Self-interstitials generated on silicon bulk surface

The self-interstitial atoms in silicon generated by the bulk surface oxidation diffuse into the bulk inside and affect the phenomena such as the diffusions and the stacking faults. The generation rate of self-interstitials (Rgen) depends on the ω power of the oxidation film growth rate dX0/dt. The physical quantity ω is important to understand the material science relevant to self-interstitials in the silicon crystal. However, the conclusive ω value is not reported, although various ω values to control the generation rate have been used. In the present study, the chemical reaction equation is analytically solved, and using the result, the oxidation stacking fault radius (r) is analytically expressed against the oxidation time (t). Comparing the obtained relation of r=r(t) with the experimental results of the stacking faults, the analytical expression of ω is determined and the physical meaning of ω is clarified. Furthermore, the temperature dependence of ω is also numerically determined.