Two-dimensional energy-dependent models for the simulation of substrate current in submicron MOSFET's

Two-dimensional energy-dependent substrate current models are described for NMOS and PMOS devices that have been developed using a multi-contour approach. The new models offer a significant improvement in the calculation of substrate current due to a more accurate calculation of the average energy as compared to the local-field model. The models are implemented in a post-processing manner by applying a one-dimensional energy conservation equation to each of many current contours in order to generate a two-dimensional representation of average energy and impact ionization rate, that is then integrated to calculate the substrate current. The new models have been compared to substrate current characteristics of a variety of NMOS and PMOS devices for a wide range of bias conditions and channel lengths, and very good agreement has been obtained with a single set of model parameters. An additional significance of this work is the enhancement of the standard multi-contour model by an energy-sink term that results in an improved prediction of the impact ionization process in PMOSFET's.>