Abnormal diffusion behaviors of Cu atoms in van der Waals layered material MoS2

We investigated the diffusion properties of metal atoms in van der Waals layered materials using first-principles calculations combined with group theory analysis. We found that there is an abnormal diffusion behavior of Cu in MoS2, which originated from the competition of the electronic and strain energies. Although the atom diffusing in bulk MoS2 constantly changes the symmetry of the system with reduced electronic energy due to p-d coupling between occupied Cu d and unoccupied anion p states, the strain energy is dominant. As a result, the energy barrier of metal atoms is mainly determined by their size, making the diffusion rate of Cu faster than those of other metal atoms. Nevertheless, in the monolayer MoS2, the strain energy is negligible and the electronic coupling is significant, so that the strong d-d coupling between occupied Cu d and unoccupied cation d states leads to the highest diffusion barrier of Cu atoms.