Method for improving efficiency of dynamic overlay compensation metrology based on hermite interpolation

Abstract

The application provides a dynamic overlay compensation measurement efficiency improving method based on Hermite interpolation, relates to the technical field of semiconductor chip manufacturing, adopts a two-dimensional Hermite interpolation technology through partial measurement, significantly breaks through the efficiency bottleneck of full measurement in traditional overlay control, and the traditional method needs to measure all shot points of a wafer, is time-consuming and reduces the throughput of a production line, and only m key shot points are measured in the scheme, about 80% of the measurement workload is reduced, and the throughput is improved by several times.The creativity lies in that the Hermite interpolation generates a smooth full-wafer difference distribution by using difference and derivative, the error is controlled within ±1nm, and the precision is comparable to that of full measurement.The optimized sampling plan further ensures the coverage of key areas and makes up for the limitations of partial measurement.This dual optimization of efficiency and precision not only reduces the burden of the measurement equipment, but also provides a feasible and efficient control scheme for advanced nodes, and has a significant breakthrough significance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of semiconductor chip manufacturing, in particular to a dynamic overlay compensation measurement efficiency improvement method based on Hermite interpolation. BACKGROUND

[0002] In semiconductor manufacturing, overlay control is the key to ensuring that the offset between different alignment layers (overlay) meets the process specifications, especially at advanced nodes (such as below 3nm), the overlay tolerance budget is reduced to a few nanometers.

[0003] The prior art has the following technical problems when in use:

[0004] Problem one, the traditional method relies on full measurement of all shot points on the wafer to ensure accuracy, but as the number of shot points increases (for example, a 12-inch wafer may have hundreds of shot points), the measurement time is significantly prolonged, directly reducing the production line throughput, the high load of the measurement equipment not only increases the cost, but also affects the economy due to the decrease in wafer area utilization (more metrology marks need to be inserted), this low efficiency problem contradicts the demand for high precision and high throughput at advanced nodes, limiting the production scale and process optimization;

[0005] Problem two, the traditional overlay compensation relies on a static reference map (such as the fixed overlay distribution of initial measurement), and adjusts the exposure parameters through a simple feedback / forward mechanism, in actual production, wafer-to-wafer variation and process drift cause the overlay distribution to change dynamically over time, the static reference cannot reflect these changes in real time, the compensation accuracy gradually decreases, especially in complex processes, the overlay deviation problem is aggravated, affecting yield and process stability. SUMMARY

[0006] Technical problems solved

[0007] In view of the deficiencies of the prior art, the present application provides a dynamic overlay compensation measurement efficiency improvement method based on Hermite interpolation, which solves the following problems:

[0008] 1. The contradiction between the low efficiency of the traditional full measurement method and the demand for overlay control at advanced nodes;

[0009] 2. The problem that the traditional static compensation cannot adapt to the dynamics of wafer-to-wafer variation and process drift;

[0010] 3. The problem of lack of cross-platform advertising effect coordination optimization.

[0011] Technical solutions

[0012] To achieve the above objectives, the present invention provides the following technical solution: a method for improving measurement efficiency through dynamic overlay compensation based on Hermite interpolation, the method comprising the following:

[0013] Sp1: Select at least one reference wafer from the batch, perform overlay measurements on all its points, and generate a baseline overlay map, represented as follows: ,in For the first The location coordinates of each point , The total number of firing points depends on the wafer size and process design (e.g., a 12-inch wafer may have hundreds of firing points). The horizontal position Vertical position;

[0014] Sp2: For each production wafer, select based on a predefined sampling plan. Overlay measurements were performed on each of the partial shooting points, among which... Furthermore, the sampling plan ensures that the measurement points cover all areas of the wafer and supports derivative estimation. The measurement results are expressed as follows: ,in, The overlay value of the measurement points on the production wafer, in nm. For the first The coordinates of each measurement point are in millimeters.

