LAMP

Motivation

Extreme Ultraviolet (EUV) lithography has become the foundation of advanced semiconductor device manufacturing, enabling the continuation of Moore’s law through the use of 13.5 nm wavelength light. While this shorter wavelength makes it possible to achieve the resolution required for next-generation technology nodes, it also significantly raises the cost and complexity of the lithography infrastructure. In particular, actinic photomask inspection—ensuring that EUV masks are free of nanoscale defects—remains a critical bottleneck. Conventional imaging-based inspection systems rely on sophisticated optics that must operate at EUV wavelengths. These systems are expensive to build, require regular upgrades to keep pace with scaling demands, and are difficult to deploy cost-effectively at scale. As an alternative, lensless imaging methods such as ptychography have emerged. They offer high-fidelity reconstructions without the need for imaging optics, making them attractive for EUV inspection. However, their practical use is hindered by two major challenges: (i) ptychography requires dense scanning with large overlap between probe positions, leading to long acquisition times and substantial data storage requirements, and (ii) standard iterative solvers such as Difference Map (DifMap) converge slowly, needing many iterations to achieve accurate reconstructions. These limitations make it impractical to use ptychography directly for high-throughput mask inspection. Therefore, there is a strong need for novel computational frameworks that retain the reconstruction fidelity of ptychography while drastically reducing its data acquisition demands and computational burden. Developing such a cost-effective and scalable solution for EUV mask inspection would not only lower infrastructure costs but also have a substantial impact on the reliability and pace of future semiconductor technology development.

Proposed Approach | Solution

We introduce Ptycho-LDM, a hybrid deep learning-based framework for efficient and accurate phase retrieval of EUV photomasks. The framework integrates a physics-informed ptychographic reconstruction with a conditional Latent Diffusion Model (LDM), a generative model capable of refining reconstructions in a low-dimensional latent space. Unlike traditional DifMap solvers, which require many probe positions and iterations, our method uses a two-step strategy. First, we obtain a coarse spatial reconstruction through a resource-constrained DifMap run, using fewer probe positions and iterations. This initial reconstruction captures the broad structure of the photomask but lacks fine details. In the second step, Ptycho-LDM refines this coarse reconstruction by leveraging the generative prior of the LDM, trained to model the distribution of photomask patterns. Working in latent space allows the model to add missing structural details with high computational efficiency, reducing both inference time and memory requirements. This hybrid strategy combines the strengths of physics-based and data-driven approaches: the ptychographic step ensures physical consistency with the diffraction data, while the diffusion prior contributes domain-specific knowledge to improve reconstruction quality. As a result, Ptycho-LDM is able to deliver high-fidelity reconstructions even in measurement-limited regimes where DifMap alone fails to converge.

Contributions‍

Our work makes the following key contributions:

• We propose Ptycho-LDM, a novel hybrid framework that integrates DifMap with a conditional Latent Diffusion Model for EUV photomask phase retrieval, enabling fast and accurate reconstructions.
• We demonstrate that Ptycho-LDM achieves high-quality results with significantly fewer probe positions and iterations, offering substantial improvements in both throughput and computational efficiency.
• Experiments on both noisy synthetic data and real actinic patterned mask inspection (APMI) measurements confirm the robustness of the approach, recovering fine structure and nanometer-scale defects beyond the capability of DifMap alone.
  By combining generative modeling with physics-based priors, we set a new benchmark for scalable, high-throughput EUV mask inspection, while also establishing a framework that can be extended to other ptychographic imaging applications such as ptycho-tomography.

Figure 1: (a) Existing ptychographic algorithms, such as Difference Map [3], require significantly longer reconstruction times due to two primary computational bottlenecks: the number of iterations (K) needed for Fourier and complex object updates, and the number of probe positions (J) required to acquire a sufficient number of diffraction patterns for high-quality phase retrieval. (b) In contrast, our proposed Ptycho-LDM achieves significantly faster reconstruction by leveraging the state-of-the-art generative capabilities and faster sampling of conditional Latent Diffusion Models (LDMs), seamlessly integrated with a physics-based ptychographic iterative approach. Most importantly, the proposed Ptycho-LDM framework requires significantly fewer probe positions, enabling much faster and high-quality image reconstruction.

Figure 2: Qualitative comparison of the reconstructed photomask (masked region for evaluation). The first and third rows show the ground-truth (left, blue colormap), Difference Map (center, green colormap), and our proposed Ptycho-LDM reconstructions (right, green colormap). The second and fourth rows show the magnified views of the rectangular regions highlighted in the first and third rows, respectively. The first and second rows show reconstructions from noise-free measurements (diffraction patterns), while the third and fourth rows present reconstructions from noisy measurements both for DifMap and Ptycho-LDM (w/ Noise, w/ Training). Despite conditioning on noisy measurements, Ptycho-LDM achieves higher-quality reconstructions compared to the DifMap baseline. Both the Difference Map and Ptycho-LDM use 5 probe positions and 1000 iterations.

Impact

‍The impact of this work lies in enabling a practical and scalable pathway for next-generation EUV photomask inspection. By integrating physics-based ptychographic reconstruction with conditional latent diffusion models, Ptycho-LDM delivers high-fidelity defect detection with substantially fewer probe positions and iterations. This directly reduces data acquisition time and computational demand, addressing two of the most critical barriers to the adoption of ptychography in semiconductor metrology. In doing so, the framework not only lowers infrastructure costs but also supports higher throughput and faster inspection cycles—capabilities essential for keeping pace with shrinking technology nodes. More broadly, the combination of generative modeling and physics-informed algorithms introduces a new paradigm for semiconductor inspection, one that is robust to noise, adaptable to real-world measurements, and extensible to other imaging modalities.