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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