[0015] Sp3: Calculation The difference between the overlay of each measurement point and the corresponding point on the baseline overlay map ,in, For the first The overlay difference at each measurement point, in nm. To generate wafer measurement values, The base overlay value;

[0016] Sp4: Estimation via the finite difference method The partial derivative of the difference between the measurement points with respect to the wafer position coordinates, for measurement points with neighboring measurement points. and neighboring points The derivative is calculated based on the difference in value and position between adjacent firing points:

[0017]

[0018]

[0019] in, It is the reciprocal of the difference in the x-direction, with units of nm / mm; is the partial derivative in y direction, unit: nm / mm; is the difference value of the neighboring shot k, unit: nm, is the distance difference in x direction, unit: mm, is the distance difference in y direction, unit: mm, for the shot without neighboring measurement shot, the derivative is set as the process default value ;

[0020] Sp5: based on the difference value and the estimated partial derivative ,a two-dimensional Hermite interpolation technique is used to interpolate the difference value of the unmeasured shot , to generate a smooth difference value distribution;

[0021] Sp6: according to the reference overlay map and the interpolated difference value, the complete overlay map of each production wafer is calculated, wherein for each shot , ;

[0022] Sp7: after processing a predetermined number of production wafers, the reference overlay map is dynamically updated by calculating the average value of the complete overlay map, that is , to adapt to the process change;

[0023] Preferably, the sampling plan in step Sp2 is generated by an optimization algorithm, and the optimization algorithm aims to minimize the global error of Hermite interpolation :

[0024]

[0025] wherein, the global interpolation error, unit: nm 2 , measures the difference value accuracy, is the interpolated difference value, unit: nm, is the total number of shots, is the true difference value, which is dynamically adjusted based on the spatial distribution of the shots on the wafer and the process variation characteristics to adjust the position of the measurement shot.

[0026] Preferably, in step Sp4, for the shot with neighboring measurement shot, the weighted finite difference method is used to calculate the partial derivative:

[0027]

[0028] wherein, is the shot a set of neighboring points of the shot j, a set of neighboring points of the shot j;

[0029]

[0030] a normalized weight based on the distance between neighboring shots and a process uniformity parameter to improve the local adaptability of the derivative estimation.

[0031] Preferably, the two-dimensional Hermite interpolation technique in step Sp5 employs piecewise cubic Hermite splines, with the interpolation function in the form of:

[0032]

[0033] wherein, is a constant term, is a first-order term coefficient with a unit of nm / mm, is a second-order term coefficient with a unit of nm / mm 2 , is a third-order term coefficient with a unit of nm / mm 3 , is an offset relative to the start of the interval with a unit of mm, and is calculated on each piecewise interval wherein the coefficient , , , is determined by , and the neighboring point values, and a virtual derivative value is introduced at the boundary shot to enhance the interpolation smoothness.

[0034] Preferably, in step Sp6, when calculating the complete overlay map, a constraint condition is imposed on wherein, is the upper limit of the process specification, and when exceeded, triggers local re-measurement to correct the interpolation result.

[0035] Preferably, in step Sp7, when dynamically updating the reference overlay map, a weighted average mechanism is introduced, with the calculation formula being:

[0036]

[0037] wherein, is the value of the updated reference overlay with a unit of nm, the number of production wafers, is the Zhang Jingyuan's overlay estimate, The weights decay over time. As a decay factor, to adapt to short-term process drift more quickly, the full overlay map of newer production wafers is given higher weight to adapt to short-term process drift more quickly.

[0038] Preferably, the optimization algorithm further incorporates historical measurement data and uses a machine learning model to predict the variance of highly variable regions:

[0039]

[0040] in, The variance of the overlay at the location, in nm. 2 Indicates the degree of variation. For the historical overlay value, For the mean, choose first. Higher injection points are used for measurement to improve the robustness of interpolation to inter-wafer differences.

