First-principles Prediction of Carrier Mobility in Semiconductor Nanowires Based on the Spatially Dependent Boltzmann Transport Equation

Abstract

Carrier mobility in bulk semiconductors is typically governed by electron-phonon (e-ph) scattering. In nanostructures, spatial confinement can lead to significant surface scattering, lowering mobility and breaking the spatial homogeneity assumption of conventional models. In this work, a fully ab initio framework based on the spatially dependent Boltzmann transport equation for one-dimensional nanowires is developed. We apply it to Si and GaN assuming diffusive surface scattering, and reveal the mobility-diameter relation: $μ_\mathrm{1D} = μ_\mathrm{bulk} \left[1-\left(d/d_0\right)^{-β}\right]$. The parameter $d_0$, comparable to the carrier mean free path, defines a boundary layer exhibiting a considerable mobility gradient, and also quantifies the competition between e-ph and surface scattering together with $β$. We further discuss the effects of orientation, cross-sectional shape, and temperature. Moreover, experimental data are generally lower than our predictions, possibly due to structural imperfections, systematic errors from measurements, etc. Therefore, our theoretical method can provide an intrinsic benchmark toward optimized experimental realizations.

Figures (5)

• Figure 1: Diameter-dependent room-temperature carrier mobility in nanowires with circular cross-sections and different crystallographic orientations. The horizontal dashed or dotted lines denote the corresponding bulk mobility values.
• Figure 2: Three-dimensional visualization of direction-dependent carrier MFP at room temperature. Each point on the surface corresponds to a crystallographic direction, with the radial distance and color indicating the averaged MFP weighted by carrier density.
• Figure 3: Cross-sectional distribution of room-temperature carrier mobility for nanowires with different diameters and cross-sectional shapes. The silver arrows indicate the fitted $d_0$ based on eq \ref{['eq:mob-diameter']} (not shown if $d_0 \ll d$). Crystallographic orientations are $<$100$>$ for Si and $<$0001$>$ for GaN. Percentages are with respect to the bulk value.
• Figure 4: Cross-sectional distribution of room-temperature carrier mobility for nanowires with different crystallographic orientations and cross-sectional shapes. The white dashed lines represent the contour of $\mu = 0.9\mu_\mathrm{bulk}$. Percentages are with respect to the bulk value.
• Figure 5: Temperature-dependent carrier mobilities in circular nanowires with selected diameters. Crystallographic orientations are $<$100$>$ for Si and $<$0001$>$ for GaN. The results of bulk materials are provided for comparison, which are fitted to the power law $\mu \propto T^{-\alpha}$.