A bare silicon wafer defect image enhancement method based on double polarization rotation sequence

Abstract

The application relates to a bare silicon wafer defect image enhancement method based on a dual-polarization rotation sequence, which comprises the following steps: collecting s-polarization component and p-polarization component reflected light images to obtain a dual-polarization rotation sequence image; constructing a polarization weight matrix W based on the gray difference between the s-polarization component and the p-polarization component of each spatial pixel in the dual-polarization rotation sequence image; decomposing the dual-polarization rotation sequence image into a background low-rank component L and a foreground sparse component S; mapping the foreground sparse component S into a two-dimensional defect map F and calculating a polarization confidence P, a rotation confidence C and a statistical confidence E; calculating a joint noise index N according to the local gray entropy H1 of each spatial pixel in the sequence formed by the rotation angle and the polarization confidence P; processing the two-dimensional defect map F by using the polarization confidence P, the rotation confidence C, the statistical confidence E and the joint noise index N, and outputting an enhanced image. The application can enhance the image and improve the defect detection accuracy.

Description

Technical Field

[0001] This invention relates to the field of semiconductor inspection technology, and in particular to a method for enhancing images of defects in bare silicon wafers based on a dual polarization rotation sequence. Background Technology

[0002] In the detection of surface defects on bare silicon semiconductor wafers, the surface under test has no circuit pattern as a spatial reference background, and the image background is globally uniformly distributed, which makes it easy for submicron-level defect signals to be submerged in background fluctuations and noise.

[0003] In existing technologies, single-frame, single-channel image acquisition is employed. Traditional image enhancement methods first suppress random noise through filtering or multi-frame averaging, and then enhance contrast through histogram equalization. However, while filtering or multi-frame averaging smooths out random noise, it also blurs submicron-level defect edges. When enhancing contrast, it stretches weak defect signals while simultaneously amplifying residual noise, leading to numerous false defects in subsequent threshold segmentation. Furthermore, bare silicon wafer inspection is typically configured on a rotating platform, where the fixed noise inherent in the imaging system exhibits the same grayscale representation as real defects in a single frame image, thus reducing detection accuracy.

[0004] Therefore, it is necessary to provide a new method for enhancing images of defects in bare silicon wafers based on a dual polarization rotation sequence to solve the aforementioned problems in the prior art. Summary of the Invention

[0005] The technical problem this application aims to solve is how to provide a bare silicon wafer defect image enhancement method based on a dual polarization rotation sequence to enhance images and improve defect detection accuracy.

[0006] To address the aforementioned technical problems, according to embodiments of this application, a method for enhancing bare silicon wafer defect images based on a dual-polarization rotation sequence is provided, comprising the following steps: driving the wafer to rotate at fixed angular intervals, synchronously acquiring reflected light images of the s-polarization component and the p-polarization component at each rotation angle formed by the angular intervals to obtain a dual-polarization rotation sequence image; calculating the average polarization difference degree D of each spatial pixel based on the grayscale difference between the s-polarization component and the p-polarization component in the dual-polarization rotation sequence image, and constructing a polarization weight matrix W; decomposing the dual-polarization rotation sequence image into a low-rank background component L and a low-rank foreground component L. The sparse component S is subjected to rotational low-rank constraints and local entropy constraints during the decomposition process, and polarization-weighted sparse constraints are applied based on the polarization weight matrix W to output the foreground sparse component S. The foreground sparse component S is mapped to a two-dimensional defect map F, and the polarization confidence P, rotation confidence C, and statistical confidence E are calculated. The joint noise index N is calculated based on the local gray-level entropy H1 of each spatial pixel in the sequence formed by the rotation angle and the polarization confidence P. The two-dimensional defect map F is processed using the polarization confidence P, the rotation confidence C, the statistical confidence E, and the joint noise index N to output an enhanced image.

[0007] According to an embodiment of this application, calculating the average polarization difference D of each spatial pixel includes: for each spatial pixel, obtaining the normalized grayscale difference between the s-polarization component and the p-polarization component at each rotation angle; averaging the multiple normalized grayscale differences to obtain the average polarization difference D of each spatial pixel; and comparing the average polarization difference D with a preset polarization difference threshold to determine whether the spatial pixel is a polarization aberration pixel.

[0008] According to an embodiment of this application, before decomposing the dual-polarization rotation sequence image into a low-rank background component L and a sparse foreground component S, the method further includes: selecting a known defect-free standard bare silicon wafer and acquiring a dual-polarization rotation sequence image as a background template under the same acquisition conditions; performing low-rank matrix decomposition on the background template to obtain the background component of the background template; dividing the background component into multiple local spatial windows, statistically calculating the gray-level histogram and window gray-level entropy H2 within each local spatial window, and using the maximum value of the window gray-level entropy H2 as the upper limit threshold of the background entropy. The local entropy constraint is used to set the upper limit threshold of the background entropy. As a boundary, for the low-rank background component L, if it exceeds the upper limit threshold of the background entropy within any local spatial window. Constrain the relevant parts.

