Wafer overlay error measurement method based on sub-pixel edge positioning
Patent Information
- Application Number
- CN202610841985.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-11
- Publication Date
- 2026-08-28
AI Technical Summary
[0005]本申请目的是为了解决针对传统对称高斯拟合模型在处理实际晶圆标记边缘梯度非对称及图像噪声干扰时容易产生拟合失真，导致亚像素边缘定位精度受限，最终套刻误差量测准确性差的问题，本申请提供一种基于亚像素边缘定位的晶圆套刻误差测量方法
[0058] This application provides a wafer overlay error measurement method based on subpixel edge localization for box-in-box overlay error measurement. This method achieves subpixel-level measurement of wafer overlay errors through six steps: preprocessing, angle correction, edge region truncation, gradient extraction and coarse localization, weighted asymmetric Gaussian fitting, and rotation reuse. The weighted asymmetric Gaussian fitting allows independent values for the standard deviations on both sides during subpixel edge localization, solving the problem of peak values shifting to the gentler side when the edge gradient is asymmetric in traditional symmetric models.
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Figure CN122652907A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of semiconductor optical inspection and machine vision technology. Background Technology
[0002] In semiconductor lithography, overlay error refers to the positional offset of the current lithographic layer pattern relative to the previous layer pattern. As the feature size of integrated circuits continues to shrink to the nanometer scale, the allowable range of overlay error also shrinks accordingly, and its measurement accuracy directly affects the final chip performance and mass production yield. Overlay error measurement typically employs optical imaging, calculating the relative offset between the inner and outer frames by photographing dedicated overlay marks on the wafer. Current mainstream overlay error measurement methods mostly rely on the alignment system built into the lithography machine or specialized overlay measurement equipment. The underlying algorithms of these devices generally use a symmetrical Gaussian fitting model to perform sub-pixel localization of the mark edges, assuming that the edge gradient signal follows a Gaussian distribution with equal standard deviations on both sides, and using the peak position of the curve fitting as the sub-pixel coordinate of the edge.
[0003] However, in actual wafer manufacturing processes, the aforementioned symmetry assumptions face serious challenges. On the one hand, process fluctuations such as etching, deposition, and chemical mechanical polishing, as well as non-uniform illumination of the imaging system, can cause the edge transition zone of the actual wafer marker to exhibit a significant left-right asymmetry. Forcing asymmetric gradients to conform to a symmetrical curve using symmetrical Gaussian fitting inevitably leads to fitting distortion, with the fitting peak position deviating from the true edge center, causing sub-pixel positioning deviations. On the other hand, wafer marker images inevitably introduce high-frequency random noise, quantization errors, and environmental stray light interference during imaging and transmission. Traditional symmetrical Gaussian fitting is highly sensitive to noise; when the signal-to-noise ratio is low, the fitting results fluctuate significantly, further reducing the stability and repeatability of sub-pixel positioning. Furthermore, existing technologies include overlay error measurement methods based on commercial software such as Halcon. However, their underlying edge positioning algorithms are not publicly available and rely on symmetry assumptions, making it difficult to customize and optimize for specific wafer processes and failing to clearly address the fitting distortion problem caused by edge gradient asymmetry.
[0004] In summary, the existing technology has the following main technical problems: the traditional symmetric Gaussian fitting model is prone to fitting distortion when dealing with the asymmetry of the actual wafer mark edge gradient and image noise interference, which leads to limited sub-pixel edge positioning accuracy and poor accuracy of overlay error measurement. These problems urgently need to be solved. Summary of the Invention
[0005] The purpose of this application is to address the problem that traditional symmetric Gaussian fitting models are prone to fitting distortion when dealing with the asymmetry of actual wafer mark edge gradients and image noise interference, resulting in limited subpixel edge positioning accuracy and ultimately poor accuracy in overlay error measurement. This application provides a wafer overlay error measurement method based on subpixel edge positioning.
[0006] A wafer overlay error measurement method based on sub-pixel edge positioning includes:
[0007] S1. Preprocess the original wafer marker image to obtain the initial binary image of the wafer marker, where the wafer marker is a rectangular frame;
[0008] S2. Extract the closed contour from the initial binary image, calculate the initial center coordinates and deflection angle of the closed contour with the largest area using the minimum bounding rectangle, and then perform angle correction on the original wafer marking image and the initial binary image through affine transformation; the markings corresponding to the largest and smallest closed contours are the outer frame and the inner frame, respectively;
[0009] S3. Determine the regions of interest (ROIs) on the left and right edges of the inner and outer frames in the corrected binary image, and extract the corresponding ROIs from the corrected original wafer marking image.
[0010] S4. Extract one-dimensional gradient signals along the column direction for each edge region of interest. Extract the fitting interval from all one-dimensional gradient signals with the position of the maximum gradient magnitude as the center, and select the maximum gradient magnitude sequence corresponding to the edge region of interest.
