CN113343182A - Theoretical spectral data optimization method and system, electronic equipment and measurement method - Google Patents
Theoretical spectral data optimization method and system, electronic equipment and measurement method Download PDFInfo
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Abstract
The invention provides an optimization method, a system, electronic equipment and a measurement method of theoretical spectral data, wherein the optimization method comprises the following steps: obtaining a sample model with a periodic structure in the direction X, Y; acquiring a convergence order pair set of the sample model in the direction X, Y; setting a convergence level secondary pair group; traversing the convergence level pair group in the convergence level pair set to obtain the mean square error removal of each convergence level pair in the convergence level pair group; comparing the removed mean square error with a first threshold value, and filtering all convergence level pairs corresponding to the removed mean square error smaller than the first threshold value to form an optimized level pair set; and acquiring theoretical spectral data corresponding to the optimized level pair set. According to the method, the convergence level pairs with smaller mean square error are removed from the convergence level pair set through first threshold filtering, and the number of the optimized convergence level pair set is less than that of the original convergence level pair set, so that the calculation efficiency of theoretical spectral data is effectively improved.
Description
Technical Field
The present invention relates to the field of optical measurements; in particular, it relates to the field of optical critical dimension measurement; and more particularly, to a method, system, electronic device and measurement method for optimizing theoretical spectral data.
Background
The Optical Critical Dimension (OCD) technology estimates the specific morphological parameters of a sample by acquiring a scattering signal of a periodic structure of a specific measured region of the sample and a model of the sample, can meet the requirements of realizing rapid and accurate measurement in a new process and a new technology, has non-contact and non-destructive properties, and is widely applied to the semiconductor manufacturing industry and Optical measurement. The principle of the optical critical dimension measurement technology can be generally described as follows: firstly, establishing a theoretical spectrum database corresponding to the appearance model of the sample, and then, obtaining scattering signals of the periodic structure of the specific detected area of the sample and matching the scattering signals with the parameters of the theoretical spectrum database so as to estimate the specific appearance parameters of the sample. In the process of establishing a theoretical spectrum database corresponding to a sample morphology model, an algorithm used for calculating theoretical spectrum data is a strict Coupled Wave Analysis (RCWA) algorithm. The RCWA algorithm flow is that a dielectric function of a sample and a Fourier series expansion of an electromagnetic field of a sample area are substituted into a Maxwell equation set, and the electric field of an incident area is solved by using the continuous condition of the electromagnetic field, so that the reflection coefficient of the sample is obtained. And traversing each wavelength point, and calculating the reflection coefficient of the sample corresponding to the wavelength point by using an RCWA algorithm so as to obtain theoretical spectral data of the sample.
Specifically, in the RCWA algorithm: for a sample model with a periodic structure in both the X direction and the Y direction, generally, fourier series expansion is performed on different optical characteristic parameters (e.g., dielectric function, electric field, and magnetic field) in the X direction and the Y direction of the sample model, the fourier series expansion is performed from negative infinite order to positive infinite order, the order of the order needs to be truncated in the actual application of the RCWA algorithm, the maximum order of truncation is called as a truncation order, that is, in the actual application, the fourier series expansion performed on the optical characteristic parameters is only performed to the truncation order. And because of the two directions of X and Y, there are two truncation orders; therefore, the method comprises the following steps:
the value of the order m in the X direction can be an integer from-Nx to Nx;
the value of the order n in the Y direction can be an integer from-Ny to Ny; the X-direction truncation order is denoted as Nx, and the Y-direction truncation order is denoted as Ny.
Thus, the combination of one X-direction order m and one Y-direction order n is referred to as an order pair and is denoted by (m, n). Because the level in the X direction has a plurality of values, the level in the Y direction also has a plurality of values, so the combination of the levels has a plurality, the different level pairs are combined to form a level pair set, the level pair set is the pairwise combination of the level in the X direction and the level in the Y direction, and is marked as: { (m, n) | -Nx ≦ m ≦ Nx, -Ny ≦ n ≦ Ny }, where the truncation order in the X direction is denoted as Nx, and the truncation order in the Y direction is denoted as Ny.
