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.