Significant reduction of lattice thermal conductivity by electron-phonon interaction in silicon with high carrier concentrations: a first-principles study

Abstract: Electron-phonon interaction has been well known to create major resistance to electron transport in metals and semiconductors, whereas less studies were directed to its effect on the phonon transport, especially in semiconductors. We calculate the phonon lifetimes due to scattering with electrons (or holes), combine them with the intrinsic lifetimes due to the anharmonic phonon-phonon interaction, all from first-principles, and evaluate the effect of the electron-phonon interaction on the lattice thermal conductivity of silicon. Unexpectedly, we find a significant reduction of the lattice thermal conductivity at room temperature as the carrier concentration goes above 1e19 cm-3 (the reduction reaches up to 45% in p-type silicon at around 1e21 cm-3), a range of great technological relevance to thermoelectric materials.

Insights into the Electron-Phonon Interaction Effect on Silicon's Thermal Conductivity

This paper investigates the impact of electron-phonon interactions (EPI) on phonon transport in silicon at elevated carrier concentrations, providing a comprehensive first-principles study of how EPI influences lattice thermal conductivity. Although previous research has extensively documented the effects of EPI on electron transport, its impact on phonon transport—particularly in semiconductors—has been less explored. The study breaks new ground by revealing a significant reduction in lattice thermal conductivity, up to 45% in p-type silicon at carrier concentrations around (10^{21} \text{ cm}^{-3}), at standard room temperature conditions.

Methodology

The study employs a robust methodology combining first-principles calculations to assess phonon lifetimes impacted by electron-phonon scattering alongside anharmonic phonon-phonon interactions. Utilizing density functional theory (DFT) and density functional perturbation theory (DFPT), the paper integrates these interactions via the EPW code with highly dense k- and q-point meshes for enhanced convergency. The phonon lifetime calculations leverage a field-theoretical approach to derive values from the imaginary part of the phonon self-energy, which are then used to compute lattice thermal conductivity using Mattiessen’s rule.

Key Findings

1. Phonon Scattering Dynamics: The study delineates how phonons near the Brillouin zone center are more susceptible to scattering via intravalley processes, with intervalley processes contributing in the conduction band for electrons. In contrast, intervalley processes are absent in valence bands for holes, resulting in differential scattering behaviors between electrons and holes.

2. Comparison with Phonon-Phonon Interactions: While EPI scattering rates are negligible at low carrier concentrations ((<10^{18}\text{ cm}^{-3}\)), they become comparable to phonon-phonon scattering rates at higher concentrations (\(>10^{19} \text{ cm}^{-3})), particularly affecting low-frequency phonons crucial for carrying heat.

3. Lattice Thermal Conductivity: At carrier concentrations exceeding (10^{19}\text{ cm}^{-3}), EPI significantly impairs thermal conductivity of silicon, with a substantial impact observed up to a 45% reduction noted in high carrier concentration regimes. Holes outperform electrons in scattering efficiency due to isotropy in hole pockets compared to anisotropic electron pockets.

Implications and Future Developments

The research reshapes the understanding of thermal transport in semiconductors and offers profound implications for the field of thermoelectrics, particularly concerning heavily-doped semiconductors. The results suggest that EPI contributes to technological strategies aimed at reducing lattice thermal conductivity. This insight could direct future endeavors in optimizing thermoelectric design through material engineering and carrier concentration manipulation.

In conclusion, this paper extends the theoretical framework around EPI effects in semiconductors, providing a critical perspective previously underestimated at technologically relevant carrier densities. Future research could explore the broader application of these findings across different materials and consider experimental methodologies to verify these computational predictions. The development of more sophisticated EPI models could further advance the validation of new thermoelectric materials and enhance energy conversion systems.