A visual coordinate calibration method for patternless wafer inspection

Abstract

This application relates to a visual coordinate calibration method for patternless wafer inspection, comprising the following steps: acquiring a reference speckle image; moving the wafer through multiple sets of different movements, acquiring multiple frames of motion-blurred speckle images during camera exposure; dividing each frame of motion-blurred speckle image into local regions, obtaining the motion-blurred trajectory geometric parameters for each local region, including the motion-blurred trajectory length, direction, and center position; obtaining the speckle displacement field based on the reference speckle image and the motion-blurred speckle image; determining the distortion parameters of the vision system based on the motion-blurred trajectory geometric parameters; determining the geometric error parameters of wafer movement based on the speckle displacement field and the center position of the motion-blurred trajectory; and obtaining visual coordinates based on the distortion parameters and the geometric error parameters. This invention enables coordinate calibration on the surface of patternless wafers.

Description

Technical Field

[0001] This invention relates to the field of semiconductor technology, and in particular to a visual coordinate calibration method for patternless wafer inspection. Background Technology

[0002] In semiconductor integrated circuit manufacturing processes, surface defect detection and film thickness measurement of unpatterned bare silicon wafers require the establishment of a high-precision mapping relationship between the pixel coordinates of the visual imaging system and the physical coordinates of the stage.

[0003] In the existing technology, the surface of bare silicon wafers lacks circuit pattern textures that can be directly tracked by image algorithms, and the detection chamber is usually in a vacuum or clean environment, making it impossible to introduce external calibration boards or artificial calibration objects. This makes traditional visual calibration methods based on checkerboard patterns or feature points unsuitable for direct application.

[0004] Therefore, it is necessary to provide a new visual coordinate calibration method for patternless wafer inspection to solve the above-mentioned problems in the prior art. Summary of the Invention

[0005] The technical problem to be solved by this application is how to provide a visual coordinate calibration method for patternless wafer inspection that enables coordinate calibration on the surface of a patternless wafer.

[0006] To address the aforementioned technical problems, according to embodiments of this application, a visual coordinate calibration method for patternless wafer inspection is provided, comprising the following steps: irradiating the wafer with a single-mode laser to form a reference speckle image; driving the wafer to perform multiple sets of different movements, acquiring multiple frames of motion-blurred speckle images during camera exposure; dividing each frame of the motion-blurred speckle image into local regions, obtaining the motion-blurred trajectory geometric parameters of each local region, the motion-blurred trajectory geometric parameters including the motion-blurred trajectory length, motion-blurred trajectory direction, and motion-blurred trajectory center position; obtaining a speckle displacement field based on the reference speckle image and the motion-blurred speckle image; determining the distortion parameters of the vision system based on the motion-blurred trajectory geometric parameters; determining the geometric error parameters of wafer movement based on the speckle displacement field and the motion-blurred trajectory center position; and obtaining visual coordinates based on the distortion parameters and the geometric error parameters.

[0007] According to an embodiment of this application, the step of irradiating a wafer with a single-mode laser to form a reference speckle image includes: setting a beam expander group in the optical path of the single-mode laser so that the laser speckle pattern of the single-mode laser covers the field of view to be calibrated; and using short exposure to acquire the laser speckle pattern to form the reference speckle image.

[0008] According to embodiments of this application, the step of driving the wafer to perform multiple sets of different movements and acquiring multiple frames of motion-blurred speckle images during camera exposure includes: controlling the stage to drive the wafer to translate at a constant speed along the X direction, or controlling the stage to drive the wafer to translate at a constant speed along the Y direction, to change the position of the wafer so that the motion-blurred trajectory appears at different radial distances on the image plane; controlling the stage to drive the wafer to rotate around the Z-axis at a constant angular velocity, and acquiring multiple frames of motion-blurred speckle images during camera exposure at multiple rotation phases to obtain the Abbe arm error and rotational eccentricity of the stage; and controlling the stage to simultaneously translate along the X direction and rotate around the Z-axis, and acquiring multiple frames of motion-blurred speckle images during camera exposure to obtain the interaxial non-perpendicularity between the X-axis and Y-axis of the stage.

[0009] According to an embodiment of this application, the step of dividing each frame of motion-blurred speckle image into local regions and obtaining the geometric parameters of the motion-blurred trajectory of each local region includes: dividing each frame of motion-blurred speckle image into multiple local sub-regions, each local sub-region having a pixel size of 64*64, and maintaining a 45-55% overlap rate between adjacent local sub-regions; performing a discrete Fourier transform on each local sub-region to detect null positions in the spectrum, obtaining the length of the motion-blurred trajectory based on the null positions, and determining the direction of the motion-blurred trajectory based on the peak value of the spectrum energy distribution in polar coordinates; using the center pixel coordinates of the local sub-region as the center position of the motion-blurred trajectory; and correcting the length and direction of the motion-blurred trajectory using the autocorrelation function of the speckle pattern.

[0010] According to an embodiment of this application, obtaining the speckle displacement field based on the reference speckle image and the motion-blurred speckle image includes: performing Wiener filtering deconvolution on a local sub-region of the motion-blurred speckle image to obtain a restored speckle pattern; performing normalized cross-correlation operation between the restored speckle pattern and the local sub-region, and obtaining the speckle displacement field through pixel interpolation and peak fitting; performing consistency verification on the speckle displacement field, and if the angle between the displacement direction and the trajectory direction exceeds 15 degrees, or the ratio of the displacement amplitude to the length of the motion-blurred trajectory exceeds a preset range, then the displacement is discarded.

