Monte Carlo Simulation

In this book, the author begins with the elementary theory of Markov chains and very progressively brings the reader to the more advanced topics. He gives a useful review of probability that makes the book self-contained, and provides an appendix with detailed proofs of all the prerequisites from calculus, algebra, and number theory. A number of carefully chosen problems of varying difficulty are proposed at the close of each chapter, and the mathematics are slowly and carefully developed, in order to make self-study easier. The author treats the classic topics of Markov chain theory, both in discrete time and continuous time, as well as the connected topics such as finite Gibbs fields, nonhomogeneous Markov chains, discrete- time regenerative processes, Monte Carlo simulation, simulated annealing, and queuing theory. The result is an up-to-date textbook on stochastic processes. Students and researchers in operations research and electrical engineering, as well as in physics and biology, will find it very accessible and relevant.

This book provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems. It contains standard material usually considered in Monte Carlo simulation as well as new material such as variance reduction techniques, regenerative simulation, and Monte Carlo optimization.

Particle simulation of semiconductor devices is a rather new field which has started to catch the interest of the world's scientific community. It represents a time-continuous solution of Boltzmann's transport equation, or its quantum mechanical equivalent, and the field equation, without encountering the usual numerical problems associated with the direct solution.

This book discusses the general principles of the Monte Carlo method with an emphasis on techniques to decrease simulation time and increase accuracy.

Monte Carlo simulation is now a well established method for studying semiconductor devices and is particularly well suited to highlighting physical mechanisms and exploring material properties. Not surprisingly, the more completely the material properties are built into the simulation, up to and including the use of a full band structure, the more powerful is the method. Indeed, it is now becoming increasingly clear that phenomena such as reliabil­ ity related hot-electron effects in MOSFETs cannot be understood satisfac­ torily without using full band Monte Carlo. The IBM simulator DAMOCLES, therefore, represents a landmark of great significance. DAMOCLES sums up the total of Monte Carlo device modeling experience of the past, and reaches with its capabilities and opportunities into the distant future. This book, therefore, begins with a description of the IBM simulator. The second chapter gives an advanced introduction to the physical basis for Monte Carlo simulations and an outlook on why complex effects such as collisional broadening and intracollisional field effects can be important and how they can be included in the simulations. References to more basic intro­ the book. The third chapter ductory material can be found throughout describes a typical relationship of Monte Carlo simulations to experimental data and indicates a major difficulty, the vast number of deformation poten­ tials required to simulate transport throughout the entire Brillouin zone. The fourth chapter addresses possible further extensions of the Monte Carlo approach and subtleties of the electron-electron interaction.

This book provides a comprehensive overview of these methods, discussing their fundamental aspects and their applications in solving a large array of problems. It is a useful reference for scholars, researchers, and students in pure and applied mathematics, physical sciences, engineering and technology, computer science, numerical analysis, scientific computing, and the general sciences.