Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices

Progress in today's high-technology industries is strongly associated with the development of new mathematical tools. A typical illustration of this partnership is the mathematical modelling and numerical simulation of electric circuits and semiconductor devices. At the second Oberwolfach conference devoted to this important and timely field, scientists from around the world, mainly applied mathematicians and electrical engineers from industry and universities, presented their new results. Their contributions, forming the body of this work, cover electric circuit simulation, device simulation and process simulation. Discussions on experiences with standard software packages and improvements of such packages are included. In the semiconductor area special lectures were given on new modelling approaches, numerical techniques and existence and uniqueness results. In this connection, mention is made, for example, of mixed finite element methods, an extension of the Baliga-Patankar technique for a three dimensional simulation, and the connection between semiconductor equations and the Boltzmann equations.

Contenu

Circuit Simulation.- A new efficient numerical integration scheme for highly oscillatory electric circuits.- Numerische Lösung von hierarchisch strukturierten Systemen von Algebro-Differentialgleichungen.- Partitioning and multirate strategies in latent electric circuits.- Circuit simulation - an application for parallel ODE solvers?.- Numerical stability criteria for differential-algebraic systems.- Analysis of linear time-invariant networks in the frequency domain.- Limit cycle computation of oscillating electric circuits.- Timestep control for charge conserving integration in circuit simulation.- Ein Zusammenhang zwischen Waveformrelaxation und Iterationsverfahren für nichtlinear gestörte Gleichungen.- Multilevel-Newton-Verfahren in der Transientenanalyse elektrischer Netzwerke.- Transientensimulation elektrischer Netwerke mit TRBDF.- The transient behavior of an oscillator.- Device Simulation.- Numerical simulation of the carrier transport in semiconductor devices on the base of an energy model.- On uniqueness of solutions to the drift-diffusion-model of semiconductor devices.- On restrictions for discretizations of the simplified linearized van Roosbroeck's equations.- Mixed finite element discretization of continuity equations arising in semiconductor device simulation.- A piecewise linear Petrov-Galerkin analysis of the box-method.- Stability analysis of thermocapillary convection in semiconductor crystal growth.- The method of Baliga-Patankar and 3-D device simulation.- A mass conserving moving grid method for dopant simulation.- Numerical approaches to the kinetic semiconductor equations.- The non-stationary semiconductor model with bounded convective velocity and generation/recombination term.