Two-dimensional array type overlay error optical measurement mark design method and system

Abstract

The invention discloses a two-dimensional array type overlay error optical measurement mark design method and system, and relates to the technical field of integrated circuit process measurement. The method comprises the following steps: designing a two-dimensional array type overlay error optical measurement mark, and constructing an overlay error characterization method; constructing a multi-objective optimization model based on the characterization method; solving the multi-objective optimization model by using a multi-objective multivariate universe optimization algorithm to obtain an optimal marking structure; according to the multi-target multivariate universe optimization algorithm, 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-target multivariate universe algorithm. According to the invention, overlay errors in two directions can be synchronously measured through the two-dimensional array type overlay mark, and the measurement performance of the mark is improved based on the structural optimization design.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of integrated circuit process measurement technology, in particular to a two-dimensional array type overlay error optical measurement mark design method and system. BACKGROUND

[0002] In the field of integrated circuit manufacturing, as the chip process develops to 7nm, 5nm and more advanced nodes, the circuit pattern complexity and integration density surge. As the core of lithography, overlay metrology needs to control the overlay error within 30% of the key line width, otherwise it will cause electrical failures such as metal interconnection misplacement, contact hole offset, etc., resulting in short circuit, open circuit and other defects, directly affecting the chip yield, increasing the manufacturing cost and research and development cycle.

[0003] The existing overlay metrology technology mainly includes IBO based on imaging and DBO based on diffraction. IBO is widely used due to its intuitive principle and simple operation, but it is difficult to meet the 0.45nm precision requirement at 22nm and below process nodes due to the optical resolution limit. DBO determines the overlay error by measuring the diffraction light intensity, breaks through the optical resolution limit, and effectively reduces various measurement errors. The eDBO measurement method is simple and accurate, but the one-dimensional grating mark used by the traditional eDBO can only produce diffraction signals in the direction perpendicular to the grating groove, so two sets of gratings with perpendicular groove directions are needed to measure the x and y direction overlay errors, which increases the production cost and measurement time. The two-dimensional periodic structure mark can produce diffraction signals in x and y directions at the same time, reduce the number of marks, improve the measurement efficiency, and provide a new direction for overlay measurement.

[0004] However, the measurement performance of the two-dimensional periodic structure mark is highly dependent on its size parameters, such as duty cycle, height, etc. The measurement sensitivity reflects the response ability of the measurement signal to the size change of the overlay error, and the accuracy depends on the linearity of the measurement signal and the size change of the overlay error. Unreasonable size parameter settings will result in insufficient diffraction signal strength, reduced measurement sensitivity, and also destroy the linearity between the diffraction signal and the overlay error, resulting in large deviations in the measurement results of eDBO based on the linear assumption. Therefore, optimizing the size parameters of the two-dimensional structure mark becomes the key to improving the overlay error measurement accuracy and reliability. SUMMARY

[0005] The purpose of the present application is to provide a two-dimensional array type overlay error optical measurement mark design method and system, which aims to solve or improve at least one of the above technical problems.

[0006] To achieve the above purpose, the present application provides the following scheme: A two-dimensional array type overlay error optical measurement mark design method, comprising: 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; A method for characterizing overlay error is constructed based on the aforementioned two-dimensional array-type optical measurement marks for overlay error; 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; 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.

[0007] 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.

[0008] Optionally, the method for characterizing the overlay error specifically includes: Calculate the transverse overlay error using the following two formulas respectively. Vertical overlay error : ; in: , , , ; 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. (0,-1) order reflected light intensity of mark 1, (0,1) order reflected light intensity of mark 2, (0,-1) order reflected light intensity of mark 2.

[0009] Optionally, in the multi-objective optimization model, each objective function is specifically represented as: The first objective function is: ; wherein, represents the difference of the lateral diffraction difference between two marks, represents the difference of the lateral overlay error between two marks; The second objective function is: ; wherein, the maximum deviation is the maximum vertical distance of the measured data points ASX and the fitting straight line ASX_fit, the full range is is the difference between the maximum and minimum values of the output data; the fitting straight line ASX_fit is a linear model obtained by least squares fitting of the measured data points ASX and the lateral overlay error OVLX ; The third objective function is: ; wherein, represents the difference of the longitudinal diffraction difference between two marks, represents the difference of the longitudinal overlay error between two marks; The fourth objective function is: ; wherein, the maximum deviation is the maximum vertical distance of the measured data points ASY and the fitting straight line ASY_fit, the full range is is the difference between the maximum and minimum values of the output data; the fitting straight line ASY_fit is a linear model obtained by least squares fitting of the measured data points ASY and the longitudinal overlay error OVLY .