[0011] According to an embodiment of this application, determining the distortion parameters of the visual system based on the geometric parameters of the motion-blurred trajectory includes: determining the radial distortion coefficient based on the relationship between the length of the motion-blurred trajectory and the radial distance; determining the tangential distortion coefficient based on the residual between the direction of the motion-blurred trajectory and the ideal direction; and determining the principal point coordinates based on the symmetry of the distribution of the length of the motion-blurred trajectory near the principal point.

[0012] According to an embodiment of this application, determining the geometric error parameters of the wafer movement based on the speckle displacement field and the trajectory center position includes: determining the Abbe arm error based on the deviation between the center position of the motion fuzzy trajectory and the ideal circular trajectory; determining the interaxial non-perpendicularity based on the deflection of the motion fuzzy trajectory direction relative to the command direction; and determining the rotational eccentricity based on the vortex center position of the speckle displacement field.

[0013] According to an embodiment of this application, obtaining visual coordinates based on the distortion parameter and the geometric error parameter includes: fixing the geometric error parameter to zero, optimizing the distortion parameter based on the geometric parameters of the motion blur trajectory; fixing the optimized distortion parameter, optimizing the geometric error parameter based on the speckle displacement field; using the optimized distortion parameter and the optimized geometric error parameter as initial values, jointly optimizing the distortion parameter and the geometric error parameter until the change in the distortion parameter is less than a first preset threshold and the change in the geometric error parameter is less than a second preset threshold; establishing a mapping relationship between pixel coordinates and physical coordinates to obtain the visual coordinates.

[0014] According to an embodiment of this application, before the joint optimization, the method further includes: calculating a second-order partial derivative submatrix A with respect to the distortion parameters and a second-order partial derivative submatrix B with respect to the geometric error parameters; if the ratio of the maximum eigenvalue to the minimum eigenvalue of each of the second-order partial derivative submatrix A and the second-order partial derivative submatrix B is less than... ,and Where a is an element of the second-order partial derivative submatrix A, b is an element of the second-order partial derivative submatrix B, and c is an element of the cross submatrix of the second-order partial derivative submatrix A and the second-order partial derivative submatrix B; then it is determined that the distortion parameter and the geometric error parameter of the wafer movement can be independently identified.

[0015] According to an embodiment of this application, after obtaining the visual coordinates, the method further includes: using the distortion parameters and geometric error parameters in the visual coordinates to predict the geometric parameters and speckle displacement of the motion blur trajectory that was not optimized, to obtain predicted values; comparing the predicted values ​​with the measured values; if... and ,in, The predicted length of the motion-blurred trajectory, N represents the measured length of the motion-blurred trajectory, and N is the total number of sampling points for the length of the motion-blurred trajectory. For the predicted speckle displacement, Let M be the measured speckle displacement, and M be the total number of sampling points for the speckle displacement; then the calibration accuracy is deemed to meet the requirements.

[0016] By employing the above technical solution, a single-mode laser irradiates the surface of a bare silicon wafer. The micro-roughness of the bare silicon surface causes scattering interference of coherent light, forming a stable laser speckle pattern. This creates a texture recognizable by algorithms on a surface without circuit patterns, meeting the pattern requirements for visual calibration without the need for external calibration objects. By actively controlling the stage to perform multiple sets of different movements, the wafer motion information is encoded into the geometric parameters of the blurred motion trajectory and the speckle displacement field in the motion-blurred speckle image during camera exposure. This transforms the motion blur that needs to be suppressed in traditional imaging into a geometric information carrier, thus realizing the distortion correction of the visual system. Orthogonal separation and joint optimization calibration of parameters and stage geometric error parameters; a staged optimization strategy is adopted, first fixing the geometric error parameters and optimizing the distortion parameters, then fixing the distortion parameters and optimizing the geometric error parameters, and finally using the results of both as initial values ​​for joint optimization. This avoids the local minima and unidentifiable problems caused by iterating multiple parameters from zero initial values ​​at the same time, and improves the stability and accuracy of calibration convergence. At the same time, the entire calibration process does not rely on an external calibration board and will not damage the cleanliness of the vacuum chamber. It is suitable for patternless bare silicon wafer inspection scenarios and provides a reliable positioning benchmark for wafer surface defect detection and film thickness measurement. Attached Figure Description

[0017] Figure 1 This is a step diagram of a visual coordinate calibration method 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 visual coordinate calibration method for patternless wafer inspection. This method addresses the problem of limited pixel coordinate to physical coordinate mapping accuracy in patternless bare silicon wafer inspection scenarios due to the lack of traceable textures and the inability to introduce external calibration objects. Specifically, in scenarios where there are no circuit patterns on the bare silicon wafer surface and no external calibration objects within the detection cavity, the visual imaging system and the stage motion system are jointly calibrated to establish a mapping relationship between pixel coordinates and physical coordinates. This provides a positioning reference for wafer surface defect detection and film thickness measurement. The visual coordinate calibration method includes the following steps: S1. Use a single-mode laser to irradiate the wafer to form a reference speckle image; specifically, on the surface of a patternless bare silicon wafer, the coherent light illumination of the single-mode laser can convert the roughness of the wafer surface into a speckle pattern, thereby providing a reference for subsequent calibration without relying on external calibration objects.

[0021] S2. Drive the wafer to perform multiple sets of different movements and acquire multiple frames of motion-blurred speckle images during camera exposure. Specifically, by actively introducing controllable motion, the motion information of the wafer is encoded into geometric information in the motion-blurred speckle image, thereby transforming the factors that traditionally lead to imaging degradation into carriers of geometric information, which facilitates the subsequent separation of visual distortion and stage error.

