Linear-accelerator-based applications like x-ray free electron lasers, ultrafast electron diffraction, electron beam cooling, and energy recovery linacs use photoemission-based cathodes in photoinjectors for electron sources. Most of these photocathodes are typically grown as polycrystalline materials with disordered surfaces. In order to understand the mechanism of photoemission from such cathodes and completely exploit their photoemissive properties, it is important to develop a photoemission formalism that properly describes the subtleties of these cathodes. The Dowell-Schmerge (D-S) model often used to describe the properties of such cathodes gives the correct trends for photoemission properties like the quantum efficiency (QE) and the mean transverse energy (MTE) for metals; however, it is based on several unphysical assumptions. In the present work, we use Spicer's three-step photoemission formalism to develop a photoemission model that results in the same trends for QE and MTE as the D-S model without the need for any unphysical assumptions and is applicable to defective thin-film semiconductor cathodes along with metal cathodes. As an example, we apply our model to Cs3Sb thin films and show that their near-threshold QE and MTE performance is largely explained by the exponentially decaying defect density of states near the valence band maximum. © 2023 Author(s).