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Effects of quantum corrections and isotope scattering on silicon thermal properties

A quantum correction procedure is proposed to correct silicon thermal properties estimated with molecular dynamics (MD). The procedure considers the energy quantization per mode basis and the anharmonic nature of the potential energy function (including the thermal expansion of the crystal) and is applied to reported thermal properties of silicon estimated with MD in ref. [11], such as temperature, specific heat and thermal conductivity. The procedure facilitates the use of these properties as input to faster numerical methods, such as those based on the Boltzmann transport equation under the single relaxation time approximation. In addition, the effect of isotope scattering is included in reported values of phonon-phonon relaxation times. The effects of the correction procedure and the scattering with isotopes are analyzed in terms of the change of phonon specific heat, mean free path and thermal conductivity. We have found that the application of quantum corrections yields a significant reduction in the contribution of high-frequency modes to the overall thermal conductivity. This contribution is further reduced by the inclusion of isotope scattering. At 220 K, the total contribution of optical modes reduces from 12.3 % (before quantum corrections) to 5.8 %; and to 2 % when the isotope scattering is also considered. The quantum corrections and the inclusion of isotope scattering are found to bring the estimated thermal conductivity into close agreement with experimental values. The relative contributions of the acoustic and optical modes after quantum corrections agrees very well with recently reported ab initio results.