1st Edition

Computational Electronics Semiclassical and Quantum Device Modeling and Simulation

    782 Pages 422 B/W Illustrations
    by CRC Press

    Starting with the simplest semiclassical approaches and ending with the description of complex fully quantum-mechanical methods for quantum transport analysis of state-of-the-art devices, Computational Electronics: Semiclassical and Quantum Device Modeling and Simulation provides a comprehensive overview of the essential techniques and methods for effectively analyzing transport in semiconductor devices.

    With the transistor reaching its limits and new device designs and paradigms of operation being explored, this timely resource delivers the simulation methods needed to properly model state-of-the-art nanoscale devices. The first part examines semiclassical transport methods, including drift-diffusion, hydrodynamic, and Monte Carlo methods for solving the Boltzmann transport equation. Details regarding numerical implementation and sample codes are provided as templates for sophisticated simulation software.

    The second part introduces the density gradient method, quantum hydrodynamics, and the concept of effective potentials used to account for quantum-mechanical space quantization effects in particle-based simulators. Highlighting the need for quantum transport approaches, it describes various quantum effects that appear in current and future devices being mass-produced or fabricated as a proof of concept. In this context, it introduces the concept of effective potential used to approximately include quantum-mechanical space-quantization effects within the semiclassical particle-based device simulation scheme.

    Addressing the practical aspects of computational electronics, this authoritative resource concludes by addressing some of the open questions related to quantum transport not covered in most books. Complete with self-study problems and numerous examples throughout, this book supplies readers with the practical understanding required to create their own simulators.

    Introduction to Computational Electronics
    Si-Based Nanoelectronics
    Heterostructure Devices in III–V or II–VI Technology
    Modeling of Nanoscale Devices
    The Content of This Book

    Introductory Concepts
    Crystal Structure
    Semiconductors
    Band Structure
    Preparation of Semiconductor Materials
    Effective Mass
    Density of States
    Electron Mobility
    Semiconductor Statistics
    Semiconductor Devices

    Semiclassical Transport Theory
    Approximations for the Distribution Function
    Boltzmann Transport Equation
    Relaxation-Time Approximation
    Rode’s Iterative Method
    Scattering Mechanisms: Brief Description
    Implementation of the Rode Method for 6H-SiC Mobility Calculation

    The Drift-Diffusion Equations and Their Numerical Solution
    Drift-Diffusion Model Derivation
    Drift-Diffusion Application Example

    Hydrodynamic Modeling
    Introduction
    Extensions of the Drift-Diffusion Model
    Stratton’s Approach
    Hydrodynamic (Balance, Bløtekjær) Equations Model
    The Need for Commercial Semiconductor Device Modeling Tools
    State-of-the-Art Commercial Packages
    The Advantages and Disadvantages of Hydrodynamic Models: Simulations of Different Generation FD SOI Devices

    Particle-Based Device Simulation Methods
    Direct Solution of Boltzmann Transport Equation: Monte Carlo Method
    Multi-Carrier Effects
    Device Simulations
    Coulomb Force Treatment within a Particle-Based Device Simulation Scheme
    Representative Simulation Results of Multiparticle and Discrete Impurity Effects

    Modeling Thermal Effects in Nano-Devices
    Some General Aspects of Heat Conduction
    Classical Heat Conduction in Solids
    Form of the Heat Source Term
    Modeling Heating Effects with Commercial Simulation Packages
    The ASU Particle-Based Approach to Lattice Heating in Nanoscale Devices
    Open Problems

    Quantum Corrections to Semiclassical Approaches
    One-Dimensional Quantum-Mechanical Space Quantization
    Quantum Corrections to Drift-Diffusion and Hydrodynamic Simulators
    The Effective Potential Approach in Conjunction with Particle-Based Simulations
    Description of Gate Current Models Used in Device Simulations
    Monte Carlo—k _ p—1D Schrödinger Solver for Modeling Transport in p-Channel Strained SiGe Devices

    Quantum Transport in Semiconductor Systems
    Tunneling
    General Notation
    Transfer Matrix Approach
    Landauer Formula and Usuki Method

    Far-From-Equilibrium Quantum Transport
    Mixed States and Distribution Function
    Irreversible Processes and MASTER Equations
    The Wigner Distribution Function
    Green’s Functions
    Nonequilibrium Keldysh Green’s Functions
    Low Field Transport in Strained-Si Inversion Layers
    NEGF in a Quasi-1D Formulation
    Quantum Transport in 1D—Resonant Tunneling Diodes
    Coherent High-Field Transport in 2D and 3D

    Conclusions

    Appendix A: Electronic Band Structure Calculation
    Appendix B: Poisson Equation Solvers
    Appendix C: Computational Electromagnetics
    Appendix D: Stationary and Time-Dependent Perturbation Theory

    Each chapter concludes with "Problems" and "References"

    Biography

    Dragica Vasileska, Stephen M. Goodnick, Gerhard Klimeck