Thermal conductivity of amorphous and crystalline Ge and GeTe films

The thermal conductivity of 2000-9000-\AA{}-thick amorphous and crystalline films of Ge and GeTe has been measured in the temperature range 100-550\ifmmode^\circ\else\textdegree\fi{}K. No thickness dependence has been observed in these films down to 2000 \AA{}. The results show that crystalline Ge and amorphous Ge and GeTe films have a negligible electronic contribution in the measured thermal conductivity. However, as expected, crystalline GeTe films exhibit significant electronic contribution which is \ensuremath{\sim}25% of the measured value of the thermal conductivity. The thermal conductivity of both amorphous Ge and GeTe increases slowly with increasing temperature in contrast to the rapid decrease in the crystalline films. In the latter case, the lattice component of the thermal conductivity decreases approximately inversely with temperature. The observed temperature dependence of the thermal conductivity can be understood on the basis of a combination of (i) umklapp-scattering mechanism, (ii) scattering due to defects, and (iii) scattering by grain boundaries. The last term, which is primarily responsible for the observed thermal resistance in the case of amorphous films, leads to a temperature-independent phonon mean free path. The observed increase of thermal conductivity with temperature for amorphous films is, therefore, attributed to the increase of specific heat with temperature. The values of the phonon mean free path in amorphous films as deduced from the thermal-conductivity data are \ensuremath{\sim}3 \AA{} in amorphous GeTe and \ensuremath{\sim}5 \AA{} in amorphous Ge films. These values suggest a relatively longer short-range order (coherently scattering regions) in amorphous Ge, as compared with amorphous GeTe.