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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.

Allowance for traps in certain space‐charge environments produces changes in the mathematical formalism which make it difficult to determine spatial variations in potential and the negative‐positive charge distribution. The trap‐free model for the blocking electrode can be extended into this realm by appropriate accommodation of the equations of continuity for specified kinetics of the trap system. The tendency of traps seems to be a moderation of the spatial fall‐off of potential with more gradual build‐up and decay of the charge densities. The nonlinear Poisson equation has been solved analytically by the development of powerful series methods, demonstrating that machine integration can be avoided.