Germanium-on-silicon (Ge-on-Si) single photon avalanche diodes (SPADs) operating in the short-wave infrared (SWIR) have various applications such as long-range eye-safe LIDAR, quantum imaging, and quantum key distribution. These SPADs offer compatibility with Si foundries and potential cost advantages over existing InGaAs/InP devices. However, cooling is necessary to reduce dark-count rates (DCR), which limits photon absorption at 1550 nm wavelength. To address this, we propose integrating a photonic crystal (PC) nano-hole array structure on the Ge absorber layer. While this technique has shown enhanced responsivity in linear Ge detectors, its potential in Ge-on-Si SPADs remains unexplored. Our simulations consider temperature dependence and the impact of electric-field hot-spots on dark count rates. Through these simulations, we have identified means of enhancing single-photon detection efficiency (SPDE) without adversely affecting DCR. We predict significant improvements in performance, including at least a 2.5x enhancement in absorption efficiency.