The influence of polarisation and image charges on electron- impurity scattering in high degeneracy, nanometre scale silicon wrap-round gate MOSFETs

Atomistic impurities in the channel of a nano-wire silicon MOSFET with wrap- round gate and highly doped and degenerate source and drain are shown to be strongly screened by polarisation (image charge effects) arising from carriers that are confined to source and drain when the channel screening length exceeds the channel length. The image charge effects on a given atomistic ionized impurity depend significantly on its location in the channel. The model is based on an exact analysis of the Poisson equation using Fourier-Bessel analysis in cylindrical coordinates. Close to source or drain the analytically computed total and differential scattering rates correspond to a form of dipole scattering. The source and drain may separately or together contribute to the screening of the atomistic impurity depending on its location and the channel screening length. The net effect of the infinite sequence of fully developed screened image charges induced by the atomistic impurity is to substantially reduce impurity scattering by at least an order of magnitude and to enhance the back scattering. The theory is illustrated for a 5 nm channel device