Application of position-averaged convergent beam electron diffraction to determine the thickness of ultra-thin materials

The precise thickness determination of free-standing two-dimensional (2D) materials-such as few-layer graphene and molybdenum disulfide (MoS₂)-is achieved using position-averaged convergent beam electron diffraction (PACBED). Experimental PACBED patterns are quantitatively compared with simulated patterns using two distinct evaluation methods: (1) a difference value method (DVM) based on pixel-wise contrast comparison, and (2) a convolutional neural network (CNN) trained on simulated data to predict layer thickness. Optical contrast measurements serve as an independent reference for validating the PACBED-based thickness determination in the few-layer regime. For samples ranging from monolayers up to three layers, both methods demonstrate exact agreement, and up to 10 layers, deviations were not exceeding a single layer. In the further extended thickness range of up to approximately 50 layers, consistent results are obtained, with deviations of no more than two layers between methods. These results confirm that PACBED, combined with either DVM or CNN-based evaluation, offers a reliable, accurate, and non-destructive method for quantifying the thickness of 2D inorganic materials in transmission electron microscopy.