Measuring vacancy-type defect density in monolayer MoS$_2$

Two-dimensional (2D) materials are being widely researched for their interesting electronic properties. Their optoelectronic, mechanical and thermal properties can be finely modulated using a variety of methods, including strain, passivation, doping, and tuning of defect density. However, measuring defect densities, such as those associated with vacancy-type point defects, is inherently very difficult in atomically thin materials. Here we show that helium atom micro-diffraction can be used to measure defect density in ~15x20$μ$m monolayer MoS$_2$, 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, favourable signal scaling with lateral resolution makes wafer-scale characterisation immediately possible.