Optimization method, apparatus and system for characterizing overlay error in photolithography process

Abstract

This application relates to the field of overlay measurement technology in integrated circuit photolithography processes, and discloses an optimized characterization method, apparatus, and system for overlay errors in photolithography processes. The method includes: acquiring DBO samples; calculating various indices of the electromagnetic field simulation minimization characterization quantities to optimize the performance of the measurement configuration and determining the optimal measurement configuration set; performing Mueller matrix measurement under the optimal measurement configuration set and matching it with the simulated Mueller matrix; performing polar decomposition on the Mueller matrix obtained from actual measurements at each wavelength point in the optimal measurement configuration set; calculating the intrinsic polarization state at each wavelength point in the optimal measurement configuration set; and averaging and weighting the characterization quantities of the intrinsic polarization states obtained at each wavelength point in the optimal measurement configuration set, followed by OVL solution to obtain the overlay error. Compared with traditional methods, this application significantly improves the accuracy of characterizing overlay errors in photolithography processes and exhibits better robustness.

Description

Technical Field

[0001] This application relates to the field of overlay measurement technology for integrated circuit photolithography processes, and in particular to an optimized characterization method, apparatus and system for overlay errors in photolithography processes. Background Technology

[0002] Photolithography is one of the most complex and critical processes in integrated circuit manufacturing, and overlay error is a crucial indicator of photolithography quality. Overlay error refers to the alignment error between the current layer (the pattern retained on the photoresist after exposure and development) and the reference layer (the existing pattern on the wafer) during exposure; it is essentially the relative offset from the designed position of the current layer. Generally, overlay error should be less than approximately 20%-30% of the critical dimension (CD). Large overlay errors will lead to poor device yields. Therefore, accurate measurement of critical dimensions is paramount in semiconductor manufacturing, and precise measurement of overlay error is particularly important.

[0003] Diffraction-based overlay error measurement (DBO), also known as scattering-based overlay error measurement (SCOL), is one of the main technical approaches for measuring overlay errors. DBO methods are mainly divided into two types: mDBO and eDBO. As indicated in the technical solution with patent publication number CN103472004A, the mDBO method requires real-time solution of complex partial differential equations to construct the optical model of the overlay mark, thus making it difficult to meet the time requirements for in-situ overlay error measurement.

[0004] Traditional eDBO methods mainly rely on the local linear relationship between the proposed light intensity characterization and the overlay error to measure the overlay error. Compared with traditional light intensity information, the Mueller matrix can obtain a 4×4 order zero-order diffraction Mueller matrix under each measurement configuration, which contains richer optical information. The measurement of the overlay error δ can be converted into the measurement of the Mueller matrix corresponding to the zero-order diffracted light, and the characterization can be found from it. The overlay error can be solved by using the linear relationship between the characterization and the overlay error δ. For example, there is a linear empirical extraction method based on the off-diagonal elements of the Mueller matrix for measuring the overlay error of three-dimensional complex overlay structures (YNKim et al., Opt. Express, Vol. 17(23), pp. 21336-21343, 2009), and there is an empirical extraction method based on the off-diagonal elements of the Mueller matrix for measuring the overlay error of one-dimensional overlay structures (J. Li et al., Proc. SPIE, Vol. 7638, pp. 78382C1-78382C10). Meanwhile, the technical solutions disclosed in patents CN202310116536.9, CN202110470725.7, CN202011056590.1, and CN201210544767.1 all mention the eDBO method using the Mueller matrix. However, existing methods have limitations in some aspects, such as a small linear range, low sensitivity, poor robustness, and inapplicability at an azimuth angle of 90°.

[0005] Therefore, there is an urgent need to construct an overlay characterization scheme with good linearity, sensitivity and robustness. Summary of the Invention

[0006] To address the aforementioned issues, this application provides an optimized characterization method, apparatus, and system for photolithography process overlay errors, thereby constructing a characterization quantity with better linearity, sensitivity, and robustness.

[0007] To achieve the above objectives, the technical solution adopted in this application is as follows:

[0008] In a first aspect, this application provides an optimized characterization method for overlay errors in photolithography processes, the method comprising:

[0009] Obtain DBO samples, calculate various indices of the electromagnetic field simulation minimized characterization quantities to optimize the performance of the measurement configuration, and determine the optimal measurement configuration set;

[0010] Under the optimal measurement configuration set, the Mueller matrix is ​​measured, and the measured Mueller matrix is ​​matched with the Mueller matrix obtained from the simulation.

