A numerical study of the current, field, and carrier density distributions within a photoconductive detector is presented. The photodetector, an interdigitated Schottky barrier diode, is made with metallic fingers of alternating voltage bias on a thin semiconductor layer grown on a transparent dielectric substrate. The Poisson and continuity equations for electrons and holes are treated in two dimensions. A modified successive line overrelaxation method, faster than the capacitance matrix method, is developed as the Poisson solver. A simple alternative to the Scharfetter-Gummel treatment of current density is also introduced. We investigate steady-state cases with and without optical illumination, and transient responses to picosecond optical pulses. The steady-state current Shows near saturation with increasing voltage, as observed experimentally. The calculated typical response of a silicon detector to a picosecond optical pulse is a current pulse lasting on the order of 10 ps.