[0009] According to an embodiment of this application, constructing the polarization weight matrix W includes obtaining the polarization weight of each spatial pixel based on the average polarization difference D. , ,in, For scale parameters, For the first The spatial pixel in the first Polarization weights at rotation angles; the polarization weights The value range is greater than 0 and less than or equal to 1; when the average polarization difference D is 0, the polarization weight is 1; when the average polarization difference D increases, the polarization weight decreases and approaches 0; multiple polarization weights The polarization weight matrix W is formed by arranging the elements.

[0010] According to an embodiment of this application, the step of decomposing the dual-polarization rotation sequence image into a low-rank background component L and a sparse foreground component S includes constructing a joint objective function. Where Y is the observation matrix; ⊙ represents element-wise multiplication; R(L) is the low-rank rotation constraint term; This is a polarization-weighted sparse constraint term; , , These are the weight coefficients of the corresponding constraint terms; the joint objective function is solved using the alternating direction multiplier method, and the background low-rank component L and the foreground sparse component S are output.

[0011] According to an embodiment of this application, the step of mapping the foreground sparse component S to a two-dimensional defect map F and calculating the polarization confidence P, rotation confidence C, and statistical confidence E includes: arranging the foreground sparse component S into a two-dimensional image according to the spatial positions corresponding to each spatial pixel; performing bilinear interpolation on the two-dimensional image to obtain the two-dimensional defect map F; selecting a square region of a preset size as the local statistical window of each spatial pixel; and calculating the local mean of each local statistical window. With local standard deviation The average polarization difference D, the grayscale amplitude of the two-dimensional defect map F, and the local noise base reference are used as a reference for local noise. The polarization confidence P, rotation confidence C, and statistical confidence E are calculated based on the average polarization difference D, the grayscale amplitude of the two-dimensional defect map F, and the local noise base reference.

[0012] According to an embodiment of this application, the calculation of polarization confidence P, rotation confidence C, and statistical confidence E based on the average polarization difference D, the grayscale amplitude of the two-dimensional defect map F, and the local noise substrate reference includes the following steps: the polarization confidence P, rotation confidence C, and statistical confidence E are calculated using the following formulas. , , ,in, and All are calibration parameters; The standard deviation of the two-dimensional defect map F; To avoid division by zero constants.

[0013] According to an embodiment of this application, the step of calculating the joint noise index N based on the local gray-level entropy H1 of each spatial pixel in the sequence formed by the rotation angle and the polarization confidence P includes: calculating the complement of the polarization confidence P; and multiplying the local gray-level entropy H1 by the complement to obtain the joint noise index N.

[0014] According to an embodiment of this application, processing the two-dimensional defect map F using the polarization confidence level P, the rotation confidence level C, the statistical confidence level E, and the joint noise index N includes constructing a gain parameter G. ,in, This is the upper limit of the maximum gain. The noise suppression intensity is determined by multiplying the gain parameter G of each spatial pixel by its grayscale value in the two-dimensional defect map F to output the enhanced image.

[0015] According to embodiments of this application, the method further includes calculating the local gray-level entropy H1. For each spatial pixel, the gray-level values ​​collected sequentially under all rotation angles are arranged in angular order to form a rotation angle sequence. The information entropy is calculated based on the frequency of occurrence of each gray level in the rotation angle sequence to obtain the local gray-level entropy H1. ,in, Let be the frequency of occurrence of gray level t in the rotation angle sequence, where t is a gray level ranging from 0 to 255. To avoid constants whose logarithmic argument is zero.

[0016] By employing the above technical solution, the inherent dual-polarization reflection characteristics of bare silicon wafers, the rotation of bare silicon wafers, and surface statistical uniformity are transformed into joint constraint conditions. Noise suppression and contrast enhancement are achieved through the gain operator G, thus solving the problem of the trade-off between noise suppression and contrast enhancement in patternless image enhancement of bare silicon wafers. Furthermore, the rotational low-rank constraint is used to classify fixed-pattern noise with angular periodicity into the background, solving the problem in existing detection methods where multi-frame averaging cannot eliminate fixed-pattern noise. In addition, the mutual verification of three independent confidence levels—polarization, rotation, and statistics—avoids the amplification of false defects caused by a single threshold, reducing the false detection rate. Attached Figure Description

[0017] Figure 1 This is a step diagram of a method for enhancing images of defects in a bare silicon wafer according to an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by those skilled in the art. The terms "comprising" and similar expressions used herein mean that the element or object preceding the word covers the element or object listed after the word and its equivalents, but does not exclude other elements or objects.