[0011] S5. Sub-pixel edge localization is achieved by using weighted asymmetric Gaussian fitting based on all maximum gradient magnitude sequences, and the X-direction overlay error is calculated.
[0012] S6. Rotate the original wafer marking image by 90° and repeat S1 to S5. Use the X-direction overlay error obtained at this time as the Y-direction overlay error before rotation. Combine the X-direction and Y-direction overlay errors to output a two-dimensional overlay error.
[0013] Preferably, in step S1, the initial binary image of the wafer marker is obtained as follows:
[0014] The original wafer marker image is subjected to Gaussian blur denoising, and then adaptive threshold binarization is performed based on the Otsu algorithm to obtain the initial binary image of the wafer marker.
[0015] Preferably, the affine transformation is implemented as follows:
[0016] ;
[0017] in, These represent the x and y coordinates of any pixel in the original wafer marker image or the initial binary image. These are the x and y coordinates of the initial center coordinates, respectively. For the deflection angle, They are respectively for The horizontal and vertical coordinates after angle correction.
[0018] Preferably, in step S3, the method for determining the regions of interest (ROIs) at the left and right edges of the inner and outer frames in the corrected binary image includes:
[0019] Determine the circumscribed rectangles of the inner and outer frames, based on the coordinates of the upper left corner inflection point of the corresponding circumscribed rectangles. ,width and height Determine the regions of interest along the left and right edges of the frame, specifically:
[0020] Each edge region of interest is a rectangle;
[0021] The width of the region of interest on the left and right edges of the frame is defined as follows: Both the pixel count and height are 100. Pixel;
[0022] The x-coordinate of the pixel corresponding to the upper left corner inflection point of the region of interest on the left edge of the frame. ;
[0023] The x-coordinate of the pixel corresponding to the upper left corner of the region of interest on the right edge of the frame ;
[0024] The vertical coordinates of the pixels corresponding to the upper left corner inflection points of the regions of interest on the left and right edges of the frame are both... ;
[0025] according to Determine the region of interest at the left edge of the frame, based on Determine the region of interest at the right edge of the frame;
[0026] in, The coordinates of the upper left corner inflection point of the inner or outer frame's circumscribed rectangle are the x and y coordinates, respectively. For edge scaling factor, It is the horizontal offset in pixels, and .
[0027] Preferably, in step S4, the method for extracting one-dimensional gradient signals along the column direction for each edge region of interest, and selecting the maximum gradient magnitude sequence corresponding to the edge region of interest by truncating the fitting interval centered on the position of the maximum gradient magnitude from all one-dimensional gradient signals, includes:
[0028] S41. Project the region of interest along the column direction for each edge, calculate the average gray value of the pixels column by column, and use the average gray value of the pixels in each column as a one-dimensional gradient signal to construct the one-dimensional gradient signal sequence corresponding to the region of interest.
[0029] S42, Based on preset smoothing coefficient Determine the first to fourth recursive filter coefficients of the Deriche algorithm , , and ;
[0030] S43. Using the Deriche algorithm, perform forward and backward causal recursive filtering on the one-dimensional gradient signal sequence to obtain the forward and backward filtered signals of each one-dimensional gradient signal.
[0031] S44. Based on the forward and backward filtered signals of the same one-dimensional gradient signal, calculate the gradient magnitude of the one-dimensional gradient signal to obtain the gradient magnitude sequence of the edge region of interest.
[0032] S45. Search for the x-coordinate of the position corresponding to the maximum gradient magnitude in the gradient magnitude sequence of the region of interest at the edge. Use this coordinate as the coarse edge center, and expand to the left and right from the pixel corresponding to this edge center. 1 pixel, extract continuous The interval containing the horizontal coordinates of each pixel is taken as the fitting interval. The sequence of gradient magnitudes of the nine pixels corresponding to this fitting interval is taken as the maximum gradient magnitude sequence corresponding to the edge region of interest.
[0033] Preferably, in step S41, ;in,
[0034] For the first Average grayscale value of each column pixel. , The width of the region of interest at the edge; and , For the edge region of interest, For the edge region of interest, the first Line number Column pixel grayscale values;
[0035] In step S42, ;in, It is a natural constant;
[0036] In step S43,
[0037] The expression for the forward-filtered signal of each one-dimensional gradient signal is:
[0038] ;
[0039] The expression for the back-filtered signal of each one-dimensional gradient signal is:
[0040] ;
[0041] in, , and They are the 1st, 2nd and 3rd respectively. The forward-filtered signal of a one-dimensional gradient signal; , and The first , and The back-filtered signal of a one-dimensional gradient signal;
[0042] In S44, the implementation methods for calculating the gradient magnitude of the one-dimensional gradient signal based on the forward and backward filtered signals of the same one-dimensional gradient signal to obtain the gradient magnitude sequence of the region of interest at the edge include:
[0043] ;
[0044] ;
[0045] in, For the first The gradient magnitude of a one-dimensional gradient signal. The gradient magnitude sequence of the region of interest at the edge. The first The forward and backward filtered signals of a one-dimensional gradient signal.
