Machine learning for layer number identification of black phosphorus based on Raman spectra

Black phosphorus (BP) is a novel two-dimensional (2D) material with tunable electronic and optical properties. Thickness is a pivotal parameter in defining the electronic, optical, and thermal properties of 2D crystals. Determining the thickness of a material is crucial to studying its properties. However, conventional characterization methods for the directly determination of thick layers of BP are complex and inefficient. In this paper, we propose a machine learning (ML)-based method that can efficiently and accurately determine the layer number of BP. The features of the three characteristic peaks (Ag1,B2g, andAg2) were extracted from the Raman spectra, including peak position, intensity, full width at half maximum, and integrated intensity. Subsequently, we found that the intensity ratio of the substrate (Si) peak to the Raman mode is crucial to predicting the number of layers by feature importance analysis. This study makes a key contribution by presenting, for the first time, a comparative analysis of multiple ML algorithms for identifying the layer number of BP. Furthermore, it identifies a specific set of discriminative features tailored for BP's Raman spectra. Finally, by synergistically augmenting the dataset and refining the model architecture, we effectively mitigated the performance limitations imposed by the small dataset. The performance of the model is evaluated based onR2, mean square error, and mean absolute error, where theR2of all algorithms is not less than 0.9. ML models can accurately predict the number of layers of BP material. ML algorithms can automatically learn from the data and optimize the algorithm to improve the efficiency and accuracy of the model. This not only reduces the analysis burden on researchers but also promotes the in-depth application of artificial intelligence in 2D material characterization.