A method and system for designing optical measurement marks for two-dimensional array overlay error

Abstract

This invention discloses a design method and system for two-dimensional array-type optical measurement marks for overlay errors, relating to the field of integrated circuit process measurement technology. The method includes: designing two-dimensional array-type optical measurement marks for overlay errors and constructing a characterization method for overlay errors; constructing a multi-objective optimization model based on the characterization method; solving the multi-objective optimization model using a multi-objective multiverse optimization algorithm to obtain the optimal mark structure; the multi-objective multiverse optimization algorithm incorporates a Latin hypercube initialization method, a fitness evaluation mechanism based on the NMPSO algorithm, and a dynamic adjustment strategy for the external archive size into the original multi-objective multiverse algorithm. This invention enables simultaneous measurement of overlay errors in two directions using two-dimensional array-type overlay marks, and improves the measurement performance of the marks based on structural optimization design.

Description

Technical Field

[0001] This invention relates to the field of integrated circuit process measurement technology, and in particular to a design method and system for two-dimensional array-type optical measurement marks for overlay error. Background Technology

[0002] In the field of integrated circuit manufacturing, as chip manufacturing processes advance to 7nm, 5nm and more advanced nodes, the complexity of circuit patterns and integration density are increasing dramatically. As the core of photolithography, overlay measurement must control the overlay error within 30% of the critical linewidth; otherwise, it will cause electrical failures such as metal interconnect misalignment and contact hole offset, resulting in defects such as short circuits and open circuits, directly affecting chip yield and increasing manufacturing costs and R&D cycles.

[0003] Existing overlay metrology technologies mainly include imaging-based interpolation (IBO) and diffraction-based diffraction (DBO). IBO is widely used due to its intuitive principle and ease of operation, but at process nodes of 22nm and below, the optical resolution limit makes it difficult to meet the 0.45nm accuracy requirement. DBO determines overlay error by measuring diffracted light intensity, overcoming the optical resolution limitation and effectively reducing various measurement errors. Among these, eDBO is simple and accurate in calculation, but traditional eDBO uses one-dimensional grating marks that only generate diffraction signals in the direction perpendicular to the grating grooves. Therefore, two sets of gratings perpendicular to the groove directions are required to measure the overlay error in the x and y directions, increasing production costs and measurement time. Two-dimensional periodic structure marks can generate diffraction signals simultaneously in the x and y directions, reducing the number of marks, improving measurement efficiency, and providing a new direction for overlay measurement.

[0004] However, the measurement performance of two-dimensional periodic structural markers is highly dependent on their dimensional parameters, such as duty cycle and height. Measurement sensitivity reflects the ability of the measurement signal to respond to changes in the magnitude of overlay error, while accuracy depends on the linearity between the measurement signal and changes in the magnitude of overlay error. Inappropriate dimensional parameter settings can lead to insufficient diffraction signal intensity, reduced measurement sensitivity, and disruption of the linear relationship between the diffraction signal and overlay error, resulting in significant deviations in the measurement results of eDBO based on the linear assumption. Therefore, optimizing the dimensional parameters of two-dimensional structural markers is crucial for improving the accuracy and reliability of overlay error measurement. Summary of the Invention

[0005] The purpose of this invention is to provide a design method and system for two-dimensional array-type optical measurement marks for overlay error, aiming to solve or improve at least one of the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A method for designing two-dimensional array-type optical measurement marks for overlay error includes:

[0008] Design a two-dimensional array type optical measurement mark for overlay error; the two-dimensional array type optical measurement mark for overlay error includes, from top to bottom, a grating etched with photoresist, a silicon dioxide thin film, a photoresist filling layer, a silicon grating and a silicon substrate;

[0009] A method for characterizing overlay error is constructed based on the aforementioned two-dimensional array-type optical measurement marks for overlay error;

[0010] A multi-objective optimization model is constructed based on the aforementioned characterization method; the multi-objective optimization model includes a first objective function that aims to maximize lateral measurement sensitivity, a second objective function that aims to minimize lateral measurement linear error, a third objective function that aims to maximize longitudinal measurement sensitivity, and a fourth objective function that aims to minimize longitudinal measurement linear error;

[0011] The multi-objective multiverse optimization algorithm is used to solve the multi-objective optimization model to obtain the optimal labeling structure. The multi-objective multiverse optimization algorithm is to introduce the Latin hypercube initialization method, the fitness evaluation mechanism based on the NMPSO algorithm, and the external archive size dynamic adjustment strategy into the original multi-objective multiverse algorithm.

