential conductance across the junction has strong dependence on the density of states in the 1-D electrode. The propo sed magnetic field induced Luttinger Liquid theory15 states that: for magnetic field induced LL connected to 3D reservoirs by tunnel barriers: dI/dV Ta(B) (when e V << kBT ), (4-1a) dI/dV Va(B) (when e V >> kBT ). (4-1b)

PAGE 55

43 The reason that a semimetal is used as the electrode of interest is that, the magnetic field for the semimetals to reach the ultraquantum limit is relatively obtainable. For example, ~10 Tesla is needed to drive bism uth into the ultra-quant um regime. For most metals however, the magnetic field needed will be >104 Tesla, because of their high Fermi energies and large cyclotron masses. 4.2 Experimental Tunnel junctions are made on freshly cleaved bismuth crystals. A big piece of precut bismuth crystal is dropped into liquid nitrogen bath. After the bismuth crystal equilibrates with the liquid nitrogen, a Razor blade was us ed to cleave the crystal and expose a fresh and smooth surface of the tr igonal plane. The piece of cleaved bismuth with smooth surface was then taken out of th e liquid nitrogen bath and warmed up in pure nitrogen gas flow. Through this way, the cl eaved surface will maintain its freshness and there will be no condensation on th e surface when it is warming up. On the surface of bismuth, we have 2 me thods for making tunnel junctions. Figure 4-1 shows the procedure usi ng photolithography to make tunne l junction on top of the semimetal surface. First of all, we define an undercut photore sist pattern on top of the junction area we choose. Then a thick layer of AlOx was RF sputte r deposited onto the sample as separation layer. This layer pr events shorting outside the tunneling area resulting from the surface roughness, and from the force of the contact leads. Then we performed lift-off and opened up the tunneling area. Then we deposit the tunnel barrier, followed by the counter-electrode, through shad ow masks. Finally we pasted gold wire on top of the counter-electrode above the separation layer.

PAGE 56

44 Figure 4-1. Procedure for making tunne l junctions on bulk semimetal using photolithography technique.

PAGE 57

45 This method using photolithography is conve nient for defining the junction area. Using the precise alignment function of the phot omask aligner, it is easy to find the ideal smooth junction area and place the photoresist pattern on top of it. The shortcoming of this method is that after liftoff, there is always some residue of photoresist left on the surface. The residue can be mostly clean ed by prolonged treatment with UV ozone cleaner (~40 minutes). But the cleaning process can cause unwanted oxidation. Figure 4-2 shows another way we used to make junctions on the surface of semimetals. This is what we called mica mask method. Essentially it is a shadow mask method used in RF sputtering. Through conve ntional shadow masks, sputtering fails to yield sharp edges due to the high Ar pressure during the deposition. Here in the mica mask method, an extremely thin mica foil is pl aced on top of the semimetal. The sheet of mica will attach itself by Van der waals for ce to the semimetals surface. We can also attach another layer of mica on top of it to get an undercut. Then we RF sputter thick AlOx film as a separation layer. After rem oving the mica foils, we get a very sharp edge of the AlOx film, due to the intimate contac t of the mica mask to the semimetal surface. Then we deposit the tunneling barrier and th e counter-electrode, a nd finally put on the gold wires as measurement leads. The mica mask method, without using a ny lithography technique, is fast and convenient. Also, there is no contamination from the resi st polymers to the junction surface. The shortcoming of the mica mask method is that, w ithout lithography and precise alignment, it is relatively ha rd to obtain well de fined tunneling area. Figure 4-3 shows the microscope picture of a tunnel junction made on the surface of bulk bismuth.

PAGE 58

46 Figure 4-2. Procedure for making tunnel j unctions on bulk semimetal using mica mask method. Figure 4-3. Microscopic picture of a Bi(bulk)-A lOx-Pb tunnel junction.

PAGE 59

47 Measurements of the tunnel junctions are ca rried out in a He3 refrigerator with an 18 Tesla superconducting magnet in the Natio nal High Magnetic Field Labs (NHMFL). Differential conductance,dV dI /, is measured using a double lock-in amplifier technique, in which one lock-in amplifier is used together with a feedback circuit to keep the small AC (500Hz) excitation voltage, dV across the tunnel junction constant, while the other lock-in amplifier measures the AC voltage respon se of a standard resistor in series with the junction, from which dI can be calculated. A slow DC ramping signal is summed with the AC excitation voltage to apply the bi as voltage across the tunnel junction. 4.3 Results and discussion Figure 4-4 shows the magneto-tunneling re sult for a Bi(bulk)-AlOx-Pb tunnel junction made through mica mask method. Th e figure shows the differential tunneling conductance vs. bias voltage in different magnetic fields. The inset shows the Pb superconducting gap, from which we can s ee that the junction has low leakage and reasonable good quality. The differential conductance vs. bias vo ltage sweep shows an asymmetric V shaped background, resulting from the asymmetry in the energy dependence of the density of states in bismuth. On top of the background there are small features of oscillations. The oscillati ons, which are most pronounced in the -20 to 20 mV range, show no obvious magnetic field depe ndence and are characterized by 2nd derivative conductance 2 2d V I d to be mostly symmetric with the bias voltage. Hence they do not likely correspond to the density of states features in bismuth, but ratherto phonon excitations.

PAGE 60

48 Figure 4-4. Differential conducta nce as a function of bias voltage in indicated strong magnetic fields at 300mk. Inset: Pb superconducting gap feature in zero magnetic field at 300mK. Figure 4-5. Differential conducta nce at low bias voltage in the magnetic fields indicated in the legend. -80-60-40-20020406080 400 600 2T 4T 8T 14TdI/dV (Arb. unit)V (mV) -4-2024 0 1 2 dI/dV (Arb. unit)V (mV)-3-2-1012 3 2T 4T 8T 14TdI/dV (Arb. unit)V (mV)

PAGE 61

49 Figure 4-5 shows the differential conductan ce at near zero bias voltage. In zero magnetic field, the differential conductance s hows a peak at zero bias. As the magnetic field increases, the peak at zero bias sepa rates into two peaks, which move towards higher bias voltages and leaves a valley at zero bias. The change of dI/dV with magnetic field appears to be as if the field opens up a gap at the Fermi level. The feature observed at low bias voltages can be expl ained by considering the Zeeman splitting of the spins. Since Tesla eVB/ 10 8 5 ~5, the g factor corresponds to our experimentally observed splitting (e.g., ~1 .6mV at 14 Tesla) is ~2. Another possible mechanism for the low bias voltage feature is the field induced Luttinger liquid behavior. In this picture, the strong magnetic field opens up a Coulomb gap at the Fermi energy. The Luttinger liquid behavior enhances the density of states in the gap. Detailed analysis requires knowledge of the classical background of the differential conductance. Tilting of magnetic field is required to tell if the zero bias feature is a spin effect or an orbital effect. Except for the features at bias voltage mV V 3 a major feature of the differential conductance show in Figure 4-4 is the lack of field dependence. The curves we took at 2, 4, 8 and 14 tesla overlap almost perfectly. Th is result contradicts the prediction from the field induced Luttinger liquid theory, in which the magnetic field dependence enters the power factors of the power law dependence. There are also some concerns about our measurements. For example, the surface stat es in bismuth might prevent the tunneling measurements from probing the intrinsi c properties of bismuth single crystal.

PAGE 62

50 CHAPTER 5 ACHIEVING LARGE MAGNETORESISTANCE IN BISMUTH THIN FILMS 5.1 Introduction Semimetal bismuth has been interest of study for many years, because of it many special properties. Figure 5-1 shows the Fermi surface a nd the brillouin zone of rombohedral bismuth. The highly anisotropic Fermi surface consists of tiny hole pockets and electron pockets, which occupy only a fe w thousandth of the volume of the Brillouin zone. Hence bismuth has very low carrier density (~1023 m-3) and low Fermi energy (~25meV). Also because of the small Fe rmi momentum, the chance of phonon scattering is very low. Hence bismuth has an ex tremely long phonon mean free path at low temperatures (~mm at 4.2K). Figure 5-1. Fermi surface and Brillo uin zone of rom bohedral bismuth

PAGE 63

51 These unusual properties of bulk single cr ystal bismuth give rise to a huge magnetoresistance.17-19 Figure 5-2(a) shows the magne tic field dependence of the resistivity at 5K for single crystal (99.9995% pure) bulk bism uth. At the 7 Tesla, the resistivity is 6 orders of ma gnitude higher than the zero fiel d resistivity. Figure 5-2 (b) shows the temperature dependence of resist ivity in zero magnetic field. Bulk single crystal bismuth is metallic, with resistivity decreasing with decreasing temperature. Figure 5-2. (a): Magnetic fiel d dependence of the reisistivity at 5K for bulk single crystal bismuth; (b) resistivity as function of temperature in zero magnetic field. The extremely large magneto-resistance ma kes bismuth a promising candidate for applications, such as magnetic field sensors. Many efforts have been carried out in order to make bismuth thin films that have quality comparable to the bulk material.20-22 However, it was found that bismuth thin films made by normal technique, such as thermal evaporation, yield bismuth film s with very small magnetoresistance.23, 24 These 050100150200250300 0.0 2.0x10-74.0x10-76.0x10-78.0x10-7 Resistivity ( m)T (K) -8-6-4-202468 0.000 0.005 0.010 0.015 R es i s ti v it y ( m ) B (T)

PAGE 64

52 films may even behave in a non-metallic manner with the resist ance increasing with decreasing temperature. Figure 5-3. (a): Magnetic fiel d dependence of the reisistivity at 5K for a 1.5um bismuth film thermally evaporated onto glass subs trate; (b) resistiv ity as function of temperature in zero magnetic field. Figure 5-3 shows the typical transport behavior of thermally evaporated bismuth thin films on glass substrates (thickness between 800~10000A). The resistance generally increases with decreasing temperature. And th e magnetoresistance at low temperatures is much lower (MR(7T)<10) than that of the bulk bismuth (MR(7T)~105). The major reason for the differences betw een bulk single crystal bismuth and the bismuth films is the small grain size in the films. The gains, generally with size of ~1000A, are actually not small co mpare to that of normal metals. However, bismuth has a very long phonon mean free path, due to th e small Fermi momentum. Application of the Matthiessens rule shows that the scattering in the films is dominated by temperature independent gain boundary scatte ring (except when the temperature is very high, e.g. higher than room temperature, and the phonon m ean free path is shorter than the grain -8-6-4-202468 1x10-52x10-53x10-54x10-5 R es i s ti v it y ( m ) B (T)0100200300 3x10-66x10-69x10-61x10-5 Resistivity ( m)T (K )

PAGE 65

53 size). The temperature dependence of the resis tivity is mainly from that of the carrier concentration, which, due to the small Ferm i energy of bismuth, decreases significantly as the temperature drops. Magnetoresistance in bismuth films is al so limited by grain boundary scattering. This can be illustrated from a simplified 2-band model, in which the electrons and holes are compensated, and the resistivity in the magnetic field simply goes like: 2 2 2 2) ( ~ ) 0 ( ~ ) 0 ( ) 0 ( ) ( c HH R H (5.1) Hence the small relaxation time due to gr ain boundaries scatte ring leads to small magnetoresistance. To make high quality bismuth thin films, it is necessary to make the grain sizes large. A judicious combination of lattice-matc hed substrates and caref ully regulated postdeposition thermal annealing provides a strate gy for growing bismut h films with large grains. In early work on bismuth films thermally deposited onto mica substrates,23 it was found that post deposition annealing close to the bismuth melting temperature caused the helium temperature resistance to decrease by a factor of 15 when compared with unannealed films. In addition, MR for fiel ds perpendicular to the film surface is significantly improved with a nnealing. Epitaxial films of bismuth having a trigonal orientation have been grown on BaF2(111) (3.6% lattice mismatch)25 and CdTe(111) (0.7% lattice mismatch). 22 In the latter case, post-deposi tion annealing at 3 C below the melting temperature of Bi lead to significant increases in the MR. An alternative approach, which has been found to give large MR in Bi films 1-20 m thick, is the technique of electro-chemi cal deposition from aqueous solutions of Bi(NO3)3 5H2O .20, 21 An underlying Au layer, patterned onto a silicon substrate, serves as

PAGE 66

54 the working electrode for the electrodeposition. As is the case for vacuum-deposited Bi films, 22, 23 post-deposition annealing of the electrodeposited films close to the melting temperature of Bi leads to a small resistivity and a large increase in MR (2.5 at room temperature and 3800 at 5K for the thickest 20um film in a perpendicular 5T magnetic field 20). For technological applications, elec trodeposition is economical and well suited for large-scale production. Similar advantag e would likewise hold fo r thermal deposition, provided ultrahigh vacuum and specialized gr oeth techniques, such as MBE, are not required. We studied the thermally deposited bismut h films on pre-deposite d gold thin films followed by post-annealing processes. We find that, upon annealing, the Au from the Au underlayer rapidly diffuses into th e bismuth, giving rise to a f ilm with large-crystal grains oriented with trigonal axis perpendicu lar to the plane of the film and having magnetotransport properties comparable to those grown by el ectro-depositions.20, 21 We show that improvements of MR are only for annealing temperature higher than the 241 C eutectic temperature of the BiAu so lid solution and below the 271 C melting temperature of Bi. This 30 C annealing window provides considerable latitude when compared to the narrow annealing window of a few C confirmed here and reported previously for pure Bi films.23 5.2 Experimental All of our samples are prepared by th ermally evaporating 99.999% pure Bi onto pre-cleaned glass substrates at 5E-7 torr base pressure. In the cases where heated substrates are needed, the substrates are glued onto a variac controlled heater with silver paste. Then the shadow mask is glued onto th e substrates using the same silver paste.

PAGE 67

55 Substrate temperature is read from a thermometer, and is manually controlled by adjusting the output vo ltage of the variac. Three categories of samples are prepared: (I) two pure bismuth films (1 um thick) grown at 150 C, followed by annealing at 265C and 270 C for 6 hours; (II) three bismuth films (1 um thick) grown simultaneous ly on pre-deposited gold films (350 ) at 150 C, followed by annealing at 238 C, 243C and 251 C, respectively for 6 hours; (III) bismuth films (1 um) grown on pre-deposited gold films (350) at room temperature, followed by annealing at 251 C for 6 hours. A nnealing is performed in a quartz vacuum tube furnace with temperature calibrated with respect to the observed melting of a small bismuth crystal placed in close proximity to the samples. Measurements of resistance vs. temperature at different magnetic fields are carried out in a Quantum Design Physical Property Me asurement System (PPMS). In all of the measurements, the magnetic field is applied perpendicular to the film. 5.3 Results and Discussion We characterized the crystal structure of the Bi/Au films by X-ray diffraction. Figure 5-4 shows the X-ray diffraction pattern of bismuth (00l) planes. The sharp lines indicate that the film is well c-axis oriented. The inset of Figure 5-4 shows a schematic of the relevant portion of th e Bi(Au) phase diagram.26 A small amount of gold in Bismuth reduces the melting point, and the lowest melti ng temperature, the eutectic temperature, occurs at 241 C for the Bi.868Au.132 compostion. In our experiment, the mass ratio of the Bi and Au is controlled by the thickness of the 2 films. Thus a pre-deposited 360--thick Au layer mixed by annealing into a 1-um-thi ck Bi film represents a solid solution (vertical dashed line) with stoichiometry Bi0.93Au0.07. All of the Bi/Au films here are at this composition.

PAGE 68

56 Figure 5-4. X-ray diffraction pa ttern for a 4-um-thick Bi/A u film grown at 150 C and annealed at 251C. Inset: the relevant portion of the Bi/Au phase diagram and corresponding annealing temp eratures (indicated by the crosses) for Bi and Bi/Au films discussed in this chapter. Figure 5-5 shows the resistance vs. temp erature at 0 and 5 Tesla for the two category-I pure bismuth films (no Au unde rlayer) annealed at 265 C and 270 C, respectively. We note that a small difference of annealing temperature at close to the 271 C melting point of bismuth produces a drastic change of the properties of the films. The film annealed at 270 C just starts to melt a nd is recrystalized during the slow cool-down. As observed through the quartz tube, the film develops a shiny surface just below the melting temperature, but at higher temperat ure begins to fully melt and ball up. The positive slope in the resistance-temperature cu rve in zero magnetic field indicates that the film is metallic. Also, at 5T, the MR=286 at 5K indicates the good quality of the film. 020406080100120 0 1000 2000 3000 4000 5000 Intensity2*theta Bi_Au (00l)

PAGE 69

57 Figure 5-5. Temperature dependence of the resi stivity at 0 and 5T for two category-I Bi films In contrast, the film annealed at 265 C does not change its appearance during the annealing process. The resistance of this f ilm shows a characteristic minimum at near 200K 23 and then increases as the temperature is further lowered. In addition, the MR of this film is much smaller than the on e annealed at 270 C through out the whole temperature range. These results are in accord with previous studies,22, 23 which have shown that post-annealing at melting point fo llowed by re-crystallization is an effective way to get high quality bismuth films. Howeve r, the temperature control must be accurate to a few C and must not be allowed to go above the melting point where there will be a loss of film adhesion leading to agglomer ation and discontinu ity between grains. 050100150200250300 1 10 100 B B A A B = 0T B = 5TSheet Resistance ()Temperature (K) A) TG = 20C, TA = 265C B) TG = 20C, TA = 270C

PAGE 70

58 Figure 5-6. Temperature dependence of the resi stivity at 0 and 5T for three category-II films grown simultaneously on 150 C substrates and them annealed separately at respective temp eratures of 238, 243 and 251 C. For samples in category-II, the presence of a gold underlayer l eads to completely different behavior. Figure 5-6 shows the effect of annealing temperature on the quality of these films. The three Bi(1um)-Au(350) films are grown at 150 C, and then annealed at 238 C, 243C and 251C respectively, as indicat ed by the crosses in the Fig.5-4 inset. Prior to each post-deposition anneal, a gol d color can be observed from the back side of each glass substrate. Afer 243 C a nd 251 C anneal, the gold color is gone and the underside of each Bi/Au film is silver color and indistinguishable from the underside of a pure Bi film. These color changes indicate th at during the annealing, the gold atoms no longer remain segregated beneath the bismuth film but diffuse into the bismuth. For an annealing temperature of 238 C, which is belo w the eutectic temperature of 241 C, all of the film remains in the solid form, and th e surface texture of the film does not change 0100200300 1 10 100 B = 0T B = 5T C C B B A A A) TG = 150C, TA = 238C B) TG = 150C, TA = 243C C) TG = 150C, TA = 251CSheet Resistance ()Temperature (K)

PAGE 71

59 during the anneal. In addition, the temperat ure dependent resistance is nonmetallic and the 5K MR is low (MR=37). In contrast for the two anneals above the eutectic temperature, the films undergo a definite cha nge in appearance in which they become shiny and remain metallic after cooldown, th e temperature-dependant resistance becomes progressively more metallic, and both f ilms exhibit significantly larger MR. MR(5K)=130 for the 243 C anneal and MR (5K)=327 for the 251 C anneal. We note that the MR of our 251 C a nnealed Bi/Au film is highe r than the MR(5K)=250 of a comparable 1-um-thick single-crys tal film grown by electrodeposition.20, 21 Further increase of the annealing temperature to s lightly above 160 C but well below the 271 C Bi melting temperature leads to sever melti ng and loss of electrical connectivity, as would be expected from the in tersection of the vert ical dashed line with the solid/liquid phase boundary shown in the Figure 5-4 inset. The plots in Figure 5-7 for the category -III films show the effect of growth temperature on transport properties for the sa me anneal conditions. The film grown at 150 C shows metallic temperature dependen ce at zero field and has MR(5K)=327. The film grown at room temperature however, shows rather complicated temperatureresistance dependence. The resistance drops a little bit as the te mperature sweep from 300K to about 200K, then increase a lot fr om 200K to 5K. The resistance-temperature curve suggests that the film has grain sizes comparable to phonon mean free path at 200~300K. At low temperatures, the grain boundary scattering dominates and the resistance increases due to decrease of ca rrier concentration. The magnetoresistance of the room temperature grown film, MR(5K) = 34, is also significantly lower than the film grown at 150 C. For pure Bi films grown on CdTe substrates, growth temperature in the

PAGE 72

60 range of 80 C to 220 C are requi red to obtain epitaxial behavior.22 For our Bi/Au films, the higher growth temperature promotes the grow th of larger grains, thus facilitating the effectiveness of the annealing procedure by star ting with larger grains We also note, as show by x-ray diffraction pattern in Figure 54 for a 4-um-thick Bi/Au film grown at 150 C and annealed at 251 C, that the anneal ed films exhibit a pronounced single-crystal orientation with trigonal axis oriented perpendicular to the film plane. Similar behavior has been noted for annealed electrodposited films. Figure 5-7. Temperature dependence of the re sistivity at 0 and 5T for two category-III films Optical microscopy verifies a smoother t opography and larger grain size (1-10um) for the films annealed at high temperature and exhibiting a large MR. This result is consistent with the aforementioned conclusions that large grain size achieved either by epitaxy and/or annealing is a pr erequisite for large MR. The primary factors that affect 0100200300 1 10 100 B = 5T B = 0T B B A ASheet Resistance ()Temperature (K) A) TG = 150C, TA = 252C B) TG = 20C, TA = 252C

PAGE 73

61 the quality of Bi/Au films are the growth te mperature and the annealing temperature. A moderate growth temperature (~150 C) encour ages the formation of large grains, but should not be so high as to cause the film to agglomerate and to become discontinuous. Table 5-1. Summary of re sults for different bismuth film growth conditions Sample Growth temperature Annealing temperature Metallic MR (5K : 300K) 265 C N 39 : 3 Pure Bi 150 C 270 C Y 283 : 4 Room temp. 251 C N 34 : 3 238 C N 37 : 3 243 C N 130 : 3 Bi (1um)Au(350) 150 C 251 C Y 327 : 3 We summarize our results in Table 1.The e ffect of the diffusion of the Au into Bi during the post-deposition annealing proce ss can be qualitatively understood by referring to the phase diagram depicted in the Figure 5-4 inset. If equ ilibrium is assumed, then for isothermal (tie line) drawn at a given anneal ing temperature, applic ation of the lever rule for binary phase diagram will determine a gold-rich melted phase and a bismuthrich solid (unmelted) phase. It is the presen ce of this melted phase that facilitates grain boundary migration and grain growth resulting in the high MR that we have observed. We suspect that this melted phase is most likely associated with grain boundaries although detail microcompositional analysis w ould be necessary to verify such a scenario. In oversimplified terms, the Au can be t hought as a lubricant that facilitates the growth of large grains during the post-depos ition anneal. However, one should not forget that Au is a impurity that gives rise to in creased carrier scattering and associated lower MR, thereby preventing the MR from appro aching the hig values reported in single crystals.17, 19 Accordingly, the use of annealed Bi/A u bilayers to obtain large MR requires

PAGE 74

62 judicious balance between using enough gold to assure large grain growth, but not using too much gold that additional scattering co mpromises that MR. We believe that these considerations also apply to the Bi/Au films deposited by electrodeposition technique reported previously by Yang et al. 20, 21

PAGE 75

63 CHAPTER 6 METALLIC SURFACE STATES IN ULTRA-THIN BISMUTH FILMS 6.1 Introduction: Physics of th e Ultra-Thin Bismuth Films Bismuth, like many other semimetals, has a very long electron wavelength, due to its low Fermi energy (~25 meV) and small effective mass (~0.005me). One can estimate the wavelength to be: 2 *10 ~ 2 ~f eE m h When the size of sample is comparable or smaller than this length scale, one will need to consider the effect of the sample boundary on the band structure. This is where the so-c alled quantum size effect become important. Bismuth provides great convenience in studying the quantum size effect in many aspects. Ultra thin bismuth films, with their thicknesses comparable to the electron wave length (~ 300 ), have been of great interest in the study of the qua ntum size effect and semimetal-semiconductor transition. Ogrin, Lutski, and Elinson, in their study of the magnetotransport of the bismuth thin films in 1965,27 produced the first clear experimental evidence for quantum size effect in any solids. Oscillat ory behaviors in both resistivity and Hall coefficient were observed with decreasing film thickness, due to the quasi-2D sub-bands passing across the Fermi le vel. Since then, quantum size effect in bismuth thin films has been intensively studied both theoretically and experimentally.28-34 The existence of the thickness dependent quasi-2D sub-bands resulting from quantum confinement has been generally accepted. One important prediction as a result of the quantum size effect is the so-called semimetal-to-semiconductor (SMSC) transition The SMSC transition happens when the

PAGE 76

64 energy shift due to the quantum confinemen t becomes large enough so that the lowest electron sub-band rises above the top of the hi ghest hole sub-band, due to their difference band masses. The critical thickness of the thin film for the transition to happen, given by most of the theoretical calcul ation, is between 230 ~340 .28, 35, 36 Figure 6-1. Illustration of semimetal-to-semicinductor transition. Despite the numerous experimental investig ations carried out to look for the SMSC transition,27, 28, 31, 37-40 the existence of the SMSC tr ansition remains ambiguous. Chu and co-workers argued against the SMSC transi tion, and proposed theory that the boundary condition for the electron wave function is that the gradient of the wave function (rather than the wave function itself) vanish at the sample boundary. Hence the ground state electron and hole energies depend only weakly on the thickness of the films, and the conduction band and the valence band remains overlaped. The arguments against the SMSC transiti on mainly focused on the lack of sharp transitions in transport properties (resistivit y, Hall coefficient, magnetoresistance).

PAGE 77

65 Hoffman et al., in their work that stand for the SMSC transition, pointed out that the main reason for the absence of the sharp transition in the previous works is that people failed to take into account the effect of the surface carrier and surface conduc tivity, which may be important and even dominating when the bismuth films are very thin.39 The simple model that takes into account the surf ace carrier is that the surface ac ts like a high carrier density conductor in parallel with the bulk part of th e film, and the averaged carrier concentration is simply:d n n ns i/ where inand sn are bulk intrinsic carr ier density and surface sheet carrier density.38 When the film is thin, ns will dominate, and the effect of the surface conductivity has to be seriously considered. Further evidences of metallic surface states were found in a very different bismuth system. In 1991, B. Weitzel and H. Mickl itz discovered superconductivity in granular systems built from rhom bohedral Bi clusters.41 They explained their result as surface superconductivity due to the strongly increase d surface density of states and suggested photoelectron spectroscopic study on bismuth surfaces to further confirm their proposal. Angle resolved photoemission spectroscopy (A RPES) since then had been a major tool people used to probe th e surfaces of bismuth. The experiments were carried out by several groups.42-47 Consistent results were obtained, indicating the existence of metallic surface states in bismuth (111) and (110) surf aces. Christian R. Ast and Hartmut Horchst reported in 2001 a surface carrier density associ ated with the surface st ate of Bi (111) to have sheet densities of 2 1310 1 1 cm psfor holes and 2 1210 5 5 cm ns for electrons.47 In 2003, Gayone et. al reported their study on the temperature dependence of the surface states linewidth and the str ong energy dependence of the electron-phonon coupling strength on Bi (100) surface.48

PAGE 78

66 6.2 Transport Properties of th e Ultra-Thin Bismuth Films 6.2.1 Experimental Bismuth films are thermally evaporated from 99.9999% pure bulk bismuth in a high vacuum chamber of ~6E-7 torr at a rate of 1~2 /sec, through shadow masks. In the cases where in situ measurements are required, bismuth or gold contact pads are thermally evaporated through shadow masks. Then the substrate pre-deposited with contact pads is fixed onto a special designed sample holder, where the Hall-bar shadow mask is installed aligned with the contact pads, and the gold wires are attached to the contacts and connected to leads which enable electrical measurements from outside the vacuum chamber. Tunnel junctions on thin bismuth films we re made using standard cross stripe geometry. Mica is used as substrate and bismuth is used for base electrodes, so that lattice match between bismuth and mica can be achieved. AlOx is used for tunnel barriers. Lead is used for top electrodes, so that when th e samples are cooled down to below the lead superconducting temperature, the superconductin g gap can be used to characterize the quality of the junction. In making of a Bi-AlOxPb junction, a thin bismuth film stripe as base electrode is deposited onto mica substrate through a sha dow mask. The film is then taken out of the vacuum chamber, and the sh adow mask is removed. The film is then immediately put back into vacuum, and the aluminum oxide tunnel barrier (~ 10 ) is coated through thermal evaporation of aluminum in the oxygen pressure of 2E-5 torr, at a rate of about 1 /sec. A cross stripe of lead as counter electrode is then deposited through a shadow mask. Typical working j unction resistances are in the range of 10~10000

PAGE 79

67 6.2.2 Metallic Surface States In the study of the Bi/Au f ilms, the thicknesses of thes e films are in the order micrometers. Films with these thicknesses can be treated as bulk polycrystal bismuth, in a sense that theres no band structure change due to the quantum confinement, and the surface effect is not significant. When the (pure) bismuth films get really thin (e.g., thickness ~ Fermi wavelength), quantum size effect will take place, and the effect of the surface states needs to be seriously considered. Figure 6-2 shows the temperature depende nce of resistivity, for films with thicknesses indicated in the legend. 050100150200250300 5.0x10-66.0x10-67.0x10-68.0x10-69.0x10-61.0x10-5 (m)T (K)150310400 Figure 6-2. Resistivity vs. temperature for Bi film with indicated thicknesses. It can be seen from the figure that, for films with thickness ~400, the resistivity increases as the temperature drops, and r eaches a maximum at ~40K. As the film becomes thinner, the temperature for the resistivity maximum shifts higher. Also the

PAGE 80

68 resistivity in the low temper ature region (say, T <150K) decr eases with decreasing film thickness. For the films with thickness < 150 the resistivity drops monotonically from room temperature with decreasing temper ature, showing metallic behavior. The metallic behavior (positive R-T slope) can be explained by considering the existence of the metallic surface states. A simp lified model is to treat the whole film as two separate films in parallel: a very thin me tallic-like film on the surface with sheet resistance Rs and thickness ts and the intrins ic film underneath it with resistivity i and thickness st t. The measured resistivity for is then t t t Ri s s 1) ( 1 The resistivity of the bulk (i ntrinsic) part of the film,i has negative R-T slope. And when the film is thick, it has low re sistance and hence will dominate the total resistance of the film. When the film gets thin, the contribution of the metallic surface becomes increasingly important, and the R-T curve starts to show a maximum, which moves to higher and higher temperature with decreasing film thickness. Eventually, when the film thickness reaches 150A or thi nner, the surface states will dominate the temperature dependence and the R-T cu rve shows positive slope throughout the temperature range of measurements (4.5K~300K). The magneto-transport of ultra-thin bism uth films is studied under the framework of classical muti-band model, as described in the previous chapters. The classical magnetoresistance of the ultra thin bismut h film can be roughly estimated to be ~2) ( c. Here, the small thickness of the films leads to very short mean free path of grain boundary scattering, and hence a very small MR.

PAGE 81

69 -6-4-20246 0.000 0.005 0.010 0.015 0.020 MRB (T) 310180 Figure 6-3. Magnetoresistance vs. magnetic fiel d at 5K for two Bi films with indicated thicknesses. Figure 6-3 shows the MR of two bismuth films with thicknesses 180 and 310 It can be seen from the figure that the classical MR increases with the film thickness, due to the increasing grain size with the film thickne ss. The sharp dip at low fields can not be explained by classical theory, and is due to anti-localization, orig inating from the strong spin-orbit interaction in bismuth. The in-balance or non-compensa tion of the positive and nega tive carriers in the thin bismuth films is revealed by the field de pendence of the Hall resistivity. Figure 6-3 shows the field dependence of Hall resistivit y at indicated temperatures for 2 bismuth thin films, 180 and 400 thick. For both film s, the measured Hall resistivities are not linear with the magnetic field. Also the zero field slope of the Hall resistivity has strong temperature dependence. For the 180 film, the low field xy vs. field curve even changes sign from 5K to 150K.

PAGE 82

70 02468 -4x10-8-2x10-80 2x10-84x10-86x10-88x10-8 xy (m)B (T)150K 75K 5K 02468 0 2x10-74x10-76x10-7 150K 75Kxy (m)B (T)5K Figure 6-4. Hall Resistivity vs magnetic field at indicated temperatures for (a) 180 and (b) 400 Bi films The Hall resistivity xy observed can be qualitati vely understood through the simple 2-band model expression, (b) 400 (a) 180

PAGE 83

71 2 2 2 1 2 2 1 2 1 2 2 2 1 3 2 1 2 1) ( ) ( B R R B R R B R R R Rxy (6-1) We can see that, for a 2-band system with electron band and hole band, the Hall resistivity is in general not linear with the ma gnetic field. Also the Hall resistivity itself does not give enough information about the in-b and carrier concentration of each band. From Equation 6-1, we get the low field a nd high field limit of the Hall resistivity: 2 2 1 2 1 2 2 2 1) ( ) ( ) 0 ( B R R Hxy (6-2a) 2 1 2 1) ( R R B R R Hxy (6-2b) Hence the zero field Hall resistance slope by itself does not give any information on the carrier density of the films. In fact it does not even give the information about whether the film is n-type or p-type, due to the complication from the in-band resistivity (or mobility). However, the high-field limit of the Hall resistance does indicate the carrier type of the film (or, the sign of 2 1R R ). The change of slope (even the sign of the slope) from low field to high field gives rise to the curvature observed in the Hall resistivity measurement. One can see from the xy vs. field curves that, even though the low field data shows strong temperature dependence (e ven change of sign), the sign of the extrapolated high field limit of the Hall resi stivity slope is temperature and thickness independent, indicating the type of the films, n-type in this case, does not change with temperature, nor the film thickness. A more detailed analys is of the Hall resistivity data yields information about the un-balance of the carriers, defi ned by the compensation factor: h e h en n n n And the

PAGE 84

72 thickness and temperature depe ndence of the Hall resistivity can be qualitatively understood by considering the change of compen sation factor (due to the n-type surface states) with temperature and thickness. To simulate the field dependence of the Hall resistivity, we adopt a 4-band model, with a bulk electron band, a bulk hole band, a surface electron band, and a surface hole band. Figure 6-5 shows the simulation results for the magnetic field dependence of the Ha ll resistivity for 180 thick and 400 thick bismuth films. In the simulation, we assume that the mobility of the carriers does not change with temperature, due to the fact that the grain boundary scattering dominates over phonon scattering. Because of the compli cation of the energy band quantization due to the quantum size effect, we can not calcula te in detail the temperature dependence of the carrier density. In the simulation, we assume different values of carrier density for the bulk part of the films, and assume the sheet surface carrier density to be temperature and thickness independent. The parameters used in the simulations are listed below: Table 6-1. Parameters for the simulating th e effect of thickness and temperature on the magnetic field dependence of the Hall resistivity in ultra-thin Bi films Surface (10) In the film Carrier density ns (m-2) Mobility s (1 1 2 s V m) Carrier density ni (m-3) Mobility s (1 1 2 s V m) e1710 2 03 01 ) 10 5 (23 a 0.119 400 h1710 4 1 0.036 ) 10 5 (23 a 0.138 e1710 2 03 01 ) 10 5 (23 a 0.056 180 h1710 4 1 0.036 ) 10 5 (23 a 0.063 Note from the listed parameters that: 1) the surface sheet carrier density and mobility are the same for both films; 2) in bulk (intrinsic ) part of the films, the carrier density of electrons is equal to that of the holes; 3) since we cannot ca lculate the carrier density in the films, we modulate its number by adjusting the parameter a

PAGE 85

73 012345678 -6x10-8-4x10-8-2x10-80 2x10-8 a=1.5 a=0.8 a=0.3Hall Resistivity ( m)B ( T ) a=0.01 012345678 -1x10-70 1x10-72x10-73x10-7 Hall Resistivity ( m)B (T)a=1.5 a=0.8 a=0.3 a=0.01 Figure 6-5. Simulated Hall Resistivity vs. magne tic field at indicated temperatures for (a) 180 and (b) 400 Bi films, with fitti ng parameters described in the text. (a) 180 (b) 400

PAGE 86

74 Comparing the calculated magnetic field de pendence of the Hall resistivity with the data, we see that the simulations yield the major features in the experimental results. From the simulations, we get the physical picture about the carriers in the ultra-thin films. The bulk part of the film is compensated, like in bulk bismuth. The surface of the film, however, has a high sheet carrier density and is uncompensated. As the film gets thinner, or the temperature gets lower, the number of compensated carriers in the bulk part of the film decreases. Hence the degree of un-compen sation, due to the existence of the uncompensated surface carrier, will increase. 6.3 Control of the Surface States All the bismuth films discussed in the prev ious section are measured after removal from the vacuum chamber. Even though the oxi dation of bismuth at room temperature is insignificant, we will still need to consider the effect of oxygen on the surface of the film. For comparison, we have carried out in-situ measurements on bismuth thin films. A thin bismuth film is deposited onto a mica s ubstrate pre-deposited with contact pads, and measured without breaking vacuum. The substr ate is mounted on a cold stage and cooled down from room temperature to ~100K, and th e resistance vs. temperature is recorded. The sample is then warmed up to room temperature, and a small amount of oxygen is introduced into the chamber for 10 minutes. The chamber is then evacuated, and the sample is cooled down again to 100 K, w ith resistance vs. temperature recorded. The in-situ measurement of freshly deposited bi smuth films shows that for ultrathin bismuth films measured in vacuum, the resistance increases with decreasing temperature. What is different for the ultrathin bismuth films from the thicker bismuth films (~um) is that, the ratio of the resistance in crease, say, R(100K)/R(300K), is much smaller in the ultra-thin bismuth films (<10% ) than in the thicker films (~200%). Hence

PAGE 87

75 the existence of the metallic surface states is intrinsic, wh ile the sheet carrier density originated from the surface states is ve ry sensitive to the surface condition. We have seen that oxygen has a significant effect on the surface states. To study the surface terminated ultra-thin bismuth film, we coated the bismuth f ilms with Ge. Ge is known to be a material that, when deposited as thin films, creates dangling bounds and nucleation sites. When thin metals films are deposited onto predeposited atomically smooth Ge thin films, the metal film grow th nucleates at the Ge dangling bounds. Thus the metal films tend to be very smooth. Here we deposit a few monolayers to Ge ri ght after the deposition of bismuth thin film, without breaking vacuum. The idea is that the dangling bounds of the Ge film may bind with the surface states in the bismuth f ilm, and terminate the surface of the bismuth film from being affected by the air. Figure 6-6. Temperature dependence of re sistivity for Bi(100) and Bi(100)/Ge. Figure 6-6 shows the resistance vs. temper ature curves of two 100 thick bismuth films simultaneously grown and measured. Th e only difference betw een the 2 films is 050100150200250300 1.2x1031.3x1031.4x103 Bi (100) Bi (100)/Ge (8)Resistance ( )T(K)

PAGE 88

76 that, one sample is coated with a few angstrom of Ge in situ right after the deposition of bismuth film. The two samples show comple tely different temperature dependence of resistance. The bare bismuth film shows pos itive resistance-temperature slope, while Ge coated film shows negative resistance-temperature slope. We also coated the bare bismuth film with Ge after its taken out of vacuum. No significant change of transport behavior was observed. We conclude that the change happens at the Bi-Ge interface, rather than in the Ge film itself. The Hall resistivity measurements provide more information on the in-balance of the carriers. From Figure 6-7, we can read ily see the big differe nces in the carrier distribution between the bare and the Ge co ated bismuth films. Comparison with Figure 6-4 reveals that the magnetic field dependen ce of the Hall resistivity for the bare 100 Bi film at 75K, 150K and 250K resembles that of the bare 180 Bi film at 5K, 75K and 150K. And the magnetic field dependence of the Hall resistivity for the Ge coated 100 Bi film at 75K, 150K and 250K resembles that of the bare 400 Bi film at 5K, 75K and 150K (the smaller curvature here is due to th e smaller mobility in the thinner films). This comparison suggests that the Ge coated Bi film has better compensation than the bare Bi film with the same thickness. Simulations results with a 4-band model de scribed earlier are s hown in Figure 6-8, with fitting parameters listed in table 6-2. Note from the listed parameters that: 1) the effect of the surface carrier is adjusted by sett ing the thickness of the surface layer; 2) in bulk (intrinsic) part of the film s, the carrier density of electrons is equal to that of the holes; 3) The carrier density of the bulk (i ntrinsic) part of the film is modulated by adjusting parameter a.