[0011] Perform polar decomposition on the Mueller matrix obtained from the actual measurements at each wavelength point in the optimal measurement configuration set;

[0012] Calculate the intrinsic polarization state of each wavelength point in the optimal measurement configuration set;

[0013] After averaging and weighting the intrinsic polarization state characteristics obtained at each wavelength point in the optimal measurement configuration set, the OVL solution is performed to obtain the overlay error.

[0014] Furthermore, DBO samples are obtained, and various indices of the electromagnetic field simulation minimization parameters are calculated to optimize the performance of the measurement configuration and determine the optimal measurement configuration set, including:

[0015] The metrics are denoted as {L, -S, Ro}. Measurement configurations are optimized by minimizing {L, -S, Ro} to obtain the Pareto optimal solution as the best measurement configuration set; where L is the linearity, and L = ||f OVL±d -k(OVL±d)||, where f is the true indicator curve, k is the slope, OVL is the overlay error, d is the artificially introduced bias, and S is the sensitivity. Ro represents robustness. σ is the standard deviation of a set of data, and μ is the mean of the average of the set of data.

[0016] Furthermore, Mueller matrix measurements were performed using a broadband ellipsometry under the optimal measurement configuration set.

[0017] Furthermore, the process of calculating the polar decomposition of the Mueller matrix obtained from the actual measurements at each wavelength point in the optimal measurement configuration set is expressed as follows:

[0018] M = M Δ M R M D

[0019] In the formula, M is the measured Mueller matrix. M D It is the bidirectional attenuation matrix of the sample amplitude with respect to the incident light, used to represent the differential loss between orthogonal polarization eigenstates; M R It is the phase delay matrix of the sample with respect to the incident light, used to represent the differential phase delay between two eigenstates; M Δ It is the depolarization matrix of the sample with respect to the incident light; D represents the bidirectional attenuation vector, P Δ Let m denote the polarization vector, T denote the matrix transpose, and m D This indicates that by deleting M D M is obtained from the first row and first column. D A 3x3 submatrix, mR This indicates that by deleting M R M is obtained from the first row and first column. R A 3x3 submatrix, m Δ This indicates that by deleting M Δ M is obtained from the first row and first column. Δ A 3x3 submatrix.

[0020] Furthermore, M is calculated using the following formula. D and M R :

[0021]

[0022] Where D = (M 12 M 13 M 14 ) T M 12 M 13 M 14 These represent the second, third, and fourth elements of the first row of the Mueller matrix, M, respectively. D I is the double-decaying vector of M, D′ is the unit vector along D, and I is the 3×3 identity matrix.

[0023] Furthermore, the intrinsic polarization state at each wavelength point in the calculated optimal measurement configuration set is expressed as:

[0024]

[0025] In the formula, α = (1, a1, a2, a3) represents the intrinsic polarization state, and M R It is the difference delay matrix of the sample with respect to the incident light, where a1, a2, and a3 represent the second, third, and fourth elements in the normalized intrinsic polarization state, respectively, and a2 in the intrinsic polarization state is used as a characterization quantity.

[0026] The calculation expressions for each element of the intrinsic polarization state are as follows:

[0027]

[0028] In the formula, Represents the phase delay function, δ ij It is the Kronecker function, ∈ ijk It is a substitution symbol (Levi–Civitaper mutation symbol), (m R ) ij It is m R The element in the i-th row and j-th column, a i It is the i+1 element in the intrinsic polarization state, a j It is the j+1 element in the intrinsic polarization state, ak It is the k+1 element in the intrinsic polarization state, and i is (m R ) ij Element in m R The corresponding row number in the middle, j is (m R ) ij Element in m R The corresponding column number, k is the indicator variable.

[0029] Furthermore, after averaging and weighting the intrinsic polarization state characteristics obtained at each wavelength point in the optimal measurement configuration set, OVL is performed to obtain the formula for calculating the overlay error, which is expressed as:

[0030]

[0031] In the formula, OVL represents the measured overlay error, and d represents the artificially introduced bias. It is a characterization quantity measured under the corresponding d+OVL marking.

