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.<
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