[0012] Optionally, in the two-dimensional array type overlay error optical measurement mark, both the photoresist-etched grating and the silicon grating are two-dimensional periodic orthogonal gratings, and there is a relative offset between them.

[0013] Optionally, the method for characterizing the overlay error specifically includes:

[0014] Calculate the transverse overlay error using the following two formulas respectively. Vertical overlay error :

[0015] ;

[0016] in: , , , ;

[0017] In the formula, and Indicates the scaling factor. This indicates the lateral diffraction difference of marker 1. This indicates the lateral diffraction difference of marker 2. This represents the intensity of the reflected light at order (1,0) marked 1. This represents the intensity of the reflected light at order (-1,0) marked 1. This represents the intensity of the (1,0) order reflected light of marker 2. This represents the intensity of the (-1,0) order reflected light of marker 2; This indicates the longitudinal diffraction difference of marker 1. This indicates the longitudinal diffraction difference of marker 2. This represents the intensity of the reflected light at order (0,1) marked 1. This represents the intensity of the reflected light of order (0, -1) marked 1. This represents the intensity of the reflected light at order (0,1) of marker 2. This represents the intensity of the reflected light of order (0, -1) marked 2.

[0018] Optionally, in the multi-objective optimization model, each objective function is specifically expressed as follows:

[0019] The first objective function is:

[0020] ;

[0021] in, This represents the difference in lateral diffraction between two markers. This represents the difference in lateral overprinting error between two marks;

[0022] The second objective function is:

[0023] ;

[0024] Among them, the maximum deviation The maximum perpendicular distance between the measured data point ASX and the fitted line ASX_fit, within the full-scale range. The maximum and minimum values ​​of the output data are the difference between them; the fitted line ASX_fit is the sum of the measured data points ASX and the lateral overlay error. OVLX A linear model obtained by fitting using the least squares method;

[0025] The third objective function is:

[0026] ;

[0027] in, This represents the difference in longitudinal diffraction between two markers. This represents the difference in longitudinal overprinting error between two marks;

[0028] The fourth objective function is:

[0029] ;

[0030] Among them, the maximum deviation The maximum perpendicular distance between the measured data point ASY and the fitted line ASY_fit, within the full-scale range. The maximum and minimum values ​​of the output data are represented by ASY_fit; the fitted line ASY_fit is the sum of the measured data points ASY and the longitudinal overlay error. OVLY The linear model obtained by fitting using the least squares method.

[0031] Optionally, the multi-objective multiverse optimization algorithm specifically includes:

[0032] Population initialization is performed based on the Latin hypercube sampling method. The variable space is divided into N non-overlapping sub-intervals. Each sub-interval is sampled independently with equal probability to ensure that the sampling points are evenly distributed throughout the distribution interval.

[0033] The fitness calculation method based on the NMPSO algorithm is used to evaluate the quality of solutions in the external archive. Based on the quality evaluation results, a leader particle is assigned to each particle through multiple roulette wheel betting methods to promote the population to evolve towards the entire Pareto front and avoid the population evolution getting stuck in local optima.

[0034] A dynamic adjustment strategy is implemented for the size of the external archive. When the number of non-dominated solutions surges in a four-objective scenario, the archive capacity is linearly reduced with each iteration to achieve a balance in resource allocation between global exploration and local development under high-dimensional objectives.

[0035] For the updated external archive, if the number of solutions in the archive exceeds the current generation archive size, the fitness calculation method based on the NMPSO algorithm is used to evaluate the quality of the solutions, and poor solutions are deleted until the number of solutions in the archive does not exceed the current generation archive size.

