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

• Published in: Applicable analysis Vol. 100; no. 4; pp. 893 - 922
• Main Authors: Hrizi, Mourad, Hassine, Maatoug
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 12.03.2021; Taylor & Francis Ltd
• Subjects: Dirichlet problem; Inverse problem; Inverse problems; Kohn-Vogelius formulation; noniterative reconstruction method; Reconstruction; Semiconductor devices; Sensitivity analysis; topological sensitivity analysis; Topology optimization; Transistors
• ISSN: 0003-6811; 1563-504X
• DOI: 10.1080/00036811.2019.1623393

In this paper, we study the inverse problem of reconstructing an interior interface appearing in an elliptic equation in a bounded domain Ω 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.