Various dark matter search experiments employ phonon-based crystal detectors operated at cryogenic temperatures. Some of these detectors, including certain silicon detectors used by the SuperCDMS Collaboration, are able to achieve single-charge sensitivity when a voltage bias is applied across the detector. The total amount of phonon energy measured by such a detector is proportional to the number of electron-hole pairs created by the interaction. However, crystal impurities and surface effects can cause propagating charges to either become trapped inside the crystal or create additional unpaired charges, producing non-quantized measured energy as a result. A new analytical model for describing these detector response effects in phonon-based crystal detectors is presented. This model improves upon previous versions by demonstrating how the detector response, and thus the measured energy spectrum, is expected to differ depending on the source of events. We use this model to extract detector response parameters for SuperCDMS HVeV detectors, and illustrate how this robust modelling can help statistically discriminate between sources of events in order to improve the sensitivity of dark matter search experiments.