Preface viii
1 Quantum mechanics 1
1.1 Introduction to quantum mechanics 1
1.1.1 The double slit experiment 1
1.1.2 Basic concepts of quantum mechanics 4
1.1.3 Schrodinger's equation 10
1.2 Basic quantum physics problems 13
1.2.1 Free particle 13
1.2.2 Particle in a one-dimensional box 14
Reference 17
2 Basics of tunnelling 18
2.1 Understanding tunnelling 18
2.1.1 Qualitative description 18
2.1.2 Rectangular barrier 20
2.2 WKB approximation 23
2.3 Landauer's tunnelling formula 26
2.4 Advanced tunnelling models 29
2.4.1 Non-local tunnelling models 30
2.4.2 Local tunnelling models 30
References 38
3 The tunnel FET 39
3.1 Device structure 39
3.1.1 The need for tunnel FETs 39
3.1.2 Basic TFET structure 41
3.2 Qualitative behaviour 42
3.2.1 Band diagram 42
3.2.2 Device characteristics 52
3.2.3 Performance dependence on device parameters 59
3.3 Types of TFETs 63
3.3.1 Planar TFETs 63
3.3.2 Three-dimensional TFETs 70
3.3.3 Carbon nanotube and graphene TFETs 72
3.3.4 Point versus line tunnelling in TFETs 73
3.4 Other steep subthreshold transistors 74
References 74
4 Drain current modelling of tunnel FET: the task and its challenges 78
4.1 Introduction 78
4.2 TFET modelling approach 81
4.2.1 Finding the value of ψC 82
4.2.2 Modelling the surface potential in the source-channel junction 83
4.2.3 Finding the tunnelling current 85
4.3 MOSFET modelling approach 87
References 89
5 Modelling the surface potential in TFETs 90
5.1 The pseudo-2D method 91
5.1.1 Parabolic approximation of potential distribution 91
5.1.2 Solving the 2D Poisson equation using parabolic approximation 94
5.1.3 Solution for the surface potential 95
5.2 The variational approach 98
5.2.1 The variational form of Poisson's equation 99
5.2.2 Solution of the variational form of Poisson's equation in a TFET 101
5.3 The infinite series solution 107
5.3.1 Solving the 2D Poisson equation using separation of variables 107
5.3.2 Solution of the homogeneous boundary value problem 109
5.3.3 The solution to the 2D Poisson equation in a TFET 112
5.3.4 The infinite series solution to Poisson's equation in a TFET 114
5.4 Extension of surface potential models to different TFET structures 119
5.4.1 DG TFET 119
5.4.2 GAA TFET 122
5.4.3 Dual material gate TFET 125
5.5 The effect of localised charges on the surface potential 131
5.6 Surface potential in the depletion regions 132
5.7 Use of smoothing functions in the surface potential models 135
References 137
6 Modelling the drain current 140
6.1 Non-local methods 142
6.1.1 Landauer's tunnelling formula in TFETs 142
6.1.2 WKB approximation in TFETs 143
6.1.3 Obtaining the drain current 144
6.2 Local methods 147
6.2.1 Numerical integration 148
6.2.2 Shortest tunnelling length 148
6.2.3 Constant polynomial term assumption 150
6.2.4 Tangent line approximation 152
6.3 Threshold voltage models 157
6.3.1 Constant current method 158
6.3.2 Constant tunnelling length 159
6.3.3 Transconductance change (TC) method 160
References 161
7 Device simulation using ATLAS 163
7.1 Simulations using ATLAS 164
7.1.1 Inputs and outputs 165
7.1.2 Structure specification 166
7.1.3 Material parameters and model specification 169
7.1.4 Numerical method specification 170
7.1.5 Solution specification 170
7.2 Analysis of simulation results 171
7.3 SOI MOSFET example 174
Reference 180
8 Simulation of TFETs 181
8.1 SOI TFET 181
8.2 Other tunnelling models 188
8.2.1 Schenk band-to-band tunnelling model 188
8.2.2 Non-local band-to-band tunnelling 188
8.3 Gate all around nanowire TFET 190
References 193
Index 194