[0036] The present invention also provides a two-dimensional array type optical measurement mark design system for overlay error, comprising:

[0037] A marking design unit is used to design a two-dimensional array type optical measurement mark for overlay error; the two-dimensional array type optical measurement mark for overlay error includes, from top to bottom, a photoresist-etched grating, a silicon dioxide thin film, a photoresist filling layer, a silicon grating, and a silicon substrate.

[0038] The characterization method construction unit is used to construct a characterization method for overlay error based on the two-dimensional array-type overlay error optical measurement mark;

[0039] The model building unit is used to build a multi-objective optimization model based on the representation method; the multi-objective optimization model includes a first objective function with the objective of maximizing lateral measurement sensitivity, a second objective function with the objective of minimizing lateral measurement linear error, a third objective function with the objective of maximizing longitudinal measurement sensitivity, and a fourth objective function with the objective of minimizing longitudinal measurement linear error;

[0040] The model solving unit is used to solve the multi-objective optimization model using the multi-objective multiverse optimization algorithm to obtain the optimal label structure. The multi-objective multiverse optimization algorithm is to introduce the Latin hypercube initialization method, the fitness evaluation mechanism based on the NMPSO algorithm, and the external archive size dynamic adjustment strategy into the original multi-objective multiverse algorithm.

[0041] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0042] This invention discloses a design method and system for two-dimensional array-type optical measurement marks for overlay error. The method includes: First, designing a two-dimensional array-type overlay mark and proposing an overlay error characterization method based on this mark, thereby achieving simultaneous measurement of overlay errors in two directions using two marks. Second, based on the proposed characterization method, constructing an evaluation criterion for the performance of the overlay characterization quantity, considering linearity and sensitivity in both measurement directions, and establishing a four-objective optimization model. Then, for the four-objective optimization scenario, an improved multi-objective multiverse algorithm is proposed by introducing a Latin hypercube initialization method, the fitness evaluation mechanism of the NMPSO algorithm, and a dynamic adjustment strategy for the external archive size. Finally, solving the established optimization model yields the optimized mark structure. The proposed method simultaneously measures overlay errors in two directions using a two-dimensional array-type overlay mark and improves the measurement performance of the mark based on structural optimization design. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a schematic diagram of a two-dimensional marker model in this embodiment; wherein, (a) is a schematic diagram of a single marker; and (b) is a schematic diagram of a group of markers.

[0045] Figure 2 This is a diagram showing the relationship between the characterization quantity and the overlay error in this embodiment; wherein, (a) is the relationship between the lateral characterization quantity and the lateral overlay error; and (b) is the relationship between the longitudinal characterization quantity and the longitudinal overlay error.

[0046] Figure 3 The flowchart of the improved multi-objective multiverse algorithm in this embodiment is shown below.

[0047] Figure 4 This is a schematic diagram illustrating the improved leader selection in this embodiment;

[0048] Figure 5 This is a schematic diagram of the improved external archive maintenance strategy in this embodiment;

[0049] Figure 6 This is an image showing the optimization results based on the improved multi-objective multiverse algorithm in this embodiment. Detailed Implementation

[0050] 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.

[0051] The purpose of this invention is to provide a design method and system for two-dimensional array-type optical measurement marks for overlay error, aiming to solve or improve at least one of the above-mentioned technical problems.

[0052] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0053] like Figures 1-6 As shown, this invention provides a method for designing two-dimensional array-type optical measurement marks for overlay error, comprising:

[0054] Step 1: Design a two-dimensional array-type overlay marking model:

[0055] The incident light wavelength was set to 532 nm, and it was incident perpendicularly. The specific dimensional parameters are shown in Table 1. The size of both the transverse and longitudinal periods is 1 μm, satisfying the existence condition of first-order diffraction. The labels from top to bottom are as follows: the first layer is a photoresist-etched grating (upper grating layer), the second layer is a silicon dioxide thin film (first thin film dielectric layer), the third layer is a photoresist-filled layer (second thin film dielectric layer), the fourth layer is a silicon grating (lower grating layer), and the bottom layer is a silicon substrate (substrate layer).

