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

Abstract

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.

Keywords:

• Inverse problem
• noniterative reconstruction method
• Kohn–Vogelius formulation
• topological sensitivity analysis
• topology optimization

2010 Mathematics Subject Classifications:

• 49N45
• 49Q10
• 49Q12
• 65M32

Acknowledgements

The authors wish to thank the referee for his/her useful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.