Quantifying the thickness of WTe₂ using atomic-resolution STEM simulations and supervised machine learning

For two-dimensional (2D) materials, the exact thickness of the material often dictates its physical and chemical properties. The 2D quantum material WTe2 possesses properties that vary significantly from a single layer to multiple layers, yet it has a complicated crystal structure that makes it difficult to differentiate thicknesses in atomic-resolution images. Furthermore, its air sensitivity and susceptibility to electron beam-induced damage heighten the need for direct ways to determine the thickness and atomic structure without acquiring multiple measurements or transferring samples in ambient atmosphere. Here, we demonstrate a new method to identify the thickness up to ten van der Waals layers in T-d-WTe2 using atomic-resolution high-angle annular dark-field scanning transmission electron microscopy image simulation. Our approach is based on analyzing the intensity line profiles of overlapping atomic columns and building a standard neural network model from the line profile features. We observe that it is possible to clearly distinguish between even and odd thicknesses (up to seven layers), without using machine learning, by comparing the deconvoluted peak intensity ratios or the area ratios. The standard neural network model trained on the line profile features allows thicknesses to be distinguished up to ten layers and exhibits an accuracy of up to 94% in the presence of Gaussian and Poisson noise. This method efficiently quantifies thicknesses in T-d-WTe2, can be extended to related 2D materials, and provides a pathway to characterize precise atomic structures, including local thickness variations and atomic defects, for few-layer 2D materials with overlapping atomic column positions.