SparseC-AFM: a deep learning method for fast and accurate characterization of MoS$_2$ with C-AFM

The increasing use of two-dimensional (2D) materials in nanoelectronics demands robust metrology techniques for electrical characterization, especially for large-scale production. While atomic force microscopy (AFM) techniques like conductive AFM (C-AFM) offer high accuracy, they suffer from slow data acquisition speeds due to the raster scanning process. To address this, we introduce SparseC-AFM, a deep learning model that rapidly and accurately reconstructs conductivity maps of 2D materials like MoS$_2$ from sparse C-AFM scans. Our approach is robust across various scanning modes, substrates, and experimental conditions. We report a comparison between (a) classic flow implementation, where a high pixel density C-AFM image (e.g., 15 minutes to collect) is manually parsed to extract relevant material parameters, and (b) our SparseC-AFM method, which achieves the same operation using data that requires substantially less acquisition time (e.g., under 5 minutes). SparseC-AFM enables efficient extraction of critical material parameters in MoS$_2$, including film coverage, defect density, and identification of crystalline island boundaries, edges, and cracks. We achieve over 11x reduction in acquisition time compared to manual extraction from a full-resolution C-AFM image. Moreover, we demonstrate that our model-predicted samples exhibit remarkably similar electrical properties to full-resolution data gathered using classic-flow scanning. This work represents a significant step toward translating AI-assisted 2D material characterization from laboratory research to industrial fabrication. Code and model weights are available at github.com/UNITES-Lab/sparse-cafm.

💡 Research Summary

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The paper addresses a critical bottleneck in the electrical metrology of two‑dimensional (2D) materials: the long acquisition time required by conductive atomic force microscopy (C‑AFM). High‑resolution C‑AFM typically needs a dense raster scan (256–512 lines, 5–10 nm/pixel) that takes 15–30 minutes per image, which is impractical for large‑scale production and rapid failure analysis. To overcome this limitation, the authors introduce SparseC‑AFM, a deep‑learning‑driven workflow that reconstructs full‑resolution conductivity maps from sparsely sampled C‑AFM data.

Key contributions

1. Data collection strategy – MoS₂ monolayers grown by plasma‑enhanced chemical vapor deposition (PECVD) on Si/SiO₂ were measured with a Park NX‑Hivac AFM in contact mode. Dual‑channel data (topography and current) were recorded at full resolution (512 × 512, 2 µm × 2 µm) and at three lower resolutions (256 × 256, 128 × 128, 64 × 64). Measurements were performed under high vacuum (10⁻⁵ torr) and ambient conditions using conductive PPP‑CONTSCPt probes.

2. Model architecture – The up‑sampling network, named Sparse‑C‑AFM, builds on the SwinIR design. An initial shallow convolution extracts low‑level features, followed by six Residual Swin Transformer Blocks (RSTB) and six Shifted‑Window Transformer Layers (STL) that capture both local and global dependencies with modest computational cost. A final reconstruction head combines shallow and deep features via skip connections and up‑sampling convolutions to produce a high‑resolution output. The network is trained with an L1 pixel‑wise loss; optional PSNR/SSIM‑based auxiliary losses can be added.

3. Training protocol – Random crops (256, 384 px) and standard augmentations (rotation, color jitter) increase data diversity. Training runs on a single NVIDIA A6000 GPU for 200 epochs, with batch sizes of 16 (×2 up‑sampling), 16 (×4) and 4 (×8). The Adam optimizer uses a learning rate of 1e‑5, β₁ = 0.9, β₂ = 0.99. A small set of full‑resolution scans is retained for rapid fine‑tuning when the workflow is deployed on a new wafer or a different material.

4. Performance evaluation –
   Reconstruction quality: For 4× up‑sampling (data reduction factor 16) the model achieves PSNR ≈ 30 dB and SSIM ≈ 0.92; for 8× up‑sampling (factor 64) PSNR ≈ 27 dB and SSIM ≈ 0.88. These numbers surpass or match prior sparse‑AFM methods such as Gaussian Process Regression (GPR) and RNAN, the former being computationally infeasible at high sparsity.
   Electrical‑property fidelity: A physics‑informed Python script extracts scalar metrics (mean current, coverage percentage, defect‑area, island‑boundary length) from both ground‑truth and reconstructed current maps. SparseC‑AFM predictions differ by < 5 % in mean current and reduce defect‑area estimation error by more than 60 % compared with the raw sparse inputs.
   Speed: Inference takes ~0.2 s per 512 × 512 map on the same GPU, orders of magnitude faster than GPR (minutes) and comparable to real‑time video‑rate processing.

5. Industrial relevance – The workflow delivers an >11× reduction in acquisition time (from ~15 min to < 5 min) while preserving the quantitative information needed for process control (film coverage, defect density, grain‑boundary mapping). Because the method uses the same AFM hardware and scanning protocol, it is non‑intrusive and can be integrated into existing metrology lines with minimal disruption. The model adapts quickly to new substrates, vacuum/ambient conditions, and even to other TMDs (e.g., WS₂) after a brief fine‑tuning phase.

6. Limitations and future directions – The current study focuses on MoS₂; extending to a broader library of 2D materials, multi‑physics AFM modalities (e.g., peak‑force, Kelvin probe) and multi‑modal data fusion remains to be explored. Very high defect densities or abrupt conductivity changes can challenge the reconstruction accuracy; incorporating physics‑based constraints into the loss function or using hybrid model‑based/data‑driven approaches could improve robustness. Finally, deploying the model on edge devices (industrial PLCs, embedded GPUs) will be essential for fully autonomous, on‑line metrology.

Conclusion – SparseC‑AFM demonstrates that deep‑learning‑based super‑resolution can effectively replace dense C‑AFM scans, delivering near‑identical electrical characterization while drastically cutting measurement time and cost. This advancement bridges the gap between laboratory‑scale 2D‑material research and high‑throughput industrial fabrication, paving the way for AI‑assisted metrology in next‑generation semiconductor manufacturing.