Measurement algorithm for wafer alignment based on principal component analysis.

We propose a novel measurement algorithm for wafer alignment technology based on principal component analysis (PCA) of a mark image. The waveform of the mark is extracted from the enlarged mark image, which is collected by CCD. The position of the mark center on the CCD can be calculated based on the extracted waveform. By applying PCA to the mark image, the first principal component containing position information of the mark can be obtained. Therefore PCA can be used to extract the waveform from the mark image. Compared with the typical waveform extraction method (the summed projection (SP) method), the proposed PCA method can use the position information contained in the mark image more effectively. Through simulation and experiment, it is proved that the proposed PCA method can improve the contrast of the normalized waveform, and then improve the alignment accuracy.

Sub-pixel position estimation algorithm based on Gaussian fitting and sampling theorem interpolation for wafer alignment.

Wafer alignment is the core technique of lithographic tools. Image-processing-based wafer alignment techniques are commonly used in lithographic tools. An alignment algorithm is used to analyze the alignment mark image for obtaining the mark position. The accuracy and speed of the alignment algorithm are very important for guaranteeing the overlay and throughput of lithographic tools. The most commonly used algorithm in image-processing-based alignment techniques is the self-correlation method. This method has a high accuracy, but the calculation is complex, and the calculation speed is slow. In this paper, we propose a sub-pixel position estimation algorithm based on Gaussian fitting and sampling theorem interpolation. The algorithm first reconstructs the alignment signal by sampling theorem interpolation and then obtains the sub-pixel position of the mark by Gaussian fitting. The accuracy and robustness of the algorithm are verified by testing the simulated marks and experimentally captured marks. The repeat accuracy can reach 1/100 pixels, which is in the same level with the self-correlation method. The calculation speed is highly improved compared with the self-correlation method, which needs only about 1/3 of even short calculation time.

Alignment mark optimization for improving signal-to-noise ratio of wafer alignment signal.

Phase diffraction gratings are widely used as alignment marks in wafer alignment systems. A higher alignment accuracy can be obtained by using higher diffraction orders of the alignment mark. Meanwhile, the alignment accuracy is also affected by the signal-to-noise ratio (SNR) of the alignment signal. The diffraction efficiency of the alignment mark is significantly reduced in the practical lithography process because of the strong absorption of the opaque film stacks on the mark surface, especially the metal layer. The reduction of the diffraction efficiency leads to a deterioration of the SNR of the alignment signal. An equal subsegmented phase grating is usually used to improve the diffraction efficiency of higher odd orders, so as to improve the SNR of the corresponding alignment signal. However, there is still a relatively high diffraction efficiency of the zeroth and even orders of such a grating. They will affect the SNR of the alignment signal of odd diffraction orders, which are usually used to measure mark position. In this paper, we propose a method to improve the diffraction efficiency of odd orders for a subsegmented phase grating through optimizing the structure of the alignment mark. Moreover, the diffraction efficiency of the zeroth and even orders, which are not used in the measurement process of mark position, are sufficiently reduced. Simulation results indicate that the SNR of the alignment signal was obviously improved by the proposed method, which is very helpful for improving alignment accuracy.

Calibration method of overlay measurement error caused by asymmetric mark.

With the process nodes extending to sub-10-nm in advanced semiconductor manufacturing, the overlay requirements keep progressively scaling down, which makes it very important to measure overlay precisely for monitoring on-product performance. The overlay mark being asymmetrical when generated via the lithography process, this asymmetry will be slightly variated even in the same process or same lot, and it will bring overlay measurement error. In general, the wafer alignment data are used for correcting this overlay measurement error, utilizing its wavelengths and polarizations dependence. However, there is a residual error that cannot be removed because the structures of the wafer alignment mark and overlay mark are different and are affected by the process differently. In this paper, a new method is proposed for calibrating the overlay measurement error introduced by the asymmetric mark, which is based on the relationship between measurement data of the overlay mark and the single layer mark. The validity is verified by simulation with different types of asymmetric mark. It is very useful for improving overlay measurement accuracy and for understanding how the overlay measurement error is affected by the asymmetric mark.

Underwater Object Segmentation Based on Optical Features.

Underwater optical environments are seriously affected by various optical inputs, such as artificial light, sky light, and ambient scattered light. The latter two can block underwater object segmentation tasks, since they inhibit the emergence of objects of interest and distort image information, while artificial light can contribute to segmentation. Artificial light often focuses on the object of interest, and, therefore, we can initially identify the region of target objects if the collimation of artificial light is recognized. Based on this concept, we propose an optical feature extraction, calculation, and decision method to identify the collimated region of artificial light as a candidate object region. Then, the second phase employs a level set method to segment the objects of interest within the candidate region. This two-phase structure largely removes background noise and highlights the outline of underwater objects. We test the performance of the method with diverse underwater datasets, demonstrating that it outperforms previous methods.

Monocular Vision-Based Underwater Object Detection.

