We investigate four monolayer transition metal dichalcogenides (TMDs) - MoS₂, WS₂, MoSe₂, and WSe₂ - transferred to silicon substrates as possible sub-nanometer copper diffusion barriers compatible with back-end-of-line temperatures. Based on top-down scanning electron microscope (SEM) and cross-section transmission electron microscope imaging, we demonstrate that the W-based TMDs act as diffusion barriers up to 360°C, while Mo-based TMDs fail at temperatures as low as 300°C. Analysis by SEM indicates that points of failure occur as pinholes, suggesting that mechanical damage may be the origin of failure. Further analysis by X-ray photoemission spectroscopy on as-grown TMDs reveals all four to be chemically unaffected by copper at temperatures as high as 600°C, indicating that directly-grown TMDs still have potential as sub-nanometer diffusion barriers.