<%BANNER%>

Schottky Barrier Modulation at Graphene/Semiconductor Interfaces

Permanent Link: http://ufdc.ufl.edu/UFE0044924/00001

Material Information

Title: Schottky Barrier Modulation at Graphene/Semiconductor Interfaces Engineering Field Permeable Semimetal Electrodes
Physical Description: 1 online resource (226 p.)
Language: english
Creator: Lemaitre, Maxime G
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: graphene -- schottky -- triode -- vfet
Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Conventional electronic circuits rely on semiconductor heterojunctions for dynamic switching, while metal/semiconductor interfaces are reserved for static contacts.  A third class of interface which allows for dynamic switching is also possible:  the semimetal/semiconductor interface.  The contact barrier at this interface is modulated by a gate field which shifts the work function of the semimetal electrode, and thins the depletion width in the semiconducting channel.  Graphene and carbon nanotube networks exhibit the required semimetallic band structure and low density of electronic states needed for transistors operating by this mechanism.  The aim of this thesis is to develop field-transparent graphene electrodes for gated Schottky barrier transistors. Some contributions to graphene growth methods are also reported: (1) increases to the average graphene domain size – from nano to millimeter scale – by adjustment of the chemical vapor deposition growth parameters; and (2) the first demonstration of site-selective growth of graphene on silicon carbide.  A process for the improved transfer of graphene to insulating substrates with the use of protective metal thin-films is also presented.   Preliminary device results focus on the two-terminal rectification behavior of junctions between graphene and conventional inorganic semiconductors (Si, GaAs, GaN, and SiC).  These reveal an unusual voltage-dependence of the Schottky barrier height in reverse-bias operation.  A modified diode equation is presented to account for the bias-induced Fermi level shifts in the graphene.   Three-terminal Schottky-junction devices are fabricated, demonstrating gate-field control of the reverse-bias current.  The transconductance is attributed primarily to modulation of the contact barrier height between the graphene and the inorganic semiconductor due to gate-field induced Fermi level shifts in the graphene electrode. Vertical, organic, field-effect transistors – analogous to the inorganic, three-terminal Schottky devices – are fabricated using continuous graphene source electrodes.  In subsequent devices, the gate-field permeability of the semimetal source electrode is modified by introducing micron-scale pores into the graphene.  The pores boost the device performance, which scales with the areal pore density, by taking advantage of both barrier height lowering (thermionic emission) and local barrier thinning (tunneling).  These devices exhibit high On/Off ratios and record output current densities for organic transistors, exceeding 106 and 200mA/cm2, respectively.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Maxime G Lemaitre.
Thesis: Thesis (Ph.D.)--University of Florida, 2013.
Local: Adviser: Hummel, Rolf E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0044924:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044924/00001

Material Information

Title: Schottky Barrier Modulation at Graphene/Semiconductor Interfaces Engineering Field Permeable Semimetal Electrodes
Physical Description: 1 online resource (226 p.)
Language: english
Creator: Lemaitre, Maxime G
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: graphene -- schottky -- triode -- vfet
Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Conventional electronic circuits rely on semiconductor heterojunctions for dynamic switching, while metal/semiconductor interfaces are reserved for static contacts.  A third class of interface which allows for dynamic switching is also possible:  the semimetal/semiconductor interface.  The contact barrier at this interface is modulated by a gate field which shifts the work function of the semimetal electrode, and thins the depletion width in the semiconducting channel.  Graphene and carbon nanotube networks exhibit the required semimetallic band structure and low density of electronic states needed for transistors operating by this mechanism.  The aim of this thesis is to develop field-transparent graphene electrodes for gated Schottky barrier transistors. Some contributions to graphene growth methods are also reported: (1) increases to the average graphene domain size – from nano to millimeter scale – by adjustment of the chemical vapor deposition growth parameters; and (2) the first demonstration of site-selective growth of graphene on silicon carbide.  A process for the improved transfer of graphene to insulating substrates with the use of protective metal thin-films is also presented.   Preliminary device results focus on the two-terminal rectification behavior of junctions between graphene and conventional inorganic semiconductors (Si, GaAs, GaN, and SiC).  These reveal an unusual voltage-dependence of the Schottky barrier height in reverse-bias operation.  A modified diode equation is presented to account for the bias-induced Fermi level shifts in the graphene.   Three-terminal Schottky-junction devices are fabricated, demonstrating gate-field control of the reverse-bias current.  The transconductance is attributed primarily to modulation of the contact barrier height between the graphene and the inorganic semiconductor due to gate-field induced Fermi level shifts in the graphene electrode. Vertical, organic, field-effect transistors – analogous to the inorganic, three-terminal Schottky devices – are fabricated using continuous graphene source electrodes.  In subsequent devices, the gate-field permeability of the semimetal source electrode is modified by introducing micron-scale pores into the graphene.  The pores boost the device performance, which scales with the areal pore density, by taking advantage of both barrier height lowering (thermionic emission) and local barrier thinning (tunneling).  These devices exhibit high On/Off ratios and record output current densities for organic transistors, exceeding 106 and 200mA/cm2, respectively.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Maxime G Lemaitre.
Thesis: Thesis (Ph.D.)--University of Florida, 2013.
Local: Adviser: Hummel, Rolf E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0044924:00001


This item has the following downloads:


Full Text

PAGE 1

1 SCHOTTK Y BARRIER MODULATION AT SEMIMETAL /SEMICONDUCTOR INTERFACES : ENGINEERING FIELD PERMEABLE GRAPHENE ELECTRODES By MAXIME GREGORY LEMAITRE 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 2013

PAGE 2

2 2013 Maxime Gregory Lemaitre

PAGE 3

3 To Mom, Dad, and Cecilia To those whose patience persisted despite a fo ndness on my part for draggi ng both feet and stomping on all the crunchy leaves along the way For Jaime

PAGE 4

4 ACKNOWLEDGMENTS I would like to begin by acknowledging my friend and Doctovater R olf Hummel Four years ago, I came to him wi th a proposal to work on a new ly discovered ele ctronic material, known as graphene. After some concerned deliberation and possibly against his better judgment, Dr. Hummel granted me the freedom to work independently on the synthesis of this novel two dimensional material. Nor did h is support did not stop at my formal education ; he was a dedicated moral and emotional advisor without whom I could not have successfully navigated this phase of my life. Although I thought of myself as a bit of a rogue scientist, I was incredibly fortunate to have the he lp a several advisors Professors Andrew Rinzler Bill Appleton, and Brent Gila contributed their financial support and inspired much of the research in this thesis with their own ideas. Between them, my four advisors taught me nearly everything I know a bout materials science and experimental methods I wou ld also like to thank professor Demiitri Maslov for taking special interest in teaching me fundamental condensed matter physics. I am thankful to have had so many trusting mentors willing to give me the freedom to try my own ideas, but ready to help when things went sideways. I would like to thank my undergraduate research advisors Drs. Moonsub Shim, Jian Min Zuo and John Rogers. I am especially grateful to Dr. Congjun Wang who inspired me to conti nue on to graduate school and tirelessly answered all of my questions about science, never asking for more in return than our friendship. I would also like to acknowledge all the lab mates with whom I had the pleasure of working with over the years, especi ally Sefa a ttin Tongay, Evan Do noghue, Mitch

PAGE 5

5 McCarthy, and Bo Liu. I also am grateful to Thierry Dubroca, a companion and colleague in many entrepreneurial adventures. I have had the pleasure of doing science alongside some great friends : Bill Hammond, S ergey Maslov, Andrew Wasson, Gregory Dudder, Michael Hartel, Blake Darby, Robele Bekele, Brad Yates, and Philip Draa Their support made my graduate years truly enjoyable. Outside of the sphere of academic life, I must thank Duane Wiedor and Walt Lifsey. As great friends and mentors, t hey saw potential past the lengthy adolescent stage of my life, and helped to gently guide me towards adulthood Most importantly they never denied me an opportunity to prove myself. Finally, I owe the greatest amount of love an d gratitude to my family. Their constant love is the most important reason for any success I have had. I cannot hope to provide an accurate account of all they have done or what it means to me. To my family and a ll the p eople who have contributed to me finally arriving to this point, this work is graciously dedicated.

PAGE 6

6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 LIST OF ABBREVIATIONS ................................ ................................ ........................... 13 ABSTRACT ................................ ................................ ................................ ................... 15 C HAPTER 1 MOTIVATIONS ................................ ................................ ................................ ....... 17 1.1 A New ................................ ................................ ........... 17 1.2 Under the (Atomic) Sheets ................................ ................................ .............. 18 1.3 Flipping the Switch ................................ ................................ .......................... 19 1.4 Statement of Thesis ................................ ................................ ........................ 21 2 TEC HNICAL BACKGROUND ................................ ................................ ................. 22 2.1 Electronic Properties of Graphene ................................ ................................ .. 22 2.1.1 Carbon Hybridization ................................ ................................ ............. 23 2.1.2 Crystal Structure ................................ ................................ .................... 23 2.1.3 Electronic Band Structure ................................ ................................ ...... 25 2.1.4 Density of States ................................ ................................ ................... 32 2.1.5 Intrinsic Charge Carrier Properties ................................ ........................ 33 2.1.6 Extrinsic Carrier Properties ................................ ................................ .... 39 2.2 Graphene Growth Techniques ................................ ................................ ........ 43 2.2.1 Catalytic Chemical Vapor Deposition ................................ .................... 43 2.2.2 Silicon Carbide Decomposition ................................ .............................. 48 2.3 Raman Spectroscopy ................................ ................................ ...................... 52 2.3.1 Basics of Inelastic Optical Scattering ................................ ..................... 52 2.3.2 Spectroscopy of Graphene ................................ ................................ .... 54 2.4 Organic versus Inorganic Transport Phenomena ................................ ............ 56 2.4.1 Isolated States, Localized Levels, and Continuous Energy Bands ........ 56 2.4.2 Carrier concentration ................................ ................................ ............. 59 2.4.3 Bulk Conduction ................................ ................................ .................... 60 2.5 Conventional Schottky Barriers ................................ ................................ ....... 61 2.5.1 Metal Semiconductor Interfaces at Thermal Equilibrium: Schottky Barrier Formatio n ................................ ................................ .......................... 62 2.5.2 Thermionic, Diffusive, and Field Emission Theory .............................. 63 2.5.3 Deviations from Ideality ................................ ................................ ......... 66 2.5.4 Ohmic Contacts ................................ ................................ ..................... 67

PAGE 7

7 3 GRAPHENE SYNTHESIS AND TRANSFER TECHNIQUES ................................ 90 3.1 Introduct ion ................................ ................................ ................................ ..... 90 3.2 Toward Macroscale Domain Growth via Chemical Vapor Deposition ............. 90 3.2.1 Low Vacuum Catalytic Chemical Vapor Deposi tion ............................... 91 3.2.2 Chemical Mechanical Polishing ................................ ............................. 96 3.3 Rethinking Graphene Transfer ................................ ................................ ........ 97 3.3.1 Hot Clamping and Vapor Dissolution ................................ ..................... 98 3.3.2 Protective Metallic Support Layers ................................ ...................... 100 3.4 Field Transparent Semimetallic Films: Porous Graphene ............................. 102 3.5 Drawing Graphene on SiC via Ion Implantation ................................ ........... 103 3.5.1 Thermal Epit axial Growth ................................ ................................ .... 104 3.5.2 Laser Induced Epitaxial Growth ................................ ........................... 110 3.5.3 Catalytic Effects of Implantation Species ................................ ............. 112 3.6 Concluding Remarks ................................ ................................ ..................... 115 4 GRAPHENE/INORGANIC SEMICONDUCTOR INTERFACES ............................ 140 4.1 Introduction ................................ ................................ ................................ ... 140 4.2 Schottky Junctions on Technologically Relevant Semiconductors ................ 141 4.2.1 Fabricating Graphene Dio des on Si, GaAs, GaN, and SiC .................. 142 4.2.2 Extracting Barrier Heights from Electrical Measurements ................... 147 4.3 Deviations from Ther mionic Emission Theory ................................ .............. 150 4.4 Gated Schottky Junctions on Si: Continuous Graphene Case ...................... 157 4.5 Concluding Remarks ................................ ................................ ..................... 161 5 GRAPHENE/ORGANIC SEMICONDUCTOR INTERFACES ............................... 181 5.1 Introduction ................................ ................................ ................................ ... 181 5.2 Graphene Enabled Vertical Field Effect Transistors ................................ ..... 181 5.3 Tuning the Field Permeability of the Graphene Electrode ............................. 185 5.4 Comparisons to Other Porous Electrodes ................................ ..................... 1 86 5.4.1 Metal versus Semimetal Porous Electrodes ................................ ........ 186 5.4.2 Porous Graphene v ersus Dilute Carbon Nanotubes ............................ 188 5.5 Concluding Remarks ................................ ................................ ..................... 189 6 CONCLUSIONS AND PROSPECTIVE ................................ ................................ 201 APPENDIX: LIST OF PUBLICATIONS ................................ ................................ ..... 203 LIST OF REFERENCES ................................ ................................ ............................. 204 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 225

PAGE 8

8 LIST OF TABLES Table page 4 1 Extracted SBHs, doping densities, and corresponding graphene work function values on various graphene/ semiconductor junctions. ....................... 175

PAGE 9

9 LIST OF FIGURES Figure page 2 1 The hybridization of carbon ................................ ................................ ................ 69 2 2 A honeycomb latt ice of carbon atoms in graphene ................................ ............. 70 2 3 Tight binding approximation of the graphene electronic energy band diagram .. 71 2 4 Angle resolved photoemission spectroscopy of the graphe ne electron e nergy dispersion ................................ ................................ ................................ ........... 72 2 5 The continuously tunable Fermi level o f graphene ................................ ............. 73 2 6 Quantum numbers in graphene Pseudospin and isospin ................................ 74 2 7 Klein tunneling in graphe ne ................................ ................................ ................ 75 2 8 Magneto oscillations in graphene ................................ ................................ ....... 76 2 9 Fractional qu antum hall effect in graphene ................................ ......................... 77 2 10 Sensitivity of the low density of states of grap hene to electronic potentials ....... 78 2 11 Quantum transport phenomena in grap hene nanoribbon s ................................ 79 2 12 Stacking graphene ................................ ................................ .............................. 80 2 13 Diagram of the kinetic processes during catalytic chemical vapor deposition .... 81 2 14 Growth modes of graphene on metal substrates with various degrees of carbon solubility ................................ ................................ ................................ .. 82 2 15 Growth modes of graphene on the different faces of SiC ................................ .. 83 2 16 Diagram of the Raman scattering process ................................ ......................... 84 2 17 The doubl e resonance process in graphene ................................ ..................... 85 2 18 Transport mechanisms in organ ic and inorganic semiconductors ...................... 86 2 19 Schematic of an n type Schottky barrier at thermal equilibrium .......................... 87 2 20 Band bending and current transport for MS junctions to n and p type semiconductor s at various biasing conditions ................................ ..................... 88 2 21 Diagram of image force lowering effect on a biased n type diode ...................... 89

PAGE 10

10 3 1 Home built CVD system ................................ ................................ ................... 117 3 2 Delet erious SiO x particles originati ng from the quartz tube furnace ................. 118 3 3 SEM characteriza tion of macroscale graphene domains in a partially grown film on Cu ................................ ................................ ................................ ......... 119 3 4 Protected surface reconstruction u nder graphene films on copper ................... 120 3 5 AFM characteriza tion of a partia lly grown graphene film on Cu ....................... 121 3 6 Histogram of the sheet resistance values for CVD grown films g rown under diffe rent conditions ................................ ................................ ........................... 122 3 7 Atomic force microscopy characterization of copper foils before and after chemical mechanical polishing ................................ ................................ ......... 123 3 8 SEM characterization copper foils before and afte r chemical mechanical polishing ................................ ................................ ................................ ........... 124 3 9 Schematic of the improved graphene transfe r proces s ................................ .... 125 3 10 Hot clamping and vapor bath technique for increased transfer yields .............. 126 3 11 Facile method for the lithography free fabricating of porous graphene ............. 127 3 12 Raman chara cterization of the impro ved graphene t ransfer metho d ................ 128 3 13 Continuity and roughness of graphene transferred using a protective metal film ................................ ................................ ................................ .................... 129 3 14 Comparison of the Raman peak intensities for graphene samples tra nsferred to SiO2 with and without an Au protective layer ................................ ............... 130 3 15 Method for obtaining hole statistics for t he ransom porous graphene films ...... 131 3 16 Site selective graphitization of SiC via ion implantation a nd thermal or laser annealing ................................ ................................ ................................ .......... 132 3 17 Raman spectra of Au and Si implant ed and annealed SiC. ............................. 133 3 18 Characterization of ion implanted SiC, befor e and after thermal annealing ...... 134 3 19 Graphene nanoribb ons grown by ion implantation ................................ ........... 135 3 20 Drawing graphene on SiC via ion implantation ................................ ................ 136 3 21 Characterization of a selectively graphitized region of SiC after ArF pulses at ................................ ................................ ................................ ......... 137

PAGE 11

11 3 22 Growth of FLG with nanoscale features by Au ion beam lithography and PLA 138 3 23 Onset of graphitization with increasing laser fluences for various implantation species as evid enced by Raman ................................ ................................ ...... 139 4 1 Fabrication and electrical characterization of graphene/inor ganic semiconductor junctions ................................ ................................ ................... 162 4 2 Raman characterization of graphene on technologically relevant semiconductors ................................ ................................ ................................ 163 4 3 In situ bias dependent Raman spectra ta ken on graphene/GaN junctions ....... 164 4 4 Hall tr ansport of transferred graphene ................................ .............................. 165 4 5 Graphene/Silicon Schottky diode: Room temperat ure transport characteristics ................................ ................................ ................................ ... 166 4 6 Graphene/GaAs Schottky diode: Room temper ature transport characteristic s 167 4 7 Graphene/GaN Schottky diode: Room temper ature transport characteristics .. 168 4 8 Graphene/GaN Schottky diode: Room temperat ure transport characteristics .. 169 4 9 Temperature dependent graphene/ n Si diode characteristic s .......................... 170 4 10 Temperature dependent graphe ne/Ga As diode characteristics ....................... 171 4 11 Temperature dependent gra phene/GaN diode characteristics ......................... 172 4 12 Temperature dependent gra phene/SiC diode characteristics .......................... 173 4 13 Capacitance measurements ................................ ................................ ............. 174 4 14 Band diagrams for graphene/inorganic sem iconductor Schottky diodes. ......... 176 4 15 The diode characteristics for the graphene/ p Si junction used for the three termina l Schottky barrier transistor. ................................ ................................ 177 4 16 Band bending schematic for a three terminal, gate field mod ulate d Schottky barrier transi stor ................................ ................................ ............................... 178 4 17 Output characteristics of a three terminal graphe ne/ p S i Schottky barrier transistor ................................ ................................ ................................ ........... 179 4 18 Compar ison of the reverse and forward bias modes of Schott ky barrier transistor operatio n ................................ ................................ ........................... 180 5 1 The G VFET architecture and drive scheme ................................ .................... 192

PAGE 12

12 5 2 Two and three terminal device s with semimetal/ organic semiconductor junctions ................................ ................................ ................................ ........... 193 5 3 Energy level diagram for a GVFET at the graphene semiconducting channel interface for constant drain voltage and three distinct gate voltages ................ 194 5 4 Field permeable graphene electro des with various pore densities ................... 196 5 5 Device perform a nce of field permeable G VFETs ................................ ............ 197 5 6 Fabrication of graphene and Ag electrodes w ith comparable pore densities .... 198 5 7 Comparison of VFETs constructed with porous graphen e versus porous Ag electrodes ................................ ................................ ................................ ......... 199 5 8 Comparison of graphene and carbon nanotube enabled VFETs with all other device layers the s ame ................................ ................................ .................... 200

PAGE 13

13 LIST OF ABBREVIATION S 2DEG 2 D IMENSIONAL E LECTRON G AS AJA A BRUPT J UNCTION A PPROXIMATION AFM A TOMIC F ORCE M ICROSCOPY APCVD A MBIENT P RESSURE C HEMICAL V A POR D EPOSITION ARPES A NGLE R ESOLVED P HOTO E MISSION S PECTROSCOPY BLG B I L AYER G RAPHENE BZ B RILLOUIN Z ONE DOS D ENSITY O F S TATES CNT C ARBON N ANO T UBE CVD C HEMICAL V APOR D EPOSITION EDS E NERGY D ISPERSIVE S PECTROMETRY HBN H EXAGONAL B ORON N ITRIDE HEMT H IGH E LECTRO N M OBILITY T RANSISTOR FD F ERMI D IRAC FET F IELD E FFECT T RANSISTOR FE F IELD E MISSION FIB F OCUSED I ON B EAM LPCVD L OW P RESSURE C HEMICAL V APOR D EPOSITION MB M AXWELL B OLTZMANN MESFET M ETAL S EMICONDUCTOR F IELD E FFECT T RANSISTOR MLG M ULTI L AYER G RAPHENE MG M ONOLAY ER G RAPHITE MOS M ETAL O XIDE S EMICONDUCTOR MS M ETAL /S EMICONDUCTOR

PAGE 14

14 NN N EAREST N EIGHBOR NNN N EXT N EAREST N EIGHBOR RTA R APID T HERMAL A NNEALING PECVD P LASMA E NHANCED C HEMICAL V APOR D EPOSITION PID P ROPORTIONAL I NTEGRAL D ERIVATIVE PPMS P HYSICAL P ROPERTIES M EASURE MENT S YSTEM SB S CHOTTKY B ARRIER SBH S CHOTTKY B ARRIER H EIGHT SCCM S TANDARD C UBIC C ENTIMETERS PER M INUTE SCLC S PACE C HARGE L IMITED C URRENT S D HO S HUBNIKOV DE H AAS O SCILLATIONS SE S ECONDARY E LECTRON SLG S INGLE L AYER G RAPHENE STM S CANNING T UNNELING M ICROSCOPY S WNT S INGLE W ALLED C ARBON N ANOTUBE TB T IGHT B INDING TE T HERMIONIC E MISSION TFE T HE R MIONIC F IELD E MISSION UHV U LTRA H IGH V ACUUM UV U LTRA V IOLET QED Q UANTUM E LECTRODYNAMICS

PAGE 15

15 Abstract of Dissertation Presented to the Graduate School of the University of Fl orida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SCHOTTK Y BARRIER MODULATION AT SEMIMETAL /SEMICONDUCTOR INTERFACES : ENGINEERING FIELD PERMEABLE GRAPHENE ELECTRODES By Maxime Gregory Lemaitre May 2013 Chair: Rolf Hummel Major: Materials Science and Engineering Conventional electronic circuits rely on semiconductor heterojunction s for dynamic switching while metal/ semi conductor interfaces are reserved for static contacts. A third class of interface which allows for d yna mic switching is also possible : the semimetal/semiconductor interface. The contact barrier at this interface is modulated by a gate field which shift s the work function of the semimetal electrode, and thins the depletion width in the semiconducting channel. Graphene and carbon nanotube networks exhibit the required semimetallic band structure and low density of electronic states needed for transistors operating by this mechanism The aim of this thesis is to develop field transparen t graphene ele ctrode s for gated Schottky barrier transistors Some c ontributions to graphene growth methods are also repor ted : (1) increases to the average graphene domain size from nano to millimeter scale by adjustment of the chemical vapor depositio n growth parameters ; and (2) the first demonstration of site selective growth of graphene on silicon carbide A p rocess for the improved transfer of graphene to insulating substrates with the use of protective metal thin films is also presented

PAGE 16

16 Prelimi nary device res ults focus on the two terminal rectification behavior of j unctions between graphene and conventional inorganic semiconductors (Si, GaAs, GaN, and SiC ) These reveal an unusual voltage dependence of the Schottky barrier height in reverse bia s operation A modified diode equation is presented to account for the bias induced Fermi level shifts in the graphene Three terminal Schottky junction devices are fabricated demonstrating g ate field control of the reverse bias current The t ranscond uctance is attributed primarily to modulation of the contact barrier height between the graphene and the in or ganic semiconductor due to gate field induced Fermi level shifts in the graphene electrode. V ertical organic field effect transistors analogous to the inorganic, three terminal Schottky device s are fabricated using continuous graphene source electrodes In subsequent devices t he gate field permeability of the semimetal source electrode is modified by introducing micron scale pores into the gr aphene. The p ores boost the device performance which scales with the areal pore density by taking advantage of b oth barrier height lowering (thermionic emission) and local barrier thinning (tunneling) These d evices exhibit high On/Off ratios and recor d output current densities for organic transistors, exceeding 10 6 and 200mA /cm 2 respectively.

PAGE 17

17 CHAPTER 1 MOTIVATION S 1.1 A New ish Wonder Material Fullerenes were first discovered in 1985, 1 c arbon nanot ubes in 1991 2 T he single atomic layer building block of these finite graphitic structures known as graphene, was not isolated until 2004. 3 Shortly after its discovery, the scientific press was quick to prophesize an end to the reign of Silicon in electronics prompting speculation about the future site According to the li terature, there is scarcely a field of study that might not be revolutionized by graphene: ultrafast electronics, 4,5 anticorrosion coatings, 6 transparent conductors, 7,8 solar cells 9,10 desalinization membranes, 11 sensors, 12 flexible displays, 13,14 DNA sequencing. 15 The fanfare surrounding grap hene will not surprise those who participated in carb on research at the end of the 20 st century. Similar ly prophetic declarations were also made a decade earlier about carbon nanotubes and C 60 films. There is no doubt that graphitic carbons possess unique or at least, rare material characteristics. Collectively, these m aterials hold nearly every performance record for electrical conductivity mechanical strength and chemical stability Obliging a certain level of amnesia among researchers for earlier w ork done with nanotubes and fullerenes, t he novelty of graphene over its predecessors is two fold: (1) a continuous planar geometry and (2) a single massless Dirac fermion energy band structure. T he planar structure of graphene makes it more compatibl e with existing thin fi lm micro fabrication techniques, while the behavior of its carriers makes it a unique material system from which to study relativistic quantum particles with bench top laboratory equipment. G raphene has also motivated the wider sear ch for other two dimensional

PAGE 18

18 materials To date, small single layer flakes of several classes of materials have been isolated, including nitrides (hexagonal BN), 16 chalcogenides (MoS 2 TaS 2 TiS 2 WS 2 Nb Se 2 Bi 2 Te 3 ), 17 19 and oxides (Bi 2 Sr 2 CaCu 2 O x Titania, VO 5 ). 20 22 Unfortunately, all unsupported two dimensional systems are inherently unstable and therefore not naturally occurring. R eliabl e large scale synthesis of 2D materials remains a challenge and the critical step towards future applications 1.2 Under the ( Atomic ) Sheets In the 1930s, Landau and Peierls presented thermodynamic arguments, disputing the existence of 2 D materials 23,24 The argument s state that at any finite temperature, divergent thermodynamic fluctuations lead to atomic displacements on the order of the interatomic distance thus preventing 2 D crystal formation. 25 In addition, large edge to surface ratio s during nucleation are energetically unfavorable and would typically lead to a phase transformation towards a more stable allotrope. These predictions were supported by over 70 years of experimental evidence from which free standing 2 D struc tures w ere conspicuously absent. The revolution came when ph ysi cists Andre Geim and Kostya Novoselov at Manchester University used the so to cleave 2 D graphene from 3 D graphite. 3,20 They used ordinary tape to peel away thin layers from slabs of natural graphite Then they exfoliated even thinner flakes by rubbing the tape on the surface of an oxidized silicon wafer. A small fraction of the flakes left on the wafer surface turned out to be single layer graphene A serendipitous choice of ox ide thickness allowed the single layers to be found in an optical microscope by a faint interference contrast

PAGE 19

19 Although this m echanical exfoliation technique is suitable for one off physics experiments it is not scalable for industrial applications An a lternative approach takes advantage of an old trick of crystal growth the concept that 2 D structures can be st able if formed as part of a 3 D matrix. I t turns out that by this method graphene can be grown on top of catalytic bulk materials with a high degree of crystallinity The quality of the graphene growth is of course dependent on growth conditions and the choice of substrate. M etals seem to be the best catalyst s for producing large areas of high quality graphene but research into growth conditio ns is still in its infancy Regrettably, the conductive nature of metallic substrates obscures the unique electronic p roperties of the graphene The key is carefully t ransferring graphene to the right underlying substrate 1.3 Flipping the Switch Swit c hing electrical currents, on to off, is the basic function of logic and power amplification circuitry. To that end, a revolution in electronics came in 1906 with the invention of the thermionic triode. 26 For the first time, current flow could be controlled by an electric field a voltage induced deflection of electrons rather than a mechanical switch. It took nearly half a century to discover a solid state analog. Building on new insights about the physics of interfaces, 27 32 Bardeen, Shockley, and Brattain invented the field effect transistor. 33 35 Switching was now controlled by the voltage induced modulation of the energy barrier at the junction of two semiconductors. N early all modern transistor s still operate on some variation of the semiconductor/semiconductor junction. Generally, these juncti ons occur between differently doped regions in a single semiconductor crystal The current transport across these junctions i s well understood and can be precisely tuned by adjusting

PAGE 20

20 doping level. M eta l/semiconductor junctions play an important role as current rectifiers and as contacts to these traditional devices. To a first approximation the work function difference betwe en a metal and a semiconductor dictates the transport across their junction, determining whether the contact will be Ohmic or have a Schottky barrier to electrical transport. 36,37 Unlike semiconductor junctions, conventional Schottky bar riers are static and cannot be modulated. Me tals possess a large density of electronic states (DOS), requiring the addition/subtraction of large amounts of charge to induce appreciable shifts in their work functions (like the water level in a large lake, much water must be added to change the level perceptibly). This picture changes dramatically for low DOS semi metals like carbon nanotubes and graphene for which charge addition/subtraction induces mu ch more dramatic work function shifts (for a tall narrow glass, little water is needed to change the level appreciably). Since the work function in these materials can be changed in response to gating fields, these low DOS carbon based semi metals, placed in contact with a semiconductor, admit a new mechanism f or current modulation by the gate field control of their trans junction transport. That is, by tuning of the Schottky barrier height. Another, more subtle, mechanism is also at play here. The semimetal source electrode, by virtue of its low DOS, is par tly permeable to the gate field. This allows the semiconductor Fermi level to be tuned as well. A shift in the semiconductor Fermi level corresponds to a change in the Schottky barrier width. As shown in this thesis, t he inclusion of small pores into th e semimetal can enhance the field permeability of the electrode, and thus increases the magnitude of the current across the junction.

PAGE 21

21 1. 4 Statement of Thesis The purpose of this research is to advance our understanding of semimetal/semiconductor interfac es and develop gated Schottky barrier transistors using field permeable graphene electrodes. Improved graphene growth and transfer techniques supporting the fabrication of these devices ar e also reported. The principal experimental outcomes are as summa rized below: Growth of single layer graphene f ilms on copper via chemical vapo r deposition with large contiguous domains, exceeding in area. An i mproved technique for graphene transfer to insulating substrates using protective metal layers. Site selective growth of few layer graphene directly on SiC substrates by ion implantation and thermal or pulsed laser annealing. L arge area rectifying contacts between graphene and several technological ly relevant semiconductors (Si, GaAs, GaN, and SiC) A p r oof of concept gate modulated Graphene/Si Schottky bar rier transistor. Gate field permeable graphene electrodes for enhanced barrier modulation at semimetal/semiconductor interfaces. G raphene enabled vertical organic field effect transistor with record s etting current densities for an organic device

PAGE 22

22 CHAPTER 2 TECHNICAL BACKGROUND Publication of graphene related literature has been prolific since the discovery of electronically isolated graphene in 2004. In less than half a dozen years, the field has produced hundreds of patents and se veral thousand publications, generating more than 50,000 citations per year. 38 Here we will give a brief synopsis of only the theoretical and experime ntal results that are most relevant to the Schottky barrier devices described in this thesis Our review will focus on the elementary electroni c properties of graphene and established epitaxial growth techniques. We go on to describe t he principles of Raman spectroscopy a widely used technique for characterizing low dimensional graphitic allotr opes A comparison of the transport processes in orga nic and inorganic semiconductor crystals is pro vided to elucidate the crucial differences between the devices fabricated in Chapters 4 and 5 Finally, we describe the mechanisms for current transport a cross metal/semiconductor junctions as a starting point for understanding our unconventional Schottky devices 2.1 Electronic Properties of Graphene This section will address the fundamental electronic properties of graphene T he properties most relevan t to our devices the semimetallic band structure and the low density of states (DOS) will be explicitly derived (S ections 2.1.3 and 2.1.4 ) in order to clarify their origin This is followed by a brief survey of the intrinsic and extrinsic electronic p roperties of graphene. We precede this discussion with a brief mention of orbital hybridization in carbon ( Fig. 2 1 ). This process, by which the electron distributions spontaneously superpose themselves, is responsible for the s pectacular variety of carbon allotropes that exist in nature

PAGE 23

23 2.1.1 Carbon Hybridization In the ground state, an isolated carbon atom has 6 electrons in the configuration. In the presence of other atoms, it is energetically favorable for the second electron in the state to fill the third state. At this point, there are 4 unpaired electronic states and a supe rposition of states is possible such that the carbon atom can form single double or triple bonds. These various bond conformations allow carbon to form lattices of all possible dimensionality (linear chains, planar sheets, or diamond bulk). The state equations for the cas e of hybridized graphene are written as follows, (2 1) (2 2) (2 3) represent ing the three bonds evenly spaced in the plane by 120 the remaining unpaired orbital is perpendicular to the sheet, (2 4) 2.1.2 Crystal Structure The atom s in graphene are ar ranged in a planar structure of hexagonal rings with an average carbon carbon bond lengt h of ~ 1.42 It is convenient to think of this honeycomb like atomic arrangement as consisting of two interpenetrating hexagonal sublattices The trigonal planar str ucture is covalently bonded via three hybridized bonds, while the remaining orbital i s hybridized to form the conjugated and bands. The resonant covalent double bonds are extremely rigid and lend strength to the graphene while the d e localized electrons contribute to i ts electrical conductivity.

