Phase Stability and Electronic Structure of In-Free Photovoltaic Materials: Cu₂ZnSiSe₄, Cu₂ZnGeSe₄, and Cu₂ZnSnSe₄

We have theoretically evaluated phase stability and electronic structure of Cu₂ZnSiSe₄ and Cu₂ZnGeSe₄ and compared the results with those of Cu₂ZnSnSe₄. The enthalpies of formation for kesterite (KS), stannite (ST), and wurtz-stannite (WST) phases of Cu₂ZnSiSe₄, Cu₂ZnGeSe₄, and Cu₂ZnSnSe₄ (CZTSe) were calculated by first-principles calculations. In these three compounds, the KS phase is more stable than the ST and WST phases. The theoretical band gaps of KS-type Cu₂ZnSiSe₄ (1.48 eV) and Cu₂ZnGeSe₄ (1.10 eV) are wider than that of KS-type Cu₂ZnSnSe₄ (0.63 eV). The valence band maximum (VBM) of KS-type Cu₂ZnIVSe₄ consists of antibonding orbital of Cu 3d and Se 4p, while the conduction band minimum (CBM) consist of antibonding orbital of IV ns and Se 4p. The VBMs of Cu 3d + Se 4p in Cu₂ZnSiSe₄ and Cu₂ZnGeSe₄ are similar to that in Cu₂ZnSnSe₄. Therefore, the energy levels of VBMs in Cu₂ZnIVSe₄ (IV = Si, Ge) do not change so much compared with that of CZTSe. On the other hand, the energy levels of CBMs of IV ns + Se 4p in Cu₂ZnSiSe₄ and Cu₂ZnGeSe₄ become higher than that in Cu₂ZnSnSe₄. These trends in the electronic structures are explained by the schematic molecular orbital diagrams of tetrahedral CuSe₄^7-, ZnSe₄^6-, and IVSe₄^4- (IV = Si, Ge, Sn) clusters.