ON USING COLLOCATION IN 3 DIMENSIONS AND SOLVING A MODEL SEMICONDUCTOR PROBLEM

A research code has been written to solve an elliptic system of couple d nonlinear partial differential equations of conservation form on a r ectangularly shaped three-dimensional domain. The code uses the method of collocation of Gauss points with tricubic Hermite piecewise contin uous polynomial basis functions. The system of equations is solved by iteration. The system of nonlinear equations is linearized, and the sy stem of linear equations is solved by iterative methods. When the matr ix of the collocation equations is duly modified by using a scaled blo ck-limited partial pivoting procedure of Gauss elimination, it is foun d that the rate of convergence of the iterative method is significantl y improved and that a solution becomes possible. The code is used to s olve Poisson's equation for a model semiconductor problem. The electri c potential distribution is calculated in a metaloxide-semiconductor s tructure that is important to the fabrication of electron devices.