PAGE 89

77 012345678 -2x10-8-1x10-80 1x10-82x10-83x10-8 250K 150KHall Resistivity ( m)B (T)75K 012345678 0.0 5.0x10-81.0x10-71.5x10-7 250K 150K 75KHall Resistivity ( m)B (T) Figure 6-7. Hall Resistivity vs. magnetic field at indicated te mperatures for (a) Bi(100) and (b) Bi(100)/Ge films. (a) (b)

PAGE 90

78 012345678 -2x10-8-1x10-80 1x10-8 Hall Resistivity ( m)B (T)a=4.0 a=1.5 a=0.8 012345678 0 5x10-81x10-72x10-7 a=4.0 a=1.5Hall Resistivity ( m)B (T)a=0.8 Figure 6-8. Simulated Hall Resistivity vs. magne tic field at indicated temperatures for (a) Bi(100) and (b) Bi(100)/G e films, with parameters described in the text. (b) (a)

PAGE 91

79 Table 6-2. Parameters for the simulating th e effect of Ge coating on the magnetic field dependence of the Hall resistivity in ultra-thin Bi films Surface (3 for Bi/Ge, 10 for Bi) In the film (100) Carrier density ns (m-2) Mobility s (1 1 2 s V m ) Carrier density ni (m-3) Mobility s (1 1 2 s V m ) e 1710 2 03 01 ) 10 5 (23 a 0.047 Bi/G e h 1710 4 1 0.036 ) 10 5 (23 a 0.054 e 1710 2 03 01 ) 10 5 (23 a 0.047 Bi h 1710 4 1 0.036 ) 10 5 (23 a 0.054 The simulations suggest that, the effect of the Ge layer on the Hall resistivity is equivalent to reducing the density of the surface carriers. It is also due to the reduction or neutralization of the metallic su rface states so that th e carriers in the bulk part of the films again dominate the transport and give rise to the negative resistance-temperature slope shown in Figure 6-6. The mechanism through which exposure of the bismuth film to th e air increases the surface sheet carrier density is still not known. However we believe that results obtained from the Ge coated bismuth ultra-thin films opens the possibility of passivating the surface and even neutralizing surface states These results should be important for studying the nanoscopic bismuth systems, such as bismuth nanowires, in which the effect of the surface state becomes very significant.

PAGE 92

80 CHAPTER 7 SURFACE SUPERCONDUCTIVITY IN ULTRA-THIN BISMUTH FILMS 7.1 Transport Evidence In the previous chapter, we have studied the effect of the meta llic surface states on the transport of ultra-thin bismuth films. For the films of certain thickness, a closer look at the transport data at low temperatures re veals some very un-expected features. Figure 7-1 shows the zoom-in of the temperature de pendence of the resistance for a 15nm thick bismuth film. We can clear see a sharp drop of the resistance at about 5.6K. The inset shows the magnetic field dependence of resistan ce for the same film. We also see a sharp decrease of R below some critical field of ~200mT. Figure 7-1. Resistance vs. temperature in ze ro magnetic field for a 15nm bismuth film. Inset: resistance vs. magnetic field at 4.5K for the same sample. 6810 760 764 768 R ()T ( K ) -1.0-0.50.00.51.0 760 765 770 R( )B (T)

PAGE 93

81 The sharp feature of resist ance change has been observe d reproducibly in samples with thickness within certain ranges. The re sistance will either jump down or jump up below a critical temperature and critical field by very small amount. Figure 7-2 here shows an example in which the resistance ju mps up at below a cri tical temperature and critical field. Figure 7-2. Example of resistance increases during the transition. The main figure shows resistance vs. temperature in zero magnetic field for a 15nm bismuth film. Inset: resistance vs. magnetic field at 4.5K for the same sample. We also observed sharp feature of re sistance increase or decrease in the Hall resistivity measurements (see Figure 7-3). Si nce the features are even with the magnetic field, they are really from the longitudina l resistance pickup due to the misalignment of the Hall leads. But the change of resistance at the transition is mu ch bigger percentage wise. We also find that the critical field for such feature decreases with increasing 68 798.0 798.5 799.0 799.5 R ( )T ( K ) -1.0-0.50.00.51.0 801 804 R ()B (T)

PAGE 94

82 temperature, and the relation satisfies th e T dependence of the critical field in superconductors: 21 ) 0 ( ) (c c cT T B T B (7.1) Figure 7-3. Sharp feature of resistance change observed in Hall resistivity measurements at indicated temperatures for a 15nm thick bismuth film. Inset: critical magnetic field as a function of T2. By measuring bismuth films with differen t thickness, we map out the thickness dependence of the critical magnetic field for the resistance transition. From Figure 7-4 we can see that at 4.5K, the transition happens for films with thickness smaller than ~16nm, and for films with thickness ~40nm. In fact th e critical field vs. th ickness plot suggests oscillating thickness dependence of the critical magnetic field. -0.50.00.51.0 0.5 1.0 1.5 4.5K 5K 6KRxy ( )B ( T ) 16182022242628 5.0x1011.0x1021.5x1022.0x102 Bc ( mT)T2 (K2)

PAGE 95

83 Figure 7-4. Film thickness dependence of the critical magnetic field at 4.5K. The features we have observed for these bi smuth films together with the absence of a full transition to a zero-resis tance state are suggestive to that superconduc tivity occurs only in certain portions of the films. The bulk rhombohedral bismuth is not superconducting ( Tc<50 mK). But there are several reported superconducting phases of bismuth: high-pressue phases of Bi called Bi II, III and V with Tc =3.9, 7.2, and 8.5K respectively,49-51 fcc Bi with Tc with Tc<4K,52 amorphous Bi with Tc=6K, and granular system of Bi clusters, with Tc ~2-6K depending on the size of the clusters.41 X-ray diffraction (XRD) analysis shows th at our films are rhombohedral. To make the amorphous bismuth films that show supe rconductivity, one need s to deposit bismuth onto liquid Helium cooled substrate. Th ese amorphous bismuth films lose their superconductivity when annealed up to room temperature. Hence we believe that 01020304050 0.0 0.2 0.4 0.6 0.8 Critical field (T)Thickness ( nm )

PAGE 96

84 amorphous phase is not the reason for th e superconductivity observed in our room temperature deposited and 200 C annealed films. 7.2 Tunneling Evidence To further probe the properties of our films, we performed tunneling measurements. The samples we studied are standard cross-bar Pb-I-Bi junctions described in chapter 6. Figure 7-5 shows th e curves of tunneling conductance vs. bias voltage at indicated different temperat ures, for a Pb-AlOx-Bi(150A) junction. -6-4-20246 0.5 1.0 1.5 10K 8K 7.1K 6.5K 5.5K 4K 0.3KdI/dV (Arb. unit)V (mV) Figure 7-5. Differential conducta nce as a function of bias voltage in the superconducting gap region at indicated te mperatures, for a Pb-AlOxBi(150) tunnel junction. A major feature of differen tial conductance at T<5.5K is the existence of two superconducting gaps. With increasing temperat ure, the two gaps move to some bias voltage in between, and the intensity of th e inner gap drops rapidly. At T>5.5K, the

PAGE 97

85 conductance spectrum recovers the shape of normal metal-in sulator-superconductor tunneling, with a single superconducting gap fr om Pb counter-electrode. With further increase of temperature, the superconducti ng gap vanishes as Pb electrode loses its superconductivity. The double gap feature in the bias voltage dependence of differential conductance is very typical for superconductor-insulator-s uperconductor (S-I-S) tunnel junction, with the DOS peaks correspond to 1+ 2 and 12, where 1 and 2 are the BCS gaps of Pb and Bi, respectively. It should be noted that the va lues of the superconducting gaps determined from the data above turn out to be bigger than what they should be (e.g.,the standard value for Pb is 1=1.4meV). Two possible reasons may cause the enhanced gap size. First of all, the sheet resistance of the bismuth film (~500 ) is comparable to the junction resistance itself, and hence will c ontribute to the measured result as a series resistor. Second, electrons may first of all tunne l into a surface state, and then lose energy when they travel into the bulk part of the film. Hence the existence of surface states may cause voltage drop at the bismuth-AlOx interface. Another surprising feature in the dI/dV vs. V characteristic is the conductance maximum for temperature lower than ~7K. This feature doesnt not reproduce for all the samples. The reason for its exis tence is not we ll understood. As a comparison, Figure 7-6 shows the s uperconducting gap feature of a Pb-AlOxBi(1000 ) tunnel junction. We see no evidence of superconductivity in the transport measurements of the 1000 thick bismuth films. The tunneli ng measurement, we also see the standard Pb superconducting gap in th e differential conductance vs. bias voltage

PAGE 98

86 sweep, but no evidence of the smaller gap seen in the sample with smaller thickness of the Bi electrode. Figure 7-6. Differential conducta nce as a function of bias vol tage in the superconducting gap region at 300mk, for a Pb-A lOx-Bi(1000) tunnel junction. We also measured the tunneling conducta nce of our samples in various magnetic fields. Shown in Figure 7-7 is the tunneli ng conductance vs. bias in different low magnetic fields perpendicular to and parallel to the junction area. For the perpendicular field, as the field increases, the gaps decrea se in size and move towards each other. In a field higher 200mT, only one gap is left. Since at 200mT, Pb already loses its superconductivity, the gap is the Bi superc onducting gap. A similar characteristic is observed in the measurements with magnetic fi eld applied parallel to the junction plane, except that the changes occur within a wide r field range. The differences between the -4-2024 0 1 2 dI/dV (Arb. unit)V (mV)

PAGE 99

87 results with magnetic field pa rallel and perpendicular to th e junction suggest that the double gap feature is not a spin effect. -6-4-20246 0.5 1.0 1.5 dI/dV (Arb. unit)V (mV)200mT 120mT 90mT 60mT 20mT 0T 40mT -6-4-20246 0.5 1.0 1.5 200mT 120mT 90mT 60mT 20mT 0TdI/dV (Arb. unit)V (mV)40mT Figure 7-7. Differential conducta nce vs. bias voltage at 300mK in indicated low magnetic fields perpendicular and para llel to the junction plane. Perp. field Para. field

PAGE 100

88 -6-4-20246 0.5 1.0 1.5 18TdI/dV (Arb. unit) V ( mV ) 10T 4T 1T 500mT 300mT -6-4-20246 0.5 1.0 1.5 10T 4T 1T 500mT 300mTdI/dV (Arb. unit)V (mV) Figure 7-8. Differential conduc tance vs. bias voltage at 300mK in indicated strong magnetic fields perpendicular and parallel to the junction plane. Para. field Perp. field

PAGE 101

89 In stronger magnetic field, the zero bias conductivity maximum disappears at ~500mT. With further increase of field, the gap feature slowly weakens out, but still can be seen even at the highest field (18T). Wh ether or not the gap-like feature in the very strong magnetic field is due to superc onductivity is still not well understood. 7.3 Possible Picture Putting together all the evidence for s uperconductivity both in transport and in tunneling measurement, we find that even t hough the resistance cha nge at the transition temperature is very small as observed in the transport measurement, the tunneling characteristic of S-I-S junction is well pronounc ed. This suggests that the overall area of the superconducting domains of the film is la rge at the surface of the film. However, these domains are only weakly coupled by mean s of tunneling. Hence for some films, the resistances exhibit sharp increase rather than decrease at the superconducting transition temperature, similar to what happens to th e tunneling resistance of a S-I-N junction at Tc. A possible model for the superconductivity is that the superconducting domains are separated from each other and normal (non-superconducting) domains by grain boundaries that serve as tunnel barriers. Depending on the th ickness and height of the barrier, the domains coupled with each ot her and the normal domains either through normal tunneling (which give s low conductance below Tc) or point contact(which gives high conductance below Tc). The average of these two kinds of effects, combined with the fact that the grain boundaries contribute to most of the film resistance, explains the small effect is observed in the transport meas urements. However, since the total area of the superconducting domains is large, pronoun ced evidence is obser ved in the tunneling measurements, which are more sensitive to the surface area than the transport

PAGE 102

90 measurements. This model can also explain th e much larger percentage resistance change observed in the Hall resistivity measurements. In those measurements, because the voltage leads are very close (the misalignmen t of the Hall leads are small), the number of grains that get averaged is small, and hence th e fluctuation of the average resistance at the superconducting transition is large. So the overa ll percentage effect of the resistance change during the tr ansition is large. Figure 7-9. A possible physical picture of surface superconduc tivity in ultra-thin bismuth films There are still many pending questions th at need to be answered. The major question that needs theoretical explanati on is, why does the s uperconducting transition happen only in films with certain thickness. Si nce the thickness depende nce of the critical magnetic field shows oscillating behavior, th e surface superconductivity might be related to quantum confinement in the ultra-thin bismuth films. Then, theoretically how does the QSE in the Bi thin films affect the su rface DOS and surface electron-phonon coupling. s n G V GG VV substrate

PAGE 103

91 CHAPTER 8 FUTURE WORK There are many interesting future directio ns that can be followed in the study of bismuth. In this chapter we will briefly show two possible directions: the low dimensional bismuth nano-structures, and the ph ysics and applications of the strong spinorbit coupling in bismuth. In the previous chapters, we have di scussed 3-D and 2-D bismuth structures. Further decreasing the dimensionality, we can envision 1-D or 0-D bismuth systems. Bismuth is a promising candidate for studying such structures mainly because bismuth has a very long Fermi wavelength. This makes it relatively easy to get reduced dimensionality without pushing the limit of the lithography technique too much. Also bismuth has very long phonon mean free path which makes it a good system for studying ballistic transport. Figure 8-1 shows some examples of the s ub-micron sized bismuth patterns we have made. All the patterns are made using sta ndard e-beam lithography technique described below: 1) A 6% copolymer is spinned onto the Si substrates at 2500 RPM for 60 sec. The coated substrate is then baked in a 140C convection furnace for 30 min. 2) A3 PMMA is spinned on top of the copolymer coated substrates at 4000 RPM for 60 sec, followed by 170C baking in a convection furnace for 30 min. 3) E-beam exposure: 30 kV beam with 30 um aperture is used. For line features, an exposure dose of 200~240 2/ cm Cis used. While for gap

PAGE 104

92 features, exposure dose of 3402/ cm C was found to give the best resolution. 4) Developing: for line features (with 200~2402/ cm Cdose), 1:1 (MIBK:IPA) developer was used, w ith developing time of 30 seconds; while for gap features, 1:3 (MIBK:IPA) developer was used, with developing time of 30 seconds. After the lithography procedure above, th e substrates with PMMA patterns were treated with oxygen glow discharge (150 mT orr oxygen, 500V) for 2 min to remove polymer and solvent residue. Then the bi smuth films are thermally deposited from 99.999% pure bismuth source, onto the Si substr ates, with typical th ickness of ~100 nm. The substrates are kept at 100 C during the deposition to achieve large grain sizes. Liftoff was carried out in 9:1 Methol yen chloride: acetone solution. For very thin bismuth films, PMMA itself, without the copolymer layer gives better resolution on bismuth patterns. In this case, A3 PMMA is spinned at ~3500 RPM onto the Si substrate, followed by 170 C baking in a convection furnace for 60 min. For exposure, 10kV beam with 30 um aperture is used, with exposure dose of ~120 2/ cm C. The patterns are developed in 1:3 (MIBK:IPA) solution for 30 sec. For thick bismuth films (>100 nm), however, copolymer layer is necessary for creating a proper undercut, thereby facilitating smooth lift-off after the metallization. To make bismuth patterns on th e insulating substrates (e.g., mica), it is necessary to deposit a thin layer of bismuth (~15 nm) be fore the e-beam lithography procedure to prevent charging. Then, after going through the lithography, metallization and lift-off procedures described above, we use ion b eam etching to remove the pre-deposited bismuth layer and open up the blank areas.

PAGE 105

93 Figure 8-1. Some examples of the sub-micr on sized bismuth patterns. (a)-(c) shows AFM amplitude images of two reservoirs, and a A-B ring patterns, respectively. (d) shows the SEM picture of a cross pattern. (a) (b) (c) (d)

PAGE 106

94 Preliminary data taken from some of thes e patterns shows some typical phenomena for the transport in the diffusive and ballistic region. Figure 8-2 shows the magnetoresistance measurement on the reservoi r pattern with two films connected by a narrow and short wire shown in Figure 8-1 (a). The resistance is generally linear with field. On top of the linear field depend ence, we can see the small, random, but reproducible fluctuations. These are universal conductance fluctuations (UCF), originated from the elastic impurity scattering in the sample in the magnetic field. Figure 8-2. Magnetic field depende nce of the resistivity for the reservoir pattern shown in Figure 8-1 (a). Inset: differential conduc tance vs. bias voltage in different magnetic fields. -20-15-10-50510152 0 1000 1050 1100 1150 1200 1250 B (T)R ()-0.020.000.02 dI/dV (Arb. unit)Vbias (V)

PAGE 107

95 The universal conductance fl uctuations are also observed in the differential conductance vs. bias voltage sweep, as shown in the inset of Figure 8-2 in which the curves are taken from the same sample. Here we also observed random fluctuations as a function of bias voltage in diffe rent fields. This is just another way of probing the UCF in that, instead of changing the phase by the ch anging magnetic field, we change the phase by changing the energy of the electrons. Fabrication of the sub-micr on or nanometer sized bismuth patterns also provide an opportunity studying the ballistic transport behavior in bismuth. For example, by making films with size comparable to the grain size, we can study th e transport inside a single grain or across a single boundary. Figure 83 shows the magnetoresistance measurements on a bismuth nano-cavity pattern. From the AFM image we can clearly see a grain boundary inside the cavity. By changing the geometry of the measurements and by changing the input signals, we can possibly study the transport across a single grain boundary. Note, for example, the more than ten times higher resistance scale for configuration A compared to configuration B. Figure 8-3. Measurements of a nano-cav ity with a single grain-boundary in it. -10-50510 55 60 65 70 75 R ()B (T) V V I I DC AC -8-6-4-202468 3.0 3.1 3.2 3.3 3.4 3.5 R ()B (T) V V I I DC AC A B

PAGE 108

96 There are still many pending problems in the study of bismuth nano-structures. First of all, as the bismuth structures are made smaller and smalle r, the effect of the surface states become more and more signifi cant. The surface states are more metallic than the bulk bismuth and will smear out the intrinsic properties (e.g., long Fermi wavelength, long phonon mean free path, quantum size effect) in the bulk part of the bismuth patterns. Hence it is very important to control the metallic surface states. Second, its difficult to make the bismuth patterns sma ll because they tend to have large crystals. We are still pushing the limit of our lithogra phy to make the sizes comparable to the Fermi wavelength. Another interesting future direction of bismuth study is about the strong spin-orbit coupling in Bi. Recently, Koroteev et.al. observed the strong spin -orbit splitting on Bi surfaces by angular resolved photo emission.53 Bi can be a very interesting material in the spintronics study. We are working on ma king magnetic tunnel junctions on bismuth surface, and studying the possibility of obser ving the spin-hall effect in bismuth.

PAGE 109

97 LIST OF REFERENCES 1. Kempa, H., Kopelevich, Y., Mrowka, F ., Setzer, A., Torres, J.H.S., Hohne, R., and Esquinazi, P., Solid St ate Communications, 2000. 115(10): p. 539. 2. Khveshchenko, D.V., Physical Review Letters, 2001. 87(24): p. 246802/1. 3. Kopelevich, Y., Torres, J.H.S., da S ilva, R.R., Mrowka, F., Kempa, H., and Esquinazi, P., Physical Review Letters, 2003. 90(15): p. 156402/1. 4. Kopelevich, Y., Lemanov, V.V., Moehleck e, S., and Torres, J.H.S., Physics of the Solid State, 1999. 41(12): p. Numbers: 1959. 5. Ashcroft, N.W. and Mermin, N.D., Solid Sate Physics 1976: Holt, Rinehart and Winston. 6. Abrikosov, A.A., Fundamentals of the Theory of Metals 1988: North-Holland. 7. Gantmakher, V.F. and Levinson, Y.B., Carrier scattering in metals and semiconductors 1987: North-Holland. 8. McClure, J.W. and Spry, W.J., Physical Review, 1968. 165(3): p. 809. 9. Smith, G.E., Baraff, G.A., and Rowell, J.M., Physical Review, 1964. 135(4A): p. A1118. 10. Brown, R.D., Physical Review B (Solid State), 1970. 2(4): p. 928. 11. Khveshchenko, D.V., Phys. Rev. Lett., 2001. 87(20): p. 206401. 12. Brandt, N.B., Schudinov, S.M., and Ponomarev, Y.G., Semimetals 1: Graphite and its compounds 1988: North-Holland. 13. Khveshchenko, D.V., Physical Review Letters, 2001. 87(20): p. 206401. 14. Matsui, T., Kambara, H., Niimi, Y., Tagami, K., Tsukada, M., and Fukuyama, H., cond-mat/0405011, 2004. 15. Biagini, C., Maslov, D.L., Reizer, M. Y., and Glazman, L.I., Europhysics Letters, 2001. 55(3): p. 383. 16. Murzin, S.S., Physics-Uspekhi, 2000. 43(4).

PAGE 110

98 17. Mangez, J.H., Issi, J.P., and Heremans, J., Physical Review B (Solid State), 1976. 14(10): p. 4381. 18. Shoenberg, D., Magnetic oscillations in metals 1984, Cambridge, UK: Cambridge. 19. Bompadre, S.G., Biagini, C., Maslov, D., and Hebard, A.F., Physical Review B (Condensed Matter and Ma terials Physics), 2001. 64(7): p. 073103/1. 20. Yang, F.Y., Liu, K., Hong, K., Reich, D.H., Searson, P.C., and Chien, C.L., Science, 1999. 284(5418): p. 1335. 21. Yang, F.Y., Kai Liu, C., C.L., and Sear son, P.C., Physical Review Letters, 1999. 82(16): p. 3328. 22. Cho, S., Kim, Y., Freeman, A.J., Wong, G.K.L., Ketterson, J.B., Olafsen, L.J., Vurgaftman, I., Meyer, J.R., and Hoffm an, C.A., Applied Physics Letters, 2001. 79(22): p. 3651. 23. Jin, B.Y., Wong, H.K., Wong, G.K., Kette rson, J.B., and Eckstein, Y., Thin Solid Films, 1983. 110(1): p. 29. 24. Beutler, D.E. and Giordano, N., Phys ical Review B (Condensed Matter), 1988. 38(1): p. 8. 25. Partin, D.L., Heremans, J., Morelli, D.T., Thrush, C.M., Olk, C.H., and Perry, T.A., Physical Review B (Condensed Matter), 1988. 38(6): p. 3818. 26. Massalski, T.B., Binary Alloy Phase Diagrams 1990, Cleveland: ASM International. 27. Ogrin, Y.F., Lutski, V.N., and Elinson, JETP Letter, 1966. 3: p. 71. 28. Chu, H.T., Henriksen, P.N., and Alex ander, J., Physical Review B (Condensed Matter and Materials Physics), 1988. 37(8): p. 3900. 29. Asahi, H., humoto, T., and Kawazu, A ., Physical Review B (Condensed Matter and Materials Physics), 1974. 9(8): p. 3347. 30. Renzi, V.D., Betti, M.G., and Mariani, C., Physical Review B (Condensed Matter), 1993. 48(7): p. 4767. 31. Garcia, N., Kao, Y.H., and Strongin, M., Physical Review B (Condensed Matter and Materials Physics), 1972. 5(6): p. 2029. 32. Hoffman, R.A. and Frankl, D.R., Phys ical Review B (Condensed Matter and Materials Physics), 1971. 3(6): p. 1825.

PAGE 111

99 33. Freeman, W.L. and Gettys, W.E., Phys ical Review B (Condensed Matter and Materials Physics), 1978. 17(2): p. 529. 34. Rogacheva, E.I., Grigorov, S.N., Nashchekina, O.N., Lyubchenko, S., and Dresselhaus, M.S., App lied Physics Letters, 2003. 82(16): p. 2628. 35. Goldfarb, I. and Tavger, B., Sov. Phys. Solid State, 1969. 11: p. 1231. 36. Chu, H.T. and Zhang, W., J. Phys. Chem. Solids, 1992. 53: p. 1059. 37. Lutski, V.N. and Kulik, L.A., JETP Letter, 1968. 8: p. 80. 38. Komnik, Y.F., Bukhshtab, E.I., Niktin, Y. V., and Andrievskii, V.V., JETP Letter, 1971. 33: p. 364. 39. Hoffman, C.A., Meyer, J.R., Bartoli, F.J., Venere, A.D., Yi, X.J., Hou, C.L., Wang, H.C., Ketterson, J.B., and Wong, G.K., Physical Review B (Condensed Matter and Materials Physics), 1993. 48(15): p. 11431. 40. Chu, H.T., Physical Review B (Conden sed Matter and Materials Physics), 1995. 51(8): p. 5532. 41. Weitzel, B. and Micklitz, H ., Physical Review Letters, 1991. 66(3): p. 385. 42. Patthey, F., Schneider, W.-D., and Mick litz, H., Physical Review B (Condensed Matter), 1994. 49(16): p. 11293. 43. Tanaka, A., Hatano, M., Takahashi, K ., Sasaki, H., Suzuki, S., and Sato, S., Physical Review B (Condensed Matter), 1999. 59(3): p. 1786. 44. Troyanovskii, A.M. and Edel'man, V.S., Journal of Experimental and Theoretical Physics, 1999. 88(6): p. Numbers: 1212. 45. Hengsberger, M., Segovia, P., Garnier, M., Purdie, D., and Baer, Y., European Physical Journal B, 2000. 17(4): p. 603. 46. Agergaard, S., Sondergaard, C., Li, H ., Nielsen, M.B., Hoffmann, S.V., Li, Z., and Hofmann, P., New Journal of Physics, 2001. 3. 47. Ast, C.R. and Hochst, H., Physical Review Letters, 2001. 87(17): p. 177602/1. 48. Gayone, J.E., Hoffman, S.V., Li, Z., and Hoffman, P., Physical Review Letters, 2003. 91(12): p. 127601. 49. Chester, P.F. and Jones, G.O., Philos. Mag., 1953. 44: p. 1281. 50. Brandt, N.B. and Ginzburg, N.J., Sov. Phys. JETP, 1961. 12: p. 1082. 51. Wittig, J., Z. Phys., 1966. 195: p. 228.

PAGE 112

100 52. Moodera, J.S. and Meservey, R., Phys ical Review B (Condensed Matter and Materials Physics), 1990. 42: p. 179. 53. Koroteev, Y.M., Bihlmayer, G., Gayone, J.E., Chulkov, E.V., Blugel, S., Echenique, P.M., and Hofmann, P ., Physical Review Letters, 2004. 93(4): p. 046403/1.

PAGE 113

101 BIOGRAPHICAL SKETCH Xu Du was born on July 16, 1974, in Chengdu, Sichuan province, P. R. China. He spent a happy childhood with hi s grandparents in Chengdu, a nd entered school in 1980. In 1982, he moved to a rural area of Sichuan an d lived with his parents. There he spent 10 years enjoying the beauty of nature and fini shing his pre-college education. As a child, Xu Du became deeply interested in math, physics, and engineering, because of the influence of his father. He spent a lot of time working on self-proposed math and physics problems, and on making airplane models a nd electronics. He was also addicted to classical guitar, which became a major pastime. In 1992, Xu Du entered Beijing University of Aeronautics and Astronautics to study mechanical engineering. Driven by his intere st, he studied the main courses for a physics major by himself, and entered the physics depa rtment at Beijing University as a graduate student in 1996. There he worked on th e structural influe nce of the high Tc superconductors and GaN, under the supe rvision of Professor Han Zhang. In 1999, Xu Du received his M..S degree in physics. He received the Alumni Fellowship and entered the University of Flor ida (UF) for his Ph.D. study. There he met his future wife, Zhihong Chen, who was also a physics graduate student. He started working under the supervision of Professor Arth ur F. Hebard in 2000. From then on, he spent 5 years enjoying the freedom of res earch. This dissertation represents the culmination of his research work during the past 5 years.


xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E20110115_AAAADT INGEST_TIME 2011-01-15T21:51:15Z PACKAGE UFE0008357_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES
FILE SIZE 25271604 DFID F20110115_AACOLK ORIGIN DEPOSITOR PATH du_x_Page_107.tif GLOBAL false PRESERVATION BIT MESSAGE_DIGEST ALGORITHM MD5
b8d48d132e39d5fad88a6f0f21d8911a
SHA-1
f35337e5d6178e321d08159651e622cd8d6699dc
1053954 F20110115_AACOKW du_x_Page_093.tif
57614406ec283b658e7cdf1a85e88737
8699140f24182c08eb13c0562601965fbdadfe99
41866 F20110115_AACOMA du_x_Page_011.pro
cd9df870cce251bfd0f0983eea796edd
18d2e7f025d5de4a96d88b4a18de1ae3801fecbc
F20110115_AACOLL du_x_Page_108.tif
647881f4ee21da9ac0a8577faf3c1b90
91cf2f85110b57bbba911294faf4fd9967f7f7ce
F20110115_AACOKX du_x_Page_094.tif
4cc25faa2fb9bd6bed226cf223204c14
b832a6e74b3925501882bc54cca5e25ad6413f0f
36198 F20110115_AACOMB du_x_Page_012.pro
e464a43a2ba302db24208d331d7be592
290b2b218b18bac8838b520525e993852f6fe598
F20110115_AACOLM du_x_Page_109.tif
d9a84f684ad26bf5a6bebe23b7a63157
776b52512d704b2d80c02fa4bdf076ca62f238a2
F20110115_AACOKY du_x_Page_095.tif
f03392e8cd7c87f482d92585d02bdf14
3b90b8520117c6979599003a537c09800f8cd822
40960 F20110115_AACOMC du_x_Page_013.pro
8a469649a73a65859f43c92d8ef5dfb2
5e544ee6a1ee292d6c999449f4a207c01eb40439
F20110115_AACOLN du_x_Page_110.tif
50dc29c3462c74862b9da261007a42b3
8e0e6ce4b49f071a59607fec3399cdced7fcd9b2
F20110115_AACOKZ du_x_Page_096.tif
fea39f917e0182112043fd7222d89b1e
138c0920a1757e3c2fe2c5a5fe6ed6d2688a3bec
49329 F20110115_AACOMD du_x_Page_014.pro
88f8dae1e4c271c7026a29fed07f8b87
b195c6e8eb8c93edc8cee8d1de124897a26739a0
F20110115_AACOLO du_x_Page_111.tif
a306314e307f88cbfceb35b96b25a7ac
99e6922bea86b6079bf1887067047753a1cb9840
F20110115_AACOLP du_x_Page_112.tif
82b61bdfee8b89e45d422ed8cb9277d7
4f1fc9381f405d9688145504f633874cc76a3c84
14579 F20110115_AACOME du_x_Page_015.pro
88d0f6081ddb9f251745c2b332750b83
20be3e0b9ed94e8d19418d8b84068dd8143a50f8
F20110115_AACOLQ du_x_Page_113.tif
d3d8bbba5eb6b6fa48517af6f37c4869
e0fd8446de3414180b6223f0a3d8e3925cbe32fd
43567 F20110115_AACOMF du_x_Page_016.pro
29a63b993e0214678e0505fc2c97f1e2
63c0a0672719f7429ff370c69a68a0b782eac878
7949 F20110115_AACOLR du_x_Page_001.pro
a71bf34971f59945a600ffe855c98dbb
320d43dd93e36afd8d18163a7e3a7027c1ccf3dd
45558 F20110115_AACOMG du_x_Page_017.pro
b35c03551f6ea52cc6695d47d65cb7d4
e466f8b342bee07ffc1349b95209d776c2e4e7d1
911 F20110115_AACOLS du_x_Page_002.pro
0e189c128fbe1f6a2b1141fb505d7193
bb245d9a2187c62378b8a013305737b567e3d6cc
48560 F20110115_AACOMH du_x_Page_018.pro
0fbd7b4235a41f81c1a50beff448fb4d
5c44fe3c3c2ed1d52092e15bfeb19ad540508460
621 F20110115_AACOLT du_x_Page_003.pro
94886542061634e3eee6ad3618d89e6b
91dc6a847fef3ee0ee5209163059769965732726
35590 F20110115_AACOMI du_x_Page_019.pro
875bfc782c1e08022fd7877c731fd06d
974cf3263a1853ccf1f00bc8129a680ef9aa2ff0
42734 F20110115_AACOLU du_x_Page_004.pro
0af25164244869a7e5a0a98253ed93eb
0ad7d4ae4609967d6168a1b4e01e5c7546cdb3f7
27958 F20110115_AACOMJ du_x_Page_020.pro
3ea93638d08c6ece035ee1c87719649f
9b554f68e14deb5db4131f40ed36861285e424c8
27337 F20110115_AACOLV du_x_Page_005.pro
cef073addcbc1ed9fcb67081f41c140b
f554c1e085d51ab4d4a5ff2a6c4e3441e66d322d
65428 F20110115_AACOLW du_x_Page_006.pro
276fecd8e9e0066b4ff323a1e37c775c
8083dec0bae44fff09484eaf04ff7e6533894c09
34907 F20110115_AACOMK du_x_Page_021.pro
b39cb88fe2ab6ffb316e12352d0bb0ee
7b622fdba18a44540abc1b6590b18b190f46f500
34134 F20110115_AACOLX du_x_Page_007.pro
f5ae135feeeca977681bfee691cea94e
768b66b71f8551ea8392cb25d2155102e418dbfd
31434 F20110115_AACONA du_x_Page_038.pro
fb5a0ecc1107c2eb57222297f0a60dcc
dd9c084225777550894e73c9c70a7e3f2c611e04
35074 F20110115_AACOML du_x_Page_022.pro
a8de03742b9075c9fbb228ed181fd412
b1871a03cf52ac4352551e243dbacd15c0902a6f
65040 F20110115_AACOLY du_x_Page_009.pro
2b4d3e1676b0de0087e37bfc304e4ab7
947b4dc1e98d360576a41004fc6df24e35abf53e
39167 F20110115_AACONB du_x_Page_039.pro
092fc1fb1b5cdd998fc02b7b645c52fb
5bd6abad852a18fc7e32281e045a4ac6d159a325
31123 F20110115_AACOMM du_x_Page_023.pro
5f72e66de8e9ab1132afaee3485d7e15
b419cd0b10753005ff5fb22857666ecef579c548
68305 F20110115_AACOLZ du_x_Page_010.pro
27274af62ea6b7e428da474e78ec986a
72901749f8987373e118a556b9fa403f4739c10a
36323 F20110115_AACONC du_x_Page_040.pro
24cdb5fb4761213a642b1d91f773801a
aea08af6b1a8bed178851a5bf1257a0363395beb
42533 F20110115_AACOMN du_x_Page_025.pro
d6d7be5b106eb2f66e8edb953048cc89
74b05ab55f9af04c4316e21693890ec562d6538e
19424 F20110115_AACOND du_x_Page_041.pro
d999807bf8e0f8b64c4fa4b6578a7e75
13cc42afaa700cc5f650758ed22ae7c93a9d49e5
27811 F20110115_AACOMO du_x_Page_026.pro
c98ba18c96a994952b809e6c44e89a38
ee10e1291df24199051413a656b64afcfb757f2f
40623 F20110115_AACONE du_x_Page_042.pro
82b53dc5dce9929e44a06d0d783af5f8
20a143e872284950b53d2b4bd5099aa05a2ba6d3
16346 F20110115_AACOMP du_x_Page_027.pro
eb2a7ee27305ac244c0b3c076210bddd
4cd96f079d6a340d104a70137e926629c554d95a
46521 F20110115_AACONF du_x_Page_043.pro
810e39d7fed42b842c0ffd6c28968ed6
b3147eaaca37b739bf194e49e3106a95f2788db4
44177 F20110115_AACOMQ du_x_Page_028.pro
5aa614d01d074663e010d9f0f61c8b7c
e5ba05baaa06dc096f9fb9ac49c160a116afe7ea
23843 F20110115_AACONG du_x_Page_044.pro
f3669e33f34f451976280484bcc10688
950adce7dc1b4f1c48e4affeaab385afb73b180f
32064 F20110115_AACOMR du_x_Page_029.pro
abe301548e8eb7295e98bc8e742e9d59
7f3363394c336e3e088551cc0a4f436e00868e46
22602 F20110115_AACONH du_x_Page_045.pro
7a418b093a2561c75636d43f202da714
904fd5165c80685e674f645d1aefe46b85be4c20
52376 F20110115_AACOMS du_x_Page_030.pro
fc8e41712ff0ae833d9e94b4ef599f56
d5afdaeda2b2290b3ba85bdfaba5ce8addab5d06
24194 F20110115_AACONI du_x_Page_046.pro
a5048cb6cc9f6cfd35d8bd16b67001f2
43c4a2b9e14795d85c0a291efcfda9d122b4c325
37491 F20110115_AACOMT du_x_Page_031.pro
04bb49665ee359d3260c12ca9cdfd575
4a642db2565ae058de512f0b83fde4046393998a
45013 F20110115_AACONJ du_x_Page_047.pro
7599ad23f84e897588fe77df18bd1c0f
a3d1cded91668aaffcc28be71ce969dcc2b01514
21312 F20110115_AACOMU du_x_Page_032.pro
bffc84908f4e31350b850e13aa642008
194e71869ea307ab03a567678547c68c220a79bf
22003 F20110115_AACONK du_x_Page_048.pro
7c114b1469f8278069ae38001da7ff11
0e530d8db4ae1f28e568f7b051daa90bfdff0fba
20424 F20110115_AACOMV du_x_Page_033.pro
f2a892381ee66ac1d10749394bf00fb7
5a959d897e6c98534773bc866008ed5d7960955c
45654 F20110115_AACOMW du_x_Page_034.pro
c423d76335daeb9330cba97efaa32202
33d952258e3c4d444b75a15d25bcf7c8f31d163b
47162 F20110115_AACOOA du_x_Page_066.pro
26629d156889d51f50b2a20de9311e96
97b3543106a0d4ac314dda59d52169504b69dbe2
46404 F20110115_AACONL du_x_Page_049.pro
0d947d8734b833fced7ae770f8194004
e8d327f5b49d34e8510843d02dac1664bd868271
46069 F20110115_AACOMX du_x_Page_035.pro
ad9f6192ecc01e8cdc308e902aa799e0
59b15a98567b8bfa24dcbc99890177abb7cf79d6
49645 F20110115_AACOOB du_x_Page_067.pro
882b4be25ec25a134dfbb5b80755511d
e43a8551b94335874a0c539c30ac8592e20af184
20969 F20110115_AACONM du_x_Page_050.pro
a326fe8db65e34690f640eb81d6c8e79
9c8b9517b1a281271aed94330a50e2463ca3d15c
41790 F20110115_AACOMY du_x_Page_036.pro
d203564dabd869544572297b5d17d96e
11045347117cadead1d3df3efcad5a486cc1426d
34268 F20110115_AACOOC du_x_Page_068.pro
934ab8dab017986e8c19d9e94478573e
9d17c4278cef1f05b9331c0dbc06189fb3c044b3
26574 F20110115_AACONN du_x_Page_051.pro
eba6b814df7a063d444e5059f96b89d4
f8791b6668b6bf59672d8fe51544446f75c0ca91
12822 F20110115_AACOMZ du_x_Page_037.pro
12bac42bf1a3d57aac6a9f406007399e
b44cc94a442fb42554fce5b1555325cd5bb6e209
28940 F20110115_AACOOD du_x_Page_069.pro
3f33e1709886d1a935ca38173cbfdfd5
2f1b72bb99285283825531bbd4562e438442db36
22998 F20110115_AACONO du_x_Page_052.pro
419c8c2ca7cdd8ca6e0a624c788d8836
3f1ec1b7bf3b1db008c4994030bd1ad380f3b8e7
39165 F20110115_AACOOE du_x_Page_070.pro
29df5fcda3c0dfc5a633e03e3f01f66e
9c5a3a6292c3128cca17ea7e55ce4b077ffcc6c5
44071 F20110115_AACONP du_x_Page_053.pro
b08a4ffb1da95b68dd1555c8d0c7e969
d62999b846d6db24cce16c537caa7f6154c65d57
50460 F20110115_AACOOF du_x_Page_071.pro
11bcb810a8a417137e5509e06b7249c6
98157907f05c652b6f25b6f11d31f419b136de7e
46197 F20110115_AACONQ du_x_Page_055.pro
e7153be802d1dafae3b2a427b3776c13
f004d7cd3047b6a81ae718e0e7d8c8c1e8344e45
45401 F20110115_AACOOG du_x_Page_072.pro
83b811601b42b46a3d09b2c21b7b3235
834108b8c3006c3661f3e7b0d5b1fa92ae7d0f36
12814 F20110115_AACONR du_x_Page_056.pro
b2e1c038dd69065b47dc1a7d829985b0
f23a5c6387b64031d6505b98c3c2b1bb7bdf6d69
8165 F20110115_AACOOH du_x_Page_074.pro
e50644230b2cf5914d6eefd47990cb4e
9fbe23c4ced7b72ef66079aa8894cc2c5be63e2c
7419 F20110115_AACONS du_x_Page_058.pro
c1f5e393448b0010ed0c4d262530eb51
829c60baa64e8fbde39f04879c5a0f2f2002b062
43212 F20110115_AACOOI du_x_Page_075.pro
febba2b07a8be43cdfae1b381a8f4683
2f1df698a2e8a0ffc29ba10fe1236b30ff4aa59e
43983 F20110115_AACONT du_x_Page_059.pro
e7a6aa56590428b31a25e74367be444a
97bf84a37dc815077a4f40f5f301879a95ce7b98
31896 F20110115_AACOOJ du_x_Page_076.pro
613e30f2f622fadec3a386cc41c18b54
27f6c74ae0803f11a6162ccdd015f291886e0fc1
11501 F20110115_AACONU du_x_Page_060.pro
63b88bcc5367c2b2c3cd3583825e0a74
9178286b8d3c2116a24b4b462e77354d121eb8e7
51961 F20110115_AACOOK du_x_Page_077.pro
f6e7003fd12a2edea5c23fa99ec4f97e
2d38a2e3e754f02c3c4b962065b3f51a15c0e5a6
45969 F20110115_AACONV du_x_Page_061.pro
84791c0dcfebe765a97c6d449931733c
3a70957d961e851a0f9ee227fc89d3da1c6e4e3b
45652 F20110115_AACOOL du_x_Page_078.pro
83c12b626f6ee33e741bf80ae2551382
b351efc7619cd84b2f58353aa927ffa47d1bfbf4
23030 F20110115_AACONW du_x_Page_062.pro
26ee747c72e2ba4ed3ff71480e50a5e4
537235ab0b8adb10bb2bcb834270c52393e0d8aa
36305 F20110115_AACONX du_x_Page_063.pro
4fb705f7c8be0f3e852a0fa79a4f1cd8
076b115801d366905a4fffab6228f92fa8d22b4b
21613 F20110115_AACOPA du_x_Page_094.pro
aa777b2ae441e7c27cd75953b2b5012d
76d0d4292e6914676db54a14469837bc6b65f766
29246 F20110115_AACOOM du_x_Page_079.pro
9236eecd89c005ebd7c5d7a1e72a415d
5e352d7a9f0936a5264bc61c836ee1533888a8b3
37106 F20110115_AACONY du_x_Page_064.pro
50cc8cedde81ae4275d8d20245e822bc
a205e08801830d6d7a85e95f923b03ba12016447
25686 F20110115_AACOPB du_x_Page_096.pro
4b15162efb378188389a834690bf7811
6d4de1a9cf46d99f444eb3475792007e337eaf17
45486 F20110115_AACOON du_x_Page_080.pro
ba990f5b2c981a6d18e9350a49e7c9d0
60528d145c5c6207dd5222093df176e5cdb114ad
48098 F20110115_AACONZ du_x_Page_065.pro
8dd2caabde1415c668e4ad96b55254ad
1916e779059ba3ff66ae589991aca1452becc971
47002 F20110115_AACOPC du_x_Page_097.pro
c36a5dfe67b3f139f311c9513e85e122
06ff85141846c25436f572eb60321070994130d0
31806 F20110115_AACOOO du_x_Page_081.pro
b6d6420cba3dcf6aa3435c33a4254b45
a0ccecf19ed046b0bc9fe2b0dac64eba0ba45127
26423 F20110115_AACOPD du_x_Page_098.pro
8fb7037cb4b2bb6f502ec6fe61610b94
2f62e58d5547f5ea82262fa6e001a6eec96fc896
44491 F20110115_AACOOP du_x_Page_083.pro
7c960dbabc2bdd9c9907c5c8216da656
4f6af4697a934a8935865d819ad3841b0ed1c8f2
11370 F20110115_AACOPE du_x_Page_099.pro
fa37593ac4edd76b67b2dbef6a4961bc
beb7af10b20bcc9c777e39db3c431af9c12104fd
52491 F20110115_AACOOQ du_x_Page_084.pro
18aa9950eb0e9d012c0b8679cd8de52e
878d53803275d58ed123fe6fce4e40000d354e0b
11082 F20110115_AACOPF du_x_Page_100.pro
9281e286f89ea199298b2086720de652
230cbd07344c66918d0410fa52c456d08b76611b
13629 F20110115_AACOOR du_x_Page_085.pro
a049a0e198bfda6727765653e466ba0a
f02211006c7d93395a45110581f5654976181e8c
50869 F20110115_AACOPG du_x_Page_101.pro
e51de70c292c96128a9b77f119520ff4
42206f09635663778a79bdf214ea758ce387791a
52799 F20110115_AACOOS du_x_Page_086.pro
15395cc6b27838925edc5210c1522b3a
424eea334762588e47b8e03181fcf31de0eebd93
32199 F20110115_AACOPH du_x_Page_102.pro
b27dfafcfdd4a51d166a6867d67b9026
1631b80260682c015c1feef4dfd6a8e90b474e67
34683 F20110115_AACOOT du_x_Page_087.pro
2716f5226d04a9b7aaae7666614ce881
1c29b3c2c795e0f6cf54fa3c4e91788b39c8792f
38546 F20110115_AACOPI du_x_Page_103.pro
bd5a66fd768de0281d445a277a3c99c0
6e22561889c47595ceeb4327fb624f732bb19a44
48764 F20110115_AACOOU du_x_Page_088.pro
a41fe882d469b9642ac9a6aedb6d9d6e
37e73c0b97594acf2a2279b88cbeebd8465a0b39
46312 F20110115_AACOPJ du_x_Page_104.pro
429ed79efb10d336d8589ca46b20f29a
dddd6a304c9a850cef5cd175dc05ac05b628b19e
10213 F20110115_AACOOV du_x_Page_089.pro
3b65601f4a4cd32ff961ed4707b1db5c
a91ca1a961b6b64416ca1e77cb752ac305ec9a96
25130 F20110115_AACOPK du_x_Page_106.pro
588d9f6071454dd8d3c047e3bb4d3968
0518959609a5e9b4c12d473828e7c138a3b135d0
13252 F20110115_AACOOW du_x_Page_090.pro
9515074ae0148034123818b5a9c11148
f9163b059f27640fc1cd76f7a15a4f129c15001e
39627 F20110115_AACOPL du_x_Page_107.pro
7737e5fafcf27080a14e71f11e5bd5f1
c4532a7ae3d927eebb882ffc17594321518bd6e7
36256 F20110115_AACOOX du_x_Page_091.pro
25691fc9f283ce8664cf7da42a93b875
21db21ac77dcbf67b36201c16c1e478f9ff54bf6
2684 F20110115_AACOQA du_x_Page_010.txt
73805fdd82ddfdbc5e619bbb913d947f
29537baaf5a592b602f7efce09523f916b73392f
30145 F20110115_AACOPM du_x_Page_108.pro
75fa8bbd1acb2934cf001326cb1573e5
ec7191b4ffb565656442a61add6c90e796467b3b
25448 F20110115_AACOOY du_x_Page_092.pro
ab9024c45fc7afdc71c87d264b76cfc7
962359b02d11af61998849ddf06752700a032e0a
1668 F20110115_AACOQB du_x_Page_011.txt
8807815ecf8376c51f51b8ad51e82384
c18d6f41ac041e2be7098ec312e4e96b6ce55b58
31206 F20110115_AACOOZ du_x_Page_093.pro
5f2a8469145a4179cfaf75f48530e227
8a743518c4425365f88702fd1f0c7f0b6f91cb18
1631 F20110115_AACOQC du_x_Page_012.txt
1bccc48c1d8ca0f9fb5a5c984596f06f
a614f0c831bb9c6e4db5f5d970fb8ba493a838fe
42056 F20110115_AACOPN du_x_Page_109.pro
445641f3434543e6ab5e24074b7efd5b
87fce83bcbba1467a18d8caf0d04a17a07dd3a4c
1742 F20110115_AACOQD du_x_Page_013.txt
7150b2b09043089c3de209c21e101ba0
b0fd1d6079559211a5b19dc873b4f1fb51c06c8d
50018 F20110115_AACOPO du_x_Page_110.pro
d1ce8905b77f12814ca54b799426cfa2
3b954a4bf6358b57eba2e23c5dec97ac38a65283
1848 F20110115_AACOQE du_x_Page_017.txt
7459f1ec9add5b7e56565a63378f6eec
579026838f47fde55cbae6d934b964c59ed74c88
53049 F20110115_AACOPP du_x_Page_111.pro
e865e6b2ad8e8b76bd85834670694537
8bb9aa7aec91f4937f07936d2a1223e15f562c34
1580 F20110115_AACOQF du_x_Page_019.txt
59733fe5b0a42f8a1f798ed4f914caa1
a6ba2dc0d621d8a4599fbacfcb830784e0176e84
7633 F20110115_AACOPQ du_x_Page_112.pro
74c3455eb4b5fe90fa2d99ebb9d48893
ea73c3cec0d3834c4c9c65a0f11cc07f85ea72f9
1483 F20110115_AACOQG du_x_Page_020.txt
e35266ce935db61aadfa23b76081c808
04ea939496da653be1fbf879cc86f9e3d809cb19
41254 F20110115_AACOPR du_x_Page_113.pro
254cc699c472d18b8da48c82973dfee6
3f6fd8705accdf1b582ad4e1afabca02a64d2f27
1735 F20110115_AACOQH du_x_Page_021.txt
bf073b1500f944c4ed9f4306a1674ad3
6d9bef92627e7365ea1f8124c0fccbb7ad06feb3
485 F20110115_AACOPS du_x_Page_001.txt
791810c67116f8b93c562b5a49b4fb17
bc2c208ca98102742b0feb67baae67ea872abb2f
1491 F20110115_AACOQI du_x_Page_022.txt
89511bfe5876245d0e5011a97c582803
9bc78722d5a8fc3471e89588932ccf5d41013244
104 F20110115_AACOPT du_x_Page_002.txt
06fe0415a16861279245dcd026c53c0c
2997fe6152dc44e12e1f88ad95c4c929e52d271c
1554 F20110115_AACOQJ du_x_Page_023.txt
43311303e14f66870cdffea8ee9105e4
d6b0440930a8ac8c0aca5b04033497b247ec169c
82 F20110115_AACOPU du_x_Page_003.txt
c0f82858de8a262db7ff805ef75df187
6ae7301f65cb9a1997bb0c25fd0a47e57186d869
1535 F20110115_AACOQK du_x_Page_024.txt
2210ff128065680b97837e47fd4b710d
60ff68e6a1104f8260343f00cbb81c5443972df8
1729 F20110115_AACOPV du_x_Page_004.txt
44948fd105391762b28685db457d94c8
3cc8e8f27c922ac2e58989fb88e1dd10485d136d
1768 F20110115_AACOQL du_x_Page_025.txt
aa9290c4d114602689c5446d6e91421b
aa6506626cd81870cbe077157765613f57c317da
1099 F20110115_AACOPW du_x_Page_005.txt
cc862dec9a58b16faa9d3b23fd69de05
75ffa555251a2e0519f4178d87cf05716f0fe644
1136 F20110115_AACORA du_x_Page_041.txt
df674ca13a965382d5660a3e1d7667d2
3bde96cda37511a27e46657c7360e6993ec9e6fd
1415 F20110115_AACOQM du_x_Page_026.txt
15ec8cce2670284130e391b8b0308728
c5aa0111b4f7fed513feca71d2098f9525b11231
2670 F20110115_AACOPX du_x_Page_006.txt
139c4ca2fd53be375f98114b01ff66b2
51393b66a19d6606ff2dbd3a4d9612182b1fe3d9
851 F20110115_AACOQN du_x_Page_027.txt
975946dfa6e82cd0e8f78078c196d1e6
edb7bf89f0a708787454188dab30357ee09dce05
1370 F20110115_AACOPY du_x_Page_007.txt
14e769f10353a283da4f11531a8a528f
0a18689990062f2e99a861abb583dfaea601cf6d
1842 F20110115_AACORB du_x_Page_042.txt
7e590f814ae57271d2d15ac1c354fa35
e7ef677c1718e6d8d884f391ac2a6c34d0ee2b48
2629 F20110115_AACOPZ du_x_Page_009.txt
1c705bd815c33d65cf14f708176fc816
e3e751d24a2f643ff2ef0215f0e6bcbd387679c4
1951 F20110115_AACORC du_x_Page_043.txt
18ab6445dfd3027db53295a79ba28eee
1c1299f5253ed9de91b92f6fffec22a12c6391d9
1844 F20110115_AACOQO du_x_Page_028.txt
5006bed899ff9f029405ce0942ed3e46
a220c58e66523dc6651b38ba36abd229bb15933c
1004 F20110115_AACORD du_x_Page_044.txt
5d76f22aaff2ff663c01a5b2e6eff407
7a4da67e1718d8d9520a080647d33a7c34600e73
F20110115_AACOQP du_x_Page_029.txt
c48649ef878fd8e5b628974783b594ce
58f0ff5ce8e45a3a2629d8bc2661c1d0581886b5
1290 F20110115_AACORE du_x_Page_045.txt
74a1f19ce50b6bac3d46e9679c663ac1
86bbd02de604ebab70dd0c06e57e78c81d0504c5
2057 F20110115_AACOQQ du_x_Page_030.txt
7eb2cd2ef4ef3c2749f1221e350f22cb
8c6f89a43b4fb832a02b64dcb3824a014942e1c6
1557 F20110115_AACORF du_x_Page_046.txt
1e0dd5e7f8fbc4b61f50635a724a3582
f7fbe568fb42ba204b217fa005354573d791d9a1
1738 F20110115_AACOQR du_x_Page_031.txt
42b8063d9c0e13b44564d69d9dad1808
126f951f69cb0b7d20456149a19f1f32516282ef
1885 F20110115_AACORG du_x_Page_047.txt
d0351383272486ca2805e6f67e662feb
421cda67c8c3c7c407fd35fbafdeff9b18626956
1582 F20110115_AACOQS du_x_Page_032.txt
cd6ef8f5714152c82a33a18b31fdfa93
2e502dcd52c6f57b4b87231e3565941080227de7
1681 F20110115_AACORH du_x_Page_048.txt
0fdef170c1bc6fdf4af17c5dc8272dd1
b65617d656ee300150027cc4f56618e05af51d8e
1080 F20110115_AACOQT du_x_Page_033.txt
0fe491a5b6d2e0dd6517e952e0a3dbb6
cf22d34beafcfdb5d5e972a03d4df5695e0bf7b2
1983 F20110115_AACORI du_x_Page_049.txt
ef866671a9a75e0f886b31e4fda928a6
0e14799d927c3d9a9859e18d3c748107155317a6
1824 F20110115_AACOQU du_x_Page_034.txt
08ec4785a702278d141c93b8a3c65740
88f99f5d8501c0f827531e2d273796c430039e9f
978 F20110115_AACORJ du_x_Page_050.txt
d3e7abfb1832cae5b7104387d6eeba22
17a9b5600a60ff6756576caa21e7303714481e2e
1826 F20110115_AACOQV du_x_Page_035.txt
519cc9818621dad19273b9b653db1e51
32b77916d1c73fd59e4583abb78e6a0451a9ab2a
1280 F20110115_AACORK du_x_Page_051.txt
73e790c2975e073763b413934d3a36d1
66a9f556e32437a1dff036309f468fbc9d98642d
1718 F20110115_AACOQW du_x_Page_036.txt
873c41ec437bc55eecccd5324c28e0c8
fd1c7b746e0a99906a6573014f6d1bb6cf58ccab
969 F20110115_AACORL du_x_Page_052.txt
3a58e251b52f22d12539781f42f5df84
a2dff5d8bea1b6c8a092cc5d4534804947da23ec
912 F20110115_AACOQX du_x_Page_037.txt
b2a93a1d3093cee34c4aa4ef659f85e8
ac514b0d0beabc20956abb2a2734c3be3b84a4aa
2118 F20110115_AACOSA du_x_Page_072.txt
2906e1c99f29dd896fbd92dbf8bee8f3
5d8673a235bb6a910e3ff5c57362f3f77c87fd9c
1827 F20110115_AACORM du_x_Page_053.txt
515c36f8dbd91edcfb6c574d551c3a7e
6444b9dacfe1aab04ab46da97e974122caa16aa1
1795 F20110115_AACOQY du_x_Page_038.txt
4501a3923a624778dbc4677b9a1203f5
04387ce4669db27ae7c52536f667e676aede3a28
2249 F20110115_AACOSB du_x_Page_073.txt
b2ffeee978333983d2ccb32567fa182a
fccc3862fa6efc5c5a212a9cc2de946e90712ee6
1843 F20110115_AACORN du_x_Page_054.txt
e3675c0781a0fb73254c2abf1aaacf14
11778da360a89cc4f6d7d02b09f2452f576820a7
1702 F20110115_AACOQZ du_x_Page_039.txt
359cf409a0cb5c4beb8aebf48b8caa5b
adae6554ffa8d49ab619b294f7bc358353e1ad46
367 F20110115_AACOSC du_x_Page_074.txt
21dfc482279a176fe8b29097950cba87
fe828d100154314028e5c19829708d596d73835f
1869 F20110115_AACORO du_x_Page_055.txt
d1cb8e0808b936c96a99683a3e69a34c
926b1736e0d9e5153423b87ef48801f724133197
1809 F20110115_AACOSD du_x_Page_075.txt
4980a9fea78d4896fb4be5088df0fa95
b4b2954923cb5e5699471c3634ed109f298de304
1343 F20110115_AACOSE du_x_Page_076.txt
23dd8f26f0171bccbddeaa807febbcd1
9e58780944f3e0ecb1127bfdea2aa4d2f37f6504
653 F20110115_AACORP du_x_Page_056.txt
a75cbf292ca16cfad7f359fe7db0a478
55e88005f2ff2801062617e818a4e3da1b979e03
1823 F20110115_AACOSF du_x_Page_078.txt
5893dc6fb97e1ad3abec6c7068229708
36e7b155bae3f924d73024c739df5f5e4499b284
1926 F20110115_AACORQ du_x_Page_057.txt
c93c21101314a8c37c6c04584047524f
b9f5dd6b2279cd5315f3a481fe37070e2a19759c
1360 F20110115_AACOSG du_x_Page_079.txt
b27f6df56a958bb940e7e63ee6708c61
8b110b82cd14de209efb1d35f92f776a9c941f4b
365 F20110115_AACORR du_x_Page_058.txt
d9403e310cadb21f9a4bb2985a1d3e23
07a7927d73bb26546eb0ba2181c12315d312991d
1935 F20110115_AACOSH du_x_Page_080.txt
5bd4f84a42daa2cc0438344bf2385212
7fb11ce17d9cb04f0a545191bb4e39c6912eebfc
1810 F20110115_AACORS du_x_Page_059.txt
549262d51507eb9d9547908d1b20c40f
3340ec1614fd6f697d4aed9cb3dc2006bc744216
1463 F20110115_AACOSI du_x_Page_081.txt
e6f62eeabca43c5072174ba27c31eb80
48a7cc6cc68298e63148b1b1e07e25f96bf68b3a
576 F20110115_AACORT du_x_Page_060.txt
e9862d58292794461c97e590d11af26a
c0170d88ce6cc7ae48af3211507329aa1659ba48
923 F20110115_AACOSJ du_x_Page_082.txt
6240fedb62d50fcca7d0c021057e40cb
c16964d90b5cb488dd34ca1bc2724479b469dc01
1828 F20110115_AACORU du_x_Page_061.txt
35074659f5cca88d899bb5edd5ea24e2
25f0c385e4c5acf19f48012242cd39e45f9ba539
2039 F20110115_AACOSK du_x_Page_083.txt
e25cfff6fa5d21e45608dfde5605b91d
75028ef615ce51e4f0759865ee6f48cb1df740ad
1701 F20110115_AACORV du_x_Page_063.txt
6e3e18769f9fd4137641e3ff1f4b46a4
f5fac7236bcbec2da41b9b014aafa1f119743780
2239 F20110115_AACOSL du_x_Page_084.txt
b95d7544b5d9e2b4e01d7b59e112e77b
147697b0b91c7266be736b3930bccfa274346809
1623 F20110115_AACORW du_x_Page_064.txt
3b3e803b741ce23ba7005bf4937b4706
9163908db370decc93b944636fb13be9a9aeb614
608 F20110115_AACOTA du_x_Page_099.txt
c2cde9443e869bcb72baf293d9bcbeed
06810814a95bde155b22e2c2eab4cf91d6eb196c
1000 F20110115_AACOSM du_x_Page_085.txt
8aecb3b4a65ded04e67854fb801d56b2
88a44e4968b792f3c6921dcc34de987525cb7cb1
1902 F20110115_AACORX du_x_Page_066.txt
ad7913c029aec14cd0f7cc179764faaa
05ed3f15ba44cc1de9a65f54cc0718a33911b6b4
1252 F20110115_AACOTB du_x_Page_100.txt
b593eb43f10424b5f1f702e2061554f6
121ea0357afeee69bd04dd09090a7294e64c2804
2112 F20110115_AACOSN du_x_Page_086.txt
08a25a16f1843c66675c02fca1475500
d63a4b402d291f1293ed327a412322de1e18d391
1793 F20110115_AACORY du_x_Page_068.txt
99bd53952e43d14e0fc9ac8f4341811e
ccb54480ca794b90a2d10a562a709bb62bcdca2e
2038 F20110115_AACOTC du_x_Page_101.txt
afa3a7fa7838a0854f58e48bffed48c3
d59b27e9491a0b36306800dec204ed3c868a0b60
1553 F20110115_AACOSO du_x_Page_087.txt
782ec731bd4ab6586d24803d04a9a1fd
f9a139fce2be55019b942ba57b05aee1aad945f4
1420 F20110115_AACORZ du_x_Page_069.txt
730bcc8d128b147a27240bef3e43257e
8376139c1ce302a675521a5d9ae642dc0016d516
1428 F20110115_AACOTD du_x_Page_102.txt
3510fb65e00ae2c946361116aeaca8d3
9a412b5bdc3d85888cff7a12a82eabe77d4e4c38
1925 F20110115_AACOSP du_x_Page_088.txt
6924703857c9493dec65ac2fe28b7e6a
b9995b548d751fc3a5cbe24cd6134a5a2724c4c3
1697 F20110115_AACOTE du_x_Page_103.txt
6895eef2493151ae7750ea03e2d0515b
dddf7331792de529440c22cf58d4eb61fee79d54
1918 F20110115_AACOTF du_x_Page_104.txt
fb6a9248ae91982b308dd7f7f7128f8d
b25062f36ed770f8805efaae8b93a18a84c01d02
812 F20110115_AACOSQ du_x_Page_089.txt
4e75422eddca0e5b6362b402084f7f93
e4216f16685ca29b07758a3a522affff97f98514
552 F20110115_AACOTG du_x_Page_105.txt
55abc57458ce0c323c8126a7d6362f28
80c3a8130c117e274f2345c0362a593e3f56b113
1069 F20110115_AACOSR du_x_Page_090.txt
690f5c39017aa97658932bd2dc14916a
69469bb66de8bdc5e99b4192c15f75c7e0be963e
1227 F20110115_AACOTH du_x_Page_106.txt
aa9288fccd8460bd25b2fe28d208adb7
223513b2b1b0e42247cf402749781a385e2d4fd1
1634 F20110115_AACOSS du_x_Page_091.txt
08cb9b95b205d6224dfea975615415fb
6831879af7a4a5419aceae8f75abebd66b6590d3
1883 F20110115_AACOTI du_x_Page_107.txt
0f42cc58217344214b383df026c6d97a
244a503051a0c3f1a7b982a6907d2dac68e9d5e1
1289 F20110115_AACOST du_x_Page_092.txt
44167cf8096708f269e29a06d6feef47
8bedc3ebe9a4c0c7219183d7b0591ddd1587924c
1209 F20110115_AACOTJ du_x_Page_108.txt
d5f8969c39d7b3837638bc97f6c23dd2
9bd42f12273205c2385d238e3559912f1aac6e2c
1579 F20110115_AACOSU du_x_Page_093.txt
8a633278629e4dd58f76a2984a5259cc
4b69a95bfa7e76fe08088d61c32f73d73b10033f
1760 F20110115_AACOTK du_x_Page_109.txt
987e00b5a82602c5c5adcc17a5460122
676fa9710a6055bee5cce6df36429ed191f12410
929 F20110115_AACOSV du_x_Page_094.txt
2cc350f0e797246d9997c270ea22556f
1571d969b4d68b81a496ee775234f533d13e4c7e
2101 F20110115_AACOTL du_x_Page_110.txt
f38fbee58a4455fceea975b812f215d9
b947180132fa2f7031d0dc88e3ee462a15f8cdb0
1382 F20110115_AACOSW du_x_Page_095.txt
f49a6f571ebb36a34b30d7e464ecb404
b273ba23446ca7df4391a04066d0d14dbb50e899
2165 F20110115_AACOTM du_x_Page_111.txt
cc9d2fe1d8de7cd7a0a4e1afb513217e
646b2f4b99c173fec7c32c01eb8ea727a340f210
1155 F20110115_AACOSX du_x_Page_096.txt
f05d53adfb9808f261007f854b5fccc8
6a0da9f3770d5af0be7bf6ffb3b75130d7c7e8ef
95734 F20110115_AACOUA du_x_Page_006.QC.jpg
0c48a40c13217e746bc0f55b90ffb08d
879d08e1f2107caa1057880ab06f09f55b1b1933
1672 F20110115_AACOTN du_x_Page_113.txt
364beb801c58fd67097ff4d24338ac9e
942d233138ff86a74ea7474772439425d7643202
1864 F20110115_AACOSY du_x_Page_097.txt
75c84d7c5a9ee7ae50b94fb073de020e
6fb092bef7050f67314c0ff1187972b9f74ee6e7
37326 F20110115_AACOUB du_x_Page_007thm.jpg
a29d670d2f415ecf535fb746c94ab8ef
7c3d2c0313d6c8eb4ee97d00ab76c5fc8b019a66
7600423 F20110115_AACOTO du_x.pdf
62c17cdf27f4f6d553ba7edcbefc9312
e4ef560add04c5baaed945662465638224847891
1205 F20110115_AACOSZ du_x_Page_098.txt
ecc1be12a0fa7a362c9e6ad7b5c2597d
b3ca0479c3bf2730584710fc672c4b5bde24a0d0
67260 F20110115_AACOUC du_x_Page_007.QC.jpg
601e6da80e581e4194edec4c7dd6e4a6
545ea62902d6c4f50435a184d247d3660399fa47
6806 F20110115_AACOTP du_x_Page_001thm.jpg
585267e71a556ec0bae3a0c77639a10c
75410f94532dbb53084e190c93ef9f54f322637e
33653 F20110115_AACOUD du_x_Page_008thm.jpg
38506521ee94b1aa2c2b5b73e973b39f
05328bc3315c4c5314a7f1876c84a88cff334f26
18319 F20110115_AACOTQ du_x_Page_001.QC.jpg
67c677fb71f8a16f308b27e407e114d3
1473eae381ff072e3a927365a3b1279d42c4c506
52582 F20110115_AACOUE du_x_Page_008.QC.jpg
d90be09eba171ab42324dfa6b5c85f6e
ffa5eacd24c2aa68b90018f53a2b244ad21b6c59
51360 F20110115_AACOUF du_x_Page_009thm.jpg
4d71e6704cb8950f17579ec0ac7627be
32c66b749d36427520043e31cf20cd3e39c90d82
3019 F20110115_AACOTR du_x_Page_002thm.jpg
b8e54d6db6949333eb3e5d7bd98d6f4a
89669e41a5c2ee3a2430edee596cc93cf9b311f4
77114 F20110115_AACPAA du_x_Page_088.QC.jpg
c6566428bb2d0c1d2a23a7b4af85a6a9
bd7addaf32ae895271544398f49cc309262b1ebd
119726 F20110115_AACOUG du_x_Page_009.QC.jpg
e714215e8e2acd1fd6162f5d54216705
dfd6c4d93119c506d77589f3ec94b46831cf1e02
5243 F20110115_AACOTS du_x_Page_002.QC.jpg
819bb8b2386318e45cef54699c6f4802
209ea193e41b92d77af30953c642b9eade1bfcc1
38659 F20110115_AACPAB du_x_Page_089thm.jpg
48336a5813e1bc038f96da9bf74bf78a
a8bda65d57999a7dcc13937422b09b1ea1c33e33
56372 F20110115_AACOUH du_x_Page_010thm.jpg
7200cd79dd81cafc14fd1946e6bec455
b82e88edfc762738e72bde948ebae4994abb2ab7
2582 F20110115_AACOTT du_x_Page_003thm.jpg
393614a2fe0a216fa5b12b70da0989e1
3d2bfd2cd9270369ad1e28e6de3c230cc5e0ae5f
58609 F20110115_AACPAC du_x_Page_089.QC.jpg
858e0f91d916f2d9db7412dddd7b00ab
35bb87af3f089637e3bd697cc7754febd3283ab2
128038 F20110115_AACOUI du_x_Page_010.QC.jpg
ad158aa272098ab7b7cc956832076de6
e005c731b418507ae7506424b10849dfda200368
4435 F20110115_AACOTU du_x_Page_003.QC.jpg
499f4b435c234254b773593395fdb31a
fa4502b55479747adfa5d8307ceef844046d4536
38238 F20110115_AACPAD du_x_Page_090thm.jpg
7e63fa4dab47afd96559f0c67cc04d47
4932c27f3cda5e77221a9361535da05235ffa3ce
45822 F20110115_AACOUJ du_x_Page_011thm.jpg
9fb84da0ff97a9d2a9addfb693381fa4
c5410ad6aabda732e88158088b07603f712698d7
21059 F20110115_AACOTV du_x_Page_004thm.jpg
fdca67cc1e5bfc9faa887338f1c2788a
e2a14e105ec117d493c49ef898c8e8b5468fcc33
16846 F20110115_AACPAE du_x_Page_091thm.jpg
f958bb817672e5d1831f967c280287e6
82d08acb6285a616565f3891b56cfa5083fc79ec
95966 F20110115_AACOUK du_x_Page_011.QC.jpg
b6acbd678daa658d04bfdb8ae4787f18
b0362225fbaa6f2879aa3c0dc0bb044de1737be2
69770 F20110115_AACOTW du_x_Page_004.QC.jpg
52f1a6b8b67b31649e9ba8fa720465f9
cee9a08ec2cae4b9a123dc90894899ac343afeef
54946 F20110115_AACPAF du_x_Page_091.QC.jpg
7e475059fe6e79213f64e73299e6d587
7a15cc8862727fbe90f77a659401d32c2ab372e9
18014 F20110115_AACOUL du_x_Page_012thm.jpg
669b93c7a0dc2eed36e1bced1874d156
3179df86c61791543f334c2d7ed73d8116ed7218
14689 F20110115_AACOTX du_x_Page_005thm.jpg
2d0aee794678161f9da7dc3d2f27ede9
8d5ea3d27c666c887f5c4e5855bf7311c10a217b
16350 F20110115_AACPAG du_x_Page_092thm.jpg
37a685c72dcfd68ed29a5af280be9a15
5535d73655f50b18c36a6563e7945841be8d93f4
15758 F20110115_AACOVA du_x_Page_020thm.jpg
64b95e4ffdcedf22970caef59794da9e
177eee6afa9736b4d65427e4f18d7b44c2ddb429
55527 F20110115_AACOUM du_x_Page_012.QC.jpg
c5ee0e0443d9fea3b6a186eb93fdc4ce
419c662761806ad9a7319b2eab672d27d8400c33
46823 F20110115_AACOTY du_x_Page_005.QC.jpg
56716de236a2cf94ef36504ac67b5b81
5a334cc2db70dbf667a813b72f500bcbaee41d45
46133 F20110115_AACPAH du_x_Page_092.QC.jpg
8f827b8636137d95d9fe990d97a3c9c9
9baff26dc0ef76e991c3b815fd195c4b4df9e6d6
39990 F20110115_AACOVB du_x_Page_020.QC.jpg
27f09c851a5da1ad22a510435dca6a97
d1b5ec98cabee6b9f3c3760e7fedb2f54bc834bc
20977 F20110115_AACOUN du_x_Page_013thm.jpg
037b7b4b48ee45fa24a331997d9c6a79
91876292841828c7233a096587c5bac46f8b57a1
18870 F20110115_AACPAI du_x_Page_093thm.jpg
2c64edffc96c486001061914dee3206b
062a92af2a71ef5bb7b8903e70b4976542962933
18534 F20110115_AACOVC du_x_Page_021thm.jpg
880454c4c9a7b509e46d35fc86abf2c7
b3dbb11b2052e81c2a35e3c47c2a76be398d6457
62012 F20110115_AACOUO du_x_Page_013.QC.jpg
8059205c282d8b82149d6faf2d14b1bd
357663f4534c23b8843554eda560907a9c66e359
46190 F20110115_AACOTZ du_x_Page_006thm.jpg
30a91c1f5561899ac3413a17992905b2
b146d728cce1aa007ae0c5c8aa5ffb0a0599b569
55773 F20110115_AACPAJ du_x_Page_093.QC.jpg
7de330497c48dbfbe44379e6bf8b6c13
dcf7c292e32c79c499dbbc930e8407e649a49aa5
47604 F20110115_AACOVD du_x_Page_021.QC.jpg
fe9289786b61a2975003659ed4c4288b
2b9def39628d0ed6a3003806cd9fcd50cc740039
24592 F20110115_AACOUP du_x_Page_014thm.jpg
c6d65108e5798ef8d6b7844874f09b27
f151a0ba15855514496d0ddaf79df919d24b4e73
42943 F20110115_AACPAK du_x_Page_094thm.jpg
0f90da4a45969d4189895db94a48dbd7
26e4f38923e3e57710031f26e88034ec41ceef36
45489 F20110115_AACOVE du_x_Page_022thm.jpg
bf4ee482d5100846ed12143d1bedf325
932f2d89af66e29e73edf06bdb4781e316d620b4
8646 F20110115_AACOUQ du_x_Page_015thm.jpg
e73d5ffda54a6c9dd6c078472ed85541
e30fe79aa43dca381f29e71b98471cb8cd51a0fc
73932 F20110115_AACPAL du_x_Page_094.QC.jpg
7163276e11dba876ac29515fb505881a
7977f567ae7f941094579ce74306a4fe3173dd0a
87114 F20110115_AACOVF du_x_Page_022.QC.jpg
3cd0d3ab996a4c3cf1ee7aa24d9d343d
9ab7bbdbd626e37a93b17a75195db50ae4974ca7
26757 F20110115_AACOUR du_x_Page_015.QC.jpg
a4b63c2250d017d4b3b20852fc5996de
