Fig. 1: Young’s modulus, fracture strength, and static fatigue.

a Schematics of defect healing and passivation of monolayer MoS₂ containing a sulfur vacancy. b Optical image of large, exfoliated monolayer MoS₂ flakes on pre-patterned Au/Ti coated SiO₂/Si substrate containing hundreds of holes. Scale bar, 20 µm. c Atomic force microscope (AFM) topographic image of monolayer MoS₂ covering multiple holes. Scale bar, 2 µm. d AFM topographic images of as-exfoliated (left) and treated (right) monolayer MoS₂ samples, each covering a hole with a diameter of 2 µm. Scale bar, 500 nm. e Schematic of the loading profiles for AFM-based monotonic and static fatigue loading. Inset shows a scanning electron microscope image of a focused ion beam (FIB)-modified single crystal diamond tip with a well-defined radius which was used to indent suspended monolayer membranes. Inset scale bar, 200 nm. f, g 2D Young’s modulus (E^2D) and 2D fracture strength (\({\sigma }_{\max }^{2D}\)), respectively, of as-exfoliated and treated MoS₂ monolayers. The central line in each box plot represents the median. The top and bottom edges of the box show the upper and lower quartiles, while the whiskers extend to the maximum and minimum non-outlier values. 30 samples each for the two monolayer MoS₂ conditions were tested. h Weibull plots of failure probability of as-exfoliated and treated MoS₂ monolayers under static fatigue loading at 85% of their respective \({\sigma }_{\max }^{2D}\). t is time in seconds, lines are linear fit with 95% confidence interval, and 50 samples each for the two monolayer MoS₂ conditions were tested. The static fatigue Weibull modulus (M) for each monolayer MoS₂ condition is shown. The gray shaded areas represent the regime of premature failure, defined as failure occurring within ~3 s of loading to a fraction of \({\sigma }_{\max }^{2D}\) (left shaded area), and the runout regime, where no failure occurred for at least 5000 s (1.39 h) (right shaded area).