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Theoretical and experimental investigation of vacancy-based doping of monolayer MoS$_2$ on oxide

Monolayer transition metal dichalcogenides are novel, gapped two-dimensional materials. Toward device applications, we consider MoS$_2$ layers on dielectrics, in particular in this work, the effect of vacancies on the electronic structure. In density-functional based simulations, we consider the effects of near-interface O vacancies in the oxide slab, and Mo or S vacancies in the MoS$_2$ layer. Band structures and atom-projected densities of states for each system and with differing oxide terminations were calculated, as well as those for the defect-free MoS$_2$-dielectrics system and for isolated dielectric layers for reference. Among our results, we find that with O vacancies, both the Hf-terminated HfO$_2$-MoS$_2$ system, and the O-terminated and H-passivated Al$_2$O$_3$-MoS$_2$ systems appear metallic due to doping of the oxide slab followed by electron transfer into the MoS$_2$, in manner analogous to modulation doping. The n-type doping of monolayer MoS$_2$ by high-k oxides with oxygen vacancies then is experimentally demonstrated by electrically and spectroscopically characterizing back-gated monolayer MoS$_2$ field effect transistors encapsulated by oxygen deficient alumina and hafnia.