An organic phototransistor (OPT) with a photomultiplication mechanism is studied, where a bulk-heterojunction of C-70 and 1,1-bis-(4-bis(4-methyl-phenyl)-amino-phenyl)-cyclohexane is used as a channel and a light-absorbing layer with an Al Schottky contact as source/drain electrodes. The light absorption in the source-side region is found to dominate the photomultiplication effect. In addition, the source electrode area that is up to 100 mu m away from the channel is identified as the most effective region in the OPTs with contact-limited operation used in this study. Therefore, to maximize the light-sensing performance of the contact-limited OPTs, we propose Corbino source/drain geometries that have a larger source electrode area than that of the drain electrode. The Corbino-type OPTs show improved photo-response properties proportional to the relative increment of the source-side area, reaching 1.7-fold higher performance in terms of photosensitivity compared to the conventional lateral-type OPTs.