Silicon wafer multi-defect decoupling weighted fitting method and device and storage medium
By using a multi-defect coupling model and a domain-weighted fitting method, the problem of multiple defects superimposed in silicon wafer inspection was solved, achieving high-precision and high-efficiency inspection, adapting to different defect scenarios, and improving inspection accuracy and efficiency.
Patent Information
- Application Number
- CN202512051364.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-31
- Publication Date
- 2026-04-14
AI Technical Summary
Existing silicon wafer inspection technologies cannot effectively decouple multiple defects, resulting in low inspection accuracy and efficiency, which cannot meet the needs of industrial mass production. In particular, in the inspection of silicon wafers with microarray lenses, it is impossible to decouple four types of defects simultaneously when multiple defects are superimposed, resulting in uneven accuracy between the edge and the center and poor versatility.
A multi-defect coupling model is used for defect pre-identification, decomposition, domain-weighted fitting, and dynamic compensation iteration. By identifying the dominant defect type through gradient and local variance, regions are divided according to the proportion of lens unit radius and assigned differentiated weights. Combined with residual feedback iterative optimization, accurate identification and efficient fitting of multiple types of defects are achieved.
It significantly improves the fitting accuracy of parameters such as radius of curvature, conic coefficient, and surface roughness, reduces detection errors, and increases detection efficiency, meeting the high-efficiency requirements of industrial mass production, and adapting to different defect scenarios without manual intervention.
Smart Images
Figure CN121860987A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of silicon wafer inspection technology, specifically to a method, equipment, and storage medium for decoupling weighted fitting of multiple defects in silicon wafers. Background Technology
[0002] In the white light interferometry inspection of silicon wafers using microarray lenses, the coexistence of multiple defects in silicon wafers during industrial mass production has become a common and unavoidable problem. These defects mainly include local deformation caused by dicing stress, edge warping caused by vacuum adsorption, global tilting caused by tooling positioning, and random depressions formed by process residues. The superposition of various defects seriously affects the inspection accuracy and efficiency.
[0003] Existing silicon wafer fitting and inspection technologies have fundamental limitations, making it difficult to meet the high precision, high efficiency, and high versatility requirements of mass production scenarios: general polynomial fitting (such as Zernike polynomial fitting) can only describe global low-order errors (such as tilt and defocus), and cannot accurately model local nonlinear defects such as ±0.3μm local protrusions caused by dicing stress, which leads to the curvature radius r deviation expanding to ±0.5% and the conic coefficient k deviation reaching ±0.08; single defect correction algorithms (such as quadratic surface compensation only for warping, and linear correction only for tilting) can only deal with single types of defects and cannot handle the superposition of multiple defects such as "tilt + dicing stress + adsorption deformation" that account for more than 60% of mass production scenarios, resulting in a measurement error of surface roughness parameter Sq exceeding 0.1μm;
[0004] Meanwhile, existing technologies lack defect identification logic and directly fit mixed defect point clouds without first distinguishing defect types. This can easily lead to misjudging dicing stress as surface features, resulting in a k-value fitting error rate exceeding 15%. Furthermore, for the inspection needs of high-load single-probe optomechanics and microarray lenses with typical specifications of 200×200 units, unit diameters of 200-1000μm, and sagittal heights of 5-70μm, existing solutions still suffer from irreconcilable contradictions such as low efficiency, inability to decouple multiple defects, poor accuracy, and weak versatility: without mechanical leveling, it is difficult to decouple four types of defects simultaneously, the k deviation can only be maintained at ±0.03~±0.05, and the r relative error is ±0.3%~±0.5%; affected by the differences in defect distribution areas, the edge Sq error is ≥0.06μm, which is far lower than the center accuracy; the fitting time of a single lens unit is 0.8~1.2s, the total inspection time of 200×200 silicon wafers is relatively long, and manual adjustment of parameters is required to adapt to different defect types and scenarios, resulting in limited versatility coverage and failing to meet the stringent requirements of industrial mass production for inspection technology. Summary of the Invention
[0005] The purpose of this invention is to provide a method, device, and storage medium for decoupling and weighted fitting of multiple defects in silicon wafers. By constructing a multi-dimensional integrated structure that includes defect pre-identification, multi-defect coupling decomposition, domain-based weighted fitting, and dynamic compensation iteration, the invention achieves accurate stripping of multiple types of defects using a multi-defect coupling model that includes tilt components, warping components, dicing stress components, and vacuum adsorption deformation components. It improves the uniformity of global fitting by dividing regions according to their radius proportions and assigning differentiated weights. It achieves scene adaptation through pre-identification and residual feedback iteration based on gradients and local variances. This invention effectively solves the technical problems of inability to decouple multiple defects, uneven accuracy between edges and centers, low detection efficiency, and weak versatility in silicon wafer inspection using microarray lenses.
