Direct determination of point-defect equilibrium concentrations

Analytical expressions, which allow the direct determination of the equilibrium concentrations of self-interstitials and vacancies from measured impurity diffusion profiles, are deduced from the equations of the kick-out and the Frank-Turnbull diffusion mechanisms. To determine the point-defect equilibrium concentrations, only diffusion profiles of appropriate elements have to be measured. The method is not restricted to semiconductors. As an example, the determination of the vacancy equilibrium concentration in silicon by means of platinum diffusion is presented. A value of approximately 4.4×${10}^{13}$ ${\mathrm{cm}}^{\mathrm{-}3}$ at 770 °C is determined for the equilibrium concentration of vacancies. A further result is the estimate of 2.2×${10}^{\mathrm{-}11}$ ${\mathrm{cm}}^2$ ${\mathrm{s}}^{\mathrm{-}1}$ for the vacancy diffusion coefficient in silicon. The generation rate of vacancies by internal sources appears to be less than 1×${10}^{\mathrm{-}5}$ ${\mathrm{s}}^{\mathrm{-}1}$ at 770°C.