Thermal Conductivity of Electron-Irradiated Silicon

Changes in the low-temperature thermal conductivity of single-crystal Si were investigated upon 2-MeV electron irradiation and annealing. The additive thermal resistivity of high-purity $p$-type Si irradiated below 60°K to maximum time-integrated fluxes $\Phi$ of 8.0×${10}^{18}$ 2-MeV e/${\mathrm{cm}}^2$ increases as $\frac{1}{K}-\frac{1}{K_0}=3.75\mathrm{}\times {10}^{-13\mathrm{}}$ ${\Phi }^{0.61}$ cm-deg/W at 47°K. The ${\Phi }^{0.61}$ dependence of the additive thermal resistivity of Si on bombardment is very similar to the ${\Phi }^{0.58}$ dependence previously observed for Ge. The magnitude of the increase is, however, much smaller than previously observed for either Ge, InSb, or GaAs. The linear concentration dependence of GaAs has been related to mass-difference strain-field scattering, whereas the nonlinear concentration dependencies of InSb, Ge, and Si suggest phonon-electron scattering. For the high-purity Si, annealing begins near 80°K, and exhibits a single dominant annealing stage near 140°K corresponding to the annealing temperature of vacancies in $p$-type Si. Measurements of the temperature dependence of the thermal conductivity indicate that the defects anneal primarily as point defects, although evidence exists for a small amount of precipitation of point defects in the annealing-temperature interval between 80 and 135°K. Sharp minima observed in the temperature dependence of the thermal conductivity of Si are similar to those previously observed in Ge and attributed to resonant scattering.