Hydrodynamical thermotransport relaxation times of semiconductor electrons via acoustic phonons

TL;DR

This paper develops a hydrodynamic model to analyze thermotransport properties of semiconductor electrons, deriving relaxation times from electron-acoustic phonon interactions and confirming Onsager symmetry in different regimes.

Contribution

It introduces a hydrodynamic framework based on the Boltzmann equation for semiconductor electrons, calculating relaxation times from microscopic scattering processes.

Findings

Relaxation times are derived considering electron-acoustic phonon interactions.

Onsager symmetry relations are validated in degenerate and non-degenerate limits.

The model provides insights into thermotransport phenomena in semiconductors.

Abstract

We propose a hydrodynamic model to study the thermotransport properties of semiconductor electrons. From the semiclassical Boltzmann equation a set of balance equations is built for the relevant fields. The electron density, the electron energy density, the electric current density and the heat flux density are considered as the basic fields of direct transport and cross effect fluxes. The kinetic relaxation times of the production terms are calculated by considering the electron-acoustic phonon interaction as the leading microscopic scattering process. To justify the long time thermalization regime, the Onsager symmetry relations are proved, both on the completely degenerate and non degenerate limits.