2d426f57d4a82da6545f25edfa76323fa730b028
17875 F20110115_AACPAM du_x_Page_095thm.jpg
489a2a5ab596cfeb47088974e8216a55
c4a066a5735ea58fb0af8fc9ab93cee1f834c53b
45537 F20110115_AACOVG du_x_Page_023thm.jpg
7f274c73f903fc5e48608f390fdd2873
255b27c43770fc610114b133db419ccd4490b251
81972 F20110115_AACPBA du_x_Page_102.QC.jpg
0a12d6ae64747b74c7f50de0fe4ea204
3c3bfa0cbe1a26440f5766ccb301496f9f5bac18
54004 F20110115_AACPAN du_x_Page_095.QC.jpg
3429f96a7dfb1ee0e3c60423d71d4cae
be312b124a0762934605227bb9581dda279d4aeb
88809 F20110115_AACOVH du_x_Page_023.QC.jpg
c738847d56b854f62f8da4a06f5930b8
0a7ed1aa9f17d770062638793786eec71a66ddcf
21659 F20110115_AACOUS du_x_Page_016thm.jpg
ca1b7708c60ecbd7e98c8252341dc9a8
a2195612cb1a835f40ebd9b3b4b9183284e6ab6a
19480 F20110115_AACPBB du_x_Page_103thm.jpg
8bdf3d7ad31ade3e2c37a3e434fccc59
2078de63e1abd8d74b2b0bf9ab3c2520bcae7a17
45112 F20110115_AACPAO du_x_Page_096thm.jpg
8c3052183755c8dec7adc0ba55b3d222
dbde67731a317a5847c71fabbe417c273879beac
44496 F20110115_AACOVI du_x_Page_024thm.jpg
e5e790df96261f25fb80642191515bba
0017c6315cca7e898aa44c4bac29eefa624156dd
69002 F20110115_AACOUT du_x_Page_016.QC.jpg
8bd7f6f49280986a96f43363fb2e8d3e
91e2966555faf9d716bef9ce72adff4d31fc8f67
59886 F20110115_AACPBC du_x_Page_103.QC.jpg
de86538e65475c906baff21289fcba9a
3a610ff0ccf09b6b9bbc7e3d59d7ba157bb413dd
84293 F20110115_AACPAP du_x_Page_096.QC.jpg
a0c55435bbc9e500dcaf43da9e501f30
e8c715157d45c566c58ec197ac7fa98088a9967c
81952 F20110115_AACOVJ du_x_Page_024.QC.jpg
11460997e2939c8f68dd9448cff7d11f
23f4bc73483466dbb6b8f45d48e95e36e2cec92a
22228 F20110115_AACOUU du_x_Page_017thm.jpg
06ed3ef269b3bf364af9dc80de3edd76
8072bbfc594d249601630c85b47a593c514f8fc6
22120 F20110115_AACPBD du_x_Page_104thm.jpg
ff84c6715a004042915b4484540f778a
40395d803554231224f4f472543738740573fb98
23862 F20110115_AACPAQ du_x_Page_097thm.jpg
f0b8d0f4cf1b1ed56041aee6a12ee29f
0ef8c5dab4ee3e53c4820b5fce0c1748dd623914
22298 F20110115_AACOVK du_x_Page_025thm.jpg
05fc89aab2dddc3c38cca6af41fe0ae3
e3bda5244aa73a23082fea011fc0be3c5d9b6dea
69527 F20110115_AACOUV du_x_Page_017.QC.jpg
bca174bf6e1edb2608689bfa0eac8da5
34aa01cacbbbc01e2fdb50902ea367d94a5016d8
70482 F20110115_AACPBE du_x_Page_104.QC.jpg
d4811f6166bebecacca96150cf2b7d54
7ca3deaa5fbf3f1a34c4563531c47edc80192336
73006 F20110115_AACPAR du_x_Page_097.QC.jpg
5474358707763b04febe5a029aa339e1
be8349b47ea00923e1452a1c67c3106a8fe64850
69670 F20110115_AACOVL du_x_Page_025.QC.jpg
3cc61a377b09fa131c9862f0ce2d8c89
a7426dce9c5b5e8e1dd1a90205a6a0e24814cd23
23700 F20110115_AACOUW du_x_Page_018thm.jpg
515efe1a8a96577fdfd22ea6603231e8
84a436f44b42c0165cbe6e546498ebf181214488
46579 F20110115_AACPBF du_x_Page_105thm.jpg
b7fb88de0a71c34308cf6bd451b88d20
bce0e5fcdc3307c41282c4ac49da19a29f065f2b
16233 F20110115_AACPAS du_x_Page_098thm.jpg
50e4eb5f06fe3e727dda4464ff1dde0e
2fd915520dc4faafeebe8cb9f37a5a79da921874
44189 F20110115_AACOVM du_x_Page_026thm.jpg
c8f34fe962d73963d664e3cd12076691
539c7afc4f47819871285b9a0e3c957fde300e68
79238 F20110115_AACOUX du_x_Page_018.QC.jpg
715c9e2aca67f9be0112b33b3a781ab2
28e24a7002c09b8825fe5fd8f3b973cf3c10cc20
92773 F20110115_AACPBG du_x_Page_105.QC.jpg
d0c5cbf687853d3fc732e36ee38ef4d8
071fdebc229307ca7f7c6445ceb008262e9e7b9e
83808 F20110115_AACOWA du_x_Page_033.QC.jpg
2e6b6402c09571ee63ab57607fc3d7a9
caf29710d80b7864f0bff4e53d07608a25748b0f
46846 F20110115_AACPAT du_x_Page_098.QC.jpg
fd43ab5e774d67b05f61f24c53d03393
9effcdc8974733ee80a354e8d0eceb2c7f11b271
40699 F20110115_AACOVN du_x_Page_027thm.jpg
4d58fe11227c4d68339ce0c2d816cbfc
a2a07ea3331733ddbd32359be61bd7bbb7390242
19484 F20110115_AACOUY du_x_Page_019thm.jpg
0e50c1135864a81445e79027ba62685c
e40bd60cebec87cc9072fee6e639420d1e7c9ffe
42138 F20110115_AACPBH du_x_Page_106thm.jpg
25a96f123d075df0260b2724be870e9a
73e1dc1c65a1cf59198b104834f8307d93e5a860
23687 F20110115_AACOWB du_x_Page_034thm.jpg
457b7f1fbcaa401bf05b8cea638d1f98
8b5b9c717a8972a46602608103da35dd3c126c44
76821 F20110115_AACPAU du_x_Page_099.QC.jpg
31f2203f416fe97929af7a68e62f7323
0dc1921d1f3f2f66a147730b91f2c901b339e185
67549 F20110115_AACOVO du_x_Page_027.QC.jpg
f10405e53b5c4ad6a53f9a2bb89d51c2
db5fad9db73c0bb9163d95c6e8d9ef6a67fe0373
57806 F20110115_AACOUZ du_x_Page_019.QC.jpg
181f209b365e53e73711bd8153f7a512
8c10a125c73a54dc1b2acc761f3987537e93d32c
76869 F20110115_AACPBI du_x_Page_106.QC.jpg
b1c98e198c5ea21686c3921dd0e4580f
bb2441d3980ee8b7119a35d552a3497a52832fbf
68093 F20110115_AACOWC du_x_Page_034.QC.jpg
656f595b34253025e2cab665914582fe
79e2dd47a5a1c0419012b9e252f819c6228ff6af
41406 F20110115_AACPAV du_x_Page_100thm.jpg
9a8131f036466ceabc972c9587ce6a84
86495496f1c72a58b5fcd097690dc93ac02ec62d
22692 F20110115_AACOVP du_x_Page_028thm.jpg
bb98287b400cacdf4db2c4a48c62d9e8
6ed2f3da98851452dd9d696f185d4baaa77bd62a
49094 F20110115_AACPBJ du_x_Page_107thm.jpg
80ca72300073dd4dcb6ce290a30f586d
aee6cfacc605eed0833b5e249dc58c00ba2b7a97
22485 F20110115_AACOWD du_x_Page_035thm.jpg
7b2400cf0fb3bcba826c9266d5034c40
2903bbea6b037e437da0ef8aecd5948e06963733
68965 F20110115_AACPAW du_x_Page_100.QC.jpg
7831adce36cbeedfad8988c283c122bf
bdc801af30b2beb8ad4105f2e7a4b047104f699c
70538 F20110115_AACOVQ du_x_Page_028.QC.jpg
ae7407c461c33ac3f124f61670a8fef5
39be2259d214eb6c024177214ea59affc8ab5be0
96804 F20110115_AACPBK du_x_Page_107.QC.jpg
f6db73382f28fbc9fb140b5d7ea94f20
192b64db702ead817dfa619a8405c9c42101eda9
73912 F20110115_AACOWE du_x_Page_035.QC.jpg
afaffed5fc14c9e233c5b03edd54cce1
5f733eae4485b67e04455a87087a339230cc4972
45477 F20110115_AACOVR du_x_Page_029thm.jpg
3c78bf66e63d0541f6aa5e82d6e612ab
c8ed746e0c8b4898845b757d24cf52c6d748528d
16024 F20110115_AACPBL du_x_Page_108thm.jpg
5eff31979247f60585e3c738e053838a
baa483939d2130d42f35e867525efca5519dbf9e
21347 F20110115_AACOWF du_x_Page_036thm.jpg
ee27ea5e3688e7ce7593fce6f5a7854c
056c335fc42021806aa048f55d4b7cfe72b035ba
24695 F20110115_AACPAX du_x_Page_101thm.jpg
5f48a77e68c7ce5473df1eb5604289d5
dde2fb85ff301a82236325640b910ac8862a03b1
88073 F20110115_AACOVS du_x_Page_029.QC.jpg
2d6841b704b1528bc37b384b51ea86e2
72b5195047491ffef0f5c57283097d5019483d9e
48483 F20110115_AACPBM du_x_Page_108.QC.jpg
8d99bfa7c209f1e17b136288d75c2170
602c0a94e3ca742bafa24a59faf411fcb584b97f
63899 F20110115_AACOWG du_x_Page_036.QC.jpg
d2b5ccee2cf1607bf76601ab0e6c9b6d
c4ea772db0d8e3d298d0f6e78cda12a01ab71cd6
77401 F20110115_AACPAY du_x_Page_101.QC.jpg
e736e1648efe9774f315f0f6290cede2
f6de62e9b655851e3d891cf4d41aab7eeb52f8b7
20628 F20110115_AACPBN du_x_Page_109thm.jpg
336b49c634dc9312ec47a68320b78237
a9f1ef68ad7a1e29f3673d380c92e773434cfc47
40016 F20110115_AACOWH du_x_Page_037thm.jpg
6995be624276ad4985e9117796d0f067
570f1a9d4820af9f611ff94e53a5494fd22f0bdd
44261 F20110115_AACPAZ du_x_Page_102thm.jpg
31c97f9447a8b2e0f7aff8b73b629f21
25df9b2f0f5402dd5662547e461dad8d667c2ba3
63983 F20110115_AACPBO du_x_Page_109.QC.jpg
d241a28e579bf6b20ddfbadf13fdfc65
2980808c6c05fc65587c081e58adde402f45435f
25158 F20110115_AACOVT du_x_Page_030thm.jpg
aaf9c82478ff5ee26e73ad0e0e1ea18f
8789c2f2220f68623a61808f3fa864258f2c902b
66510 F20110115_AACOWI du_x_Page_037.QC.jpg
00cce3c94d2b285723db5203e2102f2c
4f53b475b591163d169e3a7efc15f03858d46ffa
23475 F20110115_AACPBP du_x_Page_110thm.jpg
047d0290dbbd0a55d4ae610072f5e512
683e5f6cfe4a9989f5b457825be03846c550c971
82334 F20110115_AACOVU du_x_Page_030.QC.jpg
56d584a553d21ac54bd8ba62bab29643
02ceec885a06b192638772030df5f9ecc7b3d789
46803 F20110115_AACOWJ du_x_Page_038thm.jpg
c4feb62dabfd74e8cc6669f01c37a09d
acd44364dee5c2cb9c52d3d92795c424258de98b
70883 F20110115_AACPBQ du_x_Page_110.QC.jpg
157b7f675e7ede129a8817be3d2052ab
2cb5ed82bdcff194e0260c4d0148dd1b81c90550
20491 F20110115_AACOVV du_x_Page_031thm.jpg
ddcbe633f6eea5ac8166df314662c8e2
41815caf970c8b3aa06c716eed81632bf5ffef10
91116 F20110115_AACOWK du_x_Page_038.QC.jpg
9fefe85145ae5cc1f2dcfe43455bce45
98d2e72a09abf7cbcfd527d1d10d8a559b3c7e45
23699 F20110115_AACPBR du_x_Page_111thm.jpg
e4acb9ddbfdb487e64589177d0449436
9df6a455a57affc788a95a94d1dc702baeb86762
61354 F20110115_AACOVW du_x_Page_031.QC.jpg
39e10a206a489abfd87ff5d9d0436197
e515afa48d8990847e1b576b2f5b765fbfa1082d
19838 F20110115_AACOWL du_x_Page_039thm.jpg
d4163a384b06cbfc0ce22d5e2d246834
21fff1ca61c2e5ff4c7b31da9b64d1c76ade2519
77946 F20110115_AACPBS du_x_Page_111.QC.jpg
5c1b81e157a0a2aeebbdc4099b36e3c8
4f1c267780af6edc94497707698ae179690712e8
46737 F20110115_AACOVX du_x_Page_032thm.jpg
3a20dff2dd866d17b953d3903bcbe6e4
1b03d5382e74b9b23f07eeaaef385aedcc770df5
23188 F20110115_AACOXA du_x_Page_047thm.jpg
af8e2b2c81dfdc03cfc137b9bfcd2c9a
e9adfbefdf76a417f8618c088e569f51bb9d1cbf
62471 F20110115_AACOWM du_x_Page_039.QC.jpg
e54feed3fe86ec5bd453780b88604219
056f95f82db55a6f67305687091cac5fd2db2702
5943 F20110115_AACPBT du_x_Page_112thm.jpg
b58b9e004d2dc2577098d5b5f6f51330
b908c28327e33de2966cd5554b9546e97d8d5c1a
88319 F20110115_AACOVY du_x_Page_032.QC.jpg
382a2a56a6a08be712a43783149c0e5b
1c089b226ecf2cc7119e6b781d378b305e0d74d3
76155 F20110115_AACOXB du_x_Page_047.QC.jpg
a662b0b6313c9696e5f11544160316cc
58395a5aa5ce7565c60229a8b559da1f04fd7cd4
19501 F20110115_AACOWN du_x_Page_040thm.jpg
8b317dab4238fa53abd5ec85c19f5e55
4f233c0b75ce17e2ac159c24894e3e19b837ea4f
13783 F20110115_AACPBU du_x_Page_112.QC.jpg
7adddb93a019915f3b1d65b6cbf1ea0a
d4b3509627b5a101ba65b7648bc37197c3b7dd25
46853 F20110115_AACOVZ du_x_Page_033thm.jpg
452d1726f114c97b576143b96f82f757
ba3a48466162dcef8b29d3a5b80135c64f808aed
42745 F20110115_AACOXC du_x_Page_048thm.jpg
d199f80cbc2f3198efbd622cc7feed54
4f4225a4b5690101f4540691ba0706fc3f9ccb13
57995 F20110115_AACOWO du_x_Page_040.QC.jpg
ea58f79010e55748490de51c4d66ec9d
70d7f4d3d623a5ad316f54d650bff408280dde43
20555 F20110115_AACPBV du_x_Page_113thm.jpg
0c803c15800baf7ab985e73d1b160cba
2159e4d0d8614d18b29f394b88dda29f3a060040
70259 F20110115_AACOXD du_x_Page_048.QC.jpg
1658dcd4c06df250ebe09bfd2d760ed4
a1f8fd9eeeeb0c2733393ef20702c5b2aa68d2c3
13792 F20110115_AACOWP du_x_Page_041thm.jpg
e9b2eacbf8c444ca3c36def66d2f8b04
06f323b753c4473ce0088ef3c3ff25fdd6078ad5
67274 F20110115_AACPBW du_x_Page_113.QC.jpg
6c96c739e0d2d9db6696cddc2945cbc7
d305c75be5e74df08cbc49b6afefe5f3fe5c6ac3
23478 F20110115_AACOXE du_x_Page_049thm.jpg
fba741d098e4bdb0754d645098b6309d
accebd0b671fe94629c16dc9bfbf99588a47e5c7
37293 F20110115_AACOWQ du_x_Page_041.QC.jpg
44c1587f5392b3ff04d9828294c20271
16f55cceae582a313a9bbe50b0d18b90a33e94b2
128828 F20110115_AACPBX UFE0008357_00001.mets FULL
1c36ec02b93cc8079bb9bd82887e3ec2
324d4470829bba719f31f130a136d69a930ec4a0
69601 F20110115_AACOXF du_x_Page_049.QC.jpg
e0730d60b193ac5ced533b321ff15e19
a1e54a32d9d9f83b5a4b4598edfece2e61f58199
21678 F20110115_AACOWR du_x_Page_042thm.jpg
b0867f3f0456f1f4d957a33a5008a748
75eb9f153bffc3f6d769294a2025de2c75ce08ce
41383 F20110115_AACOXG du_x_Page_050thm.jpg
91d4a6c503cd89996b53486c23282d40
885ce9e654f598f5fdfe508b7b6a21487ce0212b
60175 F20110115_AACOWS du_x_Page_042.QC.jpg
95ea3d5540ecf028706919b7e493be6d
5cee6e86bc6bc945748e1d9aafbd4fc179c740f3
67808 F20110115_AACOXH du_x_Page_050.QC.jpg
5c3725916862a4c693d74fd1eda306a8
9c1448f6b0fa63a475f0862e5a99b99ffa0bf4a4
23865 F20110115_AACOWT du_x_Page_043thm.jpg
2a2459b192d89c7fb972ec7fdf12c55d
1c24b712f5e7f950c4f9aae52776779e2e3dead4
43961 F20110115_AACOXI du_x_Page_051thm.jpg
e72a33602e3c54748597552497f74cba
da49d32e5813a3116649173a3f9006243da5480f
196979 F20110115_AACOAA du_x_Page_018.jpg
dda8d2b2626411a83db31a6f615d6e9b
04831e757a0ce6e1559625c0a91de92862d8d081
75166 F20110115_AACOXJ du_x_Page_051.QC.jpg
c50367f86fd083096ed0a23a0eeb08ab
f0a2e4ef29468f7d8601648910820a792ac639e8
71508 F20110115_AACOWU du_x_Page_043.QC.jpg
91aa21fd45c76ac4e5a39db4e33a5d5d
7a6383a0b1b7e939c4a637805a7685d7ba05ab62
147539 F20110115_AACOAB du_x_Page_019.jpg
31c1d278ea567bbfc6093c711696d942
82c4f20b1f12debb313b1b860d31bdf4870a59a8
13180 F20110115_AACOXK du_x_Page_052thm.jpg
a1398eb7be101dae54e7e30272ac96c8
8fd1021163c0c10de66b21b681d5b308870f7a02
43965 F20110115_AACOWV du_x_Page_044thm.jpg
012790b33177c5a8eadb9c67834e0e8d
1faa6a5a25bf16d33ad95c6dd5f47aae7fa4b058
110956 F20110115_AACOAC du_x_Page_020.jpg
f4c3e721ed9867dbc53782318758cc54
527111b8c72f5e95f6f0a743a1a6cd82fdc8b932
40889 F20110115_AACOXL du_x_Page_052.QC.jpg
6013a41c3eb14a895e8c4d448bf37bb7
26c02eb23472546e54eed1f6591e95df9269fdd1
78525 F20110115_AACOWW du_x_Page_044.QC.jpg
e0cda821bdd94fb40971684e2284eada
efdf299fe295fbf24aa04af5f7dadf1d836a2c29
135167 F20110115_AACOAD du_x_Page_021.jpg
43c07ecb508da656c45b0f849d5a04e0
2177fd24a9adaab29b65fcf2e300e2d8930e11c5
75185 F20110115_AACOYA du_x_Page_061.QC.jpg
17fb34655c27b7d32ff243ba7ea91d7a
bd98c57313dada1741bf391753f9e156f05e3088
21609 F20110115_AACOXM du_x_Page_053thm.jpg
1b4b3092459434a6e4f447b7816e7d54
67192e22c89ae7ce49da71ccb1b198512eb280a5
16820 F20110115_AACOWX du_x_Page_045thm.jpg
0fe07bfbd879e2986a490c565661f8df
aa4666493acb0d5faae0a0bfd6cf9520066e0f77
184920 F20110115_AACOAE du_x_Page_022.jpg
78b803d0951839b5000ac463e9113676
7d8b2f93f02f0bf6316c861b7b957fc69e4837fd
40529 F20110115_AACOYB du_x_Page_062thm.jpg
1b5d7b08385d4b47055488acf4b9bf07
cae5bc27a546157622d0b081fe10602e2e4dde89
69162 F20110115_AACOXN du_x_Page_053.QC.jpg
b573ef53ad12dce038530991b51ff576
94011bf4e6d63118710fafba37d41af95d5b5f02
43935 F20110115_AACOWY du_x_Page_045.QC.jpg
40d80cc19aed823b504c67d6933e005a
cc282a18c099293510aee61a6f972d085c12d158
196947 F20110115_AACOAF du_x_Page_023.jpg
3a010e9265430564edaa7d1c7e140043
ea10184d972a3fdff74b85f00f31b7da8afbaf61
71256 F20110115_AACOYC du_x_Page_062.QC.jpg
afb79827f4e6c114c849cc48bf36405f
af7cbb169de8a0dadea91920c27f12fea400af84
22735 F20110115_AACOXO du_x_Page_054thm.jpg
722194998605b02a3bc64aeeaca880a7
55b3cf4acd0f76f23a350feaa2844b27c1284325
44346 F20110115_AACOWZ du_x_Page_046thm.jpg
35ae60742537e557783985d368d8419f
67d11deaf0dbab5a80973e9485195590871d6d0f
174624 F20110115_AACOAG du_x_Page_024.jpg
127d78d9b10b77a746b18bb466432015
36c9f2f4540792df2f83861562dd11a945c72e07
20497 F20110115_AACOYD du_x_Page_063thm.jpg
2e3ce62481b8b7192729a1398e3569d4
5f95bc7ad1b0191703e4843fd2fff73521f2edc9
70346 F20110115_AACOXP du_x_Page_054.QC.jpg
3acd029606a168f5c16b8835d1ca716c
20567fd9ce983d365ad5f6683c29be0fd342df2b
178052 F20110115_AACOAH du_x_Page_025.jpg
18f2668c126a8cf7673cda050b6ee5b1
071657a04aff632739226f9e98459ec15cc92011
61720 F20110115_AACOYE du_x_Page_063.QC.jpg
601f2310dc93167ca9e0be786e63b561
d8ca6a28776c5db0e6dfba851291228fef48ca74
37597 F20110115_AACOXQ du_x_Page_056thm.jpg
77ec26091d8607c156a1615812375554
83d3a3377f685ef27f98cd4edd632f69a20f7a23
168941 F20110115_AACOAI du_x_Page_026.jpg
64fafcdfc069b3abe667d5a10c2a1dee
b6e78d770c03f2f5d57de558356bb64ddf17bb5a
21650 F20110115_AACOYF du_x_Page_064thm.jpg
f8e459fc3f75258d4cdaa82d154d00f2
a45c1925ee8dd27fadeb12efffaa21edd38c823b
56084 F20110115_AACOXR du_x_Page_056.QC.jpg
2ddcbf1adf69659f52949de3ad976f9e
72c06137e7927a1cd8db7755da002da25118032b
131581 F20110115_AACOAJ du_x_Page_027.jpg
7bdf01641cb234f259caa65079382160
a4fdf4b34d42e8401d472e645ab69e1f443e5629
64970 F20110115_AACOYG du_x_Page_064.QC.jpg
2faafd35434452d78e28e583289760bf
e566fdc69f64a7bd2007221461fed9e4b23e4bdd
24312 F20110115_AACOXS du_x_Page_057thm.jpg
f42cec81ac85da30ba8810dba6a15a3a
7fb65793cfd189ff54b5af1a51907c936c2041a8
180896 F20110115_AACOAK du_x_Page_028.jpg
de17cfc7495cd935e1a6b240c2547f3d
e90ddac8ff6aa2183a8420fbf63586ba8f96f4b7
24149 F20110115_AACOYH du_x_Page_065thm.jpg
7c7a824163333164617f840db1d8b6a5
4b23eb8590357e0838e64bf0b1e5cd81de7843b5
75768 F20110115_AACOXT du_x_Page_057.QC.jpg
80a18a6a92a2c08d927f175d9641978b
17737b9a0764170551aa2d9f18ab2eae3dc22fd2
200971 F20110115_AACOAL du_x_Page_029.jpg
c54e789502eba485dd6102797018e1fb
740507e34a08532a89a6906d3a64078b854c1086
76817 F20110115_AACOYI du_x_Page_065.QC.jpg
9e89b6ee5ebec939844af2d9677828ff
0e0469a664c69e8f63ab3e6ac9dbd188b78a1211
38279 F20110115_AACOXU du_x_Page_058thm.jpg
18cd99d46f5cdeea9b1d678bed70ce7c
a4c021476990f21d3deb6c3b6d89983dccb0c8b2
172750 F20110115_AACOBA du_x_Page_046.jpg
4d5fc2e071b6bf646d1a7060f383cdd5
3c4d6da72009243a325391afc8f2b6602376f176
216704 F20110115_AACOAM du_x_Page_030.jpg
af1e33d38e9601fa643ecf8affaba83c
e34449b188ea88971bd54a2e4eb3ef0cccb24bd1
22548 F20110115_AACOYJ du_x_Page_066thm.jpg
dd9a05dff0f51c46d2c954fa63baf491
5a627ee5efbace7850d639ffc164feba69420d0d
192114 F20110115_AACOBB du_x_Page_047.jpg
c418de0bf134f5146e9783a41ba00d4d
9d7ae5d64b10eacf8a44906a81e575b4d0910f7b
161691 F20110115_AACOAN du_x_Page_031.jpg
b4845a1479dc6d0c14debbee2c8f0d30
d7727dd3718cae85d8ff1e261e84345fa8594ec2
75340 F20110115_AACOYK du_x_Page_066.QC.jpg
c336fa86548d238282c5306efc60dbe0
8f66abc4f22f91f2a9884549ef5a3eff68be1a16
22355 F20110115_AACOXV du_x_Page_059thm.jpg
e7d881418238b25e07eedf87744f7358
3f87565d0f264e0366a6c9844aacd1641b27dc75
151168 F20110115_AACOBC du_x_Page_048.jpg
e7be45adeb8c7c9a3bd8e73220808997
d465fbbc779bc7b53e7366d042bf94a5e76dea9e
171683 F20110115_AACOAO du_x_Page_033.jpg
c367d5d6433810d2ac99f02c47ae6f7d
c29feb6f81d670c406aa39d84bfe7062c00ee112
23906 F20110115_AACOYL du_x_Page_067thm.jpg
7e70cf2342a7cf4f1c39ad169888d647
e5ae6b789e03dc1e664acd4fe50c1219e734f254
67877 F20110115_AACOXW du_x_Page_059.QC.jpg
544ba1d703063508afc3bc4af86d94f9
53b4bed53d5d4b427e0e73e736b5ddc6de86c659
139058 F20110115_AACOBD du_x_Page_050.jpg
a31f2de1ac416a6dd0b6c829e175c712
b08102b2f5693d6e3187a3f6261baad699f26388
192237 F20110115_AACOAP du_x_Page_034.jpg
dda64c1b32eac16f88d339175c630ad9
8ac23e313a2083ee938fbc2ce6faabc574d24b3d
76805 F20110115_AACOYM du_x_Page_067.QC.jpg
e48bce8c9c0a311eff8db13ddf76c675
54dc158e2663e4e0853b86dd1f289bebe7a47874
41007 F20110115_AACOXX du_x_Page_060thm.jpg
f39c5f062841e3eade74163338443dd1
3221665a6242f1742614401aacf96f96f7b79bb5
164107 F20110115_AACOBE du_x_Page_051.jpg
0b7c64c14117d9a9799bbf7825b0857e
fd7ff889c4793994cd0100e4cfdba61c49b2f914
195397 F20110115_AACOAQ du_x_Page_035.jpg
3aa229b86f132df36c3e3c392af63240
dbcae755ac67220365984a883943cdf64fbeb8f3
F20110115_AACOZA du_x_Page_075thm.jpg
a484a48983f0728403559cc65b01fc34
c61b48339586538eace6fe5a3bcbf2bc8d2632c1
43380 F20110115_AACOYN du_x_Page_068thm.jpg
d575ed579349fa6c4e1b2b4ee826ad78
6e23e24f39c994814333b5d88f8aa6efc5743a55
67718 F20110115_AACOXY du_x_Page_060.QC.jpg
a10fd50945117b46883ca1295c96982c
c7015a361f051ecb24cddc0ef339043cbee57afe
101786 F20110115_AACOBF du_x_Page_052.jpg
6e3325fbcdddc6956179d13fa5fd3ca3
78169c28884ef218693a49fd4e1104c08d2a6ce9
176175 F20110115_AACOAR du_x_Page_036.jpg
09672e127c27d989170e26c9a8226a5d
bd3733626997604ca4212ad13ab7968b1de0c4b0
67729 F20110115_AACOZB du_x_Page_075.QC.jpg
bad698d1d9667882a4a4a2701078b23f
6743b289fa0603c4ce1b603a1fa1d93a5c0275f6
78765 F20110115_AACOYO du_x_Page_068.QC.jpg
7fd36bef4d8d4d69293792f5c71d8773
9dcaf6f55bb8d88cef5fc179f4b0cbe44297351b
22668 F20110115_AACOXZ du_x_Page_061thm.jpg
9d3575de99e33f9a67590e8d2dea8a0b
b64640a781ad32cb821decc5757bb6c7c4a9f26b
188781 F20110115_AACOBG du_x_Page_053.jpg
658ba015156072abe9d146738c9e841f
6918f9c55e022dfaf0a7449ee23e0d260f55c72a
130316 F20110115_AACOAS du_x_Page_037.jpg
1d7ffa5f69d0a1b5cba5ed0838c956fe
ed4f506f7b2736b14df72514ad5a09309ccc4b38
46249 F20110115_AACOZC du_x_Page_076thm.jpg
c1b24621d349b17f4a6b5efc43e42613
d016973dce54b01b035664b3be1cb9ebd9559623
45879 F20110115_AACOYP du_x_Page_069thm.jpg
519920fed47d222bcb6f8df97a3d4382
a611767a5f2b6d44c096369348525f0972138154
186184 F20110115_AACOBH du_x_Page_054.jpg
46535172fb85a6b2847f33018b748e95
9061134d787a9dab321e8dddb9d2c0157ad0975e
201420 F20110115_AACOAT du_x_Page_038.jpg
9ad250a1d40c14098b1cfe212971415d
6467f8a1abd59bc76dd01933b7f73cc885aa1524
86355 F20110115_AACOZD du_x_Page_076.QC.jpg
e7d18fb2c9740870a812648847d480a6
11f01c322ac350ac72ed56582569b67d4aa0fb40
87132 F20110115_AACOYQ du_x_Page_069.QC.jpg
92ebf35404b2a40772579750154d8335
f60fb0fc7e66df84aade5620822890bdb17c72e2
189774 F20110115_AACOBI du_x_Page_055.jpg
7be5ad5252d40038018287e2f4612c3b
76ce9ebbe368690aab897153bca5e4f87a03c3c7
141615 F20110115_AACOAU du_x_Page_040.jpg
66f2065da12b3ec2b17a7e796e89778e
624300fc31495945b90ffdff2092fe8fa5e71b8c
24723 F20110115_AACOZE du_x_Page_077thm.jpg
3ae09f5431c18515d72eff320a7c6bea
9330b181075d6f5c9d4c4c1b647f0584ce0f4583
47485 F20110115_AACOYR du_x_Page_070thm.jpg
dadf7a96e3d37b9a66221f757a967c9d
e78c205e6b93c4eb75fbcf884b0e1e486a439dd2
105680 F20110115_AACOBJ du_x_Page_056.jpg
b0f4976e611b00044d0c03931c74cb88
f165714530e1e8cf7d17b1d9b41b0ca63ecf2a44
98016 F20110115_AACOAV du_x_Page_041.jpg
bc2b9559059c83a68f363cf4b0e353f1
67e326c7a59241cf1ddde1a1631128ccd681240a
82236 F20110115_AACOZF du_x_Page_077.QC.jpg
eed2d99b470713ee23b9523463d70503
23275683ecfb87a940f35cbfd55fd3cbb5f0b616
96035 F20110115_AACOYS du_x_Page_070.QC.jpg
a4a40f60b8b1ab7628b15909f7339673
7d5be788b66c54a59c439c08e319fb8c14e7debe
203576 F20110115_AACOBK du_x_Page_057.jpg
69d50e08e2f2a10942ccf27a72c85413
974f2fd74f7eb3530426ee2ba6bee4708b787c64
162727 F20110115_AACOAW du_x_Page_042.jpg
d3a9582d7ed3991d62ac6fab0db763b6
c87726c0f080347f8a6f1cadcfac671d95ebbc0e
24040 F20110115_AACOZG du_x_Page_078thm.jpg
44e29ef63cf149608bd62be12653f6cb
21a701349f726a16c5dfec322db9aff1b83b3070
25273 F20110115_AACOYT du_x_Page_071thm.jpg
6bf7581c82bcd352f2cd5eea477fed0c
3ab1d09e5042bbcb78f149dbbc4e20001aaa3f3a
117979 F20110115_AACOBL du_x_Page_058.jpg
72f5cbc284a6ad7ba3313e11b3d9ac88
8cda255e6fbdc42559db2d8d01c71d5c26f15558
190722 F20110115_AACOAX du_x_Page_043.jpg
cfce60623ef1512b2cb09b16b0951951
7633e3e098f347551be581e910853d8c1b0c0328
72623 F20110115_AACOZH du_x_Page_078.QC.jpg
6a29ce181143e9fcd2d56681772c4ef2
d66c502744269e1741b98b257aefcc1efd1b0cad
79666 F20110115_AACOYU du_x_Page_071.QC.jpg
03ad8b440449aa49e3741fc65cab761d
bf98757eb72bd4cf5de7e3d9b343df43322cefc8
41189 F20110115_AACOCA du_x_Page_074.jpg
a08c6f1071a1f52e25eb0a02279daadf
106a85636c7884b143bc01e4cb6d7fd31134ff04
188168 F20110115_AACOBM du_x_Page_059.jpg
060df3d16033e79bb34fbb966b167ed9
492a298782c8df9639d86a916d9e5b1ef2d7473f
160442 F20110115_AACOAY du_x_Page_044.jpg
7672491a67765b42221f6e4d7b8c3467
686a85f38ca47b9a1c3881b0bdf27f9038499356
44646 F20110115_AACOZI du_x_Page_079thm.jpg
e431277e677e41680dbd5ac6340c27fb
ff97eb76025da04a3a7886c1f7ea198b104fbde7
46385 F20110115_AACOYV du_x_Page_072thm.jpg
17083ff43c6daa32f2ab7862231bc0f4
2dce761cae5625ec2a190f3f346fd9164d5f5ce9
186612 F20110115_AACOCB du_x_Page_075.jpg
e65f203ad3d9f4dadd7b59fb2f42c11f
f3347d8a019fea36cfae095d130c0f27d93c7157
132675 F20110115_AACOBN du_x_Page_060.jpg
bb4064c23f71ebb88511defd078de0c0
e4dba4302560181df5d7ea35956a879136cd3685
117908 F20110115_AACOAZ du_x_Page_045.jpg
9b066af6a59eed4d69c679d44c31813f
fe751835940623441420c85c536fccd1be3b5be3
81637 F20110115_AACOZJ du_x_Page_079.QC.jpg
60eb749386fc8a3c58a009bde5c84738
b3f11e8f98de1ffd7bd1da2f200b93ce089558c5
182217 F20110115_AACOCC du_x_Page_076.jpg
e2d312d328ef8761d7ff15905020d51b
4716a312c0a9b418b4bff8ec7378a99594d44ebc
193709 F20110115_AACOBO du_x_Page_061.jpg
bdc6f9d951e492cd53ae996c0ea24f6d
80b93c4435367a57e194544e0f95c55443782e18
23252 F20110115_AACOZK du_x_Page_080thm.jpg
289326b87dfbaa80ab70a181daf7b234
f18c4df9ea631cbeee2ea31058439487162e8a18
213214 F20110115_AACOCD du_x_Page_077.jpg
a3ac1e1a28f1a98ab28e7644c1815a8a
4ac958af41f5f547d27ad99d6ac5a6e63d9555ee
146903 F20110115_AACOBP du_x_Page_062.jpg
01ee729023e5ee66c34fccf6cbea4bc7
4605ed98075b2c991dba21c2e07af3bf76299cf1
74346 F20110115_AACOZL du_x_Page_080.QC.jpg
64adbadb42cb633cb17e93d73443228d
f9b79284f7772fe222a449b95133118806dd9d6a
90873 F20110115_AACOYW du_x_Page_072.QC.jpg
3f2b43d25048ad4e0fd98d29de7d6537
2d0f3fe941c031898f205eb87e710d52a65a38e6
193815 F20110115_AACOCE du_x_Page_078.jpg
513ac819da0266175ef09049abd58a2d
2d6bf76c23ea5333aac1991aac7086f5ac9fa1c7
168126 F20110115_AACOBQ du_x_Page_063.jpg
8d92ce519786e12428cdf492b88ac5f0
1047d1ed2a6618e266da74aa9ca6dec44bacd97a
44033 F20110115_AACOZM du_x_Page_081thm.jpg
63ce91fa1136d385f27f05193b7432ec
60822323f1025df7dabc16ed7e31484061add82e
24084 F20110115_AACOYX du_x_Page_073thm.jpg
a02a1378f769c8f91ade155a307bad63
4f733a916d03cc973a7f8f4899370993c53d958f
175183 F20110115_AACOCF du_x_Page_079.jpg
59adbbd3ffc55542725fa5add5f43e1f
ffad90bc8ade8e00ee6fdb99543b273f2e0ee182
171199 F20110115_AACOBR du_x_Page_064.jpg
5fd9aea442c58d2f6a47cdd6ec8bfc79
c246a75a938ba21c49b57f1049407f645cbb06bd
77700 F20110115_AACOZN du_x_Page_081.QC.jpg
139e7c6b547b39dcad2cce9b022585d8
75e6d9371c6fc908b6bf8e5a753d4034c71b00a7
6415 F20110115_AACOYY du_x_Page_074thm.jpg
19dde2a2928187ddf71a9397c86a5759
358a7c8e600da98c310d92bcd36b7c97757f8f9a
189131 F20110115_AACOCG du_x_Page_080.jpg
78bbea6be351761169e9956b348861e3
65347cbc3a3ea1ac6364efde2e1e12dd4292b746
200329 F20110115_AACOBS du_x_Page_065.jpg
524ec2f5754d032a66cb985ed12897b9
7d23c5af52086d436fa486e34e17b7c24f381fc0
41221 F20110115_AACOZO du_x_Page_082thm.jpg
5190c4cf55c1031f9cc7164b53038823
f6852f28e99725f7abb9460434715b8ce1b9672e
16156 F20110115_AACOYZ du_x_Page_074.QC.jpg
111cf32195b1815ec3e3372ccc974345
e73bcc349248aeb527ea5e537fadf96cc83d90e4
165842 F20110115_AACOCH du_x_Page_081.jpg
7d721e3c291c9ef908eee8450357cc69
b7d571fe5993ab0a0c63aa0656ba714044a7a59c
206878 F20110115_AACOBT du_x_Page_067.jpg
ea38ed1f64c5f03ea392b34daba49bf0
55ec1bd74cc7d1ceb4b6a274ffcc2f98b041af06
66839 F20110115_AACOZP du_x_Page_082.QC.jpg
25234f2eaf0171f5de877d3fafe2cae1
ce879ff6427a88f86bae46d8d63473f0bbeb0118
123658 F20110115_AACOCI du_x_Page_082.jpg
14b6087db3c425ff19aae7f0323c1ba0
c9e5282bb93b01452827c92c9a2c3d8c1725ff68
171681 F20110115_AACOBU du_x_Page_068.jpg
9711af6448f717db44f7443342465018
05f17f2b2a80bc17fbe65cf8a435b5df6a167821
21874 F20110115_AACOZQ du_x_Page_083thm.jpg
759680c070536a51dc1fb2f346a9f7b4
92680eaea94635d9a8f810c64f19209eeed174e3
188859 F20110115_AACOBV du_x_Page_069.jpg
d864f505959d2b881a21eecf7978171e
a5a8507cda3d5490c91e4a8f9d0c61bed3fbd999
69396 F20110115_AACOZR du_x_Page_083.QC.jpg
4ca004686e5b7d5a3ca75b99d8ee089e
2006180c4486e035a93230f778aaf2eeb7b02cd5
187195 F20110115_AACOCJ du_x_Page_083.jpg
641d150e8c8163ddb203ae8fb0a625d7
18400b21303fe3e24e2bd094c6b756cc393aaa49
217313 F20110115_AACOBW du_x_Page_070.jpg
d3c636cdadfec721319ad9b3c15b9b5a
4f1846982468023c73d927eaa396196065903525
24752 F20110115_AACOZS du_x_Page_084thm.jpg
fe1cc8dd0afde0a83ed02aadce398578
4dd6405525c8293354721fe6dd5da16bf68ebdab
218301 F20110115_AACOCK du_x_Page_084.jpg
7ee93ea68afc4695afe857a3ccc377e1
0236351563756e4a7afdf0dfc4445c7a39d0d17f
210275 F20110115_AACOBX du_x_Page_071.jpg
7ce778af0a46825cb48224cb40706974
4ecee76d2b66f69d86a3618ec3078b3989ae89ed
77996 F20110115_AACOZT du_x_Page_084.QC.jpg
923c1442e8065510ca7569801dcea24d
11f84e814ca422e3bbb52b30904a946e2e46fa58
209164 F20110115_AACODA du_x_Page_101.jpg
774e36b4ae143f7f8bc080870ad24a6a
381599129e8b822c10bfeb6774bdfa8366485db9
125315 F20110115_AACOCL du_x_Page_085.jpg
442eb245df1b23f71a31445ae3c7cf35
83daf4c22bd5a98836f659f6ddc4f27d78d6ac04
192536 F20110115_AACOBY du_x_Page_072.jpg
4838d905ff8fc2f8bdf576f6f86f352c
335346e2c04e99bf0f1af4c26ec20f0fd4db7b85
40978 F20110115_AACOZU du_x_Page_085thm.jpg
2ebb1a701f186c19aa93b35e04828633
e553604b6b119e63192dfce4d8074cc3475fe8b4
217268 F20110115_AACOCM du_x_Page_086.jpg
4d12aaf453f3d4065b78b0804c593cc9
6a188f03d806ca0c1d10100285ea3d8b67891325
205792 F20110115_AACOBZ du_x_Page_073.jpg
96de015955ff6d04fbf73dc6c7b38854
0121f0fafacb37b97492de3af8272c87c74364fa
65929 F20110115_AACOZV du_x_Page_085.QC.jpg
692190df3e7fa67bbd717e840c62e0b7
14b84ede6045adad48fbb1dbc5b9096eef264530
171365 F20110115_AACODB du_x_Page_102.jpg
0d856d2979f744850636277f121586c0
1d548dafb5c902ad5fbcaa9e508d4791ca2ef5c0
186651 F20110115_AACOCN du_x_Page_087.jpg
43725f48600f94318efda987044cbc64
189f6d39e938833f24023dc108f7a8eba6888083
1937 F20110115_AACNXI du_x_Page_065.txt
b8eb3fd6ec2463499cccad3dc4536a80
5e1695a41685cf979c1b22472ac62e746885964a
25476 F20110115_AACOZW du_x_Page_086thm.jpg
01308e91144a3abb05ba37ce1daeadfe
6f2062076d70848cce4a3c56b87ffe2420b2aee9
161436 F20110115_AACODC du_x_Page_103.jpg
502721a93de6d8352b41fce25f8bc4a8
b7d97baebdd038ce2062a1ca906ac83537cfdf3f
204712 F20110115_AACOCO du_x_Page_088.jpg
ddd2cb99432a89dfd7e9f712c8afb477
377aca8391d78e013db8b96350cc0f0d7915f287
93615 F20110115_AACNXJ du_x_Page_016.jp2
42685ea26e4444246f9fb479f702747b
49480c1720333f2b87b46beea099c166c935bb93
196485 F20110115_AACODD du_x_Page_104.jpg
f9364e9171bfa5dae78321dddf0d9c6e
67190418921429810a8d9d68b35e4e24596371af
109262 F20110115_AACOCP du_x_Page_089.jpg
b23413298c0f33bb4f5c412f84773401
cc3b0da0d1939d2b426b01ec7525bd14ed442998
76578 F20110115_AACNXK du_x_Page_073.QC.jpg
73b448087c234bf9d8a2fbb05fce0a08
6660139fb45eb880adc3727034e52b853fab1c95
44014 F20110115_AACOZX du_x_Page_087thm.jpg
2e33aee26659147c352924dc0335f480
e8c704ca57682410237b379d6978ebd1e92d07b6
250709 F20110115_AACODE du_x_Page_105.jpg
b290561c57de90ce5e6c3e80c39a4028
081206db3bfab519b89424e68f71e6ce4e92e9c2
112482 F20110115_AACOCQ du_x_Page_090.jpg
ab88b62d318927612ec97770cf1d1464
642b52b80b2efbb7652d853a8d1fb19ae2a7bd6f
F20110115_AACNXL du_x_Page_036.tif
930c671011558d062cb624570994f83f
868ac4a088305bb622786b6717673969111da85d
87118 F20110115_AACOZY du_x_Page_087.QC.jpg
a247aa49e5ac9fb4d49a3961fdf288af
5ed1371f4bfcd05e49ac19f0625a73b3d893b674
155669 F20110115_AACODF du_x_Page_106.jpg
1aa4ef67368807428a4012f7e8a55253
1a2f5107551f40f0f8be63c6eed77a6bd132585f
154250 F20110115_AACOCR du_x_Page_091.jpg
032f4c8cfe66e732b22ef26a6303e312
8f26fda6154ff7a8da2996cb1007f22e4447b893
61145 F20110115_AACNXM du_x_Page_058.QC.jpg
a0e874f9497c3b6bbe986288e77bbde9
224a7171ae4ea97bacbbcc61994ba5728ba35073
24650 F20110115_AACOZZ du_x_Page_088thm.jpg
b13b4a1da8099636e844173fb7a6cca1
20d4e32a3c7f7ab459a150e05e293d298483fb59
214079 F20110115_AACODG du_x_Page_107.jpg
e03276008d1023002b5ab73286ecf352
c9aa89da331d66ec06fd85cae6247c150068a808
66756 F20110115_AACNYA du_x_Page_015.jpg
f7a2b2d6548f664558c19174940a4794
95489bf0f1147f6921e3b30e859a3815bf5679be
123143 F20110115_AACOCS du_x_Page_092.jpg
3166d8053d9705eae3affe258e676b64
55ede5f61c68f63f1501a1c51bf87f812ebedf57
1994 F20110115_AACNXN du_x_Page_071.txt
22ff79398a90d618a7a040c4cdd42166
81bfdb7d225324e51640f20696931fa1c3ffdb3c
180272 F20110115_AACODH du_x_Page_109.jpg
349abceb927fe570ba4d478cc5e8aa53
d29f344ab83330fddcc1638870a8757809ec89f9
F20110115_AACNYB du_x_Page_041.tif
8addc005b603457a4aac0c41eb1ff2aa
b255494f98c05ca13f3e1288797001b6a3bd9974
149153 F20110115_AACOCT du_x_Page_093.jpg
df2cbd3fa09019d0804f384845e186ab
c6db4719a859e59e3bf4d117872764196d58625b
1955 F20110115_AACNXO du_x_Page_014.txt
131b179a1f6fbf3db606356e490be9b5
f097b8b5b86ddfb8733ffcaadb7c7c42a010f889
200886 F20110115_AACODI du_x_Page_110.jpg
5a329f40e6b351f01a094dd554fe0eb6
48f4a19763a65fedc228bbdae4de132eb2017bcf
