Reconstruction of contact regions in semiconductor transistors using Dirichlet-Neumann cost functional approach

In this paper, we study the inverse problem of reconstructing an interior interface appearing in an elliptic equation in a bounded domain omega from the knowledge of the boundary measurements. This problem arises from a semiconductor transistor model. We propose a new shape reconstruction procedure that is based on the Kohn-Vogelius formulation and the topological sensitivity method. The inverse problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a function. The unknown contact interface is reconstructed using a level-set curve of the topological gradient. Finally, we give several examples to show the viability of our proposed method.