Hierarchical Device Simulation: The Monte-Carlo Perspective

This monograph is the first on physics-based simulations of novel strained Si and SiGe devices. It provides an in-depth description of the full-band monte-carlo method for SiGe and discusses the common theoretical background of the drift-diffusion, hydrodynamic and Monte-Carlo models and their synergy.

This book summarizes the research of more than a decade. Its early motivation dates back to the eighties and to the memorable talks Dr. C. Moglestue (FHG Freiburg) gave on his Monte-Carlo solutions of the Boltzmann transport equation at the NASECODE conferences in Ireland. At that time numerical semiconductor device modeling basically implied the application of the drift-diffusion model. On the one hand, those talks clearly showed the potential of the Monte-Carlo model for an accurate description of many important transport issues that cannot adequately be addressed by the drift-diffusion approximation. On the other hand, they also clearly demonstrated that at that time only very few experts were able to extract useful results from a Monte-Carlo simulator. With this background, Monte-Carlo research activities were started in 1986 at the University of Aachen (RWTH Aachen), Germany. Different to many other Monte-Carlo research groups, the Monte-Carlo research in Aachen took place in an environment of active drift-diffusion and hydrodynamic model development.

Introduction References Semiclassical Transport Theory The Boltzmann Transport Equation • Balance Equations • The Microscopic Relaxation Time • Fluctuations in the Steady-State • References The Monte-Carlo Method Basic Monte-Carlo Methods • The Monte-Carlo Solver of the Boltzmann Equation • Velocity Autocorrelation Function • Basic Statistics • Convergence Estimation • References Scattering Mechanisms Phonon Scattering • Alloy Scattering • Impurity Scattering • Impact Ionization by Electrons • Surface Roughness Scattering • References Full-Band Structure Basic Properties of the Band Structure of Relaxed Silicon • Basic Properties of the Band Structure of Strained SiGe • k-Space Grid • Calculation of the Density of States • Mass Tensor Evaluation • Particle Motion in Phase-Space • Selection of a Final State in k-Space • References Device Simulation Device Discretization • Band Edges • Poisson Equation • Self-Consistent Device Simulation • Nonlinear Poisson Equation • Nonself-Consistent Device Simulation • Statistical Enhancement • Terminal Current Estimation • Contact Resistance • Normalization of Physical Quantities • References Momentum-Based Transport Models The Hydrodynamic Model • Small-Signal Analysis • Noise Analysis • The Drift-Diffusion Model • Transport and Noise Parameter Simulation • References Stochastic Properties of Monte-Carlo Device Simulations Stochastic Error • In-Advance CPU Time Estimation • References Results N+ NN+ and P+ PP+ Structures • MOSFETs • SiGe HBTs Subject Index