Edge-breakdown free InP-InGaAs avalanche photodiodes (APDs) for 10-Gb/s operation were fabricated. Two-dimensional current profiles were measured to investigate the edge breakdown on double-stepped planar APDs. The edge breakdown prominent at high gain increased with the absorption layer thickness for a fixed multiplication thickness (0.25 mum). The edge breakdown was suppressed for 0.4-mum absorption layer at the gain of ten. A simple physical model was proposed to predict the results successfully. To suppress the edge breakdown, the multiplication layer thickness should be selected so that the breakdown voltage is minimum at the selected thickness.