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This paper gives a concise overview of some existing methods for the solution of the nonlinear Poisson equation in semiconductors. A method for the solution of this equation was recently proposed in this journal by I. D. Mayergoyz [J. Appl. Phys. 59, 195 (1986)]. Soon afterwards, an improved version was described by W. Keller [J. Appl. Phys. 61, 5189 (1987)]. Both methods are classified within the perspective of the existing methods. Moreover, Keller’s method is further improved by the introduction of scaled variables and by using red-black ordening to allow for overrelaxation. All advantages of the two methods are maintained. An illustrative example shows an improvement in solution speed of at least a factor of 5.6.

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