[0041] Preferably, in step Sp1, selecting Zhang Reference Wafer And through principal component analysis (PCA) Zhang Jingyuan's overlay measurement results Perform feature extraction and calculate principal components. ,and The weights of the first principal components are used to generate a more representative baseline overlay map. ,in, The first principal component, measured in nm, is used to extract the main features of the overlay through principal component analysis (PCA). For reference wafer count, , For the first Zhang Jingyuan's weighting technique on the first principal component was calculated using PCA. For the first Zhang reference wafer at the injection point The value of overlay, in nm.

[0042] Preferably, the piecewise cubic Hermite splines incorporate a regularization term during interpolation, with the objective function being:

[0043]

[0044] in, The regularization objective function is given in nm. 2 , to measure the actual difference of shots in nm, is a regularization parameter to constrain the second derivative of the interpolation curve to reduce overfitting and improve compensation accuracy.

[0045] Preferably, the method further comprises a step Sp8, after generating the complete overlay map, calculating a wafer stress distribution based on the estimated overlay distribution:

[0046]

[0047] wherein, is the wafer stress distribution in Pascals, is the stress conversion factor, is the Laplace operator, and dynamically adjusting the subsequent exposure parameters:

[0048]

[0049] wherein, is the adjusted exposure parameter to optimize overlay control, wherein is the adjustment factor.

[0050] Advantages

[0051] The present application provides a dynamic overlay compensation measurement efficiency improvement method based on Hermite interpolation. Has the following advantages:

[0052] 1、The present application adopts partial measurement combined with two-dimensional Hermite interpolation technology, which significantly breaks through the efficiency bottleneck of full measurement in traditional overlay control. The traditional method needs to measure all shots of the wafer, which is time-consuming and reduces the production line throughput. However, the present application only measures m key shots, reducing about 80% of the measurement workload, and the throughput can be improved by several times. The creativity lies in that Hermite interpolation uses difference and derivative , to generate a smooth full-wafer difference distribution with an error controlled within ±1nm, which is comparable to the full measurement accuracy. The optimized sampling plan further ensures key area coverage, making up for the limitations of partial measurement. This dual optimization of efficiency and accuracy not only reduces the burden on measurement equipment, but also provides a feasible and efficient control scheme for advanced nodes, which has a significant breakthrough significance.

[0053] 2. An innovative closed-loop control mechanism is constructed through dynamic benchmark updates and stress feedback adjustments, overcoming the shortcomings of traditional static compensation in adapting to process drift. Traditional methods rely on a fixed benchmark, making it difficult to cope with inter-wafer variations and short-term drift. This solution updates the benchmark every w wafers and is based on overlay distribution. By calculating stress and dynamically adjusting exposure parameters, this closed-loop design reduces overlay deviation by approximately 10%-15% and improves long-term stability by about 20%, performing particularly well in complex processes such as multiple exposures. The innovation lies in the combination of regularized interpolation and variation prediction, ensuring interpolation robustness while stress feedback optimizes subsequent exposures, forming an adaptive control chain. This provides a highly robust solution for semiconductor manufacturing, driving improvements in process consistency and yield. Attached Figure Description

[0054] Figure 1 This is a diagram illustrating the method steps of the present invention;

[0055] Figure 2 This is the initial 3D surface distribution map of the baseline overlay map of this invention;

[0056] Figure 3 This is a comparison diagram of the discrete measurement points of the present invention;

[0057] Figure 4 This is a difference discrete comparison diagram of the present invention;

[0058] Figure 5 This is a Hermite interpolation distribution diagram for the present invention. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and 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. Specific Implementation Example 1:

[0061] like Figure 1 to Figure 5 As shown, a method for improving measurement efficiency based on Hermite interpolation dynamic overlay compensation includes the following:

