Diffusion of Helium in Silicon, Germanium, and Diamond

Abstract

The diffusion coefficients D of helium in silicon, germanium, and diamond were determined from the rate of evolution of helium upon heating boron‐doped crystals after slow neutron irradiation: $$\mathrm{He\; in\; C}{\mathrm{:\hspace{0.17em}\hspace{0.17em}D}}_{\mathrm{He}}^{\mathrm{C}}{\text{=7.0×10}}^{\text{−4}}\exp \text{\hspace{0.17em}(−23.4±4.9\hspace{0.17em}}\mathrm{kcal}{\text{/RT),\hspace{0.17em}\hspace{0.17em}1510}}^{\circ }{\text{<T<2470}}^{\circ }\mathrm{K};$$ $$\mathrm{He\; in\; Si}{\mathrm{:\hspace{0.17em}\hspace{0.17em}D}}_{\mathrm{He}}^{\mathrm{Si}}{\text{=5.1×10}}^{\text{−4}}\exp \text{(−13.4±1.8\hspace{0.17em}}\mathrm{kcal}{\text{/RT),\hspace{0.17em}\hspace{0.17em}740}}^{\circ }{\text{<T<1250}}^{\circ }\mathrm{K};$$ $$\mathrm{He\; in\; Ge}{\mathrm{:\hspace{0.17em}\hspace{0.17em}D}}_{\mathrm{He}}^{\mathrm{Ge}}{\text{=1.8×10}}^{\text{−3}}\exp \text{(−14.0±1.8\hspace{0.17em}}\mathrm{kcal}{\text{/RT),\hspace{0.17em}\hspace{0.17em}800}}^{\circ }{\text{<T<1130}}^{\circ }\mathrm{K}.$$ The 90% confidence level for the activation energies is indicated. Experiments in which helium was introduced into silicon by ion bombardment from a discharge plasma gave values of D concordant with the above. The activation energies were calculated theoretically from the differences in interaction energies of the helium in the interstitial site and at the saddle point between two such sites. An exp‐6 potential was used with parameters estimated from inert‐gas interactions. The theoretical E values were C: 24.8, Si: 6.7, and Ge: 6.4 kcal. The pre‐exponential factors D₀ as calculated from the vibration frequencies of the interstitial helium were about 10 times higher than the observed.