The problem investigated relates to the use of Chebyshev parameters 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, ϕ n, ϕ p – quasi Fermy’s levels for electrons and holes, respectively. The problem is further complicated by the fact that the border conditions are of two types: the Dirichlet conditions and the Neumman conditions, which act on different portions of the border. The subproblems that were solved in this research are: discretization of nonlinear differential equations, separation of obtained algebraic systems and linearization of system equations. The obtained linear algebraic systems have symmetric, positively defined and rare (five diagonal) matrices. To solve them many iterative methods can be applied, in this research the Chebyshev two-layer parameter method will be applied.