1945 F20110115_AACNYC du_x_Page_018.txt
8c6a1daa0a3d66737c95be4e681f7dca
b53de768b2f44949795fcb91445419aa899ae166
152401 F20110115_AACOCU du_x_Page_094.jpg
74fce8e19a327b0c3a1a4f508e677089
ff97be9b2d48a9bc2753e06daca42d3232cb373f
70431 F20110115_AACNXP du_x_Page_055.QC.jpg
8da11fc9260645feb94ad4d54151a1ff
e17abaa52fa68c22ce1b69700d5b73f72431d632
225524 F20110115_AACODJ du_x_Page_111.jpg
40d182c2c26699f86ca4b98052f72fa5
3e4fed6c26d25db34b389c4d4680e91ac2d39a65
984238 F20110115_AACNYD du_x_Page_007.jp2
3e52861a3f58e1b331662e11e68bfd48
f290e6b95916bacb2e8e1f26bc604763150b63dc
141843 F20110115_AACOCV du_x_Page_095.jpg
67e7ce19c2a29bdb9331df13cd2bd09b
ca8dae18c80216097fa400835067bcc523951a9f
82137 F20110115_AACNXQ du_x_Page_026.QC.jpg
bcd378b209454355c872c675f64ac314
0567b7988cae547f41742b9dfbb80b09d978d499
40181 F20110115_AACODK du_x_Page_112.jpg
52ed51ae6ed8811ff9947c43a409af25
cb6ea10d6cc010ba23031e3de52603044bd5b137
1860 F20110115_AACNYE du_x_Page_070.txt
80d64ae739a52ee755ae2c4af36ce4e6
69d20246820653ff192f95daa87b463e32fdd23f
196134 F20110115_AACOCW du_x_Page_097.jpg
d3cd00645cca9479f8fcadebfe08753b
5b222bf60bb47c56d55a4846d15d819635701fd0
99706 F20110115_AACNXR du_x_Page_035.jp2
0dc604c833bfc9d77306e9129bcb7e8c
f0a4feb4eb4d7f5ca23935759f070c7259cc21fa
97394 F20110115_AACOEA du_x_Page_017.jp2
72c3554e0aaded2ee31b455ea19724be
03743599ca32d09ba90063d34ab7cf611d47ed4e
178253 F20110115_AACODL du_x_Page_113.jpg
bba27073471306c628c0ee455378af3f
15d53bf34efe4d15b3416bae2d7db4fb53296cde
81487 F20110115_AACNYF du_x_Page_086.QC.jpg
e0510cd3b4ed7ebbe3d0835634fe0b2c
2fc06f5b110a281bf54924712c2dacfd0b913990
125765 F20110115_AACOCX du_x_Page_098.jpg
5a8a9933aa7a8913e1ee1ecd2dca69e4
8ea7adffe4afef31c054ae9784ece2f7cb5e31b9
50597 F20110115_AACNXS du_x_Page_073.pro
6a820c4b8ae76dc21f607dff0a0a96a6
05deb3e4af6fb55438e350ccd0eb2891d1674343
100689 F20110115_AACOEB du_x_Page_018.jp2
e27130e419039133f432a5ebcb517993
d76981dda8c54b084b19283435989f408f7f92bb
23351 F20110115_AACODM du_x_Page_001.jp2
159337dcaa65019d7462efc1160b7689
6811f4c9d5c813bdad17542d82b9d39b2ee36e8f
44244 F20110115_AACNYG du_x_Page_099thm.jpg
e37be8910c4afa36151e9bf295d612c2
40f33fafb31ddab2f3b028ccfa9850e1bf45a23c
161175 F20110115_AACOCY du_x_Page_099.jpg
36e67f7f38659e3ed132d868f1f9db76
540cb86ac3240b98254f2b768fc497bb5bf31f0b
48406 F20110115_AACNXT du_x_Page_057.pro
2740a74ef6d8765061ff6f729a68e293
acfeab87ca54bda1fbe81518235bb967d0d733a9
4980 F20110115_AACODN du_x_Page_002.jp2
7086c073d1a041e109da5fb879b51844
c469257c645aa5865c53e7cc795e23c8e3e19fca
2006 F20110115_AACNYH du_x_Page_067.txt
a0c4e147e412f3e6f13ea33c44cd4c48
d028a013f277e21b4415c15cba4b88ef579d39fa
140787 F20110115_AACOCZ du_x_Page_100.jpg
c05d202718d5151842f296ebd01f951b
83a8e46cb2cc65f8dc5958ab49a58b47650572a0
1015569 F20110115_AACNXU du_x_Page_038.jp2
c7941f29f9ecf7c85e7d2d94e8c339d9
21de3dea3c87d1b3ab93c36b6d1d115d4e5630ca
77604 F20110115_AACOEC du_x_Page_019.jp2
8ddead05348a14af0b2cf0ccabe98af0
9c085d18c48b9af2c5e76ab41cb84015a75df5c3
4105 F20110115_AACODO du_x_Page_003.jp2
88b7867b168fe9bd66f69695fcdabcef
4ec5d027a194ef49d75e9435bf08675c9af9231d
690 F20110115_AACNYI du_x_Page_008.txt
8dbb880dfa5bb0d294ff23f46f9b6739
73971963b31325cccc8600a311b8cbe8e02604d1
126969 F20110115_AACNXV du_x_Page_108.jpg
b80fcc7d1199594e720f1c64e0a7e419
13d4e9e4649500dfe68268ea169524e2b78a03d6
56393 F20110115_AACOED du_x_Page_020.jp2
8e63a56638e5ac561796bdb25c5ab837
c0ba714b6fdd7db6e736fd3ff91a469e4a05035a
92484 F20110115_AACODP du_x_Page_004.jp2
f2c977196eb0feba516f3bd92c82d1d9
63f45c4dbf04491b3d8455449fda3a4a7958f9ae
183875 F20110115_AACNYJ du_x_Page_004.jpg
7a3248149962467fe337a038abf9f5ff
33a36f20e9ee453b9ff4f2dc563b91cc116dbb46
70175 F20110115_AACOEE du_x_Page_021.jp2
7af6e325399cf07b2617b041a60e96bc
7bab70039daedba74dffaf9f813ef3293ec3171f
62498 F20110115_AACODQ du_x_Page_005.jp2
ca127cfa13aa93a09ab89ebbbb362123
db7c837c1b872e01ec58f4cce6f24222da3c35eb
44815 F20110115_AACNYK du_x_Page_054.pro
3523db1fb66a478a5ad0bec9c12dd63b
df0becf3dfa9ccf2c4acc1800e38752ad14081fe
30394 F20110115_AACNXW du_x_Page_095.pro
7f6362d910566651d65502fcc13bf02e
35e40b1b7d172c2b160ff84035b44b598dc71224
842953 F20110115_AACOEF du_x_Page_022.jp2
a9d90ab67c596ec7d0a652114fc57e99
175352beeccfbf05c5f2da89a27cf09fdfde3b42
1051983 F20110115_AACODR du_x_Page_006.jp2
9171283b7a0f05ac172f8ac7f9b44415
67088630f615c95cf7eb1ba8ffbf6d66b5a0ccea
58644 F20110115_AACNYL du_x_Page_090.QC.jpg
477fdfcb0456e00c60a794dc4f0c3d7c
65fba5e976885adf4905b6466bf1a0028d666548
F20110115_AACNXX du_x_Page_024.tif
4e7852d0dca646ff6320bb55ba22c705
28ea0f4b2ce037782f7aa6280ed64833e5ab2c50
952463 F20110115_AACOEG du_x_Page_023.jp2
e12eec3765dbc9b4b5fbf95d5fcd1386
c599e7567a820568af2e50ce22cd4a56a51602e9
1785 F20110115_AACNZA du_x_Page_016.txt
d479473a2ff60ecaf44fbf45050fac72
ca18dd8213c88ebd9e0245cb078a88743726995a
629124 F20110115_AACODS du_x_Page_008.jp2
b854d5ac0a22b8cd96ca3d4fb4a99c6d
de3d6ff24f92c9d1d345751400df5de011e277b8
622 F20110115_AACNYM du_x_Page_015.txt
3428798d61c9455444136c7d6f0a0828
773759ba193ac2455d0710b0c4fbbd35bd0305c5
99192 F20110115_AACNXY du_x_Page_049.jp2
52fabf065efb7618ef106ed647d59072
903e2bf3f3c0b5f059f903799eaaa658726db4b4
735284 F20110115_AACOEH du_x_Page_024.jp2
a2cb6bf2dc0aa9707a75374576ff9aec
49378004dd32ae2e19d44f5ef12547109ce31ff6
197282 F20110115_AACNZB du_x_Page_066.jpg
8c8be367204606daf39fa90698dcbe80
7795999fa4675ae3cb4106d9d5b36bc92169a168
1051957 F20110115_AACODT du_x_Page_009.jp2
756968991720fa83bf6e8dc5fac4ab5e
65181ac6537a73068bcb5ddcd8d13a7147b897d5
32313 F20110115_AACNYN du_x_Page_024.pro
12a812e42e80992eb46ba1acead2ecef
7011a26e0c6ab95507602c18c6529c06efbd4841
15875 F20110115_AACNXZ du_x_Page_008.pro
ecf62715b1398c6c0011ecb0020be3d3
c2d92ddea47de43252d0bb396ce1d5e33b79714f
91798 F20110115_AACOEI du_x_Page_025.jp2
d07bffd0cfcf2494af534cbe7e779642
5c84fc7b4255af5f6904fa1fa86382f67ad5fa58
13109 F20110115_AACNZC du_x_Page_082.pro
d3377e0abb69cd7362815c4c4d4cb748
c20c6352d752667299e39c14f9327a2545447441
1051974 F20110115_AACODU du_x_Page_010.jp2
4bda64f21c71a7ea27aa1ece9afa1e0a
acb0e15719ea0e43be765e3c80545fb0bf6a174f
F20110115_AACNYO du_x_Page_091.tif
932e546663d17970e25314e60f46c27d
7fc85ad3e919939518cf8802dd0a022ffd93611c
706492 F20110115_AACOEJ du_x_Page_026.jp2
c9ba3d5c5713e6968efe28662052cf80
03e2a2866962071b49ba5580cf0ce1e858163978
1192 F20110115_AACNZD du_x_Page_062.txt
f668f71be8966a773f043bfd95086512
140b3255c35266a06dec3562255cae4fed1831ce
1051973 F20110115_AACODV du_x_Page_011.jp2
089b9f4cb8844bacd765061f2bb457f1
60ec548352bf71d7a0087abaeb9ae6772dd8730f
739430 F20110115_AACNYP du_x_Page_068.jp2
78b92cc7edcb3b26c81118e02a32684a
008edd8b5680e4311703d061f9d8411fd64908e9
567715 F20110115_AACOEK du_x_Page_027.jp2
447565b09abd19d3af82169c63f7fa65
572f7cd04ecab02d53b4e99376d5eeb21f5f089c
359 F20110115_AACNZE du_x_Page_112.txt
c7a5d40301eda46cd25bb264af4f911a
ce1b842d57f17d50ce886b51b72d79573a172add
79909 F20110115_AACODW du_x_Page_012.jp2
214f9ace20c64496abbc7b3719e19412
698ca4ccec2837d049245bac86bc3823c19570c5
F20110115_AACNYQ du_x_Page_076.tif
8d9c701436536c3df620df1ada7b3b1e
8aaa5897138c51dcc63c7f61e1b7c862c0ce56d6
92245 F20110115_AACOEL du_x_Page_028.jp2
90f2694113a64e1c6e7d0acc7234c2fb
c24ca891a9abfcb8a3b97938b70b7ea38e7e50e1
F20110115_AACNZF du_x_Page_050.tif
7b24bd9c41dacc4538468098b7700ce8
c690661d739e3cc83ad2750aa766cf3cdf6c0cda
88598 F20110115_AACODX du_x_Page_013.jp2
a9cdefdede28fd41d5e1cdf2e1f55d01
631a1a4e98c1cd8eb0f78ba6c40cd4d3f89deea2
9095 F20110115_AACNYR du_x_Page_105.pro
4989fd39f3527e253466c2c99c5ea780
30cecd3c2961be29a2709e595b2dfd0e3a24e581
56735 F20110115_AACOFA du_x_Page_045.jp2
f4f80cd78d85e306a55c6ec81ff9d2e4
adc12f0b766f7dd16c344e1d7353e6eb66fbb7d3
1007332 F20110115_AACOEM du_x_Page_029.jp2
d6e904e804bc1f77dd11dc30ffbbd150
f4b4a19e6fa2304e186b03546cccf412c4b95e5d
2047 F20110115_AACNZG du_x_Page_077.txt
bddadfba882e38735ca100170b2389e0
995559214beb356f22bf0e5b7cf4ef566f8d5a8a
107227 F20110115_AACODY du_x_Page_014.jp2
ea2fe6270f14b89b42329de185085795
f463f9f000c657749bc71fa3ff85613f9b68fbed
1675 F20110115_AACNYS du_x_Page_040.txt
68203cf4ffb72adfde9200f6ce6c6609
bb7d0c2ff6a6bbfcb210c7a3a7e002e29e163aab
888155 F20110115_AACOFB du_x_Page_046.jp2
9172ac05fe4d6c191564d2498b3fc279
ffbe7172bf0cc630ca75cef6f889b86d4f3c3c65
111169 F20110115_AACOEN du_x_Page_030.jp2
c754965f7cc86bb683aefce10ae1e95d
695239856c2ba1ede058a5498b49e068dbe6fef5
23033 F20110115_AACNZH du_x_Page_055thm.jpg
7b1f2ba2c39e28f2e16d06cf12fcbb8f
f95a1b1eb4bfa4a82521db850bf775a413734604
34295 F20110115_AACODZ du_x_Page_015.jp2
38f14d65dbdb808b6cc00d3f3b3ecf3a
ec76b50b30bf625ba1528cff42f275cba0de3e3a
79934 F20110115_AACNYT du_x_Page_046.QC.jpg
242820ecdb4b37731ae811ebe18260f0
38bb2ac1a86b0e40b35e9c33371de47d91189548
96224 F20110115_AACOFC du_x_Page_047.jp2
ecf5c41c41dfd38e3507dc8f77f77e06
f026a0b4a38ef5532b5e4d71d5a382518b8c8416
82125 F20110115_AACOEO du_x_Page_031.jp2
fab1d802dbc7faedcc913a090bbd0917
18b00d56230436eeef9bcc853570144013059fe1
166813 F20110115_AACNZI UFE0008357_00001.xml
0ef49eb568eeb41533c9d7706dd1619b
a4c245e44174e01a3121b3d290fb1975d2c083f2
192041 F20110115_AACNYU du_x_Page_049.jpg
e3df8d7af02b99456b487c996f886e10
5a45e87a6b1ebb52c467d2af326734fd3d6e6a46
1051967 F20110115_AACOEP du_x_Page_032.jp2
19ce4f22a1c08365a064be8dab583625
e64e964797f14780cb5db95ae724ce5f4218b1d9
185333 F20110115_AACNYV du_x_Page_096.jpg
411830d86e878f379434ec167c06be11
054625ee3291434faf3c7993090e3c7be2615f52
719679 F20110115_AACOFD du_x_Page_048.jp2
4590be908c13a60b60a1589a57db97a2
fe90f9c2aedc1398a6e083b2afdf7a69be607b6c
700909 F20110115_AACOEQ du_x_Page_033.jp2
d69cac527b0ca9d80e94cca8f6c6d50b
29c22a202b4a4ae02e22eb35567cf3eb409c6119
166636 F20110115_AACNYW du_x_Page_039.jpg
499d8c753509ad6241874a157b9a4ea1
aad5a4e1a2321ead1279bb9b34839732608a4c18
576187 F20110115_AACOFE du_x_Page_050.jp2
221ab5381511afe225f3d8cca1e51b3d
62fa62aa65bfb41a1cf958117ea543e518f94ad1
99264 F20110115_AACOER du_x_Page_034.jp2
4ec6327272e830b51ec0087b12953657
9dc924a80e56d3d5ea89b43e80dee96b619e4e11
53375 F20110115_AACNZL du_x_Page_001.jpg
1eac503b607d8435c08a89399a4f9084
bf0b6c9b1751d842936493e8a4b12202fc29e6ca
803751 F20110115_AACOFF du_x_Page_051.jp2
c7392b85d067bcee6c2da33ce09fb748
2b5df61d44177a31883a707a81858b316773484b
89589 F20110115_AACOES du_x_Page_036.jp2
5cf55fcb3f15d618a83c4bb04c2e063e
519dba432825eb5a3474431881f1a5316eef3988
13500 F20110115_AACNZM du_x_Page_002.jpg
33899b41396738c1ee27d896d9a9d02a
20c0c239edaa35ec234e085207e6f8780420cb48
75635 F20110115_AACNYX du_x_Page_014.QC.jpg
22434fc4fb14ebcb77443a74de0e498c
c18596b55339196ed1f4c61bf1f566f32304de3c
52510 F20110115_AACOFG du_x_Page_052.jp2
f0dd50996087f24ca069971e666364a9
df0a249b144c0f2bec4df70117c35cc92b261139
663901 F20110115_AACOET du_x_Page_037.jp2
642e7e4b05116cc2d4ed9aa56418590d
3d520557ab45b6e24a306edb81aa264feae5c1da
11912 F20110115_AACNZN du_x_Page_003.jpg
e97ae89a72c4ba0bd7ec170daae06ec1
898eb86a54a23f481f15284f70f28a3a8fcd9d32
203036 F20110115_AACNYY du_x_Page_032.jpg
9271d0c164f7064a538435833c19c194
d096e8121c07363caa6f0ddd90dca639f3147439
93983 F20110115_AACOFH du_x_Page_053.jp2
ba5e8411089e2f3b3312305cbe77a7c1
ebdd7a193c0958983f5775440a89762f4cae7082
84960 F20110115_AACOEU du_x_Page_039.jp2
640e8c8f8e3c17ddbfd51dc8164f1967
b25c3cd1cc20679cf08537e1c0e19c4df352718c
120360 F20110115_AACNZO du_x_Page_005.jpg
f074ec32a183f8607f735749da66ca2b
f414d376927d99fd30510c1637dd58e7ae34982f
690172 F20110115_AACNYZ du_x_Page_106.jp2
fa48fcc6a7603ca56cba60121ae63da3
d86668f6899cfd775e299f0f5d0e0bdf239ba7a2
95203 F20110115_AACOFI du_x_Page_054.jp2
154f9f1d6e6a3d70c29460fdd78f448f
386ac863103748233735310c737df11ddb87fc95
75385 F20110115_AACOEV du_x_Page_040.jp2
d3cc069cabbb460b910180918737320e
74de6b1001c0df9366e95f68e4da77c71d35d7d5
254457 F20110115_AACNZP du_x_Page_006.jpg
e05eb755e28c4adaa665d6e10556ed08
3f7a517f46e1be8926b1622cbabb25c3b5ea1eea
99170 F20110115_AACOFJ du_x_Page_055.jp2
aaea316bb6315809fe31351fc69e4634
f082e8665afe95fd00b6c20471e3bf3d6bc18a14
47716 F20110115_AACOEW du_x_Page_041.jp2
546399e8af21c3f57268f4c6c1740422
7ee1e43abb31f7a7a05c59491332008675ce080b
154645 F20110115_AACNZQ du_x_Page_007.jpg
04e07c122bbde22aa4eb78b505488a59
fdda5ce40b1e075c7963e923f1ba11a64d609485
445565 F20110115_AACOFK du_x_Page_056.jp2
a1061f9dfa8b753fd4842466d75430f7
eba89b27d3ab28d30af861be6220cc497ef191b1
85945 F20110115_AACOEX du_x_Page_042.jp2
db11f8ded725476914c44e5db862ad77
356ce1a955d6206304a8e7073aa44b863549ac24
105589 F20110115_AACNZR du_x_Page_008.jpg
99c5ad9fc22efad232d592f048063f79
79de7151ffa68c55b66ba3683522127062bf527b
103355 F20110115_AACOGA du_x_Page_073.jp2
1fb177dcb401d07683767931030fea04
f45bc2fd4514a4c367063c384aede483f3a71796
103196 F20110115_AACOFL du_x_Page_057.jp2
73e7e5937021d0385cf1f080cfe9b55f
8f865cdbe85793bb021513ec196f113b900f8828
99436 F20110115_AACOEY du_x_Page_043.jp2
c87ee0bfab6421cb25af8f00e857e37f
cc50451106377969b7cd4e0aa1251cf7f3098d75
302135 F20110115_AACNZS du_x_Page_009.jpg
14eb9d316bb828f1602909ff7d6235e4
99226e63d208d8b4c4997e19e11a12721f15ea6f
21292 F20110115_AACOGB du_x_Page_074.jp2
597bf5a24c11784421c748b320e272c6
c942ef341ba4f34cac432d224fc3734017673db1
507605 F20110115_AACOFM du_x_Page_058.jp2
399b17b5b6b3d0ad5acced44e3fdd4d4
c4bfc62ae3baa0a12783f19b8bfb146974b96be0
724020 F20110115_AACOEZ du_x_Page_044.jp2
a60c9956e247151c9235669eb79eeb12
e939847963a8c4595f6501dd420209eaf87f3bea
333089 F20110115_AACNZT du_x_Page_010.jpg
4a8e7299e9eb33b004902dd9e8ce7841
9a970c768ece88eb028bf6c4cb16bc7c62baadd8
94171 F20110115_AACOGC du_x_Page_075.jp2
6c674387fb95354dd24f8980a722deee
18b56fa7ad53b3efd7d673384808a18ad3a7db21
97416 F20110115_AACOFN du_x_Page_059.jp2
6447343748dabcdb81f259c631c126b7
86cefc0f440a929aa26e966b6406e63e0b672fd8
238829 F20110115_AACNZU du_x_Page_011.jpg
5a3085c5704a75ac4c4d181e6693d337
17afd07212c8d5694a65dd32cb31be1cbbf15027
817281 F20110115_AACOGD du_x_Page_076.jp2
4b008cdc65b4c8049ca317611762a369
21acf0809192ff608d06dd5c4996f3a2179aa5ad
597957 F20110115_AACOFO du_x_Page_060.jp2
3a460575ddad3e482b66a48e37447177
0549bf4b9bbdbdc83366fa749618f6974cf89951
159705 F20110115_AACNZV du_x_Page_012.jpg
7988800c131b1db0d57972b368f44af4
f67b739a56c16ff738f8474df33f4919ba2fcff8
99189 F20110115_AACOFP du_x_Page_061.jp2
7d113388f17530c792cad1516bb760d2
cce2bf473c0d9cf99db37202c3aee1813ea84fdf
169715 F20110115_AACNZW du_x_Page_013.jpg
0fb07e5a032b7044f12760b34ae53b78
c9dc0bbb14931d1231868b890ffcbd13b1861afb
110091 F20110115_AACOGE du_x_Page_077.jp2
1a17ce89263f84a17ed52fe38e0d772a
ea78c0b65e4d9d643799229e4da251e6c0b36780
654603 F20110115_AACOFQ du_x_Page_062.jp2
b67c4a24ac5c90c5902733f838223a89
f5dab9d7104d5f1338f6a5d7a6c2ee30a52fa663
204319 F20110115_AACNZX du_x_Page_014.jpg
5bc7b00d9aae3c3af41b774e801359d5
23dc94209b65bc4061ac68fbc27198fe53f5eb0c
98981 F20110115_AACOGF du_x_Page_078.jp2
b6fac9103b5207e461dd17b192ee06e6
17284a85dfb67ec751fd24d983a88a46265ca2e1
80640 F20110115_AACOFR du_x_Page_063.jp2
04ade9f1a3d4261f3d8aabb9aeb976e2
7f082e394d6a93e9b1f335bff0a225fd41caa6aa
792145 F20110115_AACOGG du_x_Page_079.jp2
0bbc24e323ab620b8ca3045f0c73d061
32dfb22060e4edb7e5b58ba9612aedfb5fb3c159
86432 F20110115_AACOFS du_x_Page_064.jp2
fa4e9a2d6998ad38ec0105f98c08ae19
8b98c256071ba86f31f8d25021a47976d561be38
182459 F20110115_AACNZY du_x_Page_016.jpg
50ccb475f21d62ee73622a16a0bbd806
309493f352cd7a7f53e7a305dda519ea2b0ccc06
96333 F20110115_AACOGH du_x_Page_080.jp2
35cc922e65d884203e9440e7636653d0
9fc5bb2d64266ba5f2f7431d2bfc35f3e96e0de3
102866 F20110115_AACOFT du_x_Page_065.jp2
b8ee3f48198b492242fc79e7c7aebca0
cbd80856b36a0affab2b69f95ca11bff18e4bf8b
186983 F20110115_AACNZZ du_x_Page_017.jpg
33f30aabb9e7559395aa356b71e8d6b6
743d91bf09d73ef38e29551653c00e60919f7969
755256 F20110115_AACOGI du_x_Page_081.jp2
9fa3c82cc84f23e480ab4a4f20a5f866
c3325b4edbe6021807b7e1773a90a171b0bbd09b
103294 F20110115_AACOFU du_x_Page_066.jp2
45e57bf3903bb6d8f7df07e4a2b70b49
29f8eb5f6c51845161ff20296c4651eef48356bc
500138 F20110115_AACOGJ du_x_Page_082.jp2
a5d0641ed8e45358557181ad948a0362
8035e90dd0a2438aec12408be707ddd470797450
106561 F20110115_AACOFV du_x_Page_067.jp2
5f124af6cbd88fabe76e36e958b6da1f
370ea4d3c2dcc3942c7d66cac469c2be9740a3bb
91088 F20110115_AACOGK du_x_Page_083.jp2
06502a18f731dc7c37190baeba14359e
ad3f63d1368db37cd87330e78d50a2c271d4aca2
928713 F20110115_AACOFW du_x_Page_069.jp2
0744685422b62e79e25f7d2324b614e9
c1b1127ab2d09a14e3abe369af421bfe95d19044
1001832 F20110115_AACOHA du_x_Page_099.jp2
80321fe0d0fcb53ecdc7764b1e210927
c0f1769f7c916a1ff1cff588c3abc909a9e5f7d4
107841 F20110115_AACOGL du_x_Page_084.jp2
fb9913c1fcd88c4df57f363779dc7d11
6025ba7dbc2c55a6bb55e670c7537298065e825c
1051942 F20110115_AACOFX du_x_Page_070.jp2
14ee5c678c75729893990ee4ca688a69
05d4539fa53b58a11a31f52302c6debd93f3217e
762735 F20110115_AACOHB du_x_Page_100.jp2
01346df51357f517a45a908ecdc54db2
fb4658492c9e855e9e9c22ff501193bdd78b1035
529590 F20110115_AACOGM du_x_Page_085.jp2
28add07c4d0eadd48cd37bc41ef0cd29
8234b1ddcc9d5a957d78fa78f7cb115720d057f9
109664 F20110115_AACOFY du_x_Page_071.jp2
e1d303577caebf1d68de1530941560b3
0bed553f989972ebdb5b945287785f95f29fcd23
108543 F20110115_AACOHC du_x_Page_101.jp2
9d5bd9a84472dea5db15e6574693d648
8b71a1d382c850c13ff74664127914e2be5ea2bf
110841 F20110115_AACOGN du_x_Page_086.jp2
6574340e4bde3cb64b7aecbfe8dc32dc
ed50c43830d8dc9e476d65438a08d70b96530ac5
969318 F20110115_AACOFZ du_x_Page_072.jp2
0ea43058f0dbd6b1bb7ac2b61c574487
9ab60c380e8712a868bd79abc0bd3b41cedc4c4c
785657 F20110115_AACOHD du_x_Page_102.jp2
ed1778ecf1361fcbdb83bdff1cb775d8
1a4bbedae4e74191e5796ce35d3fce28122687af
825072 F20110115_AACOGO du_x_Page_087.jp2
d1683a11a84e5226f5187588c02d95db
d5e1a44e34375b7837e77f7f341d73d8f083bfbf
84116 F20110115_AACOHE du_x_Page_103.jp2
cbbd14b4f9fc800b0dcf28ad3958836b
7e1d1f5200049a49927d3bc171dd5e69dea95b31
103444 F20110115_AACOGP du_x_Page_088.jp2
18f7191cc6c7ba2f8355ad7cfbc72195
d86512ccdc86228d4b058830ae31de62977ad86d
421723 F20110115_AACOGQ du_x_Page_089.jp2
d25bf05b75de4aac020bab9c5bb25804
a6c1b6516f82dc3bdfd29d2496577ea22b03abe3
101148 F20110115_AACOHF du_x_Page_104.jp2
169075d5dd0a8583354fc7c595fb1d4b
6a8bad2fb70d51a55a1e14dc8c2f91dd6b2fb754
438632 F20110115_AACOGR du_x_Page_090.jp2
341510d8be2aa09aef4dc8d043c8bc06
9fd2d0f81f30fc44ed5fdea8f39e81bc04f13acd
76418 F20110115_AACOGS du_x_Page_091.jp2
69a112e898e5edab4ffed74f8eb35941
bf35d8d2e885155768dfd11a9c8a321702527885
1051960 F20110115_AACOHG du_x_Page_105.jp2
247d61edd4cd5cb878c48d4205f8fb53
1fd1b2c807e460dc827d96f3daa3c730bf16bb97
58071 F20110115_AACOGT du_x_Page_092.jp2
025421bc7083e1aa1f6ac6e7763d9021
36ab0fd412fbfa382afbd41c2b42c254dcb72861
1051985 F20110115_AACOHH du_x_Page_107.jp2
cf5d8cefc6ec42e7919817bbec7a90f8
7bfe0a3e90f0f254c89ce4a018e371e08249de08
70565 F20110115_AACOGU du_x_Page_093.jp2
9039d83626af32c7d22aec1e8c387e86
0d775f6212b19a90079f4355ec2e63fa1ea1140b
65824 F20110115_AACOHI du_x_Page_108.jp2
c45101eed145e2a5c470cdaf9f7c3c0c
3f0ac5859557054ae5a6c43589f422dcfb750ed9
662215 F20110115_AACOGV du_x_Page_094.jp2
8aa1359e8e27a91913c787b3d67c3ed0
2ed2a8b3e52254cbe101543c1101e2bbeef23f87
89773 F20110115_AACOHJ du_x_Page_109.jp2
ae6cef403c0a0c3434d4b8d8572e2e36
101ebeefb3c8f71db5f6e869d194e7e7f463c054
67674 F20110115_AACOGW du_x_Page_095.jp2
73cd0b4ba4185ff4b9c77afb995d8dd9
5851384aa687173e5f00b041207d565479a49c01
104749 F20110115_AACOHK du_x_Page_110.jp2
da0d6366973cdbeddbcba0e949149ca1
f70c9b6254ea48ff10ec83359aad6785b540f625
941153 F20110115_AACOGX du_x_Page_096.jp2
ad1ad49fb2fb81152ea2848ee4add37a
94e6590641e4d73fee94e32a70d393b77f95f215
F20110115_AACOIA du_x_Page_013.tif
57f3807cfbf8bc6366af67c131cad935
1b11dfe3cd6c38b83961c4955a63f10ced654f6c
108981 F20110115_AACOHL du_x_Page_111.jp2
82d166a154d081b7b1f3f1a1a431972c
c38717801bb4c86f9bd34af39a0106badf0e5c89
102534 F20110115_AACOGY du_x_Page_097.jp2
ed56fc96a15e8391e897a4df296c4c4b
c7789bc85a3886e7ee988d2bc183b013b8e8549b
F20110115_AACOIB du_x_Page_014.tif
d210d2ba9c121f22be40d386f976bc3f
89950a202f0016d01d4cd37c9ac46bae7113de4c
19273 F20110115_AACOHM du_x_Page_112.jp2
0b48c4e6032136274a0d0996629ac327
df45be036e91977d2ffc5ca700773df86fa516d1
63075 F20110115_AACOGZ du_x_Page_098.jp2
c656acc1c6034fa57e0bd84c44040d60
16f05c9830aad81a79d06c951ccde250ed702fb2
F20110115_AACOIC du_x_Page_015.tif
84898736a2bddc5f6f813aef99fcc4d2
d711a0e62450dc22a19b4bc3ff86caba47c832c4
89795 F20110115_AACOHN du_x_Page_113.jp2
1533917660a088c5ccb785f70764853f
bc301f3b13399153c643fe92d60294b787449c17
F20110115_AACOID du_x_Page_016.tif
6e45a8b7819adae5593ff1218c8628f8
b526901d608f9ea84febce94b541f36a632ad178
F20110115_AACOHO du_x_Page_001.tif
0f19674632c69522f70ee507c3cfcbaf
9820539f833cb949a1b2751093385ef34483e797
F20110115_AACOIE du_x_Page_017.tif
83c27ccd864e6e8eaecbdf3c24466ef1
afb1d12a42e84c496bc27c1d93a79f818ce22c4a
F20110115_AACOHP du_x_Page_002.tif
fa5f2eb7b5732f0b6adb5e0d0eb5b0a8
fef816b01a0edd3597c33714c1e319e1bc70ef70
F20110115_AACOIF du_x_Page_018.tif
904cf77b0f15490486e5619c6023b037
c25aa8e191813c518bb1fe49d4d88640aba947eb
F20110115_AACOHQ du_x_Page_003.tif
74beeb5a3ce03a4b5a6dcb5885bd7acb
411b54d0c57a665ee7877e3f9f37f01b7c2cc8b3
F20110115_AACOHR du_x_Page_004.tif
ebe39382caa70e26dbf15b051d8d70f9
9d8b06bc12e9e8c6f89b1a81ad2fc6bfc9786273
F20110115_AACOIG du_x_Page_019.tif
dbd06ca3c49dd7709f1400b3cecb1bc3
dd6d0580b83216f3a9e7a28c5f67613863db9bc1
F20110115_AACOHS du_x_Page_005.tif
c7d619f774bdb611d1edaaac590dde64
a6527770160261b55e83190f85640ac00f0f417d
F20110115_AACOIH du_x_Page_020.tif
015af344eea7488e494c65955255c414
1639c6a7f1686cb623de1aefd29f44f47b9d52d3
F20110115_AACOHT du_x_Page_006.tif
c8f58e1abf835004c329612ffc136d07
44dedae0b779c05bf11927f5ea4e969c14d68161
F20110115_AACOII du_x_Page_021.tif
9cbfa22f91e181fb4c1bc1cc4dbeae98
466f6d057c4f431fc5b31c28a5dfe060dcafbc67
F20110115_AACOHU du_x_Page_007.tif
c80621105a1a6151c6ab6663dcd1f296
9eb475da6690f5faeb31a7b449b853e7f3cfb340
F20110115_AACOIJ du_x_Page_022.tif
b9c41bd340b399fd0cb9f1cc7c168d45
aadab5944bad60f13f35785a2b3e172953e527a5
F20110115_AACOHV du_x_Page_008.tif
c2c9e372095b264cb26cd45e3a4ffe47
17a75fb11b87288cbb52119df55010d90f4ecf80
F20110115_AACOIK du_x_Page_023.tif
8078120fb137fae0aac7b244c9b4375c
4cca2711e6db900f57a3c1e0f1ffc79033e036f2
F20110115_AACOHW du_x_Page_009.tif
eff60032719641ab67cc997d48dc2718
bb20195ba073a6e6a7b197d8e79ebdf3af928477
F20110115_AACOJA du_x_Page_042.tif
4297567cddca6382f3a7ae44594c9c00
af9f92262f3cd69f5f61141759bb598401c27c51
F20110115_AACOIL du_x_Page_025.tif
f8150685e8ebc9cfd2c67b2b944b5b5f
a848d89e2639c203253e2df7930472a1acc5299c
F20110115_AACOHX du_x_Page_010.tif
2826767c78a033f9bc279cafbb067177
9240909f8421360a22474aa9f4850f27ab9e4ce9
F20110115_AACOJB du_x_Page_043.tif
15f9db79aadb6722a3b6ab4152f32c95
1485d3e19fcda4a517bc5900166a1aedb01c8114
F20110115_AACOIM du_x_Page_026.tif
b3645fd0d765dc04f89958d305fc7a4e
5cd6a1bac6c3936e7ac5995e232089a680301601
F20110115_AACOHY du_x_Page_011.tif
ceed9d45d3ac3c56dd05f92f3061ee41
672c5571704d15b7693a588c8e332f3d37d21a6e
F20110115_AACOJC du_x_Page_044.tif
a995ab0459b62f109c2e87e98730ea18
62f9ec410c57da7c9d8730a5f57683aaa2a4feee
F20110115_AACOIN du_x_Page_027.tif
22ced98065ddf80e47a8e1d10d3f102b
05d80c429cb8741aee210f6b6e445925dfb35ffb
F20110115_AACOHZ du_x_Page_012.tif
27850de64ddf9d1922b20e23b519efcb
92fbefd2657a6b6fede910a486c38c5199ec9d15
F20110115_AACOJD du_x_Page_045.tif
40dd06033a0e282dfdf1462056bd2664
2a880b48bd060b7f594ef255358751de4610ed95
F20110115_AACOIO du_x_Page_028.tif
9f91522d016ae9d5ace4f453db8a0d2c
98d0e4097da5a15df33395f85928173055ed352a
F20110115_AACOJE du_x_Page_046.tif
1b2d4ac53fd6d9888afed57f3abb119a
15e368afbb22cfdbfb07c787ca1d841c4b8526aa
F20110115_AACOIP du_x_Page_029.tif
36b221c9f5b0753520ca8317142f976f
bb03d754707b5e3784d087817a29eed4dd831481
F20110115_AACOJF du_x_Page_047.tif
2bf982e74e0688fd4f7a5bc36adb9f71
0d57c45ad246c5dfd4885cd4768256850c9eed24
F20110115_AACOIQ du_x_Page_030.tif
dbd5c495eec23456585ea0d8c2daa8cc
1819e395ca55b61469055a68854c42a8e71bf6e3
F20110115_AACOJG du_x_Page_048.tif
e5a6240e6f1463c0ca6303327d102e3b
22577c20f50de174bd32074bb19ed9aab160cb71
F20110115_AACOIR du_x_Page_031.tif
7c2842bdf7438076ab38c6c39c6cfa17
bf642116f97ca18eda15da7abea01e15793818db
F20110115_AACOIS du_x_Page_032.tif
951e462dd2df245ff33c9cb064719ac0
29fb5be44cc7f766c6277627bc17f702afa0dcae
F20110115_AACOJH du_x_Page_049.tif
b526d208e811b52d6f16dd7dcaa01f24
b05ce4cff84c74fc96527865d06c6153db111842
F20110115_AACOIT du_x_Page_033.tif
90ca471b8f74e1846478493db328671c
7c773e3fb970e822b7ba6df67094126f30fc4b8f
F20110115_AACOJI du_x_Page_051.tif
cc4544bd9429f2844792efb297543342
26b04b8aaa1ce98bcb47f2c83f8f5c0b2d9e84c0
F20110115_AACOIU du_x_Page_034.tif
997e9575e15fe305f7b6d88c907f7fd4
26e1591d47545777a0d79e65043cda6a7c28d3a1
F20110115_AACOJJ du_x_Page_052.tif
910ed40d5781f309309d4d55c3dea8d9
e79e1ef8d9280b359c8394161e3881cfed074d67
F20110115_AACOIV du_x_Page_035.tif
d712f33c444dc31dc431435dac73c39c
3d6e4cbf5caeb1c8c90c7bcefa55eeeb3302b14c
F20110115_AACOJK du_x_Page_053.tif
91cc8df94ad9be679c1d7bd1f8b3ea7f
0a49d65d401c8358ffad431fca593ab3737aff97
F20110115_AACOIW du_x_Page_037.tif
7a71febb4d39b738240ee8faf50ff529
5b629b7d5685051de1e6e5b5951c3783e1f2da77
F20110115_AACOJL du_x_Page_054.tif
456c5522d85fe205de7a915b6c47dc0f
fdffdb9f355ccff3d88330af0079be2aa6d481b5
F20110115_AACOIX du_x_Page_038.tif
83b031810f7670b3ee5826f3f19688f1
1cec92473867f7797619dc8b9f833d24efad5437
F20110115_AACOKA du_x_Page_069.tif
b617d23fc9df655437d5f7efee2ce957
b83caf68ea9ade43df3b9622cd337be665e957e2
F20110115_AACOJM du_x_Page_055.tif
b5ff95b86141b195d5b2b1645b073ddd
b3a19b83c5933b9d4feb62b95576ccc059967d4b
F20110115_AACOIY du_x_Page_039.tif
0feef4a431018dbc794583df2e3fc90a
d5325a63db3ae263a67d0dc99a905923ac3a3970
F20110115_AACOKB du_x_Page_070.tif
f6848dba6c717ec097aa5791157a97f3
7837bb3f012297204e75e06913b9d61185850bb2
F20110115_AACOJN du_x_Page_056.tif
cfb9baf497f8f05426a432ff963e6c60
cbecd2b8a52c5e7b6f6878996dedef7b76699cbe
F20110115_AACOIZ du_x_Page_040.tif
26e7d86ff73a745557f5831b6d11b095
3dd73a96e4200950f23158942b8f805f4073e5cd
F20110115_AACOKC du_x_Page_071.tif
7eb1b811b36822b2b0eda98c17d9c651
47b821c990da7c0390d1edd0537818732dc1a9c4
F20110115_AACOJO du_x_Page_057.tif
8dcfcb61c58ed8e02144f5864670e3cc
3a8db825082baa5b37ecf0d6eb7b8fe5f284ab0e
F20110115_AACOKD du_x_Page_072.tif
46e6ecd3187597eb43757330dbb3e02f
5166d1e542f44f1d4a0dcd60e3206df8414b1637
F20110115_AACOJP du_x_Page_058.tif
05f5422ff3a01faf5ffe812db5dc0487
b4164c4da762c89cab70a71f77cc5650bcac876d
F20110115_AACOKE du_x_Page_073.tif
554166deee22b6543613a96a460c8b56
5a2880280ed7c9c0adc3576117c67073d575862b
F20110115_AACOJQ du_x_Page_059.tif
667975611ecf34756a4184b7f75f85bd
53cf3d703b647bf79800da06d0fbe4a173162a4f
F20110115_AACOKF du_x_Page_074.tif
43aa7dd1ae0903554936c4e54afff1fe
61d4fa73b11464788991417066b68724a0e15f9b
F20110115_AACOJR du_x_Page_060.tif
0a8351ec31b143069cbe8fcba20b3b5d
50e65a6ff32b88a5f024cc020caf5d7fd3f7b8e8
F20110115_AACOKG du_x_Page_075.tif
4ec56a018561da7156515cebb2b13cf4
3728abb580e953c1b84db8a94bc7ddf15002572b
F20110115_AACOJS du_x_Page_061.tif
905e08634ce32db7d7c8d8232a506cc9
0814425c95eb149bc1a64de61c24cc1796bce96d
F20110115_AACOKH du_x_Page_077.tif
a69a9f2577ab6ef33c3ceae691f797b1
55d0133799f233c41c79d565033add57176de73a
F20110115_AACOJT du_x_Page_062.tif
e3f3a1ce41b982578a64ee98eee47933
81d7b85b412eb59c4116f7ed13e779874f4f88a2
F20110115_AACOJU du_x_Page_063.tif
3cb1738532f8006f856afe238fbf805e
a3b32e752cb0c069b65d94eb6663d634ca35dc4c
F20110115_AACOKI du_x_Page_078.tif
208a0be6cde37a2c9dbb3c8e31989546
90718aa1a4e6e6e54ec2d7179836be44f5c2686a
F20110115_AACOJV du_x_Page_064.tif
91c0324803b81d193e797582781231b2
c697059f90cc5dcad547d8dfb32e9e06faa4499d
F20110115_AACOKJ du_x_Page_079.tif
e673cd38f19d604ee117092774550d78
a5bf56a967fc05ee13c969584cbe09618494936b
F20110115_AACOJW du_x_Page_065.tif
aac9c6f96910384a72c08706649563e6
1c27f2d1bddc257afc8a7bd0029e029eba21b64c
F20110115_AACOKK du_x_Page_080.tif
17577e293870b5cd3b2f50b48543c952
0c72b1ebba4d7564619e10e29c3323d63df4cabe
F20110115_AACOJX du_x_Page_066.tif
3cfeeea3372f8619e9f6d0a83a6d59a4
d5d287f86c9e81aa40cace3626c2c7604988be3e
F20110115_AACOLA du_x_Page_097.tif
2cac2d5ee3aa793959c412c542a6c5bb
b75a7c317adf2b5bc972e1bee15b6bbd73fc90ac
F20110115_AACOKL du_x_Page_081.tif
9d724767f469a1f0e9e9b5ef58cfdca7
23bf55b05aa05e15a1c8478ab1d14e935916dd09
F20110115_AACOJY du_x_Page_067.tif
7a22e37c666e1cab939bda4e04b9d407
3d0fde252da02e61753d9ef79f7f8f389ce2ab8a
F20110115_AACOLB du_x_Page_098.tif
49c52a6e5aaaeb97e49eab4aafe2107e
2daccea7039d2ef5c8aa8184bd900823666dc26d
F20110115_AACOKM du_x_Page_082.tif
635723e5a90b4d3edef26bc910385403
0bd63b20791e40288b934dcc1bfba3d9b6a92fb2
F20110115_AACOJZ du_x_Page_068.tif
5310da3a7e58aad8955b0fd398d5e9dd
5f2257a25f0f8c919ce28fb07762fc03311630d2
F20110115_AACOLC du_x_Page_099.tif
246404fdb4e15c9fbc6bc5cfc43ef6c1
ffbddb85f716394d842706daefc3936029021237
F20110115_AACOKN du_x_Page_083.tif
a47c6d8cf459cba5933997a41105b366
3dc89d8c97900ff7886a92a4089080b363e80334
F20110115_AACOLD du_x_Page_100.tif
8b7269073315be35d97fb88ef5321edb
f6a6078391cf3f04eb055634c64391a7087c3420
F20110115_AACOKO du_x_Page_084.tif
fee3918aeddb54dcf4719e4ee49c9bca
0e3a82aba1d0f25b7b44a36414a481f7c1c82b41
F20110115_AACOLE du_x_Page_101.tif
3109f58b8700b1886bb5f279d196c9af
bd41b75eff74c2e97110ee2dcc32a8cf1bf873c8
F20110115_AACOKP du_x_Page_085.tif
0356622a8692f9e910fc9bbe0385fa31
3b682763015ef70d86f8dab76b0d864573de5e9e
F20110115_AACOLF du_x_Page_102.tif
b18f1e792d4a1f210d3defd8f2e0a8fa
1fcea0d2552d5ec243b83bd1acc4d2e758269a7c
F20110115_AACOKQ du_x_Page_086.tif
336ae9e86fc496e1ac0aa321319fa706
cdf08844522932d55f7f5316c28658c7a778088a
F20110115_AACOLG du_x_Page_103.tif
885cab7b6aad3c6c9f87137b9378e985
a26af96ecd4eaf526904554bbec0e2d9672f6ada
F20110115_AACOKR du_x_Page_087.tif
87caee0e7aa536e60df22a6c55f4bccd
b71591e333df99f07517ee24b1549b4bcd7faa0e
F20110115_AACOLH du_x_Page_104.tif
5c71e8bd8b22e45ed7958144ba3fc9e8
ff3c67c91d8df9ebb2b85fd70f41abb55124d901
F20110115_AACOKS du_x_Page_088.tif
498a0e903bf8bd2a07f93489dbfcba2e
ab8c383e05825e9835ce0c2c4c9c842a0433f83f
F20110115_AACOLI du_x_Page_105.tif
4e4caf4134cc3f3257140c367daa4cc9
79fd8b2871e5443476532ba5989fe6a749f48f3a
F20110115_AACOKT du_x_Page_089.tif
3f3e336c33b3e4f55680e06926948136
b24b3ba8c7899dda32980fa7b746307a48d701f4
F20110115_AACOKU du_x_Page_090.tif
de89f3a93bfc1c4ba5b14a8b42dad7c5
7efc0f77e8cd2b16311f3de45efebe723ca3cb67
F20110115_AACOLJ du_x_Page_106.tif
f7c561b3b9977b1803914af33b3f76b4
2fe64d7c235befcaf9acad564026a25ab1a632a8
F20110115_AACOKV du_x_Page_092.tif
6aa841e98d35c72ee8a11b4844eda087
a1b32d28bdb6e591c38fb8391e5389b6d6c9d599


