Electron Transport in Silicon Nanowires: The Role of Acoustic Phonon Confinement and Surface Roughness Scattering

We investigate the effects of electron and acoustic-phonon confinement on the low-field electron mobility of thin square silicon nanowires (SiNWs) that are surrounded by SiO$_2$ and gated. We employ a self-consistent Poisson-Schr\"{o}dinger-Monte Carlo solver that accounts for scattering due to acoustic phonons (confined and bulk), intervalley phonons, and the Si/SiO$_2$ surface roughness. The wires considered have cross sections between 3 $\times$ 3 nm$^2$ and 8 $\times$ 8 nm$^2$. For larger wires, as expected, the dependence of the mobility on the transverse field from the gate is pronounced. At low transverse fields, where phonon scattering dominates, scattering from confined acoustic phonons results in about a 10% decrease of the mobility with respect to the bulk phonon approximation. As the wire cross-section decreases, the electron mobility drops because the detrimental increase in both electron--acoustic phonon and electron--surface roughness scattering rates overshadows the beneficial volume inversion and subband modulation. For wires thinner than 5 $\times$ 5 nm$^2$, surface roughness scattering dominates regardless of the transverse field applied and leads to a monotonic decrease of the electron mobility with decreasing SiNWs cross section.