In this theoretical Letter, we examine the influence of dimensionality, size reduction, and heat-transport direction on the phonon-drag contribution to the Seebeck coefficient of silicon nanostructures. Phonon-drag contribution, which arises from the momentum transfer between out-of-equilibrium phonon populations and charge carriers, significantly enhances the thermoelectric coefficient. Our implementation of the phonon-drag term accounts for the anisotropy of nanostructures, such as thin films and nanowires through the boundary- and momentum-resolved phonon lifetime. Our approach also takes into account the spin-orbit coupling, which turns out to be crucial for hole transport. We reliably quantify the phonon-drag contribution at various doping levels, temperatures, and nanostructure geometries for both electrons and holes in silicon nanostructures. Our results support the recent experimental findings, showing that a part of phonon-drag contribution survives in 100-nm silicon nanostructures.

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• Electron-phonon coupling
• First-principles calculations
• Seebeck effect
• Spin-orbit coupling
• Transport phenomena
• Doped semiconductors
• Nanostructures