The Wigner Monte Carlo Method for Nanoelectronic Devices

The emergence of nanoelectronics has led us to renew the concepts of transport theory used in semiconductor device physics and the engineering community. It has become crucial to question the traditional semi-classical view of charge carrier transport and to adequately take into account the wave-like nature of electrons by considering not only their coherent evolution but also the out-of-equilibrium states and the scattering effects.

This book gives an overview of the quantum transport approaches for nanodevices and focuses on the Wigner formalism. It details the implementation of a particle-based Monte Carlo solution of the Wigner transport equation and how the technique is applied to typical devices exhibiting quantum phenomena, such as the resonant tunnelling diode, the ultra-short silicon MOSFET and the carbon nanotube transistor. In the final part, decoherence theory is used to explain the emergence of the semi-classical transport in nanodevices.

Symbols ix

Abbreviations xiii

Introduction xv

Acknowledgements xxi

Chapter 1. Theoretical Framework of Quantum Transport in Semiconductors and Devices 1

1.1. The fundamentals: a brief introduction to phonons, quasi-electrons and envelope functions 2

1.2. The semi-classical approach of transport 11

1.3. The quantum treatment of envelope functions 16

1.4. The two main problems of quantum transport 29

Chapter 2. Particle-based Monte Carlo Approach to Wigner-Boltzmann Device Simulation 57

2.1. The particle Monte Carlo technique to solve the BTE 59

2.2. Extension of the particle Monte Carlo technique to the WBTE: principles 71

2.3. Simple validations via two typical cases 83

2.4. Conclusion 86

Chapter 3. Application of the Wigner Monte Carlo Method to RTD, MOSFET and CNTFET 89

3.1. The resonant tunneling diode (RTD) 90

3.2. The double-gate metal-oxide-semiconductor field-effect transistor (DG-MOSFET) 99

3.3. The carbon nanotube field-effect transistor (CNTFET) 134

3.4. Conclusion 148

Chapter 4. Decoherence and Transition from Quantum to Semi-classical Transport 151

4.1. Simple illustration of the decoherence mechanism 152

4.2. Coherence and decoherence of Gaussian wave packets in GaAs 157

4.3. Coherence and decoherence in RTD: transition between semi-classical and quantum regions 171

4.4. Quantum coherence and decoherence in DG-MOSFET 175

4.5. Conclusion 180

Conclusion 183

Appendix A. Average Value of Operators in the Wigner Formalism 187

Appendix B. Boundaries of the Wigner Potential 189

Appendix C. Hartree Wave Function 191

Appendix D. Asymmetry Between Phonon Absorption and Emission Rates 193

Appendix E. Quantum Brownian Motion 195

Appendix F. Purity in the Wigner formalism 201

Appendix G. Propagation of a Free Wave Packet Subject to Quantum Brownian Motion 203

Appendix H. Coherence Length at Thermal Equilibrium 205

Bibliography 207

Index 241

Damien Querlioz, University of Paris-Sud, Orsay, France.

Philippe Dollfus, University of Paris-Sud, Orsay, France.