Finite and boundary element approach to process simulation with conjugate gradient-based method

An efficient numerical scheme for obtaining the two dimensional impurity profile and structural features of the semiconductor devices is proposed. The finite element method (FEM) is used to solve the drift-diffusion equation of impurities in silicon. The thermal oxidation using a model based on steady-state oxidant diffusion is dealt with the boundary element method (BEM). Both methods are employed for calculating the complicated geometry and the boundary conditions in the simulation, where these methods are simultaneously used for the oxidizing condition. For the finite element analysis, mass lumping is introduced to get the stable result. The matrix obtained is asymmetric and irregular sparse, the matrix is solved by the Conjugate Gradient-Squared method (CGS) with preconditioning-conditioning (Incomplete LDU factorization). Thus a more economical calculation method is obtained than the conventional FEM and BEM analysis, using Gaussian elimination method.