[0046] Preferably, in step S5, sub-pixel edge localization is achieved by weighted asymmetric Gaussian fitting based on all maximum gradient magnitude sequences, and the overlay error in the X direction is calculated using the following methods:
[0047] S51. Preprocess the sequences of each maximum gradient magnitude to obtain the preprocessed gradient magnitude sequences. ,exist Search for the maximum gradient magnitude and its corresponding x-coordinate ,Should Maximum gradient magnitude The horizontal coordinate of the corresponding pixel under coarse positioning; where, The th in the current maximum gradient magnitude sequence The preprocessed gradient magnitude corresponding to each gradient magnitude; ; This represents the total number of gradient magnitudes in the sequence of maximum gradient magnitudes. ;
[0048] S52, according to and Determine the first The intensity weight corresponding to each preprocessed gradient magnitude ;
[0049] S53. Use an asymmetric Gaussian function to model the data within the fitting interval and construct a given parameter vector. The asymmetric Gaussian model ;
[0050] , All of these are parameters to be optimized, and represent the magnitude parameter, the peak center x-coordinate parameter of the asymmetric Gaussian model, the left half-axis standard deviation parameter of the asymmetric Gaussian function, and the right half-axis standard deviation parameter of the asymmetric Gaussian function, respectively. For transpose, The th in the current maximum gradient magnitude sequence The x-coordinate of the pixel corresponding to each gradient magnitude;
[0051] S54, Based on the intensity weights and asymmetric Gaussian model Construct a weighted least squares cost function ;
[0052] S55. Using the Levenberg-Marquardt algorithm, a vector is formed from the initial values of the parameters to be optimized. Starting from the cost function The optimal given parameter vector is obtained through iterative optimization, and the peak center x-coordinate parameter of the optimal asymmetric Gaussian model in the optimal given parameter vector is taken as the maximum gradient magnitude. The corresponding pixel's x-coordinate under fine positioning, and this fine positioning x-coordinate is used as the x-coordinate of the center pixel of the current edge region of interest;
[0053] S56. Take the average value of the x-coordinates of the center pixels of the regions of interest on the left and right edges of the inner frame and the average value of the x-coordinates of the center pixels of the regions of interest on the left and right edges of the outer frame, and use them as the x-coordinates of the center pixels in the horizontal direction of the inner and outer frames, respectively; calculate the deviation between the x-coordinates of the center pixels in the horizontal direction of the inner and outer frames, and use it as the overlay error in the X direction.
[0054] Preferably, .
[0055] Preferably, .
[0056] Preferably, The initial values are all ,and .
[0057] The beneficial effects of this application are:
[0058] This application provides a wafer overlay error measurement method based on subpixel edge localization for box-in-box overlay error measurement. This method achieves subpixel-level measurement of wafer overlay errors through six steps: preprocessing, angle correction, edge region truncation, gradient extraction and coarse localization, weighted asymmetric Gaussian fitting, and rotation reuse. The weighted asymmetric Gaussian fitting allows independent values for the standard deviations on both sides during subpixel edge localization, solving the problem of peak values shifting to the gentler side when the edge gradient is asymmetric in traditional symmetric models.
[0059] By introducing an intensity weighting mechanism and Deriche filtering to smooth the gradient signal, and combining it with asymmetric modeling of left and right double standard deviations, sub-pixel-level details of gradient features are extracted in depth, optimizing the gradient peak finding performance and achieving sub-pixel-level precision edge positioning. This method improves the accuracy and reliability of overlay error measurement, providing a more precise technical means for process control in semiconductor manufacturing. Specific effects include:
[0060] 1. Adapts to asymmetric edges: It adopts a left and right double standard deviation asymmetric Gaussian model, which can fit the asymmetric morphology of the actual wafer mark edge transition zone, effectively solving the fitting distortion problem caused by traditional symmetric models.
[0061] 2. Strong noise resistance: The introduction of an intensity weighting mechanism gives feature points with high signal-to-noise ratio and high gradient intensity greater decision weight, effectively removing the interference of noise outliers and enhancing the robustness of the fit.
[0062] 3. Excellent gradient smoothing and edge preservation: Deriche recursive filtering is used to smooth the one-dimensional gradient signal, which preserves the sharpness of the edges and gradient details to the greatest extent while suppressing high-frequency noise.
[0063] 4. Transparent and customizable algorithm: It does not rely on commercial software, the algorithm is completely open, and the parameters can be optimized for specific wafer processes.
