Toward automated classification of monolayer versus few-layer nanomaterials using texture analysis and neural networks

Two-dimensional transition metal dichalcogenides (2D TMDs) exhibit exceptional electronic, optical, optoelectronic, spintronic, and mechanical properties that make them strong candidates for future lightweight, flexible, and efficient devices. Despite progress, large-area homogeneous, high-quality growth remains a critical goal, requiring extensive characterization of each sample (layer number, defects, grain size, doping), which is time-consuming and can hinder research and manufacturing. TMDs undergo an indirect-to-direct bandgap transition from bulk to monolayer, enabling thickness identification via photoluminescence (PL) intensity and Raman mode positions/separations; however, comprehensive spectroscopic analysis for every region limits throughput. A rapid optical method to scan large areas and identify homogeneity in layer number, defects, and grains would accelerate progress toward full-chip device production. This study investigates whether microscopic image texture contains sufficient information to automatically distinguish monolayer from few-layer MoS2 and WS2, aiming for a fast, robust, and non-destructive thickness categorization approach suitable for industrial standards.

Prior automated layer identification approaches largely rely on pixel optical intensity (gray or RGB), which is sensitive to acquisition conditions and dynamic range, and may require extensive pre-processing. Examples include using RGB spectral fingerprints and image processing filters to map 2D materials (Jessen et al.), machine-learning classification of optical features without spectroscopy (Masubuchi & Machida), and trainable analyses of RGB information (Lin et al.). Fresnel-law-based simulations with machine learning leveraged optical contrast, RGB, and color differences (Li et al.), and image reconstruction to standardize illuminants/cameras for layer identification across MoS2, WS2, and WSe2 (Lei et al.). These intensity-dependent methods overlook inter-pixel relationships that can reveal characteristic patterns. Texture Analysis (TA) quantitatively evaluates pixel interdependencies and has been widely applied across imaging modalities. First-order TA (GLH) measures gray level distributions; second-order (GLCOM) quantifies joint gray level occurrences at specified distances/angles; higher-order (RLM) characterizes run lengths of identical gray levels, reflecting texture granularity. Given TA’s robustness and reproducibility, it is a promising avenue for automated layer classification in 2D TMDs.

Materials and data acquisition: MoS2 and WS2 were grown by atmospheric-pressure CVD in a two-inch tube furnace. MoO3 (or WO3) precursor (5 mg) was placed on a graphite holder; Si/SiO2 substrates (100 or 300 nm SiO2) were placed face down 1–2 cm from the powder at the furnace center. Sulfur/selenium chalcogen was heated to 300 °C when the furnace reached the growth temperature (780 °C for Mo-based, 850 °C for W-based). Argon flow was 50 sccm during the initial 5 min ramp, then 10 sccm until removal. Growth time was 10–15 min from sulfur melt onset; the furnace cooled naturally. Optical images (white light; various magnifications/NA) were collected. Raman and PL (Witec confocal, 50×, NA 0.85, 532 nm, 0.9 mW, room temperature) were used to label monolayer versus few-layer regions. Multiple optical images of CVD-grown MoS2 and WS2 on Si/SiO2 were analyzed. Dataset and preprocessing: Texture analysis was performed on 28 regions for MoS2 and 19 regions for WS2. Images were equalized to standardize gray-level dynamic range and minimize brightness variation. Regions were manually delineated to avoid edges; each region contained approximately 2000–4000 pixels. Texture feature extraction: Three TA methods were used. (1) GLH (first-order): gray-level frequency distribution; features such as mean, variance, skewness, kurtosis, and percentiles. (2) GLCOM (second-order): co-occurrence matrices C(d,θ)(i,j) computed for distances d = 1–5 pixels and angles θ = 0°, 45°, 90°, 135°, capturing joint occurrences and yielding features describing homogeneity and correlation (e.g., correlation, contrast, sum variance). (3) RLM (higher-order): run-length matrices R(i,l) computed in four directions (horizontal, vertical, 45°, 135°) quantifying runs of identical gray levels, with features reflecting granularity (e.g., gray-level non-uniformity, run-length non-uniformity, long/short run emphasis, fraction of image in runs). Feature selection and classification: For each TA method, the Fisher coefficient was used to automatically select and rank the most discriminant features for monolayer vs few-layer classification. GLH produced 9 features (all used); GLCOM and RLM each contributed the top 10 features. Classifiers: (a) Artificial Neural Network (ANN): feedforward network with input layer of 10 nodes (or 9 for GLH), first hidden layer of 1 neuron, second hidden layer of 2 neurons, and 2-node output layer. Training used backpropagation to adjust synaptic weights. (b) Linear Discriminant Analysis (LDA) served as a benchmark, using the same selected features to compute linear projections maximizing between-class to within-class scatter. Software: TA, Fisher selection, ANN, and LDA were implemented using MaZda-B11 (v4.5) and MATLAB R2018b.

