Optimization method, device and measurement method for theoretical spectral data

Abstract

The application provides a method, device and method for optimizing theoretical spectrum data, the method for optimizing theoretical spectrum data comprising: obtaining a sample model, the sample model having a periodic structure in X and Y directions; obtaining a set of convergence order pairs of the sample model in the X and Y directions; obtaining a relative distribution of an optical characteristic parameter of each order pair in the set of convergence order pairs relative to a (0, 0) order pair or an absolute distribution of the optical characteristic parameter of each order pair, and establishing a data table according to the relative distribution or the absolute distribution; screening data in the data table, and the order pair corresponding to the data meeting a preset condition being an optimized order pair; and obtaining theoretical spectrum data corresponding to the optimized order pair based on an RCWA algorithm. The application improves the efficiency of solving theoretical spectrum data.

Description

Technical Field

[0001] This invention relates to the field of optical critical dimension measurement technology, and in particular to a method, device and measurement method for optimizing theoretical spectral data. Background Technology

[0002] Optical Critical Dimension (OCD) technology estimates the specific morphological parameters of a sample by acquiring the scattering signal of the periodic structure of a specific measured area and the sample model. It can meet the needs of rapid and accurate measurement in new processes and technologies, and is non-contact and non-destructive, and is widely used in the semiconductor manufacturing industry and optical measurement.

[0003] Optical critical dimension measurement technology can be summarized into two steps: the spectral acquisition process, which involves acquiring the scattering signal of the sample and processing it into a measurement spectrum; and the spectral matching process, which involves establishing a morphological model of the sample and finding a specific theoretical spectrum to achieve the best match with the measurement spectrum, thereby determining its morphological parameters. The algorithm used to calculate the theoretical spectrum is Rigorous Coupled Wave Analysis (RCWA).

[0004] In the process of spectral matching, one approach is to establish a theoretical spectral database corresponding to the morphological model of the sample, and then search for the theoretical spectrum that best matches the measured spectrum from the theoretical spectral database to determine the morphological parameters of the sample. Another approach is to use regression to find a specific theoretical spectrum to achieve the best match with the measured spectrum, thereby determining the morphological parameters of the sample.

[0005] For two-dimensional samples, the RCWA algorithm performs Fourier series expansions of the dielectric constant, electric field, and magnetic field in two orthogonal directions, typically the x and y directions, as follows:

[0006]

[0007] Fourier series expansions range from negative infinity to positive infinity. In practical applications of the RCWA algorithm, due to computational resource limitations, it's necessary to truncate the series. The highest truncation order is called the truncation order. In practical applications, the Fourier series expansions of the dielectric constant, electric field, and magnetic field can be performed down to the truncation order, as follows:

[0008]

[0009] Since the above formula covers two directions, two cutoff orders are required. The cutoff order in the x-direction is denoted as N. x The truncation order in the y-direction is denoted as N. y The order m in the x-direction can take the value -N. x To N x The integer n in the y-direction can take values ​​of -N. y To N y An integer. A combination consisting of an x-direction order *m* and a y-direction order *n* is called an order pair, denoted as (m, n). Since the x-direction order has multiple values ​​and the y-direction order also has multiple values, there are multiple combinations of them, and therefore multiple order pairs. These different order pairs form a set of order pairs. In the prior art, the set of order pairs is the pairwise combination of x-direction orders and y-direction orders, denoted as {(m, n)|-N}. x ≤m≤N x -N y ≤n≤N y The original set of order pairs is used to obtain the convergent set of order pairs by performing convergence analysis on the original set of order pairs. This is existing technology and will not be elaborated here. Based on the convergent set of order pairs, Fourier series expansions are performed on the dielectric function, electric field, and magnetic field. Then, the RCWA algorithm is applied to calculate the theoretical spectrum. Therefore, one set of order pairs corresponds to one theoretical spectrum.

[0010] On the one hand, when calculating the theoretical spectrum, the more order pairs of the Fourier series used, the greater the accuracy of the RCWA algorithm in calculating the theoretical spectrum, but the greater the computational cost and the lower the computational efficiency. On the other hand, the fewer order pairs of the Fourier series used, the smaller the computational cost and the higher the computational efficiency of the RCWA algorithm in calculating the theoretical spectrum, but this will lead to a decrease in the accuracy of the RCWA algorithm in calculating the theoretical spectrum.

[0011] Therefore, this invention proposes an optimization method, device, and measurement method for theoretical spectral data, which optimizes the convergence order set and improves the efficiency of solving theoretical spectral data. Summary of the Invention

[0012] This invention proposes an optimization method, device, and measurement method for theoretical spectral data. By optimizing the convergence order set, the efficiency of solving theoretical spectral data is improved.

[0013] In a first aspect, the present invention provides a method for optimizing theoretical spectral data, comprising: acquiring a sample model having a periodic structure in both the X and Y directions; performing Fourier series expansion on the optical characteristic parameters of the sample model along the X and Y directions to obtain a set of convergent order pairs of the optical characteristic parameters in the X and Y directions; acquiring the relative distribution of the optical characteristic parameters of each order pair in the set of convergent order pairs relative to the (0,0) order pair or the absolute distribution of the optical characteristic parameters of each order pair, and establishing a data table based on the relative distribution or the absolute distribution; filtering the data in the data table according to preset conditions, identifying the order pairs corresponding to the data that meet the preset conditions as optimized order pairs, and obtaining a set of optimized order pairs based on the optimized order pairs; and acquiring the theoretical spectral data corresponding to the set of optimized order pairs based on a rigorous coupled-wave analysis method.

[0014] Its beneficial effects are as follows: by selecting optimized order pairs through the preset conditions, and obtaining theoretical spectral data through the set of optimized order pairs and the RCWA algorithm, the efficiency of solving the theoretical spectral data is improved, thereby improving the efficiency of creating the theoretical spectral database.