[0010] Optionally, the multi-objective multi-universe optimization algorithm specifically includes: Latin hypercube sampling method is used for population initialization, and the variable space is equally divided into N non-overlapping subintervals, and independent equal probability sampling is performed on each subinterval to ensure that the sampling points are uniformly distributed in the entire distribution interval. The quality of solutions in the external archive is evaluated by using a fitness calculation method based on the NMPSO algorithm, and based on the quality evaluation result, a leader particle is assigned to each particle through multiple roulette methods, so that the population evolves towards the entire Pareto frontier, and the population evolution is prevented from falling into a local optimum. A dynamic adjustment strategy is implemented for the size of the external archive, and when the number of non-dominated solutions increases sharply in the four-target scene, the archive capacity is linearly decreased with iterations to balance the resource allocation between global exploration and local development under high-dimensional targets. For the updated external archive, if the number of solutions in the archive exceeds the archive size of the current generation, the quality of the solutions is evaluated by using a fitness calculation method based on the NMPSO algorithm, and the poor solutions are deleted until the number of solutions in the archive does not exceed the archive size of the current generation.

[0011] The application also provides a two-dimensional array type overlay error optical measurement mark design system, comprising: A mark design unit is used to design a two-dimensional array type overlay error optical measurement mark, wherein the two-dimensional array type overlay error optical measurement mark comprises gratings etched by photoresist, silicon dioxide films, photoresist filling layers, silicon gratings and silicon substrates arranged in sequence from top to bottom. A representation method construction unit is used to construct a representation method of overlay error based on the two-dimensional array type overlay error optical measurement mark. A model construction unit is used to construct a multi-objective optimization model based on the representation method, wherein 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. A model solving unit is used to solve the multi-objective optimization model by using a multi-objective multi-universe optimization algorithm to obtain an optimal mark structure, wherein the multi-objective multi-universe optimization algorithm is a Latin hypercube initialization method, a fitness evaluation mechanism based on the NMPSO algorithm and a dynamic adjustment strategy of the size of the external archive introduced in the original multi-objective multi-universe algorithm.

[0012] According to the specific embodiments of the application, the following technical effects are achieved: The application discloses a design method and system for a two-dimensional array type overlay error optical measurement mark, and the method comprises the following steps: firstly, a two-dimensional array type overlay mark is designed, and an overlay error characterization method based on the mark is proposed, so that the synchronous measurement of overlay errors in two directions is realized through double marks. Secondly, according to the proposed characterization method, an evaluation criterion for overlay characterization performance is constructed, the linearity and sensitivity in two measurement directions are considered, a four-target optimization model is established. Then, for the four-target optimization scene, an improved multi-objective multi-universe algorithm is proposed by introducing a Latin hypercube initialization method, a fitness evaluation mechanism of NMPSO algorithm and a dynamic adjustment strategy of external archive size. Finally, the optimization model is solved, and the optimized mark structure is obtained. The method synchronously measures overlay errors in two directions through the two-dimensional array type overlay mark, and the measurement performance of the mark is improved based on the structure optimization design. BRIEF DESCRIPTION OF DRAWINGS

[0013] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments. Obviously, the drawings described in the following only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0014] Figure 1 It is a two-dimensional mark model schematic diagram in the embodiment; wherein, the part (a) is a single mark schematic diagram; the part (b) is a group of mark schematic diagram; Figure 2 It is a relationship diagram between the characterization quantity and the overlay error in the embodiment; wherein, the part (a) is a relationship diagram between the transverse characterization quantity and the transverse overlay error; the part (b) is a relationship between the longitudinal characterization quantity and the longitudinal overlay error; Figure 3 It is a flow chart of the improved multi-objective multi-universe algorithm in the embodiment Figure 4 It is an improved leader selection schematic diagram in the embodiment; Figure 5 It is an improved external archive maintenance strategy schematic diagram in the embodiment; Figure 6 It is an optimization result diagram based on the improved multi-objective multi-universe algorithm in the embodiment. DETAILED DESCRIPTION

[0015] With reference to the drawings and embodiments of the present application, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of the present application.