[0064] 5. High measurement accuracy: Through sub-pixel level edge positioning, it can break through the limitation of physical pixel resolution, resolve the true continuous coordinates within the pixel gap, and realize high-precision overlay error measurement. Attached Figure Description
[0065] Figure 1 This is a flowchart of the wafer overlay error measurement method based on sub-pixel edge positioning described in this application;
[0066] Figure 2 It is the original wafer marker image;
[0067] Figure 3This is a schematic diagram of the corresponding edge regions of interest extracted from the corrected original wafer marking image; where the red and green areas are the edge regions of interest of the outer frame and the inner frame, respectively;
[0068] Figure 4 This is a schematic diagram of the closed contour extracted from the initial binary image;
[0069] Figure 5 It is a schematic diagram of the smallest bounding rectangle of the closed contour with the largest area. Detailed Implementation
[0070] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.
[0071] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.
[0072] The present application will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the application.
[0073] Specific Implementation Method 1: Combination Figure 1 This embodiment describes a wafer overlay error measurement method based on sub-pixel edge positioning, which includes:
[0074] S1. Preprocessing:
[0075] Preprocess the original wafer marker image to obtain an initial binary image of the wafer marker, where the wafer marker is a rectangular frame; see [link to documentation]. Figure 2 ;
[0076] This step is used to resolve noise interference and reduce the initial impact of noise on edge localization.
[0077] S2, Angle Correction:
[0078] See Figure 4 The closed contour is extracted from the initial binary image. The initial center coordinates and deflection angle of the closed contour with the largest area are calculated using the minimum bounding rectangle. Then, the angle is corrected by affine transformation of the original wafer marking image and the initial binary image. The markings corresponding to the largest and smallest closed contours are the outer frame and the inner frame, respectively.
[0079] This step is used to resolve gradient extraction bias caused by marker tilt, ensuring that the subsequently extracted one-dimensional gradient signal truly reflects the edge morphology and avoids pseudo-gradient interference introduced by tilt.
[0080] S3, Extract the region of interest at the edge:
[0081] Determine the regions of interest (ROIs) for the left and right edges of the inner and outer frames in the corrected binary image, and extract the corresponding ROIs from the corrected original wafer marker image; see [link to relevant documentation]. Figure 3 ;
[0082] This step addresses noise interference in irrelevant regions by precisely truncating the regions of interest at the left and right edges of the inner and outer bounding boxes, limiting the analysis scope to the vicinity of the edge transition zone. This removes noise from flat areas far from the edges, reducing the computational cost of subsequent fitting, and more importantly, avoiding interference from large-amplitude noise points in irrelevant regions on the gradient peak search.
[0083] S4. Extract gradients and cut off the fitting interval, then filter out the sequence of maximum gradient magnitudes corresponding to the regions of interest at the edges:
[0084] One-dimensional gradient signals are extracted along the column direction for each edge region of interest. The fitting interval is truncated from all one-dimensional gradient signals with the position of the maximum gradient magnitude as the center, and the maximum gradient magnitude sequence corresponding to the edge region of interest is selected.
[0085] This step truncates the fitting interval with the location of the maximum gradient magnitude as the center. This ensures that the data window for subsequent subpixel fitting focuses on the core region of the edge transition zone and stays away from noise interference in flat areas.
[0086] S5 and X-direction overlay error calculation:
[0087] Sub-pixel edge localization is achieved by using weighted asymmetric Gaussian fitting based on all maximum gradient magnitude sequences, and the X-direction overlay error is calculated.
[0088] This step is used to address fitting distortion caused by asymmetric edge gradients and interference from noise points. Asymmetric Gaussian fitting is introduced to solve asymmetric fitting distortion, and weighting methods are introduced to resolve noise interference.
[0089] S6, X-direction overlay error calculation and synthesis:
[0090] Rotate the original wafer marking image by 90° and repeat steps S1 to S5. Use the X-direction overlay error obtained at this time as the Y-direction overlay error before rotation. Combine the X-direction and Y-direction overlay errors to output a two-dimensional overlay error.
[0091] In this step, rotating the image by 90° makes the Y-axis edge of the original image horizontal, allowing the same gradient extraction and fitting process to be reused. This mechanism ensures that the X and Y directions use the exact same algorithm parameters and accuracy, avoiding the inconsistencies that would result from designing a separate algorithm for the Y direction.
[0092] Furthermore, in step S1, the initial binary image of the wafer marker is obtained as follows:
[0093] The original wafer marker image is subjected to Gaussian blur denoising, and then adaptive threshold binarization is performed based on the Otsu algorithm to obtain the initial binary image of the wafer marker.
[0094] In the above process, Gaussian blur is applied to the original wafer marker image to denoise it, suppressing high-frequency random noise introduced during imaging and transmission. Otsu adaptive threshold binarization separates the marker from the background, providing clean input for subsequent contour extraction. This is the first line of defense against noise, reducing the initial impact of noise on edge localization.
[0095] Furthermore, the implementation method of affine transformation is given as follows:
[0096] ;
[0097] in, These represent the x and y coordinates of any pixel in the original wafer marker image or the initial binary image. These are the x and y coordinates of the initial center coordinates, respectively. For the deflection angle, They are respectively for The horizontal and vertical coordinates after angle correction.
