Advanced Physical Models for Silicon Device Simulation

ISBN-13: 9783709173343 / Angielski / Miękka / 2012 / 354 str.

Andreas Schenk

Opis

Device simulation has two main purposes: to understand and depict the physical processes in the interior of a device, and to make reliable predictions of the behavior of an anticipated new device generation. Towards these goals the quality of the physical models is decisive. The introductory chapter of this book contains a critical review on models for silicon device simulators, which rely on moments of the Boltzmann equation. With reference to fundamental experimental and theoretical work an extensive collection of widely used models is discussed in terms of physical accuracy and application results. This review shows that the quality and efficiency of the phys ical models, which have been developed for the purpose of numerical simulation over the last three decades, is sufficient for many applications. Nevertheless, the basic understanding of the microscopic processes, as well as the uniqueness and accuracy of the models are still unsatisfactory. Hence, the following chapters of the book deal with the derivation of physics-based models from a microscopic level, also using new approaches of "taylored quantum-mechanics." Each model is compared with experimental data and applied to a number of simulation exam ples. The problems when starting from "first principles" and making the models suitable for a device simulator will also be demonstrated. We will show that demands for rapid computation and numerical robustness require a compromise between physical soundness and analytical simplicity, and that the attainable accuracy is limited by the complexity of the problems."

Recenzje

"... this is a well produced book, written in a easy to read style, and will also be a very useful primer for someone starting out the field who wants to know what can and cannot be done, and a useful source of reference for experienced users ..." Microelectronics Journal

Spis treści

1 Simulation of Silicon Devices: An Overview.- 1.1 Transport Models.- 1.1.1 Quantum Transport.- 1.1.2 Boltzmann Equation.- 1.1.3 Method of Moments.- 1.1.3.1 Transport Models.- 1.1.4 Thermodynamic Approach.- 1.2 Review of Physical Models for Drift-Diffusion Equations.- 1.2.1 Effective Intrinsic Density.- 1.2.1.1 Effective Masses and Effective Densities of States.- 1.2.1.2 Intrinsic Gap and Intrinsic Carrier Density.- 1.2.1.3 Band Gap Narrowing: Theoretical Models.- 1.2.1.4 Band Gap Narrowing: Empirical Models.- 1.2.1.5 Effective Intrinsic Density with Fermi Statistics.- 1.2.2 Mobility.- 1.2.2.1 Theoretical Background.- 1.2.2.2 Empirical Models for the Low Field Mobility.- 1.2.2.3 Empirical High-Field Corrections.- 1.2.2.4 Some Remarks.- 1.2.3 Generation-Recombination.- 1.2.3.1 Shockley-Read-Hall Recombination.- 1.2.3.2 Auger Recombination.- 1.2.3.3 Impact Ionization.- 1.3 Simulation Example: Gated Diode.- References.- 2 Mobility Model for Hydrodynamic Transport Equations.- 2.1 Analytical Model of the Electron Mobility.- 2.1.1 Variational Method with a Heated Maxwellian.- 2.1.2 Scattering Mechanisms.- 2.1.2.1 Intravalley Acoustic-Phonon Scattering.- 2.1.2.2 Intervalley Scattering.- 2.1.2.3 Impurity Scattering.- 2.1.3 Analytical Results for the Partial Mobilities.- 2.1.3.1 Non-Elastic Approach for Intravalley Acoustic-Phonon Scattering.- 2.1.3.2 Intervalley Scattering.- 2.1.3.3 Impurity Scattering Including Dispersive Screening.- 2.2 Parameter Fit and Comparison with Experimental Data.- 2.2.1 Fit Procedure.- 2.2.2 Dependence on Ambient Temperature.- 2.2.3 Dependence on Carrier Temperature, Velocity Saturation.- 2.2.4 Doping Dependence.- 2.3 Hole Mobility.- 2.3.1 Band Model.- 2.3.2 Analytical Model for the Hole Mobility.- 2.3.3 Dependence on Ambient Temperature, Carrier Temperature, and Doping.- 2.4 Simulation Results.- References.- 3 Advanced Generation-Recombination Models.- 3.1 Band-to-Band Tunneling.- 3.1.1 Microscopic Model.- 3.1.1.1 Kubo Formalism for the Tunneling Conductivity.- 3.1.1.2 Direct (Zero Phonon) Transitions.- 3.1.1.3 Indirect (Phonon-Assisted) Transitions.- 3.1.2 Model for Device Simulation.- 3.1.2.1 Simplifications.- 3.1.2.2 Comparison of Direct and Indirect Band-to-Band Tunneling.- 3.1.3 Field and Angular Dependence.- 3.2 Defect-Assisted Tunneling.- 3.2.1 Field Enhancement Factors for SRH Lifetimes.- 3.2.2 Simplified Models of the Field Enhancement.- 3.2.2.1 High-Temperature Approximation.- 3.2.2.2 Low-Temperature Approximation.- 3.2.3 On the Temperature Dependence of SRH Lifetimes.- 3.2.3.1 High-Temperature Approximation.- 3.2.3.2 Low-Temperature Approximation.- 3.2.4 Example: The Gold Acceptor in Silicon.- 3.3 Numerical Simulation of Tunnel Generation Currents.- 3.3.1 Band-to-Band Tunneling versus Defect-Assisted Tunneling.- 3.3.2 Local versus Nonlocal Description.- 3.4 Coupled Defect-Level Recombination.- 3.4.1 Theory of Coupled Defect-Level Recombination.- 3.4.1.1 Steady-State Recombination Rate.- 3.4.1.2 Field-Enhancement of the Coupled Defect-Level Rate.- 3.4.2 Simulation of LPE-Grown Junctions.- 3.4.3 Effect of Different Two-Level Systems.- References.- 4 Metal-Semiconductor Contact.- 4.1 Emission Current Through a Parabolic Barrier.- 4.2 Interpolation Scheme for the Transmission Probability.- 4.3 Analytical Model of the Contact Current.- 4.4 Boundary Conditions for Device Simulation.- 4.5 Comparison with Measurements.- 4.6 Results of Numerical Simulation.- 4.6.1 Implementation.- 4.6.2 Schottky nin Diode.- 4.6.3 Merged pin/Schottky (MPS) Diode.- References.- 5 Modeling Transport Across Thin Dielectric Barriers.- 5.1 One-Step Tunneling.- 5.1.1 Transmission Probability.- 5.1.2 I (V)-Characteristics of Direct and FN Tunneling.- 5.2 Two-Step Multiphonon-Assisted Tunneling.- 5.3 Resonant Tunneling.- 5.4 Comparison of Two-Step Zero-Phonon Tunneling and Resonant Tunneling.- 5.5 Simulation of the Long-Term Charge Loss in EPROMs.- 5.5.1 Measurements.- 5.5.2 Simulated Field and High-Temperature Dependence of the Leakage Current.- 5.5.3 Comparison of Various Loss Mechanisms.- References.- 6 Summary and Outlook.- References.- Appendices.- B Evaluation of a Double Integral.- C Transmission Probability for a Parabolic Barrier.- D Asymptotic Forms and Interpolation of Cylinder Functions.- E Energy Limit for Gaussian Approximation.- G Probability of Resonant Tunneling.- References.- List of Figures.- List of Tables.