[0022] S3. Divide each frame of motion-blurred speckle image into local regions and obtain the motion-blurred trajectory geometric parameters of each local region. The motion-blurred trajectory geometric parameters include the motion-blurred trajectory length, motion-blurred trajectory direction, and motion-blurred trajectory center position. Specifically, extract the motion-blurred trajectory geometric parameters from the motion-blurred speckle image to provide observation data for visual distortion parameters and platform geometric error parameters.

[0023] S4. Obtain the speckle displacement field based on the reference speckle image and the motion-blurred speckle image; specifically, by obtaining the speckle displacement field, rigid constraints can be provided for the identification of the geometric error of the platform.

[0024] S5. Determine the distortion parameters of the vision system based on the geometric parameters of the motion fuzzy trajectory; confirm the distortion parameters of the vision system without introducing an external calibration plate, thus avoiding damage to the cleanliness of the vacuum chamber by external calibration objects.

[0025] S6. Determine the geometric error parameters of wafer movement based on the speckle displacement field and the center position of the motion fuzzy trajectory. Specifically, the Abbe arm error, inter-axis non-perpendicularity, and rotational eccentricity of the stage can be inverted based on the speckle displacement field and the center position of the motion fuzzy trajectory, thereby determining the geometric error parameters of wafer movement.

[0026] S7. Obtain visual coordinates based on distortion parameters and geometric error parameters.

[0027] In some embodiments, a reference speckle image is formed by irradiating the wafer with a single-mode laser. This includes setting a beam expander group (known to those skilled in the art, and not described in detail here) in the optical path of the single-mode laser so that the laser speckle pattern of the single-mode laser covers the field of view to be calibrated; and using short exposure to acquire the laser speckle pattern to form the reference speckle image. Specifically, the coherence length of the single-mode laser is greater than the optical path difference between the scattered light waves from different regions of the bare silicon surface. The scattered light waves from different regions of the bare silicon surface undergo stable interference, and their phase difference is determined by the surface micro-height undulations. Since the surface roughness remains constant during the detection process, the interference result forms a stable speckle pattern with a bright and dark granular structure. This speckle pattern can be regarded as a random code of the wafer surface micro-height function modulated by a coherent optical system, with different spatial positions... The speckle patterns are independent of each other; therefore, in the scenario of inspecting patternless bare silicon wafers, single-mode laser irradiation can create patterns on the surface without circuit patterns that can be recognized by subsequent algorithms, thereby reducing the dependence on external calibration objects. More specifically, during the calibration process, a beam expander group is set in the optical path of the single-mode laser so that the speckle pattern formed by the laser irradiation on the wafer surface covers the field of view to be calibrated, that is, covers the entire wafer or the part of the wafer to be calibrated, to ensure the uniformity of the speckle pattern in the calibration area and avoid insufficient contrast of the speckle pattern at the edge of the field of view due to illumination attenuation. In addition, a short exposure of the camera (the camera exposure time is set to be less than the stage micro-vibration period) is used to acquire the reference speckle image to avoid motion blur introduced by stage micro-movement or environmental vibration during the exposure, and to ensure that the speckle particles of the reference speckle image are clear.

[0028] In some embodiments, the wafer is driven to perform multiple sets of different movements to acquire multiple frames of motion-blurred speckle images during camera exposure. This includes controlling the stage to move the wafer at a constant speed along the X-direction, or controlling the stage to move the wafer at a constant speed along the Y-direction, to change the wafer's position so that the motion blur trajectory appears at different radial distances from the camera's image plane. This allows sampling of the spatial variation of visual distortion throughout the entire field of view to be calibrated. Tangential distortion and interaxial non-perpendicularity both cause a deflection of the blur direction, but their deflection patterns are different. Therefore, it is necessary to rely on two positive axes in the X and Y directions. The movement in the intersecting directions distinguishes them; the stage is controlled to drive the wafer to rotate around the Z-axis at a constant angular velocity, and multiple frames of motion-blurred speckle images are acquired during camera exposure at multiple rotation phases. During the rotation, any Abbe arm error will cause a systematic shift in the circumferential trajectory, and rotational eccentricity will cause the center position to deviate from the command origin, thus facilitating the acquisition of the stage's Abbe arm error and rotational eccentricity; the stage is controlled to drive the wafer to simultaneously translate along the X-direction and rotate around the Z-axis, and multiple frames of motion-blurred speckle images are acquired during camera exposure to obtain the interaxial non-perpendicularity between the stage's X-axis and Y-axis. Specifically, on the surface of a patternless bare silicon wafer, the motion blur state that traditional calibration methods need to avoid can serve as a carrier of aggregate information in this embodiment. During the calibration process, the stage is made to move at a constant speed during exposure, and the speckle particles form a motion blur trajectory along the motion direction on the image plane. The direction and length of this motion blur trajectory directly reflect the motion direction and displacement of the wafer during the stage-driven motion. Since the speckle itself has random texture, the blurred image still retains grayscale variations, which facilitates subsequent analysis. Specifically, the X direction is parallel to the X-axis of the coordinate system, the Y direction is parallel to the Y-axis of the coordinate system, and the Z direction is parallel to the Z-axis of the coordinate system.

[0029] In some specific embodiments, when the X and Y directions are not perpendicular, the translation command in the X direction will generate an additional displacement in the Y direction, which manifests as a deflection in an ambiguous direction; the stage is controlled at a constant speed. Moving along the X direction, the camera exposure time is recorded as The unit is seconds, representing the stage displacement during the exposure period. The displacement The pixel displacement on the image plane is preferably 5 to 20 pixels. If the displacement is too small, the length of the motion blur trajectory is insufficient and it is difficult to estimate stably from the noise. If the displacement is too large, the motion blur trajectory is over-widened, causing the motion blur trajectories of different speckle particles to overlap, thus destroying the uniqueness of the speckle.

