4.7 The Onion Model

To obtain a complete mobility model for device simulation, this high-field behavior has to be combined with mobility models incorporating the effects dominant at low driving field, such as impurity scattering and surface roughness scattering. This approach, sometimes referred to as the onion model, starts with a proper expression for the lattice mobility, and adds then the effects of impurity scattering, surface scattering, and finally velocity saturation. Using this notion, the presented high-field model can be combined with any low-field model incorporating the aforementioned scattering effects. Note that effects such as surface scattering and velocity saturation are dominant in different device regions. Surface roughness scattering is most effective for carriers confined in a channel, where the driving field is low. On the other hand, high driving fields occur in the pinch-off region, where carriers are no longer quantized in sub-bands, but behave bulk like. Indeed, the transition region of moderate driving fields, where a significant fraction of carriers is still quantized and already moderate carrier heating takes place, the error of this onion type model may be somewhat higher than in the low-field and high-field limits.