Technical Report CS0649

Authors: I. Efrat and M. Israeli
Abstract: The operation of semiconductor devices is often governed by thin transition layers, either near the boundary, or at internal junctions: These regions of large g~adients pose tough requirements for the discretization scheme, which is used for the numerical solution of the governing POE's. These layers are conventionally resolved ~y extreme local mesh refinement. It has been pointed out that P-N junctions can be effectively discretized by the Scharfetter - Gummel scheme. This method exploits the smoothness of currents through junctions. There has been no similarly successful way to resolve thin channels. We have developed an asymptotic solution of the channel region of MOSFET devices. The aspect ratio of the channel is taken as a small parameter. The layer approximation is imbedded in a hybrid scheme, which computes a correction to the analytic approximation by controlvolu. me discretization. The hybrid method can reach any required accuracy, but overcomes the neces~ity of highly refined grid in the cha'1nel. MOSFET simulations which normally require vast grids were accurately performed by the hybrid method at a drastically reduced cost.
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