A MULTIGRID PRECONDITIONER FOR THE SEMICONDUCTOR EQUATIONS

A multigrid preconditioned conjugate gradient algorithm is introduced into a semiconductor device modeling code DANCIR. This code simulates a wide variety of semiconductor devices by numerically solving the dri ft-diffusion equations. The most time-consuming aspect of the simulati on is the solution of three Linear systems within each iteration of th e Gummel method. The original version of DANCIR uses a conjugate gradi ent iteration preconditioned by an incomplete Cholesky factorization. In this paper, we consider the replacement of the Cholesky preconditio ner by a multigrid preconditioner. To adapt the multigrid method to th e drift-diffusion equations, interpolation, projection, and coarse gri d discretization operators need to be developed. These operators must take into account a number of physical aspects that are present in typ ical devices: wide-scale variation in the partial differential equatio n (PDE) coefficients, small-scale phenomena such as contact points, an d an oxide layer. Additionally, suitable relaxation procedures must be designed that give good smoothing numbers in the presence of anisotro pic behavior. The resulting method is compared with the Cholesky preco nditioner on a variety of devices in terms of iterations, storage, and run time.