Avalanche photodiodes are provided, wherein the APDs provide both high optical coupling efficiency and low dark count rate. The APDs are formed such that their cap layer has an active region of sufficient width to enable high optical coupling efficiency but the APD still exhibits a low dark count rate. These cap layers have a device area with an active region and an edge region, wherein the size of the active region is substantially matched to the mode-field diameter of an optical beam, and wherein the size of the edge region is made small so as to reduce the number of defects included. These APD designs maintain a substantially uniform gain and breakdown voltage, as necessary for practical use.