Thermal Conductivity of Ge-Si Alloys at High-Temperatures

Abstract

The phonon contribution as well as the electronic dipolar contribution towards the thermal resistance of Si-Ge alloys containing 5 and 30% of silicon have been calculated in the temperature range 300 to 1200°K. The contributions of longitudinal phonons and transverse phonons are computed separately. Since much of the heat is carried by low-frequency phonons, the influence of this modification of phonon spectra is not very substantial. The phonon contribution as calculated theoretically is in good agreement with the experimental results up to about 800°K. The electronic contribution to the thermal resistance which becomes important at and above 800°K decreases with increase in temperature while the phonon contribution increases with increase in temperature. This explains the presence of a peak in the thermal-resistivity-versus-temperature plot, which is more pronounced in the alloy containing 30% silicon. Good agreement between theory and experiment is obtained in the temperature range 800 to 1200°K when the theoretical values of the sum of the electronic dipolar and lattice thermal conductivities are compared with the experimental values of the thermal conductivity minus the electronic polar thermal conductivity. The present analysis also reveals the nonuniform distribution of Si in the alloy.