Small angle X-ray scattering (SAXS) is a powerful tool to measure structural features on the order of 1-100 nm. Due to high measurement accuracy and strong penetrability, SAXS attracts much attention to characterizing the complex three-dimensional (3D) structure information of periodic nanostructures in integrated circuit (IC) and has been successfully applied to high aspect ratio (HAR) structures, such as 3D-NAND and DRAM. SAXS for IC inline metrology is mostly based on compact X-ray sources. Limited by the brightness of compact X-ray sources, SAXS measurement requires a long exposure time to improve the signal-to-noise (SNR) of SAXS signals. Since the integration effect of long exposure time, numerous cosmic rays are inevitably introduced in the SAXS measurement pattern. As a typical kind of noise that is not correlated with SAXS signals, cosmic rays appear in SAXS patterns randomly and cause signal distortion, which has a negative effect on nanostructure information extraction. However, for lack of making full use of the signal's periodicity information, present cosmic ray rejection algorithms cannot accurately identify and remove the cosmic rays that have a real influence on SAXS signals in the measurement pattern. A new cosmic ray rejection method is needed for SAXS measurement patterns of periodic nanostructures, which will help improve the SNR of SAXS patterns and the performance of nanostructure information extraction.
We propose a cosmic ray rejection method for the SAXS measurement pattern of periodic nanostructure. First, a pattern sequence including many short exposure SAXS measurement patterns of periodic nanostructure samples is generated in the same measurement conditions. Then, the coordinates of the periodic scattering signals are calculated by taking the periodic information of the nanostructure as physical prior, and cosmic rays existing in the effective signal area for each diffraction order in each scattering pattern are identified. After removing the abnormal frames influenced by cosmic rays from the pattern sequence, the SAXS measurement pattern after cosmic ray rejection is obtained by summing the remaining frames of the pattern sequence. The pattern sequence including 500 short exposure SAXS measurement patterns of periodic nanostructure samples is used to evaluate the performance of the proposed method. The precision, miss rate, and false alarm rate of cosmic ray detection results of the pattern sequence are calculated. Meanwhile, two existing methods for cosmic ray rejection of Laplacian edge detection and multi-frame median pixel rejection are selected as the comparison method, and the SAXS measurement pattern sequence is removed from cosmic rays by adopting the two comparison methods and the proposed method. The mean square error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM) of the pattern sequence before and after cosmic ray rejection by three methods are calculated respectively. Since the influence of cosmic rays and Poisson noise on the SAXS measurement pattern is relative to the exposure time, the competitive relationships between two kinds of noise and cosmic ray rejection performances of the proposed method in different exposure times are analyzed. This is realized by calculating the relationship of PSNR of the pattern sequence before and after denoising by three methods respectively, and the number of frames included in the sequence.
According to the confusion matrix calculated based on the cosmic ray detection results of the pattern sequence including 500 short exposure SAXS measurement patterns (Fig. 4), the precision, miss rate, and false alarm rate are 87.67%, 4.93%, and 5.18%, respectively. Compared with the two comparison methods, the pattern sequence denoised by this method has the best cosmic ray rejection effect, and the MSE, PSNR, and SSIM of the method are all optimal (Fig. 5 and Table 1). Especially, PSNR of the pattern sequence increases by 5.55 dB after removing cosmic rays by this method. When the number of frames included in the pattern sequence is low and equivalent to exposure time, Poisson noise is dominant and the PSNR of the pattern sequence is so low that we need more exposure time. When the number of frames increases to about 200, cosmic rays seriously restrict the upper limit of the PSNR of the scattering pattern. However, the PSNR of the pattern sequence after denoising by this method still increases with the rising number of frames, and the growth rate of the PSNR is significantly higher than comparison methods (Fig. 6).
We propose a method for cosmic ray rejection in the SAXS measurement pattern of periodic nanostructures. The pattern sequence including 500 short exposure SAXS measurement patterns of periodic nanostructure samples is simulated and removed from cosmic rays by this method. According to the cosmic ray detection results, the miss rate and false alarm rate are both only about 5%, which proves that the proposed method has a sound detection effect on cosmic rays for the single frame scattering pattern. Meanwhile, the PSNR of the pattern sequence increases by 5.55 dB after removing cosmic rays by the proposed method. The PSNR gain greatly improves the extraction reliability and accuracy of the periodic nanostructure information. By analyzing the competitive relationship between Poisson noise and cosmic rays and evaluating the cosmic ray rejection performance of the proposed method in different exposure time, we find that this method can break the upper limit of PSNR caused by cosmic rays and improve PSNR of scattering pattern continuously. This proves that this method can obtain excellent PSNR gain in the long exposure integration condition. In principle, the proposed method provides a reliable cosmic ray rejection scheme for SAXS measurement patterns of periodic nanostructures, improving the detection SNR of SAXS patterns effectively. This method features a simple principle and fast operation and thus has practical significance to improve the inline metrology performance of SAXS.