[0015] Optionally, the set of convergent order pairs is a set of order pairs obtained after performing convergence analysis on the optical property parameters, wherein the optical property parameters include any one of dielectric constant, electric field, and magnetic field. Its advantage is that the present invention allows for the selection of appropriate optical property parameters according to actual conditions.

[0016] Optionally, obtaining the relative distribution of optical characteristic parameters of each order pair in the convergent order pair set relative to the (0,0) order pair or the absolute distribution of the optical characteristic parameters of each order pair, and establishing a data table based on the relative distribution or the absolute distribution, includes: performing layering processing on the sample model according to the morphological characteristics of the sample model; obtaining the power of s of the modulus of the Fourier coefficient of at least one medium layer of each order pair relative to the (0,0) order pair under at least one wavelength condition or the power of s of the modulus of the Fourier coefficient of at least one medium layer of each order pair under at least one wavelength condition, where s is a positive integer; and establishing a data table based on the power of s of the modulus of the Fourier coefficient of at least one medium layer of each order pair relative to the (0,0) order pair under at least one wavelength condition or the power of s of the modulus of the Fourier coefficient of at least one medium layer of each order pair under at least one wavelength condition. Its beneficial effect is that the solution efficiency of theoretical spectral data can be adjusted by setting the value of s. The value of s is directly proportional to the solution efficiency of theoretical spectral data. That is, the larger the value of s is, the higher the solution efficiency of theoretical spectral data.

[0017] Further optionally, obtaining the power of the s-th power of the Fourier coefficient of the optical characteristic parameter of at least one dielectric layer of each order pair under at least one wavelength condition relative to the (0,0) order pair, or the power of the s-th power of the Fourier coefficient of the optical characteristic parameter of at least one dielectric layer of each order pair under at least one wavelength condition, includes: obtaining the power of the s-th power of the Fourier coefficient of the dielectric constant of at least one dielectric layer of each order pair under at least one wavelength condition relative to the (0,0) order pair, or the power of the s-th power of the Fourier coefficient of the dielectric constant of at least one dielectric layer of each order pair under at least one wavelength condition.

[0018] Further optionally, obtaining the power of s of the magnitude of the Fourier coefficient of the optical characteristic parameter of at least one dielectric layer of each order pair under at least one wavelength condition relative to the (0,0) order pair, or the power of s of the magnitude of the Fourier coefficient of the optical characteristic parameter of at least one dielectric layer of each order pair under at least one wavelength condition, includes: obtaining the sum of the power of s of the magnitude of the Fourier coefficient of the X component of the electric field or magnetic field of at least one dielectric layer of each order pair under at least one wavelength condition relative to the (0,0) order pair and the power of s of the magnitude of the Fourier coefficient of the Y component of the electric field or magnetic field, or the power of s of the magnitude of the Fourier coefficient of the X component of the electric field or magnetic field of at least one dielectric layer of each order pair under at least one wavelength condition and the power of s of the magnitude of the Fourier coefficient of the Y component of the electric field or magnetic field.

[0019] Optionally, establishing a data table based on the power of the s-th power of the modulus of the Fourier coefficients of the optical characteristic parameters of each order pair under at least one wavelength condition and at least one medium layer, relative to the (0,0) order pair, includes: when the wavelength condition or the number of layers is greater than or equal to two, obtaining the maximum or average value of the power of the s-th power of the modulus of the Fourier coefficients of the optical characteristic parameters of each order pair under at least one wavelength condition and at least one layer, or obtaining the maximum or average value of the power of the s-th power of the modulus of the Fourier coefficients of the optical characteristic parameters of each order pair under at least one wavelength condition and at least one layer; traversing all order pairs, and establishing the data table with the maximum or average value corresponding to each order pair. The beneficial effect is that the maximum value ensures a larger weight for the corresponding order pair, and the average value ensures a smaller deviation in the weight of the corresponding order pair; both can provide accuracy in the solution process.

[0020] Optionally, the step of filtering the data in the data table according to preset conditions, and identifying the level pairs corresponding to the data that meet the preset conditions as optimized level pairs, includes: setting a first threshold and a second threshold; when the mean square error between the theoretical spectrum of the level pair corresponding to the data in the data table that is greater than or equal to the first threshold and the theoretical spectrum corresponding to the convergent level pair set is less than or equal to the second threshold, the level pair is an optimized level pair.

[0021] Optionally, the step of filtering the data in the data table according to preset conditions, and identifying the level pairs corresponding to the data that meet the preset conditions as optimized level pairs, includes: sorting the data in the data table by size; setting a filtering ratio and a second threshold; and when the mean square error between the theoretical spectrum of the level pair corresponding to the larger data in the data table and the theoretical spectrum corresponding to the convergent level pair set is less than or equal to the second threshold, the level pair is considered an optimized level pair.

[0022] In a second aspect, the present invention provides a measurement method, comprising: establishing a theoretical spectral database corresponding to the sample model according to the method described in any one of the first aspects; wherein the theoretical spectral database includes morphological parameters of the sample model and theoretical spectral data corresponding to the morphological parameters; obtaining measurement spectral data of the measurement region corresponding to the sample to be tested; and determining the morphological parameters of the measurement region corresponding to the sample to be tested based on the measurement spectral data and the theoretical spectral database.

[0023] Thirdly, the present invention provides an electronic device including a memory and a processor, wherein the memory stores a computer program executable on the processor, and when the computer program is executed by the processor, causes the processor to perform the method as described in any one of the first or third aspects.

