Rene Pinnau Fachbereich Mathematik

This paper intends to give a comprehensive overview on the basic mathe-matical tools which are presently used in optimal semiconductor design. Focussing on the drift diusion model for semiconductor devices we col-lect available results concerning the solvability of design problems and present for the rst time results on the uniqueness of optimal designs. We discuss the construction of descent algorithms employing the ad-joint state and investigate their numerical performance. The feasibility of this approach is underlined by various numerical examples. Key words. Optimal semiconductor design, adjoints, existence, uniqueness, nu-merics, gradient algorithm AMS(MOS) subject classication. 35J50, 49J20, 49K20 1