- Best overall performance was achieved by RLM features with ANN: 89% accuracy for MoS2 and 95% for WS2. - GLCOM features with LDA achieved high accuracy for MoS2 (89%) but not for WS2 (79%). - With GLH input features, ANN outperformed LDA (MoS2: 79% vs 57%; WS2: 79% vs 79%). - With RLM input features, ANN outperformed LDA for both materials (MoS2: 89% vs 75%; WS2: 95% vs 68%). - Discriminative features: For MoS2, top RLM features included grey level non-uniformity (all directions), run length non-uniformity (all directions), long/short run emphasis. For MoS2 GLCOM, correlation at specific (d,θ) and contrast were top. For WS2, top RLM features were long run emphasis (all directions), grey level non-uniformity (multiple directions), and fraction of image in runs. For WS2 GLCOM, difference variance and contrast at specific (d,θ) dominated. - Overall, higher-order RLM features better captured texture granularity differentiating monolayer vs few-layer regions, especially when paired with ANN.

Results indicate that higher-order texture features (RLM) that quantify granularity and run properties are more informative for distinguishing monolayer from few-layer nanostructures than second-order homogeneity measures (GLCOM) or first-order intensity statistics (GLH). ANN generally leveraged GLH and RLM features more effectively, while LDA paired better with GLCOM features, suggesting that the classifier’s mathematical model influences how well class separability is emphasized for different feature types. The superior performance of RLM+ANN, particularly for WS2, supports the premise that subtle higher-order textural patterns present in optical micrographs correlate with layer thickness. In contrast, GLH is sensitive to illumination, scaling, and substrate-induced interference effects, making it less reliable without stringent standardization. Although the detailed linkage of second/higher-order TA features to specific physical crystal patterns is not confirmed, the lamellar, repeating structures in MoS2 and WS2 likely contribute to the discriminability captured by RLM. These findings provide guidance for selecting TA methods and classifiers for automated nanolayer thickness categorization, favoring higher-order texture descriptors and neural networks for robust performance.

Automated classification of monolayer versus few-layer MoS2 and WS2 from optical microscopy images was achieved using texture analysis and machine learning. Among tested combinations, RLM features with an ANN classifier provided the highest accuracies (MoS2: 89%; WS2: 95%), while GLCOM with LDA performed well for MoS2. GLH-based approaches were less accurate and more sensitive to imaging conditions. The study suggests RLM as a superior method to quantify microscopic texture associated with nanolayer thickness, enabling fast, non-destructive, and scalable characterization suitable for large-area samples. Future work should relate texture features more explicitly to the underlying physical and chemical properties, enhancing interpretability and generalizability.

- Intensity-based GLH features are susceptible to illumination conditions, gray-level scaling, and substrate variations; equalization was required, and robustness to uncontrolled imaging conditions may be limited. - The relationship between second/higher-order texture features and specific molecular/crystal structures is not confirmed, limiting physical interpretability. - Dataset size was modest (28 regions for MoS2, 19 for WS2), with manually delineated regions, which may affect generalizability. - The study focused on MoS2 and WS2 on Si/SiO2 substrates; performance on other TMDs or substrates was not evaluated. - Imaging was performed under specific optical setups; cross-instrument and cross-condition robustness was not systematically tested.