PAGE 24

24 The honeycomb lattice of graphene is illustrated in Figure 2 2 W e designate the real space Bravais lattice vectors of the A sublattice ( centered at ) (2 5 ) and the thre e nearest neighbor vectors such that, (2 6 ) where is the carbon carbon bond length. We see that the local arrangement of atoms surrounding a give n site on the A sublattice ( for example) is the mirror image of that for a corresponding site on the B sublattice ( ). The full honeycomb structure is completed only when the sublattices are brought together, creating a unit cell of two inequivalent atoms. The reciprocal space lattice vectors of both sublattices (2 7 ) are indistinguishable in phase space since the y are symmetric and differ by only a translation. Sites on the reciprocal lat tice represent physically equivalent wavevectors, such that waves propagating in the crystal lattice scatter ed by these wavevectors retain their phase (up to a factor according to, (2 8) where is a Dirac delta function whose value is 1 for and 0 for However, t he first Brillou i n zone (BZ) an area defined by bisecting the primitive reciprocal space lattice vectors (shaded area in Fig. 2 2B ) consists of inequivalent wave vectors that may not be connected by translation symmetry It is a subtle point that the shape of the BZ has nothing to do with the presence of two sublattices, and is instead the consequence of any single hexagonal lattice. T he corners of the first BZ a re designated by the and points

PAGE 25

25 (2 9) These p oints have special significance and are referred to as the Dirac points As we will see, it is at these points in the reciprocal lattice that the b ands intersect to form highly symmetric conical dispersions. The presence of two inequivalent sublattices (or alternatively, two basis atoms) will prove to be the unique electronic properties 2.1.3 Electronic Band Str ucture Graphene is a semimetal with extraordinary electronic properties. Here we will illustrate how an approximate model of the semimetallic band structure can be obtained using the tight binding (TB) formulation. This derivation illustrates how the un ique features of the graphene dispersion relation arise as a result of the honeycomb lattice consisting of a two atom basis T he interested reader can find additional detail s in several more complete discussions on the subject. 39 42 The TB approximation treat s the crystal as a s imple summation of the discrete at om ic potentials, while contributions to the potential energy term from the other atoms in the crystal are treated perturbatively. In other words, it assumes that electrons in a crystal behave much like the bound electrons in an isolated atom, and thus the full periodic potential of the lattice can be approximated by the atomic Hamiltonian and an additional corrective term which vanishes near the lattice points (2 10) The electron wavefunctions, which are eigenvalue solutions of the Schrdinger equation employing this Hamilt onian, represent atomic orbitals. The total Hamiltonian for all electrons in the lattice is then,

PAGE 26

26 (2 11) and is treated as a linear combination of atomic orbitals (LCAO). The Hamiltonian for an electron at pos i tion is defined (2 12) where the vector represents all the sites in the Bravais lattice, is the electron mass, and is the 2D Laplacian gradient operator. The additional contributi on s from neigh boring atoms to the single atom ic potential are accounted for by for all sites where A unique consequence of the honeycomb lattice of graphene is that the unit cell consists of two atoms which cannot be related to each other via a translation oper ation. As a result the A and B sublattices must be treated independently, and t he wavefunctions generated as a linear superposition of the eigenfunctions of both, (2 13) where are the unit cell wavefunc tions in the momentum basis, are the wave functions associated with 2 orbitals of each sublattice and and are c omplex functions of the wa ve vector Adapting the wavefunction solution to the single atom case, we can designate trail wavefunctions for both sublattices of the form, (2 14) Because the Hamilto nian is invariant with respect to translations of the periodicity of the Bravais lattice, these are Bloch functions that obey the following relation, (2 15)

PAGE 27

27 Although such translations are symmetric and commute with the Hamiltonian that is not the case for translations that relate one sublattice to the other along the nearest neighbor vectors (i.e. ) This is the reason the sublattices must be treated independently. The electronic ban d structure of solids is often represented as a plot of the available energy states versus the reciprocal space wavevector. In order to do this we will solve the Schrdinger equation, (2 16) using the trial wavefunctions described above normalized by the standard condition, (2 17) We multiply both sides of the Schrdinger equation by the complex conjugate of the trial wavefunction and rewrit e it in mat r ix form using Dirac notation, (2 18) The Hamiltonian matrix is now defined as, (2 19) a nd because the trial wa vefunctions for the A and B sublattices are not orthogonal we define a matrix, to account for the finite overlap of wavefunctions centered at the two basis atoms in the unit cell, (2 20) The diagonal elements of the overlap matrix, are equal to unity since the wavefunctions are assumed to be normalized, and though it is often the case that the

PAGE 28

28 off diagonal terms are neglected for simplicity, their contribution is equivalent to that of the next nearest neighbor corrections. The inclusion of these terms results in a slight electron hole asymmetry (i.e. the effective mass of electrons is smaller than that of holes i n graphene). We start by following the general procedure for any quantum mechanical eigenvalue problem, that is by evaluating, (2 21) Since we know that the eigenfunctions are finite and represent the real wavefunctions (i.e. orbitals ) in the crystal, the condition that must be sat isfied for non zero wavefunctions is thus (2 22) Th is characteristic equation has two solutions one for each of the atoms in the unit cell with each solution representing an energy band in space. The discrete energy levels within the bands result from the linear combination of a ll electrons in the lattice. The elements of the Hamiltonian matrix can be re defined such that (2 23) where the and indices represent A and B sublattices, and r epresents the hopping probability between nearest ( ) and next nearest neighbors ( ). The tight binding approximation is sufficiently accurate in the low energy regime that more complex terms involving longer range hopping probabilities and higher order overlaps can be ignored. Using this notation, the characteristic equation for the eigenvalue problem becomes, (2 24) We define three physically significant scalars,

PAGE 29

29 (2 25) (2 26) (2 27) where and represent the and hopping amplitudes, and the overlap magnitude, respectively. Values for these terms can be extracted from ab initio numerical calculations or fitting with experimental data (see below). The elements of the hopping and overlap matrices are given by the following expressions: (2 28) (2 29) (2 30) w here is the sum of the phase factors and the diagonal elements of are unity. Evaluating the characteristic equation (2 31) yields two solutions for the energy dispersi on in k space (representing and ) (2 32) expanding to (2 33) Finally, by d ot ting the wavevector components with the vectors we arrive at the complete expression:

PAGE 30

30 (2 34) From t his result we can discern several of the important features of graphene To help visualize the implications of this equation, the full electronic dispersion relation was plotted in Figure 2 3A as energy (in units of ) versus the x and y components of the wavevector ( plotted using Mathematica 7.0 Student Edition 43 ) We notice immediately that valence a nd conduction bands (or the and bands, respectively) come together at a single point at each of the and symmetry points. Since each orbital is occupied by one electron of spin for each atom in the unit cell, the energy bands of intrinsic graphene are exactly half full and the intrinsic Fermi level is defined to be at the intersection of the bands (the Dirac points). Near these intersection points, the energy varies linearly with momentum to form a semimetal for which the DOS at the Dirac point is exa ctly zero (See Figure 2 3B ). This is in contrast to conventional 2D metals in which the bands intersect to form a Fermi surface (defined by a line), or a semiconductor in which the Fermi level lies between t wo energy bands. The results of the tight binding approximation for graphene have been confirmed by a variety of experimental techniques the most striking coming from angle resolved photoemission spectroscopy (ARPES). The technique is based on the ene rgy conservation between an incident monochromatic photon and the resultant photoexcited carrier that is expelled from the lattice. The electrons are ejected from the valence band with a measureable energy and angular momentum, from which the spectral fun ction can be determined. ARPES yields a representation of the DOS and the energy band dispersion in reciprocal space (See Figure 2 4 ). Fitting to these experimental results provides accurate estimates for the and overlap function values.

PAGE 31

31 If we consider only low energy excitations about the Fermi level, then we can expand the full dispersion around the Dirac points (for arriving at the famous relation, (2 35 ) where the Fermi velocity is a constant defined by, and roughly equal to th the speed of light. The second order terms become negligible for small values of and can be ignored for energies less than from the Fermi level. This result is remarkably different from the typical case for 2D metals, in which bands are parabolic (2 36) but also, as a result the Fermi velocity of charge carriers v aries substantially as a function of energy, Of direct consequence for our devices is the ability to continuous ly tune the Fermi level or more precisely, the carrier concentration of graphene via the electric field effect. The semimetal lic band structure ensures that there is no break in available carrier states and allows for nearly symmetric ambipolar be havior. Carriers can be added or removed, by applying a voltage between graphene and an electrically insulated gate el ectrode (See Figure 2 5 ). This is analogous to the charge accumulation on a parallel plate capacitor. The number of carriers induced in the graphene sheet as a function of gate voltage can be approximated by, (2 37)

PAGE 32

32 w here is the permittivity of free space, is the dielectric constant, is the dielectric thickness, and is the charge of an electron. Since the DOS at the Dirac point is exactly zero (see Section 2.1.3), the total free carrier concentration is equal to the number of field induced charges. Approximately, 10 12 carriers per square centimeter can be induced in this way before the low energy band approximation is no longer valid. 2.1.4 Density of States A direct consequence of the low energy spectrum of graphene is a density of electronic states that is also linear in energy. At the Dirac points, the DOS actually becomes zero and therefore there are no free charge carr iers at these points. The resulting low DOS around the intrinsic Fermi energy is of great relevance to our devices Below we will estimate carrier concentrations for intrinsic graphene and derive the density of states within the low energy limit In ge neral, the density of electronic states, is defined, (2 38) where is the number of one electron energy levels found at energy in the n th band For each band, t his can be expanded into an integral over the primitive unit cell in reciprocal space, (2 39) the dimensionless term account ing for a one dimensional Fermi surface We can then use the low energy linear dispersion relation to get an integral in t erms of energy, (2 40) From here we arrive at the total density of electronic states by multiplying by the degeneracy of four resulting from the two energy bands and spin states

PAGE 33

33 (2 41) We notice that for an energy zero, which corresponds to the intrinsic Fermi energy, the density of states in also zero. Furthermore, because the number of states increases only linearly the electronic properties o f graphene are characterized by its intrinsically low DOS. This is in contrast to typically two dimensional metals for which the DOS is a series of successive step functions To illustrate the low DOS in graphene, we can compare the maximum carrier conce ntration of gated graphene ( ~ ), to the density of carbon atoms in a single sheet ( ). This shows that only one conduction electron (or hole) exists per roughly one thousand carbon atoms. It should be noted that the DOS of graphe ne is more complex when calculated for the full energy range of the dispersion relation. 45 I n this case there are points of discontinuity known as van Ho ve singularities, that arise at the symmetry points. This is the result of the local slope of the dispersion being zero at the saddle points between the Dirac cones. At these points, the derivative of the energy (found in the denominator of the full D OS expression) becomes zero and leads to an asymptotic increase in the density of states. Similar van Hove singularities are known to exist in carbon nanotubes as a result of quantum confinement in the radial direction. 2.1.5 Intrinsic Charge Carrier Pr operties Many unusual phenomena both of the theoretically predicted and totally unexpected variety, have already been observed experimentally in graphene Many of these properties are a direct result of the unique band dispersion that we deriv ed previous ly (Section 2.1.3 ). Th e outcome of the derivation is a dispersion relation of

PAGE 34

34 graphene that is a simple linear function of momentum (for energies ) This dispersion is analogous to th e eigenvalue solution of the re lativistic Dirac equation for a m assless fermion : 46 (2 42) A minor exception is that the speed of light must be replaced by the Fermi velocity, which in graphe ne turns out to be roughly Before we can explore some of the more unusual phenomena in graphene, we must first make this analogy to massless relativistic particles more explicit. You may recall that the linear dispersion is a direct result of the symmetry of the hexagonal crystal structure. The unit cell of graphene consists of two inequivalent sublattices and between whic h quantum mechanical hopping occur s This leads to the form ation of two energy bands which intersect to form conical di spersions at the points in reciprocal space. 47 In typical condensed matter systems, electrons and hole s are described by two distinct Schrdinger equ ations; h owever, in graphene we treat the bands as two components of the same Schrdinger equation (one for each sublattic e, as we saw in the TB approximation). A lternatively the bands can be described by a single Dirac Hamiltonian matrix By making the substitu tion into the effective Hamiltonian, we can define the local Hamiltonian for the conical dispersion at the K point (also referred to as a valley in reciprocal space), (2 43) where represents the set of Pauli matrices th at act to define the contributions from the two sublattices: (2 44)

PAGE 35

35 Furthermore, we must account for the contribution from both valleys ( and ) The full basis is thus, (2 45) in which for example, represents the contribution to the total wavefunction from just the K valley and the A sublattice. The complete Hamiltonian is then a 4 x 4 block matrix, (2 46) where is the Pauli matrix assigned to the valley (K point) index Traditionally, the Pauli matrices serve as the index for the electron spin, however, in this case the matrices serve to d istinguish the two fold degeneracy for 3 distinct degr ees of freedom: (1) electron spin, up and down, (2) sublattice index and and (3) valley index, and In following with the quantum number terminology, the Pauli matrices corresponding to the sublattice index are often labeled as pseudospin and the valley index is called isospin Th e symmetry of the Pauli matrices has surprising implications for the carrier properties of graphene. This signifies that the particles are interconnected in a manner analogous to charg e conjugation symmetry in QED. 48 It is useful in this case to picture a simplified model based on t w o sinusoi dal bands that are out of phase by a factor of (See Figure 2 6 ) Typically the electron (hole) state s found above (below) the intersection point are completely separate, but in graphene the electron states on the left (right) share a band with the hole stat es to the right ( left) and vice versa. This

PAGE 36

36 c harge conjugation implies that in graphene the wave equations of electrons and holes of momentum and respectively, are coupled. 23 The relativistic behavior of particles allows for very peculiar physical phenomena to be observed in graphene. O ne of the most exotic is Klein tunneling the perfect transmission of relativistic particles through arbitrarily high and wide potential barriers via a variation of the process known as quantum tunneling. 48,49 In the case of relativistic chiral particles, tunneling occurs due to energy matching of the wavefunction of the incident hole with that of the conjugate electron at the barrier ( Fig. 2 7 ). This occurs when the projection of the pseudospin along the direction of motion is matched for two conjugate particles (electron /hole pair) scattered at a potential barrier in a phenomenon te rmed chirality 50 The example in Fig ure 2 7 depicts a hole incident on a potential ba rrier of arbitrary dimension. The conjugate electron carries the charge across the barrier before being converted back to a hole state of equal energy at the other side. For electrons (holes), t he values for are defined as negative (positive) to the left (right) of where the two bands intersect Assuming that the barrier height is larger relative to the Fermi energy, the transmission probability is a pproximately, (2 47) where is the angle of incidence, is the component of the momentum normal to the barrier, and is the barrier width. Note that f or the transmissi on probability is unity! This so called gedanken tunneling may explain another anomalous property of graphene finite minimum conductivity. Graphene does not exhibit an insulating state even at the Dirac point where the semimetallic electronic structur e and a vanishing

PAGE 37

37 density of states would suggest zero average carrier density. In fact, at the zero carrier limit the conductivity approaches the universal conductivity quantum, 51 It is well established that disorder in 2 D crystals induces local potential barriers which cause the n junctions). 52 This is known as Anderson localization and leads to a metal insulator transition at finite tempera tures. Surface measurements with a scanning single electron probe concluded that the local disorder length scale was approximately 30nm 53 The instrument was able to resolve randomly distributed regions of posit ive and negative charge Chiral tunneling in graphene, however, allows particles trapped in these through the material thus suppressing localization. 54 This resul t is worrisome in the context of electronic devices which, much like a leaky faucet, must be turned off complete ly to avoid waste. Ultimately, t his characteristic may limit the potential of graphene as a candidate material to replace silicon in convention al electronic devices and should motivate the need to develop alternative device architectures for graphene based circuitry The existence of massless Dirac fermions in graphene can be confirmed experimentally by applying a magnetic field and carefully m easuring periodic fluctuation s in observable quantities (i.e. conductance quantum capacitance, etc.) For example, the value for can be obtained by the carrier density dependence of the cyclotron mass, which is semi classically defined as follows: (2 48)

PAGE 38

38 Here is the 2D area of the cyclotron orbits in space and is defi ned as Using the linear dispersion relation we find, (2 49) Values for the effective cyclotron mass are obtained from the temperature dependence of the Shubnikov de Haas oscillations (SdHO) in mesoscale conductance measurements at various magneti c and gate fields (see Figure 2 8 A ). This procedure uncovers a square root dependence of the cyclotron mass with respec t to carrier density ( Fig. 2 8 C ), which is expected for massless Dirac particles, and for which the Fermi velocity is a fitting parameter, (2 50) Magneto oscillations can also reveal more subtle behavior of the carriers in graphene, such as, a rguably the most studied effect in graphene the fractional quantum Hall effect (QH E). 55 This phenomenon is observed by measuring the longitudinal resistance, under magnetic field for varying induced carrier concentrations For weak magnetic fields ( ), the resulting SdH Oscillations represent broadened Landau Levels whose quantization cannot easily be distinguished. However, as the magnetic fiel d becomes more intense (B>8T), the Landau Levels become discretized for SdH oscillations where the longitudinal resistivity falls to ze ro. 56 Under these conditions, the QHE can be observed by plotting the Hall conductivity, versus the gate voltage or carrier concentration (the latter is shown in Figure 2 9 ). Hall conductivity is calculated from the me asured resistivity, as follows: 57 (2 51)

PAGE 39

39 an d is plotted in increments of Single layer graphene is unique in that it exhibits conductivity plateaux at half integer values ( etc ) of these quantize d units, with th e first plateaux at 58 Unconventional QHE behavior is also observed in bi layer graphene which exhibits plateaux at full integer values but no plateau at the origin. This effect is well explained for systems consisting of relativistic particles for which the Landau quantization resembles the behavior predicted by QED theor y further validating the Dirac nature of particles in graphene. 59 Therefo re, by analyzing the QHE of the samples it is possible to unambiguously identify high quality single and bi layer graphene samples from these measurements. In addition, this leads to the significant result that at zero energy the Landau level is shared eq ually by electrons and holes providing an interesting system for probing exciton interactions 2.1.6 Extrinsic Carrier Properties Electrons in graphene are bipolar: they are at the same time exceedingly sensitive to their surroundings, but decidedly ch emically inert. The cause of this behavior is orbital hybridization and the result is a chemical ly stable material with electronic properties that are readily modified. In the basal plane of graphene and graphite carbon atoms are strongly bound to the ir neighbors by the overlapping orbitals ( bonds) These robust bon ds are strong er than those found in diamond, and chemically inert in most ambients up to several hundred degrees Celsius. 60 I t turns out however, that isolated sheets are more reactive than their supported counterparts in graphite 61 Spontaneous ripples observed in suspended graphene 62 indicate regions of local curvature where a reduce d activation barrier for che mical bonding can be expected. Despite the enhanced activity of the in

PAGE 40

40 plane carbon atoms in graphene, at ambient conditions, chemistry is limit ed to edge and defect sites where broken aromatic chains are naturally susceptible to reactions with the environment. 63 In contrast to the bound electrons, t he charge carriers in graphene are found in delocalized orbitals oriented perpendicular to the surface. Thanks to the 2D nature of graphene, the surrounding potential landscape is never more than a D ebye length away so that carriers prox imal to an external charge will interact with it. The low DOS limits self screening effects and implies that the nearby charge of even a single molecule can be sensed by observing deviations in the average energy of electrons on the Fermi surface. 64 This is analogous to a transfer of charge into or out of the graphene sheet, raising or lowering the Fermi level, and thus changing the total carrier concentration of the graphene. Accordingly, t he carrier density in graphene can be t ailored in a number of different ways : atomic or molecular charge transfer doping 65 71 substitution al doping, 72 76 contact to metals, 77,78 substrate interactions 79 82 or application of a gate field 3,47,83 It should be not ed that the carrier mobilities in graphene remain high at device relevant carrier concentrations ( ) 84 making it a candidate channel material for high speed transistors. The room tem perature mobility of graphene on SiO 2 has been shown to exceed 85 limited primarily by the scattering originating from the SiO 2 surface. 84 By eliminating the influence of this extrinsic scattering the room temperature mobility can reach values almost double that of semiconducting carbon nanotubes. 86 Reducing the temperature to limit acoustic phonon scattering, mobilities e xceeding for graphene on hexagonal

PAGE 41

41 Boron Nitride, 87 for suspended graphene 88 and for graphene on HOPG 89 have been observed. These values surpass even th os e of nearl y perfect compound semiconductor crystals like InSb, 90 and 2 dimensional electron gases (2 DEGs ) found in complex AlGaAs/GaAs heterostructures at milli Kelvin te mperatures 91 Indeed, ballistic transport has been observed in graphene devices for which th e mean free path is several orders of magnitude longer ( ) than typical device dimensions. 92 Some relevant experimental re sults showcasing an array of experimental techniques, are summarized in Figure 2 10 To find application as a channel material for transistor devices it is necessary to be able to switch the conductivity of the graphene channel on and off. A consequence of the chiral behavior of its charge carriers is that this cannot be done by electrostatic gating alone Inducing a band gap would create insulating states into which the Fermi energy could be tuned, thus reducing the conductiv ity to zero (at zero temperature). One method by which a band gap can be generated, termed quantum confinement reduces the graphene sheet to a thin 1 D wire. This is akin to the quantum mechanical particle in a box problem. The energy levels are q uanti zed in the lateral dimension of the wire creating forbidden states near the Dirac point. 93,94 Han et al. first demonstrated this effect in graphene nanoribbons fabri cated by e beam lithography ( Fig. 2 11A ) 95 For nanoribbons that are less than 25nm in diameter, an energy gap is formed that is proportional to the inverse of the ribbon width : 96 (2 52 ) The situation is complicated by e dge effects arising from the abrupt change in bond character of atoms near the edges. 97 Carefully experimental study of the temperature

PAGE 42

42 dependent scaling properties of the gapped nanoribbons suggests that the gap is primarily due to defect induced localized states. 98 100 True quantum transport phenomena, such as Coulomb bl ockade and Fabry Perot interference (See Figure 2 11B ) 101 are only observed when atomically smooth edges are created carbon nanotubes 102 104 or crystallographic tearing 105 Stacking sh eets of graphene to form bi tri and multi layers also yield s non trivial alter ations to the band structure ( Fig. 2 12 ) Electrons in bilayer graphene (BLG) behave like massive fermions while retaining their semimetallic chiral nature. Trilayer graphene exhibits a band overlap. Five or more layers are generally consider ed to behave like bulk g raphite for the following reasons: (1) T he Debye screening length in the c plane direction is 106 which is equiva lent to two layers. As such, the middle layer is completely screened from the interfaces ; (2) For the same reason, five layers cannot be gated (even with a top and bottom gate) due t o shunting through the bulk; (3) The existence of several massive and massless particle species makes it difficult to deconvolute the transport behavior ; ( 4 ) The conduction and valance band overlap (>30meV for three layers) leads to metallic conduction. Sta c king order also plays an important role in the electronic properties of multilayer graphene Bernal, or AB A stacked, layers behave differently from turbostratic or rotationally (random rotations) stacked graphene. For single layer graphene the local potential landscape is identical for the two atoms in the unit cell. This is in contrast to a sheet of hexagonal Boron Nitride ( h BN) where the broken sublattice symmetry results in a wide bandgap semiconductor Similarly, if graphene is placed on top of hBN, the interaction with the local periodic potenti al of the hBN

PAGE 43

43 substrate causes the A and B atoms in the graphene lattice to become inequ ivalent (a second order effect), resulting in a bandgap. 82,107 S tacking can also alter the local potential landscape and under t he right conditions lead to a symmetry breaking in layered graphene For instance, i f a perpendicular electric field is applied to Bernal stacked bilayer graphene the symmetry breaking also induces a small bandgap. By contrast, t he in plane electronic pr operties of rotationally stacked graphene actually resemble th ose of decoupled single layer graphene sheets in series. 108 2.2 Graphene Growth Techniques It is not surprising that the fabrication of a single atomic laye r of carbon pose s a number of significant technical challen ges. However, since the discovery of electrically isolated grap hene in 2004, graphene has been produced rather unexpectedly by a variety of methods and under a wide range of conditions This section will describe the fundamental mechanisms for graphe ne growth by the most common of these methods: catalytic chemical vapor deposition and silicon carbide decomposition. A brief overview of the standard technique for transferring graphene from these growth sub strates to more technologically relevant insu lating substrates will also be presented. 2.2.1 Catalytic Chemical Vapor Deposition Chemical vapor deposition (CVD) is a process for depositing highly ordered, solid, thin film materials from gaseous chemical precursors. Purified precursor materials ar e volatized typically thermally, but also with the assistance of inductive fields and pumped through a reaction chamber, where they are adsorbed onto the desired substrate. The surface of the substrate often acts as a catalyst to promote the decomposi tion of the precursor species and the formation of a stable solid film. Unused precursor and reaction by products are swept out of the chamber by the continuous gas

PAGE 44

44 flow. In this manner, uniform films of a wide array of materials can be deposited with a great deal of control. Before graphene, c atalytic CVD was well studied as the predominant growth technique for high quality carbon nanotubes. 113,114 Samples ranging from isolated single walled nanotubes, 115 to arrays, 116 and high densit y vertically aligned films 117 have been grown via this method. C ontrol of electronic struct ure, 118 growth mode, 119 yield, 117,120 and selective growth of single or multi wall nanotubes 119 was achieved by varying the substrate, catalyst and growth conditions This range of control makes the technique ideal for the synthesis of large area graphene. In fact, t he growth of graphitic material through vapor phase depos ition is not a new concept. E vidence for the growth of few layer graphite systems existed as early as 1976 121 and w as further explored by surface scientists during the following decade. 122 125 Small s ingle layer samples were found routinely on single crystals of Pt(111), 126,127 Co(0001), 128 Ni(111), 122 Ru(0001) 129 and Ir(111) 130,131 in ultra high vacuum (UHV) with various carbon feedstock. This studied almost exclusively as an ideal surface for calibrating STM prob es a possible rational e for the lack of reference to these early studies in the literature. Today, growth of monolayer graphene is typically carried out in a horizontal tube furnace using methane as the carbon feedstock and hydrogen as a reducing carrier gas ( Fig. 2 13 ) Pressures down to and temperatures around are common. Here we will discuss the fundam ental processes controlling the nucleation and growth of these graphene films on polycrystalline metal su bstrates.

PAGE 45

45 The amount of carbon that is supplied to the catalyst surface is limited by the mass transport across the fluid flow boundary layer and by the rate of carbon sequestration ( by graphene growth or diffusion into the bulk). 132 The mass flux across the boundary layer is given by, ( 2 53 ) where is the gas flux coefficient, is the gaseous carbon species concentration, and is the surface carbon concentration. The diffusivity of carbon in the boundary layer increases rapidly as the total pressure drops, and because the boundary layer ( ) thickness changes only sl ightly, the flux coefficient also increases with decreasing pressure, The practical result is two growth regimes, a supply limited growth at ambient pressure CVD (APCVD) conditions, and a surface reaction limited growth for low pressure CVD (LPCVD). Once the carbon has reached the surface, t wo growth modes are possible for CVD grown graphene : surface catalysis or segregation The former involves a metal catalyst with a carbon solid solubility that remains very low ) even at elevated temperatures. In this case, the carbon does not diffuse in to the bulk and the entire reaction takes place at the surface ( Fig 2 14A ) The role of the catalyst substrate in this process is three fold: (1) hydrocarbon d ecomposition, surface diffusion, and catalysis. The process is strongly self limiting due to the decrease in catalyst reactivity as a function of graphene coverage. Hydrocarbon adsorption and subsequent decomposition is necessarily reduced as the graphen e layer prevents further access to the catalyst surface.

PAGE 46

46 For catalyst s with a greater affinity for carbon the situation is different. Although, the same surface reactions are free to take place, a t high temperatures i t is energetically favorable for car bon to diffuse into the bulk of me tals like Ni and Co ( Fig. 2 14B ) As a result the total amount of carbon available to the catalytic syste m is not self limiting. Upon cooling, the carbon is rejected from the lattice due to the temperature dependent solubility at which point a surface driven catalytic reaction to form graphite can take place The thickness of the graphite is dependent on the amount of carbon that has diffused into the metal and on the details of the cooling cy cle. 133 If the rate of cooling is very high, then the diffusion is quenched an d the carbon is frozen into the lattice at non equilibrium concentrations. On the other hand, if the cooling rate is to o slow, then carbon atoms diffusing throughout the bulk towards the surface are likely to encounter other carbon interstitials to form p airs and eventually cluster. This is especially true at grain boundaries and dislocations where the solubility is higher and anomalous diffusion can occur. If the cooling rate is just right, roughly then the carbon is expelled quickly to the surface w h ere it has enough thermal energy for bond formation. The growth kinetics for surface cataly sis and segregation involve similar thin film growth processes: adsorption/desorption (adsorbate density ), surface and bulk diffusion, cluster formation nucleation and attachment/detachment (domain growth ). 134 Each of these processes is temperature and pressure dependent and sensitive to the relative concentrations of the precursor gases. F or a given temper ature and pressure the adsorbate concentration will reach an equilibrium value determined by the sticking coefficient for precursor molecules and the rate of catalytic cracking (i.e. conversion of,

PAGE 47

47 for example, methane into a carbon adatom and four atomic hydrogen ) Locally however, thermal fluctuations or defects will result in regions of critical supersaturation and lead to the formation of stable graphene nuclei. 135,136 As the nuclei grow they deplete the carbon concentration in the adjacent regions, thereby reducing the probability of further nucleation. The nuclei c ontinue to grow rapidly until the remaining supersaturated carbon species ar e incorporated into graphene domains and the domains coalesce. In both the surface and segregation processes, the adsorbed carbon atoms left on the surface after decomposition, or rejected from the bulk during cooling are free to roam the surface, diffusing rapidly at the high growth temperatures. The carbon atoms rapidly form dimers and m ove on to form metastable rings, chains, or clusters as they collect passi ng carbon adso rbates. What these larger structures give up in surface mobility they make up for with a lower potential barrier for bonding to the edge of existing graphene domain s. 135 This may be explained by the stepwise decoupling of the carbon molecules from the metal surface. As carbon atoms bond together to fo rm pairs and then more complex structures, they substitute their bonds to the catalyst with new C C bonds. This allows the molecules to sit higher above the surface further relaxing the bond overlap. These molecules or clusters are now more likely to bri dge the spatial and energetic gap and bond to the graphene edge However, these catalytic processes can run in both directions. With sufficient thermal energy the metal can catalyze methane production by reacting atomic hydrogen with carbon adatoms, meta stable clusters, and edge sites (preferentially etching metastable defect sites) This allows for

PAGE 48

48 a natural clean up process to take place in which the graphene domains are constantly being etched away as they grow, eventually resulting in more perfect d omains Imperfections in the graphene films are generally found at the intersection of domains separated by small angle tilt boundaries, which are decorated with edge defects. 137,138 These zero dimensional edge defects are manifested as single pentagon or heptagon structures that stitch toget her the graphene domains. Transport across these orientationally disordered domain boundaries is limited by the series resistance contribution of the domain boundary. 139 An industria lly viable catalyst must be cost effective (polycrystalline) semicondu ctor process compatible (common etchant) self limiting (low carbon solid solubility), thermally stable ( high carbon surface diffusivity ), and strongly catalytic (metallic). Of the com monly available transition metals, only copper satisfies all of these requirements. Copper has exceptionally low carbon solubility levels even at elevated temperatures (see Figure 2 14C ). This allows copper to be annealed very near its melting point maximizing surface diffusion and catalytic activity without incorporating significant amounts of carbon. Even i nexpensive foils o f rolled polycrystalline copper are suitable for growth because t he graphene sheets can be continu ous over terrace edges and substrate grain boundaries Furthermore, by appropriately tuning the growth conditions, it is possible to obtain large single crystals of graphene on copper 140 142 2.2.2 Silicon Carbide Decomposition An alternative method to producing electronically isolated graphene is to grow it direct ly on an insulating substrate. Ultrathin graphitic film growth on hexagonal SiC substrates was first observed in 1975 144 but has more recently been pioneered for

PAGE 49

49 electronic applications by t he DeHeer group at Georgia Tech. 145,146 The technique requires a nnealing pristine SiC wafers to temperatures in excess of in a UHV environment. During annealing, prefer ential sublimation of the Si atoms leaves behind a carbon rich surface which readily catalyzes into graphit e. 147 The process leads to the a thin buffer layer. 148 This so called epitaxial graphene can be patterned and electrically contacted directly on the insulating growth substrate. A wide range of silicon carbide surfaces are available as growth substrates. Several c rystalline polym orphs differentiated by the order and orientation of layer stacking ( categorized by A, B, and C repeat unit s ) are common for grap hene growth : hexagonal 4H (ABCB) 146 and 6H (ABCACB) 149 and cubic 3C (ABC) 150 The growth properties are strongly dependent on the substrate polytype Additionally, SiC has two inequivalent polar crystal fac es, known as the Si face ( ) and the C face ( ) Graphene growth is strikingly different on th ese two faces. For similar growth conditions, the former produces few layer graphene with a single azimuthal orientation with respect to the substrate, 151 while the latter produces thicker rotationally disordered layers (see Fig ure 2 15A ) 152 Careful p reparation of the SiC surface and control of th e ambient conditions is crucial to the growth of high quality graphene. Prior to growth, h igh temperature etching of the SiC surface with atomic h ydrogen can create clean, smooth micron scale terraces with atomic step edges. 153 However, t his now pristine surface undergoes dramatic surface reconstruct ions during the subsequent annealing process es 154 The typical surface phase p rogression for the Si face in UHV is as follows: (a) Si rich ( )

PAGE 50

50 phase below (b) intermediate, ( ) phase near (c) intermediate, ( ) phase near (d ) carbon rich buffer layer ( ) phase above and ( e) graphene epitaxy near The uniformity and grain size of the graphene is related to the continuity of the intermediate phases and carbon rich buffer layer The exact structure of the buffer layer is the subject of some debate, but is generally ac cepted to consist of a graphene like array of carbon atoms that are bound to the underlying SiC lattice. 155 The continuity of the buffer layer is critical to reducing the occurrence of deep pits during the subsequent growth phase. 156 It may also help to decouple the graphite overlayers from the SiC substrate. Better c o ntrol of the surface morphology during these phase transitions should in principle improve the quality of graphen e epitaxy. Under UHV conditions, t he SiC phase transitions occur far from equilibrium ( i.e. during Si sublimation) and can result in highly non uniform growth. The situation is improved by supplying a background vapor pressure of Ar 157 or s i lane 158 to bring the system closer to thermodynamic equilibrium. This can also be achieved by confinement controlled growth in which the substrate is heated in a sealed graphite crucible with a controlled leak. 159 As the silicon sublimates, the pressure in these vesicles builds, ultimately reaching an equilibrium vapor pressure thus inhib iting further sublimation. Subsequent graphene nucleation is suppressed until much higher temperatures ( ) are reached. T he increased reaction temperatures in these equilibrium pressure cells enhance surface diffusion and allow for more complete su rface reconstruction s The resulting surfaces are free of etch pits and exhibit large ( )

PAGE 51

51 terraces ( ), separated only by short ( ) edge planes, roughly the height of one SiC unit cell. G raphene nucleation has been observed to occur p referentially on certain crystallographic planes. T he ( ) plane s characteristic of step edges after H 2 etching consist primarily of dangling bonds which may reduce the activation energy for silicon sublimation 16 0 Growth along these edges is typically not self limiting (even for the Si terminated face) and domains are gene rally small and defective compared with the graphene n ucleated on ( ) terraces or vicinal planes. 161,162 The reduced activation energy required for growth at the edges can be used to fabricate self assembled graphene nanoribbons along the step edges; 163 however, this also results in significant thickness variation across the wafer ( Fig. 2 15B ) Furthermore, instabilities at the ( )/( ) plane junction arising from the competition between capillary smoothing and curvature drive n edge roughening can result in finger like growth on the ( ) terraces. 164 These effect s can a lso be controlled somewhat by the presence of an inert atmosphere and Si background vapor pressure Multilayer growth in epitaxial grap hene, it turns out, may not be a significant issue due to the nature of layer stacking. In contrast to the AB stacking in HOPG, graphene on the carbon terminated face of 4H SiC grows with a high density of rotational stacking faults Adjacent carbon sheets that are rotationally stacked become electronically decoupled and thus preserve the Dirac like carrier behavior of a single sheet of graphene. 108 As a result, nearly perfect linear dispersions half integer quantization, and ultrahigh mobilities have been observed on SiC grown multi layer g raphene. 112,165

PAGE 52

52 Top gated devices made directly from these substrates consistently exhibit the highest field effect mobilities ( ) for SiC grown graphene. Cost and complexity may ultimately limit e pitaxial graphene to a subset of electronic applications. Particularly for high power, high temperature electronics for which the robust SiC substrate is well suited. 166 The growth of SiC as tha t of any compound semiconductor remains a challenge due to the increased number of kinetic processes that exist in binary crystals This is most easily illustrated by the relative wafer costs compared to elemental semiconductors ( ). The additional requirements for ultrapure processing conditions (up to UHV) and large thermal budgets subsequently required to form graphene may further limit the use of this material to application s in harsh environments 2.3 Raman Spectro scopy 2.3.1 Basics of Inelastic Optical Scattering Light interactions with matter can provide rapid, quantitative, non destructive, characterization of materials. Raman spectroscopy is based on inelastic scattering arising from electron phonon interacti ons. I ncoming electromagnetic waves interact with quantized lattice vibrations by polarizing the electr on distributions in atomic bonds. In other words, t he incident light causes the electron cloud to oscillate which in turn causes the atoms to vibrate Th is interaction with the lattice vibrations absorbs or augments the energy of the electron s depending on the available vibrational modes and quantum selection rules When the electron s finally relax and scatter a photon it will have a different energy than the incident photon The resulting change in frequency, known as the Raman shift, provides characteristic information about the atomic constitution, bonding character, and impurity concentration of the material

PAGE 53

53 Figure 2 16 illustrates the Raman scattering mechanism. Diagrammatically, we see that the incident light is absorbed by the molecule or bond, promoting it into a virtual excited state. Statistically, the system will return to the initial state in a radiative pro cess known as Rayleigh scattering however, some probability ( ) exists that it will relax to a different state by coupling to an optical phonon If the final state has more energy than the ground state (phonon is created ) the emitted photon is red shifted (Stokes shift) Less likely, is a transition from which the electron cloud gain s energy (phonon is annihilated) and emit s a blue shifted photon (anti Stokes shift). Since the probability of phonon creation and annihilation is determined by Bose Einstein stat istics, the relative intensity of the shifts is propo rtional to: 16 7 (2 54 ) where n is the number of phonons with energy, Therefore, barring certain cases where quantum selection rules or photoluminescent interference precludes its use, Stokes Raman is prefer able due to the higher signal intensity. Finally, if the incident excitation energy coincides with an electronic transition, then the process is resonant and the intensity is enhanced. The electron phonon interaction is analogous to the classical damped, forced, harmonic oscillator, where the damping energy is related to the polarizability and the driving force is equivalent to the oscillating electric field created by the incident light. For perturbatively damped systems such as this, the resulting peak s approach Lorentzian functions, with line widths that are inversely proportional to the phonon lifetime. 168 The peak intensity is a complex fun ction of the polariz ability, which itself is time dependent and a fu nction of the vibrational mode.

