Highly efficient computer algorithm for identifying layer thickness of atomically thin 2D materials

The fields of layered material research, such as transition-metal dichalcogenides (TMDs), have demonstrated that the optical, electrical and mechanical properties strongly depend on the layer number N. Thus, efficient and accurate determination of N is the most crucial step before the associated device fabrication. An existing experimental technique using an optical microscope is the most widely used one to identify N. However, a critical drawback of this approach is that it relies on extensive laboratory experiences to estimate N; it requires a very time-consuming image-searching task assisted by human eyes and secondary measurements such as atomic force microscopy and Raman spectroscopy, which are necessary to ensure N. In this work, we introduce a computer algorithm based on the image analysis of a quantized optical contrast. We show that our algorithm can apply to a wide variety of layered materials, including graphene, MoS₂, and WS₂ regardless of substrates. The algorithm largely consists of two parts. First, it sets up an appropriate boundary between target flakes and substrate. Second, to compute N, it automatically calculates the optical contrast using an adaptive RGB estimation process between each target, which results in a matrix with different integer Ns and returns a matrix map of Ns onto the target flake position. Using a conventional desktop computational power, the time taken to display the final N matrix was 1.8 s on average for the image size of 1280 pixels by 960 pixels and obtained a high accuracy of 90% (six estimation errors among 62 samples) when compared to the other methods. To show the effectiveness of our algorithm, we also apply it to TMD flakes transferred on optically transparent c-axis sapphire substrates and obtain a similar result of the accuracy of 94% (two estimation errors among 34 samples).