Thermal Conductivity of Gallium Arsenide at Low Temperatures

The thermal conductivities of gallium arsenide single crystals doped with tellurium and chromium have been measured from 2 to 90°K. The tellurium-doped crystal shows normal behavior in agreement with the findings of other workers. At low temperatures, the thermal conductivity of this crystal follows a $T^3$ behavior indicative of boundary scattering limiting the phonon mean free path. The phonon mean free path in this temperature region, calculated from experimental results, agrees fairly well with that obtained from Casimir's formula. The thermal conductivity of the chromium-doped sample also shows a $T^3$ behavior at the lowest temperatures. However, the phonon mean free path observed experimentally is more than an order of magnitude less than that given by Casimir's formula. The chromium-doped sample shows, in addition, evidence of an anomalous, possibly a resonant, phonon scattering in the region of temperatures 4-10°K with a peak at 6.5°K. Possible reasons for this are discussed.