First Principles Theory of the Lattice Thermal Conductivity of Semiconductors

Abstract

Using density functional perturbation theory and a full solution of the linearized phonon Boltzmann transport equation (BTE), a parameter-free theory of semiconductor thermal properties is developed. The approximations and shortcomings of previous approaches to thermal conductivity calculations are investigated. The use of empirical interatomic potentials in the BTE approach is shown to give poor agreement with measured values of thermal conductivity. By using the adiabatic bond charge model, the importance of accurate descriptions of phonon dispersions is highlighted. The extremely limited capacity of previous theoretical techniques in the realm of thermal conductivity prediction is highlighted; this is due to a dependence on adjustable parameters. Density functional perturbation theory is coupled with an iterative solution to the full Boltzmann transport equation creating a theoretical construct where thermal conductivity prediction becomes possible. Validation of the approach is demonstrated through the calculation of a range of thermal properties for a set of polar and non-polar semiconductors which are compared with measured values. The agreement between theory and measurement is very good, confirming the promise of the theoretical approach. Due to the significant computational effort required by the parameter-free calculations, new forms for room temperature relaxation time approximations are derived. The resulting forms produce thermal conductivity values in very good agreement with the ab initio data across a wide temperature range. It is therefore shown that accurate relaxation time approximations can be developed, fixing the adjustable parameters to the ab initio theory avoiding any comparison with measured data. This approach improves the accuracy of phonon relaxation times compared with previous models.