Density functional theory study of stable configurations of substitutional and interstitial C and Sn atoms in Si and Ge crystals

Group IV semiconductor compounds, e.g., Si and Ge containing substitutional C (Cs) and/or Sn (Sns) atoms (mono-doping and co-doping) with contents of several % are attracting attention for application to solar cells because they are good for the environment and have an affinity with Si materials. In this study, we evaluate the stable configurations of C and/or Sn atoms in Si (Ge) crystals with a focus on the formation of interstitial C (Ci) atoms by means of density functional theory calculations. The Hakoniwa method proposed by Kamiyama et al. (2016) is applied to a 64-atom supercell to obtain the thermal equilibrium ratio of Ci to the total C atoms. The results of the analysis are fourfold. First, the isolated Cs atom is stabler than the isolated Ci atom in both Si and Ge crystals, and it is stabler in Si than in Ge. The isolated Sns atom is much stabler that Sni as well, but it is stabler in Ge than Si. Second, a Ci atom is formed in a [0 0 1] oriented Ci-Cs pair in Ge crystals with the ratio of 7.7% to total C atoms at 450 °C when the concentration of uniformly distributed C atoms is about 3%. Third, the difference of the formation energy of Ci and Cs in Si decreases to about 0.3 eV with an increase in the concentration of uniformly distributed C atoms up to 6%. Fourth, the co-doping of C and Sn suppresses the formation of Ci atoms in Si and Ge crystals. The results obtained here are useful for the prediction of possible atomic configurations of C and/or Sn in Si and Ge for solar cell application.