Catalyst-free, direct heteroepitaxial growth of vertical InAs nanowires on Si(111) substrates was accomplished over a large area by metal-organic chemical vapor deposition. Nanowires showed very uniform diameters and a zinc blende crystal structure. The heterojunctions formed at the interface between the n-type InAs nanowires and the p-type Si substrate were exploited to fabricate vertical array photodiode devices which showed an excellent rectification ratio and low reverse leakage current. Temperature-dependent current transport across the heterojunctions was studied theoretically and experimentally in the dark and under AM 1.5 illumination. When operated in photovoltaic mode, the open-circuit voltage was found to increase linearly with decreasing temperature while the energy conversion efficiency changed nonmonotonically with a maximum of 2.5% at 110 K. Modeling of the nanowire/substrate heterojunctions showed good agreement with the experimental observations, and allowed determining the conduction band offset between the InAs nanowires and Si to be 0.10-0.15 eV. The external quantum efficiency and photoresponsivity profiles of the device showed a broad spectral response from the visible to the infrared region, indicating potential applications as a broad band photovoltaic cell or a visible-infrared dual-band photodetector.