An optimization approach to a finite dimensional parameter estimation problem in semiconductor device design

In this paper the parameter selection in semiconductor device design is posed as an optimization problem: given an ideal voltage-current (V-I) characteristic, find one or more physical and geometrical parameters such that the V-I characteristic of the device matches the ideal one optimally with respect to a prescribed performance criterion. The voltage-current characteristic of a semiconductor device is governed by a set of nonlinear partial differential equations (PDE), and thus a black-box approach is taken for the numerical solution of the PDEs. Various existing numerical methods are proposed for the solution of the nonlinear optimization problem. The Jacobian of the cost function is ill-conditioned and a scaling technique is thus proposed to stabilize the resulting linear system. Numerical experiments, performed to show the usefulness of this approach, demonstrate that the approach always gives optimal or near-optimal solutions to the test problems in both two and three dimensions. (C) 1999 Academic Press.