Structures for a single-photon avalanche diode and methods of forming a structure for a single-photon avalanche diode. The structure includes a semiconductor substrate having a top surface, a semiconductor layer on the top surface of the semiconductor substrate, a light-absorbing layer on a portion of the semiconductor layer, and a doped region in the portion of the semiconductor layer. The doped region is positioned in the portion of the semiconductor layer adjacent to the light-absorbing layer.