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We investigate the band bending that occurs at the interface between a disordered organic semiconductor and a metal electrode. Ultraviolet photoemission spectroscopy measurements of thin organic layers on conducting substrates have revealed band bending within a few nanometers of the interface. It has been proposed that this is caused by the transfer of carriers from the substrate into empty states in the organic film. Here we numerically model this process by simulating a film with a given density of states in thermal equilibrium with a metallic substrate. Comparing the model with various published experiments, we demonstrate that the observed band bending can be explained equally well by either energetic relaxation of charge carriers on a timescale longer than photoemission (polaronic relaxation) or by a Gaussian density of states representing energetic disorder. In the former case, our results suggest that the thermal injection of carriers to higher-energy states has led observers to overestimate the relaxation energy by as much as several hundred meV. We also show that band-bending effects due to disorder are expected to significantly reduce the open-circuit voltage in organic photovoltaic devices, and we quantify the relationship between the amount of voltage loss and the degree of disorder. [ABSTRACT FROM AUTHOR]