PAGE 54

54 Raman spectra are plotted as the intensity of the scattered light versus the Raman shift ( ) in inverse wavenumbers ( ) Lasers are commonly used as excitation sources because they are monochromatic and their intensity make s up for low scattering prob abilities Very efficient notch or edge filters are used to block the Rayleigh scattered light so that high gain photodet ectors can be used to capture low intensity Raman features. 2.3.2 Spectroscopy of Graphene Raman is a low probability process that is best suited to study surfaces like graphene. Surface sensitivity can be tuned somewhat by the choice of incident radiation, while quantum selection rules determine the coupling cross section s for interactions between specific inciden t wavelengths and the vib rational modes of the lattice. Three characteristic Raman peaks are generally used to investigate the thickness, crystalline size, defect density and doping level of graphene : the G band ( ), the D band ( ), and the 2D ba nd ( ) The graphite mode (G band) is characteristic of the in plane stretching in carbon s The associated quantized vibrational modes are the longitudinal optic (LO) phonon and the in plane transverse optic (iTO) phonon. 169 The peak positions for these two phonon modes are highly sensitive to strain, so although they overlap exactly for graphene, they become split for carbon nanotubes and strained graphene. 170 The G band position is also highly sensitive to doping (Fermi level shifts) This is due to the strong electron phonon coup ling that arises from the inability of the electron cloud to keep up with the high frequenc y in plane atomic vibrations ( non adiabatic relaxation ). 171

PAGE 55

55 This makes the G band ideal for probing work function shifts in graphene as a result of chemical doping or field effect modulation. The 2D band (al band ) is the result of a double resonance process by which a phonon scatters the system between two electronic states. 167 This is in contrast with more common non resonant (no electronic transitions) and singly resonant (one photoexcited elec tronic transition) processes, and can occur with one or two scattering phonons. In the first case ( Fig. 2 17A ) an electron is photo excited into the conduction band of the graphene and immediately transitions to another electron ic conduction state by scatter ing a phonon, Since the DOS of graphene is continuous, the re is always an available state above the Fermi level into which the electron can transition before relaxing back to the valence band by scatterin g a photon. In o rder to conserve momentum (excluding symmetry breaking disorder) a second phonon must backscatter the electron into a virtual state with the same wavevector as the initial photoexcitation ( Fig. 2 17B ). It turns out that the Ram an shift for the DR process is highly dependent on excitation energy causing the peak position to increase with increasing laser energy. The DR process provides a powerful method of probing the band structure of graphene 172 In this way, the 2D band can be used to ident ify the number of layers as the electronic structure changes from a sin gle Dirac cone for graphene, to several parabolic bands for bilayer and multilayer graphene. 173,174 As the number of layers increases, the shape of the 2D band transforms from a single Lorentzian to multiple overlapping peaks for multilayer graphene The electronic band structure is also highly sensitive to changes in layer stacking 175,176 substrate 177,178 and environmental effects 109

PAGE 56

56 The Raman disorder mode s ( D band s) are the result of symmetry breaking in the two dimensional graphene lattice. The sensitivity of phonon modes and electronic structure to the local lattice symmetry make Raman spectroscopy attractive for probi ng defect structures in carbons. The requirement for conservation of momentum in the electron phonon scattering process can be mediated by elastic scattering with a defect. 167 For this reason, the single phonon D peak is found at roughly half the frequency shift of the two phonon 2 D peak. Both zero and one dimensional defect structures have been extensively studied in graphene. The evolution of the D peak as a function of ion bombardment reveals that the average distance between point defects can be accurately determined from the ratio. 179 I n the immediate vicinity of a defect (~1nm) the D band arises in resp onse to structural disorder that destroys the local phonon dispersion and at longer length scales ( ) mixing of Bloch states at the edge of the Brillouin zone causes a further enhancement of the D band. 180 Studies of two dimensional defects in graphite have produced similar approximations for crystallite size. 181,182 By comparing the Raman and X ray diffraction (XRD) spectra of nanographite samples with different domain sizes, it has been d etermined that the ratio is inversely proportional to the domain size. 183 This e ffect is mirrored in thin graphite and graphene samples and holds for domain s up to 500nm in diameter which makes Raman well suited to study the growth and nucleation of graphene 184 2.4 Organic versus Inorganic Transport Phenomena 2.4.1 Isolated States, Localized Levels, and Continuous Energy Bands Electr ons in an atom are confined to discrete energy levels determined by the rules of quantum mechanics. As two atoms are brought together, the wavefunctions of

PAGE 57

57 the valence electrons become superimposed forming symmetric (bonding) and asymmetric (anti bonding ) energy levels. Interactions between multiple atoms in a molecule cause these levels to split eventually forming bands with a finite distribution of en ergy levels (equal to the number of electrons in the molecule) In contrast, t he continuous energy ba nd s in crystalline semiconductor s arise from the interaction of valence electrons with the (nearly infinite) periodic potential of the lattice. Molecular or polymeric crystals provide a hybrid of these models, as periodic intermolecular interactions give rise to continuous band like behavior. Therefore, t he relevant electronic transport mechanisms for most semiconductors can be di vided into two categories : (1) localized hopping transport, and (2) delocalized band transport. The carrier wavefunctions in organics are typically localized on individual small molecules or linear segments of a polymer chain. The intra molecular transport in organic molecules can be quite efficient due to the delocalization of conjugated states. Conjugated systems exhibit extr aordinary conductivity when taken to the quasi infinite limit, like sheets of graphene, 185 nanotubes, 186 or carbon chains. 187 However, most molecules are small compared to the probe (device channel) length, and therefore th e conduction is d ominated by a much slower, thermally assisted hopping mechanism. Phonon s provide additional kinetic energy to carriers that are localized by the disorder in the organic crystal. This additional energy al lows the carriers to overcome potential barriers a ssociated with non uniform arra ngements of molecules ( Fig. 2 18 A ). For systems with strong electron phonon coupling (i.e. organic semiconductors) the temperature dependence of the mobility is given by: (2 55)

PAGE 58

58 where is an experimental parameter with a typical value between and 188 At low temperature or high fields, the hopping becomes dominated by tunneling between neighboring states, and the mobility found to be: (2 56) w here is the electric field and is the perm ittivity of the semiconductor. Typically room temperature mobilities for organic semiconductors are in the range of to 189 Semi p eriodic orbital overlap between molecules or polymer chains can occur if they are arranged with a high degree of crystallinit y. In such cases, band like transport can take place although the mobility is reduced compared to inorganic crystals due to the limited bandwidth (i.e. number of energy levels available) for the carriers to to as the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO). The long range periodicity of inorganic crystals gives rise to the formation of continuous energy bands. 190,191 The ca rrier mobility in conventional semiconductors is a function of this band structure and limited by electron phonon and ionized impurity scattering Specific ally, we can define an effective mass, for carriers which depends on the curvature of the Fermi surface: (2 57) Taking into account acoustic and optical phonon scattering, the carrier mobility can then be approximated by: 192 (2 58)

PAGE 59

59 We observ e from this that carriers are highly delocalized their DeBroglie wavelengths ranging from to and limited by intrinsic phonon scattering at elevated temperatur es ( Fig. 2 18 B ) This is in stark contrast to the phonon assisted behavior observed in organics, but as we are about to see, another important distinction exists between these two classes of semiconductors. 2.4.2 Carrier conc entration The conductivity of inorganic semiconductors is in large part determined by the equilibrium majority carrier concentration On the other hand, t his picture does not hold for organics which have a very limited number of intrinsic carriers ( ) 193 For the case of inorganic semiconductors, the intrinsic carrier density is a temperature dependent function of the bandgap and the density of states: (2 59) where the thermodynamic function, F(E), is the Fermi Dirac distribution. This can be evaluated approximately as, (2 60) with th e effective density of states give n by The Fermi level for intrinsic semiconductors is found near the midpoint of the bandgap. A shift in either direction indicates an imbalance of free charge carriers. This can be accomplished by adding a relativ ely small number of immobile dopant species to do nate to or accept charge carriers from the bulk semiconductor. Both types of semiconductors can be doped to increase the carrier con centration and thus increase their conductivities. To accomplish this, sub stitutional and interstitial atoms of a different valency are implanted into inorganic semiconductors. Enough

PAGE 60

60 energy is present at room temperature to ionize these dopants and add to the free carrier concentration. The situation is more complex for disor dered organic systems. Organic systems are generally doped by adding small concentrations of donor or acceptor molecules, however in addition to inducing carriers, these dopant molecules increase the disorder in the system 194 Increasing the spatial and energetic disorder eventually counteracts any increas e in conductivity expected from doping. 195 Furthermore, due to the low permittivity of organic semiconductors, long range Coulombic interaction s between the dopant and the charge carrier are possible. 2.4.3 Bulk Conduction Co nductance is defined by the dynamic behavior of charge carriers subject to an electric field The total current density for a semiconduc tor is the sum of the field driven and diffusion currents: 192 (2 61) Here, is Einstein relationship between mobi lity and diffusivity. The total carrier concentrations are modified by injection, generation/recombinati on processes, is valid only when the equilibrium carrier concentration is large compare d to carrier injection (i.e inorganic semiconductors). Organic semiconductors on the other ha nd, behave more like insulators in that they have very low equilibrium carrier concentrations and a low permittivity This results in vanishing diffusion current s and space charge limited current s (SCLC) under high bias conditions SCLC occurs when in jected carriers are slow to move away from the interface and the strong Coulombic repulsion between unipolar carriers repels additional charge injection The injected current is thus limited by the space charge build up,

PAGE 61

61 which is strongly dependent on the voltage and channel length as expressed by the Mott Gurney Law : 196 (2 62) This neglects the effect of trap states which are filled in the low bias regime and subsequently released under higher applied fields. The situation is complicated f urther by the formation of dipoles at the injection interface. 197 Because the SCLC current is concentration independent, it is a useful tool for characterizing the mobility of organic materials, so long as unipolar injection is guaranteed. 2.5 Conventional Schottky Barriers The i nterface between a metal and a semiconductor plays a critical role in semiconductor devic e physics. T he charge transport across such an interface is largely dictated by the relative level of the metal work function and the semiconductor Fermi energy 36,37 T he offset of these levels determines the magnitude of the conduction barrier at the interface and whether the passage of carriers across the junction will be rectifying (S c hottky) or resistive (Ohmic) in nature. Anisotropic barriers t o electrical conduction were first observed by Braun, in 1874, when measuring the current across a fine metal wire in contact with the surface of a small lead sulfide crystal. 198 Early radio receivers in fact w ere based on these so called point contact rectifiers 199 although a clear understanding of the physical phenomenon was not established until years later 2 00 Today rectifying metal semiconductor contacts are commonly used for DC and high frequency applications, solar cells and photodetectors, and a s the gate electrode in metal semiconductor fiel d effect transistors (MESFETs) and high electron mobility tran sistors (HEMTs)

PAGE 62

62 2 .5 .1 Metal Semiconductor Interfaces at Thermal Equilibrium: Schottky Barrier Formation An accurate picture of how a barrier is formed when a metal and a semiconductor come into contact is necessary to un derstand the transport across s uch a junction If a metal and an n type semiconductor (see Figure 2 19 ) are brought into electrical contact, electrons will flow from the semiconductor into the metal until thermal equilibrium is reached and the chemical potent ials of the two sides are balanced (i.e the Fermi level of the semiconductor and the work function of the metal are aligned). A n energy barrier, now exists at the interface of the two materials. If the barrier is small ( ), t hen the metal and semiconductor will conduct current with only a small linear contact resistance. For large barriers the conduction behavior is non linear, accommodating large currents in forward bias but only negligible current in reverse bias. For the ideal case, the details of the interface can be ignored and the magnitude of the barrier is defined as follows: (2 63 ) (2 64 ) where and are the semiconductor bandgap and electron affinity, respectively, and is the metal work function. As the c harges move across the junction during equilibratio n, a space charge region is established in the semiconductor result ing in a steady state built in potential that opposes additional accumulation of charges near the interface. In order for the Fermi energy of the two materials to remain coincident, t he semiconductor energy bands must bend (according to the Poisson relation) away from their equilibrium flat band levels by an amount equal to the built in potential For an abrupt junction (AJA) t his band bending has a c

PAGE 63

63 (2 65 ) where is the permittivity of free space, is the applied field, is the electron charge, and is the carrier density. The charge accumulat ion on the metal surface opposes that in t he semiconductor depletion width and creates a junction capacitance. I n reverse bias the barrier to conduction causes additional charges to accumulate near the interface. The junction capacitance is therefore a functi on of the bias voltage and written a s, (2 66 ) where is the space charge density. Barrier height and doping concentration can be extracted from plots of the junction capacitance as a function of bias voltage ( ). 2.5 .2 Thermionic Diffusive, and Field Emission Theory Charge transport across an MS junction can occur via t hree basic processes: (1) Thermally activated emission over the barrier, 200 (2 ) Diffusion of carriers a cross the depletion region 36 or (3 ) quantum mechanical tunneling through the barrier. 201 All of these processes are majority carrier do minated for barriers larger than Thermionic emission (TE) takes place whe n carriers with energy exceeding the conduction band energy at the MS interface ( ) travel across the junction. If we ignore recombinat ion and fast decay processes, then the barrier can be approximated as an abrupt junction with a constant quasi Fermi level throughout the depletion region. The current density is then obtained by summing the contribution of these energetic carriers:

PAGE 64

64 (2 67 ) where is the component of the carrier velocity along the bias direction. And is the electron density for an infinitesimal energy range, given by: (2 68 ) f or which is the density of states, and is the Fermi Dirac distribution function. Assuming a non degenerately doped semiconductor with parabolic energy bands, the TE current density from the semiconductor to the metal for a given applie d bias is defined by: (2 69 ) where is the Richardson cons tant, which accounts for the dispersion relation of the semiconductor. 202 Since the barrier height is fixed for carriers traveling from the metal to the semiconductor, the corresponding current density is, (2 70 ) Finally, by summing these opposing terms we arrive at the total thermionic current density, (2 71 ) E xcept for the saturation current which is principally determined by the barrier height instead of the band gap, the diode equation is very similar to the transport equation for a junction. Most high mobility sem iconductors, such as Si and GaAs are adequately described by this theory So far, we have neglected t he diffusion of carriers across the depletion region, but for low mobility or disordered semiconductors, this is the dominant forward bias

PAGE 65

65 conduction me chanism The current density in the depletion region is dependent on the electric field (drift) and the carrier concentration gradient (diffusion), according to the following equation: (2 72 ) where is the electron diffusion coefficient and is the electron mobility, and t he local electric field is determined by the shape of the depletion region Integrating the c urrent density over the entire depletion region, (2 73 ) and assuming that the carrier concentrations at the boundaries remain at equilibrium, we arrive at the expression of current dens ity for diffusion theory: (2 74 ) The electric field reaches a maximum, at the MS interface and is dependent on the m agnitude of the applied bias. As a result, this expression is similar to that for TE, except that the saturation current density is more strongly influenced by the applied bias and less dependent on temperature. For a given barrier width, a fini te probability also exists that carriers will travel through the barrier as a result of quantum mechanical tunneling That probability becomes appreciable for narrow depletion widths (i.e. degenerate doping or large bias voltages) and low temperatures. I n general this field emission (FE) current is proportional to the quantum mechanical transmission coefficient multiplied by the initial and final state occupancy probabilities By integrating over all energy levels up to the

PAGE 66

66 barrier height we get the the rmionic field emission current (TFE), that is the total tunneling current : (2 75 ) Full analytical expressions for FE and TFE are complex 192 and are omitted here, but we can make a few comments regarding their behavior. Field emission is strongly dependent on applied bias and nearly independent of temperature. This is especially true for th e case of reverse bias, where large voltages can significantly narrow the depletion width and generate very large tunnel currents The TFE current includes not only the tunneling of carriers at the Fermi level, but also the tunneling of thermally excited carriers for which the tunneling barrier (i.e. the depletion width) is narrower. A summary of the expected band bending and idealized current transport mechanisms for various bias conditions is pictured in Figure 2 20 2.5 .3 D eviations from Ideality There are several factors that cause device operation to deviate from these theoretical models. We can add a voltage dependent coefficient to the diode equation, termed an ideality factor to account for these deviations: (2 76 ) The value of the can be determined from the forward bias slope of a versus plot. The ideality factor varies with bias voltage, so typically a range is giv en, with unity representing an ideal diode. Currents across the junction can be affected by several factors including defects in the depletion region that lead to carrier recom bination o ptical/phonon scattering 203,204 and quantum m echanical reflection 205 The existence of s urface states in the

PAGE 67

67 semiconductor can also play a crucial role in determining the barrier height. When the metal and semiconductor are brought into contact, the two come to thermal equilibrium by allowing charges to flow from the metal into the semiconductor. If however, t here are enough unoccupied surface states to accommodate these additional charges, then the Fermi level of the semiconductor remains largely unchanged. As a result of this Fermi level pinning covalently bonded semiconductors, which generally exhibit a hi gher density of surface states than ionic semiconductors, more often exhibit barrier heights that are independent of the choice of metal. 206 The barrier height can also be dependent on applied bias. The charge carriers near the interface of the semiconductor can induce image charges in the metal of opposite polarity. The Coulomb force between t he carrier and its image charge contributes to the potential energy of the carrier and corresponds to a shift in the effective barrier heig ht. The barrier becomes rounded, reaching a maximum value near the interface, but inside the depletion region. The change in barrier height is given by: (2 77 ) The potential energy of the carriers in the semiconductor is dependent on the electric field, and therefore the barrier shift is dependent on the applied bias voltage. Consequently, the image force lowering (Schottky Effect ) is amplified in reverse bias and reduced in forward bias (see Figure 2 21 ). 2.5 .4 Ohmic Contacts In order for any semiconductor device to be of use, it must ultimately be coupled to a metallic contact so that the current can be transmitted with minimal dissipative resistance. A low contact barrier allows charges in the semiconductor to pass

PAGE 68

68 (relatively) unobstructed into a metal contact. These so called Ohmic contacts are ubiquitous in solid state physics and behave like con ducting leads with a characteristic defined by: (2 78 ) This expression can be evaluated analytically, and is proportional to, (2 79 ) for the c ase of low doping concentrations. In this regime, the resistance is proportional to barrier height alone and the contact is TE limited. It turns out that this barrier height can be substantial and thus highly temperature dependent. As the doping concent ration in the semiconductor increases, the contact barrier height decreases and the resistance is dictated by tunneling across the interface, (2 80 ) The contact resistance in either case is reduced by minimizing the work function and Fermi level offset while maximizing the semiconductor carrier density. This is sometimes difficult to accomplish for wide ba nd gap semiconductors with very deep valence bands. Often, degenerately doped layers or heter ojunctions are used to reduce the barrier to injection. Alternatively, rapid thermal annealing (RTA) of the MS interface to induce interdiffusion and a metallurg ical alloying reaction can result in stable and consistent Ohmic contacts on most semiconductors.

PAGE 69

69 Figure 2 1. The hybridization of carbon. Various configurations of the 2s and 2p orbitals form sp1 hybridized linear carbon chains (resonant triple bonds) sp2 hybridized planar carbon sheets (conjugated double bonds), and sp3 hybridized diamond lattice carbon (strongly covalent single bonds).

PAGE 70

70 Figure 2 2. A honeycomb lattice of carbon atoms in graphene. A) The real space Bravais lattice of graphene co nsisting of two interpenetrating hexagonal sublattices (blue and yellow atoms). The primitive lattice vectors are labeled for the yellow sublattice. The nearest and the next nearest neighbors of the atom labeled are designated by the blue and yellow dotted circles, respectively. B) The reciprocal space lattice is rotated by a factor of relative to the Bravais lattice. The primitive lattice vectors are labeled and the and points located at the edges of the first Brillouin zone (shaded region). The unique linear dispersion of graphene is the result of a unit cell consisting of two inequivalent points in reciprocal space.

PAGE 71

71 Figure 2 3. Tight binding approximation of the graphene electronic ene rgy band diagram. A) The full graphene electronic dispersion relation for the first one and a half Brillouin zones (BZ).The calculation includes a wavefunction overlap term, and non zero nearest neighbor and next nearest neighbor hopping amplitudes. Sever al of the high symmetry points in the BZ are labeled for convenience. B) Close up of the linear dispersion in the low energy regime, The Fermi level for undoped graphene is found at these intersections of the conduction and valence band. C) Plot of the constant energy contours in the conduction band as a function of the wavevector components and D) 2D section of the full dispersion along the high symmetry wavevectors (connecting ), illustrating the intersection of the and energy bands at the and points at the edge of the first BZ [Produced with Wolfram Mathematica 7.0, Ref. 43 ].

PAGE 72

72 Figure 2 4. Angle resolved photoemission spectroscopy of the graphene electron energy dispersion. A) A 2D section of the valence band along the high symmetry points. The Fermi level is above the Dirac point because the graphene is slightly electron doped. B D) Constant energy contours of the first Brillouin zone for energies coincident with the Fermi level, the Dirac points, and 1eV below the Dirac points, respectively. The halos are a result of the hexagonal SiC substrate [reproduced with permission from Ref. 44 ].

PAGE 73

73 Figure 2 5. The continuously tunable Fermi level of graphe ne. Ambipolar carriers can be generated in graphene by applying an electric field from an electrically insulating gate electrode. Electrons (holes) are induced in the graphene by a positive (negative) gate voltage, increasing the total number of charge c arriers and thus reducing the in plane resistance of the film. Because the bands of semimetallic graphene are joined at the Dirac point, the Fermi level of the graphene can be tuned continuously [Reproduced with permission from Ref. 3 ].

PAGE 74

74 Figure 2 6. Quantum numbers in graphene Pseudospin and isospin Two additional degrees of freedom in graphene result from the degeneracy of the band contributions of the two inequivalent sublattices (A and B) and the two conical valleys and ). Pauli matrices are used to index these c ontributions to the effective Hamiltonian: pseudospin for the sublattices, and isospin for the valleys. A simplified interpretation of the bands is used to illustrate the conjugation of the electrons and holes belonging to the same energy bands.

PAGE 75

75 Figure 2 7. Klein tunneling in graphene. An unperturbed graphene sheet (top) is subject to a square potential resulting in a p n p junction (bottom). The chiral nature of the relativistic massless fermions allows them to tunnel through potential barri ers of arbitrary height and width. Upon reaching the potential barrier, the incident hole (traveling left to right) conjugates with an electron of matching pseudospin and opposite momentum. The conduction electron travels across the barrier and is conver ted back into a chiral conjugate hole resulting in perfect transmission and a net current.

PAGE 76

76 Figure 2 8. Magneto oscillations in graphene. Shubnikov de Haas oscillations in the transport properties of graphene have been used to confirm the Dirac like n ature of particles in graphene. (A) The transverse component of the resistance is plotted versus increasing magnetic field, where the period of the oscillations is proportional to the cross sectional area of the Fermi surface. (B) The change in longitud inal conductance as a function of applied gate voltage (T= 20K, 80K, and 140K, for blue, green, and red, respectively). The periodicity is determined by the degeneracy of the Landau levels in graphene ( ). These plots can be used to extrac t key parameters such as the cyclotron mass, (C). [Reproduced with permission from Ref. 51 ]

PAGE 77

77 Figure 2 9 Fractional quantum hall e ff ect in g raphene. The Landau quantization of the longitudinal resistance (left, green) and transverse conductance (right, red) measured at B=14T and 4K for graphene (bilayer graphene in the inset). The plateaus in conductance occur at anomalous half integ er for the case of graphene. [Reproduced with permission from Ref. 51 ]

PAGE 78

78 Fi gure 2 10. Sensitivity of the low density of s tate s of g ra phen e to electronic p otentials. (A) Raman spectrograph of ionic liquid gated graphene. The position of the G band is related to the Fermi level of the graphene and thus is related to gate field. (B) The transfer curves of a graphene sensor as it is exp osed to concentrations of NO 2 The device was used to monitor the adsorption of various gases down to a single molecule. (3) Molecular doping of graphene with TFSA ( ( CF 3 SO 2 ) 2 NH ) can be observed by monitoring the carrier concentrations in a Hall conducti vity measurement. (4) STM images of a substitutional nitrogen atom in a graphene lattice p doped by incorporation of N 2 in the CVD growth process. [Reproduced with permission from Refs. 109,64,71,76 ]

PAGE 79

79 Figure 2 11. Quantum transport phenomena in graphene n anoribbons. (A) Lithographically patterned and oxygen etched graphene nanoconstrictions. (B) The magnitude of the disorder induced transport gap in the nanoribbons is inversely proportional to the width of the ribbon. (C) Schematic of the distinction between transport gap and a confinement gap in a nanoribbon with significant edge disorder. (D) A 14nm nanoribbon with pristine nanotube by exposure to an oxygen plasma. (E) Coherent interference and coulomb blockade phenomena observed in the gated differential conductance behavior in the vicinity of the band gap. The nanoribbon exhibits negligible edge disorder. [Reproduced with permission from Refs. 96,101,105,100 ]

PAGE 80

80 Figure 2 12. Stacking g raphene. (A) Inducing a bandgap in bi layer graphene by applying a perpendicular electric fi eld (displacement field). (B) Optical absorption spectra for a gated bilayer device with several displacement fields. The increase in absorption and shift in energy is very clear for the stronger displacement fields, and fits the tight binding approximat ion (right panel). The decrease in absorption for energies immediately below the band gap is also expected since those states are now forbidden. (C) Hall resistance for a trilayer graphene device confirming the conduction and valence band overlap that oc curs in samples with three or more layers. (D) ARPES measurement of the dispersion for 11 layer rotationally stacked epitaxial graphene on C face SiC (only the first 3 layers are visible). The dispersion is a superposition of several single layer graphe ne dispersions as is expected for completely decoupled graphene sheets. [Reproduced with permission from Refs. 110 112 ]

PAGE 81

81 Figure 2 13. Diagram of the kinetic processes during catalytic chemical vapor deposition. The main processes in catalytic CVD growth of graphene are as follows: (i) in flux of the reaction products into the hot zone; (ii) diffusion of molecules across the fluid boundary layer; (iii) catalytic cracking of the carbon feedstock; (iv) surface diffusion; (v) metastable dimer and chain forma tion; (vi) nucleation of graphene domains; and finally, (vii) domain growth.

PAGE 82

82 Figure 2 14. Growth modes of graphene on metal substrates with various degrees of carbon solubility. (A) Growth on Cu proceeds by surface catalysis and is generally self lim iting, while (B) on Ni the growth is dominated by segregation of carbon to the surface during cooling, leading to multilayer growth. Grain boundaries and dislocations serve as carbon sinks (especially for Ni) and nucleation points. These disparate growth modes are the result of the five order of magnitude difference in the solubility of carbon in Cu versus Ni (C and D, respectively). [Reproduced with permission from Ref. 143 ]

PAGE 83

83 Figure 2 15. Growth modes of graphene on the different faces of SiC. (A) Thermal decomposition on the c face of 4H SiC (ABCB stacki ng) yields multilayer graphene with rotational stacking faults that allow the sheets to become electronic decoupled from each other. Fewer layers grow on the Si face, but they are generally AB stacked and electronically coupled like the sheets in HOPG. ( B) Growth proceeds faster on the terrace edges, leading to non uniform growth.

PAGE 84

84 Figure 2 16. Diagram of the Raman scattering process. Incident radiation causes the electron cloud to oscillate, thereby promoting the system into a virtual excited state. The system typically rela xes back to the initial state, emitting a photon of equal energy, in a process known as Rayleigh scattering. In rare cases, the oscillating electron cloud will lose (gain) energy by coupling to an allowed vibrational mode of the system and scatter a red ( blue) shifted photon.

PAGE 85

85 Figure 2 17. The double resonance process in graphene. (A) The defect mediated one phonon, and (B) the momentum conserved two phonon intravalley DR processes. (C) The dispersive nature of the DR process. The Raman peak associ ated with this process is dependent on the excitation energy.

PAGE 86

86 Figure 2 18. Transport mechanisms in organic and inorganic semiconductors. (A) Thermally mediated hopping transport in which carriers are localized by disorder and require additional ener an adjacent site. (B) Band transport, in which delocalized carriers are free to move by diffusion or in response to a field. Phonons and lattice defects act as scattering centers that limit the mobility of the carriers.

PAGE 87

87 Figure 2 19. Schematic of an n type Schottky barrier at thermal equilibrium.

PAGE 88

88 Figure 2 20. Band bending and current transport for MS junctions to n and p type semiconductors at various biasing conditions: (A) Thermal equilibrium, (B) forward bias, (C) reverse bias (D) breakdown.

PAGE 89

89 Figure 2 21. Diagram of image force lowering effect on a biased n type diode. The carriers in the semiconductor induce charges in the metal that lower the Schottky barrier. The barrier shift is bias dependent affecting the transport across the junction.

