Role of Dimensionality and Size in Controlling the Drag Seebeck Coefficient of Doped Silicon Nanostructures: A Fundamental Understanding*

In this theoretical study, we examine the influence of dimensionality, size reduction, and heat- transport direction on the phonon-drag contribution to the Seebeck coefficient of silicon nanos- tructures. Phonon-drag contribution, which arises from the momentum transfer between out-of- equilibrium phonon populations and charge carriers, significantly enhances the thermoelectric coef- ficient. 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.