[0056] Table 1. Marking size parameters

[0057]

[0058] In a single mark, the upper and lower grating layers are identical, both being two-dimensional periodic orthogonal gratings, such as... Figure 1 As shown in (a). There is a relative offset D between the upper and lower grating layers. This D is decomposed along the array direction into a horizontal offset and a vertical offset, i.e. In addition, when the light source is incident perpendicularly, the transverse and longitudinal period sizes of the grating must satisfy the conditions for the existence of first-order diffraction.

[0059] The measurement requires a set of markers, consisting of two markers with a preset offset of ±d. Due to the overlay error OVL, the actual offsets of the two markers are ( )and( ),like Figure 1 As shown in (b).

[0060] Figure 2 (a) shows the relationship between the lateral diffraction difference ASX and the lateral overlay error OVLX. Figure 2 Figure (b) shows the relationship between the longitudinal diffraction difference (ASY) and the longitudinal overlay error (OVLY). It can be seen that both parameters exhibit a linear relationship with the overlay error in the measurement direction. Further research revealed that even when overlay error is introduced in the non-overlay measurement direction, the above linear relationship remains essentially stable (see Figure [link to figure]). Figure 2 Based on this characteristic, the overlay error in the two directions can be measured independently using different characterization parameters.

[0061] Step 2, Method for characterizing overlay error:

[0062] Calculate the transverse overlay error using the following two formulas respectively. Vertical overlay error :

[0063] ;

[0064] in: , , , .

[0065] In the above formula, and Indicates the scaling factor. This indicates the lateral diffraction difference of marker 1. This indicates the lateral diffraction difference of marker 2. This represents the intensity of the reflected light at order (1,0) marked 1. This represents the intensity of the reflected light at order (-1,0) marked 1. This represents the intensity of the (1,0) order reflected light of marker 2. This represents the intensity of the (-1,0) order reflected light of marker 2; This indicates the longitudinal diffraction difference of marker 1. This indicates the longitudinal diffraction difference of marker 2. This represents the intensity of the reflected light at order (0,1) marked 1. This represents the intensity of the reflected light of order (0, -1) marked 1. This represents the intensity of the reflected light at order (0,1) of marker 2. This represents the intensity of the reflected light of order (0, -1) marked 2.

[0066] When calculating the overlay error based on the above formula, the accuracy mainly depends on the linearity between the characterization quantity and the overlay error, as well as the measurement noise. The influence of noise is primarily related to the sensitivity between the characterization quantity and the overlay error. Higher sensitivity results in smaller errors due to noise, and vice versa. Since the linearity and sensitivity of the marker are related to its structure, the measurement performance of the marker is improved by optimizing the transverse linewidth dx and the longitudinal linewidth dy of the grating. The structural variables dx and dy range from 0.3 μm to 0.7 μm.

[0067] Step 3, construct the objective function model:

[0068] Objective function 1: Maximizing lateral measurement sensitivity is expressed as:

[0069] ;

[0070] Objective function 2: Minimizing the linear error of lateral measurement is expressed as:

[0071] ;

[0072] Where: maximum deviation The maximum perpendicular distance between the measured data point ASX and the fitted line ASX_fit, within the full-scale range. The maximum and minimum values ​​of the output data are represented by ASX_fit, which is a linear model obtained by fitting the measured data points ASX with the transverse overlay error OVLX using the least squares method.

[0073] Objective function 3: The maximum lateral measurement sensitivity is expressed as:

[0074] ;

[0075] Objective function 4: Minimizing the linear error of longitudinal measurement is expressed as:

[0076] ;

[0077] Among them, the maximum deviation The maximum perpendicular distance between the measured data point ASY and the fitted line ASY_fit, within the full-scale range. The maximum and minimum values ​​of the output data are represented by ASY_fit; the fitted line ASY_fit is the sum of the measured data points ASY and the longitudinal overlay error. OVLYThe linear model obtained by fitting using the least squares method.

[0078] Step 4: Construct an approximate model of the objective function based on the adaptive sampling kriging method:

[0079] Step 4.1: Based on the optimal Latin hypercube sampling experimental design method, in the sample space... An initial sample set is generated internally, and the response values ​​are calculated using electromagnetic fields. The dataset is then divided into a training set and a training set in a 7:3 ratio. An initial Kriging model is constructed based on constant basis functions and the ARD squared exponential kernel function, and its prediction function is expressed as:

[0080] ;

[0081] in, It is a constant. To satisfy the second-order stationarity assumption of the Gaussian stochastic process, the kernel function parameters are optimized through maximum likelihood estimation.