[0016] The present application aims to provide a two-dimensional array type overlay error optical measurement mark design method and system, which aims to solve or improve at least one of the above technical problems.

[0017] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0018] As shown in Figures 1-6 , the present application provides a two-dimensional array type overlay error optical measurement mark design method, comprising: Step 1, design a two-dimensional array type overlay mark model: The incident light wavelength is set to 532 nm, the incident light is perpendicular, and the specific size parameters are shown in Table 1. The lateral period and longitudinal period are both 1 um, which meets the existence condition of first-order diffraction. From top to bottom, the first layer is a grating etched by photoresist (upper grating layer), the second layer is a silicon dioxide film (first thin film medium layer), the third layer is a photoresist filling layer (second thin film medium layer), the fourth layer is a silicon grating (lower grating layer), and the bottom is a silicon substrate (substrate layer).

[0019] Table 1 Size parameters of the mark

[0020] In a single mark, the upper and lower gratings are the same, both of which are two-dimensional periodic orthogonal gratings, as shown in Figure 1 (a). Among them, there is a relative offset D between the upper and lower gratings, which is decomposed into lateral offset and longitudinal offset along the array direction, i.e. In addition, when the light source is vertically incident, the lateral period size and longitudinal period size of the grating need to meet the existence condition of first-order diffraction.

[0021] A set of marks is needed for measurement, which is composed of two marks with a preset offset of ±d. Due to the overlay error OVL, the actual offset of the two marks is (d+OVL) and (d-OVL), respectively, as shown in (b). Figure 1

[0022] Figure 2 ​​Fig. 2 is a graph showing the relationship between the lateral diffraction difference ASX and the lateral overlay error OVLX of the mark (a), Figure 2 Fig. 3 is a graph showing the relationship between the longitudinal diffraction difference ASY and the longitudinal overlay error OVLY of the mark (b), which shows that the two quantities are linearly related to the overlay error in the measurement direction. Further research shows that even if an overlay error is introduced in a non-overlay measurement direction, the above linear relationship can still be basically maintained (see Fig. 4). Figure 2 Based on this characteristic, the overlay errors in the two directions can be independently measured by different quantities.

[0023] Step 2: Characterization method of overlay error: The lateral overlay error OVLX is calculated according to the following formula: The longitudinal overlay error OVLY is calculated according to the following formula: Wherein: , , , .

[0024] In the above formula, and represent the proportionality factor, represents the lateral diffraction difference of the mark 1, represents the lateral diffraction difference of the mark 2, represents the (1, 0) order reflected light intensity of the mark 1, represents the (-1, 0) order reflected light intensity of the mark 1, represents the (1, 0) order reflected light intensity of the mark 2, represents the (-1, 0) order reflected light intensity of the mark 2; represents the longitudinal diffraction difference of the mark 1, represents the longitudinal diffraction difference of the mark 2, represents the (0, 1) order reflected light intensity of the mark 1, represents the (0, -1) order reflected light intensity of the mark 1, represents the (0, 1) order reflected light intensity of the mark 2, represents the (0, -1) order reflected light intensity of the mark 2.

[0025] ​​When solving overlay error based on the above formula, the solving accuracy mainly depends on the linearity between the characterization quantity and the overlay error and the measurement noise. The influence of the noise mainly relates to the sensitivity between the characterization quantity and the overlay error. The greater the sensitivity, the smaller the solving error caused by the noise; the smaller the sensitivity, the smaller the solving error caused by the noise. Because the linearity and the sensitivity of the mark are related to the mark structure, the transverse line width dx and the longitudinal line width dy of the grating are optimized to improve the measurement performance of the mark. The range of the structure variables dx and dy is 0.3 um to 0.7 um.

[0026] Step 3, constructing a target function model: Target function 1: maximum transverse measurement sensitivity is expressed as: ; Target function 2: minimum transverse measurement linearity error is expressed as: ; In the formula: maximum deviation is the maximum vertical distance between the measured data point ASX and the fitted straight line ASX_fit, and the full range is the difference between the maximum value and the minimum value of the output data; the fitted straight line ASX_fit is a linear model obtained by fitting the measured data point ASX and the transverse overlay error OVLX through the least square method.

