Optimized numerical models for semiconductor devices: Part I

This article presents some results from a study concerned with the trade-off between efficiency of numerical computation and accuracy of numerical models for semiconductor devices. The approach taken in this study was to use nonuniform grids in the finite difference equations approximating the semiconductor partial differential equations. A constrained minimization problem was formulated which analytically optimizes the numerical models. Several performance functions were found useful in optimizing the numerical models; the one presented here matches computed and "exact" terminal current responses. An example is presented to illustrate the results obtained with this performance function. The example model optimization shows that the optimized grids should have their greatest density in the space-charge region near the junction. An interesting side result is that when one performance function is optimized, apparently other desired features are optimized for numerical models for semiconductor devices. The Fletcher-Powell optimization algorithm was used with an adjoint gradient algorithm specifically developed for this study, without which the use of nonuniform grids would not have been practical.