Co-design of III-nitride quantum dots and nanophotonic cavities for indistinguishable on-chip single-photon sources

Room-temperature solid-state III-nitride quantum dots (QDs) are an emerging platform for UV-visible quantum light sources. Despite the potential, a unified theoretical framework linking QD microscopic dynamics with nanophotonic structures remains unexplored. In this study, we develop a comprehensive computational study that bridges quantum mechanical modeling of III-nitride QDs with nanophotonic inverse design for optimized single-photon sources. By modeling the III-nitride QD dynamics as a biexciton-exciton cascade in a four-level system coupled to a cavity, we evaluate the impact of QD-cavity coupling, cavity detuning on QD dynamics, and analyze how dissipation and decoherence channels degrade photon indistinguishability. We demonstrate that by tuning the cavity resonance to the biexciton-exciton transition and engineering the Purcell factor, high indistinguishability (>99%) can be achieved in the weak coupling regime. However, entanglement concurrence is strongly limited by fine-structure splitting and cannot be recovered through Purcell enhancement alone. Guided by these insights, we use computationally efficient adjoint-based inverse design to numerically develop a suspended GaN nanobeam cavity waveguide that meets target parameters while enabling efficient photon extraction. This study reveals a fundamental trade-off between indistinguishability and photon extraction efficiency, and shows that a Purcell factor of ∼100 - with two-sided extraction efficiency of up to 66% - can be achieved with a 12-hole integrated photonic waveguide. These results provide guidelines for the co-design of integrated III-nitride quantum light sources for on-chip photonic circuits.