[0030] In some embodiments, each frame of motion-blurred speckle image is divided into local regions to obtain the motion-blurred trajectory geometric parameters of each local region. This includes dividing each frame of motion-blurred speckle image into multiple local sub-regions, each local sub-region having a pixel size of 64*64, and maintaining a 45-55% overlap rate between adjacent local sub-regions. Specifically, since the bare silicon surface has no macroscopic edges, the traditional blind zone convolution method based on step edges cannot be directly applied. Therefore, it is necessary to divide each frame of motion-blurred speckle image into multiple local sub-regions, each local sub-region having a pixel size of 64*64, and maintaining a 50% overlap rate between adjacent local sub-regions to ensure that there are no calibration blind zones within the field of view to be calibrated. For each local sub-region, a Discrete Fourier Transform is performed to detect null positions in the spectrum. The length of the motion blur trajectory is obtained based on the null positions, and the direction of the motion blur trajectory is determined based on the peak values ​​of the spectral energy distribution in polar coordinates. The center pixel coordinates of the local sub-region are used as the center position of the motion blur trajectory. In the frequency domain, uniform linear motion blur will cause periodic zeros in the modulation transfer function of the image, i.e., frequency domain nulls, forming null positions in the spectrum. Let the motion blur trajectory within the local sub-region be... Its Fourier transform satisfy:

[0031] in, ; and These are the spatial frequencies of the image in the X and Y directions, respectively, in cycles per pixel. The length of the motion blur trajectory within this sub-region, in pixels; The direction angle of the motion-blurred trajectory, in radians, is measured counterclockwise from the horizontal axis of the image; frequency domain nulls appear when... The function's independent variable is equal to an integer multiple. At the frequency, that is, at:

[0032] By detecting the first null position in the spectrum, the length of the motion-blurred trajectory can be analytically deduced.

[0033] in, The first null frequency value detected; direction of motion blur trajectory. The angle that maximizes the integration of frequency domain energy along the polar coordinates is determined by searching for the peak value of the spectral energy distribution. The center pixel coordinates of the local sub-region are used as the center position of the motion blur trajectory. The center pixel coordinates are directly determined by the row and column index when dividing the local sub-region, which is well known to those skilled in the art and will not be elaborated here.

[0034] In some specific embodiments, the autocorrelation function of the speckle pattern is used to correct the length and direction of the motion blur trajectory. Specifically, the autocorrelation function of the speckle pattern is a mathematical quantity that characterizes the similarity between the image grayscale distribution and its own translation; for a speckle image within a local sub-region, let its grayscale distribution be... Then the normalized autocorrelation function of this local subregion for:

[0035] in: , These represent the translational offset of the image in the X and Y directions, respectively, in pixels; The average gray level of the local sub-region; Let be the grayscale standard deviation of the local sub-region. Since the autocorrelation peak of a clear speckle image exhibits a sharp, approximately isotropic shape, and motion blur elongates the speckle particles along the motion blur trajectory, the autocorrelation function is stretched in the corresponding direction, and its half-width at half-maximum (WHM) is proportional to the length of the motion blur trajectory. By measuring the WHM of the autocorrelation peak in the frequency domain estimation direction, the precise length of the motion blur trajectory is deduced, correcting the trajectory length obtained from the frequency domain null detection. Simultaneously, the direction with the greatest stretching of the autocorrelation peak is the true motion blur trajectory direction, thus correcting the frequency domain estimated motion blur trajectory direction.

[0036] In some embodiments, obtaining the speckle displacement field based on a reference speckle image and a motion-blurred speckle image includes: performing Wiener filtering deconvolution on a local sub-region of the motion-blurred speckle image to obtain a restored speckle pattern; performing normalized cross-correlation between the restored speckle pattern and the local sub-region, and obtaining the speckle displacement field through pixel interpolation and peak fitting; and performing consistency verification on the speckle displacement field. If the angle between the displacement direction and the trajectory direction exceeds 15 degrees, or the ratio of the displacement amplitude to the length of the motion-blurred trajectory exceeds a preset range, the displacement is discarded. Specifically, directly performing digital speckle correlation operations on motion-blurred speckle images leads to broadening of cross-correlation peaks and decreased positioning accuracy. Therefore, Wiener filtering deconvolution is performed on local sub-regions of the motion-blurred speckle image, i.e., deconvolution is performed using a Wiener filter to obtain the recovered speckle pattern. This is well known to those skilled in the art and will not be elaborated here. This achieves the broadening of the compressed motion-blurred trajectory, restores the local contrast of speckle particles, and makes the motion-blurred speckle patterns of adjacent frames recognizable. Normalized cross-correlation operations are then performed between the recovered speckle pattern and the corresponding local sub-regions of the reference speckle image. Let the coordinates of the center of the local sub-region in the reference speckle image be... Search for the corresponding location in the motion-blurred speckle image and calculate the normalized cross-correlation coefficient.

[0037] in, For reference speckle image sub-regions at pixel locations The grayscale value at that location; For motion-blurred speckle images at offset positions The grayscale value at that location; Let be the two-dimensional displacement vector to be estimated, in pixels; The set of pixels within the sub-region; and These represent the average gray levels of the two sub-regions; and The grayscale standard deviations of the two sub-regions are respectively used. The optimal displacement vector of each local sub-region is determined by sub-pixel interpolation and peak fitting (this is well known to those skilled in the art and will not be elaborated here). The optimal displacement vectors of all local sub-regions in the full field of view are arranged according to their spatial positions to obtain the speckle displacement field. The consistency of the speckle displacement field is checked. If the angle between the displacement direction and the motion blur trajectory direction estimated in step S3 exceeds 15 degrees, or the ratio of the displacement amplitude to the length of the motion blur trajectory exceeds a preset range, the preset range is 0.8 to 1.2 times the theoretical ratio, then the displacement is removed. That is, the local sub-region itself is retained in the image, but its calculated displacement vector is discarded because it does not meet the consistency check and is not included in the subsequent calculation of the stage geometric error parameters.