[0019] The following is in conjunction with the appendix Figure 1 The specific embodiments of the present invention will be further described in detail below.

[0020] Embodiments of the present invention provide a method for enhancing images of defects in bare silicon wafers based on a dual-polarization rotation sequence, comprising the following steps: S1. Drive the wafer to rotate at fixed angular intervals, and simultaneously acquire reflected light images of the s-polarization component and the p-polarization component at the rotation angle formed by each angular interval to obtain a dual-polarization rotation sequence image; then align the obtained dual-polarization rotation sequence images in the coordinate system so that the same spatial pixel corresponds to the same position on the wafer. Specifically, since there are no circuit patterns on the surface of the bare silicon wafer as a spatial reference background, and in existing detection methods, single-frame single-channel images are not easy to distinguish between noise and defects, this embodiment uses the inherent Fresnel reflection law of the bare silicon wafer surface as a physical criterion and the rotational symmetry of the wafer surface as a geometric criterion. Wherein, s-polarization (vertical polarization) refers to the polarization component whose electric field vector direction is perpendicular to the incident surface; p-polarization (parallel polarization) refers to the polarization component whose electric field vector direction is parallel to the incident surface; and through the aforementioned acquisition, each spatial pixel simultaneously possesses three judgment conditions: polarization, angle, and grayscale, avoiding the problem of error accumulation caused by step acquisition; more specifically, in this embodiment, the rotation angle range of the fixed angle interval is 5°~10°, preferably 10°; in addition, in order to facilitate the acquisition of reflected light images of s-polarization component and p-polarization component, a polarization beam splitter is set in the illumination optical path to decompose the reflected light of the same illumination optical path into s-polarization component and p-polarization component, which is known to those skilled in the art and will not be elaborated here.

[0021] S2. Based on the grayscale difference between the s-polarization component and the p-polarization component of each spatial pixel in the dual-polarization rotation sequence image, the average polarization difference degree D of each spatial pixel is calculated, and a polarization weight matrix W is constructed. Specifically, existing detection methods perform the same processing steps on each pixel, thus failing to distinguish between isolated grayscale jumps caused by random noise and physical anomalies caused by defects. This results in defects that should be retained being erased, while noise that should be removed is retained. In this embodiment, by calculating the average polarization difference degree D, the physical reliability of each spatial pixel can be determined before decomposing the dual-polarization rotation sequence image into a low-rank background component L and a sparse foreground component S. Pixels with a large polarization difference degree are more likely to be defects, while pixels with a small polarization difference degree are more likely to be background or noise. Based on this, a polarization weight matrix W is constructed, which suppresses random noise and retains the polarization anomalies of defects, thereby reducing the occurrence of situations where noise and defects cannot be distinguished.

[0022] S3. Decompose the dual-polarization rotation sequence image into a background low-rank component L and a foreground sparse component S. Apply rotational low-rank constraints and local entropy constraints to the decomposition process, and output the foreground sparse component S after applying polarization weighted sparsity constraints based on the polarization weight matrix W. Specifically, the polarization weighted sparsity constraint, based on the polarization weight matrix W, allows pixels with large polarization differences to be retained as the foreground sparse component S, while pixels with small polarization differences are assigned to the background low-rank component L. The rotational low-rank constraint utilizes the rotation invariance of the bare silicon wafer surface to force components with angular periodicity, such as illumination gradients and fixed-mode noise, to be assigned to the background low-rank component L. The local entropy constraint is used to set a threshold value above the background entropy. As a boundary, for the low-rank background component L, if it exceeds the upper limit threshold of the background entropy within any local spatial window. The foreground sparse component S is constrained to prevent defect edges or texture artifacts from being mistaken for the background. Three constraints are applied simultaneously, ensuring that defects satisfying all three constraints are preserved in the foreground sparse component S.

[0023] S4. Map the foreground sparse component S to a two-dimensional defect map F and calculate the polarization confidence P, rotation confidence C, and statistical confidence E. Specifically, the foreground sparse component S is represented in matrix form, with rows corresponding to spatial pixels and columns corresponding to rotation angles. The foreground sparse component S needs to be mapped to a two-dimensional image according to the spatial position of each spatial pixel on the wafer surface, and the two-dimensional image is then processed to form the two-dimensional defect map F. Furthermore, a single criterion cannot distinguish all anomalies. For example, lens dust, as noise, is fixed in the image coordinate system, but after wafer coordinate registration, it exhibits positional drift in the rotation sequence, and its polarization anomaly lacks rotational consistency. In contrast, defects maintain a stable spatial position in the registered rotation sequence, and their polarization anomaly exhibits rotational consistency. Thin-film interference may show anomalies in local statistics, but its polarization response is normal. Random noise may occasionally exhibit local statistical jumps, but it is incoherently distributed in the polarization component and rotates randomly. Therefore, in this embodiment, polarization confidence P, rotation confidence C, and statistical confidence E are calculated respectively. Each pixel is examined from three directions: polarization difference, rotational sparsity, and local statistics. Polarization confidence P is used to measure the degree to which a spatial pixel deviates from Fresnel reflection law; rotation confidence C is used to measure the normalized value of the spatial pixel's grayscale amplitude relative to the global standard deviation; and statistical confidence E measures the degree to which a spatial pixel deviates from its local noise basis reference. When all three directions simultaneously support that the spatial pixel is defective, the spatial pixel is determined to be defective. That is, the possibility of misjudgment is reduced through cross-validation of the three criteria.