[0082] Step 4.2: Use the current Kriging model to predict the test set and calculate the absolute error matrix between the predicted and actual values. Sort the data directly from largest to smallest error, take the top 10 points as high error points, and define the area around them as the high error region.

[0083] Step 4.3: Within the high error region, new sample points are generated by Gaussian perturbation centered on the high error point. The perturbation amplitude is adaptively adjusted according to the interquartile range (IQR) of the input parameters to ensure dimensional consistency. The parameters are ensured to be within the range of [0.3, 0.7] by reflection method.

[0084] Step 4.4: Obtain the output value of the new sample point and add it to the training set. Retrain the Kriging model and repeat steps 4.2 to 4.4 until the prediction accuracy of the surrogate model meets the requirements.

[0085] Step 5: The improved multi-objective multiverse algorithm is obtained by introducing a Latin hypercube initialization method, a fitness evaluation mechanism based on the NMPSO algorithm, and a dynamic adjustment strategy for the external archive size. Figure 3 As shown.

[0086] In one specific implementation, this embodiment improves the multi-objective multiverse algorithm by introducing a Latin hypercube initialization method, a fitness evaluation mechanism based on the NMPSO algorithm, and a dynamic adjustment strategy for the external archive size, thereby improving performance in four-objective scenarios and avoiding getting trapped in local sparse regions.

[0087] Multi-Objective Multiverse Algorithm (MOMVO):

[0088] The population is randomly initialized in the search space as follows:

[0089] ;

[0090] in, Let j be the j-th dimension variable of the i-th individual in the population. Let j be the upper bound of the j-th dimension variable. This is the lower bound of the j-th dimension variable.

[0091] Each individual in the population represents a candidate solution to the problem, and its objective function is expressed as follows:

[0092] ;

[0093] in, Let be the i-th individual in the population, and n be the number of objective functions.

[0094] During population updates, the MOMVO algorithm defines black hole, white hole, and wormhole mechanisms, and position updates are based on the following formula:

[0095] ;

[0096] Where WEP is the probability of a wormhole existing; TDR is the travel distance rate. Let j be the j-th star in the current optimal universe. This is the value of the j-th star in the k-th universe, calculated using the roulette wheel algorithm. All are random numbers in the range [0,1].

[0097] The optimal universe is selected using the following formula:

[0098] ;

[0099] In the formula, c is a constant greater than 1; It is the number of solutions near the i-th solution in the archive region.

[0100] When the number of solutions in the external archive exceeds the size of the external archive, adjacent archive members are removed according to the following formula:

[0101] ;

[0102] Step 5.1: Using the Latin hypercube sampling (LHS)-based initialization method, stratified sampling, random sampling, and combination of sample points are performed to generate the initial cosmic population, as detailed below:

[0103] First, define the decision variable dimension D and the population size N. Then, divide each dimension into N intervals with equal probability, and let... Indicates the sample number. Represents the dimension. For each dimension... :

[0104] First, generate a random permutation. , making This represents the interval number of the i-th sample in the j-th dimension.

[0105] For each sample, the sampling point in the j-th dimension can be calculated using the following formula:

[0106] ;

[0107] in, To obtain from a uniform distribution Random numbers obtained from sampling Let j be the upper bound of the j-th dimension variable. This is the lower bound of the j-th dimension variable.

[0108] Step 5.2 utilizes the fitness evaluation mechanism of the NMPSO algorithm to estimate the fitness of external archived solutions and independently assigns a leader particle to each particle, thereby enhancing diversity while improving the algorithm's convergence performance. Figure 4 As shown.

[0109] Furthermore, the improved leader particle selection strategy includes the following steps:

[0110] Step 5.2.1, estimate the fitness of the particles in the current external archive, as follows:

[0111] 1. Four-objective normalization processing:

[0112] For each solution in external archive A The four objective function values Normalize:

[0113] ;

[0114] in, and These are the minimum and maximum values ​​of the k-th target in archive A, respectively.