In this paper, we propose an underwater object detection method using monocular vision sensors. In addition to commonly used visual features such as color and intensity, we investigate the potential of underwater object detection using light transmission information. The global contrast of various features is used to initially identify the region of interest (ROI), which is then filtered by the image segmentation method, producing the final underwater object detection results. We test the performance of our method with diverse underwater datasets. Samples of the datasets are acquired by a monocular camera with different qualities (such as resolution and focal length) and setups (viewing distance, viewing angle, and optical environment). It is demonstrated that our ROI detection method is necessary and can largely remove the background noise and significantly increase the accuracy of our underwater object detection method.

Zernike polynomials as a basis for modal fitting in lateral shearing interferometry: a discrete domain matrix transformation method.

A Zernike-polynomials-based wavefront reconstruction method for lateral shearing interferometry is proposed. Shear matrices are calculated using matrix transformation instead of mathematical derivation. Simulation results show that the shear matrices calculated using the proposed method are the same as those obtained from mathematical derivation. The advantage of the proposed method is that high order shear matrices can be obtained easily; thus, wavefront reconstruction can be extended to higher order Zernike terms, and reconstruction accuracy can be improved.

Orthonormal polynomials for annular pupil including a cross-shaped obstruction.

By nonrecursive matrix method using the Zernike circle polynomials as the basis functions, we derived a set of polynomials up to fourth order which is approximately orthonormal for optical systems with an annular pupil having a cross-shaped obstruction. The performance of the polynomials is compared with the strictly orthonormal polynomials with some numerical examples.

Analysis of lateral shearing interferometry without self-imaging limitations.

In lateral shearing interferometry, interferograms with a good contrast can be obtained at any distance without self-imaging limitations based on a modified Hartmann mask (MHM) and a randomly encoded hybrid grating (REHG). The present study analyzes and compares the diffraction orders, the contrast of carrier fringes, the available spectral bandwidth, and the wavefront measurement accuracy of the lateral shearing interferometer using MHM and REHG. Numerical simulations show that the performance of the REHG is superior to that of the MHM with respect to fringe contrast, available spectral bandwidth, and wavefront measurement accuracy. For the REGH, if the phase step of the phase chessboard is within the range of (2n+1±0.2)π, the contrast of the carrier fringes is almost invariant along the propagation axis, and the wavefront reconstruction error generated from higher diffraction orders is small enough to be neglected. Optimal quantization of the REHG is also studied. When M is equal to 2 and N is not less than 5, the quantization result can meet the requirement of the measurement accuracy.

High spatial resolution zonal wavefront reconstruction with improved initial value determination scheme for lateral shearing interferometry.

In a recent paper [J. Opt. Soc. Am. A 29, 2038 (2012)], we proposed a generalized high spatial resolution zonal wavefront reconstruction method for lateral shearing interferometry. The test wavefront can be reconstructed with high spatial resolution by using linear interpolation on a subgrid for initial values estimation. In the current paper, we utilize the difference between the Zernike polynomial fitting method and linear interpolation in determining the subgrid initial values. The validity of the proposed method is investigated through comparison with the previous high spatial resolution zonal method. Simulation results show that the proposed method is more accurate and more stable to shear ratios compared with the previous method. A comprehensive comparison of the properties of the proposed method, the previous high spatial resolution zonal method, and the modal method is performed.

Use of numerical orthogonal transformation for the Zernike analysis of lateral shearing interferograms.

A numerical orthogonal transformation method for reconstructing a wavefront by use of Zernike polynomials in lateral shearing interferometry is proposed. The difference fronts data in two perpendicular directions are fitted to numerical orthonormal polynomials instead of Zernike polynomials, and then the orthonormal coefficients are used to evaluate the Zernike coefficients of the original wavefront by use of a numerical shear matrix. Due to the fact that the dimensions of the shear matrix are finite, the high-order terms of the original wavefront above a certain order have to be neglected. One of advantages of the proposed method is that the impact of the neglected high-order terms on the outcomes of the lower-order terms can be decreased, which leads to a more accurate reconstruction result. Another advantage is that the proposed method can be applied to reconstruct a wavefront on an aperture of arbitrary shape from its difference fronts. Theoretical analysis and numerical simulations shows that the proposed method is correct and its reconstruction error is obviously smaller than that of Rimmer-Wyant method.

Generalized zonal wavefront reconstruction for high spatial resolution in lateral shearing interferometry.

A new zonal wavefront reconstruction method for lateral shearing interferometry was presented. The proposed algorithm allows shear amounts equal to arbitrary integral multiple of the sample intervals. High spatial resolution reconstruction is achieved with only two difference wavefronts measured in orthogonal shear directions. The presented algorithm was generalized to be applicable for general aperture shape by using zero padding and Gerchberg-type iterative methods. The capability of the presented algorithm was demonstrated by some numerical examples. Also, the reconstruction error was analyzed theoretically and numerically.

Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms.

Four modal methods of reconstructing a wavefront from its difference fronts based on Zernike polynomials in lateral shearing interferometry are currently available, namely the Rimmer-Wyant method, elliptical orthogonal transformation, numerical orthogonal transformation, and difference Zernike polynomial fitting. The present study compared these four methods by theoretical analysis and numerical experiments. The results show that the difference Zernike polynomial fitting method is superior to the three other methods due to its high accuracy, easy implementation, easy extension to any high order, and applicability to the reconstruction of a wavefront on an aperture of arbitrary shape. Thus, this method is recommended for use in lateral shearing interferometry for wavefront reconstruction.