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

• Published in: Japanese Journal of Applied Physics 2022-07, Vol.61 (7), p.75504
• Main Authors: Suezawa, Masashi, Iijima, Yoshiaki, Yonenaga, Ichiro
• Format: Article
• Language: English
• Subjects: Coefficients; Crystal defects; formation; Free energy; Heat of formation; interstitial; Interstitials; Lattice vacancies; migration; Point defects; Self diffusion; Silicon; thermal equilibrium concentration; Vacancies; vacancy
• ISSN: 0021-4922; 1347-4065
• DOI: 10.35848/1347-4065/ac66af

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 × 10 22 exp(6.5)exp(–3.85 eV/ k B T ) and 5 × 10 22 exp(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 −3 exp(–0.45 eV/ k B T ) and 2.5 × 10 −2 exp(–0.49 eV/ k B T ) cm 2 s −1 , respectively. The results are discussed in comparison with those reported experimentally.