Acoustical-Optical Phonon Scattering in Ge, Si, and III-V Compounds

The thermal conductivities of AlSb apd GaSb have been measured between 300 and 950°K, and of GaP between 300 and 550°K, on $n$-type samples of about ${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$ using the diffusivity technique. The room temperature thermal conductivities are 0.56 W/cm deg for AlSb, 0.33 W/cm deg for GaSb, and 0.76 W/cm deg for GaP. The electrical resistivities for AlSb and GaSb and the Seebeck coefficient for GaSb were determined as well. The lattice thermal conductivity is the dominating part in all those compounds. Its temperature dependence was found to be stronger than $T^{-1\mathrm{}}$, suggesting 4-phonon processes to be involved. To investigate the acoustical-optical phonon scattering, the experimental results on group IV elements and on III-V compounds have been correlated. The Grüneisen parameters $\gamma$ of these materials, calculated in different ways from experimental data, have been compiled. A mean value of $\gamma =0.65\mathrm{}$ is obtained. The theory of Leibfried and Schlömann, describing acoustical-acoustical 3-phonon scattering, is in good agreement with the experiment for high-phonon-energy-gap materials (e.g., AlSb). The gradual disagreement with decreasing gap is interpreted as due to acoustical-optical phonon scattering, probably of the type acoustical+acoustical=optical. This additional scattering seems to be quite substantial in low- or zero-phonon-energy-gap materials (e.g., Ge, Si, InSb, and GaAs).