Frequency dependence of the thermal conductivity of semiconductor alloys

The distribution of phonons that carry heat in crystals has typically been studied through measurements of the thermal conductivity Λ as a function of temperature or sample size. We find that Λ of semiconductor alloys also depends on the frequency of the oscillating temperature field used in the measurement and hence demonstrate a novel and experimentally convenient probe of the phonon distribution. We report the frequency dependent Λ of In0.49 Ga0.51 P, In0.53 Ga0.47 As, and Si0.4 Ge0.6 as measured by time-domain thermoreflectance over a wide range of modulation frequencies 0.1<f<10 MHz and temperatures 88<T<300 K. The reduction in Λ at high frequencies is consistent with a model calculation that assumes that phonons with mean free paths larger than the thermal penetration depth do not contribute to the thermal conductivity measured in the experiments.