Soft sphere model for electron correlation and scattering in the atomistic modelling of semiconductor devices

The atomistic modelling of silicon MOSFET devices becomes essential at deep sub-micron scales when it is no longer possible to represent the charged impurities by a continuous charge distribution with a determined doping density. Instead the spatial distribution and the actual number of dopants must be treated as discrete random variables. The present paper addresses the issue of modelling the dynamics of discrete carrier flow in a semiconductor device utilising a simple model of the carrier-carrier scattering and carrier-fixed impurity scattering which is suitable for efficient simulations of large ensembles of devices.