[0032] Secondly, this application provides an optimization characterization device for overlay error in photolithography processes, the device comprising:

[0033] The optimal configuration determination module is configured to acquire DBO samples, calculate various indices of the electromagnetic field simulation minimized characterization quantities to optimize the performance of the measurement configuration, and determine the optimal measurement configuration set.

[0034] The matrix matching module is configured to perform Mueller matrix measurements under the optimal measurement configuration set and select the measured Mueller matrix to match with the simulated Mueller matrix.

[0035] The matrix polar decomposition module is configured to perform polar decomposition on the Mueller matrix obtained from the actual measurements at each wavelength point in the optimal measurement configuration set.

[0036] The polarization state calculation module is configured to calculate the intrinsic polarization state of each wavelength point in the optimal measurement configuration set;

[0037] The overlay error solving module is configured to average and weight the intrinsic polarization state characterizations obtained at each wavelength point in the optimal measurement configuration set, and then perform OVL solving to obtain the overlay error.

[0038] Thirdly, this application provides an optimization characterization system for overlay error in photolithography processes, the system comprising: a memory for storing a computer program; and a processor for executing the computer program to implement the method described above.

[0039] This application has at least the following beneficial effects:

[0040] The characterization quantity α2 calculated in this application is not limited by the azimuth angle and can realize full-angle measurement under non-zero azimuth angle. Moreover, in characterizing the overlay error of photolithography process, it greatly improves the accuracy compared with traditional methods and has good robustness. Attached Figure Description

[0041] Figure 1 This is a flowchart of an optimization method for characterizing overlay error in a photolithography process according to an embodiment of this application.

[0042] Figure 2 This is a schematic diagram of the measurement sample marking structure according to an embodiment of this application; wherein, (a) is a cross-sectional view of the overlay marking; and (b) is a three-dimensional view of the overlay marking.

[0043] Figure 3 The following are performance diagrams at different wavelengths according to embodiments of this application, wherein (a) 200nm wavelength; (b) 400nm wavelength; (c) 600nm wavelength; (d) 800nm ​​wavelength; and (e) 1000nm wavelength.

[0044] Figure 4 This is a comparison chart of measurement errors under ideal measurement conditions according to embodiments of this application.

[0045] Figure 5 The images provided are SEM images of a real sample according to embodiments of this application and actual size diagrams marked in the FIB diagram, wherein (a) is an SEM image of the real sample; and (b) is an actual size diagram marked in the FIB diagram.

[0046] Figure 6 This is a structural diagram of an optimization characterization device for overlay error in a photolithography process according to an embodiment of this application. Detailed Implementation

[0047] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0048] The specific implementation methods of this application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0049] Example 1:

[0050] Please see Figure 1This is a flowchart of an optimization characterization method for overlay error in photolithography. The optimization characterization method for overlay error in photolithography includes steps S1 to S5, which are described in detail below.

[0051] S1. Obtain DBO samples, calculate various indices of the electromagnetic field simulation minimization characteristic to optimize the performance of the measurement configuration, and determine the optimal measurement configuration set.

[0052] In this embodiment, for a given DBO sample, electromagnetic field simulation is performed with known prior distribution information to evaluate the performance of the characterization index α2. The performance of each index can be evaluated for a series of sampling points within a given OVL range. L represents linearity, L = ||f OVL±d -k(OVL±d)||, where linear error is defined as the distance between the true indication curve f and an approximately linear function with slope k, OVL is the overlay error, d is the artificially introduced bias, and S is the sensitivity. Sensitivity is a metric used to characterize the ability of a quantitative indicator to assess small overlay errors. Ro represents robustness. Where σ is the standard deviation of a set of data, and μ is the mean of the average of the set of data. This index is designed to minimize the impact of any disturbances (e.g., small changes in the measurement wavelength λ or azimuth angle). The measurement configuration is optimized by minimizing the performance of the three indices {L, -S, Ro} to obtain a Pareto optimal solution and determine the Pareto optimal measurement configuration set.

[0053] S2, perform Mueller matrix measurement under the optimal measurement configuration set, and select the measured Mueller matrix to match the Mueller matrix obtained from simulation.

