Digital holography for non-invasive quantitative imaging of two-dimensional materials

Abstract

Digital holography has found applications in many walks of life, from medicine to metrology, due to its ability to measure complex fields. Here, we use the power of digital holography to quantitatively image two-dimensional Transition Metal Dichalcogenides (TMDs) such as MoS2 and WS2 placed on a SiO2/Si substrate and determine their complex refractive indices or layer thicknesses. By considering the different refractive indices of the TMDs as they are thinned down from bulk to monolayers and by holographically capturing both the amplitude and the phase of reflected light, single atomic layers of TMDs, about 0.7 nm thick, can be resolved. Using holography, we also predict the number of layers contained within a thick TMD flake, which shows agreement with results obtained using Atomic Force Microscopy (AFM). A Bland–Altman analysis was performed to compare our experimental results with the standard AFM measurements, yielding a limit of agreement <5 nm for samples with thicknesses ranging from 15 to 60 nm. Our technique is non-contact, non-invasive, does not require scanning, and produces a field of view of a few hundred micrometers by a few hundred micrometers in a single capture. To further our study, we also perform simulations to demonstrate how the thickness of the SiO2 layer and the laser wavelength are critical in optimizing the amplitude and phase response of a two-dimensional material. These simulations can be used as a roadmap to determine the ideal wavelength and SiO2 layer thickness that should be used to accurately determine the refractive index or thickness of any given sample.