Machine Learning Framework for Characterizing Processing-Structure Relationship in Block Copolymer Thin Films

TL;DR

The study addresses how processing conditions shape block copolymer thin-film morphology by building a high-throughput ML framework that analyzes GISAXS and AFM data. It combines a CNN-based AFM image classifier, automated GISAXS peak fitting with domain spacing $d_s = 2\pi/b$, and 2D grain-size analyses (color-wheel/Voronoi) to generate a rich morphological dataset. Regression and classification models reveal that GISAXS-derived properties are more predictable (e.g., $R^2$ up to 0.80–0.75) than AFM-derived ones, while SHAP interpretability identifies additive ratio as the key driver of domain spacing and ordering, providing physical insight into processing–structure relationships. The framework enables rapid, interpretable exploration of processing landscapes for BCP thin films and can be extended to broader chemistries and morphologies, advancing design guidance for functional polymeric materials.

Abstract

The morphology of block copolymers (BCPs) critically influences material properties and applications. This work introduces a machine learning (ML)-enabled, high-throughput framework for analyzing grazing incidence small-angle X-ray scattering (GISAXS) data and atomic force microscopy (AFM) images to characterize BCP thin film morphology. A convolutional neural network was trained to classify AFM images by morphology type, achieving 97% testing accuracy. Classified images were then analyzed to extract 2D grain size measurements from the samples in a high-throughput manner. ML models were developed to predict morphological features based on processing parameters such as solvent ratio, additive type, and additive ratio. GISAXS-based properties were predicted with strong performances ($R^2$ > 0.75), while AFM-based property predictions were less accurate ($R^2$ < 0.60), likely due to the localized nature of AFM measurements compared to the bulk information captured by GISAXS. Beyond model performance, interpretability was addressed using Shapley Additive exPlanations (SHAP). SHAP analysis revealed that the additive ratio had the largest impact on morphological predictions, where additive provides the BCP chains with increased volume to rearrange into thermodynamically favorable morphologies. This interpretability helps validate model predictions and offers insight into parameter importance. Altogether, the presented framework combining high-throughput characterization and interpretable ML offers an approach to exploring and optimizing BCP thin film morphology across a broad processing landscape.

Figures (9)

• Figure 1: Process flow for the high-throughput analysis of experimentally collected data, curated for machine learning applications and property predictions.
• Figure 2: Example peak fitting of 1D GISAXS profile, restricting the fitting functions within the peak region, indicated by the dashed box, to improve fitting of the scattering peak related to the BCP sample.
• Figure 3: Overview of the morphology agnostic, feature-based AFM image analysis process for extracting grain size. a) AFM images are classified based on domain orientation by a convolutional neural network (CNN). b) Images containing mixed-type features are segmented into dot- and line-type features. c) Color-wheel analysis of line-type images, color-coding microdomains based on orientation, then segmenting the color-coded microdomains before determining grains. d) Voronoi analysis of dot-type images, features are first isolated before applying the Voronoi analysis and identifying grains.
• Figure 4: a) Simplified architecture of the CNN used for surface feature classification. AFM images are passed through a series of convolutional blocks to extract hierarchical feature maps, which are then fed into fully connected layers to produce a probabilistic prediction over the three feature-based classes (line, dot, and mixed). b-d) SHAP-based interpretation of the CNN’s predictions at convolutional blocks 1-3. Positive SHAP values (red) highlight features that positively contribute to the predicted class, while negative SHAP values (blue) indicate features that negatively influence the prediction. e) Confusion matrix summarizing the CNN's performance on the test set.
• Figure 5: Frequency plots of a) GISAXS-measured domain spacing, b) GISAXS-measured FWHM, c) AFM-measured domain spacing, and d) AFM-measured grain size from the 202 BCP thin films. e) Pearson correlations for each processing condition input with respect to each measured output, and f) Pearson correlation heatmap of measured outputs.