Determining the maximum open circuit voltage from absorber photoluminescence in the presence of tail states

We develop a general model for sub-bandgap absorption that includes the Urbach, Franz-Keldysh, and Thomas-Fermi models as limiting forms. Combination of this absorption scheme with a generalized Kirchhoff law for spontaneous emission of photons yields a model of photoluminescence (PL) with broad applicability to many semiconductors. This model allows for full-spectrum fitting of absolute intensity PL data and outputs: (1) the functional form of sub-bandgap absorption, (2) the energy broadening term (3) the direct bandgap, (4) the local temperature, and (5) the quasi-Fermi Level Splitting (QFLS). The accuracy of the model is demonstrated by fitting the room temperature PL spectrum of GaAs. It is then applied to Cu(In,Ga)(S,Se)2 and Cu2ZnSn(S,Se)4 to reveal the nature of their tail states. The extracted QFLS is shown to accurately predict the open-circuit voltage of devices fabricated from the materials.