[0024] For the beneficial effects of the second and third aspects mentioned above, please refer to the description in the first aspect mentioned above. Attached Figure Description

[0025] Figure 1 A flowchart of a method for optimizing theoretical spectral data provided in an embodiment of the present invention;

[0026] Figure 2 A schematic diagram of a two-dimensional sample model provided in an embodiment of the present invention;

[0027] Figure 3 A schematic diagram of an optimization device for theoretical spectral data provided in an embodiment of the present invention;

[0028] Figure 4 A flowchart illustrating an embodiment of a measurement method provided by this invention;

[0029] Figure 5 This is a schematic diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0030] The technical solutions of the embodiments of this application are described below with reference to the accompanying drawings. In the description of the embodiments of this application, the terminology used in the following embodiments is for the purpose of describing specific embodiments only and is not intended to limit the application. As used in the specification and appended claims of this application, the singular expressions "a," "the," "the," "the," and "this" are intended to also include expressions such as "one or more," unless the context clearly indicates otherwise. It should also be understood that in the following embodiments of this application, "at least one" and "one or more" refer to one or more (including two). The term "and / or" is used to describe the relationship between related objects, indicating that three relationships can exist; for example, A and / or B can represent: A alone, A and B simultaneously, or B alone, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship.

[0031] References to "one embodiment" or "some embodiments" in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized. The term "connection" includes direct connections and indirect connections, unless otherwise stated. "First" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated.

[0032] In the embodiments of this application, the words "exemplarily" or "for example" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplarily" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design solutions. Specifically, the use of the words "exemplarily" or "for example" is intended to present the relevant concepts in a specific manner.

[0033] This invention provides a method for optimizing theoretical spectral data, the process of which is as follows: Figure 1 As shown, it includes:

[0034] S101: Obtain a sample model, wherein the sample model has a periodic structure in both the X and Y directions, where X and Y are coordinate axis directions;

[0035] S102: Perform Fourier series expansion on the optical property parameters of the sample model along the X and Y directions to obtain the set of convergent order pairs of the optical property parameters in the X and Y directions;

[0036] S103: Obtain the relative distribution of optical property parameters of each level pair in the convergence level pair set relative to the (0,0) level pair or the absolute distribution of optical property parameters of each level pair, and establish a data table based on the relative distribution or the absolute distribution.

[0037] S104: Filter the data in the data table according to preset conditions, and the level pairs corresponding to the data that meet the preset conditions are optimized level pairs, and obtain an optimized level pair set according to the optimized level pairs;

[0038] S105: Based on the RCWA algorithm, obtain the theoretical spectral data corresponding to the optimized order pair set.

[0039] In this embodiment, optimized order pairs are selected by filtering out the preset conditions, and theoretical spectral data are obtained by using the optimized order pair set and the RCWA algorithm, which improves the solution efficiency of the theoretical spectral data and thus improves the creation efficiency of the theoretical spectral database.

[0040] In one possible embodiment, the set of convergent order pairs is a set of order pairs obtained after performing convergence analysis on the optical property parameters, wherein the optical property parameters include any one of dielectric constant, electric field, and magnetic field. The present invention allows for the selection of appropriate optical property parameters based on actual conditions.

[0041] In another possible embodiment, obtaining the relative distribution of optical characteristic parameters of each order pair in the set of convergent order pairs relative to the (0,0) order pair or the absolute distribution of the optical characteristic parameters of each order pair, and establishing a data table based on the relative distribution or the absolute distribution, includes: performing layering processing on the sample model according to the morphological characteristics of the sample model; obtaining the power of s of the modulus of the Fourier coefficient of at least one medium layer of each order pair relative to the (0,0) order pair under at least one wavelength condition or the power of s of the modulus of the Fourier coefficient of at least one medium layer of each order pair under at least one wavelength condition, where s is a positive integer; and establishing a data table based on the power of s of the modulus of the Fourier coefficient of at least one medium layer of each order pair relative to the (0,0) order pair under at least one wavelength condition or the power of s of the modulus of the Fourier coefficient of at least one medium layer of each order pair under at least one wavelength condition. Because the sample model exhibits complex morphological features during optical parameter measurement, which affects the optical properties, it is necessary to perform layered processing on the sample model to improve the accuracy of subsequent solution results.

[0042] Specifically, the modulus of the Fourier coefficients of the optical characteristic parameters of the k layers (k≥1, i.e., at least one medium layer) of each order pair under i wavelength conditions (i≥1, i.e., at least one wavelength condition) relative to the (0,0) order pair is obtained to the power of s, or the modulus of the Fourier coefficients of the optical characteristic parameters of the k layers of each order pair under i wavelength conditions is obtained to the power of s, where k is an integer greater than or equal to 1, and i is an integer greater than or equal to 1. For example, when i = k = 1, it means selecting the power of s of the modulus of the Fourier coefficients of any one layer of optical characteristic parameters relative to the (0, 0) order pair under any wavelength condition, or the power of s of the modulus of the Fourier coefficients of any one layer of optical characteristic parameters under any wavelength condition; when i = 1 and k = K, it means selecting the power of s of the modulus of the Fourier coefficients of K layers of optical characteristic parameters relative to the (0, 0) order pair under any wavelength condition, or the power of s of the modulus of the Fourier coefficients of K layers of optical characteristic parameters under any wavelength condition, where K is the total number of layers; similarly, other cases such as i = I and k = 1, or i = I and k = K, are also possible, and will not be elaborated here, where I is the total number of wavelengths. By setting the value of s, the solution efficiency of the theoretical spectral data can be adjusted. The value of s is directly proportional to the solution efficiency of the theoretical spectral data, that is, the larger the value of s is set, the higher the solution efficiency of the theoretical spectral data.

[0043] In one possible embodiment, obtaining the power of s of the Fourier coefficient of the optical characteristic parameter of at least one dielectric layer of each order pair under at least one wavelength condition relative to the (0,0) order pair, or the power of s of the Fourier coefficient of the optical characteristic parameter of at least one dielectric layer of each order pair under at least one wavelength condition, comprises: obtaining the power of s of the Fourier coefficient of the dielectric constant of at least one dielectric layer of each order pair under at least one wavelength condition relative to the (0,0) order pair, or the power of s of the Fourier coefficient of the dielectric constant of at least one dielectric layer of each order pair under at least one wavelength condition.