[0062] Sp1: Baseline Overlay Map Generation: Establishes an initial reference baseline for the entire method, ensuring a reliable basis for comparison in subsequent steps; selects at least one reference wafer from the batch (preferably ≥2 wafers to improve representativeness), and uses a high-precision overlay metrology device (such as KLA's Archer series) to measure all of them. Measurements were taken at each point to generate a baseline overlay map. ,That For the first The location coordinates of each point , This refers to the total number of injection points (e.g., a 12-inch wafer may have 100-200 injection points, depending on the process design); measurement results. (Unit: nanometers, nm) Record the overlay value for each injection point, i.e., the offset between different alignment layers; in the preferred scheme, select k reference wafers (k is a positive integer, 2-5 wafers are recommended), and measure the overlay of each wafer. Perform principal component analysis (PCA) to calculate the first principal component. ,and The weights of the first principal components are used to generate a more representative baseline overlay map. This process first involves The overlay data of Zhang Jingyuan is input into the PCA algorithm (which can be implemented using MATLAB or Python's sklearn library), extracts the main variation patterns, removes noise and outliers, and then outputs a baseline map. The logic of the whole process is to extract the typical overlay distribution from the wafers in the early stage of the batch as a reference for subsequent production wafers, ensuring that the baseline reflects the average state and main characteristics of the process.

[0063] Sp2: Partial Measurement Functions and Processes for Production Wafers: This step reduces workload through partial measurement while ensuring data supports interpolation accuracy; for each production wafer, 1m sampling points are selected based on a predefined sampling plan. Overlay measurements were performed, and the results were as follows: (Unit: nanometer, nm), where For the first The coordinates of each measurement point are given in millimeters. The sampling plan must ensure that the 𝑚m measurement points cover all regions of the wafer (such as the center, edge, and transition region) and support derivative estimation (i.e., some measurement points have neighboring points). The sampling plan in step Sp2 is generated by an optimization algorithm that minimizes the global error of Hermite interpolation. For the goal:

[0064]

[0065] in, Global interpolation error, in nm 2 To measure the accuracy of the difference The difference between the interpolation estimates is expressed in nm. The total number of shots. The true difference is dynamically adjusted based on the spatial distribution of wafer up-shoot points and process variation characteristics. The positions of the 1m measurement points are dynamically adjusted by an optimization algorithm (such as a genetic algorithm or simulated annealing) based on the spatial distribution of the points and process variation characteristics. Specifically, the input is a wafer coordinate grid and variation estimate, and the output is the optimal set of sampling points. The optimization algorithm further combines historical measurement data and uses a machine learning model to predict the variance of high-variance regions.

[0066]

[0067] in, The variance of the overlay at the location, in nm. 2 Indicates the degree of variation. For the historical overlay value, For the mean, choose first. Higher datum points are used for measurement to improve the robustness of interpolation to inter-wafer differences. m key points are selected from the full datum grid (e.g., s=100, s=100, y=20, m=20). The measurement device records y(xj, yj)P(xj, yj) to provide input data for subsequent difference and interpolation.

[0068] Sp3: Difference Calculation Function and Process: This step calculates the deviation between the production wafer and the reference, laying the foundation for interpolation; for Calculate the overlay difference at each measurement point. ,in, For the first The overlay difference at each measurement point, in nm. To generate wafer measurement values, The base overlay value; obtained from Sp2. Read the corresponding coordinates from Sp1 Subtracting point by point, we get It captures local variations of the production wafer relative to a reference, assuming that variations in unmeasured areas can be estimated through interpolation. The difference results are directly input into Sp4 and Sp5 for derivative calculation and interpolation.

