Wavelength-multiplexed multi-mode EUV reflection ptychography based on automatic differentiation

Abstract

Ptychographic extreme ultraviolet (EUV) diffractive imaging has emerged as a promising candidate for the next generationmetrology solutions in the semiconductor industry, as it can image wafer samples in reflection geometry at the nanoscale. This technique has surged attention recently, owing to the significant progress in high-harmonic generation (HHG) EUV sources and advancements in both hardware and software for computation. In this study, a novel algorithm is introduced and tested, which enables wavelength-multiplexed reconstruction that enhances the measurement throughput and introduces data diversity, allowing the accurate characterisation of sample structures. To tackle the inherent instabilities of the HHG source, a modal approach was adopted, which represents the cross-density function of the illumination by a series of mutually incoherent and independent spatial modes. The proposed algorithm was implemented on a mainstream machine learning platform, which leverages automatic differentiation to manage the drastic growth in model complexity and expedites the computation using GPU acceleration. By optimising over 200 million parameters, we demonstrate the algorithm's capacity to accommodate experimental uncertainties and achieve a resolution approaching the diffraction limit in reflection geometry. The reconstruction of wafer samples with 20-nm high patterned gold structures on a silicon substrate highlights our ability to handle complex physical interrelations involving a multitude of parameters. These results establish ptychography as an efficient and accurate metrology tool.

Fig. 1. The ptychography process and the computational graph for the reconstruction.

a Illustration of ptychography in reflection geometry at our EUV beamline. b The computational graph for the reconstruction. f and J denote the function and the corresponding Jacobian of each sub-model. The forward path (solid arrows) predicts the diffraction pattern measured by the camera and evaluates the loss function. The backward path (dashed arrows) computes the gradients with respect to the variables in each sub-model and the two inputs of the model in an accumulative manner

Fig. 2. Performance comparison between PtyLab and PtychoFlow.

Performance comparison in execution time (a) and memory usage (b). The comparison is conducted by reconstructing the experiment dataset with two wavelengths, three illumination modes, and one sample mode per wavelength. The numbers in the figures are averaged over five runs on a Nvidia RTX A6000 GPU. *The number is obtained for the case of a single wavelength since PtyLab does not support scanning position correction in multiple wavelength reconstruction. **The number is adjusted since PtyLab only corrects the propagation distance per epoch instead of per batch. The adjustment calculates the execution time for one correction and scales it by the number of batches to match that in PtychoFlow

Fig. 3. Dual wavelengths nanostructure imaging.

a, b Ptychographic reconstructions of nanostructures on the wafer sample at wavelength 17.30 nm (a) and 17.93 nm (b). The brightness and hue of the image represent the amplitude and phase of the complex-valued object, respectively. The reconstructed objects show shifted field-of-views as the probes at different wavelengths illuminate different areas on the sample. c SEM image of the wafer sample with various types of structures and manufacturing defects for comparison. d Profile of the chirped grating in ROI 1 consisting of 200 nm, 100 nm, and 50 nm lines with varying spacing. Inset: the finest part of the chirped grating with 150 nm pitch and 50 nm linewidth. e Gratings in squared areas ROI 2 (with a manufacturing defect) and ROI 3, before (left) and after (right) refocusing for enhancing contrast. f Zoom-in of the reconstructed structures in ROI 4–6. Due to the non-uniform sample resolution in the reflection geometry, only the horizontal grating and the horizontal part of the 2D grating can be resolved

Fig. 4. 3D structure information characterisation.

a The entire field-of-view of the reconstructed complex-valued object. The ellipsoidal contours in orange and yellow mark the areas illuminated with 75% and 95% of the total photons during the scanning process, respectively. Inset: the reconstructed Siemens star with 90 spokes and a radius of 60 μm. b Distribution of pixel values in amplitude (normalised) and phase coordinates. The green circles indicate the clusters of pixels for the Si substrate and Au structures, respectively. c 3D representation of the AFM measurement and the Siemens star reconstructed by ptychography. The height is computed using the phase difference determined in b, the incident angle, the wavelength, and with prior knowledge of the materials

Fig. 5. EUV focusing optics characterisation.

a Sum of the measured diffraction patterns in logarithmic scale with zeroth order in the shape of the ellipsoidal focusing mirror and higher orders cropped in the horizontal direction due to the sample tilt in reflection geometry. Inset: zoom-in of the zeroth order in linear scale. b Reconstructed common background intensity in logarithmic scale with a clearly distinct ellipsoidal shape representing the pupil of the illumination system. Inset: zoom-in of pupil in linear scale. c, d Reconstructed pupil functions (Fourier transform of the respective reconstructed illumination probes) at wavelengths 17.30 nm (c) and 17.93 nm (d). The rectangularly shaped ROI 1–4 show the locations of the defects on the EUV focusing mirror

Fig. 6. Reflection ptychography dataset processing pipeline and the dependencies on variables.

Intertwined relations between the main steps for quantitative ptychographic imaging and the relevant variables

Fig. 7. Experimental setup for ptychography dataset acquisition using HHG EUV source.

Higher harmonics are generated in a pressurised Argon gas jet in the vicinity of the focus of an infra-red pump laser, as shown by a, and are separated from the infra-red pump laser. The HHG spectrum is calibrated using a transmission spectrometer with high-density gratings. A single harmonic can be selected with spectral filtering using a pair of Al-Zr mirrors, whose spectrum is depicted by the white dashed (one mirror) and solid (two mirrors) curves in b. The illumination beam is focused onto a patterned sample by an ellipsoidal mirror, and the resulting diffraction pattern is captured by a CCD camera sensitive to EUV photons for ptychography reconstruction