Permanent Link: http://ufdc.ufl.edu/UFE0008357/00001

Material Information

Title: Magnetotransport and Tunneling Study of the Semimetals Bismuth and Graphite
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0008357:00001

Permanent Link: http://ufdc.ufl.edu/UFE0008357/00001

Material Information

Title: Magnetotransport and Tunneling Study of the Semimetals Bismuth and Graphite
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0008357:00001


This item has the following downloads:


Full Text












MAGNETOTRANSPORT AND TUNNELING STUDY OF THE SEMIMETALS
BISMUTH AND GRAPHITE

















By

XU DU















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA


2004

































Copyright 2004

by

Xu Du



































To my parents















ACKNOWLEDGMENTS

I would like to express my sincere gratitude to the many individuals who

contributed to success of my work. First of all I would like to thank my research advisor,

Professor Arthur Hebard. Through his positive and open-minded attitude, and his

enthusiasm and optimism toward physics research, he created the legacy of the free,

vivid, intelligent, friendly and communicative research atmosphere in the lab. I feel really

lucky to be able to work in such environment. His experience, knowledge, and guidance

have been invaluable throughout my graduate career.

I would also like to thank Professor Dmitrii Maslov for his theoretic support.

Without the many useful discussions with him, and his constructive criticism, much of

my work would have gone nowhere. I would also like to express my deep appreciation to

Professor Andrew Rinzler. I truly benefited from his valuable opinions, his help with lab

facilities, and collaboration of some on his interesting and fruitful projects. I also want to

thank Professor Peter Hirschfeld, who gave me a better understanding of solid state

physics through his teaching; and Professor David Norton, for being on of my committee

members.

I am dearly thankful to current and former members of our group (Josh Kelly,

Jeremy Nesbitt, Partha Mitra, Ryan Rairigh, Sinan Selcuk, Guneeta Singh, Kevin

McCarthy, Quentin Hudspeth, Stephen Arnason, Nikoleta Theodoropoulou, and

Stephanie Getty), who provided a joyful working environment and great help. I would

especially like to thank Sinan Selcuk for his help on E-beam lithography. I also want to









thank Jamal Derakhshan (who worked as an REU student in the lab), for his help with the

bulk bismuth study.

My gratitude also goes to Professor Gray Ihas, and to Professor Amlan Biswas and

his students (Tara Dhakal, Jacob Tosado, and Sung-Hee Yun), who provided me great

help in using their facilities. I thank Zhuangchun Wu, Jennifer Sippel, and Amol Patil for

their kind help with my experiments. I also would like to thank Ronojoy Saha, for useful

discussions on high magnetic field transport. Many thanks go to the machine shop

personnel for their excellent work, which allowed my research work to move on

smoothly.

I would like to express my great appreciation and deep love to my parents for their

unconditional love and support. And finally, I would like to thank my dear wife, Zhihong

Chen, who was a graduate student in Professor Andrew Rinzler's group. Her knowledge

and intelligence have been of great help. She has shared my happiness and burden all

these years. Her love changes my life and makes me a better individual.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES .................................................... ............ .............. viii

LIST OF FIGURES ......... ......................... ...... ........ ............ ix

ABSTRACT ........ .............. ............. .. ...... .......... .......... xii

CHAPTER

1 GENERAL IN TRODU CTION ............................................................ ............... 1

2 MAGNETOTRANSPORT IN GRAPHITE ....................................... ............... 4

2.1 Overview of Classical Magnetotransport in Semimetals.......................................5
2.2 M ulti-B and M odel ................ .................................................. .....7
2.3 Sample Preparation and Characterizations............................................................9
2.3.1 Sample Preparation................... .................................. 9
2.3.2 Characterizations: Dingle Temperature and Landau Levels .....................11
2.4 Transport in the Classical R egion...................................... ........................ 17

3 MAGNETOTRANSPORT OF GRAPHITE IN THE ULTRA-QUANTUM FIELD..24

3.1 Transport D ata in the U ltra-Quantum Field................................... .....................24
3.2 In-Band Transport Behavior in the Ultra-Quantum Regime.............................27
3.3 Possible M odels in the Ultra-Quantum Regime ......................... .....................37

4 TUNNELING INTO BULK BISMUTH IN THE ULTRA-QUANTUM FIELD........41

4 .1 M o tiv atio n ........................................................................................................ 4 1
4 .2 E x p erim en ta l............................................................................................. .. 4 3
4.3 Results and D discussion .................................................... ...............47

5 ACHIEVING LARGE MAGNETORESISTANCE IN BISMUTH THIN FILMS .... 50

5 .1 In tro du ctio n ...................................... ............................ ................ 5 0
5.2 Experim mental ................................................................... .. ... ..... 54
5 .3 R esu lts an d D iscu ssion ........................................... ........................................ 55









6 METALLIC SURFACE STATES IN THE ULTRA-THIN BISMUTH FILMS........63

6.1 Introduction: Physics of the Ultra-Thin Bismuth Films ................................63
6.2 Transport Properties of the Ultra-Thin Bismuth Films............. ...............66
6 .2 .1 E x p erim ental ........... ... ....... ... .. .. ...... .. .................. .. ................ .. 66
6.2.2 M etallic Surface States .................................. ..... ............... 67
6.3 Control of the Surface States ........................................ .......................... 74

7 SURFACE SUPERCONDUCTIVITY IN ULTRA-THIN BISMUTH FILMS......... 80

7 .1 T ran sp ort E v id en ce ......... .. ............... ................. ............................................80
7.2 T unneling E evidence ........... ........................................................ ............... 84
7 .3 P o ssib le P ictu re ............................................................................................... 8 9

8 FUTURE W ORK ........... ............ ........................ .... .. ....... .............. 91

LIST OF REFEREN CES ......... .................. .............. .................................... 97

BIOGRAPHICAL SKETCH .............. ........... ................ 101
















LIST OF TABLES


Table page

1-1. Basic parameters of bismuth and graphite............... .......................1

5-1. Summary of results for different bismuth film growth conditions.........................61

6-1. Parameters for the simulating the effect of thickness and temperature on the
magnetic field dependence of the Hall resistivity in ultra-thin Bi films ................72

6-2. Parameters for the simulating the effect of Ge coating on the magnetic field
dependence of the Hall resistivity in ultra-thin Bi films .............................. 79
















LIST OF FIGURES


Figure page

2-1. Configuration of leads on graphite transport sample.................................... 10

2-2. Shubnikov-de Haas oscillations in graphite at indicated temperatures ...................11

2-3. The Landau level indices as a function of the inverse of magnetic field at different
low tem peratures ...................... .................... .. .. ........... ..... ....... 12

2-4. The amplitude of the ShdH oscillations as a function of the inverse of magnetic
fi eld at 2K ...................................................... ................... ... ....... ....... 14

2-5. Scaled ShdH oscillations amplitude as a function of the inverse of magnetic field in
different tem peratures. ........................................... ........... ..... ........15

2-6. Linear fit to the slopes of the scaled ShdH oscillation as function of temperature.. 15

2-7. Temperature dependence of the resistivity pxx for a graphite crystal in different
m magnetic fields. ....................................................................... 17

2-8. pxx and pxy versus applied magnetic field at the different temperatures .................20

2-9. Temperature dependence of mobility, relaxation time; and carrier density for the
bands indicated in the legends of each panel.. ................................................... 21

3-1. The magnetic field dependence of the longitudinal and Hall resistance of HOPG at
different tem peratures ...................... ................ .............................25

3-2. The temperature dependence of the longitudinal resistance of HOPG in different
m ag n etic fi eld s ..................................................... ................ 2 6

3-3. The ratio of the measured Hall resistance and longitudinal resistance as a function
of m magnetic field at 2K ............................................................................. .... .. 29

3-4. The Landau band dispersion relation of graphite in 12 Tesla field, calculated using
the SW M cC m odel. ............................................. .........................32

3-5. Estimation of carrier un-compensation in different magnetic fields at 2K ..............33

3-6. Shape of the in-band resistivity as a function of magnetic field at the indicated
tem peratures. .........................................................................34









3-8. Logarithmic plot of the shape of the in-band conductivity as function of
temperature in different strong magnetic fields ....................................... .......... 36

3-9. Model of the field induced Luttinger liquid with dressed impurity scattering........38

3-10. Scaled in-band conductivity as a function of temperature in magnetic fields above
th e U Q L .......................................................................... 3 9

4-1. Procedure for making tunnel junctions on bulk semimetal using photolithography
tech n iqu e. ......................................................... ................ 4 4

4-2. Mica mask method for making tunnel junctions on bulk semimetal.....................46

4-3. Microscopic picture of a Bi(bulk)-AlOx-Pb tunnel junction............................... 46

4-4. Differential conductance as a function of bias voltage in indicated strong magnetic
fields at 300m k. .......................................................................48

4-5. Differential conductance at low bias voltage in the magnetic fields indicated in the
leg en d .............................................................................. 4 8

5-1. Fermi surface and Brillouin zone of rombohedral bismuth ....................................50

5-2. Magnetotransport behavior of bulk single crystal bismuth. .....................................51

5-3. Magnetotransport behavior of a bismuth thin film .......................................... 52

5-4. X-ray diffraction pattern for a 4-um-thick Bi/Au film ..........................................56

5-5. Resistivity vs. temperature at 0 and 5T for two category-I Bi films ......................57

5-6. Resistivity vs. temperature at 0 and 5T for three category-II Bi films ...................58

5-7. Resistivity vs. temperature at 0 and 5T for two category-III Bi films....................60

6-1. Illustration of semimetal-to-semicinductor transition. ...........................................64

6-2. Resistivity vs. temperature for Bi film with indicated thicknesses. .......................67

6-3. Magnetoresistance at 5K for two different thicknesses Bi films..............................69

6-4. Hall Resistivity vs. magnetic field for (a) 180A and (b) 400A Bi films ..................70

6-5. Simulated Hall Resistivity vs. magnetic field for Bi(180A) and Bi(400A). ............73

6-6. Temperature dependence of resistivity for Bi(100A) and Bi(100A)/Ge..................75

6-7. Hall Resistivity vs. magnetic field for (a) Bi(100A) and (b) Bi(100A)/Ge ............77









6-8. Simulated Hall Resistivity vs. magnetic field for Bi(100A) and Bi(100A)/Ge ........78

7-1. Resistance vs. temperature in zero magnetic field for a 15nm bismuth film.. .........80

7-2. Example of resistance increases during the transition...........................................81

7-3. Sharp feature of resistance change observed in Hall resistivity measurements.......82

7-4. Film thickness dependence of the critical magnetic field at 4.5K .........................83

7-5. Differential conductance as a function of bias voltage in the superconducting gap
region for a Pb-AlOx-Bi(150A) tunnel junction. ............................................ 84

7-6. Differential conductance as a function of bias voltage in the superconducting gap
region at 300mk for a Pb-AlOx-Bi(1000A) tunnel junction...............................86

7-7. Differential conductance vs. bias voltage at 300mK in indicated low magnetic fields
perpendicular and parallel to the junction plane. ............. ....................... ......... 87

7-8. Differential conductance vs. bias voltage at 300mK in indicated strong magnetic
fields perpendicular and parallel to the junction plane.......................................... 88

7-9. A possible picture of surface superconductivity in ultra-thin bismuth films ..........90

8-1. Some examples of the sub-micron sized bismuth patterns ........... ...............93

8-2. Magnetic field dependence of the resistivity for a reservoir pattern ......................94

8-3. Measurements of a nano-cavity with a single grain-boundary in it .......................95















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

MAGNETOTRANSPORT AND TUNNELING STUDY OF THE SEMIMETALS
BISMUTH AND GRAPHITE

By

Xu Du

December 2004

Chair: Arthur F. Hebard
Major Department: Physics

Magnetotransport and tunneling studies on bulk crystals, thin films and patterned

nanostructures of semimetals reveal a surprising range of interesting behaviors. In our

study of ultrathin bismuth films, we found that the transport behavior is greatly affected

by the presence of metallic surface states, which become evident in the thinnest films and

are presumed to be responsible for a surface superconducting state seen in tunneling and

transport anomalies. We also studied bulk samples of both of these semimetals in

magnetic fields high enough to place all the carriers in the lowest Landau level. In this

ultraquantum regime, the apparent re-entrance in graphite from insulating to

metallic/superconducting behavior at low temperatures corresponds to the in-band

insulating behavior of carriers within a semiclassical 2-band model framework. This

analysis brings into question recently proposed explanations of a field-induced metal-

insulating transition and magnetic-field-induced superconducting fluctuations in graphite.














CHAPTER 1
GENERAL INTRODUCTION

A semimetal is a semiconductor with a small conduction band-valence band

overlap (instead of a gap). Semimetals have low Fermi energy. In contrast to

semiconductors, which are insulators at zero temperature (T = 0) where the carrier

concentration n = 0, semimetals have a finite conductivity at T = 0 where n is finite

because of the nonzero overlap of the conduction and valence bands. Semimetals are

metallic, with both electrons and holes contributing to electric conduction. Graphite and

bismuth are typical semimetals, with low Fermi energies and low carrier concentrations.

Table 1-1. Basic parameters of bismuth and graphite
Ef (meV) Carrier concentration (m 3)
(ne=np)
Bismuth -30 1023
Graphite -22 -1024


Semimetals have been of interest for many years, in many different aspects. A

major aspect of semimetal study is magnetotransport. Because of their small values of

carrier concentration, semimetals can be driven into the ultra-quantum regime, when only

the lowest Landau level remains occupied, with a magnetic field of-10 Tesla. In

addition, light cyclotron masses me in certain orientations of semimetals result in higher

cyclotron frequencies (eB/mn ) ensuring that quantum magneto-oscillations can be

observed in moderate magnetic fields and at moderate temperatures. High purity allows

the oscillations to survive the effects of disorder. Magnetotransport study of semimetals

in strong magnetic field allowed the Fermi surface to be mapped by quantum oscillations









in semimetals. In applications, the extremely large magnetoresistance of semimetals

makes them promising candidates for magnetic field sensors.

Another major aspect of semimetal study originated from the long Fermi

wavelength. By making bismuth thin films with thicknesses comparable to a Fermi

wavelength, one could study the energy band quantization because of quantum

confinement. Also, since the band mass is bigger for electrons than holes, as the size of

the bismuth structure decreases, the speed at which the conduction band shifts up will be

faster than that of the valence band. At a certain point, a gap opens up, and the

semimetal-semiconductor transition should happen. Existence of the transition has been

studied for many years, and is still not conclusive; mainly because of the existence of the

surface states, that smear out any sharp features of the transition.

Evidence of metallic surface states were found in films of superconducting bismuth

clusters, which indicates surface superconductivity because of the strongly increased

surface density of states. Further evidence of metallic surface states was found by angle

resolved photoemission spectroscopy (ARPES).

Our study of semimetals focused on two major aspects: 1) magnetotransport and

tunneling study of bulk single-crystal bismuth and graphite; and 2) the effect of bismuth

surface states on transport and bismuth surface superconductivity.

In the following chapters, we will show the motivation and our work on each aspect

of our study. Chapter 2 first of all describes the theoretic background of transport

behavior in semimetals. Then it explains the experimental details, sample characterization

and low field transport behavior analysis of graphite. Chapter 3 explains the high

magnetic field transport behavior of graphite, and proposes possible theoretic models.






3


Chapter 4 describes the magneto-tunneling measurements on bulk bismuth tunnel

junctions. Chapter 5 explains our work on achieving large magnetoresistance in Bi-Au

thin films. Chapter 6 describes the effect of the metallic surface states on the transport

properties of ultra-thin bismuth films. Chapter 7 describes the surface superconductivity

behavior we observed in the ultra-thin bismuth films. Chapter 8 discusses some possible

interesting future works on bismuth, including nano-meter sized bismuth structures and

spintronics applications.














CHAPTER 2
MAGNETOTRANSPORT IN GRAPHITE

Graphite is a typical semimetal, with a low Fermi energy (-22 meV) and low

carrier concentration (-3 x 1024 3 ). The zero-temperature conductivity in graphite

results from the small overlap between the conduction band and the valence band. The

Fermi level lies in the middle of the overlap, which makes graphite a typical compensated

2-band material.

Transport properties of graphite had been studied intensively since 1950s.

Recently, interest in magnetotransport in graphite was renewed because of the

observation of an effect that looks like a magnetic-field-induced metal-insulator

transition: the metallic temperature-dependence of the in-plane resistivity in zero field

turns into an insulating-like one when a magnetic field of a few tens of mTesla is applied

perpendicular to the basal (ab) plane. Increasing the field to about 1 Tesla produces a re-

entrance of the metallic behavior. It has been proposed that the low-field effect is caused

by a magnetic-field-induced excitonic insulator transition of Dirac fermions, 1,2 whereas

the high-field behavior is a manifestation of field-induced superconductivity.3' 4 It has

also been suggested that the apparent metal-insulator transition in graphite is similar to

that in 2D heterostructures (although the latter is driven by a field parallel to the

conducting plane). To elucidate these issues, we performed detailed measurements of

magnetoresistance in graphite and found data quite similar to data reported in 1-4 over

comparable temperature and field ranges. However, our interpretation is significantly

different from theirs.









2.1 Overview of Classical Magnetotransport in Semimetals

A combination of some unique features specific to semimetals [i.e., low carrier

density, high purity, small effective mass and equal number of electrons and holes

(compensation)] led to an unusual temperature dependence of the magnetoresistance even

in classically strong fields, defined by the condition

h/r < hco < kT (2-1)

where r is a scattering time of the carriers. Here we qualitatively compare a semimetal

with a conventional, high-density, uncompensated metal. To begin with, if the Fermi

surface is isotropic, a metal does not exhibit magnetoresistance because of the

cancellation between the longitudinal and Hall components of the electric field.5 In real,

anisotropic metals, this cancellation is broken, and as a result, magnetoresistance is finite

and proportional to (cor)2 in weak magnetic fields (oc <<1). In stronger fields

(oiz >> 1), classical magnetoresistance saturates.6 In contrast (Equation 2-14),

magnetoresistance of a compensated semimetal grows as B2 in both weak- and strong-

field regions.

In addition to the saturation effect described above, another factor that makes the

magnetoresistance much smaller in conventional metals than in semimetals is the higher

scattering rates and hence the smaller values of )ctz The impurity scattering rate in

semimetals is smaller than in conventional metals simply because semimetals are

typically much cleaner materials. The lower carrier density of semimetals also reduces

the rates of electron-phonon scattering compared to that of conventional metals. For

temperatures above the transport Debye temperature, which separates the regions of the









T- and T5 laws in the resistivity, 0 hkFS / k, where kF is the Fermi wave vector

and s is the speed of sound (both properly averaged over the Fermi surface), one can

estimate the electron-phonon scattering rate7 as

r 1 (ka,)(m* /m)k,T/h (2-2)

where a, is the atomic lattice constant, and m* and mo are respectively the effective mass

and the bare electron mass. In a conventional metal, kFaO 1 and m* i m In this case,

O is of the order of the thermodynamic Debye temperature hs /k Ba -few 100 K and

1/ r >> hAkT. Barring numerical factors, h / r < kT cannot be satisfied in a typical

metal. This means that as soon as it enters the classically strong field region,

magnetoresistance saturates and quantum magneto-oscillations start to show up. In a

low-carrier-density material (kFa <<1), 0' is much smaller (for Bi and graphite

O ~ few K) and also 1/ << h IkBT, which ensures that the inequality (2-1) can be

satisfied. Therefore, in a low-carrier-density compensated semimetal a wide interval of

temperatures and magnetic fields exists in which a) the scattering time is linear in T, in

accordance with Equation 2-2, b) we are in the regime of classically strong

magnetoresistance with essentially no signatures of quantum magneto-oscillations, as

specified by the inequality (2-1), and c) the magnetoresistance is large.

An additional feature that is crucial for interpreting the experimental data is that

the Fermi energies of graphite (EF = 22 meV)8 and bismuth (EF = 30 meV [holes])9 are

relatively low; and the temperature dependence of the resistivity is therefore a function of


SInequality (1) can be satisfied in a typical metal for T << R, when the (transport) time
1/ Ttr oc T << T. For an uncompensated metal, however, magnetoresistance saturates in this regime.









two temperature-dependent quantities, n(T) and -c(T). That materials are pure helps to

ensure that electron-phonon scattering is a dominant mechanism for resistance (in a

doped semiconductor, impurity scattering dominates).

2.2 Multi-Band Model

In the semiclassical theory of conduction in metals, DC electrical conductivity in a

multi-band system (in absence of a magnetic field) is described by

='-"(n) (2-3)
n
(n) = e2 dk r,n (k)) (k)i (k)(- f (k) (2-4)



where f is the Fermi function, and ( K) c(k)

h f

Since f 0, except when E is within kT of e, filled bands have no
OE

contribution to the conductivity. Only those partly filled bands that are close to the Fermi

level contribute to the conductivity.

In the presence of a classically strong magnetic field B = Bz (the Landau energy

level quantization is negligible), for an isotropic system in which all the occupied orbits

are closed, there will be no magnetoresistance because of the cancellation of Lorentz

force by the Hall components of the electric field. If an external electric field E = Exp is

applied, the induced current density will be j = coEx, where o0 is the in-plane zero

magnetic field conductivity. The Hall component of the electric field will be generated:

Ey = (o)r)E Then the definition: j = a E, hence










-oOE E
0 = ( (o or)Ex (2-5)
0 0

will yield

U0- 0-- C0D cT
1+(Ocr)2 1+(Or3)2
-C(o T (2-6)
or= 0
l+ (oc)2 1+((C0 )2
o o 1z (0)



This, in terms of resistivity, which is experimentally measured, is simply

p" -RB 0
p(B) = u(B) = RB pO 0 (2-7)
0 0 p"


where R = -is the Hall coefficient. Note that the longitudinal components of the
ne

resistivity have no field dependence.

Now consider such a system with more than one band. Each band contributes to the

conductivity of the system in parallel with the other bands. Then the total resistivity is in

terms of the resistivity of each band:



p p, Z RB p, 0 (2-8)
0 0 p:)


Even without calculating the resistivity above in detail, we can readily see that the

magnetic field dependence (which belongs to the off-diagonal components in the

resistivity tensor of each single band) may enter into the diagonal components of the total









resistivity. Thus the multiband system can have magnetoresistance even though none of

its band has magnetoresistance by itself.

For the simple (and most useful) case of a 2-band system, the resulting longitudinal

resistivity and Hall resistivity are:

p1, p (1 + pz)+(R p2 + R 1)B2 a)
p (2-9a)
(p1 + p22 +(R +R)2 B2

RR R(R, + R2)B3 + (2R2 +P2 R )B
p 2 (2-9b)
p(p + p2)2 +(R1 +R22 B2

For a system of more than 2 bands, it is convenient to describe the contribution of

each band in terms of conductivity. In a simple Drude model,

2 = u, (2-10a)
1 + (,B)2

enj ,2B
U e = (2-10b)
1 + (p, B)2

where, n, and /, are carrier density and mobility of the ith band. From the conductivity

tensor, we can then calculate the measured values of resistivy and Hall constant:

o, (B) a (B)/B
p(B) = xx and RH (B) = x(
U2 (B) + c2 (B) r2 (B) + U 2 (B)

2.3 Sample Preparation and Characterizations

2.3.1 Sample Preparation

The sample used in the study, a rectangular shaped highly oriented pyrolytic

graphite, with dimensions 2.4 mm wide by 8 mm long by 0.5 mm thick, was cut from a

bulk piece of highly oriented pyrolytic graphite (HOPG) using wire saw.









The HOPG sample has a mosaic spread, determined by X-rays, of 2 degrees. After

the sample was cut, it was glued onto a glass substrate. Figure 2-1 shows the

configuration of the measurement leads on the sample. The 4-terminal measurement leads

were connected to the sample applying silver paint. Because of the high in-plane/out-of-

plane conductivity ratio in layered graphite, we found it necessary to place the current

leads uniformly in contact with the sides of the sample. Thin-foil indium was coated

uniformly with silver paint, and was attached to the graphite end plates as current leads.

Gold wires with tiny loops were silver pasted with -2 mm separation to the edges of the

sample as voltage leads.

V" Hall











I+ V+ V- I-



Figure 2-1. Configuration of leads on graphite transport sample

Resistance measurements at 17 Hz were carried out using a Linear Research 700

resistance bridge. The sample was measured over the temperature range 2K- 350K in

fields as high as 17.5 Tesla. Low magnetic field measurements were carried out in a

Quantum Design Physical Property Measurement System (PPMS) with a 7 Tesla magnet.

High magnetic field measurements were carried out in a He3 refrigerator with a 17.5

Tesla magnet in the National High Magnetic Field Labs (NHFML). In all measurements,








the magnetic fields were applied perpendicular to the graphite basal plane (i.e., parallel to

the c-axis).

2.3.2 Characterizations: Dingle Temperature and Landau Levels

In the presence of strong magnetic fields, the energy bands of graphite split up into

Landau levels. With increasing magnetic fields, the interval between Landau levels

increases: As = ho)A = heB /m, where o), is the cyclotron frequency, and m is the

cyclotron mass When a Landau level moves across the Fermi surface, sharp features of

conductivity change appear. This caused the oscillatory behavior of resistivity in the

magnetic field sweep (Shubnikov-de Haas oscillations).


0.00 *
--.--2K f\. '""""'---

-5K


-0.05- -1


0. -

-0.10 4 1
0.2

0.0 -
-1 0 1 2 3 4 5 6 7 8
-0.15 B (Tesla)

0.0 0.5 1.0

1/B(Tesla-1)

Figure 2-2. Shubnikov-de Haas oscillations in graphite at indicated temperatures. The
oscillations are obtained by subtracting the background magnetoresistance
from the resistance vs. magnetic field curves. The inset shows the resistance
as a function of magnetic field at 2K.






12


Given the Fermi energy Ef, the number of Landau levels below the Fermi energy

Es
can be estimated as N = 1+ r Hence the period at which the one Landau level
heB / mI

moves across the Fermi surface goes like 1/B. As the magnetic field increases, every time

one Landau level shifts across the Fermi level, the resistivity will decrease because of the

high density of states at the bottom of the Landau band. And a valley will show up in the

resistivty vs. magnetic field plot. By plotting the valley positions of the ShdH oscillations

vs. 1/B, one gets evenly spaced points. By labeling these points one can count the number

of Landau levels lying below or across the Fermi surface. Since the band structure does

not change with temperature, the valley positions measured at different temperatures

should overlap well. Figure 2-3 below shows the Landau level indices as a function of the

inverse of magnetic fields at different low temperatures.




8 *
)* 2K
S7 M 5K
> A 10K
-J 6 -

5 -




2 -



0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

1/B (Tesla1)

Figure 2-3. The Landau level indices as a function of the inverse of magnetic field at
different low temperatures









Figure 2-2 shows that the ShdH oscillations are most pronounced at very low

temperatures (kT << hio)). At higher temperatures, the oscillations are smeared by

phonon scattering. The relation between the amplitude of the ShdH oscillations and

temperature T at magnetic field B is shown in Equation 2-11.10


Ao B-52 exp a(T+ Td) (2-11)
B

Here Td, the Dingle temperature, describes the temperature-independent scattering

from impurities and dislocations. Dingle temperature is a useful parameter in

characterizing the quality of the graphite sample. The lower the Dingle temperature, the

less imperfection the sample has.

Dingle temperature can be measured from conductance-field sweep at different

temperatures. First, the background of the conductance vs. field curves is subtracted out,

and the oscillatory part is plotted vs. 1/B. Then the oscillation amplitudes are obtained by

subtracting the envelope curves of the oscillations valleys from the envelope curves for

the peaks (Figure 2-4).

Since only the shapes of those curves are important, we used arbitrary smooth

functions to fit the envelope curves. This method of interpolation give much more precise

oscillation amplitude values than simply subtracting the resistance values at the valleys

from those at the adjacent peaks (which do not correspond to the same field).

After we get the amplitudes of the oscillations Aosc, we plot Ao B5/2 vs. 1/B,

and obtain straight lines in AocB5/2 vs. 1/B plots ((Figure 2-5)). The slopes of the

straight lines, according to Equation 2-11, simply correspond to a(T + T, ).









0.45 ., 1. ,


0.40


0.35 0


L 0.30 -
030.5






o 01
0.25 -




0.15 -
0.0 0.5 1.0 1.5 2.0
1/B (Tesia 1)
0.10 1 1 1 1 1 ,1
0.4 0.6 0.8 1.0 1.2 1.4 1.6

1/B

Figure 2-4. The amplitude of the ShdH oscillations as a function of the inverse of
magnetic field at 2K, obtained by subtracting the bottom envelope curves
from the top envelope curve of the oscillations, as indicated in the inset.

We then plot the values of the slopes vs. their corresponding temperatures, and

perform a linear equation fitting to the curve. The fitted straight line then intersects with

the negative side of the temperature axis, with the offset being the Dingle temperature Td.

For the graphite used in our study, the Dingle temperature we got from the analysis

described above is about 4.5K. This result suggests that the smearing of the ShdH

oscillations by the imperfections in the HOPG corresponds to the thermal smearing of

4.5K.












2K
0 5K
S10K
e 15K












0.4 0.6 0.8 1.0 1.2 1.4 1.6

1/B (Tesla1)


Figure 2-5. Scaled ShdH oscillations amplitude: Ln(AocB5/2),
of magnetic field in different temperatures.


as function of the inverse


-4x104


-6x104 -


0 2 4 6 8 10

T(K)


12 14 16


Figure 2-6. Linear fit to the slopes of the scaled ShdH oscillation as function of
temperature.