[0006] This invention is achieved through the following technical solution:
[0007] A weighted fitting method for decoupling multiple defects in silicon wafers includes the following steps:
[0008] S1. Obtain the raw point cloud data of the silicon wafer;
[0009] S2. Calculate the gradient G and local variance Var(z) of the original point cloud data to identify the dominant defect type;
[0010] S3. Based on the aforementioned defect-dominant type, the original point cloud data is decomposed using a multi-defect coupling model to remove multiple defect components and noise, thereby obtaining a true surface point cloud.
[0011] S4. Divide the region according to the ratio of the lens unit radius and assign differential weights, and perform weighted fitting on the real surface point cloud to obtain the initial fitting parameters;
[0012] S5. Based on the residual feedback of the initial fitting parameters, dynamically adjust the defect weights and iteratively optimize S3-S4 until the convergence condition is met, and output the final fitting result.
[0013] In this solution, a coherent process of point cloud acquisition, defect pre-identification, multi-defect coupling decomposition, domain-weighted fitting, and dynamic iterative optimization is employed. First, the gradient G and local variance Var(z) are used to accurately identify the dominant defect type. Then, a multi-defect coupling model is used to effectively separate multiple defect components from noise, avoiding parameter distortion caused by defect confusion in traditional fitting techniques. Furthermore, by dividing the region according to the proportion of lens unit radius and assigning differentiated weights, the fitting contribution of edge regions and other areas significantly affected by defects is enhanced, solving the industry pain point of uneven accuracy across the entire domain. Finally, based on residual feedback, the defect weights are dynamically adjusted and iteratively optimized, ensuring the algorithm's adaptability to different defect scenarios such as "tilt-dominated" and "stress-dominated". It can adapt to the vast majority of silicon wafer inspection needs in mass production without manual intervention. This not only significantly improves the fitting accuracy of the radius of curvature r, conic coefficient k, and surface roughness parameter Sq, and controls the detection error in multi-defect superposition scenarios to an extremely low level, but also ensures inspection efficiency through optimized process design. The fitting time of a single lens unit and the total inspection time of the silicon wafer both meet the high-efficiency requirements of industrial mass production.
[0014] Furthermore, in step S2, the gradient G includes the gradient in the X direction. gradient in the Y direction The local variance Var(z) is expressed as Var(z) = E[(zE[z])²];
[0015] Among them, when G>0.01μm / μm, it is determined to be tilt-dominant, and when Var(z)>0.005μm², it is determined to be stress-dominant.
[0016] Furthermore, in step S3, the multi-defect coupling model includes a tilt component. Warp component Scrap stress components Vacuum adsorption deformation component , True face shape components and noise components Its expression is:
[0017] .
[0018] Furthermore, the tilt component For the linear terms in the X / Y directions, the expression is: ,in The tilt coefficient is obtained by fitting the height values of the four corner points of the point cloud edge.
[0019] Furthermore, the warping component The expression is: ,in, The warpage coefficient is obtained by fitting the quadratic and quartic terms using the least squares method after removing 5% of the point cloud data from the edges, with a fit of ≥0.996.
[0020] Furthermore, the dicing stress component The expression is The stress center was located by the peak value of the local variance of the point cloud. c, d, and f are obtained by fitting the point cloud of the peak region.
[0021] Furthermore, the vacuum adsorption deformation component The expression is , where g is the adsorption coefficient, which is obtained by fitting the difference value by comparing the point clouds of standard silicon wafers with and without adsorption.
[0022] Furthermore, the noise component Eliminate by combining 3×3 median filtering and Gaussian filtering.
[0023] Furthermore, in step S4, the rules for region division and weight setting are as follows:
[0024] Central region: ρ≤0.6R, weight w=1.0, sampling point ratio 35%, fitting residual <0.004um;
[0025] Transition region: 0.6R < ρ ≤ 0.85R, weight w = 1.2, sampling point ratio 50%, fitting residual < 0.003um;
[0026] Edge region: ρ>0.85R, weight w≥1.5, sampling point ratio 15%, fitting residual <0.005um, and edge derivative constraint is added; ρ is the radial distance from any point in the lens unit to the center.