[0044] In one possible embodiment, obtaining the power of s of the magnitude of the Fourier coefficient of the optical characteristic parameter of at least one dielectric layer of each order pair under at least one wavelength condition relative to the (0,0) order pair, or the power of s of the magnitude of the Fourier coefficient of the optical characteristic parameter of at least one dielectric layer of each order pair under at least one wavelength condition, comprises: obtaining the sum of the power of s of the magnitude of the Fourier coefficient of the X component of the electric field or magnetic field of at least one dielectric layer of each order pair under at least one wavelength condition relative to the (0,0) order pair and the power of s of the magnitude of the Fourier coefficient of the Y component of the electric field or magnetic field, or the sum of the power of s of the magnitude of the Fourier coefficient of the X component of the electric field or magnetic field of at least one dielectric layer of each order pair under at least one wavelength condition and the power of s of the magnitude of the Fourier coefficient of the Y component of the electric field or magnetic field.

[0045] In one possible embodiment, establishing a data table based on the power of s of the modulus of the Fourier coefficients of the optical characteristic parameters of each order pair under at least one wavelength condition and at least one medium layer, relative to the (0,0) order pair, or the power of s of the modulus of the Fourier coefficients of the optical characteristic parameters of each order pair under at least one wavelength condition and at least one medium layer, includes: when the wavelength condition or the number of layers is greater than or equal to two (i.e., I≥2 or K≥2), obtaining the maximum or average value of the power of s of the modulus of the Fourier coefficients of the optical characteristic parameters of each order pair under at least one wavelength condition and at least one layer, or obtaining the maximum or average value of the power of s of the modulus of the Fourier coefficients of the optical characteristic parameters of each order pair under at least one wavelength condition and at least one layer; traversing all the order pairs, and establishing the data table with the maximum or average value corresponding to the order pairs. The maximum value can ensure that the weight of the corresponding order pair is larger, and the average value can ensure that the deviation of the weight of the corresponding order pair is smaller, both of which can improve the accuracy of the solution process.

[0046] In another possible embodiment, the step of filtering the data in the data table according to preset conditions, and identifying the level pairs corresponding to the data that meet the preset conditions as optimized level pairs, includes: setting a first threshold and a second threshold. When the mean square error between the theoretical spectrum of the level pair corresponding to the data in the data table that is greater than or equal to the first threshold and the theoretical spectrum corresponding to the convergent level pair set is less than or equal to the second threshold, the level pair is considered an optimized level pair. Optionally, the value range of the second threshold mentioned in this application is 1e-10 to 1e-4. Setting the first and second thresholds ensures the accuracy of the theoretical spectral data and improves the efficiency of solving the theoretical spectral data.

[0047] In another possible embodiment, the step of filtering the data in the data table according to preset conditions, and identifying the level pairs corresponding to the data that meet the preset conditions as optimized level pairs, includes: sorting the data in the data table by size; setting a filtering ratio and a second threshold; when the mean square error between the theoretical spectrum of the level pair corresponding to the larger data in the data table and the theoretical spectrum corresponding to the convergent level pair set is less than or equal to the second threshold, the level pair is considered an optimized level pair. In this embodiment, the filtering ratio is the proportion of the data to be filtered in the data table, and the data to be filtered is the data in the data table sorted by size and truncated according to the filtering ratio. Specifically, when the data table includes 100 data points and the filtering ratio is 40%, the data in the data table needs to be sorted from largest to smallest, and then the data in the first 40 positions of the sorted data needs to be filtered out. Setting a filtering ratio and a second threshold can ensure the accuracy of the theoretical spectral data and improve the efficiency of solving the theoretical spectral data.

[0048] To explain the invention in this application in more detail, specific examples are provided below:

[0049] Option 1: Obtain the normalized version of the modulus of the Fourier coefficient of the dielectric constant of each order pair in the set of convergent order pairs relative to the (0,0) order pair, which is the power of the modulus of the Fourier coefficient of the dielectric constant (where s is a positive integer). The maximum or average value, or the s-th power of the modulus of the Fourier coefficient of the dielectric constant of each order pair in the set of convergent order pairs |ε mn | s The maximum or average value; traversing all the convergent order pairs, the maximum or average value corresponding to each order pair is used to obtain an absolute medium distribution |ε. mn | s or relative distribution of media The data table. Rank pairs are filtered based on a set first threshold, or based on the absolute distribution of the medium |ε. mn | s or relative distribution of media The data corresponding to the data in the data table are sorted from largest to smallest, and the level pairs corresponding to the top-ranked data are selected as the optimized level pairs according to the filtering ratio.

[0050] Specifically, in optical measurements, on the one hand, under the illumination of incident light, the medium will exhibit an optical response. The parameters of the incident light include its wavelength, and the parameters of the medium include its dielectric constant. Specifically, the dielectric constant of the medium is related to the wavelength of the incident light. On the other hand, in optical measurements, the morphology of the sample may exhibit complex characteristics, requiring morphological segmentation. For each layer of the medium, the distribution of the medium is generally different. When the medium is periodically repeating in the x and y directions, ε(x, y) is the dielectric constant of the medium, a periodic function, and ε(x, y) is known. Let the period of the medium in the x-direction be p. x The period in the y-direction is p y Then ε(x, y) = ε(x + a*p) x y+b*p y ), a, b are integers. In rigorous coupled-wave analysis, it is necessary to perform a Fourier series expansion of ε(x, y) and truncate it. mn The Fourier coefficients of the dielectric constant are given below, where m and n are integers:

[0051]

[0052] A larger Fourier coefficient of the dielectric constant corresponding to an order pair indicates a greater weight for that order pair. Therefore, a larger weight for the selected order pairs leads to better convergence. The Fourier coefficients of the dielectric constants corresponding to at least one order pair in at least one dielectric layer under at least one wavelength condition are obtained. Since the magnitude of the Fourier coefficients of the dielectric constants corresponding to each order pair is different under different dielectric layers under different wavelength conditions, the absolute dielectric distribution |ε| of each order pair is selected. mn | s or relative distribution of media The maximum value is used to ensure the maximum weight of the order pair, or the average value of the absolute or relative distribution of the medium for each order pair is selected to ensure the minimum deviation of the weight of the order pair. By traversing the maximum or average value corresponding to all order pairs, a data table of all order pairs is obtained. Then, order pairs are filtered according to preset conditions. On the one hand, order pairs can be filtered according to a set first threshold; on the other hand, the data in the data table can be sorted from largest to smallest, and the order pairs corresponding to the top-ranked data can be selected according to the filtering ratio to obtain an optimized set of order pairs. Based on the optimized set of order pairs, Fourier series expansions are performed on the dielectric constant, electric field, and magnetic field, and the RCWA algorithm is applied to calculate the theoretical spectrum, which significantly improves efficiency.

