Density Functional Theory Calculations of Atomic Configurations and Bandgaps of C-, Ge-, and Sn-Doped Si Crystals for Solar Cells

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Poly-Si crystals are mainly used in solar cells because of their low cost. Here, the zones of sensitivity to wavelengths in sunlight should be expanded to increase the engineering efficiency of solar cells. Group IV compound semiconductors films, e.g., Si (Ge) films doped with C, Ge (C, Si), and/or Sn atoms with contents of several %, on a Si or Ge substrate have been identified as potential solutions to this technical problem. In this study, we calculated the formation energy of each atomic configuration of C, Ge, and Sn atoms in Si by using density functional theory. The “Hakoniwa” method proposed by Kamiyama et al. [Materials Science in Semiconductor Processing, 43, 209 (2016)] was applied to a 64-atom supercell of Si including up to three atoms of C, Ge, and/or Sn (up to 4.56%) in order to obtain the ratio of each atomic configuration and the average value of the Si bandgaps. Not only the conventional generalized gradient approximation (GGA) but also the screened-exchange local-density approximation (sX-LDA) functional was used to obtain more reliable Si bandgaps. The results of the analysis are fourfold. First, two C (Sn) atoms are energetically stable when they are 3rd, 4th, 6th, 7th, and 9th neighbors of each other, while the stability of two Ge atoms is independent of the atomic configuration. Second, C and Ge (Sn) atoms are stable when they are 2nd, 5th, and 8th (1st and 8th) neighbors, while the stability of Sn and Ge atoms is independent of the atomic configuration. Third, the Si bandgap depends (does not depend) on the atomic configuration when Si includes C and/or Sn atoms (Ge atoms). Uniformly mono-doping C by up to 4.68% and Ge (Sn) by up to 3.12% decreased the average value of the Si bandgaps. C doping decreased the Si bandgap the most, while Ge doping decreased it the least. Fourth, uniformly co-doping C and Sn in a 1:1 ratio (C and Ge 1:1, Ge and Sn 1:1) at 1.56% also decreased the Si bandgap. The results shown here will be useful for predicting the bandgap for a given content of Si crystals, which is important for the solar cell application.