[0054] In this embodiment, a broadband ellipsometry is used to measure the Mueller matrix under the optimal measurement configuration set. Then, the measured Mueller matrix is ​​selected and matched with the simulated Mueller matrix.

[0055] S3, perform polar decomposition on the Mueller matrix obtained from the actual measurements at each wavelength point in the optimal measurement configuration set.

[0056] In this embodiment, the Mueller matrix obtained from the actual measurement at each wavelength point in the Pareto front solution is subjected to polar decomposition. The specific process of polar decomposition is as follows:

[0057] M = M Δ M R M D

[0058] in M DIt is the bidirectional attenuation matrix of the sample amplitude with respect to the incident light, used to represent the differential loss between orthogonal polarization eigenstates; M R It is the phase delay matrix of the sample with respect to the incident light, used to represent the differential phase delay between two eigenstates; M Δ It is the depolarization matrix of the sample with respect to the incident light; D represents the bidirectional attenuation vector, P Δ This represents the polarization vector. In the experiment, the depolarization matrix M... Δ It can be extracted separately from the measured Mueller matrix, and for M D No effect. Therefore, with the non-de-biased matrix M Δ The Mueller matrix M′ is analyzed. The bidirectional attenuation matrix M... D and phase delay matrix M R It can be obtained through the following formula:

[0059]

[0060] Where D = (M 12 M 13 M 14 ) T M 12 M 13 M 14 These represent the second, third, and fourth elements of the first row of the Mueller matrix, M, respectively. D I is the double-decaying vector of M, D′ is the unit vector along D, and I is the 3×3 identity matrix.

[0061] S4 calculates the intrinsic polarization state of each wavelength point in the optimal measurement configuration set.

[0062] In this embodiment, the intrinsic polarization state at each wavelength point in the Pareto front solution is calculated, and the expression is as follows:

[0063]

[0064] Where α = (1, a1, a2, a3) represents the intrinsic polarization states, a1, a2, and a3 represent the second, third, and fourth elements in the normalized intrinsic polarization states, respectively, and M... R This is the difference delay matrix of the sample with respect to the incident light. The calculation expressions for each element of the intrinsic polarization state are as follows:

[0065]

[0066] In the formula, Represents the phase delay function, δ ij It is the Kronecker function, ∈ ijkIt is a substitution symbol (Levi–Civita permutation symbol), (m R ) ij It is m R The element in the i-th row and j-th column, a i It is the i+1 element in the intrinsic polarization state, a j It is the j+1 element in the intrinsic polarization state, a k It is the k+1 element in the intrinsic polarization state, and i is (m R ) ij Element in m R The corresponding row number in the middle, j is (m R ) ij Element in m R The corresponding column number, k is the indicator variable.

[0067] S5. After averaging and weighting the characterization quantities of the intrinsic polarization state obtained from each wavelength point in the optimal measurement configuration set, OVL solution is performed to obtain the overlay error.

[0068] In this embodiment, the overlay error can be measured by measuring several DBO samples with opposite artificially introduced biases d and -d. The calculation formula is as follows:

[0069]

[0070] In the formula, OVL represents the measured overlay error, and d represents the artificially introduced bias. It is a characterization quantity measured under the corresponding d+OVL marking.

[0071] Example 2:

[0072] This application provides a specific embodiment of the method for optimizing the overlay error of photolithography processes, based on the method described in Embodiment 1. The parameters of the sample selected in this embodiment are explained below:

[0073] The structural design and material selection referenced existing research, such as Figure 2 As shown. More detailed parameter values ​​are shown in Table 1. Here, the total offset δ includes the preset offset (d) and the overlay error (ε) generated during manufacturing. The former is fixed, while the latter varies according to simulation requirements. Two opposite preset offsets are considered in the simulation. The linewidth or critical dimension (CD) of the two grating layers is the same. The optical constants of Si and SiO2 are taken from [reference needed]. The Tauc-Lorentz model is used to represent the dielectric constant of the photoresist (PR), where A, Eg, E0, C, and ε-∞ are set to 21.1496 eV, 3.4597 eV, 9.9492 eV, 0.9877 eV, and 1.4268, respectively.

