A new hybrid method for shape optimization with application to semiconductor equations

Abstract

<p style='text-indent:20px;'>The aim of this work is to reconstruct the depletion region in pn junction. Starting with famous drift diffusion model, we establish the simplified equation for the considered semiconductor. There we call the shape optimization technique to formulate a minimization problem from the inverse problem at hand. The existence of an optimal solution of the optimization problem is proved. The proposed numerical algorithm is a combined Domain Decomposition method with an efficient hybrid conjugate gradient guided by differential evolution heuristic algorithm, the finite element method is used to discretize the state equation. At the end we establish several numerical examples, to prove the validity of theoretical results using the proposed algorithm, in addition we show some simulation of the depletion region approximation under two different functioning modes.</p>

A fuzzy particle swarm optimization method with application to shape design problem

“…Mozaffari et al [21] employed the imperialist competitive algorithm along with the conjugate gradient method and boundary element method to identify two interfaces. In [10], a hybrid differential evolution and quasi-Newton method were employed to approximate the depletion region in a pn junction semiconductor device.…”

An Efficient Numerical Scheme Based on Radial Basis Functions and a Hybrid Quasi-Newton Method for a Nonlinear Shape Optimization Problem

“…Hybrid methods have been lately used to solve several applications in inverse problems. In [8], the authors propose conjugate gradient guided with differential evolution to minimize a shape optimization problem derived from a bilateral free boundaries problem. The same authors, in [9], manipulate the genetic algorithm to find the best initial guess for the conjugate gradient, applied to an optimal control problem of bilateral free boundaries.…”