I-

S-8x104



-1x105


T, = 4.5 +1K


I I I I I I I I I I I I I I I


I I I I I I I I









ShdH oscillations also provide information about the Fermi surface. By measuring

ShdH oscillations in different magnetic field orientations, one can map out the extremal

of the Fermi surface. For graphite, by measuring ShdH oscillations and calculating the

volume of the Fermi pockets, we can then calculate the carrier concentration.

Here we simplify the problem by treating the Fermi surface of graphite as ellipsoids

with anisotropy ratio r. By measuring the ShdH oscillations with magnetic field parallel

to the c-axis of graphite, we get the period of the quantum oscillations to be

he
A(B') == (2-12)
E me

,where mc is the cyclotron mass for magnetic field along the c-axis. This provides the

information about the area of the extremal cross section of the Fermi surface with a plane

perpendicular to the magnetic field: Sx,, = 27i mc (in momentum space). Given the

anisotropy ratio r7, we can then calculate the volume of the ellipsoid and hence the

carrier concentration:


n /4 27N[A(B-1)]3/2 (2-13)


where N = 6 is the number of ellipsoids in the Brillouin zone. Taking 7 12-17, the

carrier concentration calculated from the measured oscillations period is

n 2 3 x 1024m3 This number corresponds to the zero temperature carrier

concentration in graphite. At low enough temperatures, one can separate the ShdH

oscillations periods from electrons and holes, and calculate the carrier concentration for

the two different carriers. Also, for each carrier group, there will be two sets of

oscillations because of the spins. At 2K however, we are not yet able to distinguish the









different periods result from the small effective mass difference between electrons and

holes, and from the spin splitting.

2.4 Transport in the Classical Region

In this section, we present a detailed study of low field magnetotransport in

graphite and show that the "unusual" behavior of the temperature and field-dependent

resistance, such as shown in Figure 2-7, can be described in a straightforward way by a

simple multi-band model that takes into account contributions to the conductivity from

the electron and hole carriers associated with the overlapping valence and conduction

bands.


1 E-6


0---
E


X
X
a-


1E-7


1E-8


100

T (K)


150


200


Figure 2-7. Temperature dependence of the resistivity px for a graphite crystal plotted on
a logarithmic axis at the magnetic fields indicated in the legend. The solid
lines are the fits to the data using the six parameters derived from the three
bands described in the text. The shadowed region on the inset and its mapping
onto the data in the main panel are described in the text.


1.5

1.0
I II
0.5

0.0
0 50 100 150 200
T (K)

* 0 mT
20 mT
40 mT
v 60 mT
80 mT
o 100 mT
A 200 mT









We use the qualifier "unusual" in describing the data of Figure 2-7, since on

lowering the temperature the resistance increases as it does in an insulator but then

saturates at lower temperatures. The non-trivial explanations of Kopelevich et.al 34 rely

heavily on such features as the Dirac spectrum of fermions and almost two-dimensional

transport, which are unique for graphite but not for Bi. That Bi and graphite behave

similarly suggests that these features are not responsible for the observed phenomena.

Our explanation for the insulating-like behavior in a magnetic field does not require more

exotic explanations of a magnetic-field-induced opening of an excitonic gap in the

spectrum of interacting quasiparticles.11 Instead, we propose that the uniqueness of the

low magnetic field transport behavior of semimetals lies in the existence of a wide

interval of temperatures and magnetic fields defined by the inequalities of Equation 2-1.

Our analysis of the experimental data confirms the inequalities .

Both pxx and py (see Figure 2-8) were measured in magnetic fields up to 0.2 Tesla

at different temperatures. A small field-symmetric component caused by slightly

misaligned electrodes was subtracted from the pxy(B) data. To fit the data, we adopt a

standard multi-band model.5 Each band has two parameters: resistivity p' and Hall

coefficient R, = Yq, where q, = +e is the charge of the carrier. In agreement with


earlier studies, we fix the number of bands to three.1 Two of the bands are the majority

electron and hole bands, and the third one is the minority hole band. Although the

presence of the third band is not essential for a qualitative understanding of the data, it is

necessary for explaining fine features in pxy. Our fitting routine incorporates both pxx(B)

and pxy(B) simultaneously by adjusting the six unknown parameters independently, until

the differences between the fitting curves and the experimental data are minimized.






19


Because the majority carriers in graphite derive from Fermi surfaces that have six-

fold rotational symmetry about the c-axis, we only need to deal with the 2x2

magnetoconductivity tensor with elements ,xx and cxy.

P, RB
Here, we define the conductivity ca R + ,RB and the
p2 + (RB)2 p2 +(RB)2 a

resistivity p, = m /nZe21, for the ithband. The total conductivity is simply a sum of the

contributions from all the bands: i = V ~r. The observable resistivity tensor is obtained
1=1..3

by inverting a p= :1

Qualitatively, the unusual temperature dependence of px displayed in Figure 2-7

can be understood for a simple case of a two-band semimetals, where p, reduces to


= PePh(Pe + Ph)+ (PRh + Ph Re) (2-14)
(Pe + Ph) +(R +Rh)2B2

Here pe (Ph) and R (Rh) are resistivity and Hall coefficient for the electron (hole) band,

respectively.

Assuming that pe,h oc Ta with a > 0, we find that for perfect compensation (i.e.,

ne = nh, where ne and nh are carrier density for the electron band and the hole band

respectively), Re = -Rh = R and the 2-band resistivity described by Equation 2-14 can

be decomposed into two contributions: a field-independent term o T" and a field-

dependent term oc R2 (T)B2 Ta At high T, the first term dominates and metallic

behavior ensues. At low T, R(T) oc 1/n(T) saturates and the second term dominates,

giving insulating behavior.














10-6





107
S5K 0 40K

15K v 100K
v 20K 100K
o 25K A 200K
10-8 1--
0.00 0.05 0.10 0.15 0.20
B (T)

3.0xl 07
.4x1- 5K o 40K
1.4x10" -
2.5x10.7 12x1- 10K 70K
15K v 100K
1.0x10io- 20K 150K
2.0x10.7 ~ 8.0x10 25K 4 200K
S 6.0x10

E 1.5x10-7 42x10
2.0x10i-
0.0
Q. 1.0x107 -2.0x10
0.00 0.01 0.02 0.03

5.0x10 -8


0.0


0.00 0.05 0.10 0.15 0.20
B (T)


Figure 2-8. xx and pxy versus applied magnetic field at the temperatures indicated in the
legend. The solid lines are determined by a fitting procedure described in the
text. The inset in the py plot magnifies the low-field region where the
contribution from the minority band is important.









350
S300
250
E 200
150
100
0 50
E 0

1.8E12
1.5
1.2
S 0.9
(D
c/ 0.6
T 0.3
0.0

10E24

E 8.0

S 6.0
(D
-0 4.0
(D
*E 2.0
0.0
0.0


50 100 150
Temperature


200


Figure 2-9. Temperature dependence of the fitting parameters: A) mobility; B) relaxation
time; and C) carrier density, for the bands indicated in the legends of each
panel.

The actual situation is somewhat more complicated because of the T-dependence of

the carrier concentration, the presence of the third band, and an imperfect compensation


'A I I I I
A --- band 1
-- -- band 2
-a-A- band 3


--- A b
A I



- -i- band 1 5
-*- band 2
-A- band 3








--- band 1
-*e- band 2
-A- band 3

C









between the majority bands. Results for the temperature-dependent fitting parameters are

shown in Figure 2-9, where band 1 corresponds to majority holes, band 2 to majority

electrons and band 3 to minority holes. The insulating-like behavior of the carrier density

with a tendency towards saturation at low temperatures is well reproduced. For the

majority bands, 1 and 2, the carrier concentrations are approximately equal and similar in

magnitude to literature values.12 The slope of the linear-in-T part of 1 = aexpkT/h

with axp = 0.065(3) (dashed line in Figure 2-9, panel A) is consistent with the electron-

phonon mechanism of scattering. To see this, we adopt a simple model in which carriers

occupying the ellipsoidal Fermi surface with parameters mab (equal to 0.055mo and 0.04

mo for electrons and majority holes, correspondingly), me (equal to 3mo and 6mo,

correspondingly) interact with longitudinal phonons via a deformation potential,

characterized by the coupling constant D (equal to 27.9 eV). In this model, the slope in

the linear-in-T dependence of r is given by7

theory= (2 /z) EFD2 /O S p h3 (2-15)

where m*= (mm)1/3 0.21mo both for electrons and holes, po = 2.27g/cm3 is the

mass density of graphite, and S = 2 x 106 cm / s is the speed of sound in the ab-plane.

(The numerical values of all parameters are taken from standard reference on graphite12)

With the above choice of parameters, atheo = 0.052 for both types of carriers. This value

is within 20% of the value found experimentally. Given the simplicity of the model and

uncertainty in many material parameters, especially the value of D, such an agreement

between the theory and experiment is quite satisfactory.









The solid lines through the data points in Figure 2-7 are calculated from the

temperature-dependent fitting parameters derived from our three-band analysis and

plotted in Figure 2-8. The shaded region (II) depicted in the inset of Figure 2-7 represents

those temperatures and fields that satisfy the inequalities of Equation 2-1. In region (I)

ShdH oscillations can be seen at sufficiently low T (our sample has a Dingle temperature

of 5K), and in region(II) the magnetoresistance is low. The boundary between (I) and (II)

reflects the rightmost of the inequality 2-1 and is determined by the relation

T > rheB/m *, where 7 = 5 has been chosen to represent the ratio kT/hIoi. A larger

value of 7 would decrease the slope of this boundary and diminish the area of (II). The

boundary between (II) and (III) reflects the leftmost inequality of 2-1 and is determined

by the relation B > m / e (T) where 1/r (T) is obtained from experimental fitting

parameters (Figure 2-9). In the main panel of Figure 2-7, we superimpose region (II),

again as shaded area, on the p,(T,B) data. Below the lower boundary co) < 1, and the

magnetoresistance is relatively small. The upper boundary is determined by the locus of

(B,T) points satisfying the rightmost inequality of 2-1 for 7 = 5. Clearly region (II),

constrained by the inequality 2-1, overlaps well with the metal-insulating like behavior of

graphite. We thus conclude that the semimetals graphite and, by implication, bismuth

share the common features of high purity, low carrier density, small effective mass and

near perfect compensation, and accordingly obey the unique energy scale constraints that

allow pronounced metal-insulating behavior accompanied by anomalously high

magnetoresi stance.














CHAPTER 3
MAGNETOTRANSPORT OF GRAPHITE IN THE ULTRA-QUANTUM FIELD

3.1 Transport Data in the Ultra-Quantum Field

The inequality discussed in chapter 2: h / z < Aho < kT defines two limits that are

satisfied within a wide temperature range in semimetals: h / r < hoi, (or o),z > 1) gives

rise to the large magnetoresistance in the semimetals; hoai < kT defines the "classically

strong" magnetic field (weak field), in which the number of Landau levels below the

Fermi level is so large that the quantum oscillations are well smeared by temperature,

hence the effect of quantization of the energy bands is negligible.

In stronger magnetic fields, there are only few Landau levels below the Fermi level

and A), < kBT is no longer satisfied. Eventually, when the magnetic field is so strong

that all the conduction electrons are all in the lowest Landau level, the so-called ultra-

quantum limit is reached. Above the ultra-quantum limit, the energy of the electrons is

fully quantized in the plane perpendicular to the field. The movement along the field lines

is free; hence the electrons in the system assume movement with spiral trajectories along

the field lines. Ideally, in the absence of scattering and interaction, a system in the ultra-

quantum regime should have zero conductance in the plane perpendicular to the magnetic

field, because the Lorentzian force confines the movement of the electron to the spiral

trajectories. However, with interactions and scattering, the electron can move along the

plane perpendicular to the field lines in a diffusive manner.









Figure 3-1 shows the strong magnetic field magneto-transport data taken from the

same HOPG used in the low magnetic field study.


0 5 10 15 20
B (T)


15K
B /20K
7.5K
10K

5K
40K



70K






0 5 10 15 20

B (T)


Figure 3-1. The magnetic field dependence of the
of HOPG at different temperatures


A) longitudinal; and B) Hall resistance


20K
15K
40K
10K
S7.5K
-5K
70K


1500


1200


900


S600


300


40




E
x20





0









2000



1500



S1000 17.5T
cn 16T
S/ 4T
12T
500 /10T
8T
6T
4T
0 I 1 T,
0 20 40 60 80 100

T (K)

Figure 3-2. The temperature dependence of the longitudinal resistance of HOPG in
different magnetic fields

From the magnetic field dependence of the longitudinal resistance data, we see that

the resistance increases roughly linearly with magnetic field, and tends to saturate in very

high magnetic field (>10 Tesla). For the curves taken at very low temperatures (T <15K),

we see ShdH oscillations on top of the magnetoresistance. The Hall resistance has much

smaller values than the longitudinal resistance in high magnetic fields, and has rather

complicated field dependence.

We are most interested in the temperature dependence of the resistance in different

strong magnetic fields. Here we see that, the resistance increases with decreasing

temperature for T >30K, similar to what is observed in the low (classical) magnetic

fields. For T <30K, however, the resistance plunges down with decreasing temperature in

strong magnetic fields.









The "metallic" behavior observed in strong magnetic fields and low temperatures

can not be explained by semi-classical transport theory. It was proposed that the high-

field transport behavior is a manifestation of field-induced superconductivity4. However,

we find a more conventional interpretation by considering graphite as a multi-band

system. Our strategy of analyzing the data relies on obtaining in-band transport behavior

from the experimentally measured data using the multi-band model. Then we will try to

understand the in-band transport, which represents the intrinsic physics of the graphite

system.

3.2 In-band Transport Behavior in the Ultra-Quantum Regime

In strong magnetic fields, the multi-band model still applies, except that we can no

longer take the resistivity and Hall coefficient of each single band to be field-independent

parameters, because of the strong quantum effect. Instead of curve fitting with field

independent parameters, we need to start by simplifying the multi-band model. Since the

contribution of the minority band vanishes in high fields, we can apply the simple 2-band

model, in which:

P1 2(1P + P2)+(pR2 + 2R )B2
(p1 + p2)2 +(R + R2)2B2

RR,(R, +R,)B3 +(Rp2 +R2p12)B
P (p + p2) +(RI +R,)2B2

Now we make the assumptions that, in high magnetic fields, the system is nearly

compensated, and the resistivities of each band are very close:

P2 P (3-la)

R, -R R (3-1b)









We will see that these assumptions are valid when applied to the experimental data

in high magnetic fields. With the simplification above, we have

p2 +RzB2
p, = 2p (3-2a)
4p2 + 2B2

-R2B2+p2
y = SB 2 (3-2b)
4p2+ 2B2

where 8 R1 + R2 is the difference of the electron and hole Hall coefficients.

The ratio of the two numerator terms p and RB in high magnetic fields gives rise

to two different pictures of transport properties in this region. In the first picture, we

assume that the magnetoresistance shown in px is mostly from the magnetoresistance of

each single band. An extreme case of this picture is when: p >> RB, and hence:

p, =p12 and p, = B/4.

In this case, the longitudinal resistivity of the 2-band system is essentially the same

as that of each single band. Accordingly, we see that in this picture, we do need the non-

trivial explanations for the non-saturating MR in a system with closed orbits, i.e., field

induced metal-insulator transition (MIT) and re-entrance to metallic behavior in

quantizing magetic fields.1-4, 13

In the second picture, we assume that the MR shown in px is mostly from the

diagonal (Hall) resistivity, (RB)2 >> p2 (or (o Zr)2 >> 1). Then the simplified forms of

the high field limit resistivities are:

2R2pB2
2R2B2 (3-3a)
4p2 +52B2










3R2B3
S4p2 +2B2


The ratio of the two measured parameters,





0.1





x

X 0.01







1E-3


- is plotted in the figure below:
p, 2p


6 12
BT)
Figure 3-3. The ratio of the measured Hall resistance and longitudinal resistance as a
function of magnetic field at 2K.

CB
It can be seen in the figure that, the ratio <<1 for field above the ultra-
P

quantum limit. This rules out the possibility ofun-compensation (i.e., 3 0 ) as a

mechanism for the "re-entrant" behavior in high magnetic fields and low temperatures,

since the second term in the denominator of both p, and p, can be neglected.

Now we have a even more simplified form of px and p :


R2B2
p, = (3-4a)
2p


(3-3b)









R2B3
P, = -- (3-4b)
4p2

It can be seen from these relations above that, the transport behavior in the second

picture is drastically different from that in the first picture. The 2-band longitudinal

resistivity is now proportional to the reciprocal of the resistivity of each single band!

Therefore the "re-entrance" to metallic behavior of the 2-band system as measured by

px would really correspond to a cross over from metallic to insulating behavior for each

band (as measured by p1,2) as the temperature drops.

The criterion for the second picture to be valid is that: RB >> p must be satisfied.

In relatively low magnetic fields (say, B 0.1 Tesla), taking the values of p 10 8 and

R ~ 10 6, we see that this criteria is well satisfied. Hence we are confident in ruling out

any non-trivial MIT mechanism in explaining the MIT-like behavior. Despite the

complicated field-dependence of p, the major mechanism for MR is the Hall resistivity

term RB.

R2B2
In very strong magnetic field, RB >> p is required for the result p, = to be
2p

valid. Hence we require that p >> RB. In the range of the magnetic field we are

studying, the carrier concentration increases slowly with increasing field12, hence the in-

band Hall coefficient R decreases with increasing field. Taking the experimentally

measured p, ~ 3 x 10-4 Om, and R < 10-6 QmT1, we can see that px >> RB is satisfied

for B ~ 10 Tesla. This indicates that our second picture is self-consistent according to the

experimental data.









From the analysis above, we see thatRB >> p is generally satisfied in the magnetic

CB
field range of our study. We also note that RB >> p and <<1 imply S << R. Hence
IP

our assumption that the system in strong magnetic field is nearly compensated is well

consistent with the experimental results.

Till now, we haven't made any assumption on the expressions of the resistivities

and the Hall coefficients of the two bands. Ideally, if we have the complete information

on the band structure of graphite in high magnetic field and the scattering mechanisms,

we can exactly calculate the conductivity tensor using Kubo formula. Such a procedure,

however, will be extremely complicated.

In the ultra-quantum limit (UQL), the problem may get simplified by the fact that

all the carriers are in the lowest Landau level at sufficiently low temperatures:

kBT << Ahco Ef This can be understood by examining the Landau band structure of

graphite in the ultra-quantum limit field.

The energy band quantization due to the magnetic field can be calculated using the

classical tight-binding SWMcC model.12 The dispersion relation from the calculation

shows that, in magnetic fields, each energy band separates into different Landau bands.

With increasing magnetic field, all other conduction bands and valence band move

further and further away from each other and from the Fermi level, while the lowest

(zeroth) Landau bands remains field in-dependent. For field above the ultra-quantum

limit (- 8 Telsa for graphite), the Fermi level runs across only the lowest (zeroth)

conduction band and valence band, which are the only Landau bands that contribute to

the conduction. Figure 3-4 shows the Landau band structure of graphite in 12 Tesla field,









obtained from the classical band structure calculation (SWMcC model). The field

independence of the zeroth Landau bands was confirmed by the recent high magnetic

field scan tunneling spectroscopy measurements on HOPG.14


0.10


0.05



0.00


-0.05


-0.10 1I / I iI
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Pzco/2


Figure 3-4. The Landau band dispersion relation of graphite in 12 Tesla field, calculated
using the SWMcC model.

From the Landau band structure shown in Figure 3-4, we can see that in strong

magnetic field, at sufficiently low temperature: kT << hao, E, the number of the

thermally excited electrons (and holes) in the higher Landau levels is negligible, hence

we can make the approximation that he carrier concentration does not change

significantly with temperature nor magnetic field. Since the high field limit of the Hall










coefficient is simply: R = 1, R will be roughly field and temperature independent in this
ne

region (compared with the factor of two resistivity change in this region).

With the approximation above, we have enough information to separate out the in-

band resistivity using the 2-band longitudinal resistivity. We can also estimate the un-

2 R2
compensation 5 in this high B low T region, by calculating p
p B 8

Figure 3-5 below shows the values calculated from experimental data:


106
106




10s








102



2 4 6 8 10 12 14 16 18

B (Tesla)
2 R2
Figure 3-5. as function of magnetic field at 2K, calculated from the
pB 8
experimental data.

p2 -R2
The saturation of is seen in the Figure at field above 8 Tesla (UQL for
pB 8

graphite). The weak field dependence can be attributed to the combination of weak









thermal excitation and field dependence ofun-compensation, and the saturation of 3.

Using the value ofR 10-6 / T (from the band structure calculation), we can estimate

that 38 10 17 Q/T. Hence our assumption of"near compensation" is well satisfied.

From the self-consistent approximations above, we reach a very simple high

magnetic field limit (B > BUQL) result: the resistivity of each single band is proportional

RB2 2B2
to the reciprocal of the 2-band resistivity in graphite: p = -- Figure 3-6 shows B-
P1 P1

calculated from measured data. The high field part of the curve will represent the

resistivity of a single band itself under our assumption that R is field-independent in high

magnetic field.











0 0.1



-570K
-7.5K



10
15K




20K
-25K
40K
-70K

1 10

B (Tesla)

Figure 3-6. as a function of magnetic field at the indicated temperatures, calculated
R
from the experimental data.









From Figure 3-6 above we can clearly see the tendency of scaling of curves in high

magnetic fields and low temperatures (curves become parallel to each other). This

indicates that in this region, we only need to care about the contribution from the lowest

Landau band, and neglect the thermally excited carriers in the higher index number

Landau levels. Figure 3-6 also gives us a range of such regime: B >10 Tesla and T<20K.

We note that this range satisfies the inequality for temperature and field independent

carrier density: kBT << ho E (at 10T, 20K: kBT ~ 0.9meV, hoA Ef 6meV)

With this simplification, we can directly analyze the temperature dependence of

resistivity in high fields and low temperatures assuming that the carrier densities of the

two bands are temperature independent, or R is T-independent. By treating R as a T-

independent and B-independent constant, we see that the in-band resistivity has a

temperature dependence p oc B2 / p,. The in-band conductivity scaler, which contains

the intrinsic physics about the interactions and scattering of the system, is

1 pa pa neZ2
simply o- = Here since o0 and because of the week
p (RB)2 B2 m*

temperature and magnetic field dependence of n and m* in the ultra-quantum region, this


implies that the relaxation time: r ~ Figure 3-8 shows the shape of the in-band
B2

conductivity o0 vs. T using logarithmic axis.

From Figure 3-8 we see that above the UQL field and for kBT << Ah E : 1) at

fixed temperature, the in-band conductivity o- decreases with increasing magnetic field;

2) at fixed magnetic field, the in-band conductivity co decreases with decreasing


temperature.









25

20

15


10
C ^ 4T
S C 6T
8T
5 10T
12T
14T
16T
17.5T
I I I
1 10 100

T (K)


Figure 3-8. Logarithmic plot of the shape of the in-band conductivity (- ) as function
B
of temperature in different strong magnetic fields, calculated from the
experimental data.

Using o0, we can also calculate the in-band conductivity tensor:

0 a0 1 1
= C 0 (3-5a)
l+ +(OZr)2 (c )2 B2Z pZ

S0) (3-5b)
1+ (+(0or)2 ot B

Since in fixed magnetic field, the relaxation time r decreases with decreasing

1
temperature, a, ~ will increase with decreasing temperature. The In-band Hall


conductivity is independent of the relaxation time.









3.3 Possible Models in the Ultra-Quantum Regime:

At this step, we have discovered the transport behavior directly resulting from the

physics of interactions in the graphite system in UQL field. Now we will try to

understand the physics that causes this transport behavior: 1) the relaxation time r

1.
decreases with decreasing temperature; 2) a, ~ increases with decreasing


temperature. In this section, we will consider two possible models that give this kind of

transport behavior: the magnetic field induced Luttinger liquid with impurity scattering,

and phonon delocalization (dephasing).

In the model of magnetic field induced Luttinger liquid with impurity scattering,

the scattering mechanism considered is the elastic scattering of the impurities dressed

with the Friedel potential,15 as illustrated in Figure 3-9. At zero temperature, the electrons

are localized by "dressed" impurities along the direction of the field lines. The potential

of the "dressed" impurities is considered as a tunnel barrier. With increasing temperature,

because of the increasing energy of the electrons, the effective scattering cross section of

the impurities will decrease, and the probability for the electrons to tunnel trough the

"dressed" impurity potential will increase. These will lead to an increasing relaxation

time (hence o, ) with increasing temperature. The temperature dependence of

conductivity along the field direction, ou coincides with that of o With increasing

conductivity along the field direction with increasing temperature, the conductivity along

LL 1
the plane perpendicular to the field will decrease with increasing temperature: o -


Since there is also classical magnetoresistance in the x-y plane, the field induced








Luttinger liquid behavior is a "secondary" correction to the semi-classical magneto-

transport behavior: a, = o0 + aj .






4'




V z


ICc


j impurity



Friedel oscillations



Figure 3-9. Model of the field induced Luttinger liquid with dressed impurity scattering.
The model of the field induced Luttinger liquid with impurity scattering predicts

that the correction of the conductance has power law temperature dependence, with

magnetic field dependent powers: 15

0L r T ~ (B) (along the field direction), (3-6a)

SLL 1/ r T- a(B) ( perpendicular to the field). (3-6b)

A most important prediction from the model is the field dependent power factor. To

check the field dependence of the experimental data, we plot scaled in-band conductivity









ao as function of temperature in different high magnetic field above the UQL. The

conductivities are normalized at the lowest temperature point:

20 I .
-10T
-12T
-14T
16 16T
16T
-17.5T











8

1

T(K)

Figure 3-10. Scaled in-band conductivity as a function of temperature in magnetic fields
above the UQL indicated in the legend.

It can be seen from the Figure 3-10 that, for field well above the UQL, the scaled

conductivities overlap perfectly. This indicates that the magnetic field dependence and

the temperature dependence of the conductivity can be separated: o- = F(B)G(T). This

is obviously contrary to the prediction from the magnetic field induced Luttinger liquid

theory, in which the power factor of the power law temperature dependence itself

depends on the magnetic field.

Another possible model is the phonon delocalization (dephasing) model. In this

model, the electrons are delocalized by phonon scattering. Hence with increasing









temperature, the conductivity along the magnetic field increases, while the conductivity

perpendicular to the magnetic field decreases. The phonon delocalization mechanism

predicts the same trend of the temperature dependence of the conductance:16

o7 T ~ T (along the field direction), (3-7a)

o ~ 1 / Tr T- (perpendicular to the field). (3-7b)

The phonon delocalization mechanism differs from the field induced Luttinger

liquid by an exponent which is now independent of the magnetic field. So the phonon

delocalization mechanism agrees better with the experimental data. However, as far as we

know, there is no complete theory for phonon delocalization, and there is no theoretical

prediction of the values of the power factors. Further work needs to be done to

quantitatively understand the transport behavior of graphite in the UQL region.














CHAPTER 4
TUNNELING INTO BULK BISMUTH IN THE ULTRA-QUANTUM FIELD

4.1 Motivation

In the previous chapters, we have discussed the magneto-transport properties of

semimetal graphite. Graphite is a relatively simple system for transport study in a sense

that, in its hexagonal Brillouin zone, the Fermi surface comprises six cigar shaped

pockets with their long axis parallel to the c axis. Transport in graphite is roughly 2-D

due to the weak coupling between the graphene layers and large ratio of out-of-plane and

in-plane effect mass. All these factors simplify the transport study of graphite so that it

can be treated as an isotropic 2-D system, in which only two major groups of carriers,

electrons and holes (each has one single mobility), need to be considered.

Bismuth, on the other hand, is much more complicated. In the Brillouin zone of

bismuth, there are 3 electron pockets and 1 hole pocket (see Figure 5-1 in chapter 5).

None of the pockets is parallel to any of the others, hence Bismuth is 3-D in all

orientations. And in most of the orientations, every pocket contributes carriers with

different mobility. Hence in bismuth, one needs to consider up to 4 majority bands, each

with different effective mass and different mobility. This makes the magneto-transport

study of bismuth very complicated.

Rather than studying transport, we studied the magneto-tunneling properties of

bismuth in strong magnetic fields. The original intent of our work was to study the

possible high magnetic field induced 1-D (Luttinger Liquid) behavior. The tunnel

junctions used in the study comprise metal-insulator-semimetal trilayer structure. In zero









field, we are simply tunneling from a 3-D metal into a 3-D semimetal. Tunneling theory

predicts that the measured differential conductance has a very weak dependence on the

density of states of any of the electrodes and depends mainly on the properties of the

tunnel barrier. When a strong magnetic field is applied, the energy levels in the semimetal

separate into different Landau bands. When the magnetic field is strong enough so that all

the electrons in the semimetal are in the lowest Landau level, the semimetal enters the

ultra-quantum regime, and the tunneling is between a 3-D Fermi liquid in the normal

metal and "Landau tubes" in the semimetal. In this regime, the semimetal has an

essentially ID character with 1D Landau tubes aligned along the magnetic field and

perpendicular to the tunnel junction area.

For 1-D systems, one can no-longer describe the physics using the Fermi liquid

theory, because of the strong perturbation of Coulomb interaction due to the lack of

screening and phase space for scattering. Instead the 1-D system will be described by the

Luttinger liquid theory. The tunneling experiment provides an opportunity to discover the

enhanced density of states predicted by the Luttinger liquid theory.

When tunneling into a 1-D system, the tunneling theory predicts that the measured

differential conductance across the junction has strong dependence on the density of

states in the 1-D electrode. The proposed magnetic field induced Luttinger Liquid

theory15 states that: for magnetic field induced LL connected to 3D reservoirs by tunnel

barriers:

dI/dV ocT(B) (when eV << kBT), (4-la)

dI/dV ocVa(B) (when eV >> kBT). (4-1b)









The reason that a semimetal is used as the electrode of interest is that, the magnetic

field for the semimetals to reach the ultra-quantum limit is relatively obtainable. For

example, -10 Tesla is needed to drive bismuth into the ultra-quantum regime. For most

metals however, the magnetic field needed will be >104 Tesla, because of their high

Fermi energies and large cyclotron masses.

4.2 Experimental

Tunnel junctions are made on freshly cleaved bismuth crystals. A big piece of pre-

cut bismuth crystal is dropped into liquid nitrogen bath. After the bismuth crystal

equilibrates with the liquid nitrogen, a Razor blade was used to cleave the crystal and

expose a fresh and smooth surface of the trigonal plane. The piece of cleaved bismuth

with smooth surface was then taken out of the liquid nitrogen bath and warmed up in pure

nitrogen gas flow. Through this way, the cleaved surface will maintain its freshness and

there will be no condensation on the surface when it is warming up.

On the surface of bismuth, we have 2 methods for making tunnel junctions. Figure

4-1 shows the procedure using photolithography to make tunnel junction on top of the

semimetal surface. First of all, we define an undercut photoresist pattern on top of the

junction area we choose. Then a thick layer of AlOx was RF sputter deposited onto the

sample as separation layer. This layer prevents shorting outside the tunneling area

resulting from the surface roughness, and from the force of the contact leads. Then we

performed lift-off and opened up the tunneling area. Then we deposit the tunnel barrier,

followed by the counter-electrode, through shadow masks. Finally we pasted gold wire

on top of the counter-electrode above the separation layer.













UV expose


photoresist


semimetal


UV expose









semimetal


semnimetal


- opitcle mask






semimetal


photoresist


200A
Aluminum








develop


Aluminum Oxide 400A
RF sputtering


40um


semimeta


Ilift-off
l in Aceton


Stunneling barrier
semimetal Aluminum Oxide -10A
semimetal


Pb
counter
-electrode


sI- e"


semimetal


Figure 4-1. Procedure for making tunnel junctions on bulk semimetal using
photolithography technique.









This method using photolithography is convenient for defining the junction area.

Using the precise alignment function of the photomask aligner, it is easy to find the ideal

smooth junction area and place the photoresist pattern on top of it. The shortcoming of

this method is that after liftoff, there is always some residue of photoresist left on the

surface. The residue can be mostly cleaned by prolonged treatment with UV ozone

cleaner (-40 minutes). But the cleaning process can cause unwanted oxidation.

Figure 4-2 shows another way we used to make junctions on the surface of

semimetals. This is what we called mica mask method. Essentially it is a shadow mask

method used in RF sputtering. Through conventional shadow masks, sputtering fails to

yield sharp edges due to the high Ar pressure during the deposition. Here in the mica

mask method, an extremely thin mica foil is placed on top of the semimetal. The sheet of

mica will attach itself by Van der waals force to the semimetals surface. We can also

attach another layer of mica on top of it to get an undercut. Then we RF sputter thick

AlOx film as a separation layer. After removing the mica foils, we get a very sharp edge

of the AlOx film, due to the intimate contact of the mica mask to the semimetal surface.

Then we deposit the tunneling barrier and the counter-electrode, and finally put on the

gold wires as measurement leads.

The mica mask method, without using any lithography technique, is fast and

convenient. Also, there is no contamination from the resist polymers to the junction

surface. The shortcoming of the mica mask method is that, without lithography and

precise alignment, it is relatively hard to obtain well defined tunneling area.

Figure 4-3 shows the microscope picture of a tunnel junction made on the surface

of bulk bismuth.








AlOt
N lica foil S eri
Sputtering


III.


Thermnal A1C
(barrier)


iFI Pb


7+


V-


Figure 4-2. Procedure for making tunnel junctions on bulk semimetal using mica mask
method.


Figure 4-3. Microscopic picture of a Bi(bulk)-AlOx-Pb tunnel junction.









Measurements of the tunnel junctions are carried out in a He3 refrigerator with an

18 Tesla superconducting magnet in the National High Magnetic Field Labs (NHMFL).

Differential conductance, dl / dV, is measured using a double lock-in amplifier technique,

in which one lock-in amplifier is used together with a feedback circuit to keep the small

AC (500Hz) excitation voltage, dV, across the tunnel junction constant, while the other

lock-in amplifier measures the AC voltage response of a standard resistor in series with

the junction, from which dl can be calculated. A slow DC ramping signal is summed with

the AC excitation voltage to apply the bias voltage across the tunnel junction.

4.3 Results and discussion

Figure 4-4 shows the magneto-tunneling result for a Bi(bulk)-AlOx-Pb tunnel

junction made through mica mask method. The figure shows the differential tunneling

conductance vs. bias voltage in different magnetic fields. The inset shows the Pb

superconducting gap, from which we can see that the junction has low leakage and

reasonable good quality.

The differential conductance vs. bias voltage sweep shows an asymmetric "V"

shaped background, resulting from the asymmetry in the energy dependence of the

density of states in bismuth. On top of the background there are small features of

oscillations. The oscillations, which are most pronounced in the -20 to 20 mV range,

show no obvious magnetic field dependence and are characterized by 2nd derivative

d21
conductance V- to be mostly symmetric with the bias voltage. Hence they do not
dV

likely correspond to the density of states features in bismuth, but ratherto phonon

excitations.












600







400

> 400
'1


-80 -60 -40 -20 0
v (mV)


20 40 60 80


Figure 4-4. Differential conductance as a function of bias voltage in indicated strong
magnetic fields at 300mk. Inset: Pb superconducting gap feature in zero
magnetic field at 300mK.


-3 -2 -1 0
v (mV)


1 2 3


Figure 4-5. Differential conductance at low bias voltage in the magnetic fields indicated
in the legend.









Figure 4-5 shows the differential conductance at near zero bias voltage. In zero

magnetic field, the differential conductance shows a peak at zero bias. As the magnetic

field increases, the peak at zero bias separates into two peaks, which move towards

higher bias voltages and leaves a valley at zero bias. The change of dI/dV with magnetic

field appears to be as if the field opens up a gap at the Fermi level.

The feature observed at low bias voltages can be explained by considering the

Zeeman splitting of the spins. Since /u 5.8 x 105 e V / Tesla, the g factor corresponds to

our experimentally observed splitting (e.g., -1.6mV at 14 Tesla) is -2. Another possible

mechanism for the low bias voltage feature is the field induced Luttinger liquid behavior.

In this picture, the strong magnetic field opens up a Coulomb gap at the Fermi energy.

The Luttinger liquid behavior enhances the density of states in the gap. Detailed analysis

requires knowledge of the classical "background" of the differential conductance. Tilting

of magnetic field is required to tell if the zero bias feature is a spin effect or an orbital

effect.

Except for the features at bias voltage V < 3mV, a major feature of the differential

conductance show in Figure 4-4 is the lack of field dependence. The curves we took at 2,

4, 8 and 14 tesla overlap almost perfectly. This result contradicts the prediction from the

field induced Luttinger liquid theory, in which the magnetic field dependence enters the

power factors of the power law dependence. There are also some concerns about our

measurements. For example, the surface states in bismuth might prevent the tunneling

measurements from probing the intrinsic properties of bismuth single crystal.














CHAPTER 5
ACHIEVING LARGE MAGNETORESISTANCE IN BISMUTH THIN FILMS

5.1 Introduction

Semimetal bismuth has been interest of study for many years, because of it many

special properties. Figure 5-1 shows the Fermi surface and the brillouin zone of

rombohedral bismuth. The highly anisotropic Fermi surface consists of tiny hole pockets

and electron pockets, which occupy only a few thousandth of the volume of the Brillouin

zone. Hence bismuth has very low carrier density (-1023 m-3) and low Fermi energy

(-25meV). Also because of the small Fermi momentum, the chance of phonon scattering

is very low. Hence bismuth has an extremely long phonon mean free path at low

temperatures (-mm at 4.2K).


trigonal (7)

hole pocket



electron pocket (A)




bisectrix (y)
binary (x) L


Blillouin zone of Bi


Figure 5-1. Fermi surface and Brillouin zone of rombohedral bismuth









These unusual properties of bulk single crystal bismuth give rise to a huge

magnetoresistance.17-19 Figure 5-2(a) shows the magnetic field dependence of the

resistivity at 5K for single crystal (99.9995% pure) bulk bismuth. At the 7 Tesla, the

resistivity is 6 orders of magnitude higher than the zero field resistivity. Figure 5-2 (b)

shows the temperature dependence of resistivity in zero magnetic field. Bulk single

crystal bismuth is metallic, with resistivity decreasing with decreasing temperature.


-7
a&bdO
Q015 -





6r1\. I -
(0 K \-7



u o 2 o0

QOCO] QO

I lt tI t t lt lt lt I 1 I I I I1 0I I I I I
-8-6 4-2 0 2 4 6 8 0 50 101502 02503

B(1) T(0)

Figure 5-2. (a): Magnetic field dependence of the reisistivity at 5K for bulk single crystal
bismuth; (b) resistivity as function of temperature in zero magnetic field.

The extremely large magneto-resistance makes bismuth a promising candidate for

applications, such as magnetic field sensors. Many efforts have been carried out in order

to make bismuth thin films that have quality comparable to the bulk material.2022

However, it was found that bismuth thin films made by normal technique, such as

thermal evaporation, yield bismuth films with very small magnetoresistance.23 24 These









films may even behave in a non-metallic manner with the resistance increasing with

decreasing temperature.








S4 6 8 0





BdO
3& 1 1 I I -




-8-64-202468 0 100 200 300
B(1) T(H

Figure 5-3. (a): Magnetic field dependence of the reisistivity at 5K for a 1.5um bismuth
film thermally evaporated onto glass substrate; (b) resistivity as function of
temperature in zero magnetic field.

Figure 5-3 shows the typical transport behavior of thermally evaporated bismuth

thin films on glass substrates (thickness between 800-10000A). The resistance generally

increases with decreasing temperature. And the magnetoresistance at low temperatures is

much lower (MR(7T)<10) than that of the bulk bismuth (MR(7T)-105).

The major reason for the differences between bulk single crystal bismuth and the

bismuth films is the small grain size in the films. The gains, generally with size of

-1000A, are actually not small compare to that of normal metals. However, bismuth has

a very long phonon mean free path, due to the small Fermi momentum. Application of

the Matthiessen's rule shows that the scattering in the films is dominated by temperature

independent gain boundary scattering (except when the temperature is very high, e.g.

higher than room temperature, and the phonon mean free path is shorter than the grain









size). The temperature dependence of the resistivity is mainly from that of the carrier

concentration, which, due to the small Fermi energy of bismuth, decreases significantly

as the temperature drops.

