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  • Louisiana State University LSU Digital Commons

    LSU Doctoral Dissertations Graduate School

    2016

    Physical Modeling of Graphene Nanoribbon Field Effect Transistor Using Non-Equilibrium Green Function Approach for Integrated Circuit Design Yaser Mohammadi Banadaki Louisiana State University and Agricultural and Mechanical College, ymoham8@lsu.edu

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    Recommended Citation Mohammadi Banadaki, Yaser, "Physical Modeling of Graphene Nanoribbon Field Effect Transistor Using Non-Equilibrium Green Function Approach for Integrated Circuit Design" (2016). LSU Doctoral Dissertations. 1052. https://digitalcommons.lsu.edu/gradschool_dissertations/1052

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  • PHYSICAL MODELING OF GRAPHENE NANORIBBON FIELD EFFECT TRANSISTOR

    USING NON-EQUILIBRIUM GREEN FUNCTION APPROACH

    FOR INTEGRATED CIRCUIT DESIGN

    A Dissertation

    Submitted to the Graduate Faculty of the

    Louisiana State University and

    Agricultural and Mechanical College

    in partial fulfillment of the

    requirements for the degree of

    Doctor of Philosophy

    in

    The Division of Electrical and Computer Engineering

    by

    Yaser Mohammadi Banadaki

    B.S., Azad University, Tehran, Iran, 2006

    M.S., Shahid Beheshti University, Tehran, Iran, 2009

    M.S., Louisiana State University, Baton Rouge, LA 70803, U.S.A, 2016

    May 2016

  • ii

    To my loving wife,

    Safura,

    for inspiration, support and encouragement

    &

    To my wonderful daughter,

    Persia

    for being relief and awesome

  • iii

    ACKNOWLEDGEMENTS

    First of all, I would like to express my gratitude to my research advisor and mentor,

    Professor Ashok Srivastava, for sharing his wealth of experience and knowledge to further my

    education. This research would not have been possible without his guidance, suggestions, and

    support.

    My appreciation also extends to Professor Pratul K. Ajmera, Professor Jonathan P.

    Dowling, and Professor Kidong Park for providing valued advice and serving as members in my

    dissertation advisory committee.

    Thanks also to fellow students and good friends, K.M. Mohsin and M.D. Fahad, for their

    collaboration and discussion.

  • iv

    TABLE OF CONTENTS

    ACKNOWLEDGEMENTS ……………………………………………………………….... iii

    LIST OF FIGURES ………………………………………………………………………… vi

    LIST OF ABBREVIATIONS ………………………………………………………………. xii

    ABSTRACT ………………………………………………………………………………… xiv

    CHAPTER 1 INTRODUCTION ………………………………………………………… 1

    1.1 Silicon Electronics and Scaling Challenges…………………………….... 1

    1.2 Prospects of Carbon-based Electronics ………………………………….. 3

    1.3 Graphene Superlative …………………………………………………….. 5

    1.4 Fabrication of Graphene Nanoribbon ……………………………………. 8

    1.5 Modeling of Graphene Nanoribbon Field Effect Transistors ……………. 11

    1.6 Outline of Dissertation …………………………………………………… 15

    CHAPTER 2 GRAPHENE NANORIBBON FIELD EFFECT TRANSISTOR (GNRFET).. 17

    CHAPTER 3 CARRIER TRANSPORT MODEL ……………………………………….. 30

    3.1 Simulation Algorithm …………………..……………………………….. 30

    3.2 Quantum Capacitance in GNRFET …………………………………….... 40

    3.3 Computational Time ……………………………………………………... 44

    CHAPTER 4 SCALING EFFECTS ON STATIC METRICS AND SWITCHING

    ATTRIBUTE OF GNRFET …………………………………………………………………

    47

    4.1 GNRFET Structure ………….…………………………….…………….. 48

    4.2 Results and Discussion …………………………………………………… 50

    4.2.1 Scaling Effects on Static Metric of GNRFET …………………. 52

    4.2.2 Scaling Effects on Switching Attributes of GNRFET ………… 63

    CHAPTER 5 WIDTH-DEPENDENT PERFORMANCE OF GNRFET ………………...

    71

    5.1 GNRFET Structure ………………………………………………………. 73

    5.2 Results and Discussion ………………………………………………….. 75

    5.2.1 Width-dependent Static Metrics of GNRFET ………………….. 80

    5.2.2 Width-dependent Switching Attribute of GNRFET …………… 90

  • v

    CHAPTER 6 CONCLUSION AND FUTURE WORK…………………………………… 98

    6.1 Results Summary ……………………………………………………….. 98

    6.1.1 Scaling down the channel length of GNRFET ………………... 100

    6.1.2 Width-dependent performance of GNRFET…………………… 101

    6.2 Recommendation for Future Works…………………………………….. 104

    REFERENCES……………………………………………………………………………….

    106

    APPENDIX A. MATLAB CODES FOR GNRFET NEGF MODEL ……………………… 118

    APPENDIX B. LETTER OF PERMISSION FOR FIGURE 2.3(c) ………………………... 131

    VITA ………………………………………………………………………………………... 132

  • vi

    LIST OF FIGURES

    Figure 1.1: Integrated Circuit scaling history and projection [6] ………..…………….... 2

    Figure 1.2: Three Carbon allotropes, (a) buckyball, discovered in 1985 [8], (b) carbon

    nanotube, discovered in 1991 [9] and graphene discovered in 2004 [10].….. 4

    Figure 1.3: Logic potential solution reported by ITRS 2013 [3]…………………….…... 6

    Figure 1.4: (a) Diffusive carrier transport in long channel device and ballistic carrier

    transport in short channel device and (b) energy-position-resolved local

    density of states of a typical GNRFET simulated with NEGF formalism,

    showing three possible regions for carrier transport: (1) thermionic emission

    of carriers over the channel potential barrier, (2) direct tunneling of carriers

    through channel potential barrier, and (3) band-to-band-tunneling of

    electrons from conduction band in the drain side to the hole states in the

    channel region……………………………………………………………….. 13

    Figure 2.1: (a) Two dimensional honeycomb lattice of graphene, which consists of two

    triangular sub-lattices A and B. (b) Unit cell and lattice vectors in the

    lattice. (c) Graphene band structure and first Brillouin zone in momentum

    space. Note: The position of Dirac points, K , K  and reciprocal lattice

    vectors are also shown underneath of the graphene band structure. (d)

    Linear band near Dirac point and the position of Fermi level……………….

    18

    Figure 2.2: (a) Schematic of a field-effect transistor (FET) and symbol of graphene

    FET. (b) Large-area graphene with zero bandgap. Three Fermi levels are

    shown in E-k diagram and the correspon