Intermediate band (IB) photovoltaics have the potential to be highly efficient and cost effective solar cells. When the IB concept was proposed in 1997, there were no known intermediate band materials. In recent years, great progress has been made in developing materials with intermediate bands, though power conversion efficiencies have remained low. To understand the material requirements to increase IB device efficiencies, we must develop good models for their behavior under bias and illumination. To evaluate potential IB materials, we present a figure of merit, consisting of parameters that can be measured without solar cell fabrication. We present a new model for IB devices, including the behavior of their junctions with n- and p-type semiconductors. Using a depletion approximation, we present analytic approximations for the boundary conditions of the minority carrier diffusion equations. We compare the analytic results to Synopsys Sentaurus device models. We use this model to find the optimal thickness of the IB region based on material parameters. For sufficiently poor IB materials, the optimal thickness is zero – i.e., the device is more efficient without the IB material at all. We show the minimum value of the figure of merit required for an IB to improve the efficiency of a device, providing a clear goal for the quality of future IB materials.