PAGE 90

90 CHAPTER 3 GRAPHENE SYNTHESIS A ND TRANSFER TECHNIQU ES 3.1 Introduction T he principal challenge to fabricating the graphene based Schottky barrier devices described in the following Chapters is reliably synthesizing macroscale gr aphene on insulating substrates. This C hapter will describe two very different approaches to producing electronically isolated gr aphene. First, w e will discuss improved techniques for the low vacuum CVD growth of graphene and subsequent transfer to insul ting substrates. This method will be used to fabricate the Schottky barrier devices in Chapters 4 and 5. We also describe a method for the site selective growth of few layer graphene directly on insulating SiC substrates via ion i mplantation and t hermal or pulsed laser annealing 3.2 Toward Macroscale Domain Growth via Chemical Vapor Deposition The study of low vacuum CVD growth of graphene was initially put forth as part of rea did not begin until after the seminal works of Reina et al. (Jing Kong Group, MIT) 133 and Li et al. (Ruoff group, UT Austin). 207 Improvements to these original techniques have since I gratefully acknowledge my collaborators for their many contributions, especially Drs. Evan Donaghue and Andrew Rinzler (Sections 3.3 & 3.4), and Drs. Sefaatin Tongay, Brent Gila, and Bill Appleton (Section 3.5). I also thank Dr. Brent Gila for his help with the initial design and modification of the LP CVD system used for these experiments. Finally, I acknowledge the help of Drs. Rajiv Singh and Purushottam Kumar for chemical mechanical polishing of the copper foils. The work presented in this Chapte r is based in part on published results. The published manuscripts and figures have been modified from their original format: Sections 3.3 & 3.4 : Improved Transfer of Graphene for Gated Schottky Junction, Vertical, Organic, Field Effect Transistors. AC S Nano 2012 6 9095 Section 3.5 : Drawing Graphene Nanoribbons on SiC by Ion Implantation. Applied Physics Letters 2012 100 073501; Site Selective Graphitization of SiC via Ion Implantation and Pulsed Laser Annealing. Applied Physics Letters 2012 10 0 193105

PAGE 91

91 come in rapid succession, often being developed independently by several groups in parallel. The techniques described here were refined over the course of several years inspired by and sometimes a nticipating the literature. Despite the pace of improvement, the reproducibility required for large scale integration necessitates further improvements to these techniques. As such, the focus here will be to highlight data that contribute s to our unders tanding of fundamental growth mechanisms 3.2.1 Low Vacuum Catalytic Chemical Vapor Deposition It may be understood that a continuous two dimensional crystal should in theory, be able to grow on a smooth meta l l ic surface. It is much less trivial to ass ume that this growth could occur in the presence of crystal defects, surface roughness, thermal fluctuations, and near ambient base pressures. Still, it proves worthwhile to explore such low vacuum technique s to avoid the cost and complexity of ultra high vacuum. Here, b y low vacuum, we mean operating pressures that can be achieved with a single roughing pump and standard O ring seals. The home built LPCVD system ( Fig. 3 1 ) used in these experiments was designed to maximize the range of processing conditions that could be studied We will briefly describe the primary components of the system, starting from the gas sources. The system allows for mixtures of up to five interchangeable i nlet gases, and is typically stocked with ni trogen, forming gas ( ), hydrogen, methane, and a mixture ( ) of (all supplied by Airgas, >99.99% purity). The tanks are housed in a fume hood ( ) serving as a gas cabinet, and rigged with pneumatic emergency shut off valves. A firs t level of particle filters ( Swagelok, SS 4FWS 05 ) ensures that large particulates do not enter the calibrated flow meters. High precision

PAGE 92

92 rotometers (Matheson Tri gas, FM 1050 series) control the flow rates of the gases down to standard cubi c centimeters per minute ( sccm ) A second stage high purity particle filter ( T.E.M. Filter Company TEM915 ) ensures that no contaminant s are introduced to the chamber during processing. The diameter quartz tube (TGP, 35X38) serves as the grow th chamber and is coupled to the gas lines via Viton sealed quick conne ct couplings (LDS Vacuum, NW 40 Q150 ) and flanges and fittings (A&N, QF 40 XXX) The clam shell tube furnace (Lindberg, ) has a uniform hot zone capable of reaching The rmal cycling is controlled by a 16 stage, digital, proportional integral derivative (PID) feedback temperature controller (Yokogawa, UP150 VN) The outlet has a check valve (Swagelok, SS CHS4 1/3) rated at to prevent a hazardous pressure build up in the tube. The tube outlet is coupled to a unio n cross allowing the exhaust to go to the standard roughing pump, an external turbo pump for experiments requiring or through a double bubbler (ARS) for atmospheric growth. T he roughing pump system is connected via a right angle poppet valve ( A&N LPAV150 CF ) that allows the tube to be held under vacuum for extended periods Total p ressure can be adjusted manually from to with a bellows valve (Swagelo k SS 4BRW ) on the outlet. The mechanical pump vents directly into the laboratory fume hood. A liquid nitrogen trap (A&N, VSCI 80 QF40) prevents pump oil vapors from back flowing into reaction chamber during growth. A filtered purge valve (Swagelok, SS 4P 4) allows the system to be vented manually. The gas lines are all stainless steel tubing coupled by stainless steel Swagelok tube fittings.

PAGE 93

93 The operational procedure for the CVD system is stated here, in brief : (1) Load the samples into th e quartz tube and pump the system down to below ; (2 ) purge all the necessary gas lines for at ; (3) slow ly ramp ( ) to in a reducing or inert ambient to degas sample and chamber; (4) ramp ( ) to to burn off carbon residue; (5 ) perform CVD growth (see standard procedure below) ; (6 ) cool in reducing or inert ambient ( ) until the thermocouple reads below (actual substrate temperature is ); (7 ) close pump bellows valve an d turn off gas flow; (8 ) vent chamber with the p urge valve and unload sample; (9 ) Pump down tube and close pump bellows valve to keeping the tube under vacuum until the next use. The quartz tube s are kept under vacuum to prevent oxidation of the sublimate d copper in the cold zones. Early growth runs were often plagued by micron scale particulates ( Fig. 3 2 ), which were identified as SiO x particles by energy dispersive spectrometry (EDS) analysis Since these are not present on th e sampl es prior to growth, we conclude that the se particulates must originate from the quartz tube. A tantalum enclosure h as subsequently been used to prevent these particles from depositin g on the growth substrate. Tantalum was chosen based on the follo wing merits: it has a high melting point and good mechanical stability ; it is a good oxygen scavenger; it has a low sticking coefficient for Cu, and it is inexpensive. The enclosure also creates a small diffusion mediated reaction chamber isolated from th e turbulent fluid flow in the tube. In 2011, Li et al. 140 found increased grain size s of single layer graphene on the inside of copper foil enclosures formed by rolling and crimping the foil. Rather than crimp our CMP polished copper foil substrates, flat pieces ar e placed inside covered tantalum boats (R.D. Mathis

PAGE 94

94 Company, SB 4/SB 4A) which also improves ease of handling and reproducibility The boats are wrapped with and placed down stream from folded sheet s of fresh tantalum foil ( ) that act as dispos able oxygen scavengers (see Figure 3 1B and C ). Although the precise growth conditi ons used in each experiment vary all standard CVD growths in this thesis unless otherwise noted are based on the fol lowing recipe (beginning from step 5 of the operational procedure described above) After a soak at t he tem perature is ramped slowly to for to avoid overshoot. The samples are then annealed for at to promote Cu grain growth (mean grain size s exceed ed 5mm 2 as determined by optical microscopy). An initial low density nucleation and slow g rowth phase is performed at for with a mixture of and at a total pressure of and flows of and respectively. To guarantee f ull coverage the temperature was dropped to for while increasing the total pressure and methane flow to and respectively. This increases the nucle ation rate between graphene domains and allows large single crystals to be stitched together by smaller domains. We have used a number of techniques to charact erize our graphene sheets. Raman spectroscopy is a fast, non destructive technique that is ideal for distinguishing single layer graphene from multi layer graphene and graphite, 173 and for characterizing disorder, stacking symmetry, and doping of the graphitic films. 184 Raman spectra were acquired with a Horiba Jobin Yvon LabRAM Aramis system using a excitation laser, 1 ND filter, (for mapping) and (for individual spectra) line diffraction gratings, integration times, and averaging. Figure 3 12 shows a typical spectrum for graphene grown on Cu via o ur standard recipe (above) There is no

PAGE 95

95 discernible D peak and the indicative of single layer graphene. The uniformity of the samples can be determined by acquiring spatial Raman map s of the growth substrate Every film that we gro w is compared to previous growth s by acquir ing a minimum of three Raman maps at separate locations along the foil (typically arrays with spacing in and ) Althou gh our films are highly uniform, occasionally we observe local regions of m ultilayer or disorder ed growth. E lectron microscopy is a pow erful tool for understanding graphene growth kinetics Contrast between single layers of graphene and bare Cu can be observed at low voltages ( ) and is attributed to secondary electron (SE) attenuation 208 However, i f the Cu sample has had time to develop a native oxide, charge accumulation in the oxide during imaging results in a drastically enhanced contrast mechanism. Indeed, Jia et al. found that annealing partially grown Cu samples in air is enough to make graphene domains visible by both optical and electron microscopy. 209 In Figure 3 3 very large single crystal domains of graphene are shown on lightly oxidized copper. The gr ains shown here were grown in a process developed after our standard growth technique, in which the hydrogen partial pressure is increased by an order of magnitude while the methane partial pressure remains as low as possible in our system ( ). The domains shown here are approaching the millimeter scale ( ). Further dilution and more careful surface preparation should yield even larger single crystal domains by limiting the nucleation rate. Interestingly, single lay ers of graphene can also be observed by AFM directly on copper using the same annealing technique as described above. In Figure 3 3 and 3 4 the copper protect s the underlying surface reconstruction prov id es a strong contrast

PAGE 96

96 with the surround oxide layer. The terrace dimensions vary greatly depending on the Cu crystal orientation and growth conditions, but the AFM line scan reveals that they are not atomic steps, but rather tens of nanometers in height ( Fig 3 4 B ). Ultimately, these graphene films are used as conductive electrodes, and as such e lectrical characterization of our transferred films is crucial We have performed sheet resistance measurements for graphene grown by o ur standard recipe and compared it t o the baseline growth technique published by Li et al. 207 Figure 3 6 compares the sheet resistance values for 4 0 transferred films of graphene grown using original method and our standard recipe. The films are transferred onto SiO 2 wafe rs using th hot clamping method described in section 3.3.1. A four point Van der Pauw electrode configuration was evaporated (40nm Au) onto the transfer red films. The decrease in sheet resistance can be attributed to the larger single crystal domains exp ected of our standard growth technique. This reduces the number of grain boundaries in the electronic path and thus increases the scattering t ime and mobility values 3.2.2 Chemical Mechanical Polishing Remarkably, graphene domains have been shown to gr ow over step edges and micron scale surface features. Unfortunately features commensurate with the topography of a rough substrate often lead to wrinkling and tearing of the graphene sheets during transfer. Wrinkles are especially harmful for devices th at build vertically on top of graphene, as these can result in highly conductive shorting pathways. Surface roughness also promotes defects and nucleation by providing localized regions of high curvature and a high density of carbon sinks The origin of the roughness for most commercially available foils is the rolling process by which they are manufactured. The situation can be improved dramatically by planarizing the surface prior to annealing and

PAGE 97

97 graphene growth. In an attempt to improve the uniform ity and suppress nucleation we investigated the chemical mec hanical polishing. Copper foils ( purity, Alfa Aesar ) thick were chemically mechanically polished (CMP) at Sinmat Inc. on a Buehler E comet 300/Automet 250 bench top polisher u sing a Suba IV pad (Eminess). The CMP slurry was prepared with colloidal silica ( nominal particle size) in a solution, using benzotriazole as a corrosion inhibitor, and citric acid as a complexin g agent. The acidity of the slurry was adjusted to a pH of using NH 4 OH. Polishing was done with a down pressure of ( ) the platen and head rotating at and respectively, and a slurry flow rate of Approximately of copper were polished away to achieve a smooth surface. Foils were subsequently exposed to a dilute HF ( DI:HF) solution to etch away residual slurry particulates and rinsed in pure DI water. The results of the polishin g can be seen in the representative AFM images in Figure 3 7 A s a result of the CMP polishing, the large features in the Cu foil are completely eliminated and the roughness is drastically reduced from an RMS value of t o This change can also be seen in larger scale SEM images of the foils ( Fig 3 8 A ), where the rolling grooves are readily apparent prior to polishing. The planarized films are so smooth that they provide very little c ontrast for SEM imaging ( Fig 3 8 A Inset). 3.3 Rethinking Graphene Transfer Transferring graphene from the metallic growth substrates remains a challenge for device synthesis. Most conventional transfer techniques are based on the method first

PAGE 98

98 demonstrated by Reina et al. 133 By this met hod, a polymeric s upport layer, typically poly methyl methacrylate ( PMMA ) or poly dimethyl siloxane ( PDMS) is spun and cured directly onto the metal/graphene substrate. The metal is then etched away (HNO 3 or Fe 2 (NO) 3 for Ni and Cu, respectively), leaving the polymer suppor ted graphene floating in the etch solution. The film is re trieve d from the solution using the desired substrate. The final step is to dissolve away the polymeric support layer leaving behind the graphene film on the target substrate. Despite the simplici ty of this technique, results are difficult to reproduce and yields are generally very low. Complete removal of the polymeric (specifically PMMA) support has proved to be nearly impossible without damaging the underlying graphene. Furthermore, the proces s induces defects in the graphene a s observed by an increas ed Raman D peak relative to as grown graphene (on Cu ). Several modifications have been proposed in the literature to improve on this primitive transfer method but none have been successful in ful ly eliminating the defects induced by the transfer process. 210 216 Here we report on a transfer process (depicted in Figure 3 9 ) that increases transf er yields, significantly reduces di sorder, eliminates of polymeric residues, and reduces vertical protrusions that can act as shorting pathways in vertically integrated devices. The process modifications are divided into two parts: (1) Improvements to the physical transfer process, and (2) the addition of a protective metal support layer. 3.3 .1 Hot Clamping and Vapor Dissolution Poor transfer yields during our early efforts lead us to develop a better technique for adhering the graphene/PMMA films to the target substrate. Our technique is modeled after a method used by Wu et al. for transferring large area nanotube films to

PAGE 99

99 arbitrary substrates. Similar to the existing method, o ur process begins by spin coating a polymeric support layer onto the as grown graphene/Cu wafer. The copper foil is mounted onto a PDMS/glass substrate and a thick film of PMMA (MicroChem, in Anisole) is sp u n cast at for The foil is removed from the PDMS/glass substrate and cured at for to ensure the complete solven t evaporation. We use a perchloric based, commercial, electronic grad e etchant solution (Transene, APD 100 ), rather than aqueous iron (III) nitrate ( ) to remove the copper film. This eliminates the Fe 2 O 3 particles that wer e observed in transferred films. After etching the copper growth substrate the graphene /PMMA sandwich is adhered, graphene side down, to a p + Si/ 200nm SiO 2 /BCB substrate using a drop of electronic grade isopropyl alcohol ( IPA ) to wet the surface of the wafe r The BCB is a benzocyclobutene derivative that had previou sly been spun coat onto the SiO 2 and thermally cross linked to leave an thick hydrophobic layer on the dielectric. This layer e xcludes water adsorption from the ambient which has been implicated in charge trap generation on oxide dielectrics, degrading device performance. 217 The transferred substrates are covered with a thin porous filter membrane ( Sterlitech ) and a block of porous Teflon and a handclamp ( ) is used to sandwich the stack between two stainl ess steel blocks ( Fig. 3 10 ) The clamped samples are then annealed for at Hot clamping near the glass transition temperature causes the PMMA to reflow, slowly relieving some of the stress build up in the film. Th e heat and uniform pressure allows the IPA time to dry and improves the transfer yields dramatically.

PAGE 100

100 After removing the samples from the clamps, the PMMA is slowly dissolved using an acetone vapor bath ( Fig 3 10 B and C ) The substrates are placed on a water cooled condensation stage inside of a sealed vapor pot which is heated to roughly ( just below the boiling point of acetone). The vapor bath slowly dissolves the PMMA, minimizing the stress es propagated by the swelling of the polymer. After the samples are removed and cleaned by successive acetone, chloroform, and IPA b aths. Finally, before device fabrication begins, s amples are baked on a hot plate in the glovebox at for to dedope (i.e. clean) the graphene film ( doping is attributed to hydroxyl radicals and H 2 O) 3.3 .2 Protective Metallic Support La yers Transfer of CVD grown graphene from the copper growth substrate was further improved by depositing a thin layer ( 100 nm) of Au as a protective layer before spinning the PMMA support film ensuring a post transfer surface that is free of difficult to remove polymeric residue. The thin metallic layer avoids strain induced by the swelling of the PMMA film during the more conventional transfer process. This is especially important at domain boundaries where chemical bonding between the polymeric chains and the graphene is favorable. 63 Figure 3 11 illustrates the procedure for transferring and patterning graphene using an Au thin film as a protective layer and etch mask. Gold was thermally evaporated at a thickness of through a round ed rectangular shadow mask onto the graphene grown on the polished copper foils, followed by spin coating the PMMA. The Au served as an etch mask while the PMMA and excess graphene around the go ld

PAGE 101

101 mask were dry etched in an O 2 plas ma thus defining the edge of the graphene source electrode. An iodide based gold etchant subsequently removed the mask layer. Gold strips ( ) were evaporated onto the graphene that grew on the polished side of the foil followed by a thick film of PMMA (MicroChem, in Anisole) sp u n cast at for and baked at for The uncoated graphene grown on the unpolished backside of the Cu was etched in an O 2 plasma and the Cu was etched away in a perc h lori c solution (Transene, APD 100) bath. The resulting PMMA /Au/graphene sandwich w as trimmed leaving some unprotected graphene surrounding the Au protected regions and rinsed in DI water and IPA The residue PMMA and excess graphene is removed by an O 2 pl asma ash for and the gold was etched in an iodide solution (Transene, Au TFA Etchant). Figure 3 12 compares the quality of the graphene transferred with a nd without the use of a pinhole free, protective Au layer. Raman spec troscopy provides a comparative measure of graphitic materials, capable of distinguishing single layer graphene from multi layer graphene and graphite, 173 and characterizing disorder, crystalline grain size, stacking symmetry, and doping of the graphene films. 177,184,218 The D to G band intensity ratios are shown versus the FWHM of the 2D band overtone for distinct points for the graphene films transferred with and without the use of the gold protective layer. The D band was below the n oise threshold, and the 2D FWHM was substantially reduced in the majority of measured spots for the Au protected films. Raman maps of the films were also taken to demonstrate the spatial homogeneity of t he films. These maps ( Fig 3 14 ) are consistent with the random samplings in that the D peak is nearly imperceptible for the Au transferred graphene. Scanning electron (SEM)

PAGE 102

102 and atomic force micrographs (AFM) of films transferred by the two methods are shown in Figure 3 13 The films transferred using the gold protective layer are continuous, without the polymer residue, micro tears, and wrinkles characteristic of the standard PMMA transfer ( see Fig. 3 13 ). 3.4 Field Transp arent Semimetallic Films : Porous Graphene Although limited, graphene exhibits some intrinsic permeability to electric fields due to its low density of states. Simulations by Regan et al. show that for typical gate field strengths, single layer graphene on ly partially screens the gate field. 219 The field permeability decreases for multi layers, leaving the field complete ly screened for four or more layers. The addition of small pores to the graphene allows for a large portion of the gate field to pass t hrough the graphene. Here we describe a technique to generate small holes in planar graphene sheets for use as gate fie ld permeable electrodes. Micron scale holes with a crudely controlled density were produced in graphene by varying the thickness of the Au mask layer. Thin Au layers possess sub micron pinholes, with a through hole density that depends on the layer thickn ess. During the dry etch of the PMMA, reactive oxygen radicals penetrate these holes to etch the graphene and underlying BCB, leaving behind circular holes in the graphene with an average diameter of The diameters of these holes are self limiting due to the increasing diffusion path length for counter propagating oxygen and reaction products in the confined space between the Au and the SiO 2 as the etched region grows. The hole distribution s were measured via SEM prior to incorporating them as electrode s in Schottky barrier devices. Figures 3 15 B and C illustrate the process for counting the holes from SEM images. The measured areal hole densities in the graphene used to

PAGE 103

103 build the G VFETs to be discussed in Section 5.3 are and with average hole diameters of respectively. Despite the relative simplicity of this technique, reproducible hole densities are difficult to achieve, necessitating ex situ SEM analysis of each sample to confirm the exact hole distributions. Additionall y, the eventual agglomeration of holes limits the practical hole density to approximately 20%. This is far from the estimated porosity of electrodes made from dilute carbon nanotube networks (~80%). In order to reach these higher densities, we are explor ing a lternative techniques to reproducibly pattern the graphene sheets with ordered hole arrays, including conventional top down lithography techniques and bottom up nanopatterning techniques. 220 223 This will allow us to further explore the parameter space o f hole size, density, and distribution o n the field porosity graphene electrodes. 3.5 Drawing Graphene on SiC via Ion Implantation Although continuous large area graphene with low defect concentrations can be grown on various metal substrates u sing CVD ; this technique requires the non trivial transfer of the graphene onto insulating substrates. 133,207,224 A promising technique for forming large area graphene directly on insulating substrates is to anneal SiC single crystals at high temperatures ( ) in ultra high vacuum (UHV). 157,4 This results in Si sublimation, leaving behind a C rich interface leading to the growth of graphene suitable for the fabrication of electronic devices. 157,160 Since graphene is a zero gap semimetal, transistors that use it as a channel material must rely o n quantum confinement, 96,225 strain, 226 or perpendicula r electric field modulation 110 to open a bandgap. A dditional and often complicated processing steps,

PAGE 104

104 such as photolithography, e beam lithography, and dry etching (O 2 ) are needed to fabricate these devices This exposes the graphene sheets to various polymers and h arsh chemical/mechanical treatment, thus leading to reduced carrier mobilities and unintentional doping of the graphene. Because of it s 2D structure, preservation of the surface and interface properties is essential for maximizing device performance. He re w e report on a novel method for growing graphene with predetermined patterns directly on insulating substrates (see Figure 3 1 6 ) We show that ion implantation of a SiC substrate prior to annealing reduces the threshold energ y needed for graphitization. In this way, a focused ion beam (FIB) can be used to patterns on SiC. Thermal or pulsed laser annealing are used to selectively graphitize the surface only where ions have been implanted 3.5 .1 Thermal Epit ax ial G rowth High temperature annealing of SiC substrates ( ) causes Si atoms to sublimate This leaves behind a C rich boundary layer which catalyzes the epitaxial growth of graphene on the surface (see Section 2.2.2 for an overview) Camara et al demonstrated selective area graphene growth on SiC using a n AlN capping layer The AlN acts as a barrier to Si sublimation thus inhibiting graphene growth, while exposed regions of SiC graphitize normally above 227,228 In this section we describe a method of forming graphene patterns on 4H and 6H SiC by selectively ion implanting areas where graphene layers are desired and thermally annealing the substrates to approximately below We find that unlike the Al N capping method which l imits Si sublimation, Au and Si ion implantation into SiC enhances sublimation and lowers the graphitization tem perature of SiC from

PAGE 105

105 ( ) down to ( ) The decrease in is attributed to : (1) an increase in the Si sublimation rate, associated with broken Si C bonds and crystal damage at the SiC surface and (2) possibl e surface catalysis induced by Au ions. Annealing implanted SiC to temperatures between and results in localized graphitizatio n only in the implanted regions a s illustrated by our SEM, Raman, and Au ger electron spectroscopy (AES) measurements This selective area graphene growth by ion implantation provide s a lithography free route for patterning graphene on SiC for device appl ications. We used commercially available, semi insulating, CMP polished (Sinmat, Inc) C face 4H and 6H SiC wafers. Multi ion implantation was performed with a Raith ionLiNE lithography tool employing a n AuSi liquid metal alloy ion source (LMAIS). Sam pl es were implanted by and ions at with fluences ranging from to and to The Au and Si ions were implanted into wide na noribbons as well as and windows 229 Pristine and implanted SiC samples were annealed between in a conventional quartz tube oven with Torr base pressure. Sample temperature was measured in close proximity ( ) to the SiC samples using a C type thermocoupl e (Omega Engineering Inc., EXXC C 24 100). The epitaxial ly g rown graphene layers were characterized using AES at SEM, and micro Raman ( laser excitation) In Fig ure 3 1 7 we compare the Raman spectra of pristine SiC to the Au and Si implant ed SiC after annealing to For the unimplanted samples, the Raman spectra of the annealed 6H SiC (dashed lines) were identical to as received pristine

PAGE 106

106 SiC, implying that graphi tization did not occur at Further ann ealing of the pristine SiC initiated graphitiz ation a nd samples became conductive above W e note d that the implanted regions already began g raphitizing at well below A comparison between Raman spectra of pristine and implanted SiC annealed at sho ws striking dif ferences. Raman spectra of Au ( ) implanted 6H SiC (blue line), Si ( ) implanted 6H SiC (red line), and 4H SiC samples (not shown) exhibit three pro minent peaks (see arrows in Figure 3 1 7 A ). The G peak ( breathing phonon mode) at and 2D peak (two phonon double resonance mode) at are consistent with a surface that is graphitic in nature. The l arge D peak at suggests that graphene layers contain disorder possibly a ssociated with defects induced at the SiC surface during implantation. According to our measurements, the peak is also prese nt in graphene layers grown on pristine SiC (no implant ation) after annealing to which sugg ests that observed disorder in the implanted regions can be partially attributed to the initial quality of the SiC surfaces, surface contamination and the annealing press W e note that an increase in disorder typically reduces the scattering time and cau ses an overall reduction in the electrical conductivity thus degrading the device performance In t he presence of a large D peak comparable in intensity to the G peak ( ) other disorder modes become activated at ( peak) and ( ). Since the peak is in close proximity to the observed peak, it causes overall broadening and increase in as obse rved in Figures 3 1 7 A and B Considering the existence of and peaks and large ratio, we estimate that graphene

PAGE 107

107 doma in sizes are around 218 Finally, we note that both and the peak position depend on the laser excitation energy ( Fig. 3 17 C ). The relative disorder mode scattering cross section increases with increasing wavelength and the D peak position exhibits the energy di spersion expected for graphene ( ) In order t o test the uniformity of the graphene sheets grown on implanted SiC and to determine ca rbon bonding type, AES was performed on pristine and implanted SiC annealed at shown in Figure 3 18 A in blue and red lines, respectively. Since the pristine S iC does not graphitize at the AES spectrum shows large Si and C peaks originating from the SiC crystal with almost elemental % ratio. However, the obs erved Si and surface ox ide peaks completely disappear for the annealed and implanted samples suggesting that the graphene growth reaches full coverage on the surface consistent with micro Raman and SEM measurements ( Figs. 3 17 a nd 3 19 ). It is known that graphene growth on the C face of SiC is not self limiting and many weakly coupled graphene layers are grown without any stacking order resulting in electronically isolated graphene sheets 147 Since AES probes only a few atomic layers at the surface ( ), the absence of Si and Au peaks in Figure 3 18 implies that graphene layers are thick er than the interaction depth and that Au particles have not formed clusters or agglomerated at the surface. Figure 3 18 B shows a clo ser look at the C peak of annealed pristine SiC (blue), annealed implanted SiC (red), highly oriented pyrolytic graphite (HOPG) (black), and CVD graphene (green). T he C peak position is fixed at h owever, since the peak shape is sen sitive to the bonding character, t he first derivative of the C peak measured on annealed SiC shows a sharp peak at (blue dashed square in Fig. 3 18 )

PAGE 108

108 similar to the other repo rted carbides; while the sharp peak disappears for HOPG, CVD graphene, and graphene grown on implanted regions but instead the carbon peak of these materials displays a smooth shoulder at (black dashed square in Fig. 3 18 ). Similarities between various types of graphene and graphene grown onto implanted SiC suggest that the surface is composed of graphene layers ( bonded carbon) in agreement with the existence of prominent and peaks observed in the Raman s pectrum ( Fig. 3 17 ). SEM images of the edge of the implanted area show the transitions between the pristine and selectively graphitized SiC on 4H SiC and 6H SiC samples (see Figs. 3 19 A and B) While the unimplanted regions remain unchanged and preserve their Si:C ratio, imp lanted regions graphitize as expected from Figure 3 17 Some surface roughness and non uniformity is visible and may be attributed to the sputtering and redisposition that occurs during ion implantation. A cross sectional t ransmission electron microscopy (TEM) image ( Fig. 3 19 D ) shows that the underlying 6H SiC has completely recovered the SiC lattice structure via solid ph ase epitaxial regrowth. The SiC surface can be patterned down to nanometer dimensions limited only by the width of the focused ion beam. Figure 3 20 C shows two para llel nanoribbons (dark lines) with line widths on the order o f Arbitrary patterns can be drawn rapidly the graphene lattice structure surrounding the word, graphene, and several patterned lines down to ( Fig. 3 20 ). With regard s to the physical mechanism for lowering the graphitization temperature of SiC, we have performed additional implantation experiments with

PAGE 109

109 different implantation doses (fluences). We find that at the graphit ization is less prominent for dosages smaller than for Si, and for Au. At these fluences, e nergetic ion bombardment break s Si C bonds at the surface, enhancing the Si sublimation. Th e l ower fluences required for Au implantation to induce graphitization at (compared to Si) is due primarily to the increased surface damage created by the heavier Au ions. Preliminary studies examining graphitization of Au/SiC thin films, indica te that Au enhances graphitization at the interface pos sibly through the formation of an Au Si eutectic or a catalytic effect. Since graphene layers can also be selectively grown on SiC implanted with non catalytic Si ions these effects alone cannot acco unt for lowering the graphitization temperature. The question of ion a ctivity is addresses in section 3.5.3 In conclusion, we have demonstrated that graphene laye rs can be selectively grown on Au and Si implanted SiC at reduced temperatures Upon ion implantation, the graphitization temperature of SiC is lowered by at least allowing us to grow graphene layers selectively in the ion implanted regions at temperatures below the graphitization temperature of pristine SiC and above the grap hitization temperature of implanted SiC. Our results suggest that by varying the available parameters such as ion species, energy, dose, and sample temperature during implantation, and/or starting with better quality SiC, higher quality gra phene may be selectively grown by this method, possibly at even lower temperatures. These results offer an avenue for selective graphene growth that can be applied to graphene based devices and nanoribbon synthesis.

PAGE 110

110 3.5 .2 Laser Induced Epitaxial G rowth In this section, we integrate ion implantation and pulsed laser annealing ( PLA ) to graphitize selective areas of an SiC substrate 230 232 This approach is capable of producing arbitrary patterns of few layer graphene (FLG) over large areas with nanoscale precision, at low processin g temperatures, and in a variety of environments including air. Expanding on the thermal annealing expe riments discussed in the previous section, we show that i t is also possible to grow graphene only in the implanted areas by PLA with an ArF laser. The attractiveness of this alternative is that PLA is a non equilibrium, rapid annealing method that maintains the substrate surface near room temperature, and can be performed with short processing times in a variety of environments including air. There have been other promising reports of graphene synthesized on SiC by PLA. For example, Perrone et al 233 used a q switched Nd:YVO 4 to anneal the C face of 4H SiC in Ar and reported e vidence for graphene formation and Lee et al 234 have shown that graphene can be grown on SiC single crystals in vacuum when irradiated with pulses from a KrF excimer laser at a flu ence of To establish the P LA parameters, unimplanted regions of a SiC crystal were annealed using a JPSATM IX 260 ArF excimer laser system with m wavelength pulse duration, and repetition rate. Metal masks were inserted i n to the laser beam and imaged on the sample as squares. Eight square areas were sequentially annealed with pulses, in each region, at various fluences ranging from per pulse

PAGE 111

111 Figure 3 21 shows Raman, SEM, and AFM analyses for one such window where unimplanted SiC was laser annealed with pulses at per pulse. Graphitization is found to occur only inside the laser ann ealed window as indicated by the appearance of the so called and band s in the Raman spectrum ( Figure 3 21 B ) 235 The presence of a large band, comparable in intensity to the band is consistent with previous reports of both thermal and laser annealing of the C face of SiC. 230,234 The relative intensity of the band with respect to the silicon carbide trans verse optical phonon overtone ( ) at and the single peak L orentzian fit of the band ( position and FWHM of and respectively) indicate the presence of FLG. 235 A Raman map of the G peak ( Figure 3 21 D ) confirms that the presence of graphitic ca rbon at the surface is restrict ed to the PLA exposed area. The patchy appear ance of the Raman map may be due to surface melting of the SiC at this high laser fluence. The SEM and AFM ( Figures 3 21 C and E, respectively) measurements indicate an increase in roughness of the sample ( versus ). Resul ts of PLA on areas patterned by multi ion beam lithography (MIBL) are illustrated in Figure 3 2 2 The MionLiNE was used to pattern a 4H S iC single crystal by implanting Au ions to a fluence of The ArF la ser was then used to anneal the implanted patterns with pulses of duration at a fluence of T o demonstrate the patterning capabilities of this technique, an SEM image of two nanoscal e FLG lines is presented in Figure 3 22 A We also fabricated graphene micro arrays by maskless ion implantation that are similar to those patterned with

PAGE 112

112 conv entional methods by Lu et al. 236 to demonstrate graphene plasmonics in the terahertz range A periodic micro ribbon array composed of five lines, each wide and long, separated by was patterned on the sample ( Figure 3 22 B ) The Raman map of the band intensity ( Figure 3 22 C ) of this area shows graphitization only where the SiC was implanted 3.5 .3 Catalytic Effects of Implantation Species We al so investigated the effect of ion species on the graphitization process In order t o study the graphitization onset threshold a 4H SiC (n type) single crystal wafer was implanted over broad areas using the accelerator facilities at the Australian Nation al U niversity The implant conditions and retained dopant concentrations as measured by ion scattering were 60 keV Au at Cu at and Ge at Figure 3 23 summarizes the laser fluence thresholds for the onset of graphitization ( ) induced by PLA in air for pr istine as well as ion implanted SiC. The implantation of SiC with Si (self dopant) Ge (isoelectronic), Au (noble/catalytic), and Cu (catalytic), provided a comparison for the effect of various types of dopants, and is seen to have a s ignificant effect on the threshold fluence for graphitization It is clear from the data in Figure 3 23 that while graphitization of unimplanted SiC has a (indicated b y the shaded region in Fig. 3 23 A ) the thresholds for ion implan ted SiC can occur at fluences as low as ( Fig 3 2 3 B ) No graphitization was observed for the implanted/annealed or annealed/un implanted regions. The measurements in Figure 3 23 B suggest that the onset of graphitization occurs at lower fluences for the implanted catalytic species (Au and Cu) than for

PAGE 113

113 isoelectronic and self dopants like Ge and Si It should be noted that at these implantation conditions Au and Cu also induce more lattice damage in SiC However, c rystalline SiC (c SiC) becomes amorphous at quite low implant fluences ~ compared to the doses used in our experiments, 237 and our implantation conditions were chosen to create comparable amorphous layer thicknesses. This suggests that ion species like Au and Cu that behave as catalysts f or CVD growth of graphene may contribute catalytically to influence ho wever a more comprehensive study is needed to confirm this There appears to be a number of mechanisms contributing to the onset of SiC graphitization. When heated to high temperatures in UH V for long periods Si appears to subli mate, leading to gr aphitization. 157 If instead SiC is implanted with Au or Si the graphitization temperature is reduced significantly, the underlying SiC recrystallizes and FLG grows selectively in only the implanted regions 230 PLA experiments done by Lee et al. in UHV on unimplanted SiC initiated graphitization at about ( pulses from a KrF la ser) and the authors argue that as many as pulses could not thermally sublimate enough Si to form even a monolayer of graphene. 234 They s uggest that the laser induces photophysical Si C bond breaking that allows the Si evaporation rate at the surface to exceed equilibrium effusion flux. Our PLA experiments on Si C surface by ion im plantation with a variety of different species, demonstrate the onset of graphitization at relatively low fluences well below the melting threshold for c SiC. 238 Depending on the fluence, the non equilibr ium PLA The effects associated with the PLA of amorphous SiC

PAGE 114

114 (a SiC) have been investigated by Baeri et al. 239 who used time resolved reflectivity to measure the surface melt thresholds of a SiC formed by ion implantati on. They created various thickness amorphous layers in 6H SiC single crystals by Ar implantations, and annealed the samples with a q switched ruby laser (wavelength = ) to determine the laser fluences at which surface melting occurred. O ur experimental conditions differ somewhat but some of their conclusions and observations can be applied to analyze our experiments. They concluded that the melting point of a SiC ) is much lower than that of the crystalline phase ), a nd even lower than the temperature at which peritectic decomposition occurs ( ). As a consequence of the differences in the absorption, thermal conductivity, and diffusivity between a and c SiC their measurements and calculations conclude that t he surface melting threshold is strongly dependent on the thickness of amorphous layers raising the possibility that this may explain the trends observed in Figure 3 23 Extracting fundamental parameters f rom their measurements they are able to deduce that thin layers ( ) require high laser fluences to melt compared to only for layers thicker than But our amorphous layer thicknesses (Cu) (Au), and (Ge ) as measured by ion scattering/channe ling are too thin and our measured onset fluences are too low for melting to be probable. This further suggests that doping or catalytic effects may be responsible for the observed threshold reduction, and/ or that the mechanism does not re quire s urface melting. We have demonstrated that ion implantation combined with pulsed laser annealing offers an approach for rapid synthesis of few layer graphene, and provides great

PAGE 115

11 5 flexibility for the study of the mechanisms of SiC graphitization We observe selective graphitization of ion implanted SiC when annealed in air with an ArF pulsed laser at onset fluences far below those for unimplanted SiC. Both the ion induced damage and the implanted species are contributing factors. The laser fluence as well a s the number of pulses at a given fluence can also be used to control the amount of graphitization. Coupled with multi ion beam lithography these techniques provide a low temperature approach for direct synthesis of graphene nanostructures Future studie s will concentrate on quantifying the mechanism s contributing to graphitization and optimizing the experimental conditions for producing graphene devices and structures. 3.6 Concluding Remarks W e have describe d two method s of producing grap hene on insula ting substrates: catalytic CVD and decomposition of ion implanted SiC. Our improvements to copper based CVD growth methods have led to smoother films with macroscale single crystal graphene domains. The importance of copper substrate roughness and growth parameters (i.e. pressure, temperature, H 2 /CH 4 ratio) on nucleation density was illucidated by comparing optical and SEM images of partially grown films consisting of isolated graphene domains on oxidized copper. In addition we have demonstrated a metho d of transferring graphene with improved yields without inducing damage or leaving behind polymeric residue. The resulting graphene is free of vertical protrusions and macroscopic folds and tears which are deleterious to the vertically integrated devices in Chapter 5 Finally, we have demonstrated a facile method of creating electric field permeable graphene sheets. The porous graphene remains highly conductive but is locally permeable to electric fields, a feature that will be called upon in

PAGE 116

116 Chapter 5. Continuous and porous graphene electrodes will be important for the Schottky barrier devices that we develop in the next chapters. Ancillary to the CVD work described above, we demonstrated the site selective growth of few layer graphene films directly on insulating SiC substrates using ion implantation and laser annealing This technique allows complex graphene nanostructures to be locally formed at low substrate temperatures without the u se of lithographic patterning.