[0027] Target function 3: maximum transverse measurement sensitivity is expressed as: ; Target function 4: minimum longitudinal measurement linearity error is expressed as: ; In the formula: maximum deviation is the maximum vertical distance between the measured data point ASY and the fitted straight line ASY_fit, and the full range is the difference between the maximum value and the minimum value of the output data; the fitted straight line ASY_fit is a linear model obtained by fitting the measured data point ASY and the longitudinal overlay error OVLY through the least square method.

[0028] Step 4, constructing an approximate model of the target function based on the adaptive sampling Kriging method: Step 4.1: generating an initial sample set in the sample space based on the optimal Latin hypercube sampling test design method, obtaining the response value through electromagnetic field calculation, dividing the data set into a training set and a training set in a ratio of 7:3, and constructing an initial Kriging model based on a constant basis function and an ARD square exponential kernel function, and the prediction function is expressed as: ; where, is a constant, For Gaussian random process satisfying the second-order stationary hypothesis, the kernel function parameters are optimized by maximum likelihood estimation.

[0029] Step 4.2: Predict the test set using the current Kriging model, and calculate the absolute error matrix of the predicted value and the true value. Directly sort the error from large to small, take the top 10 points as high error points, and define the high error area around them.

[0030] Step 4.3: In the high error area, generate new sample points by Gaussian disturbance with the high error point as the center. The disturbance amplitude is adaptively adjusted according to the interquartile range (IQR) of the input parameters to ensure dimensional consistency, and the parameters are ensured to be within the range of [0.3, 0.7] by reflection method.

[0031] 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 use requirements.

[0032] Step 5: Introduce the Latin hypercube initialization method, the fitness evaluation mechanism based on NMPSO algorithm, and the external archive size dynamic adjustment strategy into the multi-objective multi-universe algorithm, to obtain the improved multi-objective multi-universe algorithm, as shown in Figure 3 .

[0033] In a specific embodiment, the present embodiment improves the multi-objective multi-universe algorithm, introduces the Latin hypercube initialization method, the fitness evaluation mechanism based on NMPSO algorithm, and the external archive size dynamic adjustment strategy, improves the performance in the four-target scenario, and avoids falling into the local sparse area.

[0034] Multi-objective multi-universe algorithm (MOMVO): Randomly initialize the population in the search space, as follows: ; where, is the jth variable of the ith individual in the population, is the upper limit of the jth variable, is the lower limit of the jth variable.

[0035] Each individual in the population represents a candidate solution to the problem, and the objective function is represented as follows: ; where, is the ith individual in the population, and n is the number of objective functions.

[0036] During population updates, the MOMVO algorithm defines black hole, white hole, and wormhole mechanisms, and position updates are based on the following formula: ; 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].

[0037] The optimal universe is selected using the following formula: ; 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.

[0038] 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: ; 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: 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... : First, generate a random permutation. , making This represents the interval number of the i-th sample in the j-th dimension.

[0039] For each sample, the sampling point in the j-th dimension can be calculated using the following formula: ; 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.

[0040] 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.

[0041] Further, the improved leader particle selection strategy comprises the following steps: Step 5.2.1, fitness estimation for particles in the current external archive, specifically as follows: 1. Four-objective normalization processing: For each solution in the external archive A , the four objective function values are normalized as: ; where and are the minimum and maximum values of the kth objective in the archive A, respectively.

[0042] 2. Diversity distance calculation: The diversity of particle distribution is calculated using the displacement density estimation (SDE), and the greater the diversity distance indicates that the solution is located in a sparse area. The calculation formula is as follows: ; where: and are the maximum and minimum displacement density estimation values in the external archive, respectively.

[0043] The displacement density estimation formula of particle is as follows: ; where .

[0044] 3. Convergence distance calculation: The convergence distance represents the distance from the normalized objective function to the ideal point , and the greater the convergence distance indicates that the solution is closer to the ideal point. The calculation formula is as follows: ; where .

