Advanced Physical Models for Silicon Device Simulation

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.

Table of Contents:
1 Simulation of Silicon Devices: An Overview.- 1.1 Transport Models.- 1.2 Review of Physical Models for Drift-Diffusion Equations.- 1.3 Simulation Example: Gated Diode.- References.- 2 Mobility Model for Hydrodynamic Transport Equations.- 2.1 Analytical Model of the Electron Mobility.- 2.2 Parameter Fit and Comparison with Experimental Data.- 2.3 Hole Mobility.- 2.4 Simulation Results.- References.- 3 Advanced Generation-Recombination Models.- 3.1 Band-to-Band Tunneling.- 3.2 Defect-Assisted Tunneling.- 3.3 Numerical Simulation of Tunnel Generation Currents.- 3.4 Coupled Defect-Level Recombination.- 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.- References.- 5 Modeling Transport Across Thin Dielectric Barriers.- 5.1 One-Step 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.- 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.