A new nonlinear relaxation scheme for solving semiconductor device equations

In most cases steady-state semiconductor device equations are solved simultaneously by Newton´s method, by Gummel´s decoupled nonlinear relaxation scheme, or a combination of both. A framework deriving such different iterative methods from underlying variable transformations is presented. Within that framework the introduction of a new variable establishes a new nonlinear relaxation scheme, which is significantly faster than Gummel´s scheme in cases where it converges slowly, thereby avoiding the drawbacks of a simultaneous solution method. This relaxation scheme has been implemented in the two-dimensional device simulator GALENE II