[0024] S5. Calculate the joint noise index N based on the local gray-level entropy H1 and polarization confidence P of each spatial pixel in the sequence formed by the rotation angle. Specifically, by calculating the joint noise index N, a suppression term opposite to the polarization confidence P, rotation confidence C, and statistical confidence E is constructed for subsequent image enhancement, thereby facilitating the image enhancement process.

[0025] S6. The two-dimensional defect image F is processed using polarization confidence P, rotation confidence C, statistical confidence E, and joint noise index N to output an enhanced image.

[0026] In some embodiments, calculating the average polarization difference D of each spatial pixel includes: for each spatial pixel, obtaining the normalized grayscale difference between its s-polarization component and p-polarization component at each rotation angle; averaging multiple normalized grayscale differences to obtain the average polarization difference D of each spatial pixel; and comparing the average polarization difference D with a preset polarization difference threshold to determine whether the spatial pixel is a polarization aberration pixel. The preset polarization difference threshold is pre-calibrated based on a standard defect-free bare silicon wafer, for example, taking the 95th percentile value of the average polarization difference D distribution in the defect-free region of a standard defect-free bare silicon wafer. In actual inspection, different wafer batches have different preset polarization difference thresholds, and calibration is required before each inspection. When the average polarization difference D exceeds the preset polarization difference threshold, the spatial pixel is determined to be a polarization aberration spatial pixel, indicating that the polarization response of the spatial pixel deviates from the Fresnel reflection law of the ideal bare silicon wafer surface, and there is a possibility of defects or noise, resulting in a large polarization difference. Otherwise, it is determined to be a spatial pixel with polarization within the normal range. By introducing this threshold, spatial pixels with abnormal polarization responses can be quickly screened out during the preprocessing stage.

[0027] In some specific embodiments, for each spatial pixel, the gray values ​​of its s-polarization component and p-polarization component at each rotation angle are obtained and denoted as follows: and ,in For spatial pixel index, The rotation angle index is used; the grayscale difference between the s-polarization component and the p-polarization component is calculated, and the grayscale difference is normalized by dividing it by the sum of the grayscale values ​​of the s-polarization component and the p-polarization component, to obtain the normalized grayscale difference at that rotation angle. ,

[0028] Wherein, v is the polarization balance coefficient pre-calibrated according to the standard defect-free bare silicon wafer, with a value range of 0.8-1.2, preferably 1.0. The polarization balance coefficient v is used to compensate for the system response difference between the s-polarization component and the p-polarization component. To avoid division by zero, for example, take... .

[0029] Normalized grayscale difference at all rotation angles Calculate the arithmetic mean to obtain the average polarization difference D for each spatial pixel.

[0030] Where A is the number of rotation angle samples.

[0031] In some embodiments, before decomposing the dual-polarization rotation sequence image into a low-rank background component L and a sparse foreground component S, the method further includes: selecting a known defect-free standard bare silicon wafer and acquiring a dual-polarization rotation sequence image as a background template under the same acquisition conditions; performing low-rank matrix decomposition on the background template to obtain the background component; dividing the background component into multiple local spatial windows, statistically analyzing the gray-level histogram within each local spatial window and calculating the window gray-level entropy H2, with the maximum value of the window gray-level entropy H2 serving as the upper limit threshold for the background entropy. Local entropy constraints are used to set the upper limit threshold of background entropy. As a boundary, for the low-rank background component L, if it exceeds the upper limit threshold of the background entropy within any local spatial window. The background template is constrained in several ways. Specifically, since the background template is a standard bare silicon wafer known to be defect-free, its surface does not have grayscale anomalies caused by defects. Therefore, the foreground sparse component S of the background template should approach zero under sparse constraints. The background low-rank component L of the background template contains interference components with angular periodicity, such as illumination gradient and fixed-pattern noise. The background template is processed using low-rank decomposition to eliminate the interference of random noise. The calculation method of window grayscale entropy H2 is the same as the subsequent calculation method of local grayscale entropy H1, which will be introduced later and will not be repeated here. In addition, by statistically analyzing the grayscale histogram and calculating the window grayscale entropy H2 in each local spatial window, the fluctuation of the background at different spatial locations can be captured, thereby providing boundary constraints for the background low-rank component L in the subsequent detection process. The maximum value of the entropy in all windows is taken as the upper limit threshold of the background entropy. This ensures that uneven background areas are also covered; if the image of the actual inspected wafer is subsequently decomposed, the gray-level entropy of the obtained low-rank background component L in some local windows exceeds the upper threshold of the background entropy. This indicates an error in the decomposition result, which may have misclassified microscopic lattice textures, thin film interference artifacts, or defect edges into the background. This allows for timely adjustment of the algorithm, preventing the decomposition algorithm from excessively classifying defect components or texture artifacts into the background in order to reduce the overall residual.