[0069] Sp4: Partial Derivative Estimation Function and Process: This step provides slope information for Hermite interpolation, ensuring smoothness and accuracy; it estimates the partial derivative using the finite difference method. The partial derivative of the difference between the measurement points with respect to the coordinates, for a measurement point with neighboring measurement points. and neighboring points The derivative is calculated based on the difference in value and position between adjacent firing points:

[0070]

[0071]

[0072] wherein, is the reciprocal of the partial derivative of the difference in the x direction, in nm / mm; is the partial derivative of the interpolated difference in the y direction, in nm / mm; is the difference of the neighboring shot k, in nm, is the difference of the distance in the x direction, in mm, is the difference of the distance in the y direction, in mm, for the shot without neighboring measurement points, the derivative is set to the process preset value ; in the preferred embodiment, the weighted finite difference method is used to calculate the partial derivative:

[0073]

[0074] wherein, is the set of neighboring points of the shot , and is the set of neighboring points of the shot j;

[0075]

[0076] is the normalized weight based on the distance , wherein the weight is determined according to the distance between the adjacent shots and the process uniformity parameter to improve the local adaptability of the derivative estimation; the weight is determined according to the distance and the process uniformity parameter (such as the flatness of the wafer area), and the near neighbor has a greater impact; in the implementation, the coordinates of and are obtained from Sp3, the neighboring points (for example, the points with a distance less than 5 mm) are identified, the weighted derivative is calculated, and the result is output to Sp5, which is the spatial trend of overlay reflected by the local difference change rate, supporting the continuity of interpolation;

[0077] Sp5: Hermite interpolation function and process: this step generates the difference of the unmeasured shot, completes the difference distribution of the whole wafer, based on the difference and the estimated partial derivative , , the two-dimensional Hermite interpolation technology is used to interpolate the difference of the unmeasured shot , to generate a smooth difference distribution, using a piecewise cubic Hermite spline, the interpolation function is in the form of:

[0078]

[0079] on each piece interval , wherein the coefficients , , , By , Determined by and adjacent point values, and introduce virtual derivative values at the boundary shot points To enhance the smoothness of interpolation, further preferably, introduce a regularization term in the interpolation process, the objective function is:

[0080]

[0081] Wherein, The regularization objective function is nm 2 , The actual difference value of the measurement shot is nm, The regularization parameter constrains the second derivative of the interpolation curve To reduce overfitting and improve compensation accuracy, input the difference and derivative from Sp3 and Sp4, calculate the two-dimensional spline using a numerical library (such as SciPy), and optimize Output , using the values and slopes of known points, smooth estimate full wafer difference, provide complete data for Sp6;

[0082] Sp6: complete overlay map generation function and process: this step synthesizes the complete overlay distribution of the production wafer, which is used for feedback control, according to the reference overlay map and the difference obtained by interpolation, the complete overlay map of each production wafer is calculated, wherein for each shot , , from Sp1, From Sp5, the optimization is to impose constraint conditions on When calculating the complete overlay map , wherein, The process specification upper limit is triggered when it is exceeded, and local re-measurement is triggered to correct the interpolation result, when, point by point addition to generate the full map, check the constraint conditions, if necessary Adjust the m and return to Sp2, combine the reference and estimated deviation to generate a full overlay distribution that meets the process requirements, and directly used for exposure machine parameter adjustment;

[0083] Sp7: reference map update function and process: this step dynamically adjusts the reference to adapt to process drift; after processing w production wafers (w is a predetermined number, such as 10), calculate the average value of the complete overlay map to update the reference: that is When updating the reference overlay map to adapt to process changes, a weighted average mechanism is introduced, and the calculation formula is:

[0084]

[0085] wherein, is the value of the updated reference overlay in nm, the number of production wafers, is the overlay estimate value of the k-th wafer, is the weight decaying over time, is the decay coefficient to adapt to short-term process drift faster, wherein the complete overlay map of the newer production wafer is given a higher weight to adapt to short-term process drift faster, from Sp6, calculate the weighted average, replace the old reference, track the process changes by periodic updates, and ensure that the reference is consistent with the current state;

[0086] Sp8: Stress distribution and exposure adjustment function and process: this step optimizes the subsequent exposure based on the overlay distribution to form a closed-loop control; after generating the complete overlay map, the wafer stress distribution is calculated based on the estimated overlay distribution:

[0087]

[0088] wherein, is the wafer stress distribution in pascal, is the stress conversion coefficient, is the Laplacian operator, and the subsequent exposure parameters are dynamically adjusted:

[0089]

[0090] wherein, is the adjusted exposure parameter to optimize overlay control, wherein is the adjustment factor, and is obtained from Sp6, calculate the stress distribution, input the exposure machine (such as ASML lithography machine) adjustment parameter, optimize the exposure through stress feedback, and reduce the overlay deviation.

[0091] The whole method starts from Sp1 initialization benchmark, and the Sp2 to Sp7 processes each production wafer in a loop, and the Sp8 optimizes the subsequent exposure to form a closed-loop control system. The core is the combination of partial measurement (Sp2) and Hermite interpolation (Sp5), supplemented by dynamic updating (Sp7) and exposure adjustment (Sp8), to realize efficient and accurate overlay control. The wafer enters the measurement device from the production line, performs Sp2 measurement, and the data is processed by Sp3-Sp6 to generate an overlay map, Sp7 updates the benchmark, and Sp8 adjusts the exposure parameters before returning to the exposure machine, and the cycle runs. The data flow from the measurement device to the calculation unit (running interpolation and optimization algorithms), and then to the exposure machine, forms a real-time control chain. Embodiment Two:

[0093] As shown in Figure 1 to Figure 5 According to the content in the above embodiments, the following content is further disclosed:

[0094] To further verify the feasibility and effect of the present application, a comparative experiment is designed for verification, and the specific content is as follows:

[0095] The existing overlay control method mainly includes the following two typical technologies:

[0096] Full measurement compensation method: overlay measurement is performed on all shot points (s) of the wafer to generate a complete overlay map, which is directly fed back to the exposure machine to adjust the parameters; high precision (error <1nm), but long measurement time, low throughput, and a large number of metrology marks are required, which reduces the wafer area utilization rate; representative literature: such as "Overlay measurement and compensation in semiconductor fabrication" (US9786569B1);

[0097] Simple partial measurement + linear interpolation method: measure part of the shot points (m < s), and use linear interpolation (such as Lagrange interpolation) to estimate the overlay value of the unmeasured points; improve efficiency, but the interpolation accuracy is low (error about 2-5nm), and the adaptability to wafer-to-wafer variation and process drift is poor; representative literature: such as "Overlay Error Compensation Using Advanced Process Control" (IEEE6609079);

[0098] The principle of the technical solution: based on partial measurement (m < s), two-dimensional Hermite interpolation is used to generate a full-wafer overlay map , combined with dynamic benchmark updating and stress feedback adjustment to realize closed-loop control;

[0099] Distinctive features: Hermite interpolation with optimized sampling: utilize difference and derivative , , combined with optimization algorithm (minimize E) and variation prediction ( ), improve interpolation accuracy and efficiency;

[0100] Dynamic closed-loop control: update reference by weighting

[0101] and stress adjustment

[0102] Adapt to process drift, high efficiency (reduce measurement by about 80%), high accuracy (error ±1nm), strong robustness (stability improved by 20%).

[0103] The experimental content is as follows:

[0104] Purpose of the experiment: verify the distinctive features of this technical solution in measurement efficiency, compensation accuracy and process robustness, compare with existing technology, highlight the innovation of Hermite interpolation and closed-loop control;

[0105] Experimental conditions and equipment: KLA overlay measurement machine (such as Archer700), ASML lithography machine (such as TWINSCAN NXT); sample: 12-inch wafer, process node 5nm, batch size 100, total number of shots s=100s=100; environment: temperature 22±1°C, humidity 45±5%, cleanliness Class 10;

[0106] Experimental group and control group:

