Inverse Problems and Imaging (IPI)

On the inverse doping profile problem

Pages: 465 - 486, Volume 6, Issue 3, August 2012      doi:10.3934/ipi.2012.6.465

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Victor Isakov - Wichita State University, 1845 Fairmount, Wichita, KS 67260-0033, United States (email)
Joseph Myers - Friends University, 2100 W University Ave, Wichita, KS 67213, United States (email)

Abstract: We obtain new analytic results for the problem of the recovery of a doped region $D$ in semiconductor devices from the total flux of electrons/holes through a part of the boundary for various applied potentials on some complementary part of the boundary. We consider the stationary two-dimensional case and we use the index of the gradient of solutions of the linear elliptic equation modeling a unipolar device. Under mild assumptions we prove local uniqueness of smooth $D$ and global uniqueness of polygonal $D$ satisfying some geometrical (star-shapednedness or convexity in some direction) assumptions. We design a nonlinear minimization algorithm for numerical solution and we demonstrate its effectiveness on some basic examples. An essential ingredient of this algorithm is a numerical solution of the direct problem by using single layer potentials.

Keywords:  Inverse problems, inverse scattering problems.
Mathematics Subject Classification:  Primary: 35R30; Secondary: 78A46.

Received: April 2011;      Revised: February 2012;      Available Online: September 2012.