[0074] Table 1: Parameter settings for DBO overlay marker samples corresponding to the simulation

[0075]

[0076] Experimental setup:

[0077] In this embodiment, the incident broadband Mueller matrix ellipsometer is simulated using the rigorously coupled wavelength analysis (RCWA) method. The incident angle is fixed at 65°, the simulation wavelength range is [200nm, 800nm], the step size is 10nm, and the azimuth angle is fixed at 10°.

[0078] Experimental band selection:

[0079] Simulations were used to evaluate the performance of the characterization index α2, optimizing the objective {L, -S, Ro}, where L is the linearity and L = ||f OVL±d -k(OVL±d)||, where linearity error is defined as the distance between the true indication curve f and an approximately linear function with slope k. S is the sensitivity. Sensitivity is a metric used to characterize the ability of a quantitative indicator to assess small overlay errors. Ro represents robustness. Where σ is the standard deviation of a set of data, and μ is the mean of the average of the set of data. This index is designed to minimize the impact of any disturbances (e.g., small variations in the measurement wavelength λ or azimuth angle). Suitable wavelength bands are selected for subsequent measurements.

[0080] Spectral matching: Perform Mueller matrix measurements under the optimal measurement configuration set, then select the measured Mueller matrix and match it with the simulated Mueller matrix;

[0081] Polar decomposition: The Mueller matrix obtained from actual measurements at each wavelength point in the Pareto front solution is decomposed into polar components, as shown in the following expression:

[0082] M = M Δ M R M D

[0083] in M D It is the bidirectional attenuation matrix of the sample amplitude with respect to the incident light, used to represent the differential loss between orthogonal polarization eigenstates; M R It is the phase delay matrix of the sample with respect to the incident light, used to represent the differential phase delay between two eigenstates; M Δ It is the depolarization matrix of the sample with respect to the incident light; D represents the bidirectional attenuation vector, P ΔThis represents the polarization vector.

[0084] Intrinsic polarization state solution: Extract the difference delay matrix from the polar decomposition results and solve for its eigenpolar polarization states, as shown in the following expression:

[0085]

[0086] α = (a1, a2, a3) represents the intrinsic polarization states, M R It is the difference delay matrix of the sample with respect to the incident light. In the experiment, the depolarization matrix M... Δ It can be extracted separately from the measured Mueller matrix and has no effect on MD. Therefore, with the debiased matrix M Δ The Mueller matrix M′ is analyzed. The bidirectional attenuation matrix M... D. and phase delay matrix M R It can be obtained through the following formula:

[0087]

[0088] Where D = (M 12 M 13 M 14 ) T I is the double-decaying vector of M, D′ is the unit vector along D, and I is the 3×3 identity matrix.

[0089] Solving for intrinsic polarization states:

[0090] The intrinsic polarization state at each wavelength point in the Pareto front solution is calculated as follows:

[0091]

[0092] α = (1, a1, a2, a3) represents the intrinsic polarization state, M R This is the difference delay matrix of the sample with respect to the incident light. The calculation expressions for each element of the intrinsic polarization state are as follows:

[0093]

[0094] in Represents the phase delay function, δ ij It is Kronecker delta, ∈ ijk It is the Levi–Civita permutation symbol.

[0095] Overlay error extraction:

[0096] After averaging and weighting the a2 obtained from each wavelength point in the Pareto front solution, the OVL solution is then performed.

[0097]

[0098] Simulation verification:

[0099] 1) Linearity verification: To quickly verify the effectiveness of this method, this implementation performs simulation verification on the above samples. Figure 3 Table 2 shows the relationship between the characterization quantity and the total offset δ at wavelengths of 200nm, 400nm, 600nm, 800nm, and 1000nm, corresponding to azimuth angles of 30°, 60°, and 90°. The specific linearity values ​​are shown in Table 2.

[0100] Table 2: Linearity R at different wavelengths and azimuth angles 2

[0101]

[0102] 2) Accuracy verification:

[0103] To quickly verify the accuracy of this method, ε was fixed at 10m, and d was varied from 5nm to 50nm. The results were compared with other methods, and the measurement error was as follows: Figure 4 As shown. Here, the a2 representation proposed in this embodiment, after being averaged and weighted, is called PE-OI. Other methods refer to the differential Mueller matrix LB' representation as LD'-OI (linear dichroism along ±45°axes, LD'-OI), while the off-diagonal elements of the Mueller matrix are called MMD-OI. Here, M is used as the reference. 13 +M 31 For example.