[0027] Furthermore, in step S4, the weighted fitting is performed by minimizing the objective function J to solve for the fitting parameters. The expression for the objective function J is:
[0028] ;
[0029] in, Here, r represents the weight of each sampling point, r is the reference radius of curvature of the lens, and k is the conic coefficient. This represents the true surface shape of the lens at each sampling point;
[0030] By taking the partial derivatives of r and k in the objective function and setting them to 0, we obtain a system of equations. We then use Newton's iteration method to solve the system and obtain the values of r and k.
[0031] Furthermore, in step S5, the dynamic weight adjustment and convergence conditions include:
[0032] The initial weights are set based on the defect pre-identification results: if G > 0.01 μm / μm, then the tilt component weights are adjusted accordingly. Other defect components have a weight of 1.0; if Var > 0.005 μm², then the tilt component weight is... Other defect components have a weight of 1.0;
[0033] Residual adjustment rule: If the residuals are concentrated in the marginal region, i.e., ρ>0.85R, then the marginal region weights are adjusted. Increase by 0.1~0.2; if the residuals are distributed globally, then the weights of the marginal regions are adjusted. Increase by 0.1;
[0034] Convergence condition: The number of iterations is ≤3, and the maximum fitting residual Err is ≤3. max ≤0.005μm.
[0035] A silicon wafer multi-defect decoupling weighted fitting device includes:
[0036] The acquisition module is used to acquire the raw point cloud data of the silicon wafer;
[0037] The identification module is used to calculate gradients and local variances to identify the dominant defect type.
[0038] The decomposition module is used to perform the multi-defect coupling model according to any one of claims 1-11 to remove defects and noise and output a realistic surface point cloud;
[0039] The fitting module is used to divide the lens unit regions and assign differential weights, and fit the real surface point cloud using the weighted least squares method.
[0040] The output module is used to adjust the defect weights based on the fitting residuals, iteratively execute the defect decomposition and fitting process, and output the final parameters.
[0041] A storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described silicon wafer multi-defect decoupling weighted fitting method.
[0042] Compared with the prior art, the present invention has the following advantages and beneficial effects:
[0043] 1. This invention uses a multi-defect coupling model to simultaneously and accurately separate four types of defects, namely tilting, warping, dicing stress, and vacuum adsorption deformation, as well as noise, avoiding parameter distortion caused by defect confusion and solving the core limitation of existing technologies that cannot handle the superposition of multiple defects.
[0044] 2. This invention adopts a design of "partitioning by radius proportion and differentiated weights" to enhance the fitting contribution of areas with significant defects such as edge regions, so that the edge Sq error is consistent with the center accuracy, solving the problem of poor edge accuracy caused by traditional global equal weight fitting, and significantly reducing the fitting error of radius of curvature r and conic coefficient k;
[0045] 3. This invention achieves automatic identification of defect-dominant types by quantizing and calculating gradient G and local variance Var(z) and determining thresholds. Combined with dynamic weight adjustment of residual feedback, it can adapt to different defect scenarios such as "tilt-dominant" and "stress-dominant" without manual intervention. Attached Figure Description
[0046] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:
[0047] Figure 1 This is a schematic diagram of the overall process of the present invention;
[0048] Figure 2 This is a diagram illustrating the architecture of step S2 of the present invention;
[0049] Figure 3 This is a defect coupling decomposition diagram of step S3 of the present invention;
[0050] Figure 4 This is a schematic diagram of the partitioning in step S4 of the present invention;
[0051] Figure 5 A logic diagram for setting the region weights in step S4 of this invention;
[0052] Figure 6 This is a schematic diagram of the dynamic compensation iteration in step S5 of the present invention. Detailed Implementation
[0053] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.