[0032] In some embodiments, constructing the polarization weight matrix W includes obtaining the polarization weight of each spatial pixel based on the average polarization difference D. , ,in, For scale parameters, For the first The spatial pixel in the first Polarization weights at rotation angles; polarization weights The value range is greater than 0 and less than or equal to 1; when the average polarization difference D is 0, the polarization weight is 1; as the average polarization difference D increases, the polarization weight decreases and approaches 0; multiple polarization weights The polarization weight matrix W is formed by arranging the pixels. Specifically, since existing detection methods perform the same processing steps for each pixel during decomposition, they cannot distinguish between random noise and real defects. Therefore, it is necessary to obtain the polarization weight of each spatial pixel. By assigning different polarization weights to each spatial pixel, it is possible to distinguish them based on the physical laws of polarization before decomposition. That is, pixels with small polarization differences (more like background or noise) have lower polarization weights. Pixels whose polarization weight approaches 1 are assigned to the background low-rank component L in subsequent decomposition; pixels with large polarization differences (more like defects) have different polarization weights. Approaching 0, it is assigned to the foreground sparse component S in subsequent decomposition; the scale parameter γ ranges from 1.0 to 5.0, preferably 2.0. During the formation of the polarization weight matrix W, the polarization weight of each spatial pixel is... Arranged into a two-dimensional matrix according to spatial pixel index i and rotation angle index j; where the polarization weight of the same spatial pixel at all rotation angles j. The same polarization weights for different spatial pixels The values ​​are determined based on their average polarization difference D.

[0033] In some embodiments, decomposing a dual-polarization rotation sequence image into a low-rank background component L and a sparse foreground component S includes constructing a joint objective function.

[0034] Where Y is the observation matrix; ⊙ represents element-wise multiplication, that is, the values ​​at corresponding positions in the two matrices are directly multiplied; R(L) is the rotation low-rank constraint term; This is a polarization-weighted sparse constraint term; , , These are the weight coefficients of the corresponding constraint terms; the joint objective function is solved using the alternating direction multiplier method, outputting the background low-rank component L and the foreground sparse component S. Specifically, existing methods typically execute the rotation low-rank constraint, polarization weighted sparse constraint, and local entropy constraint as three independent steps sequentially. This causes the error from the previous step to propagate and accumulate, resulting in a continuous increase in error. In this embodiment, each spatial pixel in the dual-polarization rotation sequence image is arranged into a two-dimensional matrix at each rotation angle according to the spatial pixel index i and the rotation angle index j, denoted as the observation matrix Y. The observation matrix Y is the total number of spatial pixels multiplied by the number of rotation angle samples A. By constructing a joint objective function, the observation matrix Y is decomposed into the background low-rank component L and the foreground sparse component S. The objective function contains four terms, the first of which is the data fidelity term, i.e. The first term is the square of the Hilbert-Schmidt norm, used to constrain the sum of the low-rank background component L and the sparse foreground component S, making it approximate the observation matrix Y, thus ensuring that the decomposition result does not deviate from the initial data. The second term is the rotational low-rank constraint term, i.e. R(L) is a rotational low-rank constraint term, which requires that the matrix rank in the direction of the rotation angle of the background low-rank component L does not exceed a preset value, for example, not exceeding 2. The first term is the corresponding weighting coefficient, with a value ranging from 0.01 to 1.0, preferably 0.1. This term is used to utilize the rotational invariance of the bare silicon wafer surface to forcibly classify components with angular periodicity, such as illumination gradients and fixed-mode noise, into the low-rank background component L; the third term is the polarization-weighted sparsity constraint term. ,in It is an L1 norm. The corresponding weighting coefficient ranges from 0.1 to 1.0, with 0.5 being preferred. This term constrains spatial pixels with large polarization differences, making them easier to be assigned to the foreground sparse component S. Spatial pixels with polarization differences in the normal range are assigned to the background. The fourth term is the local entropy constraint term. , where k is the index of the local spatial window, Let H2 be the window grayscale entropy of the k-th local spatial window. The corresponding weighting coefficient has a value range of 1.0-50, preferably 10. This term is used to constrain the window grayscale entropy H2 of the background low-rank component L within any local spatial window to not exceed the upper limit threshold of the background entropy. If the window grayscale entropy H2 of a certain local window exceeds the upper limit threshold of the background entropy, If this happens, the total value of the joint objective function will increase accordingly. However, during the calculation process, the joint objective function aims to reduce the overall objective function value by limiting the value of the local window that exceeds the upper threshold of the background entropy. A portion is redistributed to the foreground sparse component S, thus preventing defect edges or texture artifacts from being incorrectly classified into the background. Finally, the joint objective function is solved iteratively using the alternating direction multiplier method. Specifically, it can be iterated 50-200 times, preferably 100 times, until the difference between the objective function values ​​of two adjacent iterations is less than a preset tolerance, for example... It simultaneously outputs the low-rank background component L and the sparse foreground component S, thus avoiding the inherent defect of error accumulation at each level.

