Search

Abstract: We are interested in circuit simulation including distributed semiconductor models. The circuit itself is modeled by the modified nodal analysis. The stationary drift diffusion equations are used to describe the semiconductors. The complete system is then a partial differential-algebraic system. We discretize it first in space with finite elements and the Scharfetter–Gummel discretization. The resulting semi-discrete system can be analyzed as a differential-algebraic equation with properly stated leading term. We present topological index one criteria. They coincide with previous results for the non-discretized partial differential-algebraic equation. For the time discretization we use standard BDF methods (implicit Gear formulas). Finally we derive a convergence estimate for the whole partial differential-algebraic system close to equilibrium. [ABSTRACT FROM AUTHOR]

Abstract: In this work we are interested in the numerical solution of a coupled model of differential algebraic equations (DAEs) and partial differential equations (PDEs). The DAEs describe the behavior of an electrical circuit that contains semiconductor devices and the partial differential equations constitute drift-diffusion equations modelling the semiconductor devices in the circuit. After space discretization using a finite element method, the coupled system results in a differential-algebraic system with a properly stated leading term. We investigate the structure and the properties of this DAE system. In particular, we develop structural criteria for the DAE index. This is of basic interest since DAE properties like stability, existence and uniqueness of solutions depend strongly on its index. [Copyright &y& Elsevier]