[0053] Option 2: Obtain the sum of the s-th power of the magnitude of the Fourier coefficients of the electric field X component and the s-th power of the magnitude of the Fourier coefficients of the electric field Y component for each order pair in the set of convergent order pairs, i.e., |S y，mn | s +|S x，mn | s The maximum or average value, or the sum of the normalized sum of the magnitudes of the Fourier coefficients of the electric field X component and the Fourier coefficients of the electric field Y component relative to the (0,0) order, i.e., the sum of the magnitudes of the Fourier coefficients of the electric field X component and the Fourier coefficients of the electric field Y component. The maximum or average value of the electric field is used to obtain an absolute electric field distribution |S y，mn | s +|S x，mn | s or relative distribution of electric field The data table filters level pairs based on a set first threshold, or based on the absolute electric field distribution |S y，mn | s +|S x，mn | s or relative distribution of electric field The data in the corresponding data table is sorted from largest to smallest, and the level pairs corresponding to the top-ranked data are selected as the optimized level pairs according to the filtering ratio.

[0054] Option 3: Obtain the sum of the s-th power of the magnitude of the Fourier coefficient of the magnetic field X component and the s-th power of the magnitude of the Fourier coefficient of the magnetic field Y component for each order pair in the set of convergent order pairs, i.e., |U y mn | s +|U x mn | sThe maximum or average value, or the sum of the normalized sum of the magnitudes of the Fourier coefficients of the X component and the Y component of the magnetic field relative to the (0,0) order, which is the sum of the magnitudes of the Fourier coefficients of the X component and the Y component of the magnetic field. The maximum or average value of the magnetic field is used to obtain an absolute distribution of the magnetic field |U y mn | s +|U x mn | s Or the relative distribution of magnetic fields The data table filters level pairs based on a set first threshold, or based on the absolute distribution of the magnetic field |U y mn | s +|U x mn | s Or the relative distribution of magnetic fields The data in the corresponding data table is sorted from largest to smallest, and the level pairs corresponding to the top-ranked data are selected as the optimized level pairs according to the filtering ratio.

[0055] Specifically, in optical measurements, on the one hand, under the illumination of incident light, the incident light interacts with the medium, thus changing the electric field distribution of the medium. The parameters of the incident light include its wavelength; therefore, the electric field distribution of the medium is related to the wavelength of the incident light. On the other hand, in optical measurements, the morphology of the sample can exhibit complex characteristics. Therefore, in such cases, it is necessary to classify the sample morphology. For each layer, generally, due to the different distributions of the medium, the electric field distribution is different. When the medium periodically repeats in the x and y directions, the electric field is a periodic function, and the two orthogonal components of the electric field are Ex and Ey. x E y In rigorous coupled-wave analysis, it is necessary to perform a Fourier series expansion and truncation on the two orthogonal components of the electric field, where S... x，mn It is E x The Fourier coefficients, S y，mn It is E y The Fourier coefficients, where m and n are integers, are as follows:

[0056]

[0057] The larger the Fourier coefficients of the two orthogonal components of the electric field corresponding to the order pair, the greater the weight of the order pair. Therefore, the greater the weight of the selected order pair, the better the convergence of the result.

[0058] In optical measurement, incident light irradiates a sample model, generating reflected and transmitted light on the sample model's surface. The region above the sample surface is called the incident region, containing both incident light (i.e., the incident electric field) and reflected light (i.e., the reflected electric field). The region below the sample surface is called the transmission region, containing both transmitted light (i.e., the transmitted electric field). This sample region is called the grating region. At each wavelength, the reflected electric field of the incident region is calculated using the RCWA algorithm. Based on the reflected and incident electric fields and the electromagnetic field continuity condition, the distribution of the electromagnetic field of each layer in the grating region with respect to order pairs is determined. Since the Fourier coefficients of the electric field corresponding to each order pair are different under different medium layers at different wavelengths, the absolute distribution of the electric field |S| for each order pair is selected. y mn | s +|S x mn | s or relative distribution of electric field The maximum value of (s is a positive integer) is used to ensure the maximum weight of this order pair, or the average value of the absolute or relative electric field distribution of each order pair is selected to ensure the minimum deviation of the weight of the order pair. By traversing the maximum or average value corresponding to all order pairs, a data table of all order pairs is obtained. Then, order pairs are filtered according to preset conditions. On the one hand, order pairs can be filtered according to a set first threshold; on the other hand, the data in the data table can be sorted from largest to smallest, and the order pairs corresponding to the top-ranked data can be selected according to the filtering ratio to obtain an optimized set of order pairs. Based on the optimized set of order pairs, Fourier series expansions are performed on the dielectric constant, electric field, and magnetic field, and the RCWA algorithm is applied to calculate the theoretical spectrum, which significantly improves efficiency.

[0059] In optical measurement, regardless of whether it's Scheme 1 or Scheme 2, the first threshold is adjustable. The first threshold is determined based on the condition that the mean square error (MSE) of the final result and the theoretical spectrum calculated from the convergence set is less than or equal to a second threshold. When the condition that the MSE of the final result and the theoretical spectrum calculated from the convergence set is less than or equal to the second threshold is met, a smaller first threshold is better. A smaller first threshold results in fewer optimized sets of order pairs, leading to higher computational efficiency. The first threshold is a real number from 0 to 1, excluding 0. The screening ratio is also adjustable. The screening ratio is determined based on the condition that the MSE of the final result and the theoretical spectrum calculated from the convergence set is less than or equal to the second threshold. When the condition that the MSE of the final result and the theoretical spectrum calculated from the convergence set is less than or equal to the second threshold is met, a smaller screening ratio is better. A smaller screening ratio results in fewer optimized sets of order pairs, leading to higher computational efficiency. The screening ratio is a real number from 0 to 1, excluding 0.