[0104] 3) Robustness verification:

[0105] To ensure that this implementation still performs well under wavelength / azimuth oscillation, the robustness of the characterization quantity was investigated when there was a ±1° perturbation in wavelength / azimuth. The degree of robustness was expressed by the robustness index mentioned above, and the final results are shown in Table 3.

[0106] Table 3: Robustness of different characterization parameters in simulation

[0107]

[0108] Experimental verification:

[0109] To verify the effectiveness of this method, similar samples were prepared in this embodiment. Specific dimensions are shown in [reference needed]. Figure 5The FIB plot was obtained. Measurements were performed following the steps described above, and the results were compared with those of the other two characterization parameters. After PC weighting, LD'-OI yielded OVL = -15.3 nm, and MME-OI yielded OVL = -9.7 nm. The true value corresponding to FIB was -17 nm. The corresponding robustness and its various parameters are shown in Table 4.

[0110] Table 4: Robustness of different characterization parameters in the experiment

[0111]

[0112] In summary, all the experimental results above demonstrate the effectiveness of the proposed method for extracting nanostructure overlay errors based on the Mueller matrix.

[0113] Those skilled in the art will readily understand that the above-described ellipticity measurement is based on results with x and y as orthogonal directions, and is merely a preferred embodiment of the present invention. Other orthogonal directions (left circle, right circle, etc.) are not intended to limit the present invention.

[0114] Example 3:

[0115] This application also provides an optimization characterization device for overlay error in photolithography processes, such as... Figure 6 As shown, the device includes:

[0116] The optimal configuration determination module 601 is configured to acquire DBO samples, calculate various indices of the electromagnetic field simulation minimized characterization quantities to optimize the performance of the measurement configuration, and determine the optimal measurement configuration set.

[0117] The matrix matching module 602 is configured to perform Mueller matrix measurement under the optimal measurement configuration set and select the measured Mueller matrix to match with the simulated Mueller matrix;

[0118] The matrix polar decomposition module 603 is configured to perform polar decomposition on the Mueller matrix obtained by actual measurement at each wavelength point in the optimal measurement configuration set.

[0119] The polarization state calculation module 604 is configured to calculate the intrinsic polarization state of each wavelength point in the optimal measurement configuration set.

[0120] The overlay error solving module 605 is configured to average and weight the intrinsic polarization state characterization quantities obtained at each wavelength point in the optimal measurement configuration set, and then perform OVL solution to obtain the overlay error.

[0121] In some embodiments, the optimal configuration determination module is further configured to:

[0122] The metrics are denoted as {L, -S, Ro}. Measurement configurations are optimized by minimizing {L, -S, Ro} to obtain the Pareto optimal solution as the best measurement configuration set; where L is the linearity, and L = ||f OVL±d -k(OVL±d)||, where f is the true indicator curve, k is the slope, OVL is the overlay error, d is the artificially introduced bias, and S is the sensitivity. Ro represents robustness. σ is the standard deviation of a set of data, and μ is the mean of the average of the set of data.

[0123] In some embodiments, the matrix matching module is further configured to perform Mueller matrix measurements using a broadband ellipsometry under the optimal measurement configuration set.

[0124] In some embodiments, the matrix polar decomposition module is further configured to perform polar decomposition calculations on the Mueller matrix actually measured at each wavelength point in the optimal measurement configuration set, as follows:

[0125] M = M Δ M R M D

[0126] In the formula, M is the measured Mueller matrix. M D It is the bidirectional attenuation matrix of the sample amplitude with respect to the incident light, used to represent the differential loss between orthogonal polarization eigenstates; M R It is the phase delay matrix of the sample with respect to the incident light, used to represent the differential phase delay between two eigenstates; M Δ It is the depolarization matrix of the sample with respect to the incident light; D represents the bidirectional attenuation vector, P Δ Let m denote the polarization vector, T denote the matrix transpose, and m D This indicates that by deleting M D M is obtained from the first row and first column. D A 3x3 submatrix, m R This indicates that by deleting M R M is obtained from the first row and first column. R A 3x3 submatrix, m Δ This indicates that by deleting M Δ M is obtained from the first row and first column. Δ A 3x3 submatrix.

