The impact of device length on the electron's effective mobility

Within the framework of an electron transport regime classification scheme, we aim to explore the boundaries that occur between the ballistic, collision-dominated, space-charge injection, and non-space-charge injection electron transport regimes that are experienced by an electron within a semiconducting device, mapping out where these different electron transport regimes are. We do this by determining the electron's mean free path and the relevant screening length. In order to make this analysis concrete, we perform this analysis for four representative semiconductor material systems, including silicon, gallium arsenide, the 4H-phase of silicon carbide, and the wurtzite phase of gallium nitride. The entire analysis is performed using a two-dimensional approach, this being representative of the electron transport that is experienced by an electron in the vicinity of a two-dimensional electron gas. Finally, following an evaluation of the dependence of the ballistic mobility on the device length scale for all four materials, an evaluation of the effective mobility as a function of the channel-length scale is pursued, a Matthiessen-rule based approach being employed for the purposes of this analysis.