The authors present a new and efficient precondition method (ILUV-CGS), which is an incomplete LU (ILU) factorization by value instead of a sparse nonzero pattern, in conjunction with CGS iteration for solving nonsymmetric linear equations in finite-element simulation of semiconductor devices. To demonstrate the efficiency of this method, the simulations of a group of representative devices with different numerical characteristics have been carried out using the ILUV-CGS algorithm, and these are compared with those of the existing ILU-CGS method. The comparison results are in favor of using the ILUV=CGS method.>

To make the application of the finite-element method practical in semiconductor device simulation, the authors have applied the Scharfetter-Gummel (S-G) scheme in conjunction with an accurate seven-point Gaussian quadrature rule to the assembly of the finite-element stiffness matrices and the right-hand-side vector of the semiconductor equations. The key of this method lies in accurate interpolation rules, which are derived on the basis of simple device physics considerations. The inherent simplicity and flexibility in the finite element formulation make the new method applicable to multidimensional problems. The simplicity of embedding the S-G scheme in the quadrature of finite-element assembly lends itself to all kinds of finite-element methods using various elements, shape functions, and weightings. The resultant exponential functional fitting avoids high discretization errors usually incurred by the classical finite-element discretization method. Solutions with high accuracy, even on coarse mesh, and a significant speed-up of convergence rate are obtained.>