The solution of the kinetic equation for phonon heat conductivity by the method of momenta and the influence of isotopic disorder on phonon heat conductivity of germanium and silicon crystals at T=300 K

The problem of solving the kinetic equation for the heat conductivities of dielectric substances and semiconductors by the method of momenta is discussed. Microscopic models are used to estimate the effect of isotopic disorder on the thermal resistance of germanium crystals in the multimomentum approximation. The contributions of acoustic and optical phonons are taken into account. Excess thermal resistance ΔW of samples with a natural isotopic composition compared with highly enriched samples is calculated. For germanium, the theoretical and experimental Δ W values are in close agreement with each other. For silicon, the theoretical ΔWvalue is much smaller than its experimental excess thermal resistance.