[0054] Example 1
[0055] This embodiment 1 provides a decoupling weighted fitting method for multiple defects in silicon wafers, targeting the inspection of microarray lens silicon wafers commonly used in the AR / VR field. The silicon wafer has a 200×200 unit array structure, with a single lens unit diameter of 500μm (reference radius R=250μm), a designed radius of curvature r=10mm, a conic coefficient k=-1.0, and a sagitta of 35μm. The inspection scenario involves a superposition of multiple defects, including tilting, warping, scratch stress, and vacuum adsorption deformation. Figure 1 As shown, the specific implementation steps are as follows:
[0056] S1. Obtain the raw point cloud data of the silicon wafer;
[0057] Specifically, a white light interferometer was used to scan and acquire data from a single lens unit on the silicon wafer. The scanning resolution was set to 1500 points / unit, and the acquisition range was x∈[-250μm, 250μm], y∈[-250μm, 250μm], with a height measurement range of 0~2.5μm (including various defects and noise). After acquisition, the raw point cloud data was output in CSV format, containing the x-coordinate, y-coordinate, and corresponding height value of each sampling point. This step takes 0.18 seconds, which meets the design requirement of ≤0.2 seconds.
[0058] S2. Calculate the gradient G and local variance Var(z) of the original point cloud data to identify the dominant defect type;
[0059] Specifically, such as Figure 2 As shown, the gradient in the X direction of the original point cloud data is calculated. gradient in the Y direction The calculated values are Gx = 0.008 μm / μm and Gy = 0.006 μm / μm, and the combined gradient is... =0.010μm / μm;
[0060] The local variance of the original point cloud was calculated using the local variance formula Var(z)=E[(zE[z])²], where E[z] is the expected value of the height. The calculated value was Var(z)=0.006μm².
[0061] When G > 0.01 μm / μm, it is determined to be tilt-dominant; when Var(z) > 0.005 μm², it is determined to be stress-dominant. Therefore, since Var(z) = 0.006 μm² > 0.005 μm², the silicon wafer is determined to be a stress-dominant defect scenario. Simultaneously, the gradient G = 0.010 μm / μm is close to the threshold, indicating that tilt defects have a certain impact. The initial defect weight configuration is as follows: Scribing stress component weight W. stress =1.3, skew component weight W tilt =1.1, and the weights of the warpage component and the vacuum adsorption deformation component are both 1.0. This step takes 0.04s, which meets the design requirement of ≤0.05s.
[0062] S3. Based on the aforementioned defect-dominant type, the original point cloud data is decomposed using a multi-defect coupling model to remove multiple defect components and noise, thereby obtaining a true surface point cloud.
[0063] Specifically, defect stripping is performed on the original point cloud, such as... Figure 3 As shown, the original point cloud is decomposed into "four types of defect components + true surface components + noise", as shown in the following formula:
[0064] The mathematical expressions and solution methods for each component are as follows:
[0065] Inclined component : represents the linear tilt term in the X / Y directions of the silicon wafer, expressed as follows: ,in The tilt coefficient, Similarly, we can obtain , specifically, The height values of the four corner points ((250,250), (250,-250), (-250,250), (-250,-250)) of the original point cloud edge were fitted to obtain the result. =0.008μm / μm =0.006μm / μm, after stripping this component, we obtain ;
[0066] Warp component It is generated when the silicon wafer warps (a quadratic surface-type global deformation), and the expression is: First, 5% of the point cloud data at the edge (i.e., the stress-affected region with ρ>237.5μm) is removed to eliminate the stress influence. Then, the least squares method is used to fit the quadratic and quartic terms, resulting in a=0.0004μm / μm. 2 The goodness of fit is 0.997 ≥ 0.996. After removing this component, we obtain... ;
[0067] Scribing stress components For example, local higher-order deformations, such as depressions, are expressed as follows: By searching The local variance peak was located at the stress center (x0, y0) = (30 μm, 25 μm). Point cloud data in a 10 × 10 μm region surrounding this center was fitted to obtain c = 0.25 μm, d = 0.001 μm⁻², and f = 0.0003 μm / μm. 2 After stripping this component, we obtain ;
[0068] Vacuum adsorption deformation component The expression is By comparing the point cloud data of standard silicon wafers under adsorption-free and adsorbed states, the difference value was fitted to obtain an adsorption coefficient g = 0.00035 μm / μm² (within the stable mass production range of 0.0002~0.0005 μm / μm²). After removing this component, the adsorption coefficient was obtained as follows: ;
[0069] noise components The elimination was performed using a combination of 3×3 median filtering and Gaussian filtering, resulting in point cloud data containing only the true surface features. .
