Modeling of surface roughness scattering in nanowires based on atomistic wave function: Application to hole mobility in rectangular germanium nanowires

Abstract

The authors present a calculation model of surface roughness scattering (SRS) in nanowires (NWs) based on atomistic description of electronic states by an $s{p}^{3}{d}^{5}{s}^{*}$ tight-binding scheme, and then this model is applied to hole transport in rectangular cross-sectional germanium (Ge) NWs. In this SRS model, the change of electronic band structures due to width or height reduction is first computed, and then it is expressed using an equivalent potential near the surface. The perturbation corresponding to a surface roughness is calculated from this equivalent potential. Using the aforementioned SRS model, hole mobility in Ge NWs was computed taking into account phonon scattering and SRS. The impacts of SRS on hole mobility in Ge NWs were analyzed, focusing on the valence band structure and hole states of NWs. The main results are as follows. At low hole density, the impacts of SRS are strongly dependent on NW geometry, and Ge NWs with high phonon-limited hole mobility, such as rectangular cross-sectional [110]-oriented NWs with large height along the [001] direction and square cross-sectional [111]-oriented NWs, tend to be less affected by SRS. At high hole density, however, the geometry dependence of hole mobility becomes weaker. These are understood from the nature of hole states and the valence band structure.