PAGE 117

117 Figure 3 1. Home built CVD s ystem. (A) The complete system is composed of the following key components (Inset is a close up photo the quartz tube): (a) Sample loaded into the tantalum boat; (b) oxygen scavenging tantalum foil; (c) high precision flow meter bank; (d) optional bubbler s for ambient pressure growth; (e) gas cylinders in a vented fume hood; (f) clam shell tube furnace; (g) sample loading area; (h) roughing pump; (i) vacuum gauge and liquid nitrogen trap; (j) temperature control module. (B) The tantalum enclosure is loade d with a copper foil and (C) wrapped with a fresh tantalum foil (D) A piece of tantalum foil is also placed upstream of the sample to scavenge any oxygen in the reaction chamber. The fresh tantalum (top) is shiny and malleable compared to the oxidized tantalum (bottom), which becomes dark and brittle after repeated growth cycles.

PAGE 118

118 Figure 3 2. Deleterious SiO x particles originating from the quartz tube furnace. (A) Fully grown graphene on copper can be littered with SiO x particles if it is unshielded during the growth process. The density increases with increased cycling of the growth tube. (B) Large particles sometimes result in macroscale restructuring of the copper surface during growth.

PAGE 119

119 Figure 3 3. SEM characterization of macroscale graphene domains in a partially grown film on Cu. Lightly oxidizing the copper substrate enhances the visibility of the graphene domains by a charging contrast mechanism. (A) A large single layer graphene domain ( ) and, (B) a most ly single layer domain exceeding

PAGE 120

120 Figure 3 4. Protected surface reconstruction under graphene films on copper. (A) SEM image of graphene domains on copper. The ridges are terrace steps on the reconstructed copper surface. Inset: Close up of the surface steps that are preserved underneath the graphene and the disordered copper oxide surface. (B) AFM tip height image showing similar step edge reconstructions underneath the graphene domains. A line scan perpendicular to the edges reveals steps that are roughly high and for this sample.

PAGE 121

121 Figure 3 5. AFM characterization of a partially grown graphene film on Cu. The tapping mode AFM maps of (A) tip height, (B) amplitude, and (C) phase maps. The methane flow rate was increased to to ensure a high enough nucleation density for AFM imaging. The arrows indicate bilayer regions surrounding the nucleation sites.

PAGE 122

122 Figure 3 6. Histogram of the sheet resistance values for CVD grown films grown under different conditions. The 4 point Van der Pauw contact geometry ( separation) was used to obtain sheet resistance values for samples transferred to SiO 2 substrates using the hot clamping method described in Section 3.3.1.

PAGE 123

123 Figure 3 7 Atomic force microscopy characteri zation of copper foil s before and after chemical mechanical polishing. Surface height and tip amplitude profiles for as received (A and C) and CMP polished films (B and D).

PAGE 124

124 Figure 3 8. SEM characterization copper foils before and after chemical mec hanical polishing. (A) SE image of the unpolished Cu surface taken at 5KeV, and (B) Zoomed in look at the micron scale grooves that result from the rolling process. Inset: The SEM image for the polished samples is smooth and featureless.

PAGE 125

125 Figure 3 9. Schematic of the improved graphene transfer process. (a c) Continuous, defect free graphene films are grown using the process steps described in Section 3.2; (d) Au is evaporated on to p of the as grown graphene; (e ) PMMA is spun onto the gold layer; (f) Cu is etched away in perchloric acid; (g ) Films are cleaned in HF, DI water, and IPA. (h) G raphene/Au/PMMA stack is adhered to the dielectric layer on Si us ing isopropyl alcohol; (i ) The stack is clamped and heated to ; (j) PMMA dry etched away in O 2 plasma ; (k ) Au film is wet etched away leaving behind a residue free, perforated graphene sheet; (l) Films are dedoped by annealing to in an inert atmos phere.

PAGE 126

126 Figure 3 10. Hot clamping and vapor bath technique for increased transfer yields. (A) Schematic of the clamp stack. (B) Photo (side view) of the acetone vapor bath used to slowly dissolve the PMMA support layer. (C) Top view photo of the water chilled condensation plate.

PAGE 127

127 Figure 3 11 Facile method for the lithography free fabricating of porous graphene. The steps are as follows: (a) the Au film evaporated onto the as grown graphene on Cu, (b) the PMMA spin coated onto the gold layer, (c) Cu etched away, (d) graphe ne/Au/PMMA stack adhered to SiO 2 subst rate, (e) PMMA etched away in O 2 plasma (spots depict pinholes in the Au film), (f) Au film etched away leaving behind a residue free, perforated graphene sheet

PAGE 128

128 Figure 3 12. Raman chara cterization of the improved graphene transfer method. (A ) Representative Raman spectra of the PMMA and Au/PMMA transferred graphene on BCB/SiO 2 Insets are zoomed in on the D band regions (B ) Raman spectral data in the form of a cluster plot of D/G peak ratios versus the 2D band FWHMs for a graphene layer transferred using the Au protected process (black squares) and a graphene layer transferred using the conventional PMMA process (red triangles). One hundred points were recorded on each layer in a squar e array having a pitch of approximately 50 points recorded for the Au transferred layer.

PAGE 129

129 Figure 3 13. Continuity and roughness of graphene transferred using a protective metal film: (A, B) SEM (scale bars, ) and (C, D) AFM images ( ) of graphene layers transferred to SiO2 using the Au protected and t he conventional PMMA processes.

PAGE 130

130 Figure 3 14. Comparison of the Raman peak intensities for graphene samples tr ansferred to SiO 2 with and without an Au protective layer. Two Raman maps (400 points, laser spot size, excitation) of the (A) D band Intensity and (B) D to G band intensity ratio, one for each case. The Au protected samples display much impr oved characteristics versus the conventional transfer.

PAGE 131

131 Figure 3 1 5 Method for obtaining hole statistics for the ransom porous graphene films. (A) Histograms of the hole size distribution for the 4 devices tested in Section 5.3. (B) Characteristic SE M image of a porous graphene film. (C) Analysis of the hole distributions is done using computer software to count the number and size of the holes. The process is iterated over several images to ensure an accurate distribution.

PAGE 132

132 Figure 3 1 6 Site s elective graphitization of SiC via ion implantation and thermal or laser annealing. 4H SiC substrates are (A) implanted with various ions species. The implantation process creates a teardrop amorphous region below the surface (layers represent the ABCB s tacking of 4H SiC). Solid phase epitaxial regrowth of the SiC substrate is activated by (B) thermal or (C) laser annealing. The recrystallization of the SiC substrate leads to few layer graphene formation on the surface.

PAGE 133

133 Figure 3 1 7 Raman spectr a of Au and Si implanted and annealed SiC. (A ) Raman spectra measured on pristine 6H (blue dashed), Au implanted ( ) 6H (blue line), p ristine 6H (red dashed) and Si implanted ( ) 6H Si C (red line) after annealing to at pressure. (B) Raman spectra of Au implanted (blue) an d Si implanted 6H SiC (red) after subtracting the pr istine SiC background. (C) The peak Raman shift and to peak ratio measured usi ng lasers at different wavelengths.

PAGE 134

134 Figure 3 1 8 Characterization of ion implanted SiC, before and after thermal annealing. (A ) Auger electron spectra taken from to o n pristine 6H SiC (blue) and Au implanted 6H SiC (red) after annealing to (B ) Detailed Auger carbon peaks measured on pristine (blue), Au implanted (red) 6H SiC after annealing to HOPG (black), and CVD graphene on copper foil (green).

PAGE 135

135 Figure 3 1 9 Graphene nanoribbons grown by ion implantation. SEM images taken on (A) Au implanted 4H SiC, (B) Si implanted 6H SiC, and (C ) graphene nanoribbon surfaces. (D ) Cross sectional TEM images taken at the Au (protective layer) /graphene/6H SiC.

PAGE 136

136 Figure 3 20 Drawing graphene on SiC via ion implantation. 4H SiC was patterned with an Au ion beam and thermally annealed to produce few layer graphene. Inset is a map of the Raman G

PAGE 137

137 Figure 3 21 Characterization of a selectively graphitized region of SiC af ter A rF pulses at (A ) Schematic of the two step ion implantation and pulsed laser annea ling graphitization process. (B ) Raman spectra comparing a region of FLG (blue) and unannealed SiC (black). INSET: Zoom plot of band. (C) SEM (scale bar = ) and (D ) Raman band map of PLA spot i ndicating graphitization, and (E ) AFM (scale bar = ) of the annealed region.

PAGE 138

138 Figure 3 22 Growth of FLG with nanoscale features by Au i on beam lithography and PLA. (A ) SEM of and lines. (B ) Reproduction of a plasmonic terahertz metamaterial consisting of a mi cro array of wide lines. (C ) Raman band map of the metamaterial array. Scale bars are respectively.

PAGE 139

139 Figure 3 2 3 Onset of graphitization with increasing laser fluences for various implantation species as evidenced by Raman. Relative band intensities (after normalization) versus, (A ) laser flu ences on unimplanted SiC, and (B ) the graphitization onset fluence at for va rious implanted SiC samples. (C ) The full Raman spectra for each implant condition annealed at and pulses. The spectra are normalized by the shoulder at to avoid interference with the large convoluting band. INS ET: Zoom plot of the bands

PAGE 140

140 CHAPTER 4 GRAPHENE/INORGANIC S EMICONDUCTOR INTERFA CES 4.1 Introduction Investigation of graphene for use in electronic circuits has largely been limited to the semiconducting channel. 4,5,240,241 The high room temperature mobility of graphene compared with all existing semiconducting systems is widely cited as the motivation for this line of research. Unfortunately, the semimet allic band structure and charge conjugation imply that a traditional p n p ( n p n ) junction can not provide the barrier to conduction necessary to turn the device off For power or logic circuitry, a band gap must be induc ed in the graphene to allow for devices to be switched off more completely Unfortunately, this requires the graphene to be modified 242 244 or confined to quasi one dimensional wires 163,222,245 necessarily leading to a degradation o f the mobility, often by several orders of magnitude. Thi s suggests that graphene may be a more natural fit in analog electronics for which high On/Off ratios are not necessary. The alternative is to use graphene as a semimetal electrode rather than a s emiconductor. Electrodes are generally required to have a high electrical conductivity with some combination of mechanically flexibility, chemically inertness, optically transparency, and a resistance to d iffusion and electromigration. Graphene is unique in that it excels in all of these measures. No further justification should be necessary to nominat e graphene as a candidate electrode material but we will suggest another, I gratefully acknowledge my collaborators for their many contributions, especially Drs. Sefaatin Tongay, and Art Hebard (Section 4.2) and Dr. Andrew Rinzler (Section 4.3). The work presented in this Chapter is based in part on published resu lts. The published manuscript and figures have been modified from their original format: Section 4.2 4.3 : Rectification at Graphene Semiconductor Interfaces: Zero Gap Semiconductor Based Diodes Phys. Rev. X 2012 2, 011002.

PAGE 141

141 more subtle advantage: the uniquely field tunable density of states. As we wi ll show, this give s rise to anoma lous rec tification behavior and a novel operating mechanism for three terminal devices In the following sections, w e report on the rectificat ion (diode) effects observed at graphene/semiconductor interfaces on a wide vari ety of conventional semiconductors (Si, GaAs, GaN, and SiC) In addition to current voltage ( ) measurements, we utilize Hall transport capacitance voltage ( ) and electric field modulated Rama n techniques to measure previously unobserved proper ties of the graphene/semicon ductor interface. Finally, we exploit the unconventional transport properties of these rectifiers to fabricate gate modulated Schottky barrier transistors, and report on their performance. 4.2 Schottky Junctions on T echnolog ically R elevant S emiconductors L ittle is known about the interface physics at semimetal/ semicondu ctor junctions. Graphene/semiconductor junctions exhibiting rectification and photo responsive behavior have been demonstrated by transferring either CVD prepa red 246,247 or exfoliated 248,249 graphene sheets onto Si substrates. The resulting diodes show ideality factors (a measure of deviation from thermionic emission) varying from approximately ( close to the ideal value of unity ) to values in the range of approximately on exfoliated graphene implying that unconventional current injection processes exist at graphene/Si interface s Although these early results are promising, a more general st udy of the interface between graphene and various semiconductors is needed to unravel the transport mechanisms across semimetal/semiconductor interfaces.

PAGE 142

142 We begin our investigation by transferring CVD prepared graphene sheets onto a variety of technologica lly important semiconductors: n type Si, GaAs, GaN, and 4H SiC ( Fig. 4 1A and B) E quilibration of the Fermi level throughout the system gives rise to a charg e transfer between the graphene and the semiconductor, thereby creating strong rectification (cal We find t ha t the graphene Fermi level ( ) is sensitive to the equilibrium charge transfer ac ross the graphene/semiconductor interface as measured by in situ Raman spectroscopy me asurements. U nlike conventional metal/semiconductor diodes, where the Fermi level ( ) of the metal stays constant due to a high dens ity of states at the Fermi surface, small variations in charge density can significantly shift the Fermi level in graphene These variat ions become especially pronounced at high reverse bias voltages when the induced negative charge in the graphene is sufficient to increase and give rise to As a result of their unusual behavior, these diodes can serve as the basis for a new class of transistor devices ( Fig. 4 1C ) 4.2 .1 Fabricating Graphene Diodes on Si, GaAs, GaN, and SiC Our diodes are fabricated by transferring large scale graphene sheets grown by ch emical vapor deposition directly onto the semiconductor under investigation and allowing van der Waals attraction to pull the graphene into intimate contact with the semiconductor. Large area single layer graphene sheets were synthesized on Cu foils via a multistep LP CVD process similar to the process described in Chapter 3. Four noteworthy differences in the growth and transfer process should be mentioned: (1) The

PAGE 143

143 graphene was grown on thinner unpolished thick Cu foils (Puratronic, Cu) ( 2) the Cu etching was done in a solution of Fe (NO 3 ) 3 (Alfa Aesar) (3) a protective metal layer was not used during transfer, and (4) the graphene was not clamped to the substrate stack, but rather it was transferred with a drop of IPA and all owed to dry on the surface. Application of isopropyl alcohol improves the success rate of the graphene transfer and does not affect the measurements presented here. After growth and transfer, the graphene films were characterized and identified using a H oriba Yvon micro Raman spectrometer with green ( ) red ( ) and UV lasers ( ) Commercially available n type Si and n type GaAs wafers we re doped with P ( ) and Si ( ) respectively. Epilayers of n type GaN and n type 4H SiC, t hick, were grown on semi insulating sapphire substrates with S ( ) and N ( ) dopants. The doping densities ( ) of the semiconducting wafers (Table 4 1 ) were measured at usin g a Hall bar geo metry During the sample preparation and before the graphene transfer, the w afers were cleaned using standard surface cleanin g techniques. Thin native oxide formation was unavoidable given the time consuming transfer process. Ohmic contacts to the semic onductors were formed using conventional Ohmic contact recipes. 192,250 252 Multilayer Ohmic contacts were thermally grown on the back and front sid e of the semiconductor and were annealed a t high temperatures using rapid thermal annealing. After the Ohmic contact formation, a thick SiO x window was grown on various semiconductors using a plasma enhanced chemical vapor deposition system, and gold electrodes approxim ately thick wer e

PAGE 144

144 thermally evaporated onto the SiO x at A schematic fo r our graphene based diodes is shown in Fig ure 4 1 B The back side of the semiconductor substrate is covered with an Ohmic contact, and the graphene sheet is transferred o nto Cr/Au contacts deposited over the SiO x windows. The graphene contacting areas w ere squares with sides in the range of After deposit ing the graphene/PMMA films, the samples were placed in an acetone vapor rich container for periods ranging from to approximately The acetone bath allows slow removal of the PMMA films without noticeable d efo rmation of the graphene sheets. Before the graphene transfer, there is an open circuit resistance between the Au contacts and the semiconductor. After the transfer of the PMMA/graphene bilayer, the graphene makes simu ltaneous connection to the Au con tacts and the semiconducto r, as evidenc ed by the measured rectifying I V characteristics. Since the diodes made with the PMMA/graphene bilayer show essentially the same rectifying characte ristics as the samples in which the PMMA has been dissolved away, we conclude that the graphene is making intimate contact with the semiconductor. After the transfer, the graphene and semiconductor adhere to each other in an intimate van der Waals contact in the middle of the open wi ndow, and the Cr/Au contact pad provid es good electrical contact with the graphene. Our Ohmic contact arrangements allow current density versus voltage ( ) and capacitance versus voltage ( ) measurements to be taken separately. The measurements were taken in darkroom conditions using a Keithley 6430 sub fempto a mp source meter, and measurements were taken using an HP 4284A capacitance b ridge. The electric field modulated Raman measurements were made on the same configuration, h owever,

PAGE 145

145 the four terminal transport and Hall measurements were perf ormed with an intervening dielectric layer of SiO 2 using a physical property measurement system (PPMS) at room temperature in magnetic fields up to In Fig ures 4 2 (A D) we show typical Raman spectroscopy data tak en on graphene sheets grown on Cu foils by CVD deposition before and after transferring onto semiconductors. The presented sca ns have been reproduced at more than 20 random spots and a re good representations of the quality of the graphene on the Cu foils before transfer and on the semiconductor surface after transfer. In our graphene/Cu samples, we observe and a negligible peak amplitude, h owever, after the graph ene transfer to the semiconduct or substrate, we observe a small disorder mode peak ( ), while remains the same ( Fig. 4 2 B ) The increase in reflects an increase in the disorder induced during the transferring of graphene fr om the Cu growth substrate. The Raman spectrum of exfoliated graphene transferred onto Si/SiO 2 substrates has previously been studied as a function of applied bias. 109 It has been found that the and peaks of graphene ar e sensitive to the Fermi energy (carrier density) of graphene a nd allow one to estimate the bi as induced changes in Considering the typical operating voltages of Schottky junctions, the low carrier density in graphene, and the associated bias dependence of we have also measured the Raman spect rum of graphene transferred onto GaN as a function of applied bias ( ) Our Raman measurements differ from those reported by Das et al. 109 in the following three ways: (1) W e are using CVD prepared rather tha n exfoliated graphene; (2) The graphene is in direct contac t w ith GaN rather than oxidized Si; (3) This in situ measurement is a function of applied bias voltage in a Sc hottky diode, rather than gate

PAGE 146

146 voltage in a field effect transistor In Figure 4 3 we show the evolution of the Raman spectrum as a function of applied bias. While and are almost identical with the same peak positions at and in reverse bias at the band shifts higher by approximately and the band shifts lower by approximately The relative shifts in the Ram an peaks along with a reduction of the peak ratio from (at ) to (at ) imply that graphene sheets transferred onto GaN become electron doped. Considering the previous results reported on graphene/SiO 2 109 and doped graphene, 71 the shift in can be estimated to be in the range of approximately Hall measurements show that the Hall mobility of the graphene sheets used in our diodes is in the range of and that the sheets are hole doped with carrier densities in the range of ( Fig. 4 4 ). The presence of extrinsic residual p type doping is commonly observed in exfoliated ( H 2 O vapor) 3 and CVD grown graphene ( N O 3 ). 133 In both cases, annealing r educes the concentration of dopants and forces closer to the neutrality point. For our CVD prepared graphene, the presence of residual impurity doping can be attributed to a lowering of due to hole dopin g of the graphene during the Fe(NO 3 ) 3 etching transfer process. Schottky diod es are expected to pass current under forward bias (when the semiconductor is negatively biased) while becoming highly resistive in reverse bias (when the semiconductor is positively biased). As seen in Figure s 4 5 through 4 8 the ( part A ) and ( part B ) graphene/ n type semiconductor junctions are capable of display strong rectification. This rectification is a consequence of Schottky barrier formation at the interface when electrons flow from the semiconductor to the

PAGE 147

147 graphene as the Fe rmi energies equilibrate In principle, any semiconductor with electron affinity ( ) smaller than the work function of the metal can create rectification at a metal/semiconductor (M S) interface with Schottky barrier height (4 1) given by the Schottky Mott model. Electron transport over the Schottky barrier at the M/S interface is well described by thermionic emission theory with the expression : (4 2) where is the curre nt density across the graphene/ semiconductor interface, is the applied voltage, is the temperature, and is the ideality factor. 192 The pref actor, is the saturation current density and is expressed as (4 3) where is the Richardson constant. 4.2.2 Extracting Barrier Heights from Electrical Measurements When electronic tr ansport across the barrier is dominated by thermionic emission as described by Eq uation 4 1 semilogarithmic plots of the curves should display a linear region in forward bias. As seen in part B of Fig ure s 4 5 through 4 8 our measurements typically reveal decades of linearity thus allowing us to extract and for each diode. The deviations from linearity at higher bias are likely due to series resistance contributions from t he respective semiconductors. The temperature dependent da t a for the graphene/(Si, GaAs, GaN, and SiC) diode s ( Figs. 4 9 through 4 12 ) show s that, for both bias directions, a larger (smaller) current flows as the temperature is increased (decreased), and the probability of conduction electrons overcoming the barri er increases (decreases). In forward bias, the thermionic emission

PAGE 148

148 process manifests itself as a log/ l inear dependence and linear versus curves where The SBH is calculated directly from the slope of this linear dependence. By repeating these temperature dependent measurements for the four differ ent diodes, we find that the SBH ( ) values at the graphene/semiconductor interfaces are and for Si, GaAs, SiC, and GaN, respectively (Table 4 1 ). While the overall reverse current density increases as is increased, we notice that, at high reverse bias, the magni tude of the breakdown voltage decreases linearly with temperature implying that has a positive breakdown coefficient and that the junction breakdown mechanism is mainly ava lanche multiplication. 192 The variation of our ideality values in the range of has no obvious correlation to the type of semiconducting substrate. Ideality values great er than one (unity) have been attributed to (1) an image force lowering correction to the SBH, (2) a bias dependent SBH, and (3) the existence of additional current processes such as thermionic field emission across the metal/semiconductor interface. 253 Here, even though and henc e the SBH of the diode, is bias dependent, we do not expect a significant change in the SBH for forward bias since the applied bias is relatively small. However, even if the current across the M S interface is dominated by thermionic emis sion, the image force lowering alone can result in ideality values much larger than unity. 253 Therefore, ideality values exceeding unity might be associated with enhanced image force lowering across the grap hene/semiconductor interface. Schottky barrier values are well described using either the Bardeen or Schottky limits. In the Bardeen limit, the junction current is mostly governed by interface states

PAGE 149

149 which, in accumulating free charge, change the charge distributi on at the interface and cause of the semiconductor to be fixed (Fermi level pinning). Accordingly, the SBH shows weak dependence on the work function of the metals used for contacts, as found, for example, in GaAs. 192 On the other hand, the wide band gap semiconductors SiC and GaN are well described by the Schottky Mott (S M) limit (Eq. 4 1) Using the extracted values of and e lectron affinity values of approximately of approximately of approximately and of approxi mately ), we calculate (Table 4 1 ). The calculated values of the work function are typically higher than the a ccepted values (approxi mately ) of graphene when is at the Dirac point ( point). The deviation from this ideal graphene work function can be attributed to the lowering of due to hole doping of the graphene during the etching transfer process, together w ith the fact that the graphene is in physical co ntact with the gold electrodes. 77 Although the S BHs on Si, GaAs, and GaN can be roughly explai ned within the S/M model, in reality, GaAs surfaces have a high density of surface states and thus exhibit char acteristic Fermi level pinning. GaAs based diodes generally have SBHs in the range of as observed in our measurements, and proper interpretation of the SBH on GaAs/graphene junctions requires the Bardeen model. After the graphene is placed on the semiconductor surface, there is charge separation and concomitant form ation of induced dipoles at the interface. According to bond polarization theory, 254,255 the SBH is determined by charge separation at the boundary between the oute rmost layers of the metal (here, a single layer carbon sheet) and the semiconductor. Our results are in good agreement with the findings of our earlier work

PAGE 150

150 on graphite an d many layer graphene junctions where the layer in closest proximity to the semicond uctor surface is a single sheet of carbon atoms. 256,248 On the other hand, barriers formed on the 4H SiC substrates give an unphysically low value for (see Table I ) and therefore cannot be explained by either model. The deviation observed on graphene /4H SiC diodes clearly requires consideration of more advanced treatments of metal induced gap states or bond polarization. For example, since the la ttice mismatch between 4H SiC and graphene is quite small when compared to the other substrates (namely, Si, GaAs, and GaN), the coupling/interaction between the 4H SiC and graphene might be fundamentally different, and, within the bond polarization model, this difference might result in the observed deviation. 4.3 Deviations from Thermionic Emission Theory Next, we turn our attention to the revers e bias characteristics. In conventional metal/semiconductor Schottky diodes, the work function of the meta l is pinned independent of bias voltage due to the high density of states at while, in reverse (forward) bias, the Fermi energy of the semiconductor shifts down (up), allowing observed rectification via an increase (decrease) in the built in poten tial ( ). Unlike ) is a function of bias, and, for large voltage values, the SBH does no t stay constant. When Schottky diodes are forward biased, they permit large currents at bias voltages wel l below and small decreases in the Fermi level of g raphene cannot be distinguished from voltage drops associated with a series resistance. Said in another way, the deviation from linearity in the semilogarithmic plots of Fig ure 4 5 through 4 8 (part A) for forward bias could be due to a combination of a series resistance becoming important at high currents together with

PAGE 151

151 a small increase in and a downward shift in for the positively charged graphene. However, in reverse bias, where the applied vol tage can be larger than starts changing dramatically 257 and the fixed SBH assumption clearly no longer holds. In reverse bias, whe n the graphene electrodes are negati vely charged, increases and decreases, causing the SBH height to decrease as the reverse bias is increased. A s observed in the insets of Figure 4 5 through 4 8 ( part B ) this effect causes the total reverse current to increase as the magnitude of the bias is in creased, thus preventing the Schottky diode from reaching reverse current saturation. This nonsaturating reverse current has not been obse rved in graphite based Schottky junctions due to the fixed Fermi level of graphite 256 Capacitance voltage ( ) m easurements made in the reverse b ias mode are complementary to measurements and provide useful information about the distribution and density of ionized donors in the semiconductor and the magnitude of the built in potential For a uniform distribution of ionized donors within the depletion width of the semiconductor, the Schottky Mott relationship between and the reverse bias voltage satisfies the linear relationship, (4 4) which, as shown in Figure 4 13 is observed to hold for graphene/GaAs and graphene/Si junctions. Linear extrapolation to the intercept with the abscissa gives the built in potential, which is related to via the exp ression (4 5) Here, is the effective density of s tates in the conduction band, is the doping level of the semiconductor, and the s lope of the linear fitting to versus gives the

PAGE 152

152 doping density of the semiconductor. We list and values for the graphene/GaAs and graphene/ Si junctions in Table 4 I We note from Table 4 1 that the extracted values on the Si and GaAs junctions are generally higher than the values. The discrepancy between the SBHs determined by the two methods can be attributed to: (a) the existence of a thin oxide or residue at the graphene/ semiconductor interface and/or (b) Schottky barrier inhomogeneity. G raph ene sheets transferred onto SiO 2 are known to have charge puddles mostly due to the inhomogeneous doping due to surface charge traps in the substrate or from chemicals used during the graphene production or transfer process. Sinc e the SBH is sensitive to the of graphene, patches with different charge densities (doping) are expected to have an impac t on the SBH and hence on the characteristics of the graphene diodes. An imp ortant difference between and techniques is that the capacitan ce measurements probe the average junction capacitance at the interface, thereby yielding an average value for the SBH, while the measurements give a minimum value fo r the SBH, since electrons with thermionic emission probabilities exponentially sens itive to barrier heights 253 choose low barrier patches (less p doped graphene patches) ov er higher patches (more p doped graphene patches). While measurements give reasonable values of the SBH for graphene/GaAs and graphene/Si, we have not been able to obtain reliable measurements for graphene deposited on GaN and SiC because of high series resistance in these wide bandgap semiconductors The linearity of th e measurements shown in Figure 4 13 is consistent with the Schottky Mott model and the abrupt junction approximation,

PAGE 153

153 which assumes that the density of ionized donors is constant throughout the depletion width of the sem iconductor. This good agreement invites a more quantitative analysis of the Fermi energy shifts in the graphene that are the source of the nonsaturating reverse bias currents discussed in the previo us subsection. We begin by writing the electron charge d ensity per unit area on the graphene as (4 6) where (4 7) is the Schottky Mott depletion capacitance, is the number of electrons per unit area, and is the magnitude of the reverse bias voltage. Combining these two equatio ns gives the following result: (4 8) The above expression provides an estimate of the number of carriers per unit are a associated with the electric field within the depletion width, but it does not account for extrinsic residual doping described by the carrier density on the graphene before it makes contact with the semiconductor. The processing steps used to tr ansfer the CVD grown graphene from Cu substrates to semiconductor surfaces typically results in p doped material with of approximately as inferred from Hall data ( Fig. 4 4 ) taken at Accordingly, the final carrier dens ity including contributions from the as made graphene and the charge transfers associated with the Schottky barrier ( and the applied voltage ) reads as

PAGE 154

154 (4 9) Using the well ergy, we can write (4 10) w hich in combination with Eq. ( 4 5 ) becomes (4 11) T o calculate typical shifts in we use parameter values cm/s and for a typical semiconductor. Thus the Fermi energy of the as made graphene with of about is calculated from to be below the charge neutrality point, a shift assoc iated with the aforementioned p doping during processing. When the graphene is transferred onto a semi conductor, equilibration of the chemical potentials result s in a transfer of negative charge to the graphene and an increase in [calculated from Eq. ( 4 8 ) for ] to be in the range of for in the range of to The application of a typical 10 V reverse bias voltage ( Figs. 4 5 through 4 8 ) creates significantly larger Fermi energy shifts, which from Eq. ( 4 8 ) give in the range of to for the same factor of variatio n in The corresponding shifts from the pristine value of are in the range of and thus bring closer to the neutrality point. These numerical calculations show that, for our n doped semiconductors, it is relative ly easy to induce Fermi energy shifts on the order of with the application of a sufficie ntly high reverse bias voltage. Since the electron affinity of the semiconductor remains unchanged, the Schottky Mott constraint of Eq. ( 4 2 ) enforces the sa me reduction in