[0035] In some embodiments, mapping the foreground sparse component S to a two-dimensional defect map F and calculating the polarization confidence P, rotation confidence C, and statistical confidence E includes: arranging the foreground sparse component S into a two-dimensional image according to the spatial positions corresponding to each spatial pixel; performing bilinear interpolation on the two-dimensional image to obtain the two-dimensional defect map F; selecting a square region of a preset size as the local statistical window of each spatial pixel; and calculating the local mean of each local statistical window. With local standard deviation The average polarization difference D, the grayscale amplitude of the two-dimensional defect image F, and the local noise basis reference are used as the local noise basis reference. The polarization confidence P, rotation confidence C, and statistical confidence E are calculated. Specifically, the foreground sparse component S is arranged according to spatial pixel index i and rotation angle index j to form a two-dimensional image. Each spatial pixel index corresponds to a unique two-dimensional spatial coordinate in the original dual-polarization rotation sequence image. Since the rotation angle is discretely sampled, there will be discretization error. This discretization error is corrected by bilinear interpolation of the two-dimensional image to eliminate the discretization error, thus obtaining the two-dimensional defect image F.

[0036] In some embodiments, based on the average polarization difference D, the grayscale amplitude of the two-dimensional defect map F, and the local noise substrate reference, the polarization confidence P, rotation confidence C, and statistical confidence E are calculated, including the following formulas: , , ,in, and All are calibration parameters; The standard deviation of the two-dimensional defect graph F is known to those skilled in the art and will not be elaborated here. To avoid division by zero, the following parameters are used: Specifically, the polarization confidence score P measures the degree to which the corresponding spatial pixel deviates from Fresnel's law of reflection; the larger the polarization difference D, the closer the polarization confidence score P is to 1. τ is the polarization difference threshold, ranging from 0.1 to 0.3, preferably 0.2; β is the slope control parameter, ranging from 5 to 10, preferably 7, used to control the slope of the confidence curve. The rotation confidence score C measures the normalized value of the corresponding spatial pixel's grayscale amplitude relative to the global standard deviation, where |F| is the grayscale amplitude of the two-dimensional defect image F at the corresponding spatial pixel. The statistical confidence score E measures the degree to which the corresponding spatial pixel deviates from its local spatial background, where |F| is the grayscale amplitude of the two-dimensional defect image F at the corresponding spatial pixel. μ| is the absolute difference between the grayscale amplitude of the corresponding spatial pixel and the local mean, and σ is the local standard deviation; To avoid division by zero, for example, take... Only when all three criteria are met will a spatial pixel be assigned a high defect confidence level, thereby reducing the false detection rate.

[0037] In some embodiments, the joint noise index N is calculated based on the local gray-level entropy H1 and polarization confidence P of each spatial pixel in the sequence formed by the rotation angle. This includes calculating the complement of the polarization confidence P; multiplying the local gray-level entropy H1 by the complement to obtain the joint noise index N. The sum of the polarization confidence P and its complement is 1, therefore the complement is 1-P, which represents the polarization anomaly degree. Random noise exhibits disordered jumps in the rotation angle sequence, thus its local gray-level entropy H1 is high; simultaneously, random noise is incoherently distributed in the dual polarization components, not disrupting the Fresnel reflectance, thus its polarization anomaly degree is high. Real defects behave in the opposite way. By multiplying the local gray-level entropy H1 by the polarization anomaly degree, noise obtains a high noise index N, and defects obtain a low noise index N, thereby providing a noise suppression term (denominator) for the subsequent gain parameter G, thus facilitating the highlighting of defects.

