Controlling Mixed Mo/MoS$_2$ Domains on Si by Molecular Beam Epitaxy for the Hydrogen Evolution Reaction

Molybdenum disulfide (MoS$_2$) is a prototypical layered transition-metal dichalcogenide whose electrocatalytic performance is governed by a delicate balance between crystallinity, defect density, and electronic conductivity. Here we report a systematic molecular beam epitaxy (MBE) study in which annealing temperature, deposition cycle number, and Mo/S thickness ratio were independently varied to control the structural and electronic properties of MoS$_2$ thin films. The successful epitaxial growth of atomically uniform MoS$_2$ directly on Si substrates enables strong interfacial coupling and efficient charge transfer, offering a viable route toward semiconductor-integrated catalytic architectures. X-ray diffraction, Raman spectroscopy, and X-ray absorption analyses reveal that higher annealing temperatures and excessive deposition cycles enhance crystallinity but reduce edge-site density and electrical conductivity, leading to diminished hydrogen evolution reaction (HER) activity. In contrast, intermediate cycle numbers and sulfur-deficient growth conditions yield heterostructures composed of MoS$_2$ with residual metallic Mo and sulfur vacancies, which activate otherwise inert basal planes while providing conductive pathways. These defect-engineered films deliver the best catalytic performance, achieving overpotentials as low as -0.33 V at -10 mA cm$^{-2}$, enlarged electrochemical surface area (ECSA) up to 8.0 cm$^2$, and mass-based turnover frequencies exceeding 23 mmol H$_2$ g$^{-1}$ s$^{-1}$, more than double those of stoichiometric counterparts. Our findings establish sulfur stoichiometry and growth kinetics as powerful levers to tune the interplay between structural order and catalytic activity in MBE-grown MoS$_2$ and point toward a broader strategy for engineering layered catalysts at the atomic scale.