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Numerical simulation of nonlinear processes in semiconductor devices with the application of the Newtons method for linearization
Authors: Galina Sprincean
Keywords: nonlinear processes, semiconductor devices, Scharfetter-Gummel scheme, Newton’s linearization.
– 1.71 Mb
Keywords: nonlinear processes, semiconductor devices, Scharfetter-Gummel scheme, Newton’s linearization.
Abstract
This article relates to the use of Newton’s method and Scharfetter– Gummel scheme, to linearize and discretize the equations, for numerical modeling of nonlinear processes in semiconductor devices. The mathematical model of the problem represents a system of nonlinear differential equations, in the unknowns ϕ–electrostatic potential, n,p–the concentrations of electrons and holes, respectively. The problem is further complicated by the fact that the boundary conditions are of two types: the Dirichlet conditions and the Neumman conditions, which act on different portions of the boundary. The subproblems that were solved in this paper: linearization of nonlinear differential equations, using Newton’s method; discretization of equations, using Scharfetter–Gummel scheme. The obtained systems have five diagonal and nonsymmetrical matrices. The numerical method of Bi–Conjugate Gradients was used to solve the systems.Moldova State University,
Chisinau, Republic of Moldova,
E-mail:
Chisinau, Republic of Moldova,
E-mail:
Fulltext
– 1.71 Mb
Contents
- On solutions of the kinetic McKean system
- Coincidence and common fixed points theorem with an application in dynamic programming
- Free left k-nilpotent n-tuple semigroups
- Almost Periodic and Almost Automorphic Solutions of Monotone Differential Equations with a Strict Monotone First Integral*
- On semigroups of endomorphisms of universal algebras
- An analogue of Bremermann’s theorem on finding the Bergman kernel for the Cartesian product of the classical domains ℜI (m, k) and ℜII (n)
- Numerical simulation of nonlinear processes in semiconductor devices with the application of the Newtons method for linearization
