Semiconductors, Part II.- Device Modeling.- On the Child-Langmuir law for semiconductors.- A critical review of the fundamental semiconductor equations.- Physics for device simulations and its verification by measurements.- An industrial perspective on semiconductor technology modeling.- Combined device-circuit simulation for advanced semiconductor devices.- Methods of the kinetic theory of gases relevant to the kinetic models for semiconductors.- Shock waves in the hydrodynamic model for semiconductor devices.- Macroscopic and microscopic approach for the simulation of short devices.- Derivation of the high field semiconductor equations.- Energy models for one-carrier transport in semiconductor devices.- Some applications of asymptotic methods in semiconductor device modeling.- Discretization of three dimensional drift-diffusion equations by numerically stable finite elements.- Mathematical modeling of quantum wires in periodic heterojunction structures.- Numerical simulation of MOS transistors.- Scattering theory of high frequency quantum transport.- Accelerating dynamic iteration methods with application to semiconductor device simulation.- Boundary value problems in semiconductors for the stationary Vlasov-Maxwell-Boltzmann equations.- On the treatment of the collision operator for hydrodynamic models.- Adaptive methods for the solution of the Wigner-Poisson system.- The derivation of analytic device models by asymptotic methods.- Symmetric forms of energy - momentum transport models.- Analysis of the Gunn effect.- Some examples of singular perturbation problems in Device Modeling.
This IMA Volume in Mathematics and its Applications SEMICONDUCTORS, PART II is based on the proceedings of the IMA summer program "Semiconductors." Our goal was to foster interaction in this interdisciplinary field which involves electrical engineers, computer scientists, semiconductor physicists and mathematicians, from both university and industry. In particular, the program was meant to encourage the participation of numerical and mathematical analysts with backgrounds in ordinary and partial differential equations, to help get them involved in the mathematical as pects of semiconductor models and circuits. We are grateful to W.M. Coughran, Jr., Julian Cole, Peter Lloyd, and Jacob White for helping Farouk Odeh organize this activity and trust that the proceedings will provide a fitting memorial to Farouk. We also take this opportunity to thank those agencies whose financial support made the program possible: the Air Force Office of Scientific Research, the Army Research Office, the National Science Foundation, and the Office of Naval Research. A vner Friedman Willard Miller, J r. Preface to Part II Semiconductor and integrated-circuit modeling are an important part of the high technology "chip" industry, whose high-performance, low-cost microprocessors and high-density memory designs form the basis for supercomputers, engineering work stations, laptop computers, and other modern information appliances. There are a variety of differential equation problems that must be solved to facilitate such mod eling.
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