[0070] After this step was completed, the four types of defect components and noise were successfully removed. The local deformation caused by the dicing stress was reduced from the original 0.3μm to 0.002μm, the defect removal rate reached 99.3%, and the step took 0.09s, which meets the design requirement of ≤0.1s.
[0071] S4. Divide the region according to the ratio of the lens unit radius and assign differential weights, and perform weighted fitting on the real surface point cloud to obtain the initial fitting parameters;
[0072] First, such as Figure 4 and Figure 5 As shown, based on the ratio of lens unit radius ρ / R (ρ is the radial distance from the sampling point to the center), the area is divided into three regions:
[0073] Central region: ρ≤0.6R=150μm, weight w=1.0, sampling point ratio 35%, a total of 525 sampling points were selected, and the fitting residual threshold <0.004μm;
[0074] Transition region: 0.6R<ρ≤0.85R=212.5μm, weight w=1.2, sampling point ratio 50%, a total of 750 sampling points are selected, and the fitting residual threshold is <0.003μm;
[0075] Edge region: ρ > 0.85R = 212.5μm, weight w = 1.5, sampling point ratio 15%, a total of 225 sampling points were selected, the fitting residual threshold < 0.005μm, and an edge derivative constraint condition was added. To ensure no mutations occur.
[0076] Then, the fitting parameters are solved by minimizing the objective function J, which is expressed as:
[0077] ;
[0078] in, Here, r represents the weight of each sampling point, r is the reference radius of curvature of the lens, and k is the conic coefficient. The actual surface shape of the lens at each sampling point is given, and N is the total number of sampling points involved in the fitting (N=1500 in this invention).
[0079] The objective function J is constructed based on a quadratic surface and higher-order corrections. Taking the partial derivatives of r and k in the objective function and setting them to 0, we obtain a system of linear equations:
[0080] ;
[0081] The equation system was solved using Newton's iteration method (no more than 5 iterations, with each iteration taking ≤0.05s), yielding the initial fitting parameters: r=10.008mm, k=-1.007, Sq=0.083μm. This step took 0.08s, meeting the design requirement of ≤0.1s.
[0082] S5. Based on the residual feedback of the initial fitting parameters, dynamically adjust the defect weights and iteratively optimize S3-S4 until the convergence condition is met, and output the final fitting result.
[0083] Specifically, such as Figure 6 As shown, firstly, based on the initial fitting parameters (radius of curvature r, conic coefficient k, and surface roughness parameter Sq) output in step S4, and combined with the actual surface point cloud data... The fitting residual for each sampling point is calculated using the following formula: ,in The surface fitting function is constructed based on the initial parameters. It consists of a quadratic surface and higher-order correction terms, and corresponds to the weighted fitting objective function in step S4.
[0084] Calculate the maximum residual Err max =max(Err(x,y)) is used to determine whether the overall fitting accuracy meets the standard. The maximum residual Err is calculated. max =0.006μm (located at ρ=240μm in the edge region), which is greater than the convergence threshold of 0.005μm, and the residuals are concentrated in the edge region;
[0085] The distribution of residuals in different regions was statistically analyzed: the number of sampling points with residual absolute values greater than 0.003 μm in the central region (ρ≤0.6R), transition region (0.6R<ρ≤0.85R), and edge region (ρ>0.85R) was counted, and the proportion of these sampling points to the total number of sampling points in that region was calculated.
[0086] Determine the residual distribution type: If the percentage of residuals exceeding the threshold in the edge region is ≥60%, it is determined as "residuals concentrated in the edge region"; if the percentage of residuals exceeding the threshold in all three regions is between 30% and 50%, it is determined as "residuals distributed throughout the entire region"; otherwise, it is determined as "locally concentrated distribution".
[0087] Based on the defect pre-identification results (step S2) and the residual distribution analysis conclusions, the weights of various defect components and region weights are adjusted according to the following rules:
[0088] (1) Initial weight benchmark
[0089] Based on the defect dominance type determination result in step S2, set the initial weights:
[0090] If the tilt is determined to be dominant (G>0.01μm / μm), then the tilt component weights are... Other component weights ;
[0091] If the stress is determined to be dominant (Var(z)>0.005μm²), then the weight of the scribing stress component is... The remaining defect component weights ;
[0092] The initial values of the regional weights are set according to step S4: w=1.0 for the central region, w=1.2 for the transition region, and w=1.5 for the edge region.
