Threshold voltage calculation in ultra-thin film SOI MOSFETs using the effective potential

The success of the effective potential method of including quantum confinement effects in simulations of MOSFETs is based on the ability to calculate ahead of time the extent of the Gaussian wave-packet used to describe the electron. In the calculation of the Gaussian, the inversion layer is assumed to form in a triangular potential well, from which a suitable standard deviation can be obtained. The situation in an ultra-thin SOI MOSFET is slightly different, in that the potential well has a triangular bottom, but there is a significant contribution to the confinement from the rectangular barriers formed by the gate oxide and the buried oxide (BOX). For this more complex potential well, it is of interest to determine the range of applicability of the constant standard deviation effective potential model. In this work we include this effective potential model in 3D Monte Carlo calculations of the threshold voltage of ultra-thin SOI MOSFETs. We find that the effective potential recovers the expected trend in threshold voltage shift with shrinking silicon thickness, down to a thickness of approximately 3 nm.