[0045] 4. Dynamically adjust the weights α and β according to the position of the solution in the four-objective space: Calculate the average convergence distance and the average diversity distance of the particles in the archive; If (the solution is close to the ideal point): If (good diversity), then α = 1.0 and β = 0.9; If (crowded), then α = (0.6 to 1.3) and β = 1.0; If (away from ideal point): Calculate the projection distance of the "ideal point - Nadir point" line and the perpendicular distance : ; where, .

[0046] If (boundary solution), then α = β = 1.0; otherwise α = β = 0.2.

[0047] 5. Comprehensive fitness calculation: ; Step 5.2.2, roulette leader assignment based on fitness estimation, as follows: 1. Selection probability calculation: The fitness of each solution in the external archive is normalized to construct a selection probability model, with the specific calculation formula as follows: ; where, denotes the selection probability of solution in the external archive, is the fitness value of solution , and |A| is the number of solutions in the external archive.

[0048] This formula converts the fitness by standardization to map it to the probability interval, so that solutions with higher fitness have a greater selection probability, thereby laying a quantitative foundation for subsequent roulette-based selection mechanisms.

[0049] 2. Dynamic leader particle allocation: After calculating and normalizing the selection probability, a dynamic leader particle allocation strategy is implemented for each particle in the population. This strategy is based on the roulette selection mechanism and independently selects a leader particle for each particle in each iteration of the algorithm update process. In this way, particles can select the corresponding particle as their own update guide in the form of probability based on the fitness proportion of solutions in the external archive. This dynamic allocation strategy effectively breaks the limitations of traditional single leader particles, enabling the population to explore a wider solution space during the search process, significantly reducing the risk of the algorithm falling into a local optimal solution, and thus improving the global optimization performance of the algorithm in multi-objective optimization problems.

[0050] Step 5.3, using the fitness evaluation mechanism of the NMPSO algorithm and the dynamic adjustment strategy of the external archive size, the fitness of the external archive solution is estimated, thereby enhancing the diversity while improving the convergence performance of the algorithm, as shown in Figure 5

[0051] Further, the improved external archive maintenance strategy includes the following steps: Step 5.3.1, in the optimization algorithm presented in this paper, the external archive size is dynamically adjusted using a linear decreasing strategy, aiming to balance the global search ability of the algorithm and the elite individual preservation mechanism, specifically: In the initial state, the external archive size is set to 1.5 times the population size, providing sufficient storage capacity for early exploration of the solution space, avoiding premature convergence to local optima.

[0052] As the iteration process advances, the external archive size gradually decreases in a linear manner, until it converges to the size of the population, which ensures that the solution space is fully explored in the early stage of the algorithm, and the elite solution is finely selected in the later stage, effectively balancing the resource allocation between global exploration and local development in high-dimensional objectives, and accelerating the convergence speed of the algorithm. The calculation formula is as follows: ; Where, is the external archive capacity size of the current generation, N is the population size, T is the maximum number of iterations, and t is the current iteration number.

[0053] Through this linear decreasing strategy, the external archive capacity gradually decreases from 1.5N to N, and the archive size is adaptively adjusted at different stages of the algorithm, effectively improving the overall optimization performance of the algorithm.

[0054] Step 5.3.2, based on the Pareto dominance relationship, for each new solution generated in each iteration, perform the following archiving operations: Calculate the dominance relationship between the new solution and the existing solution in the external archive; If the new solution is a non-dominated solution, add it to the external archive; If there is a dominated solution in the archive, delete the dominated solution.

[0055] Step 5.3.3, after archiving, maintain the external archive, as follows: Judge the archive size, when the external archive size exceeds the external archive capacity size of the current generation, perform external archive deletion operation, calculate the fitness size of each particle in the external archive based on the calculation formula in step 5.2.1, then delete the worst particle until the external archive size does not exceed the external archive capacity size of the current generation.

[0056] ​In order to verify the improved computing performance of the algorithm, the present application selects the WFG3-8 test function, compares the performance of the improved multi-objective multi-universe algorithm (IMOMVO) with the MOMVO, NMPSO and NSGAII algorithms, all tests are independently run 30 times, the specific indicators and related parameters are shown in Table 2. Among them, the test function related settings are as follows: the number of objective functions is set to 4, the number of variables is set to 13, the population size is set to 100, and the maximum number of evaluations is set to 10000.