[0115] 2. Diversity distance calculation:

[0116] Displacement density estimation (SDE) is used to calculate the diversity of particle distribution; a larger diversity distance indicates that the solution is located in a sparse region. The calculation formula is shown below:

[0117] ;

[0118] in: and These are the maximum and minimum displacement density estimates in the external archive, respectively.

[0119] particle The formula for estimating displacement density is shown below:

[0120] ;

[0121] in, .

[0122] 3. Convergence distance calculation:

[0123] Convergence distance represents the distance from the normalized objective function to the ideal point The convergence distance is related to the solution; a larger convergence distance indicates that the solution is closer to the ideal point. The calculation formula is shown below:

[0124] ;

[0125] in, .

[0126] 4. Dynamically adjust weights α and β based on the position of the solution in the four-objective space:

[0127] Calculate the average convergence distance of particles in the archive. and average diversity distance ;

[0128] if (Solution close to the ideal point):

[0129] like (If the diversity is good), then α = 1.0 and β = 0.9;

[0130] like (Crowded), then α = (0.6 to 1.3) and β = 1.0;

[0131] if (Solution far from the ideal point):

[0132] Calculate the projected distance of the line connecting the "ideal point" and the "Nadir point". and vertical distance :

[0133] ;

[0134] in, .

[0135] like (Boundary solution), then α = β = 1.0;

[0136] Otherwise, α = β = 0.2.

[0137] 5. Overall fitness calculation:

[0138] ;

[0139] Step 5.2.2, leader assignment based on fitness estimation, is as follows:

[0140] 1. Calculate the probability of selection:

[0141] The fitness of each solution in the external archive is normalized to construct a selection probability model. The specific calculation formula is as follows:

[0142] ;

[0143] in, Characterizing the solution in the external archive The probability of choosing, To solve The fitness value, |A| is the number of solutions in the external archive.

[0144] This formula maps fitness to a probability interval by standardizing the fitness, so that solutions with higher fitness have a greater probability of being selected, thus laying a quantitative foundation for subsequent selection mechanisms based on roulette.

[0145] 2. Dynamic leader particle allocation:

[0146] After calculating and normalizing the selection probability, for each particle in the population... A dynamic leader particle allocation strategy is implemented. Based on a roulette wheel selection mechanism, this strategy allows each particle to independently select a leader particle during each iteration of the algorithm. In this way, particles can probabilistically select a corresponding particle as their update guide based on the fitness proportion of solutions in the external database. This dynamic allocation strategy effectively overcomes the limitations of the traditional single leader particle, enabling the population to explore a wider solution space during the search process, significantly reducing the risk of the algorithm getting trapped in local optima, and thus improving the global optimization performance of the algorithm in multi-objective optimization problems.

[0147] Step 5.3 utilizes the fitness evaluation mechanism and external archive size dynamic adjustment strategy of the NMPSO algorithm to estimate the fitness of external archive solutions, thereby enhancing diversity while improving the algorithm's convergence performance. Figure 5 As shown.

[0148] Furthermore, the improved external archive maintenance strategy includes the following steps:

[0149] Step 5.3.1: In the optimization algorithm proposed in this paper, the external archive size is dynamically adjusted using a linear decreasing strategy, aiming to balance the algorithm's global search capability with the elite individual retention mechanism. Specifically:

[0150] In the initial state, the external archive size is set to 1.5 times the population size to provide sufficient storage capacity for the algorithm to explore the diverse solution space in the early stage and avoid getting trapped in local optima too early.

[0151] As the iteration progresses, the size of the external archive gradually decreases linearly until it eventually converges to be equal to the population size. This setting ensures that the solution space is fully explored in the early stages of the algorithm, and focuses on fine-tuning elite solutions in the later stages. This effectively balances the resource allocation between global exploration and local development under high-dimensional objectives, accelerating the algorithm's convergence speed. The calculation formula is as follows:

[0152] ;

[0153] in, N is the external archive size for the current generation, T is the population size, and t is the maximum number of iterations.