[0093] (2) Weighting adjustment rules
[0094] The residuals are concentrated in the marginal region (ρ>0.85R): the regional weight of the marginal region is increased by 0.1 to 0.2, and the adjusted marginal region weight is ≥1.6 and ≤1.8;
[0095] If the pre-identification is stress-dominant, the additional weight W of the dicing stress component will be applied. stress Increase by 0.1; if tilt is dominant, additionally increase the weight W of the vacuum adsorption deformation component. deform Increase by 0.1;
[0096] Global residual distribution: The weight of the edge region increases by 0.1, and the weight of the transition region increases by 0.05; the weight of the warping component W... warp Increase by 0.1 to ensure the accuracy of stripping global defects;
[0097] Based on the aforementioned residual distribution calculation results, the weight of the edge region is adjusted from 1.5 to 1.6, and the weight of the dicing stress component is adjusted from 1.3 to 1.4. After completing the weight adjustment, return to step S3 and re-execute the multi-defect coupling decomposition based on the new defect weights:
[0098] The peeling priority of each component of tilt, warping, scuffing stress, and vacuum adsorption deformation is recalculated according to the adjusted weights. The higher the weight of the defect component, the stricter the fitting accuracy threshold used in the peeling process (e.g., after the weight of the tilt component is increased, the residual threshold of corner fitting is tightened from 0.005μm to 0.003μm).
[0099] After removing various defect components and noise, the updated true surface point cloud z_true' (x,y) is obtained.
[0100] Based on the updated real surface point cloud and the adjusted region weights, perform the domain-weighted fitting in step S4 to obtain new fitting parameters (r', k', Sq').
[0101] After each iteration, the process of "residual calculation - weight adjustment - decomposition and fitting" is repeated. The number of iterations is accumulated and counted. The total time for a single iteration is ≤0.1s (including 0.02s for residual calculation, 0.01s for weight adjustment, 0.04s for S3 re-decomposition, and 0.03s for S4 re-fitting). The maximum number of iterations is set to 3 to avoid excessive iterations that lead to a decrease in efficiency.
[0102] After each iteration, convergence is determined based on the following two conditions:
[0103] Maximum residual condition: the maximum residual Err after the update max' ≤0.005μm;
[0104] Iteration count condition: The cumulative number of iterations is ≤ 3.
[0105] If both of the above conditions are met simultaneously, the fit is considered convergent; if the number of iterations reaches 3 but Errr... max' If the value is still >0.005μm, an alarm message should be output, and the result of the 3rd iteration should be used as the final output; if the 3rd iteration has not been reached but Err has been satisfied... max' If the value is ≤0.005μm, the iteration can be terminated early.
[0106] After re-performing multi-defect coupling decomposition and domain-weighted fitting, the fitting parameters obtained after the second iteration are r=10.007mm, k=-1.006, Sq=0.082μm, and the maximum residual Err is... max =0.004μm≤0.005μm, and the number of iterations is 2≤3, which satisfies the convergence condition.
[0107] After the fit converges, the following results are output:
[0108] Final fitting parameters: radius of curvature r = 10.007 mm, conic coefficient k = -1.006, surface roughness parameter Sq = 0.082 μm (this step takes 0.04 s, which meets the design requirement of ≤0.05 s).
[0109] Residual data: final residual curve, average residual for each region, maximum residual Err max ;
[0110] Weight adjustment record: The adjustment values of the defect component weight and the region weight in each iteration are used to trace the fitting process;
[0111] Output format: Parameter data is stored in CSV format, and residual curves are stored in vector format, supporting integration with the subsequent data traceability module of the detection system.
[0112] Example 2
[0113] To better implement the silicon wafer multi-defect decoupling weighted fitting method in Embodiment 1 of the present invention, Embodiment 2 of the present invention also provides a silicon wafer multi-defect decoupling weighted fitting device, which includes a data acquisition module, an identification module, a decomposition module, a fitting module and an output module, and each module realizes bidirectional data interaction through a data bus;
[0114] The acquisition module, as the data input unit of the device, is used to acquire the raw point cloud data of the silicon wafer. Its structural design is adapted to mainstream microarray lens silicon wafers. After the user sets the scanning parameters through the host computer, the acquisition module drives the stage to move the area to be detected on the silicon wafer to the detection field of the white light interferometer. The white light emitted by the interferometer is reflected by the surface of the silicon wafer to form interference fringes. The interference fringes are captured by the image sensor and converted into height values. Combined with the XY axis positioning coordinates, raw point cloud data containing "x coordinate - y coordinate - height value" is generated. After preprocessing, it is transmitted to the recognition module.
