Abstract
We study a generalized Gummel iteration for the solution of an abstract optimal semiconductor design problem, which covers a wide range of semiconductor models. The algorithm is to exploit the special structure of the KKT system and it can be interpreted as a descent algorithm for an appropriately defined cost functional. This allows for a convergence proof which does not need the assumption of small biasing voltages. The algorithm is explicitly stated for the (quantum) drift diffusion model, the energy transport model and the microscopic Schrödinger–Poisson model.
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