[0098] Furthermore, in step S3, the method for determining the regions of interest (ROIs) at the left and right edges of the inner and outer frames in the corrected binary image includes:
[0099] Determine the circumscribed rectangles of the inner and outer frames, based on the coordinates of the upper left corner inflection point of the corresponding circumscribed rectangles. ,width and height Determine the regions of interest along the left and right edges of the frame, specifically:
[0100] Each edge region of interest is a rectangle;
[0101] The width of the region of interest on the left and right edges of the frame is defined as follows: Both the pixel count and height are 100. Pixel;
[0102] The x-coordinate of the pixel corresponding to the upper left corner inflection point of the region of interest on the left edge of the frame. ;
[0103] The x-coordinate of the pixel corresponding to the upper left corner of the region of interest on the right edge of the frame ;
[0104] The vertical coordinates of the pixels corresponding to the upper left corner inflection points of the regions of interest on the left and right edges of the frame are both... ;
[0105] according to Determine the region of interest at the left edge of the frame, based on Determine the region of interest at the right edge of the frame;
[0106] in, The coordinates of the upper left corner inflection point of the inner or outer frame's circumscribed rectangle are the x and y coordinates, respectively. As the marginal scaling factor, it is generally taken as , It is the horizontal offset in pixels, and .
[0107] In determining the regions of interest (ROIs) on the left and right edges of the frame, this preferred method uses the geometric parameters of the circumscribed rectangle to calculate the coordinates and size of the ROIs on the left and right edges, precisely limiting the analysis range to the edge transition zone. The left and right edges are extracted separately, avoiding interference from the top and bottom edges, the height is adaptively marked with a size, and the width is fixed, providing clean and accurate input data for subsequent gradient extraction and sub-pixel fitting.
[0108] Furthermore, in step S4, one-dimensional gradient signals are extracted along the column direction for each edge region of interest. The fitting interval is then truncated from all one-dimensional gradient signals, centered on the position of the maximum gradient magnitude, to select the sequence of maximum gradient magnitudes corresponding to that edge region of interest. The implementation methods include:
[0109] S41. Project the region of interest along the column direction for each edge, calculate the average pixel gray value column by column, and use the average pixel gray value of each column as a one-dimensional gradient signal to construct the one-dimensional gradient signal sequence corresponding to the region of interest. ;in,
[0110] For the first Average grayscale value of each column pixel. , The width of the region of interest at the edge; and , For the edge region of interest, For the edge region of interest, the first Line number Column pixel grayscale values;
[0111] Because 2D image data is large, direct calculation is too slow, and the grayscale value of a single pixel jumps around due to noise, making it easy to find incorrect edges. Therefore, this step transforms the 2D image into a 1D signal, where a region of interest at an edge originally has... OK Lieutenant General Each pixel, after projection, becomes The number of values significantly reduces the amount of data. Averaging column by column also eliminates random noise along the column direction, naturally improving the signal-to-noise ratio. In this one-dimensional signal, the value of each column reflects the overall brightness of that column from top to bottom; the edges are indicated by dramatic changes in these values.
[0112] S42, Based on preset smoothing coefficient Determine the first to fourth recursive filter coefficients of the Deriche algorithm , , and Specifically,
[0113] ;in, It is a natural constant;
[0114] Preset smoothing coefficient Used to control smoothing intensity Smaller values result in stronger noise reduction, but the edges will become wider. Larger values preserve edges well but have weaker noise reduction. They can be flexibly adjusted according to the noise level of the actual image. Therefore, [the following can be done]: The value can be 1.8, which combines the effects of both aspects.
[0115] S43. Using the Deriche algorithm, perform forward and backward causal recursive filtering on the one-dimensional gradient signal sequence to obtain the forward and backward filtered signals of each one-dimensional gradient signal; specifically...
[0116] The expression for the forward-filtered signal of each one-dimensional gradient signal is:
[0117] ;
[0118] The expression for the back-filtered signal of each one-dimensional gradient signal is:
[0119] ;
[0120] in, , and They are the 1st, 2nd and 3rd respectively. The forward-filtered signal of a one-dimensional gradient signal; , and The first , and The back-filtered signal of a one-dimensional gradient signal;
[0121] Because unidirectional filtering (only forward or only backward) causes signal phase shift, edge positions will deviate to the left or right from their true positions. Ordinary filtering methods, while smoothing noise, also flatten edges, making them blurry and reducing gradient peaks, which is detrimental to subsequent peak detection. Therefore, in this step, forward filtering is calculated from left to right, and backward filtering from right to left. The results of the two filtering processes are then combined. The filtered signal has no phase shift, and the edge positions are consistent with those of the original signal. Recursive filtering correlates the output of the current point with the output of the previous (or next) point, making the signal smoother and more continuous. Local glitches are suppressed, but the overall step changes remain, and the sharpness of the edges is preserved.