[0038] In some embodiments, the distortion parameters of the visual system are determined based on the geometric parameters of the motion-blurred trajectory. This includes determining the radial distortion coefficient based on the relationship between the length of the motion-blurred trajectory and the radial distance; determining the tangential distortion coefficient based on the residual between the direction of the motion-blurred trajectory and the ideal direction; and determining the principal point coordinates based on the symmetry of the distribution of the motion-blurred trajectory length near the principal point. Specifically, radial distortion causes changes in local magnification at different radial distances, resulting in different lengths of the motion-blurred trajectory produced by the same physical displacement in different image regions. Let the principal point coordinates of the motion-blurred speckle image be... and The unit is pixels; the radial distance of the center of a local sub-region relative to the principal point is... ,satisfy:

[0039] in, and The pixel coordinates of the center of this sub-region; the observed blur length under radial distortion. With ideal fuzzy length The relationship between them is:

[0040] in, and The radial distortion coefficient is... The unit is the negative first power of the square of each pixel. The unit is the fourth power negative one per pixel; radial distortion produces a magnification deviation in regions far from the principal point, thus stretching or compressing the blur length. Multiple sets of data collected at different radial positions through X-axis and Y-axis movement are compared... By using weighted least squares fitting, the unknown parameters can be directly solved. , , and At this point, the ideal fuzzy length The observation deviation is entirely attributed to visual distortion, determined by the known stage speed and exposure time. The tangential distortion coefficient is determined based on the residual between the motion blur trajectory direction and the ideal direction. Tangential distortion causes an azimuth-related shift in pixel coordinates, thus deflecting the blur direction. Specifically, the azimuth angle of the center of the local sub-region is set as... ,satisfy The blur direction deflection caused by tangential distortion depends on the azimuth angle of the point relative to the principal point. The tangential distortion coefficient can be solved by establishing a system of equations using the residuals of the measured blur direction (0 or 180 degrees) from the ideal direction during X-direction micro-motion and the residuals of the measured direction (90 or 270 degrees) from the ideal direction during Y-direction micro-motion. The process of establishing and solving this system of equations is well-known to those skilled in the art and will not be elaborated here. The principal point coordinates are determined based on the symmetry of the distribution of motion blur trajectory lengths near the principal point. Specifically, in the image formed by the X and Y direction movements, multiple local sub-regions symmetrically distributed relative to the candidate principal points are selected, and the difference in motion blur trajectory lengths at symmetrical positions is calculated. The candidate principal points are calculated one by one to minimize the sum of squares of the differences; the coordinates of the corresponding candidate principal points are then the principal point coordinates. The principal point coordinates refer to the pixel coordinates at the intersection of the optical axis of the optical lens and the image sensor (image plane).

[0041] In some embodiments, the geometric error parameters of wafer movement are determined based on the speckle displacement field and the position of the trajectory center, including: determining the Abbe arm error based on the deviation between the position of the motion fuzzy trajectory center and the ideal circular trajectory; determining the inter-axis non-perpendicularity based on the deflection of the motion fuzzy trajectory direction relative to the command direction; and determining the rotational eccentricity based on the position of the vortex center of the speckle displacement field. Specifically, the geometric motion error of the stage is inverted by utilizing the global rigidity pattern of the cross-frame speckle displacement field and the trajectory characteristics of the motion blur trajectory center in a pure rotation sequence. The stage geometric error manifests as a global systematic deviation in observation, and its spatial distribution pattern is distinctly different from the local radial or angular dependence of visual distortion, thus allowing for orthogonal separation from distortion parameters. The Abbe arm error is determined based on the deviation between the position of the motion blur trajectory center and the ideal circular trajectory. The Abbe arm error refers to the spatial offset between the stage rotation axis and the measurement baseline; that is, when the stage executes a pure rotation command, the wafer mounted on the stage will undergo an additional translation linearly related to the rotation angle due to the offset of the rotation center. When controlling the stage to rotate the wafer around the Z-axis at a constant angular velocity, if there were no Abbe error, the motion blur trajectory center should perform a strict circular motion around the image principal point. The existence of the Abbe error causes a linear drift term to be superimposed on this circular trajectory. Let the rotation angle during exposure be... The additional offset of the motion blur trajectory center caused by the Abbe error is:

[0042] in, and Here, represents the lengths of the Abbe arms along the X and Y axes, respectively, in mm. This offset manifests as a uniform translation linearly related to the rotation angle across all sub-regions of the field of view, independent of the position of any local sub-region. Therefore, by comparing the deviations between the center trajectory of the motion blur trajectory and the ideal circular trajectory, the image can be directly separated. and Based on the deflection of the motion fuzzy trajectory direction relative to the command direction, the inter-axis non-perpendicularity is determined. Inter-axis non-perpendicularity refers to the deviation of the actual angle between the X-axis and Y-axis of the stage from 90 degrees. When controlling the stage to simultaneously translate along the X-axis and rotate around the Z-axis while driving the wafer, if the command requires the stage to simultaneously translate and rotate along the X-axis, the inter-axis non-perpendicularity will cause the X-axis motion to generate a Y-axis component. This component manifests in the image plane as a systematic deflection of the fuzzy direction relative to the command direction. Let the command fuzzy direction be... The measured fuzzy direction is Then the deviation between the two satisfies:

[0043] in, This refers to the non-perpendicularity between axes, expressed in radians. This represents a higher-order term caused by radial distortion, which varies with radial distance. Change; due to It is a global constant, while the visual distortion term varies with... The variation can be solved directly by collecting multiple sets of data at different radial locations and using regression methods (such as stepwise regression) to separate the constant term that does not change with location from the higher-order term that changes with location. Based on the position of the vortex center in the speckle displacement field, the rotational eccentricity is determined. Rotational eccentricity refers to the two-dimensional offset between the actual rotation center of the stage and the origin of the command coordinate system. When the stage drives the wafer to rotate around the Z-axis at a constant angular velocity, the rotational eccentricity causes the physical center of the wafer to move around the eccentric circle, which in turn causes the vortex center of the cross-frame speckle displacement field to deviate from the command origin. By analyzing the position of the vortex center in the displacement field in a pure rotation sequence, the eccentricity vector can be analytically obtained. Specifically, if the pixel trajectory of a physical point in the displacement field at different rotation angles is an ellipse, the center of the ellipse is the vortex center. The difference between the coordinates of the vortex center in the pixel coordinate system and the coordinates of the command origin in the pixel coordinate system is taken as the rotational eccentricity. The rotational eccentricity is represented by a vector, which is the eccentricity vector.

[0044] In some embodiments, visual coordinates are obtained based on distortion parameters and geometric error parameters, including: Two complementary reprojection errors are defined; the first is the geometric reprojection error of the motion-blurred trajectory, based on observations of a local sub-region of a single frame; for the second... The first group of sequences For each local sub-region, define the error vector:

[0045] in, and The measured motion blur trajectory length and direction obtained in step S3; the distortion parameter is set to v. Based on the distortion parameter v and radial distance The predicted length of the motion-blurred trajectory; Based on distortion parameter v and geometric error parameter and platform movement commands Predicted motion-blurred trajectory direction; distortion parameter vector ,in and These are the focal lengths in the horizontal and vertical directions, respectively, in pixels; and Radial distortion coefficient; and The tangential distortion coefficient; and Principal point coordinates; geometric error parameter vector ,in This refers to the non-perpendicularity between axes. and For Abbe arm error, and It is a rotational eccentricity.

[0046] The second type is speckle displacement reprojection error, based on observations of corresponding point fields across frames; for the first... For the first in adjacent frames For each corresponding point, define the error:

[0047] in, The pixel displacement vector measured in step S4; To project the physical point coordinates of the wafer onto the pixel coordinates using a perspective transformation with distortion, specifically, the three-dimensional coordinates of the physical point on the wafer in the camera coordinate system are determined based on the actual motion of the stage. Normalize the three-dimensional coordinates to obtain ideal normalized coordinates. ,in , The ideal normalized coordinates are distorted according to the distortion parameters to obtain the corrected coordinates. :

[0048]

[0049] in, ; , The radial distortion coefficient is mentioned above; , The tangential distortion coefficients are used; the corrected coordinates are mapped to pixel coordinates:

[0050]

[0051] in, , The focal length of the camera, expressed in pixels; , The coordinates of the principal point are in pixels. For the first The wafer physical point coordinates corresponding to each local sub-region are initially unknown and are used as auxiliary quantities to be determined. and The first Frame and the The frame contains the actual stage motion command with errors, derived from the stage motion command. With geometric error parameters (Abbe arm error, inter-axis non-perpendicularity, and rotational eccentricity) are obtained; Construct the overall objective function E:

[0052] in, and This is the Huber robust kernel function, used to suppress the influence of local sub-regions at the edges; The physical point smoothing regularization term utilizes the known condition that the wafer is a rigid plane. It introduces an additional error into the objective function for the difference between the coordinates of the physical points on the wafer corresponding to the spatially adjacent local sub-regions. The larger the difference, the larger the objective function value, thereby making the coordinates of adjacent physical points tend to be consistent. This prevents the coordinates of each physical point from independently converging to local discrete values ​​during the optimization process, and ensures the overall continuity of the physical point coordinates on the wafer surface. and This is the regularization coefficient, used to prevent overfitting.

[0053] The two types of errors are processed separately in three stages. Specifically, the geometric parameters of the motion blur trajectory are determined only by the image content of a local sub-region of a single frame, reflecting the local deformation of the vision system's imaging at different spatial locations; while the speckle displacement field is determined by the global positional offset of the same physical point between adjacent frames, reflecting the global rigidity deviation of the stage motion. The two types of observation data have different scopes: the former is limited to a local region of a single frame, while the latter spans the global field of view between frames. Therefore, the corresponding distortion parameters and geometric error parameters can be optimized independently in stages to avoid mutual interference when the two types of parameters are iterated simultaneously, which could lead to convergence to a local minimum.

[0054] In the first stage, the geometric error parameters are fixed at zero, and the distortion parameters are optimized only using the geometric parameters of the motion fuzzy trajectory. At this time, the platform motion is regarded as ideal motion. After fixing the geometric error parameters to zero, the original joint optimization problem that required solving both the distortion parameters and the geometric error parameters is simplified into a single-variable optimization problem that only requires solving the distortion parameters. That is, the change of the motion fuzzy trajectory length with the radial distance directly constrains the radial distortion coefficient, the deflection of the motion fuzzy trajectory direction relative to the ideal direction (coordinate axis direction) directly constrains the tangential distortion coefficient, and the symmetry of the distribution of the motion fuzzy trajectory length near the principal point constrains the principal point coordinates.

[0055] In the second stage, the optimized distortion parameters are fixed, and the geometric error parameters are optimized only using the speckle displacement field. At this point, the visual projection relationship is determined, and the global rigid offset of the geometric error parameters across the frame displacement field is fully exposed: Abbe arm error manifests as a translation component in pure rotational motion that is linearly related to the rotation angle; inter-axis non-perpendicularity manifests as a constant deflection relative to the command direction during motion that simultaneously translates along the X-axis and rotates around the Z-axis; and rotational eccentricity manifests as the vortex center offset of the pure rotational sequence displacement field.