[0115] The identification module is used to calculate the gradient and local variance of the raw point cloud data, identify the dominant defect type, and provide a targeted basis for subsequent multi-defect decomposition. After the identification module receives the raw point cloud data transmitted by the acquisition module, the data calculation unit performs gradient and local variance calculations in parallel. The calculation results are transmitted to the defect type determination unit, compared with the preset threshold, to determine the dominant defect type and generate the initial weight configuration. Then, the point cloud data, the dominant defect type, and the initial weights are transmitted to the decomposition module.
[0116] The decomposition module is used to remove defects and noise based on the multi-defect coupling model and output the true surface point cloud. It is the core module for realizing multi-defect decoupling. After the decomposition module receives the data transmitted by the recognition module, the multi-defect coupling model unit calls the corresponding model expression, the defect component solving unit solves the parameters of each defect component based on the initial weight configuration, the defect stripping unit strips the four types of defect components in sequence, and the noise elimination unit filters the remaining point cloud. Finally, the true surface point cloud is obtained and transmitted to the fitting module.
[0117] The fitting module is used to divide the lens unit region and assign differential weights, and fit the real surface point cloud using the weighted least squares method. Specifically, it includes a region division calculation unit, a weight configuration unit, and a parameter solving unit. After the fitting module receives the real surface point cloud transmitted by the decomposition module, the region division unit completes the region division and sampling point allocation, the weight configuration unit assigns differential weights, the fitting model construction unit constructs the objective function, and the parameter solving unit solves the fitting parameters using the Newton iteration method. The initial fitting parameters and residual distribution are then transmitted to the output module.
[0118] The output module is used to adjust the defect weights based on the fitting residuals, iteratively execute the defect decomposition and fitting process, and output the final parameters. After the output module receives the initial fitting parameters and residual distribution transmitted by the fitting module, its internal residual calculation unit completes the residual analysis, the weight adjustment unit adjusts the weights according to the residual distribution, and the iterative convergence judgment unit judges whether the convergence condition is met. If it does not converge, the iterative process is triggered. After convergence, the final data is output through the result output interface, completing the entire fitting and detection process.
[0119] Furthermore, the embodiments of the present invention do not specifically limit the type of electronic device mentioned. The electronic device can be a mobile phone, tablet computer, personal digital assistant (PDA), wearable device, laptop computer, or other portable electronic device. Exemplary embodiments of portable electronic devices include, but are not limited to, portable electronic devices running iOS, Android, Microsoft, or other operating systems. The aforementioned portable electronic devices can also be other portable electronic devices, such as laptop computers with touch-sensitive surfaces (e.g., touch panels). It should also be understood that in some other embodiments of the present invention, the electronic device may not be a portable electronic device, but rather a desktop computer with a touch-sensitive surface (e.g., a touch panel).
[0120] Accordingly, this application also provides a computer-readable and writable storage medium for storing computer-readable programs or instructions. When the programs or instructions are executed by a processor, they can implement the steps or functions of the silicon wafer multi-defect decoupling weighted fitting method provided in the above-described method embodiments.
[0121] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.), and the computer program can be stored in a computer-readable and writable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.
[0122] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A weighted fitting method for decoupling multiple defects in silicon wafers, characterized in that, Includes the following steps: S1. Obtain the raw point cloud data of the silicon wafer; S2. Calculate the gradient G and local variance Var(z) of the original point cloud data to identify the dominant defect type; S3. Based on the aforementioned defect-dominant type, the original point cloud data is decomposed using a multi-defect coupling model to remove multiple defect components and noise, thereby obtaining a true surface point cloud. S4. Divide the region according to the ratio of the lens unit radius and assign differential weights, and perform weighted fitting on the real surface point cloud to obtain the initial fitting parameters; S5. Based on the residual feedback of the initial fitting parameters, dynamically adjust the defect weights and iteratively optimize S3-S4 until the convergence condition is met, and output the final fitting result.
2. The silicon wafer multi-defect decoupling weighted fitting method according to claim 1, characterized in that, In step S2, the gradient G includes the gradient in the X direction. gradient in the Y direction The local variance Var(z) is expressed as Var(z) = E[(zE[z])²]; Among them, when G>0.01μm / μm, it is determined to be tilt-dominant, and when Var(z)>0.005μm², it is determined to be stress-dominant.