[0154] This linear decreasing strategy gradually reduces the external archive capacity from the initial 1.5N to the final N, adaptively adjusting the archive size at different stages of the algorithm's operation, effectively improving the overall optimization performance of the algorithm.

[0155] Step 5.3.2, based on the Pareto dominance relation, perform the following archiving operation on the new solution generated in each iteration:

[0156] Calculate the dominance relationship between the new solution and existing solutions in the external archive;

[0157] If the new solution is a non-dominant solution, then add it to the external archive;

[0158] If a solution in the archive is dominated by the new solution, then delete the dominated solution.

[0159] Step 5.3.3: After archiving, maintain the external archive as follows:

[0160] The size of the external archive is determined. If the size of the external archive exceeds the capacity of the external archive in the current generation, the external archive is deleted. The fitness of each particle in the external archive is calculated based on the calculation formula in step 5.2.1. Then, the particle with the worst fitness is deleted until the size of the external archive does not exceed the capacity of the external archive in the current generation.

[0161] To verify the computational performance of the improved algorithm, this invention selected the WFG3-8 test function to compare the performance of the improved multi-objective multiverse algorithm (IMOMVO) with MOMVO, NMPSO, and NSGAII algorithms. All tests were run independently 30 times, and the specific metrics and related parameters are shown in Table 2. The test function settings were as follows: the number of objective functions was set to 4, the number of variables was set to 13, the population size was set to 100, and the maximum number of evaluations was set to 10000.

[0162] Table 2 Comparison of IGD values ​​for different algorithms under some test functions

[0163]

[0164] The inverse generational distance (IGD) is selected to evaluate the quality of the approximate Pareto front obtained by the algorithm. The formula for calculating IGD is as follows:

[0165] ;

[0166] The results show that the improved multi-objective multiverse algorithm performs well in four-objective optimization problems, slightly better than the original algorithm and commonly used algorithms. The performance results before and after optimization are shown in Table 3.

[0167] Table 3 Performance before and after label optimization

[0168]

[0169] Step 6: Solve the objective function model established in Step 3 using the improved algorithm from Step 5.

[0170] The obtained Pareto solution set is as follows Figure 6 As shown in the figure, most solutions are... and They performed well. Therefore, in the selection process based on decision-makers' preferences, and The weight is relatively small, while and The weights are relatively large. This led to the determination of the final optimal solution [dx=0.367um, dy=0.364um]. As can be seen from Table 3, the measurement performance of the markers was improved after optimization.

[0171] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0172] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A design method of an optical metrology mark for overlay error measurement in a two-dimensional array, characterized in that, Comprise: Design a two-dimensional array type overlay error optical measurement mark; the two-dimensional array type overlay error optical measurement mark comprises a grating etched with photoresist, a silicon dioxide film, a photoresist filling layer, a silicon grating and a silicon substrate arranged in turn from top to bottom; Construct an overlay error characterization method based on the two-dimensional array type overlay error optical measurement mark; the overlay error characterization method specifically comprises: The lateral overlay error is calculated according to the following two equations, respectively and the longitudinal overlay error : ； wherein: , , , ; wherein and represents a proportionality factor, represents the lateral diffraction difference of marker 1, represents the lateral diffraction difference of marker 2, represents the (1,0) order reflected light intensity of marker 1, represents the (-1,0) order reflected light intensity of marker 1, represents the (1,0) order reflected light intensity of marker 2, represents the (-1,0) order reflected light intensity of marker 2; represents the longitudinal diffraction difference of marker 1, represents the longitudinal diffraction difference of marker 2, represents the (0,1) order reflected light intensity of marker 1, represents the (0,-1) order reflected light intensity of marker 1, represents the (0,1) order reflected light intensity of marker 2, represents the (0,-1) order reflected light intensity of marker 2; Construct a multi-objective optimization model based on the characterization method; the multi-objective optimization model comprises a first objective function with the maximum lateral measurement sensitivity as the target, a second objective function with the minimum lateral measurement linear error as the target, a third objective function with the maximum longitudinal measurement sensitivity as the target, and a fourth objective function with the minimum longitudinal measurement linear error as the target; Solve the multi-objective optimization model by using a multi-objective multi-universe optimization algorithm to obtain an optimal mark structure; the multi-objective multi-universe optimization algorithm is a Latin hypercube initialization method, a fitness evaluation mechanism based on the NMPSO algorithm and an external archive size dynamic adjustment strategy introduced in the original multi-objective multi-universe optimization algorithm.