PAGE 155

155 thus leading to a greater than 5% reduction in the measured SBHs shown in Table 4 1 as determined by the in situ Raman spectroscopy measurements ( Fig. 4 3 ) is larger ( of approximately ) than our theoretical estimation ( of approximately ). The discrepancy between the theoretical estimate of and the experimental values might be attributed to (1) the existence of an interface capaci tance induced by dipoles at the graphene/semiconductor interface (within bond polarization theory), causing deviation from the ideal Schottky Mott cap acitance relation given by Equation 4 4 and (2) the estimate of using relative peak shifts in the and peak positio ns for graphene deposited on Si/SiO 2 109 which might be different than the change in Fermi level for graphene transferred onto semiconductors. As discussed in the previous sections, since the of the graphene electrode is sensitive to the applied bias across the graphene/semiconductor interface, the SBH at the interface becomes bias dependent, especially for large reverse voltages. However, extracting the SBH from characteristics u sing Equation 4 1 which involves extrapolating current density to zero bias saturation current ( ), yields the putative zero bias barrier height (Table 4 1 ). Finally we present a simple modification t o the Richardson equation (Eq. 4 1) consideri ng the shift in of graphene induced by applied bias. The modified Richardson equation preserves the original functional form of Eq. ( 4 1 ) but allows one to estimate the SBH at fixed voltages. The voltage dependent SBH [ ] can be written as (4 12)

PAGE 156

156 where is the zero bias SBH and is the correction to the SBH at fixed voltage V. The change in the Fermi energy is opposite to i.e., as seen in Fig. 4 14 Thus, for reverse bias (the addition of electron s to the graphene), we use Equations 4 5 and 4 7 together with the inequality to calculate (4 13) Adding the reverse and forward current densities, as done in s tandard treatments of the diode equation, yields the total current density across the graphene/semiconductor interface, (4 14) Here, we note that the original form of the Richardson equation is preserved, with slight modifications to the saturation current term, which is given as (4 15) with for reverse bias given b y Eq. 4 10 In our conventional analysis using Eq uation 4 1 the zero bias saturation current is extracted by extrapolating the current density to the zero bias limit. In this limit, the correction to the SBH is expected to be zero, since t he graphene is not subject to applied bias and hence the Fermi level does not shift from the original value. However, using the extrapolated zero bias saturation current density, one can extract the SBH, and one can take into account the

PAGE 157

157 correction to the SBH at fixed bias ( ) by the additional term in Eq uation 4 12 4.4 Gated Schottky Junctions on Si: Continuous Graphene Case Noting the impact that a shift in barrier height can have on rectification currents, we turn our attention to three terminal ga te field modulated Schottky barrier transistors. These devices make use of an electrically insulated gate electrode to modulate the Fermi level of the graphene. Th e electric field effect induced shift of the graphene work fun ction results in smooth chang es to the barrier height between the graphene and the semiconductor (the DOS of graphene is also smooth and continuous) Under a constant source drain bi as (i.e. forward or reverse preserving conventional diode terminology), adjusting the barrier height via a gate potential will result in a change to the current flow across the junction. In order for sufficient current modulation to occur the initial barrier height m ust not be too large compared with the graphene Fermi level shift due to gating. For this reason, we have chosen a lower doping concentration for the Silicon (p type, Boron, ) used in this experiment. Figure 4 15 confirms the rectifying behavior of the graphene/ p Si junction on which our three terminal transistors will be based. As expected, when compared to the graphene/n Si device studied in Section 4.2, the lower initial barrier height of these junctions results in higher current densities for a given bias. We still observe the onset of the non saturating reverse bi as current described in the previous section. The d iode device structure can be readily modified to yield a gated, three terminal device. A scalable top gate can be fabricated by depositing a dielectric layer and a

PAGE 158

158 metal contact directly on top of the gr aphene/semiconductor contact. This requires the graphene to be free of vertical protrusions to avoid shorting pathways through the thin dielectric layer (see Section 3.3 ). Care also needs to be taken not to damage the single layer graphene du ring the dep osition of the gate stack. Atomic layer deposition can yield very low stress, high k gate dielectrics without damaging the graphene layer, although seeding of the oxide layer may be necessary Alternatively, one off research devices can quickly be fabric ated using an ionic liquid as the gate die le ctric (see Fig. 4 1 ). 258 Here the ions rearrange in response to the applied gate voltage forming a capacitive double layer at the graphene ionic liquid interface. So long as the gate voltage is kept below the redox potential of the electrolyte no chemical reactions take place and the double layer behaves like an exceptionally thi n high dielectric The ionic liquid is ideal for gating large area graphene with folds, tents, and other conducting vertical protrusions (see Section 3.3.2 for methods to eliminate these protrusions). This technique is not well suited for measurements which require transient fields (i.e. transfer curves and dynamic switching) ; however it provides a facile method of probing the switching mechanisms in these Schottky transistors. Unlike traditional MOS transistors, the behavior of these Schottky barrier dev ices is inherently anisotropic. That is, t he bias (source drain) voltage polarity determines the mode of operation (the switching mechanism) The mechanisms for current transport across the junction are also different. In reverse bias, injection of hole s from the graphene electrode into the semiconductor occurs primarily via thermionic emission over the abrupt junction barrier, although thermionic field emission is also possible for narrow depletion widths (high doping densities, or large bias voltages,

PAGE 159

159 ). For any given semiconductor, t he barrier height is only a function of the graphene work function. This is in contrast to the forward bias mode, in which holes diffuse across the depletion region (Schottky transport) into the graphene. The barrier height for this case is determined by the flat band potential of the valence. This is a function of both the work function of the graphene as well as the source drain bias. Larger source drain bias voltages result in higher current densities and a weaker gate field modulation effect (smaller On/Off ratios). The two operating modes are schematically represented in Figure 4 16 In Figur e 4 17 we show the out put characteristics for a three terminal device in both reverse (A and B) and forward bia s (C and D) mode. The gate voltage was stepped in increments from to while carefully monitoring the gate leakage at each step to ensure that the ionic liquid had reached equilibr ium before beginning a bias sweep Voltage steps outs ide of this range were excluded due to the electrochemical breakdown that oc cu rs in the ionic liquid above a known threshold voltage ( ). Two features are immediately obvious when compa ring the performance of the operational modes: (1) the forward b ias current densit ies are much higher than those of the counterpart mode, and (2) the switching effect (i.e. the On/Off ratio) is more prominent in reverse bias. The first point is not surprising, since the current across a forward bias diode junction is naturally larger than for the reverse bias case. Less intuitive is the discrepancy in switching performance. This can be understood by looking at how the gate voltage and bias voltage effects combine to determine the barrier to hole injection from the se miconductor to the metal. The gate field applied to

PAGE 160

160 the graphene affect s the ba rrier on the semiconductor side indirectly due to the charge transfer that takes place at the junction. Thus, a positive (negative) gate bias increases (decreases) the depleti on barrier to transport. T he bias voltage imposes an offset between the Fermi level of the graphene and the semiconductor, shifting the flat band valence band level closer to the equilibrium level, consequently reducing the barrier for all gate voltages. A large gate field can also cause the depletion width in the semiconductor to narrow, increasing the field emission current across the junction in the state. This is the reason for the poor switching and high current densities in forward operated d evices. In reverse bias, the graphene Fermi level is directly related to the injection barrier height. The applied bias reduces the equilibrium barrier by lowering the Fermi level of the graphene closer to the valence band edge. At this stage, only a s mall negative gate field is needed to induce enough of a Fermi level shift to substantially increase the probability of thermionic injection. Conversely, a positive field will shift the Fermi level away from the valence band edge, thus turning the device off. Furthermore, a large bias voltage will also narrow the depletion width, leading to a disproportionate increase in the on state current (relative to the slight increase in the off state current). The two mechanisms are illustrated in Figure 4 18 The modulation of the reverse bias device is a direct result of the shift of the graphene work function with gate field. The device exhibits good switching behavior increasing with applied bias. As expected for the forward bias case, the current density lev els are higher and the On/Off ratio decreases with larger bias voltages (the applied bias reduces the depletion barrier). In this mode, the modulation is a secondary effect of the graphene work

PAGE 161

161 function shift: charge transfer across the junction causes th e valence band energy of the semiconductor to shift closer to the equilibrium value, reducing the depletion barrier height. 4.5 Concluding Remarks Rectification across semimetal/semiconductor junctions has been studied for several common semiconductors. C urrent voltage and capacitance voltage measurements were used to characterize the Schottky barriers formed when graphene is placed in intimate contact with Si, GaAs, GaN and SiC. The good agreement with Schottky Mott physics within the context of bond p olarization theory is somewhat surprising given that the Schottky Mott picture was developed for metal/semiconductor interfaces, not for the semi metal /semiconductor junctions discussed here We did observe a shift of the graphene work function resulting f rom the charge transfer across the interface during Schottky barrier formation This shift does not occur at metal/semiconductor or graphite/semiconductor interfaces, where remains fixed during Schottky barrier formatio n Due to a low density of states, the Fermi level is also sensitive small changes in charge density induced by the bias potential. The se bias induced shift s in the Fermi level result in significant de viations to the rectification behavior of the diodes in reverse bias W e have modified the thermionic emission diode equation allowing us to estimate the change in the barrier height at fixed applied bias. Three terminal devices were fabricated by exploi ting the additional barrier height modulation accessible via an applied gate field. The devices exhibit drastically different modes of operation for forward and reverse biasing of the underlying diode.

PAGE 162

162 Figure 4 1. Fabrication and electrical characte rization of graphene/inorganic semiconductor junctions. (A) Two terminal diodes are made by etching windows ( ) through the oxide layer (purple) and draping a graphene over the source contacts (gold). (B) The current voltage characteristics are measured applying a bias voltage between the grounded Ohmic back contact (brown) and graphene film. (C) Three terminal Schottky barrier transistors are gated using an ionic liquid gate.

PAGE 163

163 Figure 4 2. Raman characterization of graphene on technologic ally relevant semiconductors. Raman spectra of (A ) CVD grown graphene on Cu foils and (B ) graphene, after transfer onto various semiconductor substrates. Graphene sheets show a large ratio, and after the transfer, the graphene becomes slightly disordered. (C ) The Raman spectra peak. The black curve is the measurement on graphene/Cu and the other curves are for the graphene/semiconductor combinations as in dicated in t he legend in (B). (D ) Same as in (C ) for the Raman spectra peak.

PAGE 164

164 Figure 4 3. In situ bias dependent Raman spectra taken on graphene/GaN junctions Plotted as a function of a pplied bias: (black line), (red line), and (blue line). Blue arrows indicate the direction and magnitude of the shift in the and peak positions relative to zero bias when the diode is reverse biased.

PAGE 165

165 Figure 4 4. Hall transport of transferred graphene. vs Magnetic field ( ) taken at Typically, sample mobilities are in the range of and carrier densities (holes) are in the range of

PAGE 166

166 Figure 4 5 Graphene/Silicon Schottky diode: Room temperature transport characteristics. (A) L inear current density voltage ( ) and (B) log current density voltage ( ).

PAGE 167

167 Figure 4 6 Graphene/GaAs Schottky diode: Room temperature transport characteristics. (A) Linear current density voltage ( ) and (B) log current density vo ltage ( ).

PAGE 168

168 Figure 4 7 Graphene/GaN Schottky diode: Room temperature transport characteristics. (A) Linear current density voltage ( ) and (B) log current density voltage ( ).

PAGE 169

169 Figure 4 8 Graphene/GaN Schottky diode: Roo m temperature transport characteristics. (A) Linear current density voltage ( ) and (B) log current density voltage ( ).

PAGE 170

170 Figure 4 9. Temperature dependent graphene/ n Si diode characteristics. (A ) Plot of the temperature dependence of the current (I) versus voltage (V) curves measured across a graphene/GaAs junction from up to with intervals separating each isotherm. The arrows indicate the direction of increasing temperature. (B ) Plot of the temperature dependenc e of curves t aken on graphene/ n Si junctions at different temperatures. (C ) Extracted values from B are plotted in terms of versus

PAGE 171

171 Figure 4 10. Temperature dependent graphene/GaAs diode characteristics. (A ) Plot o f the temperature dependence of the current (I) versus voltage (V) curves measured across a graphene/GaAs junction from up to with intervals separating each isotherm. The arrows indicate the direction of increasing temperature. (B ) Pl ot of the temperature dependence of I V curves t aken on graphene/GaAs junctions at different temperatures. (C ) Extracted values from B are plotted in terms of versus

PAGE 172

172 Figure 4 11. Temperature dependent graphene/GaN diode characteristics. (A ) Plot of the temperature dependence of the current (I) versus voltage (V) curves measured across a graphene/GaAs junction from up to with intervals separating each isotherm. The arrows indicate the direction of inc reasing temperature. (B ) Plot of the temperature dependence of I V curves t aken on graphene/GaN junctions at different temperatures. (C ) Extracted values from B are plotted in terms of versus

PAGE 173

173 Figure 4 12. Temperature de pendent graphene/SiC diode characteristics. (A ) Plot of the temperature dependence of the current (I) versus voltage (V) curves measured across a graphene/GaAs junction from up to with intervals separating each isotherm. The arrows in dicate the direction of increasing temperature. (B ) Plot of the temperature dependence of I V curves t aken on graphene/SiC junctions at different temperatures. (C ) Extracted values from B are plotted in terms of versus

PAGE 174

174 Fi gure 4 13. Capacitance measurements (A ) Plots of the inverse square capacitance ( ) versus applied bias ( ) for graphene/ n Si (red squares and the markings on the left hand y axis) and for n GaAs (green circles and the markings on the right hand y axis) at and show a linear dependence, implying that the Schottky Mott model provides a good description. The interception on the abscissa gives the built in potential ( ), which can be correlated to the Schottky barrier height, whi le the slope of the linear fit gives Extracted and values are listed in Table 4 1

PAGE 175

175 Table 4 1 Extracted SBHs, doping densities, and corresponding graphene work function values on various graphene/ semiconduc tor junctions.

PAGE 176

176 Figure 4 14. Band diagrams for graphen e/inorganic semiconductor Schottky diodes. The shift of the Schottky barrier height with applied bias results in modifications to the standard thermionic emission current, especially for reverse bias case. (A) Forward, (B) zero, and (C ) reverse bias conditions are shown

PAGE 177

177 Figure 4 15. The diode characteristics for the graphene/ p Si junction used for the three terminal Schottky barrier transistor. The lower initial barrier gives rise to high er current densities than the n type device studied in Section 4.2, as seen in the (A) and plots.

PAGE 178

178 Figure 4 16. Band bending schematic for a three terminal, gate field modulated Schottky barrier transistor. The transis tor has two distinct modes of operation: the Forward (B, D, and F) and Reverse bias (A, C, and E) modes. A negative gate bias turns p type devices on, while a positive gate bias turns them off. The gate field modulation of the graphene Fermi level not on ly affects the barrier height, but also the width of the depletion region. Note that the current in forward bias mode is dominated by diffusion across the depletion region, while in reverse bias mode the current is primarily thermionic over the abrupt jun ction barrier.

PAGE 179

179 Figure 4 17. Output characteristics of a three terminal graphene/ p Si Schottky barrier transistor. The transistor can operate in both the reverse (A and B) or forward bias (C and D) mode. The modulation of the graphene Fermi level dicta tes the magnitude of current transport across the barrier. The reverse bias mode has a reasonable On/Off ratio of 100, while the forward bias mode exhibits significant non saturating current densities in both the on and off states.

PAGE 180

180 Figure 4 18. Compar ison of the reverse and forward bias modes of Schottky barrier transistor operation. (A) The forward and reverse bias operating modes of the graphene/p Si junction transistor. (B) A schematic of the two operating mechanisms. The small initial Fermi leve l shift in the graphene is due to the applied bias (forward or reverse), while the larger omnidirectional shift (red zone) is attributed to the gate field modulation of the Fermi level.

PAGE 181

181 CHAPTER 5 GRAPHENE/ORGANIC SEM ICONDUCTOR INTERFACE S 5.1 Introducti on In the last chapter, we demonstrated that the Schottky barrier at the semimetal/ inorganic semiconductor interface exhibits an anomalous non saturating reverse bias current. We also showed that this current can be modulated by a gate field. Junction s between semimetals and organic semiconductors should display similar behavior. Such control has been demonstrated in carbon nanotube enabled vertical field effect transistor s (CN VFET) where modulation of the contact barrier between a dilute nanotube so urce electrode and an organic semiconductor channel layer controls the current flow through the organic channel. 259 261 In this Chapter, we will use gra phene as the source electrode for organic diodes and VFETs We also study the effect s of tuning the porosity of the g raphene film on device performance. The arch itecture, moreover, readily lends itself to conversion to a full aperture emission light emit ting transistor, where the high on currents at low operating voltages resulted in high brightness at low power dissipation. 262 5.2 Graphene Enabled Vertical Field Effect Transistors The increasing availability of high quality graphene 133,207,141,127 and the low DOS it shares with the nanotubes makes graphene a natural candidate source electrode for similar high performance VFETs. The vertical architecture consisting of a gate, gate I gratefully acknowled ge my collaborators for their many contributions, especially Drs. Evan Donaghue and Andrew Rinzler. The work presented in this Chapter is based in part on published results. The published manuscript and figures have been modified from their original for mat: Improved Transfer of Graphene for Gated Schottky Junction, Vertical, Organic, Field Effect Transistors. ACS Nano 2012 6 9095.

PAGE 182

182 dielectric, source electrode, semiconducting channel, and drain electrode in a collinear stac k (similar to Fig ure 5 1 ) takes advantage of the very thin control layer occurring at the nanotube organic junction, allowing for short channel lengths and yieldi ng high on currents at low source drain voltage, despite the low mobility of organic semiconductors. V ertically stacking the source, channel, and drain layers makes the transistor channel length simply the thickness of the deposited channel layer. The n aturally short channel length this creates allows for large on currents, despite the use of relatively low mobility organic channel materials. For a conventional, lateral channel, TFT to achieve a comparable channel length would require (expensive) high r esolution patterning, and subject the device to short channel effects. The devices discussed here, because they rely on a distinct Schottky barrier modulation for their operation, are immune to short channel effects. The monolithic nature of graphene may p rovide intrinsic advantages in sheet resistance compared to nanotube films, 263,264 where impedance at tube tube junctions may ultimately limit device performance. The single atom thickness o f graphene in a continuous layer also affords the opportunity to disentangle the operational mechanism of these gated Schottky junction VFETs. B arrier height modulation is possible due to the low DOS of nanotubes and graphene but VFETs that use conventio nal metal source electrodes (in which the high DOS effectively precludes barrier height modulation) have also been demonstrated. 265 268 To function such devices require that the metallic source electrode be perforated thus allowing the gate field direct access to the metal semiconductor interface, where a field induced band bending thins the barrier (without barrier height lowering) to allow tunneling currents. Such band bending also

PAGE 183

183 contributes to barrier modulation in the CN VFET, where the dilute nanotube source electrode also admits the gate field to the nanotube organic interface. The nanotube based devices thus operate in a mixed fashion, taking advantage of both modes. The continuous electrode provided by grap hene can probe (principally) the effect of the barrier height modulation. Better still, by purposely inducing holes in the continuous graphene layer we can probe both modes in a single material system Here this is done to report the first organic channe l graphene enabled VFETs (G VFETs Fig. 5 2 ). We fabricate graphene/organic semiconductor junctions and VFETs using the transfer techniques described in Section 3.3 and thermally evaporated organic channel materials. Figure 5 2 shows the rectification an d transfer characteristics of the organic two and three terminal devices. The anomalous non saturating reverse bias current is observed in these organic devices. Gate field control of the reverse bias current is also evident from Fig. 5 2B An analyti cal expression for the diode current is not easily obtained for these devices due to the non linear nature of transport at organic interfaces. The devices are fabricated using the growth and transfer methods described earlier. In summary, after copper d issolution the Au coated section of the graphene/Au/PMMA sandwich was adhered, graphene side down, to a p + Si/SiO 2 /BCB substrate. BCB is a benzocyclobutene derivative that had previously been spun coat onto the SiO 2 and thermally cross linked to leave an 8 nm thick hydrophobic layer on the dielectric. This excludes water adsorption from the ambient which has been implicated in charge trap generation on oxide dielectrics, degrading device performance. 217 The Au served as an etch mask while the PMMA and excess graphene

PAGE 184

184 around the gold mask were dry etched in an O 2 plasma thus defining the edge of the graphene source electrode. An iodide based gold etchant subs equently removed the mask layer. Finally, a gold source contact was evaporated along one edge of the graphene layer completing the source electrode. The measured areal hole densities in the graphene used to build the G VFETs discussed below were 0, 2, 13 and 20% with average hole diameters of 2.2 0.6m, 2.3 0.6m, 2.5 1.0m, respectively. The organic semiconductor channel layer evaporated onto the graphene was dinaphtho [2,3 b f ]thieno[3,2 b ] thiophene (DNTT). 269 The flatness of a single layer of graphene should in principle permit even sub 100 nm channel layer thickness (with corresponding performance enhancement) wi thout incurring electrical shorts to the top drain electrode. We found however that device yields suffered when the DNTT thickness was below 250 nm. This may be a consequence of the low surface energy of graphene and crystallinity of DNTT that results in island growth incorporating pinholes and shorting paths to the subsequently deposited Au drain electrode, for thin channel layers. To ensure effectively 100% yields and to permit a direct performance comparison against comparable channel thickness Ag an d CN VFETs, a DNTT channel thickness of 500 nm was used. G VFET devices were tested with the graphene source electrode contact held at ground potential, while the drain and gate were biased relative to ground. Figure 5 5 shows typical output curves for the G VFETs with graphene source electrode areal hole densities of 0, 2, 13 and 20% ( Fig. 5 4 ). Both the on (V G = 40 V) and off (V G =+40V) states are shown. Thinner and/or higher k gate dielectrics should allow for low gate voltage operation as seen in CN VFETs that employ them. 260,262 The advantage of the

PAGE 185

185 short channel length in the vertical architecture is seen in the high on current densities at low drain voltages ( | 5| V). The on current densities clearly scale with the densit y of holes in the graphene source electrode. Figure 5 5C plots the on/off current ratio of the devices as a function of the on current density (as the drain voltages are swept from 0 to 5 V). The 20% areal hole density electrode yields on/off ratios exc eeding 10 6 Attempts to get higher hole densities (>20%) by making the protective Au layer thinner resulted in discontinuous graphene sheets. Ordered hole arrays would avoid this problem and provide a path for further device optimization. A summary of t he device characteristics versus areal hole density is plotted in Figure 5 5D 5.3 Tuning the Field Permeability of the Graphene Electrode The current modulation seen to occur with the continuous graphene electrode (over three orders of magnitude) provid es strong support for the anticipated Schottky barrier height modulation (changing principally the thermionic emission). Extrapolating from the Kevin probe measurements of Yu et al., 257 we estimate that our gate sweep results in a 0.4 0.5eV shift of the graphene work function and a commensurate modulation of the barrier height. Introducing 20% holes into the graphene source electrode yields a further 2 3 de cades of transconductance. The gate field access to the graphene DNTT interface in the vicinity of the holes additionally thins the barrier ( Fig. 5 3 ) resulting in the dramatic current enhancement. Note that barrier height modulation also plays a role in the enhanced tunneling currents since (for exampl e) within the WKB approximation the tunneling probability is proportional to : (5.1)

PAGE 186

186 where is the barrier height, the local electric field and constant. Such barrier height modulation can thus explain the dramatic performance advantage these low DOS metals (graphene, nanotubes) hav e over the conventional metal source electrode based devices. As support of this hypothesis, in the next section we present a comparison of our field transparent graphene with other porous electrode materials. 5.4 Comparisons to Other Porous Electrode s 5.4.1 Metal versus Semimetal Porous Electrodes The high DOS of conventional metal devices should preclude any gate modulation of the electrode work function, and limit the switching mechanism to the penetration of the gate field near the pores. Simila r porous metal FETs have been fabricated by the Tessler group at IIT, 266,270 however several key diffe rences prevent a direct comparison with our devices Instead, we have fabricated thin film Silver electrodes with comparable hole densities to our graphene devices. Silver was chosen for the se porous metal VFETs because it is readily evaporated and has a work function that is close to that of gra phene ( ). This ensures that the initial barrier height is the same for both electrode materials. VFETs fabricated with continuous Ag electrodes show no tr ansconductance, confirming no appreciabl e work function modulation occurs in gated me tallic electrodes. In order to accurately compare the switching performance of devices with porous electrodes, we need to ensure that the metal and semimetal electrodes have equivalent porosities. We used porous membranes to pattern both the graphene and Ag electrodes with the same pore densities ( Fig. 5 6 ). Graphene was first transferred to BCB/SiO 2 /p + Si substrates using the techniques described in Section 3.3. Then a porous membrane (Sterlitech, 200nm pores) was adhered to the graphene film using a d rop of IPA and hot clamped for 4

PAGE 187

187 hours The stack was then exposed to a brief oxygen etch (30 sec, 50 sccm O 2, 10mTorr, 30W RIE, 150W ICP) to etch away the graphene in the pores. The membranes were washed away in successive chloroform baths and rinsed wi th IPA. Finally, the graphene was annealed in an inert atmosphere. We also used the membranes as a transfer template to pattern porous Ag films. We thermally evaporated 20nm of Ag onto the membranes and then adhered to the BCB/SiO 2 /p + Si substrates usin g a drop of IPA and hot clamped for 8 hours in a N 2 glovebox to minimize the tarnishing of the silver. The membranes were washed away (see above) and the samples were immediately loaded into the evaporation chamber. Ex situ SEM characterization of the Ag and graphene films revealed areal pore densities of ~1.2% and highly uniform 200nm pores. Some residue from the porous membranes remained despite repeated solvent cleaning steps. VFETs with both Ag and graphene electrodes were then fabricated in parallel using the process described in Section 5.2. The performance of the devices is compared in Figure 5 7 The difference between metal and semimetal porous electrodes is manifested in the poor switching characteristics of the Ag VFETs. The larger current densities can be attributed to the higher conductivity of the 20nm Ag thin film (graphene has a higher mobility, but the thicker Ag electrode has a lower resistance). The relatively poor performance of the graphene device s may be the result of residual do ping from the patterning process. However u nlike for the meta l electrode, the low DOS of graphene all ows the gate field to modulate t he barrier height at the junction resulting in a two order of magnitude im provement in the On/Off ratio. This

PAGE 188

188 emphasizes the need for a better understanding of the interplay between conductivity, barrier height modulation, and field permeability. 5.4.2 Porous Graphene versus Dilute Carbon Nanotubes We also compare our graphene based transistors with state of the art devic es made with another porous semimetal material: dilute carbon nanotube networks. Comparison between the G VFET and CN VFET reveals differences that can be attributed to the morphological differences between the respective source electrodes. Figure 5 8A co mpares transfer curves for a G VFET with a 20% areal hole density graphene source electrode and a typical CN VFET fabricated on the same p + Si/SiO 2 /BCB gate electrode/gate dielectric substrates. The drain voltages are adjusted to yield comparable on curre nts at a gate voltage of 40 V. The large hysteresis seen in the nanotube based device has been explained by ambipolar charge traps in the BCB having a well defined critical field for charge exchange with the electrode. 271 This hysteresis can be minimized b y restricting the gate voltage range but here it is interesting to observe the significantly smaller hysteresis for the graphene source electrode over the same large voltage range. This is likely due to the enhanced field concentration around the nanomete r width nanotube electrodes versus the half plane like graphene electrode in the vicinity of a hole. Output curves for the two devices are plotted in Figure 5 8 B for gate voltages of 40V and drain voltages out to 10V. Compared to the nanotube device th e graphene devices exhibits a drain voltage delay of ~500 mV before current begins to flow. This may be due to the work function difference between the graphene ( 4.6 eV) and the DNTT ( 5.4 eV) generating a larger initial barrier than that between the DNTT and the nanotubes. The nitric acid purification of the nanotubes charge transfer dopes them,

PAGE 189

189 placing their work function around 4.9 eV, after which a heating step dedopes them to an estimated 4.7 to 4.8 eV. The field concentration around the nanotube s may also give them an advantage in terms of this lower turn on voltage. As the drain voltage continues to grow, the nanotube device off current begins to suffer as the drain field concentration around the nanotubes begins to extract charge despite the o ff state (+40 V) gate voltage. The planar graphene does not exhibit such degradation in the off state. The graphene electrode also excels in the on state at high drain voltage. At V D = 10V the CN VFET on current density is ~300mA/cm 2 compared to an as tounding ~1200mA/cm 2 for the graphene device. We attribute this to the lower impedance of the monolithic graphene layer versus that at tube tube contacts across the nanotube film electrode. Figure 5 8 C compares the on/off ratios for the two devices as a function of their on currents ( ) as the drain voltage is swept from 0 to 10 V. The impedance limited on current and increasing off current degrades the on/off ratio of the nanotubes device while that of the graphene device remains above 10 6 out to 10 V. 5.5 Concluding R emarks We have studied the transport properties of graphene/organic junctions and demonstrated a gate field modulated organic Schottky barrier transistor. By tuning the porosity of the graphene source electrode we show that the gate field can be used to m odulate not only the barrier height, but also the barrier width. This work also has implications for a very recently published inorganic channel graphene source electrode 272 While that device used a top gate architecture and the semiconductor was crystalline silicon, the principle of operation can be recognized to be precisely the same as the continuous graphene bottom gate, organic semico nductor devices we discuss here (unlike the case for the relatively low mobility organic

PAGE 190

190 semiconductors, the high mobility of the crystalline silicon allows the drain electrode to lie in a more remote, arbitrary location relative to the graphene source ele ctrode without loss of performance). Their (and our) Schottky junction devices exhibit a gate modulated transconductance in either the forward or reverse bias direction of the graphene/semiconductor diode. In the case of a continuous graphene source elec trode, which relies principally on barrier height modulation, they show a forward bias on off ratio of 10 5 which greatly exceeds the performance of transistors that use graphene as the channel layer. However, attaining the low off state current in the fo rward direction of the diode required an impractically low bias voltage of 0.3 V (the off state current rising much more quickly than the on state current as the bias voltage increased). In reverse bias operation their on off current ratio was only a fact or of 300, not far from the three orders of magnitude current modulation we show for the continuous graphene/organic semiconductor in reverse bias operation. As we further show, however, providing the gate field direct access to the graphene/semiconductor interface by incorporating holes or edges in the graphene electrode introduces a new tunneling mechanism that boosts the on off ratio by an additional three orders of magnitude to yield an on off ratio of By operating our holey graphene/organic c hannel devices in the reverse bias mode the off state was maintained even to large bias voltages (as expected for a diode operated in reverse bias), while the on state was dramatically boosted by tunneling through the thinned Schottky barrier in those regi ons where the gate field now had direct access to the graphene/semiconductor interface. Similar large improvements should be had by configuring graphene/silicon devices to allow gate field access when operated in reverse bias.

PAGE 191

191 Better controlled patterni ng techniques to fabricate ordered hole arrays in graphene over a wider range of densities and sizes, in conjunction with a thinning of the active channel layer thickness should offer a straightforward path to improved device performance. Optimized nanotu be devices yield their highest on/off ratios with an areal pore density of approximately 75% suggesting significant room for improvement in such organic channel graphene devices.

PAGE 192

192 Figure 5 1. The G VFET architecture and drive scheme The graphene sou rce electrode is transferred directly to a Si/ SiO 2 wafer onto which the small molecule organic semiconductor (DNTT) layer and Au drain contact are thermally evaporated. The source contact is held at ground and the bias voltage ( ) is applied between the source and d rain contacts. The Schottky barrier is modulated by a gate field that is applied by the biasing ( ) the silicon wafer with respect to the grounded source contact.

PAGE 193

193 Figure 5 2 Two and three terminal devices with semimetal/organic semic onductor junctions. (A) Rectification in a graphene/DNTT diode. (B) Transfer curve of a gate field modulated Schottky barrier transistor based on the graphene/DNTT diode.

PAGE 194

194 Figure 5 3. Energy level diagram for a GVFET at the graphene semiconducting ch annel interface for constant drain voltage and three distinct gate voltages. The black line depicts the hole injection barrier and depletion layer in the semiconductor for a continuous graphene electrode. The red dashed line depicts the same features for the case of a graphene electrode perforated with holes. For the continuous graphene case current modulation is due principally to barrier height lowering (thermionic emission).

PAGE 195

195

PAGE 196

196 Figure 5 4 Field permeable graphene electrodes with various pore densities. 50 x 50 m SEM images of the transferred graphe ne films having the indicated hole densities (0%, 2%, 15%, and 19.6%, respectively)

PAGE 197

197 Figure 5 5 Device performance of field permeable G VFETs. (A ) G VFET output curves for the off state (V G =+40V) and the on state (V G = 40V) for these graphene sour ce electrode hole densities. (B ) On/Off current ratio versus on state current density up to a drain voltage o f 5V for each hole density. (C ) On current densities and On/Off current ratios for drain voltage up to 10 V versus source electrode hole density

PAGE 198

198 F igure 5 6 Fabrication of graphene and Ag electrodes with comparable pore densities. A commercially available porous membrane with highly controlled pore density is used to pattern the electrodes. The membrane is used as an etch mask for the gra phene film (A C), and as a transfer template for the evaporated Ag film (D E).

PAGE 199

199 Figure 5 7 Comparison of VFETs constructed with porous graphene versus porous Ag electrodes. (A) Transfer and (B) output curves for both VFET architectures. The graphen e VFET exhibits a much larger transconductance and On/Off ratio. As expected, the current densities are higher for the 20nm thick Ag electrode compared to the graphene film.

PAGE 200

200 Figure 5 8 Comparison of graphene and carbon nanotube enabled VFETs w ith all other device layers the same. (A) Transfer curves for a CN VFET and the G VFET with a 20% areal hole density electrode. (B) Output curves for both devices in the on ( ) and off ( ) states up to (C) On/O ff ratios versus on current density for drain voltages to 10V.

