PDAE models of integrated circuits and perturbation analysis

Abstract

A model for a linear electric circuit containing semiconductors is presented. The modified nodal analysis leads to a differential algebraic equation (DAE) describing the electric network. The non-linear behaviour of the semiconductors is modelled by the drift diffusion equations. Coupling relations are defined and a sensitivity analysis concept that generalises the DAE index for finite systems to infinite ones is presented and applied to the resulting partial differential algebraic equation (PDAE). It is shown that the coupled system is of index 1 if the voltages applied to the semiconductors are low and the network without semiconductors is of index 1.