  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.
