Fast calculation method for small-angle X-ray scattering spectra of high-aspect-ratio nanostructures

The rapid evolution of X-ray critical dimension (XCD) metrology demands an accurate and efficient forward model that describes the interaction between incident X-rays and nanostructures under test to support high-throughput experimental data analysis. However, the intricate design of high-aspect-ratio (HAR) nanostructures poses significant computational challenges to the forward model. In this work, we propose a semi-analytical method based on Green's theorem for fast and accurate calculation of small-angle X-ray scattering spectra from HAR nanostructures. Compared with conventional numerical approaches such as the non-uniform fast Fourier transform, the proposed method significantly reduces the number of required sampling points while maintaining high numerical accuracy and stability. Benchmark simulations demonstrate that the method yields a baseline speedup of one to three orders of magnitude over existing techniques, while consistently achieving relative errors below 1%, even for geometrically complex structures. Further acceleration and optimization strategies are also discussed, through which the overall speedup can be extended to two to four orders of magnitude on the current platform. These results highlight the potential of the proposed method as a powerful tool for rapid modeling and large-scale synthetic dataset generation for advanced XCD applications.