We have recently demonstrated that GaAs nanosheets can be grown by metal-organic chemical vapor deposition （MOCVD）. Here, we investigate these nanosheets by secondary electron scanning electron microscopy （SE-SEM） and electron beam induced current （EBIC） imaging. An abrupt boundary is observed between an initial growth region and an overgrowth region in the nanosheets. The SE-SEM contrast between these two regions is attributed to the inversion of doping at the boundary. EBIC mapping reveals a p-n junction formed along the boundary between these two regions. Rectifying I-V behavior is observed across the boundary further indicating the formation of a p-n junction. The electron concentration （ND） of the initial growth region is around 1 × 10^18 cm^-3, as determined by both Hall effect measurements and low temperature photoluminescence （PL） spectroscopy. Based on the EBIC data, the minority carrier diffusion length of the nanosheets is 177 nm, which is substantially longer than the corresponding length in unpassivated GaAs nanowires measured previously.