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

Abstract

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. During the optimization process several intermediate direct problems are solved using the boundary element method (BEM). To accelerate the solutions of of these systems we use a strategy of subdividing the domain into a number of smaller subdomains [11,9]. The scheme is iterative and each subdomain is handled by a separate node in parallel. Test runs comparing the performance of the parallel with the serial code, and other numerical discussions are presented.

On the numerical approximation of some inverse problems governed by nonlinear delay differential equation

“…Furthermore, many parallel evolutionary algorithm implementations for solving optimization problems have demonstrated their success [21][22][23][24] as seen in the literature. For the implementation, we use a parallel simulation executed on a multiprocessor machine with distributed memory.…”

An hybrid finite element method for a quasi-variational inequality modeling a semiconductor

“…Under physical assumptions, we show that the system (1) -(2) leads as a limit case to a quasi-variational equation [1,12,24], given in the case of a unipolar field-effect semiconductor, by…”

“…and w d = V + on the grid (see figure 1). This IQV model is a formulation of a free boundary problem where we have to find the unknown boundary separating two sets Ω C and Ω D , corresponding to the charge neutrality region where the potential u and the Fermi quasi-potential w = M(u) are identical and the depletion region where u < w [1,22,24] The existence and uniqueness of the solution to the problem (6) -( 7) are discussed in [1] where the authors propose a technique based on topological degree theory which extends the results of [21] to cases where the solution is not regular. The solution of the quasi-variational inequality being obtained as the limit of a series of variational inequalities where the two problems ( 6) and ( 7) are decoupled…”