[0122] S44. Based on the forward and backward filtered signals of the same one-dimensional gradient signal, calculate the gradient magnitude of the one-dimensional gradient signal to obtain the gradient magnitude sequence of the region of interest at the edge; specifically,
[0123] ;
[0124] ;
[0125] in, For the first The gradient magnitude of a one-dimensional gradient signal. The gradient magnitude sequence of the region of interest at the edge. The first The forward and backward filtered signals of a one-dimensional gradient signal.
[0126] The gradient magnitude is obtained by subtracting the filtered signals from the preceding and following steps. This magnitude represents the degree of drastic change in grayscale in each column. The larger the change, the higher the magnitude; the smaller the change, the lower the magnitude. The edges are precisely where the grayscale changes are most drastic, so the peak value in the gradient magnitude sequence is the column where the edge is located. Since step S43 has already smoothed out the noise, the peak value here will not jump back and forth due to individual noise points, and the coarsely located position is stable.
[0127] S45. Search for the x-coordinate of the position corresponding to the maximum gradient magnitude in the gradient magnitude sequence of the region of interest at the edge. Use this coordinate as the coarse edge center, and expand to the left and right from the pixel corresponding to this edge center. 1 pixel, extract continuous The interval containing the x-coordinates of each pixel is used as the fitting interval. The sequence of gradient magnitudes of the nine pixels corresponding to this fitting interval is taken as the sequence of maximum gradient magnitudes corresponding to the region of interest at the edge. In practical applications, The optimal value is 9.
[0128] The peak values of the gradient magnitude sequence only provide the edge location at the integer pixel level, which is insufficient precision. To obtain sub-pixel precision, curve fitting is needed on the data near the peak values. First, use the maximum magnitude value for coarse localization to determine roughly which column the edge is in. Then, take 4 points to the left and 4 points to the right of this column as the midpoint, for a total of 9 points. These 9 points precisely cover the core area of the edge transition zone. The edge transition typically occurs within a few pixels from its inception to its conclusion.
[0129] Furthermore, S5, sub-pixel edge localization is achieved by using weighted asymmetric Gaussian fitting based on all maximum gradient magnitude sequences. The calculation of the X-direction overlay error includes the following methods:
[0130] S51. Preprocess the sequences of each maximum gradient magnitude to obtain the preprocessed gradient magnitude sequences. ,exist Search for the maximum gradient magnitude and its corresponding x-coordinate ,Should Maximum gradient magnitude The horizontal coordinate of the corresponding pixel under coarse positioning;
[0131] Specifically, the preprocessing method for each maximum gradient magnitude sequence is as follows:
[0132] Find the minimum value of the amplitude sequence within the current fitted interval. Subtract the minimum value from each amplitude within the interval to eliminate the baseline effect;
[0133] ;
[0134] , For the fitted interval, the first The x-coordinate of each pixel;
[0135] The th in the current maximum gradient magnitude sequence The preprocessed gradient magnitude corresponding to each gradient magnitude; ; This represents the total number of gradient magnitudes in the sequence of maximum gradient magnitudes. ; The optimal value is 9;
[0136] S52, according to and Determine the first The intensity weight corresponding to each preprocessed gradient magnitude ;
[0137] The intensity weighting mechanism assigns greater decision weights to feature points with high signal-to-noise ratios and high gradient strengths (points near the peak), and smaller weights to feature points with low signal-to-noise ratios and low gradient strengths (points far from the peak or affected by noise). In the subsequent weighted least squares cost function, the higher weights dominate the fitting result, effectively removing the interference of noise outliers and enhancing the robustness of the fitting.
[0138] S53. Use an asymmetric Gaussian function to model the data within the fitting interval and construct a given parameter vector. The asymmetric Gaussian model ;
[0139] ;
[0140] , All of these are parameters to be optimized, and represent the magnitude parameter, the peak center x-coordinate parameter of the asymmetric Gaussian model, the left half-axis standard deviation parameter of the asymmetric Gaussian function, and the right half-axis standard deviation parameter of the asymmetric Gaussian function, respectively. The initial values are all ,experience , For transpose, The th in the current maximum gradient magnitude sequence The x-coordinate of the pixel corresponding to each gradient magnitude;
[0141] Asymmetric Gaussian Model It allows for different widths on the left and right sides, which can fit the asymmetric morphology of the actual wafer mark edge transition zone;
[0142] S54, Based on the intensity weights and asymmetric Gaussian model Construct a weighted least squares cost function ;
[0143] .
[0144] S55. Using the Levenberg-Marquardt algorithm, a vector is formed from the initial values of the parameters to be optimized. Starting from the cost function The optimal given parameter vector is obtained through iterative optimization, and the peak center x-coordinate parameter of the optimal asymmetric Gaussian model in the optimal given parameter vector is taken as the maximum gradient magnitude. The corresponding pixel's x-coordinate under fine positioning, and this fine positioning x-coordinate is used as the x-coordinate of the center pixel of the current edge region of interest; ;
[0145] S56. Take the average value of the x-coordinates of the center pixels of the regions of interest on the left and right edges of the inner frame and the average value of the x-coordinates of the center pixels of the regions of interest on the left and right edges of the outer frame, and use them as the x-coordinates of the center pixels in the horizontal direction of the inner and outer frames, respectively; calculate the deviation between the x-coordinates of the center pixels in the horizontal direction of the inner and outer frames, and use it as the overlay error in the X direction.