[0107] Experimental group (this scheme): measure m=20 shots, use optimized sampling (minimize E and ), Hermite interpolation to generate , update every 10 wafers (𝑤=10w=10) , calculate S adjustment E;

[0108] Control group 1 (full measurement compensation method): measure all s=100 shots, no interpolation, directly generate overlay map, static reference;

[0109] Control group 2 (simple partial measurement + linear interpolation method): measure m=20 shots (random sampling), linear interpolation to generate overlay map, no update and stress adjustment;

[0110] Experimental steps:

[0111] Reference establishment: experimental group: generate Control group 1: full measurement of the first batch of 1 wafer to generate static reference; Control group 2: measurement of 20 points of the first batch of 1 wafer, linear interpolation to generate reference;

[0112] Measurement and processing: 100 wafers were processed in each group, and the measurement time was recorded;

[0113] Experimental group: optimized sampling, calculation , derivative , , update , adjust E;

[0114] Control group 1: full measurement to generate overlay map;

[0115] Control group 2: random sampling, linear interpolation to generate overlay map;

[0116] Verification: full measurement on each wafer (as true value), calculate overlay error of each group; statistical throughput (wafers per hour); simulate process drift (adjust lithography parameters), evaluate deviation change of each group;

[0117] Verification index measurement efficiency: average single wafer measurement time (seconds); compensation accuracy: overlay root mean square error (RMSE, unit: nm): ; process robustness: overlay deviation standard deviation after 100 wafers (unit: nm);

[0118] The experimental results are as follows:

[0119] Indicator Full measurement compensation method Simple partial measurement + linear interpolation method The technical solution Note Measurement time (seconds / page) 50 12 10 Optimized sampling reduces additional computing overhead RMSE (nm) 0.8 3.2 0.9 Hermite interpolation accuracy close to full measurement Throughput (pages / hour) 72 300 360 The highest efficiency, about 5 times higher Bias standard deviation (nm) 1.5 2.8 1.2 Closed-loop control improves robustness and best stability

[0120] Table 1

[0121] Result analysis:

[0122] Measurement efficiency: the measurement time of this scheme (10 seconds per wafer) is shortened by 80% compared with full measurement (50 seconds per wafer), and is slightly better than linear interpolation method (12 seconds per wafer), which verifies the high efficiency of partial measurement and optimized sampling.

[0123] Compensation accuracy: RMSE is 0.9nm, close to full measurement (0.8nm), far superior to linear interpolation (3.2nm), which proves the precision breakthrough of Hermite interpolation (including derivative and regularization).

[0124] Process robustness: deviation standard deviation 1.2nm is better than full measurement (1.5nm) and linear interpolation (2.8nm), dynamic update and stress feedback significantly improve adaptability.

[0125] The experiment verifies that the scheme has the distinguishing features in efficiency, precision and robustness, the Hermite interpolation and closed-loop control solve the bottleneck of the prior art, have the breakthrough of creativity, and are suitable for advanced semiconductor manufacturing.

[0126] It is to be noted that the relational terms herein, such as first and second, and the like, are used solely to distinguish one from another entity or action without necessarily requiring or implying any actual relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. The terms "comprises", "comprising", or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus.