[0127] In some embodiments, the matrix polar decomposition module is further configured to calculate M using the following formula. D and M R :

[0128]

[0129] In the formula, D = (M 12 M 13 M 14 ) T M 12 M 13 M 14 Let D and I represent the second, third, and fourth elements of the first row of the Mueller matrix, respectively. D′ is the unit vector along D, and I is the 3×3 identity matrix.

[0130] In some embodiments, the intrinsic polarization state of each wavelength point in the calculated optimal measurement configuration set is represented as:

[0131]

[0132] In the formula, α = (1, a1, a2, a3) represents the intrinsic polarization state, and M R It is the difference delay matrix of the sample with respect to the incident light, where a1, a2, and a3 represent the second, third, and fourth elements in the normalized intrinsic polarization state, respectively, and a2 in the intrinsic polarization state is used as a characterization quantity.

[0133] The calculation expressions for each element of the intrinsic polarization state are as follows:

[0134]

[0135] In the formula, Represents the phase delay function, δ ij It is the Kronecker function, ∈ ijk It is a substitution symbol (Levi–Civita permutation symbol), (m R ) ij It is m R The element in the i-th row and j-th column, a i It is the i+1 element in the intrinsic polarization state, a j It is the j+1 element in the intrinsic polarization state, a k It is the k+1 element in the intrinsic polarization state, and i is (m R ) ij Element in m R The corresponding row number in the middle, j is (m R ) ij Element in m R The corresponding column number, k is the indicator variable.

[0136] In some embodiments, the intrinsic polarization state characterization values ​​obtained at each wavelength point in the optimal measurement configuration set are averaged and weighted before OVL calculation, resulting in the formula for calculating the overlay error, which is expressed as follows:

[0137]

[0138] In the formula, OVL represents the measured overlay error, and d represents the artificially introduced bias. It is a characterization quantity measured under the corresponding d+OVL marking.

[0139] It should be noted that the device described in this embodiment and the method described earlier belong to the same technical concept, have the same technical principle, and can achieve the same beneficial effect, so they will not be described again here.

[0140] This application also provides an optimization characterization system for overlay error in photolithography processes. The system includes: a memory for storing a computer program; and a processor for executing the computer program to implement the method described in any of the above embodiments.

[0141] This application also provides a non-transitory computer-readable storage medium storing instructions that, when executed by a processor, perform the methods described in any of the above embodiments.

[0142] The above embodiments are only used to illustrate this application and are not intended to limit this application. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of this application. Therefore, all equivalent technical solutions also fall within the scope of this application, and the patent protection scope of this application should be defined by the claims.

Claims

1. A method for optimizing the characterization of overlay error in photolithography processes, characterized in that, The method includes; Obtain DBO samples, calculate various indices of the electromagnetic field simulation minimized characterization quantities to optimize the performance of the measurement configuration, and determine the optimal measurement configuration set; Under the optimal measurement configuration set, the Mueller matrix is ​​measured, and the measured Mueller matrix is ​​matched with the Mueller matrix obtained from the simulation. Perform polar decomposition on the Mueller matrix obtained from the actual measurements at each wavelength point in the optimal measurement configuration set; Calculate the intrinsic polarization state of each wavelength point in the optimal measurement configuration set; After averaging and weighting the intrinsic polarization state characteristics obtained at each wavelength point in the optimal measurement configuration set, the OVL solution is performed to obtain the overlay error.

2. The method for optimizing and characterizing overlay error in photolithography as described in claim 1, characterized in that, Obtain DBO samples, calculate various indices of the electromagnetic field simulation minimization characteristics to optimize the performance of the measurement configuration, and determine the optimal measurement configuration set, including: The metrics are denoted as {L, -S, Ro}. Measurement configurations are optimized by minimizing {L, -S, Ro} to obtain the Pareto optimal solution as the best measurement configuration set; where L is the linearity, and L = ||f OVL±d -k(OVL±d)||, where f is the true indicator curve, k is the slope, OVL is the overlay error, d is the artificially introduced bias, and S is the sensitivity. Ro represents robustness. σ is the standard deviation of a set of data, and μ is the mean of the average of the set of data.

