On the inverse doping profile problem

Victor Isakov; Joseph Myers

doi:10.3934/ipi.2012.6.465

Article Contents

2012, Volume 6, Issue 3: 465-486. Doi: 10.3934/ipi.2012.6.465

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On the inverse doping profile problem

Victor Isakov^1, and
Joseph Myers^2,

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

Received: March 31, 2011

Revised: January 31, 2012

Published: July 2012

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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.

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References

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