Resistive RAM, or RRAM, is one of the emerging non-volatile memory (NVM) technologies, which could be used in the near future to fill the gap in the memory hierarchy between dynamic RAM (DRAM) and Flash, or even completely replace Flash. RRAM operates faster than Flash, but is still non-volatile, which enables it to be used in a dense 3D NVM array. It is also a suitable candidate for computation-in-memory, neuromorphic computing and reconfigurable computing. However, the show stopping problem of RRAM is that it suffers from unique defects, which is the reason why RRAM is still not widely commercially adopted. These defects differ from those that appear in CMOS technology, due to the arbitrary nature of the forming process. They can not be detected by conventional tests and cause defective devices to go unnoticed. Therefore, new tests need to be developed that properly include the physics of a defective device in a RRAM model. Device-aware testing (DAT) is the state-of-the-art solution to this problem. By accounting for the unique physics of an RRAM device, DAT is able to detect unique RRAM defects. However, DAT bases its results on relatively compact electrical models, which do not account for randomness present in e.g. the forming of the filament and local temperature fluctuations. Meanwhile, many low-level physical models exist already that can model this randomness and provide accurate insights into the physical specifics of RRAM. These models do, however, hardly ever analyze the effects of defects. The contribution of this work is to expand and improve one of the state-of-the-art physical models to analyse manufacturing defects on a low, near atomic-level scale. For the first time, the characteristics of a defect can be described in the physical shape of the defect, rather than only the electrical consequences of a black box device. This enables deep level analysis and characterization of defects, the results of which improves DAT to detect even more unique defects. The model is applied to four types of RRAM-related defects: oxygen vacancy density fluctuation, oxide thickness variation, electrode roughness, and contamination by impurities. The effect of the defects on the conductivity of the device are observed and explained, and their unique non-linear behavior is confirmed by simulation. Dynamic defects are not yet included, but the model does provide an extensive static characterization of unique RRAM defects, providing insights into their behavior and improving the quality of DAT. Finally, a discussion is presented which criticizes the reproducability of the referenced defect-free model, but also shows the potential of this work's model to be improved.