On the inverse doping profile problem
Myers, Joseph Kenneth
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Isakov, Victor; Myers, Joseph. 2012. On the inverse doping profile problem. Inverse Problems and Imaging, v.6 no.3 pp.465-486
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.
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