Paper detail

Thermal conductivity of intrinsic semiconductor at elevated temperature: role of four-phonon scattering and electronic heat conduction

While using first-principles-based Boltzmann transport equation approach to predict the thermal conductivity of crystalline semiconductor materials has been a routine, the validity of the approach is seldom tested for high-temperature conditions. Most previous studies only focused on the phononic contribution, and neglected the electronic part. Meanwhile, the treatment on phonon transport is not rigorous as a few ingredients, such as four-phonon scatterings, phonon renormalization and thermal expansion, are ignored. In this paper, we present a Boltzmann transport equation study on high-temperature thermal conduction in bulk silicon by considering the effects of both phonons and electrons, and explore the role of the missing parts in the previous studies on the thermal conductivity at elevated temperature. For the phonon transport, four-phonon scattering is found to considerably reduce the thermal conductivity when the temperature is larger than 700 K, while the effects of phonon renormalization and thermal expansion on phononic thermal conductivity are negligible. Bipolar contribution to the electronic thermal conductivity calculated from first-principles is implemented for the first time. More than 25% of heat is shown to be conducted by electrons at 1500 K. The computed total thermal conductivity of silicon faithfully reproduces the measured data. The approach presented in this paper is expected to be applied to other high-temperature functional materials, and the results could serve as benchmarks and help to explain the high-temperature phonon and electron transport phenomena.