Concentrations and diffusion coefficients of thermal equilibrium point defects in silicon crystals

Abstract

The dependencies of concentrations of thermal equilibrium vacancies and interstitials on temperatures in Si crystals are determined directly, which has been a long-standing issue since the 1950s. They are evaluated by combining the formation energies and self-diffusion entropies deduced from the analyses of self-diffusion coefficients, and migration entropies deduced from diffusion coefficients of point defects. The concentrations as the number density of thermal equilibrium vacancies and interstitials at temperature T (K) are determined to be 5 × 1022exp(6.5)exp(–3.85 eV/k B T) and 5 × 1022exp(10.6)exp(–4.3 eV/k B T) cm−3, respectively. The diffusion coefficients of vacancies and interstitials are determined to be 2.7 × 10−3exp(–0.45 eV/k B T) and 2.5 × 10−2 exp(–0.49 eV/k B T) cm2 s−1, respectively. The results are discussed in comparison with those reported experimentally.