[0146] In the process of calculating the X-direction overlay error, asymmetric Gaussian modeling allows the left and right sides to independently adapt to the actual edge shape, solving the positioning deviation caused by asymmetric edges. The intensity weighting mechanism allows high signal-to-noise ratio points to dominate the fitting process, solving the fitting instability caused by noise interference. Baseline elimination, peak search, and the Levenberg-Marquardt algorithm together ensure efficient convergence and stable output of the fitting, resulting in a more accurate and stable X-direction overlay error than traditional methods.
[0147] While this application has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.
Claims
1. A wafer overlay error measurement method based on sub-pixel edge positioning, characterized in that, include: S1. Preprocess the original wafer marker image to obtain the initial binary image of the wafer marker, where the wafer marker is a rectangular frame; S2. Extract the closed contour from the initial binary image, calculate the initial center coordinates and deflection angle of the closed contour with the largest area using the minimum bounding rectangle, and then perform angle correction on the original wafer marking image and the initial binary image through affine transformation; the markings corresponding to the largest and smallest closed contours are the outer frame and the inner frame, respectively; S3. Determine the regions of interest (ROIs) on the left and right edges of the inner and outer frames in the corrected binary image, and extract the corresponding ROIs from the corrected original wafer marking image. S4. Extract one-dimensional gradient signals along the column direction for each edge region of interest. Extract the fitting interval from all one-dimensional gradient signals with the position of the maximum gradient magnitude as the center, and select the maximum gradient magnitude sequence corresponding to the edge region of interest. S5. Sub-pixel edge localization is achieved by using weighted asymmetric Gaussian fitting based on all maximum gradient magnitude sequences, and the X-direction overlay error is calculated. S6. Rotate the original wafer marking image by 90° and repeat S1 to S5. Use the X-direction overlay error obtained at this time as the Y-direction overlay error before rotation. Combine the X-direction and Y-direction overlay errors to output a two-dimensional overlay error.
2. The wafer overlay error measurement method based on sub-pixel edge positioning according to claim 1, characterized in that, In step S1, the initial binary image of the wafer marker is obtained as follows: The original wafer marker image is subjected to Gaussian blur denoising, and then adaptive threshold binarization is performed based on the Otsu algorithm to obtain the initial binary image of the wafer marker.
3. The wafer overlay error measurement method based on sub-pixel edge positioning according to claim 1, characterized in that, The affine transformation is implemented as follows: ； in, These represent the x and y coordinates of any pixel in the original wafer marker image or the initial binary image. These are the x and y coordinates of the initial center coordinates, respectively. For the deflection angle, They are respectively for The horizontal and vertical coordinates after angle correction.
4. The wafer overlay error measurement method based on sub-pixel edge positioning according to claim 1, characterized in that, In step S3, the methods for determining the regions of interest (ROIs) at the left and right edges of the inner and outer frames in the corrected binary image include: Determine the circumscribed rectangles of the inner and outer frames, based on the coordinates of the upper left corner inflection point of the corresponding circumscribed rectangles. ,width and height Determine the regions of interest along the left and right edges of the frame, specifically: Each edge region of interest is a rectangle; The width of the region of interest on the left and right edges of the frame is defined as follows: Both the pixel count and height are 100%. Pixel; The x-coordinate of the pixel corresponding to the upper left corner inflection point of the region of interest on the left edge of the frame. ; The x-coordinate of the pixel corresponding to the upper left corner inflection point of the region of interest on the right edge of the frame. ; The vertical coordinates of the pixels corresponding to the upper left corner inflection points of the regions of interest on the left and right edges of the frame are both... ; according to Determine the region of interest at the left edge of the frame, based on Determine the region of interest at the right edge of the frame; in, The coordinates of the upper left corner inflection point of the inner or outer frame's circumscribed rectangle are the x and y coordinates, respectively. For edge scaling factor, It is the horizontal offset in pixels, and .