2. The design method of claim 1, wherein, In the two-dimensional array type overlay error optical measurement mark, the grating etched with photoresist and the silicon grating are both two-dimensional periodic orthogonal gratings, and there is a relative offset between them.

3. The design method of claim 1, wherein, In the multi-objective optimization model, each objective function is specifically represented as: The first objective function is: ； wherein, represents the difference between the lateral diffraction differences of the two marks, represents the difference between the lateral overlay errors of the two marks; The second objective function is: ； where the maximum deviation is the maximum vertical distance of the measured data points ASX from the fitted straight line ASX_fit, full scale range is the difference between the maximum and minimum values of the output data; the fitted straight line ASX_fit is a linear model fitted by least squares to the measured data points ASX and the lateral overlay error OVLX is the lateral overlay error; the fitted straight line ASX_fit is a linear model fitted by least squares to the measured data points ASX. The third objective function is: ； wherein, represents the difference between the longitudinal diffraction difference of the two marks, represents the difference between the longitudinal overlay error of the two marks; The fourth objective function is: ； where the maximum deviation is the maximum vertical distance of the measured data points ASY from the fitted straight line ASY_fit, full scale range is the difference between the maximum and minimum values of the output data; the fitted straight line ASY_fit is a linear model fitted by least squares to the measured data points ASY and the longitudinal overlay error OVLY is the longitudinal overlay error.

4. The design method of claim 1, wherein, The multi-objective multi-universe optimization algorithm specifically comprises: Perform population initialization based on the Latin hypercube sampling method, divide the variable space into N non-overlapping subintervals, and independently sample each subinterval with equal probability to ensure that the sampling points are uniformly distributed in the entire distribution interval; Use the fitness calculation method based on the NMPSO algorithm to evaluate the quality of solutions in the external archive, and then assign a leader particle to each particle through multiple roulette methods based on the quality evaluation results, promote the evolution of the population to the entire Pareto frontier, and avoid the population evolution from falling into local optimum; Implement a dynamic adjustment strategy for the size of the external archive, and when the number of non-dominated solutions increases rapidly in a four-objective scenario, balance the resource allocation between global exploration and local development by linearly decreasing the archive capacity with iterations; For the updated external archive, if the number of solutions in the archive exceeds the current generation archive size, use the fitness calculation method based on the NMPSO algorithm to evaluate the quality of the solutions, and delete the poor solutions until the number of solutions in the archive does not exceed the current generation archive size.

5. A design system for optical metrology marks for overlay error measurement in a two-dimensional array, applying the method according to any one of claims 1 to 4, characterized in that, Comprise: A mark design unit for designing a two-dimensional array type overlay error optical measurement mark; the two-dimensional array type overlay error optical measurement mark comprises a grating etched with photoresist, a silicon dioxide film, a photoresist filling layer, a silicon grating and a silicon substrate arranged in turn from top to bottom; A characterization method construction unit for constructing an overlay error characterization method based on the two-dimensional array type overlay error optical measurement mark; The model construction unit is configured to construct a multi-objective optimization model based on the characterization method; the multi-objective optimization model comprises a first objective function aiming at maximizing a transverse measurement sensitivity, a second objective function aiming at minimizing a transverse measurement linear error, a third objective function aiming at maximizing a longitudinal measurement sensitivity, and a fourth objective function aiming at minimizing a longitudinal measurement linear error. The model solving unit is configured to solve the multi-objective optimization model by using a multi-objective multi-universe optimization algorithm to obtain an optimal marker structure; the multi-objective multi-universe optimization algorithm is an algorithm in which a Latin hypercube initialization method, a fitness evaluation mechanism based on an NMPSO algorithm, and an external archive size dynamic adjustment strategy are introduced into an original multi-objective multi-universe optimization algorithm.

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