Electron-phonon scattering effect on the lattice thermal conductivity of silicon nanostructures.

Nanostructuring technology has been widely employed to reduce the thermal conductivity of thermoelectric materials because of the strong phonon-boundary scattering. Optimizing the carrier concentration can not only improve the electrical properties, but also affect the lattice thermal conductivity significantly due to the electron-phonon scattering. The lattice thermal conductivity of silicon nanostructures considering electron-phonon scattering is investigated for comparing the lattice thermal conductivity reductions resulting from nanostructuring technology and the carrier concentration optimization. We performed frequency-dependent simulations of thermal transport systematically in nanowires, solid thin films and nanoporous thin films by solving the phonon Boltzmann transport equation using the discrete ordinate method. All the phonon properties are based on the first-principles calculations. The results show that the lattice thermal conductivity reduction due to the electron-phonon scattering decreases as the feature size of nanostructures goes down and could be ignored at low feature sizes (50 nm for n-type nanowires and 20 nm for p-type nanowires and n-type solid thin films) or a high porosity (0.6 for n-type 500 nm-thick nanoporous thin films) even when the carrier concentration is as high as 10 cm. Similarly, the size effect due to the phonon-boundary scattering also becomes less significant with the increase of carrier concentration. The findings provide a fundamental understanding of electron and phonon transports in nanostructures, which is important for the optimization of nanostructured thermoelectric materials.