[0056] The third stage uses the results of the first and second stages as initial values ​​to jointly optimize the distortion parameters and geometric error parameters until the relative change in the distortion parameter vector is less than a first preset threshold (e.g., 10). -6 Furthermore, the relative change in the geometric error parameter vector is less than a second preset threshold (e.g., 10). -6 At this point, the initial value is already in the global optimal neighborhood, and only local corrections are made, avoiding the local minima and unidentifiable problems caused by optimizing all parameters from zero initial values ​​at the same time.

[0057] By establishing a mapping relationship between pixel coordinates and physical coordinates, visual coordinates are obtained. Specifically, the pixel coordinates are distorted using the distortion parameters to obtain ideal imaging coordinates; the stage motion commands are error-compensated using the geometric error parameters to obtain stage motion commands; the ideal imaging coordinates and stage motion commands are combined, and a mapping relationship between pixel coordinates and wafer physical coordinates is established through coordinate transformation to obtain the visual coordinates.

[0058] In some embodiments, prior to joint optimization, the method further includes: calculating a second-order partial derivative submatrix A with respect to distortion parameters and a second-order partial derivative submatrix B with respect to geometric error parameters; if the ratio of the maximum eigenvalue to the minimum eigenvalue of each of the second-order partial derivative submatrix A and the second-order partial derivative submatrix B is less than... ,and

[0059] Where a is an element of the second-order partial derivative submatrix A, b is an element of the second-order partial derivative submatrix B, and c is an element of the cross submatrix of the second-order partial derivative submatrix A and the second-order partial derivative submatrix B. Then the distortion parameters and the geometric error parameters of wafer movement can be identified independently.

[0060] Specifically, calculate the second-order partial derivative matrix of the joint optimization objective function, i.e., the Hessian matrix H. ,in The overall objective function The first-order partial derivative matrix of all parameters to be determined; extraction Regarding distortion parameters The submatrix is ​​taken as the second-order partial derivative submatrix A, and the geometric error parameter is taken as the submatrix A. The submatrix of A and B is taken as the second-order partial derivative submatrix B; the ratio of the largest eigenvalue to the smallest eigenvalue of each of the second-order partial derivative submatrix A and B is their condition number, and the condition number is less than 1. This indicates that the submatrix is ​​a well-state matrix, and the observation equations of the corresponding parameter set are stable; This indicates that the distortion parameters and geometric error parameters are approximately block diagonal in the Hessian matrix, and the coupling between them is sufficiently low. This ensures that the distortion parameters and geometric error parameters are identifiable in the observation model, prevents errors caused by parameter coupling, and guarantees the effectiveness and reliability of the calibration results.

[0061] In some embodiments, after obtaining the visual coordinates, the method further includes: Using distortion parameters and geometric error parameters in visual coordinates, the geometric parameters and speckle displacement of motion-blurred trajectories that were not involved in optimization are predicted to obtain predicted values; Compare the predicted values ​​with the measured values; like

[0062] and

[0063] in, The length of the predicted motion-blurred trajectory, N represents the measured length of the motion-blurred trajectory, where N is the total number of sampling points for the motion-blurred trajectory length. For the predicted speckle displacement, Let M be the measured speckle displacement, and M be the total number of sampling points for the speckle displacement; then the calibration accuracy is deemed to meet the requirements. Specifically, at least one set of motion sequences not involved in the aforementioned optimization process is selected as the validation set; using the calibrated distortion parameters, the pixel coordinates of each local sub-region in the validation set and the parameters of the stage motion command (translation or rotation of the stage) are substituted into the radial distortion model and tangential distortion model described in step S5 to calculate the length and direction of the motion blur trajectory that the local sub-region should have, and the predicted values ​​of the geometric parameters of the motion blur trajectory are obtained; using the calibrated geometric error parameters, the stage motion command of each frame in the validation set is substituted into the mapping relationship between the Abbe arm error, inter-axis non-perpendicularity, and rotational eccentricity and the stage motion command described in step S6 to calculate the actual stage motion command of each frame in the validation set, and then the pixel offset of the same physical point between adjacent frames is calculated according to the mapping relationship between pixel coordinates and physical coordinates, and the physical coordinates are projected onto the pixel coordinates of adjacent frames respectively; the difference between the pixel coordinates of two frames is the predicted value of the speckle displacement; the predicted value is compared with the corresponding measured value, if ,and If the calibration accuracy meets the requirements, it is determined that the calibration accuracy meets the requirements. Using independent data that has not been optimized for verification can avoid errors caused by overfitting and ensure the accuracy of the calibration.

[0064] 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 visual coordinate calibration method for patternless wafer inspection, characterized in that, Includes the following steps: A reference speckle image is formed by irradiating the wafer with a single-mode laser; The wafer is driven to perform multiple different movements, and multiple frames of motion-blurred speckle images are captured during camera exposure; Each frame of motion-blurred speckle image is divided into local regions, and the motion-blurred trajectory geometric parameters of each local region are obtained. The motion-blurred trajectory geometric parameters include the motion-blurred trajectory length, the motion-blurred trajectory direction, and the center position of the motion-blurred trajectory. The speckle displacement field is obtained based on the reference speckle image and the motion-blurred speckle image; The distortion parameters of the vision system are determined based on the geometric parameters of the motion fuzzy trajectory. Based on the speckle displacement field and the center position of the motion fuzzy trajectory, determine the geometric error parameters of wafer movement; including: determining the Abbe arm error based on the deviation between the center position of the motion fuzzy trajectory and the ideal circular trajectory; determining the interaxial non-perpendicularity based on the deflection of the motion fuzzy trajectory direction relative to the command direction; and determining the rotational eccentricity based on the vortex center position of the speckle displacement field. The visual coordinates are obtained based on the distortion parameters and the geometric error parameters.

