Origin of layer-dependent electrical conductivity of transition metal dichalcogenides

Transition metal dichalcogenide (TMD) shows layer-dependent electrical conductivity. However, there are conflicting experimental reports on the trend of conductivity, which is attributed to originating from point defects as a function of the number of layers (NLs). Using density functional theory, we analyze the layer-dependent defect thermodynamics of $n$- and $p$-type defects in ${\mathrm{MoS}}_{2}$ and ${\mathrm{WS}}_{2}$. The shallow donor levels of hydrogen defects systematically become deep with the increasing NLs to six or seven-layers and hence reduces the $n$-type conductivity. Moreover, the deep acceptor ${V}_{\text{S}}$ in a one-layer turns into a weak shallow acceptor for six-layers. Interestingly, from eight-layers onwards, the thermodynamic defect transition levels shift towards the conduction band due to the interplay between the bonding characteristic of the localized defect state and Coulombic repulsion of the added charge in the changing dielectric environment. The study uncovers the plausible cause of the layer-dependent electrical conductivity of TMDs.