Low-Temperature Length Change Measurements of Electron-Irradiated Germanium and Silicon

Precision measurements of the change in length of high-purity germanium and silicon were made upon 2-Mev electron irradiation and annealing. Two germanium samples were irradiated at maximum temperatures of 365°K and 86°K, respectively. The first sample was irradiated at 33 μa/${\mathrm{cm}}^2$ to an integrated flux of 5.4×${10}^{19}$ electrons/${\mathrm{cm}}^2$. The specific length expansion obtained was $\frac{\Delta L}{L}=(6\mathrm{}\pm 12)\times {10}^{-26\mathrm{}}$ per 2-Mev electrons/${\mathrm{cm}}^2$. The 86°K sample was irradiated at 10 μa/${\mathrm{cm}}^2$ to an integrated flux of 3.0×${10}^{19}$ electrons/${\mathrm{cm}}^2$. The specific length expansion was (1.5±3.9)×${10}^{-25\mathrm{}}$ per 2-Mev electrons/${\mathrm{cm}}^2$. Using the Seitz-Koehler simple theory of displacement ($E_d=30\mathrm{}$ ev) and assuming no annealing at the low temperature, we calculate a concentration of displaced pairs equal to 1.6×${10}^{-3\mathrm{}}$ with a corresponding fractional atomic volume change per interstitial-vacancy of ${(f_i+f_v)}_{\mathrm{Ge}}=0.008\mathrm{}\pm 0.021$. The silicon sample was initially irradiated at ∼50°K to an integrated flux of 8.3×${10}^{18}$ electrons/${\mathrm{cm}}^2$ and further irradiated at ∼115°K to a total integrated flux of 7.9×${10}^{19}$ electrons/${\mathrm{cm}}^2$ and then annealed to room temperature. The specific length change for both bombardments was $\frac{\Delta L}{L}=(4\mathrm{}\pm 19)\times {10}^{-26\mathrm{}}$ per 2-Mev electrons/${\mathrm{cm}}^2$. The simple theory ($E_d=28\mathrm{}$ ev) predicts a concentration of displaced pairs of 4×${10}^{-3\mathrm{}}$ with a corresponding volume change per interstitial-vacancy of ${(f_i+f_v)}_{\mathrm{Si}}=0.002\mathrm{}\pm 0.011$. These values are much smaller than would be expected from previous results for deuteron and neutron irradiations of germanium. Calculations of defect cluster size distributions for electron, deuteron, and neutron irradiations of germanium are given and combined with the experimental results to indicate that the volume change per defect is nonlinear and increases as the cluster size increases. The samples were not observed to expand within the presumed error. All measurements did, however, yield a small positive value. The values for Ge and Si are very small compared with the large expansions recently observed for electron-irradiated InSb and GaAs.