Significant Reduction of Lattice Thermal Conductivity by the Electron-Phonon Interaction in Silicon with High Carrier Concentrations: A First-Principles Study

The electron-phonon interaction is well known to create major resistance to electron transport in metals and semiconductors, whereas fewer studies are directed to its effect on 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 ${10}^{19}{\mathrm{cm}}^{-3}$ (the reduction reaches up to 45% in $p$-type silicon at around ${10}^{21}{\mathrm{cm}}^{-3}$), a range of great technological relevance to thermoelectric materials.

Figure 1

The scattering rates of phonons in silicon due to the EPI by (a) electrons and (b) holes. The carrier concentration is ${10}^{21}{\mathrm{cm}}^{-3}$. The color denotes the scattering rates, and the white region indicates either there is no phonon mode, or the scattering rates are below the threshold rate of the calculation.

Figure 2

The asymptotic behaviors (lines) of the phonon scattering rates due to the EPI, calculated from the DPA, are compared with data obtained from first principles (dots) for (a) LA modes and (b) LO modes scattered by electrons and (c) LA modes and (d) LO modes scattered by holes. A $60\times 60\times 60$ $q$ mesh is used in this calculation.

Figure 3

The phonon scattering rates due to the EPI with (a) electrons and (b) holes at the carrier concentration of ${10}^{21}{\mathrm{cm}}^{-3}$ and the intrinsic phonon-phonon interaction.

Figure 4

The lattice thermal conductivity versus the carrier concentration, taking into account both the EPI and the phonon-phonon interaction. The calculation is done on a $60\times 60\times 60$ $q$ mesh for both electron-phonon and phonon-phonon calculations.

Figure 5

The phonon mean free paths with and without the EPI: (a) phonons scattered by electron and (b) phonons scattered by holes. The carrier concentration is ${10}^{21}{\mathrm{cm}}^{-3}$ in both cases.