[0060] To illustrate the invention in this application in more detail, further examples are provided below.

[0061] Two-dimensional sample model, such as Figure 2 As shown, N x =20, N y =20, the original set of order pairs is {(m, n)|-20≤m≤20, -20≤n≤20}, and convergence analysis of the original set of order pairs yields the convergent set of order pairs {(m, n)|-10≤m≤10, -10≤n≤10}. The sample has 5 layers, wavelengths ranging from 400 to 800 nm, and a step size of 10 nm. On one hand, the refractive index of the sample differs at each wavelength, resulting in a different medium distribution at each wavelength. On the other hand, the medium distribution of each layer of the sample is also different. In the above method embodiments, all m in each step are -N x To N x integers, where n is -N y To N y The integer is λ, where λ represents the wavelength and z represents the height of the layer in the Z direction. In this embodiment, taking S=1 as an example, it iterates through all layer pairs (in this embodiment, the first, second, third, fourth, and fifth layers) under all wavelength conditions (400 nm, 410 nm, 420 nm, ..., 790 nm, 800 nm) to obtain the order pairs (in this embodiment, the order pairs in the convergent order pair set {(m, n)|-10≤m≤10, -10≤n≤10}). For each order pair, this embodiment takes the relative distribution of the medium as an example to obtain the relative distribution of the medium. The maximum or average value.

[0062] When a relative distribution of the medium for all order pairs is obtained When dealing with a data table containing the maximum value, two filtering schemes can be selected to filter the data in the table. Taking s=1 as an example, specifically:

[0063] Screening Scheme 1: Taking "0.05 as the first threshold" as an example, order pairs greater than the first threshold are selected as optimized order pairs. Calculating the theoretical spectrum using the optimized order pair set takes 13 seconds; calculating the theoretical spectrum using the convergent order pair set takes 164 seconds. Therefore, the computational efficiency of this invention is improved by 92% compared to existing technologies, and the mean square error of the theoretical spectrum calculated with the convergent order pair set is 8.51e-05.

[0064] Screening Scheme 2: Sort the data in the data table from largest to smallest, and select the top 41% of order pairs from all data as optimized order pairs. Calculating the theoretical spectrum using the optimized order pair set takes 13 seconds, while calculating the theoretical spectrum using the convergent order pair set takes 164 seconds. Therefore, the computational efficiency of this invention is improved by 92% compared to existing technologies, and the mean square error of the theoretical spectrum calculated using the convergent order pair set is 8.51e-05.

[0065] When a relative distribution of the medium for all order pairs is obtained The data table contains average values, with s=1 as an example. For this data table, two filtering options can be selected to filter the data. Specifically:

[0066] Screening Scheme 1: Taking "0.05 as the first threshold" as an example, order pairs greater than the first threshold are selected as optimized order pairs. Calculating the theoretical spectrum using the optimized order pair set takes 5 seconds; calculating the theoretical spectrum using the convergent order pair set takes 164 seconds. Therefore, the computational efficiency of this invention is improved by 97% compared to existing technologies, and the mean square error of the theoretical spectrum calculated with the convergent order pair set is 0.00067.

[0067] Screening Scheme 2: Sort the order pairs from largest to smallest based on the dielectric distribution values, and select the top 29% of all order pairs as optimized order pairs. The theoretical spectrum is calculated using the optimized order pair set, taking 5 seconds. The theoretical spectrum is then calculated using the convergent order pair set. Therefore, this invention improves computational efficiency by 97% compared to existing technologies, and the mean square error of the theoretical spectrum calculated using the convergent order pair set is 0.00067.

[0068] against Figure 2 The two-dimensional sample shown in this embodiment also provides a solution. During rigorous coupled-wave analysis, under each wavelength condition, the reflected electric field of the incident region is calculated using the RCWA algorithm. Based on the reflected and incident electric fields and the electromagnetic field continuity condition, the electromagnetic field distribution of each layer (in this embodiment, the first, second, third, fourth, and fifth layers) of the grating region is determined. This embodiment uses the absolute electric field distribution as an example. For the electromagnetic field of each layer of the grating region at each wavelength, the sum of the s-th power of the modulus of the Fourier coefficients of the X-component of the electric field and the s-th power of the modulus of the Fourier coefficients of the Y-component of the electric field for each order of all layers under all wavelength conditions is calculated, i.e., |S|. y，mn | s +|S x，mn | s The maximum or average value, in this embodiment taking s = 2 as an example, that is, |S y mn | 2 +|S x mn |2 This yields a data table regarding the electric field distribution.

[0069] When we obtain the absolute electric field distribution |S| for all orders... y mn | 2 +|S x mn | 2 When dealing with a data table containing the maximum values, two filtering schemes can be selected to filter the data in the table. Specifically, filtering scheme 1: Taking "1e-4 as the first threshold" as an example, select order pairs greater than the first threshold as optimized order pairs. Calculating the theoretical spectrum using the optimized order pair set takes 38 seconds, while calculating the theoretical spectrum using the convergent order pair set takes 164 seconds. Therefore, the computational efficiency of the present invention is improved by 77% compared to the prior art, and the mean square error of the theoretical spectrum calculated with the convergent order pair set is 1.54e-05.

[0070] Screening Scheme 2: Sort the data in the data table from largest to smallest, and select the top 50% of order pairs from all data as optimized order pairs. Calculating the theoretical spectrum using the optimized order pair set takes 38 seconds, while calculating the theoretical spectrum using the convergent order pair set takes 164 seconds. Therefore, the computational efficiency of this invention is improved by 77% compared to existing technologies, and the mean square error of the theoretical spectrum calculated using the convergent order pair set is 1.54e-05.