[0038] In some embodiments, the two-dimensional defect map F is processed using polarization confidence P, rotation confidence C, statistical confidence E, and joint noise index N, including constructing a gain parameter G. ,in, This is the upper limit of the maximum gain. The noise suppression intensity is determined by multiplying the gain parameter G of each spatial pixel by its grayscale value in the 2D defect map F, outputting the enhanced image. The numerator of the gain parameter G is the product of three independent confidence levels, reaching its maximum value only when all three physical mechanisms (polarization, rotation, and statistics) are supported simultaneously. The denominator is a linear function of the joint noise exponent N plus 1; the denominator increases with the noise level. The gain parameter G is applied pixel-by-pixel to the 2D defect map F to obtain the enhanced image. In the background and noise areas, the gain parameter G approaches 1, for example, 1.02, which can be considered as 1, meaning the image grayscale is hardly amplified, achieving noise suppression. In the defect areas, the gain parameter G is greater than 1, for example, 1.2, meaning the defect grayscale is stretched and amplified, achieving contrast enhancement. Notably, when the gain parameter G is greater than 1.1, it is considered that the defect grayscale is stretched and amplified. In addition, there is a maximum gain upper limit. This parameter is used to limit the maximum amplification factor of the gain parameter G, preventing the gain from increasing indefinitely and exceeding the upper limit of the dynamic range of the detection system due to excessively high confidence levels at the defect location; its value ranges from 0.1 to 5.0, preferably 2.0. Noise suppression intensity. The value used to control the degree of noise suppression is in the range of 0.5-2.0, preferably 1.0.

[0039] In some embodiments, the method further includes calculating the local gray-level entropy H1. For each spatial pixel, the gray values ​​collected sequentially at all rotation angles are arranged in angular order to form a rotation angle sequence; the information entropy is calculated based on the frequency of occurrence of each gray level in the rotation angle sequence to obtain the local gray entropy H1.

[0040] in, Let be the frequency of occurrence of gray level t in the rotation angle sequence, where t is a gray level ranging from 0 to 255. To avoid constants whose logarithmic argument is zero, we can take... Specifically, the frequency of occurrence of each gray level is obtained by dividing the number of occurrences of each gray level by the total sequence length (number of rotation angle samples A). The information entropy is calculated based on the frequency of occurrence, resulting in the local gray-level entropy H1. Random noise exhibits disordered gray-level jumps at various rotation angles, with a dispersed gray-level distribution, and its local gray-level entropy H1 is high. Defects, on the other hand, rotate synchronously with the wafer, exist stably at various angles, and have a concentrated gray-level distribution, resulting in a low local gray-level entropy H1.

[0041] While embodiments of the present invention have been described in detail above, it will be apparent to those skilled in the art that various modifications and variations can be made to these embodiments. However, it should be understood that such modifications and variations fall within the scope and spirit of the invention as set forth in the claims. Furthermore, the invention described herein may have other embodiments and can be implemented or carried out in various ways.

Claims

1. A method for enhancing images of defects in bare silicon wafers based on a dual-polarization rotation sequence, characterized in that, Includes the following steps: The wafer is driven to rotate at fixed angular intervals, and reflected light images of s-polarization and p-polarization components are synchronously acquired at the rotation angle formed by each angular interval to obtain a dual-polarization rotation sequence image. Based on the grayscale difference between the s-polarization component and the p-polarization component of each spatial pixel in the dual-polarization rotation sequence image, the average polarization difference degree D of each spatial pixel is calculated, and a polarization weight matrix W is constructed based on the average polarization difference degree D. The dual-polarization rotation sequence image is decomposed into a background low-rank component L and a foreground sparse component S. Rotation low-rank constraints and local entropy constraints are applied to the decomposition process, and the foreground sparse component S is output after applying polarization weighted sparsity constraints based on the polarization weight matrix W. The foreground sparse component S is mapped to a two-dimensional defect map F, and the polarization confidence P, rotation confidence C, and statistical confidence E are calculated. Calculate the joint noise index N based on the local gray-level entropy H1 of each spatial pixel in the sequence formed by the rotation angle and the polarization confidence P; The two-dimensional defect image F is processed using the polarization confidence level P, the rotation confidence level C, the statistical confidence level E, and the joint noise index N to output an enhanced image.

2. The method for enhancing images of defects in bare silicon wafers according to claim 1, characterized in that, The average polarization difference D of each of the spatial pixels is calculated. include, For each spatial pixel, obtain the normalized grayscale difference between the s-polarization component and the p-polarization component at each rotation angle; The average polarization difference D of each spatial pixel is obtained by averaging the multiple normalized grayscale differences. The average polarization difference degree D is compared with a preset polarization difference threshold to determine whether the spatial pixel is a polarization anomalous pixel.