Magnetoresistance in bismuth films is also limited by grain boundary scattering.

This can be illustrated from a simplified 2-band model, in which the electrons and holes

are compensated, and the resistivity in the magnetic field simply goes like:

p(H)- p(O) RH 2H2 (r)2 (5.1)
p(O) p(0)2

Hence the small relaxation time due to grain boundaries scattering leads to small

magnetoresi stance.

To make high quality bismuth thin films, it is necessary to make the grain sizes

large. A judicious combination of lattice-matched substrates and carefully regulated post-

deposition thermal annealing provides a strategy for growing bismuth films with large

grains. In early work on bismuth films thermally deposited onto mica substrates,2 it was

found that post deposition annealing close to the bismuth melting temperature caused the

helium temperature resistance to decrease by a factor of 15 when compared with

unannealed films. In addition, MR for fields perpendicular to the film surface is

significantly improved with annealing. Epitaxial films of bismuth having a trigonal

orientation have been grown on BaF2(111) (3.6% lattice mismatch)25 and CdTe( 11)

(0.7% lattice mismatch). 22 In the latter case, post-deposition annealing at 3 oC below the

melting temperature of Bi lead to significant increases in the MR.

An alternative approach, which has been found to give large MR in Bi films 1-20

,um thick, is the technique of electro-chemical deposition from aqueous solutions of

Bi(N03)3 5H20 .20,21 An underlying Au layer, patterned onto a silicon substrate, serves as









the working electrode for the electrodeposition. As is the case for vacuum-deposited Bi

films, 22,23 post-deposition annealing of the electrodeposited films close to the melting

temperature of Bi leads to a small resistivity and a large increase in MR (2.5 at room

temperature and 3800 at 5K for the thickest 20um film in a perpendicular 5T magnetic

field 20). For technological applications, electrodeposition is economical and well suited

for large-scale production. Similar advantage would likewise hold for thermal deposition,

provided ultrahigh vacuum and specialized groeth techniques, such as MBE, are not

required.

We studied the thermally deposited bismuth films on pre-deposited gold thin films

followed by post-annealing processes. We find that, upon annealing, the Au from the Au

underlayer rapidly diffuses into the bismuth, giving rise to a film with large-crystal grains

oriented with trigonal axis perpendicular to the plane of the film and having

magnetotransport properties comparable to those grown by electro-depositions.20' 21 We

show that improvements of MR are only for annealing temperature higher than the 241

C eutectic temperature of the BiAu solid solution and below the 271 C melting

temperature of Bi. This 30 C annealing window provides considerable latitude when

compared to the narrow annealing window of a few C confirmed here and reported

previously for pure Bi films.23

5.2 Experimental

All of our samples are prepared by thermally evaporating 99.999% pure Bi onto

pre-cleaned glass substrates at 5E-7 torr base pressure. In the cases where heated

substrates are needed, the substrates are glued onto a variac controlled heater with silver

paste. Then the shadow mask is glued onto the substrates using the same silver paste.









Substrate temperature is read from a thermometer, and is manually controlled by

adjusting the output voltage of the variac.

Three categories of samples are prepared: (I) two pure bismuth films (1 um thick)

grown at 150 C, followed by annealing at 2650C and 270 C for 6 hours; (II) three

bismuth films (1 um thick) grown simultaneously on pre-deposited gold films (350 A) at

150 C, followed by annealing at 238 C, 243C and 251 C, respectively for 6 hours; (III)

bismuth films (1 um) grown on pre-deposited gold films (350A) at room temperature,

followed by annealing at 251 C for 6 hours. Annealing is performed in a quartz vacuum

tube furnace with temperature calibrated with respect to the observed melting of a small

bismuth crystal placed in close proximity to the samples.

Measurements of resistance vs. temperature at different magnetic fields are carried

out in a Quantum Design Physical Property Measurement System (PPMS). In all of the

measurements, the magnetic field is applied perpendicular to the film.

5.3 Results and Discussion

We characterized the crystal structure of the Bi/Au films by X-ray diffraction.

Figure 5-4 shows the X-ray diffraction pattern of bismuth (001) planes. The sharp lines

indicate that the film is well c-axis oriented. The inset of Figure 5-4 shows a schematic of

the relevant portion of the Bi(Au) phase diagram.26 A small amount of gold in Bismuth

reduces the melting point, and the lowest melting temperature, the eutectic temperature,

occurs at 241 C for the Bi.868Au.132 composition. In our experiment, the mass ratio of the

Bi and Au is controlled by the thickness of the 2 films. Thus a pre-deposited 360-A-thick

Au layer mixed by annealing into a 1-um-thick Bi film represents a solid solution

(vertical dashed line) with stoichiometry Bi0.93Auo.07. All of the Bi/Au films here are at

this composition.













5000 i

271 442 'C
L
4000 -



3000 r'c

.- 9O 934 1DO
BU)
Mass Percent Bismuth
w 2000



1000



0


0 20 40 60 80 100 120
2*theta


Figure 5-4. X-ray diffraction pattern for a 4-um-thick Bi/Au film grown at 150 oC and
annealed at 251 C. Inset: the relevant portion of the Bi/Au phase diagram and
corresponding annealing temperatures (indicated by the crosses) for Bi and
Bi/Au films discussed in this chapter.

Figure 5-5 shows the resistance vs. temperature at 0 and 5 Tesla for the two

category-I pure bismuth films (no Au underlayer) annealed at 265 C and 270 C,

respectively. We note that a small difference of annealing temperature at close to the 271

C melting point of bismuth produces a drastic change of the properties of the films. The

film annealed at 270 C just starts to melt and is recrystalized during the slow cool-down.

As observed through the quartz tube, the film develops a shiny surface just below the

melting temperature, but at higher temperature begins to fully melt and ball up. The

positive slope in the resistance-temperature curve in zero magnetic field indicates that the

film is metallic. Also, at 5T, the MR=286 at 5K indicates the good quality of the film.










I I I I I I I
B A A) TG = 20C, TA = 265C
B) Te = 20C, TA = 270C
S 100 A
a, : B = 5T







0 B= OT
A

B

0 50 100 150 200 250 300
Temperature (K)

Figure 5-5. Temperature dependence of the resistivity at 0 and 5T for two category-I Bi
films

In contrast, the film annealed at 265 C does not change its appearance during the

annealing process. The resistance of this film shows a characteristic minimum at near

200K 23 and then increases as the temperature is further lowered. In addition, the MR of

this film is much smaller than the one annealed at 270 C through out the whole

temperature range. These results are in accord with previous studies,22 23 which have

shown that post-annealing at melting point followed by re-crystallization is an effective

way to get high quality bismuth films. However, the temperature control must be accurate

to a few oC and must not be allowed to go above the melting point where there will be a

loss of film adhesion leading to agglomeration and discontinuity between grains.











I I I I
SB A) T. = 150C, T =238G
100 C "-.. B) T_ =150C, T =243
A' A. C)T_ = 150C, T =251
B( B=5T


S10


(-
0 A B=OT

1 -B
:C ---. ,

0 100 200 300
Temperature (K)

Figure 5-6. Temperature dependence of the resistivity at 0 and 5T for three category-II
films grown simultaneously on 150 C substrates and them annealed
separately at respective temperatures of 238, 243 and 251 C.

For samples in category-II, the presence of a gold underlayer leads to completely

different behavior. Figure 5-6 shows the effect of annealing temperature on the quality of

these films. The three Bi(lum)-Au(350A) films are grown at 150 oC, and then annealed at

238 C, 243C and 251C respectively, as indicated by the crosses in the Fig.5-4 inset.

Prior to each post-deposition anneal, a gold color can be observed from the back

side of each glass substrate. Afer 243 C and 251 C anneal, the gold color is gone and the

underside of each Bi/Au film is silver color and indistinguishable from the underside of a

pure Bi film. These color changes indicate that during the annealing, the gold atoms no

longer remain segregated beneath the bismuth film but diffuse into the bismuth. For an

annealing temperature of 238 C, which is below the eutectic temperature of 241 C, all

of the film remains in the solid form, and the surface texture of the film does not change









during the anneal. In addition, the temperature dependent resistance is nonmetallic and

the 5K MR is low (MR=37). In contrast, for the two anneals above the eutectic

temperature, the films undergo a definite change in appearance in which they become

shiny and remain metallic after cooldown, the temperature-dependant resistance becomes

progressively more metallic, and both films exhibit significantly larger MR.

MR(5K)=130 for the 243 C anneal and MR(5K)=327 for the 251 C anneal. We note

that the MR of our 251 C annealed Bi/Au film is higher than the MR(5K)=250 of a

comparable 1-um-thick "single-crystal" film grown by electrodeposition.20' 21 Further

increase of the annealing temperature to slightly above 160 C but well below the 271 C

Bi melting temperature leads to sever melting and loss of electrical connectivity, as

would be expected from the intersection of the vertical dashed line with the solid/liquid

phase boundary shown in the Figure 5-4 inset.

The plots in Figure 5-7 for the category-III films show the effect of growth

temperature on transport properties for the same anneal conditions. The film grown at

150 C shows metallic temperature dependence at zero field and has MR(5K)=327. The

film grown at room temperature however, shows rather complicated temperature-

resistance dependence. The resistance drops a little bit as the temperature sweep from

300K to about 200K, then increase a lot from 200K to 5K. The resistance-temperature

curve suggests that the film has grain sizes comparable to phonon mean free path at

200-300K. At low temperatures, the grain boundary scattering dominates and the

resistance increases due to decrease of carrier concentration. The magnetoresistance of

the room temperature grown film, MR(5K) = 34, is also significantly lower than the film

grown at 150 C. For pure Bi films grown on CdTe substrates, growth temperature in the






60


range of 80 C to 220 C are required to obtain epitaxial behavior.22 For our Bi/Au films,

the higher growth temperature promotes the growth of larger grains, thus facilitating the

effectiveness of the annealing procedure by starting with larger grains. We also note, as

show by x-ray diffraction pattern in Figure 5-4 for a 4-um-thick Bi/Au film grown at 150

C and annealed at 251 C, that the annealed films exhibit a pronounced single-crystal

orientation with trigonal axis oriented perpendicular to the film plane. Similar behavior

has been noted for annealed electrodposited films.



B A) TG = 150C, TA = 252C
100 A B) T= 20C, T = 252C
SB = 5T












0 100 200 300

Temperature (K)



Figure 5-7. Temperature dependence of the resistivity at 0 and 5T for two category-III
films

Optical microscopy verifies a smoother topography and larger grain size (1-lOum)

for the films annealed at high temperature and exhibiting a large MR. This result is

consistent with the aforementioned conclusions that large grain size achieved either by

epitaxy and/or annealing is a prerequisite for large MR. The primary factors that affect
.L_ 10
U)


r--


B

0 100 200 300
Temperature (K)



Figure 5-7. Temperature dependence of the resistivity at 0 and 5T for two category-Ill
films

Optical microscopy verifies a smoother topography and larger grain size (1-10um)

for the films annealed at high temperature and exhibiting a large MR. This result is

consistent with the aforementioned conclusions that large grain size achieved either by

epitaxy and/or annealing is a prerequisite for large MR. The primary factors that affect









the quality ofBi/Au films are the growth temperature and the annealing temperature. A

moderate growth temperature (-150 C) encourages the formation of large grains, but

should not be so high as to cause the film to agglomerate and to become discontinuous.

Table 5-1. Summary of results for different bismuth film growth conditions
Sample Growth Annealing Metallic MR (5K: 300K)
temperature temperature
Pure Bi 150 C 265 C N 39 : 3
270 C Y 283:4
Bi (lum)- Room temp. 251 C N 34: 3
Au(350A) 238 oC N 37 : 3
150 C 243 C N 130 :3
251 C Y 327:3


We summarize our results in Table 1.The effect of the diffusion of the Au into Bi

during the post-deposition annealing process can be qualitatively understood by referring

to the phase diagram depicted in the Figure 5-4 inset. If equilibrium is assumed, then for

isothermal (tie line) drawn at a given annealing temperature, application of the "lever

rule" for binary phase diagram will determine a gold-rich melted phase and a bismuth-

rich solid (unmelted) phase. It is the presence of this melted phase that facilitates grain

boundary migration and grain growth resulting in the high MR that we have observed.

We suspect that this melted phase is most likely associated with grain boundaries

although detail microcompositional analysis would be necessary to verify such a

scenario.

In oversimplified terms, the Au can be thought as a lubricant that facilitates the

growth of large grains during the post-deposition anneal. However, one should not forget

that Au is a impurity that gives rise to increased carrier scattering and associated lower

MR, thereby preventing the MR from approaching the hig values reported in single

crystals.17, 19 Accordingly, the use of annealed Bi/Au bilayers to obtain large MR requires






62


judicious balance between using enough gold to assure large grain growth, but not using

too much gold that additional scattering compromises that MR. We believe that these

considerations also apply to the Bi/Au films deposited by electrodeposition technique

reported previously by Yang et al. 20,21














CHAPTER 6
METALLIC SURFACE STATES IN ULTRA-THIN BISMUTH FILMS

6.1 Introduction: Physics of the Ultra-Thin Bismuth Films

Bismuth, like many other semimetals, has a very long electron wavelength, due to

its low Fermi energy (-25 meV) and small effective mass (-0.005me). One can estimate

h
the wavelength to be: A ~ 102 A. When the size of sample is comparable or


smaller than this length scale, one will need to consider the effect of the sample boundary

on the band structure. This is where the so-called quantum size effect become important.

Bismuth provides great convenience in studying the quantum size effect in many

aspects. Ultra thin bismuth films, with their thicknesses comparable to the electron wave

length (- 300 A), have been of great interest in the study of the quantum size effect and

semimetal-semiconductor transition. Ogrin, Lutski, and Elinson, in their study of the

magnetotransport of the bismuth thin films in 1965,27 produced the first clear

experimental evidence for quantum size effect in any solids. Oscillatory behaviors in both

resistivity and Hall coefficient were observed with decreasing film thickness, due to the

quasi-2D sub-bands passing across the Fermi level. Since then, quantum size effect in

bismuth thin films has been intensively studied both theoretically and experimentally.28-34

The existence of the thickness dependent quasi-2D sub-bands resulting from quantum

confinement has been generally accepted.

One important prediction as a result of the quantum size effect is the so-called

semimetal-to-semiconductor (SMSC) transition. The SMSC transition happens when the









energy shift due to the quantum confinement becomes large enough so that the lowest

electron sub-band rises above the top of the highest hole sub-band, due to their difference

band masses. The critical thickness of the thin film for the transition to happen, given by

most of the theoretical calculation, is between 230 -340 A.28, 35, 36










/ 38meV

13.6meV









Figure 6-1. Illustration of semimetal-to-semicinductor transition.

Despite the numerous experimental investigations carried out to look for the SMSC

transition,27 28 31 37-40 the existence of the SMSC transition remains ambiguous. Chu and

co-workers argued against the SMSC transition, and proposed theory that the boundary

condition for the electron wave function is that the gradient of the wave function (rather

than the wave function itself) vanish at the sample boundary. Hence the ground state

electron and hole energies depend only weakly on the thickness of the films, and the

conduction band and the valence band remains overlaped.

The arguments against the SMSC transition mainly focused on the lack of sharp

transitions in transport properties (resistivity, Hall coefficient, magnetoresistance...).









Hoffman et al., in their work that stand for the SMSC transition, pointed out that the main

reason for the absence of the sharp transition in the previous works is that people failed to

take into account the effect of the surface carrier and surface conductivity, which may be

important and even dominating when the bismuth films are very thin.39 The simple model

that takes into account the surface carrier is that the surface acts like a high carrier density

conductor in parallel with the bulk part of the film, and the averaged carrier concentration

is simply: n = n, + n, / d, where n, and n, are bulk intrinsic carrier density and surface

sheet carrier density.38 When the film is thin, n, will dominate, and the effect of the

surface conductivity has to be seriously considered.

Further evidences of metallic surface states were found in a very different bismuth

system. In 1991, B. Weitzel and H. Micklitz discovered superconductivity in granular

systems built from rhombohedral Bi clusters.41 They explained their result as surface

superconductivity due to the strongly increased surface density of states and suggested

photoelectron spectroscopic study on bismuth surfaces to further confirm their proposal.

Angle resolved photoemission spectroscopy (ARPES) since then had been a major

tool people used to probe the surfaces of bismuth. The experiments were carried out by

several groups.42-47 Consistent results were obtained, indicating the existence of metallic

surface states in bismuth (111) and (110) surfaces. Christian R. Ast and Hartmut Horchst

reported in 2001 a surface carrier density associated with the surface state of Bi (111) to

have sheet densities of p, = 1.1 x 1013 cm2 for holes and n = 5.5 x 1012 cm2 for

electrons.47 In 2003, Gayone et. al reported their study on the temperature dependence of

the surface states linewidth and the strong energy dependence of the electron-phonon

coupling strength on Bi (100) surface.48









6.2 Transport Properties of the Ultra-Thin Bismuth Films

6.2.1 Experimental

Bismuth films are thermally evaporated from 99.9999% pure bulk bismuth in a

high vacuum chamber of-6E-7 torr at a rate of 1-2 A/sec, through shadow masks. In the

cases where in situ measurements are required, bismuth or gold contact pads are

thermally evaporated through shadow masks. Then the substrate pre-deposited with

contact pads is fixed onto a special designed sample holder, where the Hall-bar shadow

mask is installed aligned with the contact pads, and the gold wires are attached to the

contacts and connected to leads which enable electrical measurements from outside the

vacuum chamber.

Tunnel junctions on thin bismuth films were made using standard cross stripe

geometry. Mica is used as substrate and bismuth is used for base electrodes, so that lattice

match between bismuth and mica can be achieved. AlOx is used for tunnel barriers. Lead

is used for top electrodes, so that when the samples are cooled down to below the lead

superconducting temperature, the superconducting gap can be used to characterize the

quality of the junction. In making of a Bi-AlOx-Pb junction, a thin bismuth film stripe as

base electrode is deposited onto mica substrate through a shadow mask. The film is then

taken out of the vacuum chamber, and the shadow mask is removed. The film is then

immediately put back into vacuum, and the aluminum oxide tunnel barrier (- 10 A) is

coated through thermal evaporation of aluminum in the oxygen pressure of 2E-5 torr, at a

rate of about 1 A /sec. A cross stripe of lead as counter electrode is then deposited

through a shadow mask. Typical working junction resistances are in the range of

10-10000Q.









6.2.2 Metallic Surface States

In the study of the Bi/Au films, the thicknesses of these films are in the order

micrometers. Films with these thicknesses can be treated as bulk polycrystal bismuth, in a

sense that there's no band structure change due to the quantum confinement, and the

surface effect is not significant. When the (pure) bismuth films get really thin (e.g.,

thickness Fermi wavelength), quantum size effect will take place, and the effect of the

surface states needs to be seriously considered.

Figure 6-2 shows the temperature dependence of resistivity, for films with

thicknesses indicated in the legend.

1.0x105
400A

9.0x106-


8.0x10-6 310A


S7.0x106 -

150A
6.0x106


5.0x1 06
0 50 100 150 200 250 300
T (K)

Figure 6-2. Resistivity vs. temperature for Bi film with indicated thicknesses.

It can be seen from the figure that, for films with thickness -400A, the resistivity

increases as the temperature drops, and reaches a maximum at ~40K. As the film

becomes thinner, the temperature for the resistivity maximum shifts higher. Also the









resistivity in the low temperature region (say, T <150K) decreases with decreasing film

thickness. For the films with thickness < 150 A, the resistivity drops monotonically from

room temperature with decreasing temperature, showing metallic behavior.

The metallic behavior (positive R-T slope) can be explained by considering the

existence of the metallic surface states. A simplified model is to treat the whole film as

two separate films in parallel: a very thin metallic-like film on the surface with sheet

resistance R, and thickness ts, and the "intrinsic" film underneath it with resistivity

1 (t- t_)
p, and thickness t t. The measurered resistivity for is then p = -+ t.
R, A )

The resistivity of the bulk (intrinsic) part of the film, p, has negative R-T slope.

And when the film is thick, it has low resistance and hence will dominate the total

resistance of the film. When the film gets thin, the contribution of the metallic surface

becomes increasingly important, and the R-T curve starts to show a maximum, which

moves to higher and higher temperature with decreasing film thickness. Eventually, when

the film thickness reaches 150A or thinner, the surface states will dominate the

temperature dependence and the R-T curve shows positive slope throughout the

temperature range of measurements (4.5K-300K).

The magneto-transport of ultra-thin bismuth films is studied under the framework

of classical muti-band model, as described in the previous chapters. The classical

magnetoresistance of the ultra thin bismuth film can be roughly estimated to be (mr)2.

Here, the small thickness of the films leads to very short mean free path of grain

boundary scattering, and hence a very small MR.











0.020



0.015 31 OA



s 0.010 180A



0.005



0.000

-6 -4 -2 0 2 4 6
B (T)

Figure 6-3. Magnetoresistance vs. magnetic field at 5K for two Bi films with indicated
thicknesses.

Figure 6-3 shows the MR of two bismuth films with thicknesses 180 and 310 A. It

can be seen from the figure that the classical MR increases with the film thickness, due to

the increasing grain size with the film thickness. The sharp dip at low fields can not be

explained by classical theory, and is due to anti-localization, originating from the strong

spin-orbit interaction in bismuth.

The in-balance or non-compensation of the positive and negative carriers in the thin

bismuth films is revealed by the field dependence of the Hall resistivity. Figure 6-3

shows the field dependence of Hall resistivity at indicated temperatures for 2 bismuth

thin films, 180 A and 400A thick. For both films, the measured Hall resistivities are not

linear with the magnetic field. Also the zero field slope of the Hall resistivity has strong

temperature dependence. For the 180A film, the low field p vs. field curve even


changes sign from 5K to 150K.









8x10 (a) 1s8A

6x10

4x10

S2x10 -

0- 75K

-2x10 -

-4x108 '* *
0 2 4 6 8
B(T)



6x07 (b) 400A
6x10 --
150K

4x10-7


.2x10- -
75K

0 -5K

0 2 4 6 8
B(T)


Figure 6-4. Hall Resistivity vs. magnetic field at indicated temperatures for (a) 180A and
(b) 400A Bi films
The Hall resistivity p, observed can be qualitatively understood through the

simple 2-band model expression,









RR2(R1 + R2)B3 + (R1,p2 + R2p12)B
(P1 + P2 )2 + (R, + R 2 (6-B2

We can see that, for a 2-band system with electron band and hole band, the Hall

resistivity is in general not linear with the magnetic field. Also the Hall resistivity itself

does not give enough information about the in-band carrier concentration of each band.

From Equation 6-1, we get the low field and high field limit of the Hall resistivity:

(R p 2 + R 2 )B
p, (H 0) = p2 (6-2a)
(pI + 2)2

RRzB
p (H ) = 2 (6-2b)
(R, +R2)

Hence the zero field Hall resistance slope by itself does not give any information

on the carrier density of the films. In fact, it does not even give the information about

whether the film is n-type or p-type, due to the complication from the in-band resistivity

(or mobility). However, the high-field limit of the Hall resistance does indicate the carrier

type of the film (or, the sign of R + R2). The change of slope (even the sign of the slope)

from low field to high field gives rise to the curvature observed in the Hall resistivity

measurement. One can see from the p vs. field curves that, even though the low field

data shows strong temperature dependence (even change of sign), the sign of the

extrapolated high field limit of the Hall resistivity slope is temperature and thickness

independent, indicating the type of the films, n-type in this case, does not change with

temperature, nor the film thickness.

A more detailed analysis of the Hall resistivity data yields information about the


un-balance of the carriers, defined by the compensation factor: A = -h And the
ne +nh









thickness and temperature dependence of the Hall resistivity can be qualitatively

understood by considering the change of compensation factor (due to the n-type surface

states) with temperature and thickness. To simulate the field dependence of the Hall

resistivity, we adopt a 4-band model, with a bulk electron band, a bulk hole band, a

surface electron band, and a surface hole band. Figure 6-5 shows the simulation results

for the magnetic field dependence of the Hall resistivity for 180A thick and 400 A thick

bismuth films. In the simulation, we assume that the mobility of the carriers does not

change with temperature, due to the fact that the grain boundary scattering dominates

over phonon scattering. Because of the complication of the energy band quantization due

to the quantum size effect, we can not calculate in detail the temperature dependence of

the carrier density. In the simulation, we assume different values of carrier density for the

bulk part of the films, and assume the sheet surface carrier density to be temperature and

thickness independent. The parameters used in the simulations are listed below:

Table 6-1. Parameters for the simulating the effect of thickness and temperature on the
magnetic field dependence of the Hall resistivity in ultra-thin Bi films
Surface (10A) In the film
Carrier density Mobility Carrier density Mobility
ns (m-2) / 2 -) n i (m-3) /S (m2V 1)
400A e 2x1017 0.031 ao(5x1023) 0.119
h 1.4 x 1017 0.036 a (5x1023) 0.138
180A e 2x1017 0.031 a*(5x 1023) 0.056
h 1.4 x 1017 0.036 a (5x1023) 0.063


Note from the listed parameters that: 1) the surface sheet carrier density and mobility are

the same for both films; 2) in bulk (intrinsic) part of the films, the carrier density of

electrons is equal to that of the holes; 3) since we cannot calculate the carrier density in

the films, we modulate its number by adjusting the parameter a.






73


2x10-8


a=1.5
E 0-



-2x108 a=0.8
c/)

^ -4x108 -O
c (a) 180 A a=0.3


-6x108 a=0.01
0 1 2 3 4 5 6 7 8
B (T)


3x107
(b) 400 A a=1.5

C: 2x107

> a=0.8
1, 0-7




-1x107


0 1 2 3 4 5 6 7 8
B (T)



Figure 6-5. Simulated Hall Resistivity vs. magnetic field at indicated temperatures for (a)
180A and (b) 400A Bi films, with fitting parameters described in the text.









Comparing the calculated magnetic field dependence of the Hall resistivity with

the data, we see that the simulations yield the major features in the experimental results.

From the simulations, we get the physical picture about the carriers in the ultra-thin films.

The bulk part of the film is compensated, like in bulk bismuth. The surface of the film,

however, has a high sheet carrier density and is uncompensated. As the film gets thinner,

or the temperature gets lower, the number of compensated carriers in the bulk part of the

film decreases. Hence the degree of un-compensation, due to the existence of the un-

compensated surface carrier, will increase.

6.3 Control of the Surface States

All the bismuth films discussed in the previous section are measured after removal

from the vacuum chamber. Even though the oxidation of bismuth at room temperature is

insignificant, we will still need to consider the effect of oxygen on the surface of the film.

For comparison, we have carried out in-situ measurements on bismuth thin films. A

thin bismuth film is deposited onto a mica substrate pre-deposited with contact pads, and

measured without breaking vacuum. The substrate is mounted on a cold stage and cooled

down from room temperature to -100K, and the resistance vs. temperature is recorded.

The sample is then warmed up to room temperature, and a small amount of oxygen is

introduced into the chamber for 10 minutes. The chamber is then evacuated, and the

sample is cooled down again to 100 K, with resistance vs. temperature recorded.

The in-situ measurement of freshly deposited bismuth films shows that for ultra-

thin bismuth films measured in vacuum, the resistance increases with decreasing

temperature. What is different for the ultra-thin bismuth films from the thicker bismuth

films (-um) is that, the ratio of the resistance increase, say, R(100K)/R(300K), is much

smaller in the ultra-thin bismuth films (<10%) than in the thicker films (-200%). Hence









the existence of the metallic surface states is intrinsic, while the sheet carrier density

originated from the surface states is very sensitive to the surface condition.

We have seen that oxygen has a significant effect on the surface states. To study the

surface "terminated" ultra-thin bismuth film, we coated the bismuth films with Ge. Ge is

known to be a material that, when deposited as thin films, creates dangling bounds and

nucleation sites. When thin metals films are deposited onto predeposited atomically

smooth Ge thin films, the metal film growth nucleates at the Ge dangling bounds. Thus

the metal films tend to be very smooth.

Here we deposit a few monolayers to Ge right after the deposition of bismuth thin

film, without breaking vacuum. The idea is that the dangling bounds of the Ge film may

bind with the surface states in the bismuth film, and terminate the surface of the bismuth

film from being affected by the air.


-- Bi (100A)
Bi (1 0A)/Ge (8A)
1.4x103 -



C 1.3x103



1.2x103



0 50 100 150 200 250 300
T(K)

Figure 6-6. Temperature dependence of resistivity for Bi(100A) and Bi(100A)/Ge.

Figure 6-6 shows the resistance vs. temperature curves of two 100A thick bismuth

films simultaneously grown and measured. The only difference between the 2 films is









that, one sample is coated with a few angstrom of Ge in situ, right after the deposition of

bismuth film. The two samples show completely different temperature dependence of

resistance. The bare bismuth film shows positive resistance-temperature slope, while Ge

coated film shows negative resistance-temperature slope. We also coated the bare

bismuth film with Ge after it's taken out of vacuum. No significant change of transport

behavior was observed. We conclude that the change happens at the Bi-Ge interface,

rather than in the Ge film itself.

The Hall resistivity measurements provide more information on the in-balance of

the carriers. From Figure 6-7, we can readily see the big differences in the carrier

distribution between the bare and the Ge coated bismuth films. Comparison with Figure

6-4 reveals that the magnetic field dependence of the Hall resistivity for the bare 100 A

Bi film at 75K, 150K and 250K resembles that of the bare 180 A Bi film at 5K, 75K and

150K. And the magnetic field dependence of the Hall resistivity for the Ge coated 100 A

Bi film at 75K, 150K and 250K resembles that of the bare 400 A Bi film at 5K, 75K and

150K (the smaller curvature here is due to the smaller mobility in the thinner films). This

comparison suggests that the Ge coated Bi film has better compensation than the bare Bi

film with the same thickness.

Simulations results with a 4-band model described earlier are shown in Figure 6-8,

with fitting parameters listed in table 6-2. Note from the listed parameters that: 1) the

effect of the surface carrier is adjusted by setting the thickness of the surface layer; 2) in

bulk (intrinsic) part of the films, the carrier density of electrons is equal to that of the

holes; 3) The carrier density of the bulk (intrinsic) part of the film is modulated by

adjusting parameter a.






77


3x108 -

(a) 2 50 K
-8
S2x10 -


1x108 -
UB
) 0-
^ I-150K

I -1x108 -
75K
-2x10 -8
0 1 2 3 4 5 6 7 8
B (T)


1.5x10-7
250


1.0x10-7 (b)

150K


w 5.0x10 -


75K

0.0

0 1 2 3 4 5 6 7 8
B (T)



Figure 6-7. Hall Resistivity vs. magnetic field at indicated temperatures for (a) Bi(100A)
and (b) Bi(100A)/Ge films.






78



1x10 -

a=4.0

0 -



S-1x108 -
W a=1.5
I (a)(

-2x108 a=0.8


0 1 2 3 4 5 6 7 8
B (T)



a=4.0
2x107 a=4.
(b)


> 1x10-7



5 0 a=1.5
n 5x108 -



0 a=0.8

0 1 2 3 4 5 6 7 8
B (T)




Figure 6-8. Simulated Hall Resistivity vs. magnetic field at indicated temperatures for (a)
Bi(100A) and (b) Bi(100A)/Ge films, with parameters described in the text.









Table 6-2. Parameters for the simulating the effect of Ge coating on the magnetic field
dependence of the Hall resistivity in ultra-thin Bi films
Surface (3A for Bi/Ge, 10A for In the film (100A)
Bi)
Carrier density Mobility Carrier density ni Mobility
ns (m-2) / (2V is -1) (m-3) (m V -s 1)
Bi/G e 2x1017 0.031 a (5x1023) 0.047
e h 1.4x1017 0.036 a (5x1023) 0.054
Bi e 2x1017 0.031 a (5 x 1023) 0.047
h 1.4x1017 0.036 a*(5x1023) 0.054


The simulations suggest that, the effect of the Ge layer on the Hall resistivity is

equivalent to reducing the density of the surface carriers. It is also due to the reduction or

neutralization of the metallic surface states so that the carriers in the bulk part of the films

again dominate the transport and give rise to the negative resistance-temperature slope

shown in Figure 6-6.

The mechanism through which exposure of the bismuth film to the air increases the

surface sheet carrier density is still not known. However we believe that results obtained

from the Ge coated bismuth ultra-thin films opens the possibility of passivating the

surface and even neutralizing surface states. These results should be important for

studying the nanoscopic bismuth systems, such as bismuth nanowires, in which the effect

of the surface state becomes very significant.














CHAPTER 7
SURFACE SUPERCONDUCTIVITY IN ULTRA-THIN BISMUTH FILMS

7.1 Transport Evidence

In the previous chapter, we have studied the effect of the metallic surface states on

the transport of ultra-thin bismuth films. For the films of certain thickness, a closer look

at the transport data at low temperatures reveals some very un-expected features. Figure

7-1 shows the zoom-in of the temperature dependence of the resistance for a 15nm thick

bismuth film. We can clear see a sharp drop of the resistance at about 5.6K. The inset

shows the magnetic field dependence of resistance for the same film. We also see a sharp

decrease of R below some critical field of 200mT.



768





764 770

765

I 760
760 -1.0 -0.5 0.0 0.5 1.0
II B (T)
6 (K)8 10


Figure 7-1. Resistance vs. temperature in zero magnetic field for a 15nm bismuth film.
Inset: resistance vs. magnetic field at 4.5K for the same sample.









The sharp feature of resistance change has been observed reproducibly in samples

with thickness within certain ranges. The resistance will either jump down or jump up

below a critical temperature and critical field by very small amount. Figure 7-2 here

shows an example in which the resistance jumps up at below a critical temperature and

critical field.


799.5
804



799.0 -
801



798.5
-1.0 -0.5 0.0 0.5 1.0
B (T)


798.0 '-
I i I
6 T (K) 8


Figure 7-2. Example of resistance increases during the transition. The main figure shows
resistance vs. temperature in zero magnetic field for a 15nm bismuth film.
Inset: resistance vs. magnetic field at 4.5K for the same sample.

We also observed sharp feature of resistance increase or decrease in the Hall

resistivity measurements (see Figure 7-3). Since the features are even with the magnetic

field, they are really from the longitudinal resistance pickup due to the misalignment of

the Hall leads. But the change of resistance at the transition is much bigger percentage

wise. We also find that the critical field for such feature decreases with increasing








temperature, and the relation satisfies the T dependence of the critical field in

superconductors:


B,(T)= B(O) 1 T-


1.5







0.5
0.5


(7.1)


-0.5 0.0 0.5 1.0
B (T)


Figure 7-3. Sharp feature of resistance change observed in Hall resistivity measurements
at indicated temperatures for a 15nm thick bismuth film. Inset: critical
magnetic field as a function of T2.


By measuring bismuth films with different thickness, we map out the thickness

dependence of the critical magnetic field for the resistance transition. From Figure 7-4 we

can see that at 4.5K, the transition happens for films with thickness smaller than -16nm,

and for films with thickness -40nm. In fact the critical field vs. thickness plot suggests

oscillating thickness dependence of the critical magnetic field.










0.8

A
0.6

4\A



S0.2 A


0.0- A-A- A

0 10 20 30 40 50
Thickness (nm)
Figure 7-4. Film thickness dependence of the critical magnetic field at 4.5K.


The features we have observed for these bismuth films together with the absence of

a full transition to a zero-resistance state are suggestive to that superconductivity occurs

only in certain portions of the films. The bulk rhombohedral bismuth is not

superconducting (T,<50 mK). But there are several reported superconducting phases of

bismuth: high-pressue phases of Bi called Bi II, III and V with Tc =3.9, 7.2, and 8.5K

respectively,4951 fcc Bi with T, with Tc<4K,52 amorphous Bi with T,=6K, and granular

system of Bi clusters, with T, -2-6K depending on the size of the clusters.41

X-ray diffraction (XRD) analysis shows that our films are rhombohedral. To make

the amorphous bismuth films that show superconductivity, one needs to deposit bismuth

onto liquid Helium cooled substrate. These amorphous bismuth films lose their

superconductivity when annealed up to room temperature. Hence we believe that






84


amorphous phase is not the reason for the superconductivity observed in our room

temperature deposited and 200 C annealed films.

7.2 Tunneling Evidence

To further probe the properties of our films, we performed tunneling

measurements. The samples we studied are standard cross-bar Pb-I-Bi junctions

described in chapter 6. Figure 7-5 shows the curves of tunneling conductance vs. bias

voltage at indicated different temperatures, for a Pb-AlOx-Bi(150A) junction.


1.5





1.0
0-




0.5


-6 -4 -2 0 2 4
V (mV)


Figure 7-5. Differential conductance as a function of bias voltage in the superconducting
gap region at indicated temperatures, for a Pb-AlOx-Bi(150A) tunnel junction

A major feature of differential conductance at T<5.5K is the existence of two

superconducting gaps. With increasing temperature, the two gaps move to some bias

voltage in between, and the intensity of the inner gap drops rapidly. At T>5.5K, the









conductance spectrum recovers the shape of normal metal-insulator-superconductor

tunneling, with a single superconducting gap from Pb counter-electrode. With further

increase of temperature, the superconducting gap vanishes as Pb electrode loses its

superconductivity.

The double gap feature in the bias voltage dependence of differential conductance

is very typical for superconductor-insulator-superconductor (S-I-S') tunnel junction, with

the DOS peaks correspond to Ai+ A2 and A1- A2, where A1 and A2 are the BCS gaps of Pb

and Bi, respectively. It should be noted that the values of the superconducting gaps

determined from the data above turn out to be bigger than what they should be (e.g.,the

standard value for Pb is Ai=1.4meV). Two possible reasons may cause the "enhanced"

gap size. First of all, the sheet resistance of the bismuth film (-500Q) is comparable to

the junction resistance itself, and hence will contribute to the measured result as a series

resistor. Second, electrons may first of all tunnel into a surface state, and then lose energy

when they travel into the bulk part of the film. Hence the existence of surface states may

cause voltage drop at the bismuth-AlOx interface.

Another surprising feature in the dI/dV vs. V characteristic is the conductance

maximum for temperature lower than -7K. This feature doesn't not reproduce for all the

samples. The reason for its existence is not well understood.

As a comparison, Figure 7-6 shows the superconducting gap feature of a Pb-AlOx-

Bi(1000l) tunnel junction. We see no evidence of superconductivity in the transport

measurements of the 1000A thick bismuth films. The tunneling measurement, we also see

the standard Pb superconducting gap in the differential conductance vs. bias voltage






86


sweep, but no evidence of the smaller gap seen in the sample with smaller thickness of

the Bi electrode.


2


















-4 -2 0 2 4
V (mV)

Figure 7-6. Differential conductance as a function of bias voltage in the superconducting
gap region at 300mk, for a Pb-AlOx-Bi(1000A) tunnel junction.

We also measured the tunneling conductance of our samples in various magnetic

fields. Shown in Figure 7-7 is the tunneling conductance vs. bias in different low

magnetic fields perpendicular to and parallel to the junction area. For the perpendicular

field, as the field increases, the gaps decrease in size and move towards each other. In a

field higher 200mT, only one gap is left. Since at 200mT, Pb already loses its

superconductivity, the gap is the Bi superconducting gap. A similar characteristic is

observed in the measurements with magnetic field applied parallel to the junction plane,

except that the changes occur within a wider field range. The differences between the







87


results with magnetic field parallel and perpendicular to the junction suggest that the

double gap feature is not a spin effect.


1.5



C
3
2 1.0





0.5


1.5







e-0
.-1




0.5


-4 -2 0 2
v (mV)


-4 -2 0 2 4
v (mV)


4 6


Figure 7-7. Differential conductance vs. bias voltage at 300mK in indicated low magnetic
fields perpendicular and parallel to the junction plane.







88



1.5
S300mT

500mT

1T


4 1.0
> 4T
-10T
18T

Perp. field

0.5-

-6 -4 -2 0 2 4 6
V (mV)



300mT

500mT

1T


4 1.0
> 4T
10T



Para. field
0.5

-6 -4 -2 0 2 4 6
v (mV)




Figure 7-8. Differential conductance vs. bias voltage at 300mK in indicated strong
magnetic fields perpendicular and parallel to the junction plane.