Drift-diffusion Systems: Variational Principles and Fixed Point Maps for Steady State Semiconductor Models

The mathematical semiconductor device model, consisting of the potential equation and the current continuity subsystem for the carriers, is studied from the standpoint of its decoupling fixed point map and the numerical approximate fixed point map. Variational principles will be discussed for this process and for discretizations achieved by use of generalized splines. By the choice of trial space, these capture the upwinding associated with Scharfetter-Gummel methods. An approximation calculus will be introduced in conjunction with the numerical fixed point map.