Thermal Conductivity of Electron-Irradiated Germanium

Measurements of the change in low-temperature thermal conductivity of high-purity single-crystal Ge were made upon 2-MeV electron irradiation and annealing. Strong scattering of phonons by small concentrations of radiation-induced defects is observed. The additive thermal resistivity increases as the 0.58 power of the time integrated flux $\Phi$ rather than the first power observed for GaAs. Irradiation to 3.4×${10}^{18}$ 2-MeV $\frac{e}{{\mathrm{cm}}^2}$ below 50°K gave $\frac{1}{K}-\frac{1}{K_0}=1.7\mathrm{}\times {10}^{-11\mathrm{}}{\Phi }^{0.58}$ cm-deg/W at 20°K. For $\Phi$ between ${10}^{16}$ and ${10}^{19}$ 2-MeV $\frac{e}{{\mathrm{cm}}^2}$, the magnitude of the increase in thermal resistivity of Ge is comparable to that observed for GaAs even though the lattice strain is much smaller. Strain and mass-difference scattering theories cannot explain the Ge data as they can the GaAs data. The Keyes or Pyle phonon-electron scattering theories, however, can explain the Ge results. A small amount of annealing of the additive thermal resistivity was observed to begin at 35°K in the high-purity Ge studied here. This is in agreement with the first annealing stage seen by electrical measurements in degenerate $n$-type Ge by MacKay and Klontz and in degenerate $p$-type Ge by Gobeli. Large recovery states are seen at 125 and 200°K. In the annealing-temperature interval between 140 and 200°K, the thermal conductivity is strongly dependent on electron trapping and can be significantly decreased by a short illumination which changes the charge states of the defects. This demonstrates the phonon-electron scattering nature of the thermal resistivity. Measurements of the temperature dependence of the thermal conductivity indicate that the defects anneal as point defects. The large precipitation of point defects seen in GaAs is not seen in Ge, and almost complete recovery of the radiation-induced defects occurs by 405°K. Minima are observed in the temperature dependence of the thermal conductivity, suggesting localized mode scattering.