Calculation of the thermal conductivity of nanostructured Bi$_2$Te$_3$ with the real phonon spectrum taken into account

The results of calculations of lattice thermal conductivity in bismuth telluride are presented and its decrease in a nanostructured material due to boundary scattering is estimated. Calculation is carried out using the lattice-dynamics method with the real phonon spectrum and the phonon–phonon interaction taken into account. Its results well agree with experimental data for the crystalline material. The estimates for the nanostructured material give a decrease in the thermal conductivity by 30% for grain sizes of 20 nm. Calculations by this method are compared with those obtained using approximate methods of description of the spectrum and scattering processes. It is shown that the least difference in the estimates (about 10%) can be obtained when using the approximation of a constant matrix element of phonon–phonon scattering with correction of the frequency dependence for acoustic modes.