APPLICATION OF THE COLLOCATION METHOD IN 3 DIMENSIONS TO A MODEL SEMICONDUCTOR PROBLEM

A research code has been written to solve an elliptic system of couple d non-linear partial differential equations of conservation form on a rectangularly shaped three-dimensional domain. The code uses the metho d of collocation of Gauss points with tricubic Hermite piecewise conti nuous polynomial basis functions. The system of equations is solved by iteration. The system of non-linear equations is linearized, and the system of linear equations is solved by iterative methods. When the ma trix of the collocation equations is duly modified by using a scaled b lock-limited partial pivoting procedure of Gauss elimination, it is fo und that the rate of convergence of the iterative method is significan tly improved and that a solution becomes possible. The code is used to solve Poisson's equation for a model semiconductor problem. The elect ric potential distribution is calculated in a metal-oxide-semiconducto r structure that is important to the fabrication of electron devices.