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 Lambda as a function of temperature or sample size. We find that Lambda 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 Lambda of In0.49Ga0.51P, In0.53Ga0.47As, and Si0.4Ge0.6 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 Lambda 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.