The transition between the collision-dominated and ballistic electron transport regimes as the device length is reduced: A continuum analysis

Noting that the conventional collision-dominated electron transport perspective is only relevant when the length scale over which the transit occurs is greater than the electron’s mean free path, one can conceptually partition the electron transport “space” into collision-dominated and ballistic electron transport regimes. As the boundaries between these regimes are quite porous, in this analysis, we devise a means of quantitatively examining the transition between electron transport regimes as the length scale is reduced on a continuum basis. Our approach introduces a collision-dominated fractional scattering parameter, this parameter quantifying the fraction of the total scattering rate that arises purely from bulk scattering processes, contact scattering also contributing to the total scattering rate. We pursue this analysis for two conventional semiconductors of interest, silicon and gallium arsenide. A determination of the dependence of the results on both the length scale and the crystal temperature is pursued. Finally, for the specific case of room temperature, a comparison with the results of experiment is performed.