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

Carrier mobility in bulk semiconductors is typically governed by electron-phonon (e-ph) scattering. In nanostructures, finite size leads to significant surface scattering, thus 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: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mi>D</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>u</mml:mi><mml:mi>l</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mi>β</mml:mi></mml:mrow></mml:msup><mml:mo>]</mml:mo></mml:mrow></mml:math>. The parameter <i>d</i>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 provides an intrinsic benchmark toward optimized experimental realizations.