An Index Analysis from Coupled Circuit and Device Simulation

Nowadays the semiconductor devices in an electrical circuit are modelled by equivalent circuits containing basic network elements described by algebraic and ordinary differential equations. But the correct adjustment of these circuits has become a very difficult task for the network design. Recently a new model for electrical circuits containing semiconductor devices has been proposed. In this model the differential algebraic equations (DAEs) for the basic circuit's elements are coupled to partial differential equations (PDEs), more specifically to one-dimensional Drift-Diffusion (DD) equations, modelling the semiconductor devices in it. In this work we study the index of a similar system where higher dimensional PDEs model the behaviour of the semiconductor devices in the circuit. We also show that the index of the DAE that is obtained after discretization in space of the PDEs is equal to the index of the abstract system