On the numerical solution of a free boundary identification problem

In this paper, we discuss an inverse problem of determining a part of the b oundary of the depletion region of semiconductor devices. The existence of the unique solution is proved. The unknown boundaries as well as unknown po tentials are parameterized by finite elements. Decoupling the discretized L aplace equation from the boundary conditions, we derive two algorithms to s olves this problems. The obtained nonlinear systems of algebraic equations are solved by quasi-Newton methods. Numerical experiments, including compar isons of the behaviour of the proposed algorithms when applied to two-dimen sional inverse boundary problems, are reported.