Resonant tunneling diodes (RTDs) integrated with molecular materials have demonstrated significant potential as efficient and rapid organic photodetectors (OPDs). Understanding the charge transport mechanisms in RTD-based OPDs is crucial for optimizing device performance. This paper presents a comprehensive analysis of the charge transport mechanisms in RTD-based OPDs of which the operation is based on an intuitive 4-site model. We investigate the photocurrent (Iph), quantum efficiency (QE), and responsivity of OPDs using two acceptor molecules (C60 and B80 fullerenes) and one armchair graphene nanoribbon (AGNR) as the donor molecule. Additionally, we explore key factors that influence charge transport, including molecular structure, energy levels, and device architecture. Initially, the structures underwent optimization using the density functional theory (DFT) approach implemented in the Atomistix ToolKit (ATK) package. This allowed the extraction of the states and band gap energies of AGNR-σ-C60 and AGNR-σ-B80 molecules at zero voltage, followed by calculating the optical Hamiltonian to determine transmission. Subsequently, OPDs based on the optimized molecules were modeled and simulated using the non-equilibrium Green's function (NEGF) method in MATLAB software. The generated results were then used to derive the transmission and photocurrent curves of the devices. Simulation results indicate that utilizing fullerene B80 as the acceptor in AGNR-based donor/acceptor (D/A) OPDs enhances OPD parameters such as photocurrent, QE, and responsivity, thereby offering a promising avenue for future research. Furthermore, the device exhibits significant negative differential resistance (NDR). The insights gained from this study will provide a deeper understanding of the fundamental principles governing charge transport in RTD-based OPDs of which the operation is based on an intuitive 4-site model and will inform future design strategies.