Physics-Informed Deep Neural Networks for Layer Identification of 2D Materials

Accurate identification of the number of layers in transition metal dichalcogenides (TMDs) and hexagonal boron nitride (hBN) is essential for quantum photonic qubit fabrication, as the photoluminescence yield in 2D materials is layer-dependent. However, identifying multiple layers in micron-area exfoliated flakes and few-layered samples from large-area chemical vapor deposition is time-consuming and challenging. The optical contrast of a 2D flake non-linearly correlates with the number of layers present. In this study, we employ deep-learning convolutional neural networks to uncover this correlation. We leverage Meta's open-source Segment Anything Model (SAM), trained on human vision, to analyze magnified images of 2D materials. Initial masks of bulk, few-layer, and monolayer structures are created and subsequently refined by iteratively running SAM on these masks. To gain insight into the underlying optical physics, we develop a physics-informed variational autoencoder (VAE), trained using a hybrid approach of supervised classification loss and unsupervised loss based on Fresnel equations. The models are provided with image embeddings and trained to predict layer detection and distribution. Our method offers an efficient approach to identifying the number of layers, thereby boosting quantum technologies.