Electrical transport limited by electron-phonon coupling from Boltzmann transport equation: An ab initio study of Si, Al, and MoS_2

摘要

We demonstrate the ab initio electrical transport calculation limited by electron-phonon coupling by using the full solution of the Boltzmann transport equation (BTE), which applies equally to metals and semiconductors. Numerical issues are emphasized in this work. We show that the simple linear interpolation of the electron-phonon coupling matrix elements from a relatively coarse grid to an extremely fine grid can ease the calculational burden, which makes the calculation feasible in practice. For the Brillouin zone (BZ) integration of the transition probabilities involving one 8 function, the Gaussian smearing method with a physical choice of locally adaptive broadening parameters is employed. We validate the calculation in the cases of n-type Si and Al. The calculated conductivity and mobility are in good agreement with experiments. In the metal case we also demonstrate that the Gaussian smearing method with locally adaptive broadening parameters works excellently for the BZ integration with double S functions involved in the Eliashberg spectral function and its transport variant. The simpler implementation is the advantage of the Gaussian smearing method over the tetrahedron method. The accuracy of the relaxation time approximation and the approximation made by Allen [Phys. Rev. B 17, 3725 (1978)] has been examined by comparing with the exact solution of BTE. We also apply our method to n-type monolayer MoS_2, for which a mobility of 150 cm~2 v~(-1) s~(-1) is obtained at room temperature. Moreover, the mean free paths are less than 9 nm, indicating that in the presence of grain boundaries the mobilities should not be effectively affected if the grain boundary size is tens of nanometers or larger. The ab initio approach demonstrated in this paper can be directly applied to other materials without the need for any a priori knowledge about the electron-phonon scattering processes, and can be straightforwardly extended to study cases with electron-impurity scattering.