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August  2012, 6(3): 465-486. doi: 10.3934/ipi.2012.6.465

## On the inverse doping profile problem

 1 Wichita State University, 1845 Fairmount, Wichita, KS 67260-0033, United States 2 Friends University, 2100 W University Ave, Wichita, KS 67213, United States

Received  April 2011 Revised  February 2012 Published  September 2012

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.
Citation: Victor Isakov, Joseph Myers. On the inverse doping profile problem. Inverse Problems & Imaging, 2012, 6 (3) : 465-486. doi: 10.3934/ipi.2012.6.465
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