3. The silicon wafer multi-defect decoupling weighted fitting method according to claim 1, characterized in that, In step S3, the multi-defect coupling model includes a tilt component. Warp component Scrap stress components Vacuum adsorption deformation component , True face shape components and noise components Its expression is: 。 4. The silicon wafer multi-defect decoupling weighted fitting method according to claim 3, characterized in that, The tilt component For the linear terms in the X / Y directions, the expression is: ,in The tilt coefficient is obtained by fitting the height values of the four corner points of the point cloud edge.
5. The silicon wafer multi-defect decoupling weighted fitting method according to claim 3, characterized in that, The warping component The expression is: ,in, The warpage coefficient is obtained by fitting the quadratic and quartic terms using the least squares method after removing 5% of the point cloud data from the edges, with a fit of ≥0.
996.
6. The silicon wafer multi-defect decoupling weighted fitting method according to claim 3, characterized in that, The dicing stress component The expression is The stress center was located by the peak value of the local variance of the point cloud. c, d, and f are obtained by fitting the point cloud of the peak region.
7. The silicon wafer multi-defect decoupling weighted fitting method according to claim 3, characterized in that, The vacuum adsorption deformation component The expression is , where g is the adsorption coefficient, which is obtained by fitting the difference value by comparing the point clouds of standard silicon wafers with and without adsorption.
8. The silicon wafer multi-defect decoupling weighted fitting method according to claim 3, characterized in that, The noise component Eliminate by combining 3×3 median filtering and Gaussian filtering.
9. The silicon wafer multi-defect decoupling weighted fitting method according to claim 1, characterized in that, In step S4, the rules for region division and weight setting are as follows: Central region: ρ≤0.6R, weight w=1.0, sampling point ratio 35%, fitting residual <0.004um; Transition region: 0.6R < ρ ≤ 0.85R, weight w = 1.2, sampling point ratio 50%, fitting residual < 0.003um; Edge region: ρ>0.85R, weight w≥1.5, sampling point ratio 15%, fitting residual <0.005um, and edge derivative constraint is added; ρ is the radial distance from any point in the lens unit to the center.
10. The silicon wafer multi-defect decoupling weighted fitting method according to claim 8, characterized in that, In step S4, the weighted fitting is performed by minimizing the objective function J to solve for the fitting parameters. The expression for the objective function J is: ； in, Here, r represents the weight of each sampling point, r is the reference radius of curvature of the lens, and k is the conic coefficient. This represents the true surface shape of the lens at each sampling point; By taking the partial derivatives of r and k in the objective function and setting them to 0, we obtain a system of equations. We then use Newton's iteration method to solve the system and obtain the values of r and k.
11. The silicon wafer multi-defect decoupling weighted fitting method according to claim 8, characterized in that, In step S5, the dynamic weight adjustment and convergence conditions include: The initial weights are set based on the defect pre-identification results: if G > 0.01 μm / μm, then the tilt component weights are adjusted accordingly. Other defect components have a weight of 1.0; if Var > 0.005 μm², then the tilt component weight is... Other defect components have a weight of 1.0; Residual adjustment rule: If the residuals are concentrated in the marginal region, i.e., ρ>0.85R, then the marginal region weights are adjusted. Increase by 0.1~0.2; if the residuals are distributed globally, then the weights of the marginal regions are adjusted. Increase by 0.1; Convergence condition: The number of iterations is ≤3, and the maximum fitting residual Err is ≤3. max ≤0.005μm.
12. A silicon wafer multi-defect decoupling weighted fitting device, characterized in that, include: The acquisition module is used to acquire the raw point cloud data of the silicon wafer; The identification module is used to calculate gradients and local variances to identify the dominant defect type. The decomposition module is used to perform the multi-defect coupling model according to any one of claims 1-11 to remove defects and noise and output a realistic surface point cloud; The fitting module is used to divide the lens unit regions and assign differential weights, and fit the real surface point cloud using the weighted least squares method. The output module is used to adjust the defect weights based on the fitting residuals, iteratively execute the defect decomposition and fitting process, and output the final parameters.
13. A storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the steps of the silicon wafer multi-defect decoupling weighted fitting method according to any one of claims 1 to 11.