[0057] Table 2 Comparison of IGD values of different algorithms under part of test functions

[0058] The inverse generational distance (IGD) is selected to evaluate the goodness of the approximate Pareto front obtained by the algorithm. The calculation formula of IGD is as follows: ; The results show that the improved multi-objective multi-universe algorithm performs well in the four-target optimization problem scene, slightly better than the original algorithm and the commonly used algorithm, and the performance results before and after optimization are shown in Table 3.

[0059] Table 3 Performance before and after optimization of markers

[0060] Step 6, use the improved algorithm of step 5 to solve the target function model established in step 3.

[0061] The obtained Pareto solution set is shown in Figure 6 From the figure, it can be seen that most of the solutions perform well on and Therefore, in the selection process based on the decision maker's preference, and have smaller weights, while and have larger weights. Thus the final optimal solution [dx=0.367um, dy=0.364um] is determined. From Table 3, it can be seen that the measurement performance of the marker is improved after optimization.

[0062] Each embodiment in the specification is described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same and similar parts of each embodiment can be referred to each other.

[0063] The principles and implementations of the present application are described in the specific examples in this article, and the above examples are only used to help understand the core idea of the present application; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation and application range will be changed. Therefore, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A design method of an optical metrology mark for overlay error measurement in a two-dimensional array, characterized in that, The application relates to a design method of a two-dimensional array type overlay error optical measurement mark. The two-dimensional array type overlay error optical measurement mark comprises, from top to bottom, a photoresist etched grating, a silicon dioxide film, a photoresist filling layer, a silicon grating and a silicon substrate. An overlay error characterization method is constructed based on the two-dimensional array type overlay error optical measurement mark. A multi-objective optimization model is constructed based on the characterization method; the multi-objective optimization model comprises a first objective function aiming at maximizing a lateral measurement sensitivity, a second objective function aiming at minimizing a lateral 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 multi-objective multi-universe optimization algorithm is used to solve the multi-objective optimization model, and an optimal mark structure is obtained; the multi-objective multi-universe optimization algorithm is a multi-objective multi-universe optimization 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.

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

3. The design method of claim 1, wherein, The overlay error characterization method specifically comprises the following steps. The lateral overlay error is calculated according to the following two equations, respectively and the longitudinal overlay error : ； wherein: , , , ; wherein and represents a scaling 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.

4. The design method of claim 1, wherein, In the multi-objective optimization model, each objective function is specifically represented as follows: 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 to the measured data points ASX and the lateral overlay error OVLX is a linear model fitted by least squares. 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.

5. The design method of claim 1, wherein, The multi-objective multi-universe optimization algorithm specifically comprises the following steps. The population is initialized based on a Latin hypercube sampling method; the variable space is equally divided into N non-overlapping subintervals, and independent equal-probability sampling is respectively performed on each subinterval, so that the sampling points are uniformly distributed in the entire distribution interval. An NMPSO algorithm-based fitness calculation method is used to evaluate the quality of solutions in the external archive, and based on the quality evaluation result, a leader particle is allocated to each particle through multiple roulette methods, so that the population evolves towards the entire Pareto frontier, and the population evolution is prevented from falling into a local optimum. A dynamic adjustment strategy is implemented for the size of the external archive; when the number of non-dominated solutions sharply increases in a four-target scenario, the archive capacity is linearly decreased with the iteration, so that the resource allocation between global exploration and local development under high-dimensional targets is balanced. For the updated external archive, if the number of solutions in the archive exceeds the archive size of the current generation, an NMPSO algorithm-based fitness calculation method is used to evaluate the quality of the solutions, and the poor solutions are deleted until the number of solutions in the archive does not exceed the archive size of the current generation.

6. A two-dimensional array-type optical measurement mark design system for overlay error, characterized in that, The application relates to a design method of a two-dimensional array type overlay error optical measurement mark. The two-dimensional array type overlay error optical measurement mark comprises, from top to bottom, a photoresist etched grating, a silicon dioxide film, a photoresist filling layer, a silicon grating and a silicon substrate. An overlay error characterization method is constructed based on the two-dimensional array type overlay error optical measurement mark. An overlay error characterization method is constructed 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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