**Authors:** Galina Sprincean

**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:

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