2. The visual coordinate calibration method according to claim 1, characterized in that, The method of irradiating the wafer with a single-mode laser to form a reference speckle image includes, A beam expander group is set in the optical path of the single-mode laser so that the laser speckle pattern of the single-mode laser covers the field of view to be calibrated; The reference speckle image is formed by acquiring the laser speckle pattern using a short exposure.

3. The visual coordinate calibration method according to claim 1, characterized in that, The process involves driving the wafer through multiple different movements, and acquiring multiple frames of motion-blurred speckle images during camera exposure, including... The stage is controlled to move the wafer at a constant speed along the X direction, or the stage is controlled to move the wafer at a constant speed along the Y direction, so as to change the position of the wafer and make the motion blur trajectory appear at different radial distances in the image plane. The stage is controlled to drive the wafer to rotate around the Z-axis at a constant angular velocity. Multiple frames of motion-blurred speckle images are acquired during camera exposure at multiple rotation phases to obtain the Abbe arm error and rotational eccentricity of the stage. The stage is controlled to move the wafer simultaneously along the X-axis and rotate around the Z-axis, and multiple frames of motion-blurred speckle images are acquired during camera exposure to obtain the interaxial non-perpendicularity between the X-axis and Y-axis of the stage.

4. The visual coordinate calibration method according to claim 1, characterized in that, The step of dividing each frame of motion-blurred speckle image into local regions and obtaining the motion-blurred trajectory geometric parameters of each local region includes, Each frame of motion-blurred speckle image is divided into multiple local sub-regions, each with a pixel size of 64*64, and adjacent local sub-regions maintain an overlap rate of 45-55%. A discrete Fourier transform is performed on each local sub-region to detect null positions in the spectrum. The length of the motion blur trajectory is obtained based on the null positions, and the direction of the motion blur trajectory is determined based on the peak value of the spectrum energy distribution in polar coordinates. The center pixel coordinates of the local sub-region are used as the center position of the motion blur trajectory. The length and direction of the motion blur trajectory are corrected using the autocorrelation function of the speckle pattern.

5. The visual coordinate calibration method according to claim 4, characterized in that, The step of obtaining the speckle displacement field based on the reference speckle image and the motion-blurred speckle image includes: Wiener filtering and deconvolution are applied to a local sub-region of the motion-blurred speckle image to obtain the restored speckle pattern; Normalized cross-correlation is performed between the restored speckle pattern and the local sub-region, and the speckle displacement field is obtained by pixel interpolation and peak fitting. The consistency of the speckle displacement field is checked. If the angle between the displacement direction and the trajectory direction exceeds 15 degrees, or the ratio of the displacement amplitude to the length of the motion fuzzy trajectory exceeds a preset range, the displacement is discarded.

6. The visual coordinate calibration method according to claim 1, characterized in that, Determining the distortion parameters of the visual system based on the geometric parameters of the motion-blurred trajectory includes, The radial distortion coefficient is determined based on the relationship between the length of the motion-blurred trajectory and the radial distance; The tangential distortion coefficient is determined based on the residual between the motion fuzzy trajectory direction and the ideal direction; The coordinates of the principal point are determined based on the symmetry of the distribution of the length of the motion fuzzy trajectory near the principal point.

7. The visual coordinate calibration method according to claim 1, characterized in that, The step of obtaining visual coordinates based on the distortion parameters and the geometric error parameters includes: The geometric error parameter is fixed at zero, and the distortion parameter is optimized based on the geometric parameters of the motion fuzzy trajectory; The optimized distortion parameters are fixed, and the geometric error parameters are optimized based on the speckle displacement field. The optimized distortion parameter and the optimized geometric error parameter are used as initial values ​​to jointly optimize the distortion parameter and the geometric error parameter until the change in the distortion parameter is less than a first preset threshold and the change in the geometric error parameter is less than a second preset threshold. Establish a mapping relationship between pixel coordinates and physical coordinates to obtain the visual coordinates.

8. The visual coordinate calibration method according to claim 7, characterized in that, Prior to the joint optimization, the following is also included: Calculate the second-order partial derivative submatrix A with respect to the distortion parameters and the second-order partial derivative submatrix B with respect to the geometric error parameters; If the ratio of the maximum eigenvalue to the minimum eigenvalue of both the second-order partial derivative submatrix A and the second-order partial derivative submatrix B is less than... ,and Where a is an element of the second-order partial derivative submatrix A, b is an element of the second-order partial derivative submatrix B, and c is an element of the cross submatrix of the second-order partial derivative submatrix A and the second-order partial derivative submatrix B. Then it can be determined that the distortion parameter and the geometric error parameter of the wafer movement can be independently identified.

9. The visual coordinate calibration method according to claim 7, characterized in that, After obtaining the visual coordinates, the process also includes: Using the distortion parameters and geometric error parameters in the visual coordinates, the geometric parameters and speckle displacement of the motion blur trajectory that was not optimized are predicted to obtain the predicted values; Compare the predicted values ​​with the measured values; like and in, The predicted length of the motion-blurred trajectory, N represents the measured length of the motion-blurred trajectory, and N is the total number of sampling points for the length of the motion-blurred trajectory. For the predicted speckle displacement, The measured speckle displacement is M, where M is the total number of sampling points for the speckle displacement. If the calibration accuracy meets the requirements, then it is determined that the calibration accuracy meets the requirements.

Images