[0071] When we obtain the absolute electric field distribution |S| for all orders... y mn | 2 +|S x mn | 2 When dealing with a data table containing average values, two filtering options can be selected to filter the data in the table. Specifically:

[0072] Screening Scheme 1: Taking "0.05 as the first threshold" as an example, order pairs greater than the first threshold are selected as optimized order pairs. Calculating the theoretical spectrum using the optimized order pair set takes 6 seconds, while calculating the theoretical spectrum using the convergent order pair set takes 164 seconds. Therefore, the computational efficiency of this invention is improved by 96% compared to existing technologies, and the mean square error of the theoretical spectrum calculated using the convergent order pair set is 0.0002.

[0073] Screening Scheme 2: Sort the data in the data table from largest to smallest, and select the top 27% of order pairs from all data as optimized order pairs. Calculating the theoretical spectrum using the optimized order pair set takes 6 seconds, while calculating the theoretical spectrum using the convergent order pair set takes 164 seconds. Therefore, the computational efficiency of this invention is improved by 96% compared to existing technologies, and the mean square error of the theoretical spectrum calculated using the convergent order pair set is 0.0002.

[0074] It is worth noting that in any of the above embodiments, the set first threshold is adjustable, and the determination of the first threshold is based on the fact that the mean square error of the final result and the theoretical spectrum calculated from the set of convergent order pairs is less than or equal to the second threshold. When the condition that the mean square error of the final result and the theoretical spectrum calculated from the set of convergent order pairs is less than or equal to the second threshold is met, the smaller the first threshold, the better. The smaller the first threshold, the fewer the number of optimized order pairs, and the higher the computational efficiency. The first threshold is a real number from 0 to 1, excluding 0. The screening ratio is also adjustable, and the determination of the screening ratio is based on the fact that the mean square error of the final result and the theoretical spectrum calculated from the set of convergent order pairs is less than or equal to the second threshold. When the condition that the mean square error of the final result and the theoretical spectrum calculated from the set of convergent order pairs is less than or equal to the second threshold is met, the smaller the screening ratio, the better. The smaller the screening ratio, the fewer the number of optimized order pairs, and the higher the computational efficiency. The screening ratio is a real number from 0 to 1, excluding 0.

[0075] Based on the method for optimizing theoretical spectral data described in any of the above embodiments, the present invention provides an apparatus for optimizing theoretical spectral data, such as... Figure 3 As shown, the optimization device includes: an acquisition module 301, a convergence module 302, a table building module 303, a filtering module 304, and a calculation module 305. The acquisition module 301 is used to acquire a sample model, which has a periodic structure in both the X and Y directions. The convergence module 302 acquires a set of convergence order pairs of the sample model in the X and Y directions. The table building module 303 is used to acquire the relative distribution of the optical characteristic parameters of each order pair in the set of convergence order pairs relative to the (0,0) order pair or the absolute distribution of the optical characteristic parameters of each order pair, and establishes a data table based on the relative distribution or the absolute distribution. The filtering module 304 is used to filter the data in the data table according to preset conditions, and the order pairs corresponding to the data that meet the preset conditions are optimized order pairs, and an optimized order pair set is obtained based on the optimized order pairs. The calculation module 305 is used to acquire the theoretical spectral data corresponding to the optimized order pair set based on the RCWA algorithm.

[0076] Based on the optimization method for theoretical spectral data described in any of the above embodiments, the present invention also provides a measurement method, the process of which is as follows: Figure 4 As shown, it includes:

[0077] S401: Establish a theoretical spectral database corresponding to the sample model according to the optimization method of theoretical spectral data described in any one of the above claims; wherein, the theoretical spectral database includes the morphological parameters of the sample model and the theoretical spectral data corresponding to the morphological parameters;

[0078] S402: Obtain the measurement spectral data of the corresponding measurement area of ​​the sample to be tested;

[0079] S403: Determine the morphological parameters of the measurement area corresponding to the sample to be tested based on the measured spectral data and the theoretical spectral database.

[0080] This application discloses an electronic device, such as... Figure 5 As shown, the electronic device may include: one or more processors 501; a memory 502; a display 503; one or more application programs (not shown); and one or more computer programs 504. These devices may be connected via one or more communication buses 505. The one or more computer programs 504 are stored in the memory 502 and configured to be executed by the one or more processors 501. The one or more computer programs 504 include instructions that can be used to perform the steps in the corresponding embodiments described above.

[0081] Through the above description of the embodiments, those skilled in the art will clearly understand that, for the sake of convenience and brevity, only the division of the above functional modules is used as an example. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. The specific working process of the system, device, and unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0082] In the embodiments of this application, the functional units can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0083] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, in essence, or the parts that contribute to the prior art, or all or part of the technical solutions, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as flash memory, portable hard disk, read-only memory, random access memory, magnetic disk, or optical disk.

[0084] The above description is merely a specific implementation of the embodiments of this application, but the protection scope of the embodiments of this application is not limited thereto. Any changes or substitutions within the technical scope disclosed in the embodiments of this application should be covered within the protection scope of the embodiments of this application. Therefore, the protection scope of the embodiments of this application should be determined by the protection scope of the claims.