PAGE 201

201 CHAPTER 6 CONCLU SIONS AND PROSPECTIVE The progression of results described in this thesis can be summarized as follows: (1) Techniques were developed to maximize the electrical conductivity and uniformity of large area ( ) graphene sheets and to cleanly transfer those single layer films to insulating or semiconducting substrates without inducing the usual disorder attributed to the transfer process; (2) The graphene films were transferred to common inorganic semicon ducting (Si, GaAs, GaN, SiC) to study the behavior of two terminal semimetal/semiconductor junctions (Schottky diodes) ; (3) Unusual rectification behavior structure yieldin g a modified analytical expression for the diode current across the junction; (4) These semimetal/semiconductor junctions were used as the basis for three terminal Schottky barrier transistors, operating by gate modulation of the barrier height; (5) Analog ous three terminal devices were made using Graphene/ Organic semiconductor junctions; (6) The field permeability of the semimetal electrode was tuned by patterning micron scale holes in the graphene films, thus allowing the gate field to not only shift the graphene Fermi level, but also to narrow the depletion width in the semiconductor, thus admitting a second switching mechanism. The result is an unconventional graphene based transistor with six orders of magnitude current modulation and potential for ext remely large drive currents. Since its discovery, the convention has to been to use g raphene as a semiconductor, ignoring its s emimetal character altogether. Instead of modify ing our graphene to turn it into a suitable channel material we have chosen dev ice architectures that make use of its extraordinary in trinsic properties The rectification

PAGE 202

202 effects observed for a wide variety of semiconductors suggest a bright future for graphene/semiconductor diodes particularly in applications requiring mechanical stability, optical transparency, resistance to diffusion, robustn ess at high temperatures, and demonstrated capability to embrace multiple functionalities. Rather than view the deviations from ideal Schottky diode rectification as parasitic, we have demo nstrated that this unusual behavior can be harness ed as the central operating mechanism for a new class of gate modulated Schottky barrier transistors.

PAGE 203

203 APPENDIX LIST OF PUBLICATIONS 1. Cao, Q.; Zhu, Z. T.; Lemaitre, M. G.; Xia, M. G.; Shim, M.; Rogers, J. A. Transparent Flexible Organic Thin film Transistors That Use Printed Single walled Carbon Nanotube Electrodes. Applied Physics Letters 2006 88, 113511 3. 2. Matthews, K. D.; Lemaitre, M. G.; Kim, T.; Chen, H.; Shim, M.; Zuo, J. M. Growth Modes of C arbon Nanotubes on Metal Substrates. Journal of Applied Physics 2006 100, 044309 10. 3. Tongay, S.; Lemaitre, M.; Schumann, T.; Berke, K.; Appleton, B. R.; Gila, B.; Hebard, A. F. Graphene/GaN Schottky Diodes: Stability at Elevated Temperatures. Applied P hysics Letters 2011 99, 102102 3. 4. Tongay, S.; Berke, K.; Lemaitre, M.; Nasrollahi, Z.; Tanner, D. B.; Hebard, A. F.; Appleton, B. R. Stable Hole Doping of Graphene for Low Electrical Resistance and High Optical Transparency. Nanotechnology 2011 22, 42 5701. 5. Tongay, S.; Lemaitre, M.; Miao, X.; Gila, B.; Appleton, B. R.; Hebard, A. F. Rectification at Graphene Semiconductor Interfaces: Zero Gap Semiconductor Based Diodes. Phys. Rev. X 2012 2, 011002. 6. Appleton, B. R.; Tongay, S.; Lemaitre, M.; Gila, B.; Fridmann, J.; Mazarov, P.; Sanabia, J. E.; Bauerdick, S.; Bruchhaus, L.; Mimura, R. et al. Materials Modifications Using a Multi ion Beam Processing and Lithography System. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactio ns with Materials and Atoms 2012 272, 153 157. 7. Tongay, S.; Lemaitre, M.; Fridmann, J.; Hebard, A. F.; Gila, B. P.; Appleton, B. R. Drawing Graphene Nanoribbons on SiC by Ion Implantation. Applied Physics Letters 2012 100, 073501 3. 8. Lemaitre, M. G.; Tongay, S.; Wang, X.; Venkatachalam, D. K.; Fridmann, J.; Gila, B. P.; Hebard, A. F.; Ren, F.; Elliman, R. G.; Appleton, B. R. Low temperature, Site Selective Graphitization of SiC via Ion Implantation and Pulsed Laser Annealing. Applied Physics Letters 2 012 100, 193105 4. 9. Lemaitre, M. G.; Donoghue, E. P.; McCarthy, M. A.; Liu, B.; Tongay, S.; Gila, B.; Kumar, P.; Singh, R. K.; Appleton, B. R.; Rinzler, A. G. Improved Transfer of Graphene for Gated Schottky Junction, Vertical, Organic, Field Effect Tra nsistors. ACS Nano 2012 6, 9095 9102. Reference 1 & 2 were completed at the University of Illinois at Urbana undergraduate research. The work in References 3, 4, and 6 is largely outside the scope of this thesis.

PAGE 204

204 LIST OF REFERENCES 1. Buckminsterfullerene. Nature 1985 318 162 163. 2. Iijima, S. He lical Microtubules of Graphitic Carbon. Nature 1991 354 56 58. 3. Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004 3 06 666 669. 4. Lin, Y. M.; Dimitrakopoulos, C.; Jenkins, K. A.; Farmer, D. B.; Chiu, H. Y.; Grill, A.; Avouris, P. 100 GHz Transistors from Wafer Scale Epitaxial Graphene. Science 2010 327 662 662. 5. Wu, Y.; Lin, Y.; Bol, A. A.; Jenkins, K. A.; Xia, F. ; Farmer, D. B.; Zhu, Y.; Avouris, P. High frequency, Scaled Graphene Transistors on Diamond like Carbon. Nature 2011 472 74 78. 6. Prasai, D.; Tuberquia, J. C.; Harl, R. R.; Jennings, G. K.; Bolotin, K. I. Graphene: Corrosion Inhibiting Coating. ACS Nan o 2012 6 1102 1108. 7. Kim, K. S.; Zhao, Y.; Jang, H.; Lee, S. Y.; Kim, J. M.; Kim, K. S.; Ahn, J. H.; Kim, P.; Choi, J. Y.; Hong, B. H. Large scale Pattern Growth of Graphene Films for Stretchable Transparent Electrodes. Nature 2009 457 706 710. 8. Li X.; Zhu, Y.; Cai, W.; Borysiak, M.; Han, B.; Chen, D.; Piner, R. D.; Colombo, L.; Ruoff, R. S. Transfer of Large Area Graphene Films for High Performance Transparent Conductive Electrodes. Nano Lett. 2009 9 4359 4363. 9. Wang, X.; Zhi, L.; Mullen, K. T ransparent, Conductive Graphene Electrodes for Dye Sensitized Solar Cells. Nano Lett. 2008 8 323 327. 10. Li, X.; Zhu, H.; Wang, K.; Cao, A.; Wei, J.; Li, C.; Jia, Y.; Li, Z.; Li, X.; Wu, D. Graphene On Silicon Schottky Junction Solar Cells. Advanced Mat erials 2010 22 2743 2748. 11. Cohen Tanugi, D.; Grossman, J. C. Water Desalination Across Nanoporous Graphene. Nano Lett. 2012 12 3602 3608. 12. Dan, Y.; Lu, Y.; Kybert, N. J.; Luo, Z.; Johnson, A. T. C. Intrinsic Response of Graphene Vapor Sensors. Na no Lett. 2009 9 1472 1475. 13. Lee, W. H.; Park, J.; Sim, S. H.; Jo, S. B.; Kim, K. S.; Hong, B. H.; Cho, K. Transparent Flexible Organic Transistors Based on Monolayer Graphene Electrodes on Plastic. Advanced Materials 2011 23 1752 1756.

PAGE 205

205 14. Lee, S. K .; Jang, H. Y.; Jang, S.; Choi, E.; Hong, B. H.; Lee, J.; Park, S.; Ahn, J. H. All Graphene Based Thin Film Transistors on Flexible Plastic Substrates. Nano Lett. 2012 12 3472 3476. 15. Min, S. K.; Kim, W. Y.; Cho, Y.; Kim, K. S. Fast DNA Sequencing with a Graphene based Nanochannel Device. Nature Nanotechnology 2011 6 162 165. 16. Lee, K. H.; Shin, H. J.; Lee, J.; Lee, I.; Kim, G. H.; Choi, J. Y.; Kim, S. W. Large Scale Synthesis of High Quality Hexagonal Boron Nitride Nanosheets for Large Area Graphen e Electronics. Nano Lett. 2012 12 714 718. 17. K.; Gaucher, A.; De, S.; Smith, R. J. et al. Two Dimensional Nanosheets Produced by Liquid Exfoliation of Layered Material s. Science 2011 331 568 571. 18. Zeng, Z.; Yin, Z.; Huang, X.; Li, H.; He, Q.; Lu, G.; Boey, F.; Zhang, H. Single Layer Semiconducting Nanosheets: High Yield Preparation and Device Fabrication. Angewandte Chemie International Edition 2011 50 11093 1109 7. 19. Layer MX2 Transition Metal Oxides and Dichalcogenides in a Honeycomb Like Structure. J. Phys. Chem. C 2012 116 8983 8999. 20. Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; M orozov, S. V.; Geim, A. K. Two dimensional Atomic Crystals. PNAS 2005 102 10451 10453. 21. Tanaka, T.; Ebina, Y.; Takada, K.; Kurashima, K.; Sasaki, T. Oversized Titania Nanosheet Crystallites Derived from Flux Grown Layered Titanate Single Crystals. Che m. Mater. 2003 15 3564 3568. 22. Fukuda, K.; Saida, T.; Sato, J.; Yonezawa, M.; Takasu, Y.; Sugimoto, W. NaFeO2 Related Structure and Its Electrochemical Supercapacitor Property. Inorg. Chem. 2010 49 4391 4393. 23. Peierls, R. Quelques Proprietes Typiques Des Corpses Solid. Ann. I.H. Poincare 1935 177 222. 24. Landau, L. Zur Theorie Der Phasenumwandlungen II. Phys. Z. Sowjetunion 1937 11 26 35. 25. Mermin, N. D. Crystalline Order in Two Dimensions. Phys. Rev. 1968 176 25 0 254. 26. Okamura, S. History of Electron Tubes ; IOS Press, 1994.

PAGE 206

206 27. Wilson, A. H. The Theory of Electronic Semi Conductors. Proc. R. Soc. Lond. A 1931 133 458 491. 28. Frenkel, J. Physik. Z. Sowjetunion 1935 8 185. 29. Davydov, B. J. Tech. Phys. U.S .S.R 1938 5 87. 30. Schottky, W. Z. Physik 1939 113 367. 31. Mott, N. F. The Theory of Crystal Rectifiers. Proc. R. Soc. Lond. A 1939 171 27 38. 32. Schottky, W. Z. Physik 1942 118 539. 33. Bardeen, J.; Brattain, W. H. The Transistor, A Semi Conduc tor Triode. Phys. Rev. 1948 74 230 231. 34. Bardeen, J.; Bardeen, J. Three Electrode Circuit Element Utilizing Semiconductive Materials 1950 35. Circuit Element Utilizing Semiconductive Material 1951 36. Schottky, W. Halbleitertheorie Der Sperrschicht. Naturwissenschaften 1938 26 843. 37. Mott, N. F. Note on the Contact Between a Metal and an Insulator or Semi Conductor. Mathematical Proceedings of the Cambridge Philosophical Society 1938 34 568 572. 38. Barth, A.; Marx, W. Graphene A Rising Star in View of Scientometrics. arXiv:0808.3320 2008 39. Wallace, P. R. The Band Theory of Graphite. Phys. Rev. 1947 71 622 634. 40. Reich, S.; Maultzsch, J.; Thomsen, C.; Ordejn, P. Tight binding Description of Graphene. Phys. Rev. B 2002 66 035412. 41. Fathi, D. A Review of Electronic Band Structure of Graphene and Carbon Nanotubes Using Tight Binding. Journal of Nanotechnology 2011 2011 1 6. 42. Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. The Electronic Properties of Graphene. Rev. Mod. Phys. 2009 81 109 162. 43. Mathematica ; Wolfram Research, Inc.: Champaign, IL, 2008. 44. Bostwick, A.; Ohta, T.; Seyller, T.; Horn, K.; Rotenberg, E. Quasiparticle Dynamics in Graphene. Nature Physics 2007 3 36 40.

PAGE 207

207 45. Hobson, J. P .; Nierenberg, W. A. The Statistics of a Two Dimensional, Hexagonal Net. Phys. Rev. 1953 89 662. 46. Dirac, P. A. M. The Principles of Quantum Mechanics ; Oxford University Press, 1982. 47. Zhang, Y.; Tan, Y. W.; Stormer, H. L.; Kim, P. Experimental Obser vation of the Nature 2005 438 201 204. 48. Katsnelson, M. I.; Novoselov, K. S.; Geim, A. K. Chiral Tunnelling and the Klein Paradox in Graphene. Nature Physics 2006 2 620 625. 49. Klein, O. Die Reflexi on Von Elektronen an Einem Potentialsprung Nach Der Relativistischen Dynamik Von Dirac. Zeitschrift fur Physik 1929 53 157 165. 50. Katsnelson, M. I. Graphene: Carbon in Two Dimensions ; 1st ed.; Cambridge University Press, 2012. 51. Novoselov, K. S.; Gei m, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Two dimensional Gas of Massless Dirac Fermions in Graphene. Nature 2005 438 197 200. 52. Lifshitz, I. M.; Gredeskul, S. A.; Pastur, L. A. Introductio n to the Theory of Disordered Systems ; Wiley, 1988. 53. Martin, J.; Akerman, N.; Ulbricht, G.; Lohmann, T.; Smet, J. H.; Klitzing, K. von; Yacoby, A. Observation of Electron hole Puddles in Graphene Using a Scanning Single electron Transistor. Nature Physi cs 2008 4 144 148. 54. Juan, F. de; Cortijo, A.; Vozmediano, M. A. H. Charge Inhomogeneities Due to Smooth Ripples in Graphene Sheets. Phys. Rev. B 2007 76 165409. 55. Feldman, B. E.; Krauss, B.; Smet, J. H.; Yacoby, A. Unconventional Sequence of Fract ional Quantum Hall States in Suspended Graphene. Science 2012 337 1196 1199. 56. Rose, M. E. Relativistic Electron Theory ; Wiley, 1961. 57. Kittel, C. Introduction to Solid State Physics ; John Wiley & Sons, 2004. 58. Gusynin, V. P.; Sharapov, S. G. Uncon ventional Integer Quantum Hall Effect in Graphene. Phys. Rev. Lett. 2005 95 146801. 59. Katsnelson, M. I. Zitterbewegung, Chirality, and Minimal Conductivity in Graphene. The European Physical Journal B Condensed Matter and Complex Systems 2006 51 15 7 160.

PAGE 208

208 60. Elias, D. C.; Nair, R. R.; Mohiuddin, T. M. G.; Morozov, S. V.; Blake, P.; Halsall, M. P.; Ferrari, A. C.; Boukhvalov, D. W.; Katsnelson, M. I.; Geim, A. K. et al. Control ne. Science 2009 323 610 613. 61. Liu, L.; Ryu, S.; Tomasik, M. R.; Stolyarova, E.; Jung, N.; Hybertsen, M. S.; Steigerwald, M. L.; Brus, L. E.; Flynn, G. W. Graphene Oxidation: Thickness Dependent Etching and Strong Chemical Doping. Nano Lett. 2008 8 1965 1970. 62. Meyer, J. C.; Geim, A. K.; Katsnelson, M. I.; Novoselov, K. S.; Booth, T. J.; Roth, S. The Structure of Suspended Graphene Sheets. Nature 2007 446 60 63. 63. Sharma, R.; Baik, J. H.; Perera, C. J.; Strano, M. S. Anomalously Large Reactivit y of Single Graphene Layers and Edges Toward Electron Transfer Chemistries. Nano Lett. 2010 10 398 405. 64. Schedin, F.; Geim, A. K.; Morozov, S. V.; Hill, E. W.; Blake, P.; Katsnelson, M. I.; Novoselov, K. S. Detection of Individual Gas Molecules Adsorb ed on Graphene. Nature Materials 2007 6 652 655. 65. Wehling, T. O.; Novoselov, K. S.; Morozov, S. V.; Vdovin, E. E.; Katsnelson, M. I.; Geim, A. K.; Lichtenstein, A. I. Molecular Doping of Graphene. Nano Lett. 2007 8 173 177. 66. Boukhvalov, D. W.; Ka tsnelson, M. I. Chemical Functionalization of Graphene with Defects. Nano Lett. 2008 8 4373 4379. 67. Gierz, I.; Riedl, C.; Starke, U.; Ast, C. R.; Kern, K. Atomic Hole Doping of Graphene. Nano Lett. 2008 8 4603 4607. 68. Farmer, D. B.; Golizadeh Mojar ad, R.; Perebeinos, V.; Lin, Y. M.; Tulevski, G. S.; Asymmetry in Graphene Devices. Nano Lett. 2009 9 388 392. 69. Pinto, H.; Jones, R.; Goss, J. P.; Briddon, P. R. P type Doping of G raphene with F4 TCNQ. Journal of Physics: Condensed Matter 2009 21 402001. 70. J.; Biswas, C.; Han, G. H.; Kim, E. S.; Chae, S. J.; Choi, J. Y.; Lee, Y. H. Layer by Layer Doping of Few Layer Graphene Film. ACS Nano 2010 4 4595 4600. 71. Tongay, S.; Berke, K.; Lemaitre, M.; Nasrollahi, Z.; Tanner, D. B.; Hebard, A. F.; Appleton, B. R. Stable Hole Doping of Graphene for Low Electrical Resistance and High Optical Transparency. Nanotechnology 2011 22 425701. 72. Martins, T. B.; Miwa, R H.; Silva, A. J. R. da; Fazzio, A. Electronic and Transport Properties of Boron Doped Graphene Nanoribbons. Phys. Rev. Lett. 2007 98 196803.

PAGE 209

209 73. Panchakarla, L. S.; Subrahmanyam, K. S.; Saha, S. K.; Govindaraj, A.; Krishnamurthy, H. R.; Waghmare, U. V. ; Rao, C. N. R. Synthesis, Structure, and Properties of Boron and Nitrogen Doped Graphene. Advanced Materials 2009 21 4726 4730. 74. Wang, X.; Li, X.; Zhang, L.; Yoon, Y.; Weber, P. K.; Wang, H.; Guo, J.; Dai, H. N Doping of Graphene Through Electrother mal Reactions with Ammonia. Science 2009 324 768 771. 75. Ci, L.; Song, L.; Jin, C.; Jariwala, D.; Wu, D.; Li, Y.; Srivastava, A.; Wang, Z. F.; Storr, K.; Balicas, L. et al. Atomic Layers of Hybridized Boron Nitride and Graphene Domains. Nature Materials 2010 9 430 435. 76. Zhao, L.; He, R.; Rim, K. T.; Schiros, T.; Kim, K. S.; Zhou, H.; Gutirrez, C.; Chockalingam, S. P.; Arguello, C. J.; Plov, L. et al. Visualizing Individual Nitrogen Dopants in Monolayer Graphene. Science 2011 333 999 1003. 77. G iovannetti, G.; Khomyakov, P. A.; Brocks, G.; Karpan, V. M.; Brink, J. van den; Kelly, P. J. Doping Graphene with Metal Contacts. Phys. Rev. Lett. 2008 101 026803. 78. Xia, F.; Perebeinos, V.; Lin, Y.; Wu, Y.; Avouris, P. The Origins and Limits of Metal graphene Junction Resistance. Nature Nanotechnology 2011 6 179 184. 79. Zhou, S. Y.; Gweon, G. H.; Fedorov, A. V.; First, P. N.; Heer, W. A. de; Lee, D. H.; Guinea, F.; Neto, A. H. C.; Lanzara, A. Substrate induced Bandgap Opening in Epitaxial Graphene. Nature Materials 2007 6 770 775. 80. Calizo, I.; Bao, W.; Miao, F.; Lau, C. N.; Balandin, A. A. The Effect of Substrates on the Raman Spectrum of Graphene: Graphene On sapphire and Graphene on glass. Applied Physics Letters 2007 91 201904 201904 3. 81 Faugeras, C.; Nerrire, A.; Potemski, M.; Mahmood, A.; Dujardin, E.; Berger, C.; Heer, W. A. de Few layer Graphene on SiC, Pyrolitic Graphite, and Graphene: A Raman Scattering Study. Applied Physics Letters 2008 92 011914. 82. Dean, C. R.; Young, A. F. ; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L. et al. Boron Nitride Substrates for High quality Graphene Electronics. Nature Nanotechnology 2010 5 722 726. 83. Zhang, Y.; Small, J. P.; Pontius, W. V.; Kim, P. Fabrication and Electric field dependent Transport Measurements of Mesoscopic Graphite Devices. Applied Physics Letters 2005 86 073104 073104 3. 84. Chen, J. H.; Jang, C.; Xiao, S.; Ishigami, M.; Fuhrer, M. S. Intrinsic and Extrinsic Performance Limits of Graphene Devices on SiO2. Nature Nanotechnology 2008 3 206 209.

PAGE 210

210 85. Morozov, S. V.; Novoselov, K. S.; Katsnelson, M. I.; Schedin, F.; Elias, D. C.; Jaszczak, J. A.; Geim, A. K. Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer. Ph ys. Rev. Lett. 2008 100 016602. 86. Drkop, T.; Getty, S. A.; Cobas, E.; Fuhrer, M. S. Extraordinary Mobility in Semiconducting Carbon Nanotubes. Nano Lett. 2004 4 35 39. 87. Xue, J.; Sanchez Yamagishi, J.; Bulmash, D.; Jacquod, P.; Deshpande, A.; Wata nabe, K.; Taniguchi, T.; Jarillo Herrero, P.; LeRoy, B. J. Scanning Tunnelling Microscopy and Spectroscopy of Ultra flat Graphene on Hexagonal Boron Nitride. Nature Materials 2011 10 282 285. 88. Mayorov, A. S.; Elias, D. C.; Mukhin, I. S.; Morozov, S. V .; Ponomarenko, L. A.; Novoselov, K. S.; Geim, A. K.; Gorbachev, R. V. How Close Can One Approach the Dirac Point in Graphene Experimentally? Nano Lett. 2012 89. Neugebauer, P.; Orlita, M.; Faugeras, C.; Barra, A. L.; Potemski, M. How Perfect Can Graphene Be? Phys. Rev. Lett. 2009 103 136403. 90. Hrostowski, H. J.; Morin, F. J.; Geballe, T. H.; Wheatley, G. H. Hall Effect and Conductivity of InSb. Phys. Rev. 1955 100 1672 1676. 91. Umansky, V.; Heiblum, M.; Levinson, Y.; Smet, J.; Nbler, J.; Dolev, M. MBE Growth of Ultra low Disorder 2DEG with Mobility Exceeding 35106 cm2/V s. Journal of Crystal Growth 2009 311 1658 1661. 92. Du, X.; Skachko, I.; Barker, A.; Andrei, E. Y. Approaching Ballistic Transport in Suspended Graphene. Nature Nanotechnology 2 008 3 491 495. 93. Son, Y. W.; Cohen, M. L.; Louie, S. G. Half metallic Graphene Nanoribbons. Nature 2006 444 347 349. 94. Barone, V.; Hod, O.; Scuseria, G. E. Electronic Structure and Stability of Semiconducting Graphene Nanoribbons. Nano Lett. 2006 6 2748 2754. 95. Han, M. Y.; zyilmaz, B.; Zhang, Y.; Kim, P. Energy Band Gap Engineering of Graphene Nanoribbons. Phys. Rev. Lett. 2007 98 206805. 96. zyilmaz, B.; Jarillo Herrero, P.; Efetov, D.; Kim, P. Electronic Transport in Locally Gated Graphene Nanoconstrictions. Applied Physics Letters 2007 91 192107 192107 3. 97. Son, Y. W.; Cohen, M. L.; Louie, S. G. Energy Gaps in Graphene Nanoribbons. Phys. Rev. Lett. 2006 97 216803. 98. Han, M. Y.; Brant, J. C.; Kim, P. Electron Transport in Disordered Graphene Nanoribbons. Phys. Rev. Lett. 2010 104 056801.

PAGE 211

211 99. Gallagher, P.; Todd, K.; Goldhaber Gordon, D. Disorder induced Gap Behavior in Graphene Nanoribbons. Phys. Rev. B 2010 81 115409. 100. Stampfer, C.; Gttinger, J.; Hellmller, S.; Molitor, F. ; Ensslin, K.; Ihn, T. Energy Gaps in Etched Graphene Nanoribbons. Phys. Rev. Lett. 2009 102 056403. 101. Wang, X.; Ouyang, Y.; Jiao, L.; Wang, H.; Xie, L.; Wu, J.; Guo, J.; Dai, H. Graphene Nanoribbons with Smooth Edges Behave as Quantum Wires. Nature N anotechnology 2011 6 563 567. 102. Jiao, L.; Zhang, L.; Wang, X.; Diankov, G.; Dai, H. Narrow Graphene Nanoribbons from Carbon Nanotubes. Nature 2009 458 877 880. 103. Kosynkin, D. V.; Higginbotham, A. L.; Sinitskii, A.; Lomeda, J. R.; Dimiev, A.; Pric e, B. K.; Tour, J. M. Longitudinal Unzipping of Carbon Nanotubes to Form Graphene Nanoribbons. Nature 2009 458 872 876. 104. Jiao, L.; Wang, X.; Diankov, G.; Wang, H.; Dai, H. Facile Synthesis of High quality Graphene Nanoribbons. Nature Nanotechnology 2 010 5 321 325. 105. Li, X.; Wang, X.; Zhang, L.; Lee, S.; Dai, H. Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors. Science 2008 319 1229 1232. 106. Pietronero, L.; Strssler, S.; Zeller, H. R.; Rice, M. J. Charge Distribution in c Di rection in Lamellar Graphite Acceptor Intercalation Compounds. Phys. Rev. Lett. 1978 41 763 767. 107. Giovannetti, G.; Khomyakov, P. A.; Brocks, G.; Kelly, P. J.; Brink, J. van den Substrate induced Band Gap in Graphene on Hexagonal Boron Nitride: Ab Ini tio Density Functional Calculations. Phys. Rev. B 2007 76 073103. 108. Hass, J.; Varchon, F.; Milln Otoya, J. E.; Sprinkle, M.; Sharma, N.; Heer, W. A. de; Berger, C.; First, P. N.; Magaud, L.; Conrad, E. H. Why Multilayer Graphene on 4H SiC(0001[over ]) Behaves Like a Single Sheet of Graphene. Phys. Rev. Lett. 2008 100 125504. 109. Das, A.; Pisana, S.; Chakraborty, B.; Piscanec, S.; Saha, S. K.; Waghmare, U. V.; Novoselov, K. S.; Krishnamurthy, H. R.; Geim, A. K.; Ferrari, A. C. et al. Monitoring Dop ants by Raman Scattering in an Electrochemically Top gated Graphene Transistor. Nature Nanotechnology 2008 3 210 215. 110. Zhang, Y.; Tang, T. T.; Girit, C.; Hao, Z.; Martin, M. C.; Zettl, A.; Crommie, M. F.; Shen, Y. R.; Wang, F. Direct Observation of a Widely Tunable Bandgap in Bilayer Graphene. Nature 2009 459 820 823. 111. Craciun, M. F.; Russo, S.; Yamamoto, M.; Oostinga, J. B.; Morpurgo, A. F.; Tarucha, S. Trilayer Graphene Is a Semimetal with a Gate tunable Band Overlap. Nature Nanotechnology 200 9 4 383 388.

PAGE 212

212 112. Sprinkle, M.; Siegel, D.; Hu, Y.; Hicks, J.; Tejeda, A.; Taleb Ibrahimi, A.; Fvre, P. Le; Bertran, F.; Vizzini, S.; Enriquez, H. et al. First Direct Observation of a Nearly Ideal Graphene Band Structure. Phys. Rev. Lett. 2009 103 226 803. 113. Kong, J.; Cassell, A. M.; Dai, H. Chemical Vapor Deposition of Methane for Single walled Carbon Nanotubes. Chemical Physics Letters 1998 292 567 574. 114. ncel, .; Yrm, Y. Carbon Nanotube Synthesis via the Catalytic CVD Method: A Review on the Effect of Reaction Parameters. Fullerenes, Nanotubes and Carbon Nanostructures 2006 14 17 37. 115. Kong, J.; Soh, H. T.; Cassell, A. M.; Quate, C. F.; Dai, H. Synthesis of Individual Single walled Carbon Nanotubes on Patterned Silicon Wafers. Nature 1998 395 878 881. 116. Cassell, A. M.; Raymakers, J. A.; Kong, J.; Dai, H. Large Scale CVD Synthesis of Single Walled Carbon Nanotubes. J. Phys. Chem. B 1999 103 6484 6492. 117. Ren, Z. F.; Huang, Z. P.; Xu, J. W.; Wang, J. H.; Bush, P.; Siegal, M. P.; Provencio, P. N. Synthesis of Large Arrays of Well Aligned Carbon Nanotubes on Glass. Science 1998 282 1105 1107. 118. Li, Y.; Mann, D.; Rolandi, M.; Kim, W.; Ural, A.; Hung, S.; Javey, A.; Cao, J.; Wang, D.; Yenilmez, E. et al. Preferential Growth of S emiconducting Single Walled Carbon Nanotubes by a Plasma Enhanced CVD Method. Nano Lett. 2004 4 317 321. 119. Matthews, K. D.; Lemaitre, M. G.; Kim, T.; Chen, H.; Shim, M.; Zuo, J. M. Growth Modes of Carbon Nanotubes on Metal Substrates. Journal of Appli ed Physics 2006 100 044309 044309 10. 120. Wei, Y. Y.; Eres, G.; Merkulov, V. I.; Lowndes, D. H. Effect of Catalyst Film Thickness on Carbon Nanotube Growth by Selective Area Chemical Vapor Deposition. Applied Physics Letters 2001 78 1394 1396. 121. Is ett, L. C.; Blakely, J. M. Segregation Isosteres for Carbon at the (100) Surface of Nickel. Surface Science 1976 58 397 414. 122. Eizenberg, M.; Blakely, J. M. Carbon Monolayer Phase Condensation on Ni(111). Surface Science 1979 82 228 236. 123. v, E. V.; Tontegode, A. Y. A Study of the Carbon Adlayer on Iridium. Surface Science 1985 161 373 389. 124. Aizawa, T.; Souda, R.; Otani, S.; Ishizawa, Y.; Oshima, C. Anomalous Bond of Monolayer Graphite on Transition metal Carbide Surfaces. Phys. Rev. L ett. 1990 64 768 771.

PAGE 213

213 125. Nagashima, A.; Nuka, K.; Satoh, K.; Itoh, H.; Ichinokawa, T.; Oshima, C.; Otani, S. Electronic Structure of Monolayer Graphite on Some Transition Metal Carbide Surfaces. Surface Science 1993 287 288, Part 2 609 613. 126. Land T. A.; Michely, T.; Behm, R. J.; Hemminger, J. C.; Comsa, G. STM Investigation of Single Layer Graphite Structures Produced on Pt(111) by Hydrocarbon Decomposition. Surface Science 1992 264 261 270. 127. Gao, L.; Ren, W.; Xu, H.; Jin, L.; Wang, Z.; Ma, T.; Ma, L. P.; Zhang, Z.; Fu, Q.; Peng, L. M. et al. Repeated Growth and Bubbling Transfer of Graphene with Millimetre size Single crystal Grains Using Platinum. Nature Communications 2012 3 699. 128. Vaari, J.; Lahtinen, J.; Hautojrvi, P. The Adsorpti on and Decomposition of Acetylene on Clean and K covered Co(0001). Catalysis Letters 1997 44 43 49. 129. Sutter, P. W.; Flege, J. I.; Sutter, E. A. Epitaxial Graphene on Ruthenium. Nature Materials 2008 7 406 411. 130. belman, P. J.; Michely, T. Two Dimensional Ir Cluster Lattice on a Graphene Moir on Ir(111). Phys. Rev. Lett. 2006 97 215501. 131. Coraux, J.; N`Diaye, A. T.; Busse, C.; Michely, T. Structural Coherency of Graphene on Ir(111). Nano Lett. 2008 8 565 57 0. 132. Bhaviripudi, S.; Jia, X.; Dresselhaus, M. S.; Kong, J. Role of Kinetic Factors in Chemical Vapor Deposition Synthesis of Uniform Large Area Graphene Using Copper Catalyst. Nano Lett. 2010 10 4128 4133. 133. Reina, A.; Jia, X.; Ho, J.; Nezich, D.; Son, H.; Bulovic, V.; Dresselhaus, M. S.; Kong, J. Large Area, Few Layer Graphene Films on Arbitrary Substrates by Chemical Vapor Deposition. Nano Lett. 2008 9 30 35. 134. Robinson, V. N. E.; Robins, J. L. Nucleation Kinetics of Gold Deposited onto UHV Cleaved Surfaces of NaCl and KBr. Thin Solid Films 1974 20 155 175. 135. Loginova, E.; Bartelt, N. C.; Feibelman, P. J.; McCarty, K. F. Evidence for Graphene Growth by C Cluster Attachment. New Journal of Physics 2008 10 093026. 136. Loginova, E.; Bart elt, N. C.; Feibelman, P. J.; McCarty, K. F. Factors Influencing Graphene Growth on Metal Surfaces. New Journal of Physics 2009 11 063046. 137. Huang, P. Y.; Ruiz Vargas, C. S.; Zande, A. M. van der; Whitney, W. S.; Levendorf, M. P.; Kevek, J. W.; Garg, S.; Alden, J. S.; Hustedt, C. J.; Zhu, Y. et al. Grains and Grain Boundaries in Single layer Graphene Atomic Patchwork Quilts. Nature 2011 469 389 392.

