Correcting tip-convolution artifacts for precision AFM measurements via a topography-constrained network

The functional reliability of semiconductor micro/nanostructures, from photonic crystals to MEMS, relies on nanometer-scale topographic precision. While atomic force microscopy (AFM) is vital for their characterization, its metrological accuracy is often compromised by tip-convolution artifacts that blur critical features. To address this, we propose the Topography-Constrained Attention UNet (TCA-UNet). Unlike conventional pixel-wise image restoration models, TCA-UNet incorporates a specialized topographical constraint system comprising Mean Absolute Error, Vertical Total Variation, and a Laplacian curvature-consistency term. This system is designed to enforce strict geometric fidelity with the sample's intrinsic surface morphology and roughness characteristics, thus preventing the generation of over-smoothed or non-physical surface predictions. Architecturally, we optimize the encoder-decoder framework to preserve high-frequency spatial details and integrate a gated channel attention module, enabling the network to adaptively focus on morphological features severely distorted by tip-surface interactions. Evaluated on synthetic surface datasets, TCA-UNet achieved an SSIM of 0.98-0.999 depending on the structure class, with an average PSNR improvement of 4.2-6.1 dB over a standard UNet and 8.2-12.8 dB over the EDN baseline across the three test datasets. In practical AFM measurement, evaluated over five repeated scans, it reduced the deviation of a standard grating linewidth from a sharp-tip reference from 44 nm to 5 nm. The topographical reconstruction error (MSE) of complex cone-array patterned sapphire substrates (PSS) was reduced by 52.3% over five regions, from 8.968 ± 0.008-4.274 ± 0.003 nm². The method is scale-agnostic, in that the network operates in pixel space, but shape-specific: the profile family of the sample must have been covered during training. Our framework provides a geometry-aware approach to suppressing routine imaging artifacts, supporting quantitative characterization of semiconductor devices via AFM within the stated applicability envelope.