Two-dimensional (2D) layered dielectrics offers a compelling route towards the design of next-generation ultimately compact nanoelectronics. Motivated by recent high-throughput computational prediction of LaO$X$ ($X$ = Br, Cl) as an exceptional 2D dielectrics that significantly outperforms HfO$_2$ even in the monolyaer limit, we investigate the interface properties between LaOX and the archetypal 2D semiconductors of monolayer transition metal dichacolgenides (TMDCs) $M$S$_2$ ($M$ = Mo, W) using first-principle density functional theory simulations. We show that LaO$X$ monolayers interacts weakly with $M$S$_2$ via van der Waals forces with negligible hybridization and interfacial charge transfer, thus conveniently preserving the electronic properties of 2D TMDCs upon contact formation. The conduction and valance band offsets of the interfaces exhibit a sizable value ranging from 0.7 to 1.4 eV, suggesting the capability of LaO$X$ as a gate dielectric materials. Based on Murphy-Good electron emission model, we demonstrate that LaOCl/MoS$_2$ is a versatile dielectric/semiconductor combinations that are compatible to both NMOS and PMOS applications with leakage current lower than $10^{-7}$ Acm$^{-2}$, while LaO$X$/WS$_2$ is generally compatible with PMOS application. The presence of an interfacial tunneling potential barrier at the van der Waals gap further provide an additional mechanism to suppress the leakage current. Our findings reveal the role LaO$X$ as an excellent dielectric companion to 2D TMDC and shall provide useful insights for leveraging the dielectric strength of LaO$X$ in the design of high-performance 2D nanodevices. Comment: 10 pages, 4 Figures, 3 Tables