PAGE 214

214 138. Kim, K.; Lee, Z.; Regan, W.; Kisielowski, C.; Crommie, M. F.; Zettl, A. Grain Boundary Mapping in Polycrystalline Graphene. ACS Nano 2011 5 2142 2146. 139. Tsen, A. W.; Brown, L.; Levendorf, M. P.; Ghahari, F.; Huang, P. Y.; Havener, R. W.; Ruiz Vargas, C. S.; Muller, D. A.; Kim, P.; Park, J. Tailoring Electrical Transport Across Grain Boundaries in Polycrystalline Graphene. Science 2012 336 1143 1146. 140. Li, X.; Magnuson, C. W.; Venugopal, A.; Tromp, R. M.; Hannon, J. B.; Vogel, E. M.; Colombo, L.; Ruoff, R. S. Large Area Graphene Single Crystals Grown by Low Pressure Chemical Vapor Deposition o f Methane on Copper. J. Am. Chem. Soc. 2011 133 2816 2819. 141. Wang, H.; Wang, G.; Bao, P.; Yang, S.; Zhu, W.; Xie, X.; Zhang, W. J. Controllable Synthesis of Submillimeter Single Crystal Monolayer Graphene Domains on Copper Foils by Suppressing Nucleat ion. J. Am. Chem. Soc. 2012 142. Yan, Z.; Lin, J.; Peng, Z.; Sun, Z.; Zhu, Y.; Li, L.; Xiang, C.; Samuel, E. L.; Kittrell, C.; Tour, J. M. Toward the Synthesis of Wafer Scale Single Crystal Graphene on Copper Foils. ACS Nano 2012 143. Asm ASM Handbook: V olume 3: Alloy Phase Diagrams (Asm Handbook) ; 10th ed.; ASM International, 1992. 144. Bommel, A. J. Van; Crombeen, J. E.; Tooren, A. Van LEED and Auger Electron Observations of the SiC(0001) Surface. Surface Science 1975 48 463 472. 145. Berger, C.; Song Z.; Li, T.; Li, X.; Ogbazghi, A. Y.; Feng, R.; Dai, Z.; Marchenkov, A. N.; Conrad, E. H.; First, P. N. et al. Gas Properties and a Route Toward Graphene based Nanoelectronics. J. Phys. Chem. B 2004 108 19912 1 9916. 146. Berger, C.; Song, Z.; Li, X.; Wu, X.; Brown, N.; Naud, C.; Mayou, D.; Li, T.; Hass, J.; Marchenkov, A. N. et al. Electronic Confinement and Coherence in Patterned Epitaxial Graphene. Science 2006 312 1191 1196. 147. Hass, J.; Heer, W. A. de; C onrad, E. H. The Growth and Morphology of Epitaxial Multilayer Graphene. Journal of Physics: Condensed Matter 2008 20 323202. 148. Huang, H.; Chen, W.; Chen, S.; Wee, A. T. S. Bottom up Growth of Epitaxial Graphene on 6H SiC(0001). ACS Nano 2008 2 2513 2518. 149. Emtsev, K. V.; Speck, F.; Seyller, T.; Ley, L.; Riley, J. D. Interaction, Growth, and Ordering of Epitaxial Graphene on SiC{0001} Surfaces: A Comparative Photoelectron Spectroscopy Study. Phys. Rev. B 2008 77 155303.

PAGE 215

215 150. Aristov, V. Y.; Urba nik, G.; Kummer, K.; Vyalikh, D. V.; Molodtsova, O. V.; Preobrajenski, A. B.; Zakharov, A. A.; Hess, C.; Hnke, T.; Bchner, B. et al. Graphene Synthesis on Cubic SiC/Si Wafers. Perspectives for Mass Production of Graphene Based Electronic Devices. Nano Le tt. 2010 10 992 995. 151. Virojanadara, C.; Syvjarvi, M.; Yakimova, R.; Johansson, L. I.; Zakharov, A. A.; Balasubramanian, T. Homogeneous Large area Graphene Layer Growth on 6H SiC(0001). Phys. Rev. B 2008 78 245403. 152. Luxmi; Srivastava, N.; He, G .; Feenstra, R. M.; Fisher, P. J. Comparison of Graphene Formation on C face and Si face SiC {0001} Surfaces. Phys. Rev. B 2010 82 235406. 153. Ramachandran, V.; Brady, M.; Smith, A.; Feenstra, R.; Greve, D. Preparation of Atomically Flat Surfaces on Sil icon Carbide Using Hydrogen Etching. Journal of Electronic Materials 1998 27 308 312. 154. Heer, W. A. de; Berger, C.; Wu, X.; First, P. N.; Conrad, E. H.; Li, X.; Li, T.; Sprinkle, M.; Hass, J.; Sadowski, M. L. et al. Epitaxial Graphene. Solid State Com munications 2007 143 92 100. 155. Chen, W.; Xu, H.; Liu, L.; Gao, X.; Qi, D.; Peng, G.; Tan, S. C.; Feng, Y.; Loh, K. P.; Wee, A. T. S. Atomic Structure of the 6H SiC(0 0 0 1) Nanomesh. Surface Science 2005 596 176 186. 156. Hannon, J. B.; Tromp, R. M. Pit Formation During Graphene Synthesis on SiC(0001): In Situ Electron Microscopy. Phys. Rev. B 2008 77 241404. 157. Emtsev, K. V.; Bostwick, A.; Horn, K.; Jobst, J.; Kellogg, G. L.; Ley, L.; McChesney, J. L.; Ohta, T.; Reshanov, S. A.; R|[ouml]|hrl, J. et al. Towards Wafer size Graphene Layers by Atmospheric Pressure Graphitization of Silicon Carbide. Nature Materials 2009 8 203 207. 158. Tromp, R. M.; Hannon, J. B. Thermodynamics and Kinetics of Graphene Growth on SiC(0001). Phys. Rev. Lett. 2009 10 2 106104. 159. Heer, W. A. de; Berger, C.; Ruan, M.; Sprinkle, M.; Li, X.; Hu, Y.; Zhang, B.; Hankinson, J.; Conrad, E. Large Area and Structured Epitaxial Graphene Produced by Confinement Controlled Sublimation of Silicon Carbide. PNAS 2011 160. Robinso n, J.; Weng, X.; Trumbull, K.; Cavalero, R.; Wetherington, M.; Frantz, E.; LaBella, M.; Hughes, Z.; Fanton, M.; Snyder, D. Nucleation of Epitaxial Graphene on SiC(0001). ACS Nano 2009 4 153 158. 161. Virojanadara, C.; Yakimova, R.; Osiecki, J. R.; Syvj rvi, M.; Uhrberg, R. I. G.; Johansson, L. I.; Zakharov, A. A. Substrate Orientation: A Way Towards Higher Quality Monolayer Graphene Growth on 6H SiC(0 0 0 1). Surface Science 2009 603 L87 L90.

PAGE 216

216 162. Tanaka, S.; Morita, K.; Hibino, H. Anisotropic Layer by layer Growth of Graphene on Vicinal SiC(0001) Surfaces. Phys. Rev. B 2010 81 041406. 163. Sprinkle, M.; Ruan, M.; Hu, Y.; Hankinson, J.; Rubio Roy, M.; Zhang, B.; Wu, X.; Berger, C.; Heer, W. A. de Scalable Templated Growth of Graphene Nanoribbons on Si C. Nature Nanotechnology 2010 5 727 731. 164. Borovikov, V.; Zangwill, A. Step edge Instability During Epitaxial Growth of Graphene from SiC(0001). Phys. Rev. B 2009 80 121406. 165. Wu, X.; Hu, Y.; Ruan, M.; Madiomanana, N. K.; Hankinson, J.; Sprinkle, M.; Berger, C.; Heer, W. A. de Half Integer Quantum Hall Effect in High Mobility Single Layer Epitaxial Graphene. Applied Physics Letters 2009 95 223108 223108 3. 166. Neudeck, P. Progress in Silicon Carbide Semiconductor Electronics Technology. Journal of Electronic Materials 1995 24 283 288. 167. Jorio, A.; Dresselhaus, M. S.; Saito, R.; Dresselhaus, G. Raman Spectroscopy in Graphene Related Systems ; John Wiley & Sons, 2011. 168. Alfano, R. R.; Shapiro, S. L. Optical Phonon Lifetime Measured Directly with Picosecond Pulses. Phys. Rev. Lett. 1971 26 1247 1251. 169. Samsonidze, G. G.; Barros, E. B.; Saito, R.; Jiang, J.; Dresselhaus, G.; Dresselhaus, M. S. Electron phonon Coupling Mechanism in Two dimensional Graphite and Single wall Carbon Nanotubes. Phys. Rev. B 2007 75 155420. 170. Mohiuddin, T. M. G.; Lombardo, A.; Nair, R. R.; Bonetti, A.; Savini, G.; Jalil, R.; Bonini, N.; Basko, D. M.; Galiotis, C.; Marzari, N. et al. Uniaxial Strain in Graphene by Raman Spectroscopy: G Peak Splitting, Grneis en Parameters, and Sample Orientation. Phys. Rev. B 2009 79 205433. 171. Pisana, S.; Lazzeri, M.; Casiraghi, C.; Novoselov, K. S.; Geim, A. K.; Ferrari, A. C.; Mauri, F. Breakdown of the Adiabatic Born|[ndash]|Oppenheimer Approximation in Graphene. Natur e Materials 2007 6 198 201. 172. Malard, L. M.; Nilsson, J.; Elias, D. C.; Brant, J. C.; Plentz, F.; Alves, E. S.; Castro Neto, A. H.; Pimenta, M. A. Probing the Electronic Structure of Bilayer Graphene by Raman Scattering. Phys. Rev. B 2007 76 201401. 173. Ferrari, A. C.; Meyer, J. C.; Scardaci, V.; Casiraghi, C.; Lazzeri, M.; Mauri, F.; Piscanec, S.; Jiang, D.; Novoselov, K. S.; Roth, S. et al. Raman Spectrum of Graphene and Graphene Layers. Phys. Rev. Lett. 2006 97 187401. 174. Malard, L. M.; Pimen ta, M. A.; Dresselhaus, G.; Dresselhaus, M. S. Raman Spectroscopy in Graphene. Physics Reports 2009 473 51 87.

PAGE 217

217 175. Reina, A.; Son, H.; Jiao, L.; Fan, B.; Dresselhaus, M. S.; Liu, Z.; Kong, J. Transferring and Identification of Single and Few Layer Grap hene on Arbitrary Substrates. J. Phys. Chem. C 2008 112 17741 17744. 176. Lui, C. H.; Li, Z.; Chen, Z.; Klimov, P. V.; Brus, L. E.; Heinz, T. F. Imaging Stacking Order in Few Layer Graphene. Nano Lett. 2011 11 164 169. 177. Wang, Y. Y.; Ni, Z. H.; Yu, T.; Shen, Z. X.; Wang, H. M.; Wu, Y. H.; Chen, W.; Shen Wee, A. T. Raman Studies of Monolayer Graphene: The Substrate Effect. J. Phys. Chem. C 2008 112 10637 10640. 178. Yang, R.; Huang, Q. S.; Chen, X. L.; Zhang, G. Y.; Gao, H. J. Substrate Doping Effec ts on Raman Spectrum of Epitaxial Graphene on SiC. Journal of Applied Physics 2010 107 034305 034305 5. 179. Jorio, A.; Lucchese, M. M.; Stavale, F.; Martins Ferreira, E. H.; Moutinho, M. V. O.; Capaz, R. B.; Achete, C. A. Raman Study of Ion induced Defe cts in N layer Graphene. Journal of Physics: Condensed Matter 2010 22 334204. 180. Lucchese, M. M.; Stavale, F.; Ferreira, E. H. M.; Vilani, C.; Moutinho, M. V. O.; Capaz, R. B.; Achete, C. A.; Jorio, A. Quantifying Ion induc ed Defects and Raman Relaxation Length in Graphene. Carbon 2010 48 1592 1597. 181. Tuinstra, F.; Koenig, J. L. Raman Spectrum of Graphite. The Journal of Chemical Physics 1970 53 1126 1130. 182. Tuinstra, F.; Koenig, J. L. Characterization of Graphite Fiber Surfaces with Raman Spectroscopy. Journal of Composite Materials 1970 4 492. 183. Canado, L. G.; Takai, K.; Enoki, T.; Endo, M.; Kim, Y. A.; Mizusaki, H.; Speziali, N. L.; Jorio, A.; Pimenta, M. A. Measuring the Degree of Stacking Order in Graphit e by Raman Spectroscopy. Carbon 2008 46 272 275. 184. Ferrari, A. C. Raman Spectroscopy of Graphene and Graphite: Disorder, Electron phonon Coupling, Doping and Nonadiabatic Effects. Solid State Communications 2007 143 47 57. 185. Bolotin, K. I.; Sikes K. J.; Jiang, Z.; Klima, M.; Fudenberg, G.; Hone, J.; Kim, P.; Stormer, H. L. Ultrahigh Electron Mobility in Suspended Graphene. Solid State Communications 2008 146 351 355. 186. Seidel, R. V.; Graham, A. P.; Kretz, J.; Rajasekharan, B.; Duesberg, G. S .; Liebau, M.; Unger, E.; Kreupl, F.; Hoenlein, W. Sub 20 Nm Short Channel Carbon Nanotube Transistors. Nano Lett. 2005 5 147 150. 187. Jin, C.; Lan, H.; Peng, L.; Suenaga, K.; Iijima, S. Deriving Carbon Atomic Chains from Graphene. Phys. Rev. Lett. 2009 102 205501.

PAGE 218

218 188. Horowitz, G. Organic Field Effect Transistors. Advanced Materials 1998 10 365 377. 189. Coropceanu, V.; Cornil, J.; Silva Filho, D. A. da; Olivier, Y.; Silbey, R.; Brdas, J. L. Charge Transport in Organic Semiconductors. Chem. Rev. 2 007 107 926 952. 190. Ashcroft, N. W.; Mermin, N. D. Solid State Physics ; Saunders College, 1976. 191. Harrison, W. A. Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond ; Courier Dover Publications, 1989. 192. Sze, S. M.; Ng, K. K. Physics of Semiconductor Devices ; John Wiley & Sons, 2006. 193. Pope, M.; Swenberg, C. E. Electronic Processes in Organic Crystals and Polymers ; Oxford University Press, 1999. 194. Arkhipov, V. I.; Heremans, P.; Emelianova, E. V.; Bssler, H. Ef fect of Doping on the Density of states Distribution and Carrier Hopping in Disordered Organic Semiconductors. Phys. Rev. B 2005 71 045214. 195. Bssler, H. Charge Transport in Disordered Organic Photoconductors a Monte Carlo Simulation Study. physica st atus solidi (b) 1993 175 15 56. 196. Lampert, M. A.; Mark, P. Current Injection in Solids ; Academic Press, 1970. 197. Baldo, M. A.; Forrest, S. R. Interface limited Injection in Amorphous Organic Semiconductors. Phys. Rev. B 2001 64 085201. 198. Braun, F. ber Die Stromleitung Durch Schwefelmetalle. Ann. Phys. Chem. 1874 153 556. 199. Bose, J. C. 1904 200. Bethe, H. A.; Laboratory, M. I. of T. R. Theory of the Boundary Layer of Crystal Rectifiers ; Radiation Laboratory, Massachusetts Institute of Tech nology, 1942. 201. Chang, C. Y.; Sze, S. M. Carrier Transport Across Metal semiconductor Barriers. Solid State Electronics 1970 13 727 740. 202. Crowell, C. R. The Richardson Constant for Thermionic Emission in Schottky Barrier Diodes. Solid State Electr onics 1965 8 395 399. 203. Crowell, C. R.; Sze, S. M. Electron optical phonon Scattering in the Emitter and Collector Barriers of Semiconductor metal semiconductor Structures. Solid State Electronics 1965 8 979 990. 204. Kao, C. W.; Anderson, C. L.; Cr owell, C. R. Photoelectron Injection at Metal semiconductor Interfaces. Surface Science 1980 95 321 339.

PAGE 219

219 205. Crowell, C. R.; Sze, S. M. Quantum Mechanical Reflection of Electrons at Metal Semiconductor Barriers: Electron Transport in Semiconductor Metal Semiconductor Structures. Journal of Applied Physics 1966 37 2683 2689. 206. Rideout, V. L. A Review of the Theory and Technology for Ohmic Contacts to Group III V Compound Semiconductors. Solid State Electronics 1975 18 541 550. 207. Li, X.; Cai, W.; An, J.; Kim, S.; Nah, J.; Yang, D.; Piner, R.; Velamakanni, A.; Jung, I.; Tutuc, E. et al. Large Area Synthesis of High Quality and Uniform Graphene Films on Copper Foils. Science 2009 324 1312 1314. 208. Kochat, V.; Nath Pal, A.; Sneha, E. S.; Sampathk umar, A.; Gairola, A.; Shivashankar, S. A.; Raghavan, S.; Ghosh, A. High Contrast Imaging and Thickness Determination of Graphene with In column Secondary Electron Microscopy. Journal of Applied Physics 2011 110 014315 014315 5. 209. Jia, C.; Jiang, J.; Gan, L.; Guo, X. Direct Optical Characterization of Graphene Growth and Domains on Growth Substrates. Scientific Reports 2012 2 210. Li, X.; Zhu, Y.; Cai, W.; Borysiak, M.; Han, B.; Chen, D.; Piner, R. D.; Colombo, L.; Ruoff, R. S. Transfer of Large Area Graphene Films for High Performance Transparent Conductive Electrodes. Nano Lett. 2009 9 4359 4363. 211. Bae, S.; Kim, H.; Lee, Y.; Xu, X.; Park, J. S.; Zheng, Y.; Balakrishnan, J.; Lei, T.; Kim, H. R.; Song, Y. I. et al. Roll to roll Production of 30 i nch Graphene Films for Transparent Electrodes. Nature Nanotechnology 2010 5 574 578. 212. Lee, Y.; Bae, S.; Jang, H.; Jang, S.; Zhu, S. E.; Sim, S. H.; Song, Y. I.; Hong, B. H.; Ahn, J. H. Wafer Scale Synthesis and Transfer of Graphene Films. Nano Lett. 2010 10 490 493. 213. Cheng, Z.; Zhou, Q.; Wang, C.; Li, Q.; Wang, C.; Fang, Y. Toward Intrinsic Graphene Surfaces: A Systematic Study on Thermal Annealing and Wet Chemical Treatment of SiO2 Supported Graphene Devices. Nano Lett. 2011 11 767 771. 214. Liang, X.; Sperling, B. A.; Calizo, I.; Cheng, G.; Hacker, C. A.; Zhang, Q.; Obeng, Y.; Yan, K.; Peng, H.; Li, Q. et al. Toward Clean and Crackless Transfer of Graphene. ACS Nano 2011 5 9144 9153. 215. Wang, Y.; Zheng, Y.; Xu, X.; Dubuisson, E.; Bao, Q.; Lu, J.; Loh, K. P. Electrochemical Delamination of CVD Grown Graphene Film: Toward the Recyclable Use of Copper Catalyst. ACS Nano 2011 5 9927 9933. 216. Kang, J.; Hwang, S.; Kim, J. H.; Kim, M. H.; Ryu, J.; Seo, S. J.; Hong, B. H.; Kim, M. K.; Choi, J. B. Efficient Transfer of Large Area Graphene Films onto Rigid Substrates by Hot Pressing. ACS Nano 2012

PAGE 220

220 217. Chua, L. L.; Zaumseil, J.; Chang, J. F.; Ou, E. C. W.; Ho, P. K. H.; Sirringhaus, H.; Friend, R. H. General Observation of N type Field effect Be haviour in Organic Semiconductors. Nature 2005 434 194 199. 218. Pimenta, M. A.; Dresselhaus, G.; Dresselhaus, M. S.; Canado, L. G.; Jorio, A.; Saito, R. Studying Disorder in Graphite based Systems by Raman Spectroscopy. Phys. Chem. Chem. Phys. 2006 9 1276 1290. 219. Regan, W.; Byrnes, S.; Gannett, W.; Ergen, O.; Vazquez Mena, O.; Wang, F.; Zettl, A. Screening Engineered Field Effect Solar Cells. Nano Lett. 2012 12 4300 4304. 220. Venkatesh, S.; Jiang, P.; Jiang, B. Generalized Fabrication of Two Dim ensional Non Close Packed Colloidal Crystals. Langmuir 2007 23 8231 8235. 221. Bai, J.; Zhong, X.; Jiang, S.; Huang, Y.; Duan, X. Graphene Nanomesh. Nature Nanotechnology 2010 5 190 194. 222. Cai, J.; Ruffieux, P.; Jaafar, R.; Bieri, M.; Braun, T.; Bla nkenburg, S.; Muoth, M.; Seitsonen, A. P.; Saleh, M.; Feng, X. et al. Atomically Precise Bottom up Fabrication of Graphene Nanoribbons. Nature 2010 466 470 473. 223. Tada, K.; Haruyama, J.; Yang, H. X.; Chshiev, M.; Matsui, T.; Fukuyama, H. Ferromagnetis m in Hydrogenated Graphene Nanopore Arrays. Phys. Rev. Lett. 2011 107 217203. 224. Lee, S.; Lee, K.; Zhong, Z. Wafer Scale Homogeneous Bilayer Graphene Films by Chemical Vapor Deposition. Nano Lett. 2010 10 4702 4707. 225. Han, M. Y.; zyilmaz, B.; Zha ng, Y.; Kim, P. Energy Band Gap Engineering of Graphene Nanoribbons. Phys. Rev. Lett. 2007 98 206805. 226. Ni, Z. H.; Yu, T.; Lu, Y. H.; Wang, Y. Y.; Feng, Y. P.; Shen, Z. X. Uniaxial Strain on Graphene: Raman Spectroscopy Study and Band Gap Opening. ACS Nano 2008 2 2301 2305. 227. Camara, N.; Rius, G.; Huntzinger, J. R.; Tiberj, A.; Mestres, N.; Godignon, P.; Camassel, J. Selective Epitaxial Growth of Graphene on SiC. Applied Physics Letters 2008 93 123503 123503 3. 228. Rubio Roy, M.; Zaman, F.; Hu, Y.; Berger, C.; Moseley, M. W.; Meindl, J. D.; Heer, W. A. de Structured Epitaxial Graphene Growth on SiC by Selective Graphitization Using a Patterned AlN Cap. Applied Physics Letters 2010 96 082112 082112 3.

PAGE 221

221 229. Appleton, B. R.; Tongay, S.; Lemaitre, M.; Gila, B.; Fridmann, J.; Mazarov, P.; Sanabia, J. E.; Bauerdick, S.; Bruchhaus, L.; Mimura, R. et al. Materials Modifications Using a Multi ion Beam Processing and Lithography System. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 2012 272 153 157. 230. Tongay, S.; Lemaitre, M.; Fridmann, J.; Hebard, A. F.; Gila, B. P.; Appleton, B. R. Drawing Graphene Nanoribbons on SiC by Ion Implantation. Applied Physics Letters 2012 100 073501 073501 3. 231. Appleton, B.; Gila, B. Graphene Processing for Device and Sensor Applications. 232. Appleton, B.; Gila, B.; Lemaitre, M.; Tongay, S. Ion Beam Processing of SiC and Other Materials for Fabrication of Graphene Structures. 233. Perrone, D.; Maccioni, G.; Chiolerio, A.; Martinez de Marigorta, C.; Naretto, M.; Pandolfi, P.; Martino, P.; Ricciardi, C.; Chiodoni, A.; Celasco, E. et al. Study on the Possibility of Graphene Growth on 4H silicon Carbide Surfaces via Laser Processing. Proceedings of the Fifth Int ernational WLT Conference on Laser Manufacturing 2009 234. Lee, S.; Toney, M. F.; Ko, W.; Randel, J. C.; Jung, H. J.; Munakata, K.; Lu, J.; Geballe, T. H.; Beasley, M. R.; Sinclair, R. et al. Laser Synthesized Epitaxial Graphene. ACS Nano 2010 4 7524 75 30. 235. Ni, Z. H.; Chen, W.; Fan, X. F.; Kuo, J. L.; Yu, T.; Wee, A. T. S.; Shen, Z. X. Raman Spectroscopy of Epitaxial Graphene on a SiC Substrate. Phys. Rev. B 2008 77 115416. 236. Ju, L.; Geng, B.; Horng, J.; Girit, C.; Martin, M.; Hao, Z.; Bechtel, H. A.; Liang, X.; Zettl, A.; Shen, Y. R. et al. Graphene Plasmonics for Tunable Terahertz Metamaterials. Nature Nanotechnology 2011 6 630 634. 237. Rao, M. V.; Griffiths, P.; Holland, O. W.; Kelner, G.; Freitas, J. A.; Simons, D. S.; Chi, P. H.; Ghezzo, M. Al and B Ion implantations in 6H and 3C SiC. Journal of Applied Physics 1995 77 2479 2485. 238. Mizunami, T.; Toyama, N. ArF excimer laser Annealing of 3C SiC Films diode Characteristics and Numerical Simulation. Optics & Laser Technology 2003 35 4 51 456. 239. Baeri, P.; Spinella, C.; Reitano, R. Fast Melting of Amorphous Silicon Carbide Induced by Nanosecond Laser Pulse. International Journal of Thermophysics 1999 20 1211 1221. 240. Kedzierski, J.; Pei Lan Hsu; Healey, P.; Wyatt, P. W.; Keast, C. L.; Sprinkle, M.; Berger, C.; Heer, W. A. de Epitaxial Graphene Transistors on SiC Substrates. IEEE Transactions on Electron Devices 2008 55 2078 2085.

PAGE 222

222 241. Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nature Materials 2007 6 183 191. 242. Ryu, S.; Han, M. Y.; Maultzsch, J.; Heinz, T. F.; Kim, P.; Steigerwald, M. L.; Brus, L. E. Reversible Basal Plane Hydrogenation of Graphene. Nano Lett. 2008 8 4597 4602. 243. Cheng, S. H.; Zou, K.; Okino, F.; Gutierrez, H. R.; Gupta, A.; Shen, N.; Eklund, P. C.; Sofo, J. O.; Zhu, J. Reversible Fluorination of Graphene: Evidence of a Two dimensional Wide Bandgap Semiconductor. Phys. Rev. B 2010 81 205435. 244. Nair, R. R.; Ren, W.; Jalil, R.; Riaz, I.; Kravets, V. G.; Britnell, L.; Blake, P.; Schedin, F.; Ma yorov, A. S.; Yuan, S. et al. Fluorographene: A Two Dimensional Counterpart of Teflon. Small 2010 6 2877 2884. 245. Liang, X.; Wi, S. Transport Characteristics of Multichannel Transistors Made from Densely Aligned Sub 10 Nm Half Pitch Graphene Nanoribbon s. ACS Nano 2012 246. Li, X.; Zhu, H.; Wang, K.; Cao, A.; Wei, J.; Li, C.; Jia, Y.; Li, Z.; Li, X.; Wu, D. Graphene On Silicon Schottky Junction Solar Cells. Advanced Materials 2010 22 2743 2748. 247. Fan, G.; Zhu, H.; Wang, K.; Wei, J.; Li, X.; Shu, Q. ; Guo, N.; Wu, D. Graphene/Silicon Nanowire Schottky Junction for Enhanced Light Harvesting. ACS Appl. Mater. Interfaces 2011 3 721 725. 248. Tongay, S.; Schumann, T.; Miao, X.; Appleton, B. R.; Hebard, A. F. Tuning Schottky Diodes at the Many layer grap hene/semiconductor Interface by Doping. Carbon 2011 49 2033 2038. 249. Chen, C. C.; Aykol, M.; Chang, C. C.; Levi, A. F. J.; Cronin, S. B. Graphene Silicon Schottky Diodes. Nano Lett. 2011 11 1863 1867. 250. Hao, P. H.; Wang, L. C.; Deng, F.; Lau, S. S .; Cheng, J. Y. On the Low Resistance Au/Ge/Pd Ohmic Contact to n GaAs. Journal of Applied Physics 1996 79 4211 4215. 251. Ruvimov, S.; Liliental‐ andWeber, Z.; Washburn, J.; Duxstad, K. J.; Haller, E. E.; Fan, Z. ȁ. andF.; Mohammad, S. N.; K im, W.; Botchkarev, A. E.; Morkoc, H. Microstructure of Ti/Al and Ti/Al/Ni/Au Ohmic Contacts for n GaN. Applied Physics Letters 1996 69 1556 1558. 252. Han, S. Y.; Shin, J. Y.; Lee, B. T.; Lee, J. L. Microstructural Interpretation of Ni Ohmic Contact on N type 4H SiC. Journal of Vacuum Science Technology B: Microelectronics and Nanometer Structures 2002 20 1496 1500. 253. Tung, R. T. Recent Advances in Schottky Barrier Concepts. Materials Science and Engineering: R: Reports 2001 35 1 138.

PAGE 223

223 254. Tung, R. T. Chemical Bonding and Fermi Level Pinning at Metal Semiconductor Interfaces. Phys. Rev. Lett. 2000 84 6078 6081. 255. Tung, R. T. Formation of an Electric Dipole at Metal semiconductor Interfaces. Phys. Rev. B 2001 64 205310. 256. Tongay, S.; Sch umann, T.; Hebard, A. F. Graphite Based Schottky Diodes Formed on Si, GaAs, and 4H SiC Substrates. Applied Physics Letters 2009 95 222103 222103 3. 257. Yu, Y. J.; Zhao, Y.; Ryu, S.; Brus, L. E.; Kim, K. S.; Kim, P. Tuning the Graphene Work Function by E lectric Field Effect. Nano Lett. 2009 9 3430 3434. 258. Misra, R.; McCarthy, M.; Hebard, A. F. Electric Field Gating with Ionic Liquids. Applied Physics Letters 2007 90 052905. 259. Liu, B.; McCarthy, M. A.; Yoon, Y.; Kim, D. Y.; Wu, Z.; So, F.; Hollow ay, P. H.; Reynolds, J. R.; Guo, J.; Rinzler, A. G. Carbon Nanotube Enabled Vertical Field Effect and Light Emitting Transistors. Advanced Materials 2008 20 3605 3609. 260. McCarthy, M. A.; Liu, B.; Rinzler, A. G. High Current, Low Voltage Carbon Nanotube Enabled Vertical Organic Field Effect Transistors. Nano Lett. 2010 10 3467 3472. 261. McCarthy, M. A.; Liu, B.; Jayaraman, R.; Gilbert, S. M.; Kim, D. Y.; So, F.; Rinzler, A. G. Reorientation of the High Mobility Plane in Pentacene Based Carbon Nanotube Enabled Vertical Field Effect Transistors. ACS Nano 2010 5 291 298. 262. McCarthy, M. A.; Liu, B.; Donoghue, E. P.; Kravchenko, I.; Kim, D. Y.; So, F.; Rinzler, A. G. Low Voltage, Low Power, Organic Light Emitting Transistors for Active Matrix Displays. Science 2011 332 570 573. 263. Garrett, M. P.; Ivanov, I. N.; Gerhardt, R. A.; Puretzky, A. A.; Geohegan, D. B. Separation of Junction and Bundle Resistance in Single Wall Carbon Nanotube Percolation Networks by Impedance Spectroscopy. Applied Physics Letters 2010 97 163105 163105 3. 264. De, S.; Coleman, J N. Are There Fundamental Limitations on the Sheet Resistance and Transmittance of Thin Graphene Films? ACS Nano 2010 4 2713 2720. 265. Ma, L.; Yang, Y. Unique Architecture and Concept for High performance Organic Transistors. Applied Physics Letters 20 04 85 5084 5086. 266. Ben Sasson, A. J.; Avnon, E.; Ploshnik, E.; Globerman, O.; Shenhar, R.; Frey, G. L.; Tessler, N. Patterned Electrode Vertical Field Effect Transistor Fabricated Using Block Copolymer Nanotemplates. Applied Physics Letters 2009 95 213301 213301 3.

PAGE 224

224 267. Li, S. H.; Xu, Z.; Yang, G.; Ma, L.; Yang, Y. Solution processed Poly(3 hexylthiophene) Vertical Organic Transistor. Applied Physics Letters 2008 93 213301 213301 3. 268. Jiang, J.; Sun, J.; Zhou, B.; Lu, A.; Wan, Q. Vertical Low vo ltage Oxide Transistors Gated by Microporous SiO2/LiCl Composite Solid Electrolyte with Enhanced Electric double layer Capacitance. Applied Physics Letters 2010 97 052104 052104 3. 269. Extended Het eroarenes, Dinaphtho[2,3 f]chalcogenopheno[3,2 b]chalcogenophenes, and Their Application to Field Effect Transistors. J. Am. Chem. Soc. 2007 129 2224 2225. 270. Ben Sasson, A. J.; Tessler, N. Patterned Electrode Vertical Field Effect Transistor: Theory and Experiment. Journal of Applied Physics 2011 110 044501 044501 12. 271. Liu, B.; McCarthy, M. A.; Rinzler, A. G. Non Volatile Organic Memory Elements Based on Carbon Nanotube Enabled Vertical Field Effect Transistors. Advanced Functional Materials 2010 20 3440 3445. 272. Yang, H.; Heo, J.; Park, S.; Song, H. J.; Seo, D. H.; Byun, K. E.; Kim, P.; Yoo, I.; Chung, H. J.; Kim, K. Graphene Barristor, a Triode Device with a Gate Controlled Schottky Barrier. Science 2012 336 1140 1143.

PAGE 225

225 BIOGRAPHICAL SKETCH Maxime Gregory was born to Claude and Philippe Lemaitre in 1983 in Paris, France. The family soon immigrated to th e United States where h e grew up with hi s sister, Cecilia, in suburban towns outside some of the larger Midwest ern cities The proud son of two engineers, he was heavily influen ced by his parents and their vagabond disposition In 2001, he enrolled as an engineering p hysics student at the University of Illinois at Urbana Champaign. After an inauspicious start to his undergraduate studies, he refocused during an internship at International Rectifier in southern California. It was there that he develope d an interest in semiconductor ph ysics and manufacturing. R etur n ing to the University in the spring of 2003, he was accepted into the materials s cience program thanks in no small part to a research position with Professor John Roger s working on soft lith ography He later continued his undergraduate research with Drs. Moonsub Shim and Jian min Zuo, focusing on plasma enhanced chemical vapor deposition of single walled carbon nanotub es. He received a Bachelor of Science in 2005 and moved to Florida to at tend graduate school U nderestimating the work involved and overestimating his abilities he anticipated graduating with a dissertation after a few short years at the University of Florida As might have been expected he was stymied by the hopeless com bination of grandiose ideas and lack of focus. He began working on organic electronics, before joini ng Professor Rolf He received a Master of Science for his work developing an automated explosive det ection system The effort resulted in a spin off company founded by himself and Drs. Thierry Dubroca and Hummel. In a characteristic change of course, he subsequently lobbied his

PAGE 226

226 committee for the freedom to work independently on the synthesis of a prom ising new material known as graphene He spent the following 4 years collaborating with groups in materials science, chemistry, and physics in pursuit of interest ing science. Max plans to continue working on the novel class of devic es discussed in this t hesis.