Numerical simulation and modelling of electric circuits and semiconductor devices are of primal interest in today's high technology industries. At the Oberwolfach Conference more than forty scientists from around the world, in­ cluding applied mathematicians and electrical engineers from industry and universities, presented new results in this area of growing importance. The contributions to this conference are presented in these proceedings. They include contributions on special topics of current interest in circuit and device simulation, as well as contributions that present an overview of the field. In the semiconductor area special lectures were given on mixed finite element methods and iterative procedures for the solution of large linear systems. For three dimensional models new discretization procedures including software packages were presented. Con­ nections between semiconductor equations and the Boltzmann equation were shown as well as relations to the quantum transport equation. Other issues discussed in this area include the design of simulation programs for semiconductors, vectorcomputers, and interface problems in several dimensions. Topics discussed in the area of circuit simulation include the index classification of differential-algebraic systems, connections with ill-posed problems, and regularization techniques. Split discretization procedures were given for the efficient calculation of periodic solutions of circuits taking into acount the latency. Homotopy methods and new numerical techniques for differential-algebraic systems were presented, and im­ provements of special numerical methods for standard software packages were sug­ gested. The editors VII Table of Contents Circuit Simulation Merten K.

Inhalt

Circuit Simulation.- Circuit Simulation in the Semiconductor Industry - State of the Art, Requirements and Future Development.- The Index of Differential-Algebraic Equations and its Significance for the Circuit Simulation.- Analysis and Numerical Treatment of Differential-Algebraic Systems.- Hopf Bifurcation in Differential Algebraic Equations and Applications to Circuit Simulation.- Row-Type Methods for the Integration of Electric Circuits.- Local Timestep Control for Simulating Electrical Circuits.- An improved numerical integration method in the circuit simulator SPICE2-S.- Increasing the Vector Length for Matrix Multiplication with Reduced Memory Access.- Device Simulation.- Semiconductor Equations and Analytical Models for Mosfets.- Recent Progress in Algorithms for Semiconductor Device Simulation.- A New Algorithmic Model for the Transient Semiconductor Problem.- Semiconductor Modelling Via the Boltzmann Equation.- A Numerical Method for the Simulation of Quantum Tunneling Phenomena in Solid State Semiconductors.- Modelling of Semiconductors Subject to Prescribed Currents.- Differential-Algebraic Problems and Semiconductor Device Simulation.- Algorithmic Aspects of the Hydrodynamic and Drift-Diffusion Device Models.- About the dependence of the convergence of Gummel's algorithm and its linear variants on the device geometry.- Mixed FEM for ?u = ?u.- A Mixed Finite Element Method with Tetrahedral Elements for the Semiconductor Continuity Equations.- Local oxidation of silicon - a finite element approach.- Corner Singularities of Solutions of the Potential Equation in three Dimensions.