On the numerical solution of a free boundary identification problem

Abstract

In this paper, we discuss an inverse problem of determining a part of the boundary of the depletion region of semiconductor devices. The existence of the unique solution is proved. The unknown boundaries as well as unknown potentials are parameterized by h i t e elements. Decoupling the discretized Laplace equation from the boundary conditions, we derive two algorithms to solves this problems. The obtained nonlinear systems of algebraic equations are solved by quasi-Newton methods. Numerical experiments, including comparisons of the behaviour of the proposed algorithms when applied to two-dimensional inverse boundary problems, are reported.

Reconstruction of the depletion layer in MOSFET by genetic algorithms

“…Inverse boundary identification problems are ubiquitous in medicine, engineering, industry, and other fields [1][2][3]. This kind of problem consists in finding an unknown boundary defined as a part of the domain boundary's or a boundary which separates two regions, that is called a free interface.…”

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

“…Free boundary problems are defined as the problem of finding an optimal domain satisfying a given model. Their application appears in different scientific areas such as identification of cavities and cracks in solid bodies, semiconductor framework [2,5,6,13]. In this paper we study the pn-junction [21], which is a semiconductor device considered as bipolar transistor, composed from two electrode semiconductors a p-type and n-type.…”

“…We can see that (5) has supplement boundary conditions. Thus we split problem (5) into two state problems, the first is given by: 6) with Γ N = Γ 1 ∪ Γ 3 and Γ D = Γ 2 ∪ Γ 4 , it is associated with the variational form…”

“…Now we will illustrate some numerical test for the depletion region identification. We assume that the pn junction domain is [0, 6] × [0, 2], the range of the positive and negative electrodes are [0, 3] × [0, 2] and [3,6] × [0, 2] respectively. The working of a pn-junction is governed by two mode known as the forward and the reverse biased mode.…”

Parallel solvers for the depletion region identification in metal semiconductor field effect transistors

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In this work we are interested in a sufficiently accurate approximation of the steady-state potentials in a Metal Semiconductor Field Effect Transistor (MESFET), which can be obtained with the so-called depletion region approximation (see [5]). We propose a robust method based on the shape optimization techniques to analyze and compute the depletion boundary as a function of the applied voltage and the geometry material properties of the device.

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