Transition Metal Dichalcogenides (TMDs) are perhaps the most promising substitute for graphene for building the next generation of low-dimensional functional materials. They possess naturally layered and anisotropic structures with a vanishing coefficient of friction observed in high-vacuum conditions. However, TMD-based nano-devices experience nanotribological effects in static or dynamic conditions leading to major challenges regarding their design, control, and reliability. For instance, pure Molybdenum Disulfide (MoS₂) deposited by sputtering easily oxidises into Molybdenum Trioxide (MoO₃) in humid air. Investigations in recent years have explored the doping and multi-layer design of TMDs in an attempt to alleviate the above issues. Therefore, it is necessary to understand the mechanisms governing the formation of stable TMD heterostructures to guide their experimental synthesis.

To that end, we have performed a computational investigation to study the doping of monolayer and bilayer MoS₂ and WS₂ from first principles using the Alloy Theoretic Automated Toolkit (ATAT) together with the Vienna Ab initio Simulation Package (VASP). We constructed the temperature-composition phase diagrams for a selection of dopants to provide guidelines for their experimental synthesis. Then, we characterised the mechanisms underlining the formation and stability of doped compounds in terms of electronic and dynamic descriptors. We finally provide guidelines on how to select a suitable dopant atomic type and concentration to achieve a specific target stability. The proposed methodology constitutes a general protocol to study the formation of doped layered TMDs, which can easily be extended to other layered materials. Additionally, since the search for the stabilisation mechanism and phase diagrams of doped TMD-heterostructures has no intrinsic ties to tribology, the new phases here identified may prove to be useful in other applications (e.g. optoelectronics, photovoltaics etc.).