Measuring vacancy-type defect density in monolayer semiconductors

Abstract

Two-dimensional (2D) materials have attracted wide-spread interest due to their unique and tunable properties. Their optoelectronic, mechanical, and thermal properties are greatly influenced by crystal defects, which are, in turn, used to control these properties. However, experimental quantification of the density of defects, whether deliberately introduced or inherent, is very difficult in these atomically thin materials. Here we show that helium atom micro-diffraction can be used to measure the defect density in 15x20um monolayer MoS2, a prototypical 2D semiconductor, quickly and easily compared to standard methods. We present a simple analytic model, the lattice gas equation, that fully captures the relationship between atomic Bragg diffraction intensity and defect density. The model, combined with ab initio scattering calculations, shows that our technique can immediately be applied to a wide range of 2D materials, independent of sample chemistry or structure. Additionally, wafer-scale characterization is immediately possible.

Figures (5)

• Figure 1: (a) Schematic of an atomic matter wave scattering from the outermost electron density of a 2D material. Most of the scattered flux is directed into kinematic channels (ordered, Bragg diffraction). Defects in the surface introduce disorder, resulting in some flux being scattered diffusely, following a cosine-like distribution. The ratio of ordered to disordered scattering therefore encodes the degree of order at the surface. An optical image (b) and helium micrograph (c) shows the typical sample layout.
• Figure 2: 2D diffraction scan of lowest (left) and highest (right) defect densities of monolayer MoS2 measured in this study. The native defect density (left, $0.1e14\per cm\squared$) produces more intense diffraction peaks at all orders in comparison to the high defect density (right, $1.8e14\per cm\squared$) sample. Schematics of pristine and defective ML-MoS2 surface are inset in the corresponding diffraction pattern.
• Figure 3: (a) Diffraction scans along <10> of increasing defect density ML-MoS2 acquired at $200\degreeCelsius$. (b) Fitting the lattice gas equation to the intensities of the (-20) peaks yields strong agreement with He-defect scattering cross-section $\sigma=35.8\pm5.3\angstrom\squared$.
• Figure A1: He-MoS2 potential energy surfaces at a height $z=2.5\angstrom$ from the top sulphur ionic cores, approximately the classic turning point of an incident helium atom with thermal energy. Green dots mark hollow sites and red dots mark molybdenum atoms. The pink and green arrows in (a) show the real-space lattice vectors. In (b) a sulphur vacancy is marked with a blue star.
• Figure A2: Reciprocal-space scattering distributions of defect-free (top) and defective (bottom) MoS2 (PES shown in Figure \ref{['fig:defect_PES_equipotentials']}) calculated using a close-coupled method to solve matter-wave scattering using the time-dependent Schrodinger equation ManolopoulosIterativeApproachWolken1973CollisionSurface. Using the defect-free PES the outgoing scattered flux is confined to kinematically allowed ($\bf{K}_f=\bf{K}_i+\bf{G}$) diffraction channels, constituting solely ordered diffraction. By introducing a defect to the PES the scattered flux becomes disordered and begins to populate kinematically forbidden ($\bf{K}_f\neq \bf{K}_i+\bf{G}$) channels, introducing disordered, cosine-like scattering. Reciprocal-space lattice vectors are shown in dark red/green, with their real-space counterparts in light red/green. The specular scattering condition ($\hkl(00)$ channel) is off-centre to reflect the $45°$ incidence scattering geometry in the experimental SHeM set-up used in the current work. The blue cross represents the outgoing wavevector normal to the sample surface. As defect density increases, the average outgoing wavevector will migrate from near the specular $\hkl(00)$ condition towards the blue cross.