Self-Consistent Solution of Two-Dimensional Poisson and Schrödinger Wave Equations for Nanoscale MOSFET Approaching Ballistic Limit

A numerical solution of the potential distribution of two-dimensional Poisson equation and Schrödinger wave equation under a set of boundary conditions has been obtained for a deep sub- micron and nanoscale MOSFET. The output characteristics can be found out by simply solving the two-dimensional Poisson equation under specific boundary conditions governed by the physics of the device. The channel potential profile has been presented. It is seen that the classical model underestimates the channel voltage and hence the longitudinal electric field in the channel as com- pared to that obtained through the quantum mechanical approach. For the purpose of validation, the results obtained on the basis of our model have been compared and contrasted with reported experimental result.