5. The wafer overlay error measurement method based on sub-pixel edge positioning according to claim 1, characterized in that, In step S4, one-dimensional gradient signals are extracted along the column direction for each edge region of interest. The fitting interval is then truncated from all one-dimensional gradient signals, centered on the position of the maximum gradient magnitude. The methods for selecting the maximum gradient magnitude sequence corresponding to the edge region of interest include: S41. Project the region of interest along the column direction for each edge, calculate the average gray value of the pixels column by column, and use the average gray value of the pixels in each column as a one-dimensional gradient signal to construct the one-dimensional gradient signal sequence corresponding to the region of interest. S42, Based on preset smoothing coefficient Determine the first to fourth recursive filter coefficients of the Deriche algorithm , , and ; S43. Using the Deriche algorithm, perform forward and backward causal recursive filtering on the one-dimensional gradient signal sequence to obtain the forward and backward filtered signals of each one-dimensional gradient signal. S44. Based on the forward and backward filtered signals of the same one-dimensional gradient signal, calculate the gradient magnitude of the one-dimensional gradient signal to obtain the gradient magnitude sequence of the edge region of interest. S45. Search for the x-coordinate of the position corresponding to the maximum gradient magnitude in the gradient magnitude sequence of the region of interest at the edge. Use this coordinate as the coarse edge center, and expand to the left and right from the pixel corresponding to this edge center. 1 pixel, extract continuous The interval containing the horizontal coordinates of each pixel is taken as the fitting interval. The sequence of gradient magnitudes of the nine pixels corresponding to this fitting interval is taken as the maximum gradient magnitude sequence corresponding to the edge region of interest.
6. The wafer overlay error measurement method based on sub-pixel edge positioning according to claim 5, characterized in that, In step S41, ;in, For the first Average grayscale value of each column pixel. , The width of the region of interest at the edge; and , For the edge region of interest, For the edge region of interest, the first Line number Column pixel grayscale values; In step S42, ;in, It is a natural constant; In step S43, The expression for the forward-filtered signal of each one-dimensional gradient signal is: ； The expression for the back-filtered signal of each one-dimensional gradient signal is: ； in, , and They are the 1st, 2nd and 3rd respectively. The forward-filtered signal of a one-dimensional gradient signal; , and The first , and The back-filtered signal of a one-dimensional gradient signal; In S44, the implementation methods for calculating the gradient magnitude of the one-dimensional gradient signal based on the forward and backward filtered signals of the same one-dimensional gradient signal to obtain the gradient magnitude sequence of the region of interest at the edge include: ； ； in, For the first The gradient magnitude of a one-dimensional gradient signal. The gradient magnitude sequence of the region of interest at the edge. The first The forward and backward filtered signals of a one-dimensional gradient signal.
7. The wafer overlay error measurement method based on sub-pixel edge positioning according to claim 1, characterized in that, S5. Sub-pixel edge localization is achieved using weighted asymmetric Gaussian fitting based on all maximum gradient magnitude sequences. The methods for calculating the X-direction overlay error include: S51. Preprocess the sequences of each maximum gradient magnitude to obtain the preprocessed gradient magnitude sequences. ,exist Search for the maximum gradient magnitude and its corresponding x-coordinate ,Should Maximum gradient magnitude The horizontal coordinate of the corresponding pixel under coarse positioning; where, The th in the current maximum gradient magnitude sequence The preprocessed gradient magnitude corresponding to each gradient magnitude; ; This represents the total number of gradient magnitudes in the sequence of maximum gradient magnitudes. ; S52, according to and Determine the first The intensity weight corresponding to each preprocessed gradient magnitude ; S53. Use an asymmetric Gaussian function to model the data within the fitting interval and construct a given parameter vector. The asymmetric Gaussian model ; , All of these are parameters to be optimized, and represent the magnitude parameter, the peak center x-coordinate parameter of the asymmetric Gaussian model, the left half-axis standard deviation parameter of the asymmetric Gaussian function, and the right half-axis standard deviation parameter of the asymmetric Gaussian function, respectively. For transpose, The th in the current maximum gradient magnitude sequence The x-coordinate of the pixel corresponding to each gradient magnitude; S54. Based on the intensity weights Asymmetric Gaussian Model Construct a weighted least squares cost function ; S55. Using the Levenberg-Marquardt algorithm, a vector is formed from the initial values of the parameters to be optimized. Starting from the cost function The optimal given parameter vector is obtained through iterative optimization, and the peak center x-coordinate parameter of the optimal asymmetric Gaussian model in the optimal given parameter vector is taken as the maximum gradient magnitude. The corresponding pixel's x-coordinate under fine positioning, and this fine positioning x-coordinate is used as the x-coordinate of the center pixel of the current edge region of interest; S56. Take the average value of the x-coordinates of the center pixels of the regions of interest on the left and right edges of the inner frame and the average value of the x-coordinates of the center pixels of the regions of interest on the left and right edges of the outer frame, and use them as the x-coordinates of the center pixels in the horizontal direction of the inner and outer frames, respectively; calculate the deviation between the x-coordinates of the center pixels in the horizontal direction of the inner and outer frames, and use it as the overlay error in the X direction.
8. The wafer overlay error measurement method based on sub-pixel edge positioning according to claim 7, characterized in that, 。 9. The wafer overlay error measurement method based on sub-pixel edge positioning according to claim 7, characterized in that, 。 10. The wafer overlay error measurement method based on sub-pixel edge positioning according to claim 7, characterized in that, The initial values are all ,and .