Claims

1. A method of optimizing theoretical spectral data, characterized by, The method comprises the following steps: obtaining a sample model, which has a periodic structure in both X and Y directions; performing Fourier series expansion on an optical characteristic parameter of the sample model along the X and Y directions to obtain a convergent order pair set of the optical characteristic parameter in the X and Y directions; obtaining a relative distribution of the optical characteristic parameter of each order pair in the convergent order pair set relative to the (0, 0) order pair or an absolute distribution of the optical characteristic parameter of each order pair, and establishing a data table according to the relative distribution or the absolute distribution; the step of obtaining a relative distribution of the optical characteristic parameter of each order pair in the convergent order pair set relative to the (0, 0) order pair or an absolute distribution of the optical characteristic parameter of each order pair, and establishing a data table according to the relative distribution or the absolute distribution comprises the following steps: performing hierarchical processing on the sample model according to the topographic features of the sample model; obtaining s-th powers of the modulus of the Fourier coefficients of the optical characteristic parameter of at least one medium layer of each order pair relative to the (0, 0) order pair under at least one wavelength condition or s-th powers of the modulus of the Fourier coefficients of the optical characteristic parameter of at least one medium layer of each order pair under at least one wavelength condition, wherein s is a positive integer; and establishing a data table according to the s-th powers of the modulus of the Fourier coefficients of the optical characteristic parameter of at least one medium layer of each order pair relative to the (0, 0) order pair under at least one wavelength condition or the s-th powers of the modulus of the Fourier coefficients of the optical characteristic parameter of at least one medium layer of each order pair under at least one wavelength condition; screening data in the data table according to a preset condition, wherein the order pairs corresponding to the data meeting the preset condition are optimization order pairs, and an optimization order pair set is obtained according to the optimization order pairs; obtaining theoretical spectral data corresponding to the optimization order pair set based on a rigorous coupled wave analysis method.

2. The method of optimizing theoretical spectral data according to claim 1, characterized in that, The convergent order pair set is an order pair set obtained after performing convergence analysis on an optical characteristic parameter, and the optical characteristic parameter comprises any one of a dielectric coefficient, an electric field and a magnetic field.

3. The method of optimizing theoretical spectral data according to claim 2, characterized in that, The step of obtaining s-th powers of the modulus of the Fourier coefficients of the optical characteristic parameter of at least one medium layer of each order pair relative to the (0, 0) order pair under at least one wavelength condition or s-th powers of the modulus of the Fourier coefficients of the optical characteristic parameter of at least one medium layer of each order pair under at least one wavelength condition comprises the following steps: obtaining s-th powers of the modulus of the Fourier coefficients of the dielectric coefficient of at least one medium layer of each order pair relative to the (0, 0) order pair under at least one wavelength condition or s-th powers of the modulus of the Fourier coefficients of the dielectric coefficient of at least one medium layer of each order pair under at least one wavelength condition.

4. The method of optimizing theoretical spectral data according to claim 2, characterized in that, The obtaining of the s-th power of the modulus of the Fourier coefficient of the optical characteristic parameter of the at least one medium layer corresponding to each order pair under at least one wavelength condition relative to the (0, 0) order pair or the s-th power of the modulus of the Fourier coefficient of the optical characteristic parameter of the at least one medium layer corresponding to each order pair under at least one wavelength condition comprises: The obtaining of the s-th power of the sum of the modulus of the Fourier coefficient of the X component of the electric field or the magnetic field and the modulus of the Fourier coefficient of the Y component of the electric field or the magnetic field of the at least one medium layer corresponding to each order pair under at least one wavelength condition relative to the (0, 0) order pair or the s-th power of the sum of the modulus of the Fourier coefficient of the X component of the electric field or the magnetic field and the modulus of the Fourier coefficient of the Y component of the electric field or the magnetic field of the at least one medium layer corresponding to each order pair under at least one wavelength condition.

5. The method of optimizing theoretical spectral data according to claim 2, wherein, The establishing of the data table according to the s-th power of the modulus of the Fourier coefficient of the optical characteristic parameter of the at least one medium layer corresponding to each order pair under at least one wavelength condition relative to the (0, 0) order pair or the s-th power of the modulus of the Fourier coefficient of the optical characteristic parameter of the at least one medium layer corresponding to each order pair under at least one wavelength condition comprises: When the number of the wavelength conditions or the number of the layers is greater than or equal to two, the maximum value or the average value of the s-th power of the modulus of the Fourier coefficient of the optical characteristic parameter of the at least one medium layer corresponding to each order pair under at least one wavelength condition and at least one layer relative to the (0, 0) order pair is obtained or the maximum value or the average value of the s-th power of the modulus of the Fourier coefficient of the optical characteristic parameter of the at least one medium layer corresponding to each order pair under at least one wavelength condition and at least one layer is obtained; The maximum value or the average value corresponding to each order pair is established into the data table by traversing all the order pairs.

6. The method of optimizing theoretical spectral data according to claim 1, wherein, The screening of the data in the data table according to the preset condition comprises: The first threshold value and the second threshold value are set, and when the theoretical spectrum of the order pair corresponding to the data greater than or equal to the first threshold value in the data table has a mean square error less than or equal to the second threshold value with the theoretical spectrum corresponding to the convergent order pair set, the order pair is the optimized order pair.

7. The method of optimizing a theoretical spectrum according to claim 1, wherein, The screening of the data in the data table according to the preset condition comprises: The data in the data table is sorted by size; The screening ratio and the second threshold value are set, and when the theoretical spectrum of the order pair corresponding to the data with a larger value in the data table has a mean square error less than or equal to the second threshold value with the theoretical spectrum corresponding to the convergent order pair set, the order pair is the optimized order pair.

8. A method of measurement, characterized by, It comprises: The method according to any one of claims 1 to 7 is used to establish a theoretical spectrum database corresponding to the sample model, wherein the theoretical spectrum database comprises topographic parameters of the sample model and theoretical spectrum data corresponding to the topographic parameters; Measurement spectrum data of a measurement region corresponding to a to-be-measured sample is obtained; The method according to any one of claims 1 to 7 is used to establish a theoretical spectrum database corresponding to the sample model, wherein the theoretical spectrum database comprises topographic parameters of the sample model and theoretical spectrum data corresponding to the topographic parameters; According to the measured spectrum data and the theoretical spectrum database, a topographic parameter of a corresponding measurement region of the sample to be measured is determined.

9. An electronic device, comprising: The application also provides a computer readable storage medium storing a computer program product, wherein the computer program product comprises computer executable instructions, and when the computer program product is executed on a computer, the computer is enabled to implement the method according to any one of claims 1 to 7 or 8.

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