Cross-sectional dependence of electron mobility and lattice thermal conductivity in silicon nanowires

The thermoelectric efficiency of a material depends on the ratio of its electrical and thermal conductivity. In this work, the cross-sectional dependence of electron mobility and lattice thermal conductivity in silicon nanowires has been investigated by solving the electron and phonon Boltzmann transport equations. The effects of confinement on acoustic phonon scattering (both electron - phonon and phonon - phonon) are accounted for in this study. With decreasing wire cross-section, the electron mobility shows a non-monotonic variation, whereas the lattice thermal conductivity exhibits a linear decrease. The former is a result of the decrease in intervalley and intersubband scattering due to a redistribution of electrons among the twofold-degenerate Δ₂ and fourfold-degenerate Δ₄ valley subbands when the cross-section is below 5 × 5 nm², while the latter is because of the monotonic increase of three phonon umklapp and boundary scattering with decreasing wire cross-section. Among the wires considered, those with a cross-section between 3 × 3 nm² and 4 × 4 nm² have the maximal ratio of the electron mobility to lattice thermal conductivity, and are expected to provide the maximal thermoelectric figure of merit.