[0127] Although the embodiments of the present application have been shown and described, it is to be understood that various changes, modifications, substitutions, and alterations can be made to the embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for improving the efficiency of dynamic overlay compensation metrology based on Hermite interpolation, characterized in that: The method comprises the following steps: Sp1: select at least one reference wafer from the batch, perform overlay measurement on all shots of the reference wafer, generate a reference overlay map, denoted as wherein is the position coordinate of the th set point, , is the total number of shots.​ Sp2: for each production wafer, select a partial set of shots for overlay measurement based on a predefined sampling plan, wherein , and the sampling plan ensures that the measurement shots cover each region of the wafer and support derivative estimation, and the measurement results are represented as ; Sp3: Calculate Difference between overlay of the metrology shot and overlay of the corresponding shot of the reference overlay map ; Sp4: Estimate the partial derivative of the difference of the metrology shots with respect to the wafer position coordinates by finite difference method for shots with neighboring metrology shots and neighboring shots Compute the derivative based on the difference of the neighboring shots and the position difference: ； ； For shot without neighboring metrology points, set derivative to process default value ; Sp5: difference based and estimated partial derivatives , , interpolate the difference of unmeasured shots using two-dimensional Hermite interpolation technique to generate a smooth difference distribution;​ Sp6: Calculate a complete overlay map for each production wafer based on the reference overlay map and the difference values obtained by interpolation, wherein for each shot , ; Sp7: After processing a predetermined number of production wafers, the reference overlay map is dynamically updated by calculating the average of its complete overlay maps, i.e. to accommodate process variations. to accommodate process variations.

2. The method of claim 1, wherein the overlay measurement efficiency is improved by using a Hermite interpolation-based dynamic overlay compensation. The sampling plan in the step Sp2 is generated by an optimization algorithm which dynamically adjusts based on the spatial distribution of shot points on the wafer and process variation characteristics to minimize the global error of the Hermite interpolation the position of the one metrology shot.

3. The method of claim 1, wherein the overlay measurement efficiency is improved by using a Hermite interpolation-based dynamic overlay compensation. In the step Sp4, partial derivatives are calculated for shot points with neighboring measurement points using weighted finite difference method, where weights are determined according to distances between neighboring shot points and process uniformity parameters.

4. The method of claim 1, wherein the overlay measurement efficiency is improved by using a Hermite interpolation-based dynamic overlay compensation. In the step Sp5, a two-dimensional Hermite interpolation technique is used, which adopts piecewise cubic Hermite splines to construct interpolation functions along x and y directions of the wafer respectively, and introduces virtual derivative values at boundary shot points to enhance interpolation smoothness.

5. The method of claim 1, wherein the method is a Hermite interpolation based dynamic overlay compensation metrology efficiency improvement method. In said step Sp6, when computing the complete overlay map, the overlay map is computed by Applying constraints wherein, a process specification upper line, and trigger a local re- metrology to correct the interpolation result when exceeded.

6. The method of claim 1, wherein the overlay measurement efficiency is improved by using a Hermite interpolation-based dynamic overlay compensation. In the step Sp7, when updating the reference overlay map dynamically, a weighted average mechanism is introduced, where a complete overlay map of a newer production wafer is given a higher weight to adapt to short-term process drift more quickly.

7. The method of claim 1, wherein the overlay measurement efficiency is improved by using a Hermite interpolation-based dynamic overlay compensation. In the step Sp2, the optimization algorithm further combines historical measurement data to predict high-variation regions through a machine learning model, and shot points in these regions are preferentially selected for measurement to improve the robustness of the interpolation to wafer-to-wafer differences.

8. The method of claim 1, wherein the overlay measurement efficiency is improved by using a Hermite interpolation-based dynamic overlay compensation. 8 In the step Sp1, selecting Zhang reference wafer and extracting features by principal component analysis (PCA) on the overlay measurement results of Zhang wafer to calculate principal components , and the weight of the first principal component, to generate a more representative reference overlay map .

9. The method of claim 4, wherein the method is a Hermite interpolation based dynamic overlay compensation metrology efficiency improvement method, characterized by: In the step Sp5, the piecewise cubic Hermite spline introduces a regularization term in the interpolation process to constrain the second derivative of the interpolation curve based on the physical model of the wafer, thereby reducing overfitting and improving compensation accuracy.

10. The method of claim 1, wherein the method is a Hermite interpolation based dynamic overlay compensation metrology efficiency improvement method. The method further comprises the step Sp8, after generating a complete overlay map, calculating the wafer stress distribution based on the estimated overlay distribution, and dynamically adjusting subsequent exposure parameters to optimize overlay control.

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