3. The method for enhancing images of defects in bare silicon wafers according to claim 1, characterized in that, Before decomposing the dual-polarization rotation sequence image into a background low-rank component L and a foreground sparse component S, the process also includes: A standard bare silicon wafer known to be defect-free was selected, and dual-polarization rotation sequence images were acquired under the same acquisition conditions as a background template. Perform low-rank matrix decomposition on the background template to obtain the background components of the background template; The background component is divided into multiple local spatial windows. A gray-level histogram is calculated within each local spatial window, and the window gray-level entropy H2 is calculated. The maximum value of the window gray-level entropy H2 is used as the upper limit threshold of the background entropy. ; The local entropy constraint is used to set an upper limit threshold for background entropy. As a boundary, for the low-rank background component L, if it exceeds the upper limit threshold of the background entropy within any local spatial window. Constrain the relevant parts.

4. The method for enhancing images of defects in bare silicon wafers according to claim 1, characterized in that, The construction of the polarization weight matrix W based on the average polarization difference D includes, The polarization weight of each spatial pixel is obtained based on the average polarization difference D. , in, For scale parameters, For the first The spatial pixel in the first Polarization weights at rotation angles; the polarization weights The value range is greater than 0 and less than or equal to 1; when the average polarization difference D is 0, the polarization weight is 1; when the average polarization difference D increases, the polarization weight decreases and approaches 0. Multiple polarization weights The polarization weight matrix W is formed by arranging the elements.

5. The method for enhancing images of defects in bare silicon wafers according to claim 3, characterized in that, The step of decomposing the dual-polarization rotation sequence image into a low-rank background component L and a sparse foreground component S includes, Construct a joint objective function. Where Y is the observation matrix; ⊙ represents element-wise multiplication; R(L) is the rotational low-rank constraint term; This is a polarization-weighted sparse constraint term; , , These are the weight coefficients of the corresponding constraint terms; k is the index of the local spatial window; The joint objective function is solved using the alternating direction multiplier method, and the background low-rank component L and the foreground sparse component S are output.

6. The method for enhancing images of defects in bare silicon wafers according to claim 1, characterized in that, The step of mapping the foreground sparse component S to a two-dimensional defect map F and calculating the polarization confidence P, rotation confidence C, and statistical confidence E includes, The foreground sparse components S are arranged into a two-dimensional image according to the spatial positions corresponding to each spatial pixel. The two-dimensional image is subjected to bilinear interpolation to obtain a two-dimensional defect image F; Centered on each of the spatial pixels, a square region of a preset size is selected as the local statistical window of the spatial pixels; Calculate the local mean of each of the aforementioned local statistical windows. With local standard deviation , as a local noise base reference; Based on the average polarization difference D, the grayscale amplitude of the two-dimensional defect map F, and the local noise substrate reference, the polarization confidence P, rotation confidence C, and statistical confidence E are calculated.

7. The method for enhancing images of defects in bare silicon wafers according to claim 6, characterized in that, The calculation of polarization confidence P, rotation confidence C, and statistical confidence E based on the average polarization difference D, the grayscale amplitude of the two-dimensional defect map F, and the local noise substrate reference includes: The polarization confidence score P, rotation confidence score C, and statistical confidence score E are calculated using the following formulas. in, and All are calibration parameters; The standard deviation of the two-dimensional defect map F; To avoid division by zero constants.

8. The method for enhancing images of defects in bare silicon wafers according to claim 1, characterized in that, The step of calculating the joint noise index N based on the local gray-level entropy H1 of each spatial pixel in the sequence formed by the rotation angle and the polarization confidence P includes, Calculate the complement of the polarization confidence P; Multiplying the local gray-level entropy H1 by the complement value yields the joint noise index N.

9. The method for enhancing images of defects in bare silicon wafers according to claim 1, characterized in that, The two-dimensional defect map F is processed using the polarization confidence level P, the rotation confidence level C, the statistical confidence level E, and the joint noise index N. include, Construct the gain parameter G, in, This is the upper limit of the maximum gain. Noise suppression intensity; The enhanced image is output by multiplying the gain parameter G of each spatial pixel by its grayscale value in the two-dimensional defect map F.

10. The method for enhancing images of defects in bare silicon wafers according to claim 1, characterized in that, It also includes calculating the local gray-scale entropy H1, For each spatial pixel, the gray values ​​collected sequentially at all rotation angles are arranged in angular order to form a rotation angle sequence; The information entropy is calculated based on the frequency of occurrence of each gray level in the rotation angle sequence to obtain the local gray entropy H1. in, Let be the frequency of occurrence of gray level t in the rotation angle sequence, where t is a gray level ranging from 0 to 255. To avoid constants whose logarithmic argument is zero.

Images