Frequency dependence of the thermal conductivity of semiconductor alloys

Abstract

The distribution of phonons that carry heat in crystals has typically been studied through measurements of the thermal conductivity $\ensuremath{\Lambda}$ as a function of temperature or sample size. We find that $\ensuremath{\Lambda}$ 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 $\ensuremath{\Lambda}$ of ${\mathrm{In}}_{0.49}{\mathrm{Ga}}_{0.51}\mathrm{P}$, ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$, and ${\mathrm{Si}}_{0.4}{\mathrm{Ge}}_{0.6}$ as measured by time-domain thermoreflectance over a wide range of modulation frequencies $0.1<f<10\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and temperatures $88<T<300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The reduction in $\ensuremath{\Lambda}$ 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.