A new approach to analytically solving the two-dimensional Poisson´s equation and its application in short-channel MOSFET modeling

An analytical solution for the potential distribution of the two-dimensional Poisson´s equation with the Dirichlet boundary conditions has been obtained for the MOSFET device by using Green´s function method and a new transformation technique, in which the effects of source and drain junction curvature and depth are properly considered. Based on the calculated potential distribution, the subthreshold current considering the drain-induced barrier lowering effects has been computed by a simple current equation that considers only the diffusion component with an effective length determined by the potential distribution at the SiO2-Si interface. From the calculated subthreshold current, the threshold voltage of the MOSFET´s is determined. It has been verified that the dependences of the calculated threshold voltage and subthreshold current on device channel length, drain, and substrate biases are in good agreement with those computed by whole two-dimensional numerical analysis and experimental data.