A rigorous model is developed for determining single-photon quantum efficiency (SPQE) of single-photon avalanche photodiodes (SPADs) with simple or heterojunction multiplication regions. The analysis assumes nanosecond gated-mode operation of the SPADs and that band-to-band tunneling of carriers is the dominant source of dark current in the multiplication region. The model is then utilized to optimize the SPQE as a function of the applied voltage, for a given operating temperature and multiplication-region structure and material. The model can be applied to SPADs with In0.52Al0.48As or InP multiplication regions as well as In0.52Al0.48As--InP heterojunction multiplication regions for wavelengths of 1.3 and 1.55 μm. The predictions show that the SPQE generally decreases with decreasing the multiplication-region thickness. Moreover, an InP multiplication region requires a lower breakdown electric field (and, hence, offers a higher SPQE) than that required by an In0.52Al0.48As layer of the same width. The model also shows that the fractional width of the In0.52Al0.48As layer in an In0.52Al0.48As--InP heterojunction multiplication region can be optimized to attain a maximum SPQE that is greater than that offered by an InP multiplication region. This effect becomes more pronounced in thin multiplication regions as a result of the increased significance of dead space.