We propose and demonstrate a novel process to fabricate planar avalanche photodiodes using selective area growth (SAG) followed by a single Zn diffusion through the SAG material using the same dielectric mask. The tapered surface profile of the SAG epitaxy due to the enhancement of the growth rate in the vicinity of the mask edge modifies the diffusion profile, resulting in a gradual reduction of the diffusion depth towards the outer edge of the active area. The associated reduction of the electric field counteracts the edge curvature effect sufficiently to suppress edge breakdown. For undoped InP SAG epitaxy, small areas of higher electric field occur where the mask edge is along the [1 0 0] or [0 1 0] directions, associated with the formation of enhanced ridges in the SAG material in these locations. Similar ridges are observed for Si-doped InP and InP/InGaAs/InP SAG structures, but the enhancement of the electric field in these locations is significantly lower.