Optical spectrum augmentation for machine learning powered spectroscopic ellipsometry.

As structures of semiconductors become more complex and finer, the importance of an accurate measurement system has emerged. Previous studies have suggested various methodologies to improve the accuracy. However, since multiple measuring instruments are used in mass production, repeatability and reproducibility are as important as the accuracy of the values produced by predictive models. In this study, we adopted a data augmentation approach that minimizes the physical difference between multiple measuring instruments by using the domain knowledge of the spectroscopic ellipsometry (SE) field. By modeling the photodetector misalignment as polynomials and taking into account random noise, we proposed stochastic polynomial wavelength calibration (s-PWC) which can improve the percentage of the gage repeatability and reproducibility (Gage R&R) value. In experiments, the proposed methodology was applied to train the nanostructure prediction model of a three-dimensional vertical NAND Flash memories with industrial data sets. The performance improvements before and after applying the method were evaluated. Gaussian noise augmentation (GNA) and polynomial wavelength calibration (PWC) methodologies devised based on previous studies were also evaluated for relative comparison. As a result of conducting the experiments under conditions similar to the actual production environment, the average value of the percentage of Gage R&R decreased from 10.23% to 6.3% when applying the proposed method, while the GNA and PWC methodologies reduced the values to 10.01% and 7.62%, respectively. There were no significant changes in the values of coefficient of determination (R2) and root mean square error (RMSE) when applying the three methods based on the data augmentation approach. In other words, applying s-PWC ensures that the predictive model produces consistent values for the same sample when it needs to infer data obtained from multiple measuring instruments, while maintaining R2 and RMSE. Future research on data augmentation techniques by modeling differences between other physical components might extend the explanations of the methodologies to improve R2 and RMSE of predictive models. We expect this study could provide guidelines for improving the performance of inferential models based on machine learning and SE in mass production environments.

Residual vibration reduction of white-light scanning interferometry by input shaping.

White-light scanning interferometry is widely used for precision metrology of engineering surfaces. It needs a mechanical scanning for capturing an interferogram that determines where the surface of a measured sample is located. The residual vibration during the scanning procedure distorts the interferogram and it reduces the accuracy and the precision of the system. The residual vibration becomes bigger as the proportional gain gets higher for the fast response. So it is hard to achieve the fast and precise measurement simultaneously. In this study, input shaping which convolves a reference signal with the input shaper is investigated to reduce the residual vibration of the scanning system. The step response data is analyzed using Continuous Wavelet Transform (CWT) to design the input shaper. Using proposed method, the residual vibration of the white light scanning interferometry is reduced and it achieved both faster measurement speed and more accurate measurement.

Critical dimension measurement of transparent film layers by multispectral imaging.

An optical microscopy system as a non-destructive method for measuring critical dimension (CD) is widely used for its stability and fastness. In case of transparent thin film measurement, it is hard to recognize the pattern under white light illumination due to its transparency and reflectance characteristics. In this paper, the optical measurement system using multispectral imaging for CD measurement of transparent thin film is introduced. The measurement system utilizes an Acousto-Optic Tunable Filter (AOTF) to illuminate the specimen with various monochromatic lights. The relationship between spectral reflectance and CD measurement are deduced from series of measurement experiments with two kinds of Indium Tin Oxide (ITO) patterned samples. When the difference of spectral reflectance between substrate and thin film layers is large enough to yield a large image intensity difference, the thin film layer can be distinguished from substrate, and it is possible to measure the CD of transparent thin films. This paper analyzes CD measurement of transparent thin film with reflectance theory and shows that the CD measurement of transparent thin film can be performed successfully with the proposed system within a certain wavelength range filtered by AOTF.

Microsphere-assisted hyperspectral imaging: super-resolution, non-destructive metrology for semiconductor devices.

As semiconductor devices shrink and their manufacturing processes advance, accurately measuring in-cell critical dimensions (CD) becomes increasingly crucial. Traditional test element group (TEG) measurements are becoming inadequate for representing the fine, repetitive patterns in cell blocks. Conventional non-destructive metrology technologies like optical critical dimension (OCD) are limited due to their large spot diameter of approximately 25 µm, which impedes their efficacy for detailed in-cell structural analysis. Consequently, there is a pressing need for small-spot and non-destructive metrology methods. To address this limitation, we demonstrate a microsphere-assisted hyperspectral imaging (MAHSI) system, specifically designed for small spot optical metrology with super-resolution. Utilizing microsphere-assisted super-resolution imaging, this system achieves an optical resolution of 66 nm within a field of view of 5.6 µm × 5.6 µm. This approach effectively breaks the diffraction limit, significantly enhancing the magnification of the system. The MAHSI system incorporating hyperspectral imaging with a wavelength range of 400-790 nm, enables the capture of the reflection spectrum at each camera pixel. The achieved pixel resolution, which is equivalent to the measuring spot size, is 14.4 nm/pixel and the magnification is 450X. The MAHSI system enables measurement of local uniformity in critical areas like corners and edges of DRAM cell blocks, areas previously challenging to inspect with conventional OCD methods. To our knowledge, this approach represents the first global implementation of microsphere-assisted hyperspectral imaging to address the metrology challenges in complex 3D structures of semiconductor devices.