3. The method for optimizing and characterizing overlay errors in photolithography as described in claim 1, characterized in that, The Mueller matrix was measured using a broadband ellipsometry under the optimal measurement configuration set.

4. The method for optimizing and characterizing overlay errors in photolithography as described in claim 1, characterized in that, The process of calculating the polar decomposition of the Mueller matrix obtained from the actual measurements at each wavelength point in the optimal measurement configuration set is expressed as follows: M=M Δ M R M D In the formula, M is the measured Mueller matrix. M D It is the bidirectional attenuation matrix of the sample amplitude with respect to the incident light, used to represent the differential loss between orthogonal polarization eigenstates; M R It is the phase delay matrix of the sample with respect to the incident light, used to represent the differential phase delay between two eigenstates; M Δ It is the depolarization matrix of the sample with respect to the incident light; D represents the bidirectional attenuation vector, P Δ Let m denote the polarization vector, T denote the matrix transpose, and m D This indicates that by deleting M D M is obtained from the first row and first column. D A 3x3 submatrix, m R This indicates that by deleting M R M is obtained from the first row and first column. R A 3x3 submatrix, m Δ This indicates that by deleting M Δ M is obtained from the first row and first column. Δ A 3x3 submatrix.

5. The method for optimizing and characterizing overlay error in photolithography as described in claim 4, characterized in that, M is calculated using the following formula. D and M R : In the formula, D = (M 12 M 13 M 14 ) T M 12 M 13 M 14 Let D and I represent the second, third, and fourth elements of the first row of the Mueller matrix, respectively. D′ is the unit vector along D, and I is the 3×3 identity matrix.

6. The method for optimizing and characterizing overlay errors in photolithography as described in claim 1, characterized in that, The intrinsic polarization state of each wavelength point in the calculated optimal measurement configuration set is represented as follows: In the formula, α = (1, a1, a2, a3) represents the intrinsic polarization state, and M R It is the difference delay matrix of the sample with respect to the incident light, where a1, a2, and a3 represent the second, third, and fourth elements in the normalized intrinsic polarization state, respectively, and a2 in the intrinsic polarization state is used as a characterization quantity. The calculation expressions for each element of the intrinsic polarization state are as follows: In the formula, Represents the phase delay function, δ ij It is the Kronecker function, ∈ ijk It is a substitution symbol, (m R ) ij It is m R The element corresponding to the i-th row and j-th column, a i It is the i+1 element in the intrinsic polarization state, a j It is the j+1 element in the intrinsic polarization state, a k It is the k+1 element in the intrinsic polarization state, and i is (m R ) ij Element in m R The corresponding row number in the middle, j is (m R ) ij Element in m R The corresponding column number, k is the indicator variable.

7. The method for optimizing and characterizing overlay error in photolithography as described in claim 1, characterized in that, After averaging and weighting the intrinsic polarization state characteristics obtained at each wavelength point in the optimal measurement configuration set, the OVL solution is performed to obtain the formula for calculating the overlay error, which is expressed as follows: In the formula, OVL represents the measured overlay error, and d represents the artificially introduced bias. It is a characterization quantity measured under the corresponding d+OVL marking.

8. An optimized characterization device for overlay error in photolithography processes, characterized in that, The device includes: The optimal configuration determination module is configured to acquire DBO samples, calculate various indices of the electromagnetic field simulation minimized characterization quantities to optimize the performance of the measurement configuration, and determine the optimal measurement configuration set. The matrix matching module is configured to perform Mueller matrix measurements under the optimal measurement configuration set and select the measured Mueller matrix to match with the simulated Mueller matrix. The matrix polar decomposition module is configured to perform polar decomposition on the Mueller matrix obtained from the actual measurements at each wavelength point in the optimal measurement configuration set. The polarization state calculation module is configured to calculate the intrinsic polarization state of each wavelength point in the optimal measurement configuration set; The overlay error solving module is configured to average and weight the intrinsic polarization state characterizations obtained at each wavelength point in the optimal measurement configuration set, and then perform OVL solving to obtain the overlay error.

9. An optimized characterization system for overlay error in photolithography processes, characterized in that: The system includes: Memory, used to store computer programs; A processor for executing the computer program to implement the method as described in any one of claims 1 to 7.

Images