Formulation of Ground States for 2DEG at Rough Surfaces and Application to Nonlinear Model of Surface Roughness Scattering in nMOSFETs

Electron mobility in extremely-thin-body (ETB) nanosheet channels and at cryogenic temperature is known to be dominated by surface roughness scattering. However, the conventional model of surface roughness scattering lacks accuracy because it requires the use of excessive roughness parameters to represent the experimental results. One of the main difficulties for the surface roughness scattering model is that the higher-order perturbations should be accurately included in the model because the surface roughness scattering is a strongly nonlinear phenomenon. Therefore, in this study, the formulation of ground states of two-dimensional electron gas (2DEG) at rough surfaces is derived by introducing a concept of the space-averaged perturbation Hamiltonian. This revised formulation of 2DEG at rough surfaces is different from the conventional solution for 2DEG at the flat surface. The space-averaged perturbation Hamiltonian is invisible in the linearized perturbation system, while its effect is significant in the system with the nonlinear perturbation energy. We combine the revised 2DEG formulation with a nonlinear model of surface roughness scattering and calculate the 2DEG mobility of the bulk Si and ETB Si-on-insulator (SOI) nMOSFETs. As a result, the experimental mobility of bulk and ETB SOI nMOSFETs is well explained in a wide temperature range of 4.2 to 300 K by using the roughness parameters experimentally obtained by transmission electron microscopy (TEM), which also supports the understanding of mobility at cryogenic temperature. The revised nonlinear model reveals that surface roughness scattering under the present model is 13 times stronger than that predicted by the conventional linear model.