Based on the level pair set, performing Fourier series expansion on different optical characteristic parameters, and then applying RCWA algorithm to calculate theoretical spectrum data; thus, one set of pairs of this order corresponds to one theoretical spectral data. However, the calculation efficiency and the number of the order pairs corresponding to the fourier series are in a cubic inverse relationship, so that when the theoretical spectral data are calculated: on one hand, the more the number of the level pairs corresponding to the Fourier series is used, the higher the accuracy of the RCWA algorithm in calculating the theoretical spectral data is, but the larger the calculation amount of the RCWA algorithm in calculating the theoretical spectral data is, the lower the calculation efficiency is; on the other hand, the smaller the number of the order pairs corresponding to the fourier series, the higher the calculation efficiency, but the lower the accuracy of the RCWA algorithm in calculating the theoretical spectral data. Therefore, before calculating the theoretical spectral data, convergence analysis is performed on the set of order pairs corresponding to the fourier series expansion of different optical characteristic parameters to obtain the set of convergence order pairs.
The convergence analysis aims to obtain a convergence level pair set, and the calculation efficiency can be improved under the condition of ensuring the accuracy by using the convergence level pair set to calculate the theoretical spectral data. The convergence analysis is carried out as follows:
setting a first-level threshold Nxr (positive integer) of the truncation level Nx in the X direction and a second-level threshold Nyr (positive integer) of the truncation level Ny in the Y direction, generating a reference level pair set corresponding to the first-level threshold Nxr and the second-level threshold Nyr based on pairwise combination of the level m in the X direction and the level n in the Y direction, and acquiring first theoretical spectral data corresponding to the reference level pair set based on an RCWA algorithm;
changing the truncation level Nx in the X direction and the truncation level Ny in the Y direction according to a set starting point and a set step length to enable the truncation level Nx and Ny to be respectively increased to a first level threshold Nxr and a second level threshold Nyr, obtaining an original level pair set corresponding to a group of truncation level Nx and Ny based on pairwise combination of the level m in the X direction and the level n in the Y direction, and obtaining second theoretical spectral data corresponding to the original level pair set based on an RCWA algorithm;
and calculating the Mean Square Error (MSE) between the first theoretical spectral data and the second theoretical spectral data, sequentially comparing the MSE with a preset MSE threshold value, and extracting an original level pair set corresponding to the first MSE smaller than the MSE threshold value as a convergence level pair set.
Specifically, as described above, first theoretical spectral data corresponding to the reference level pair set is calculated by using the RCWA algorithm, the X-direction truncated level Nx and the Y-direction truncated level Ny are gradually increased from a set start point (for example, 0) to the first level threshold Nxr and the second level threshold Nyr (for example, both the X direction and the Y direction are gradually increased by a step size of 1), a set of original level pair sets corresponding to the X-direction truncated level Nx and the Y-direction truncated level Ny are generated based on the pairwise combination, the RCWA algorithm is applied to calculate the mean square error MSE between the second theoretical spectral data corresponding to the set of original level pair sets and the first theoretical spectral data, and the MSE threshold is obtained according to the conditions of hardware devices, generally speaking, the larger the truncated level Nx and Ny, the more the MSE in the original level pair set, the smaller the MSE, and in the increase process of the truncated level Nx and Ny, an original level pair set corresponding to a first mean square error MSE smaller than the MSE threshold is called a convergence level pair set. In general, the convergence level pair set can be found without increasing the first level threshold Nxr and the second level threshold Nyr.
In the prior art, a convergence level pair set is obtained based on convergence analysis, theoretical spectral data is calculated based on the convergence level pair set, that is, a fourier series term corresponding to the convergence level pair set is retained when fourier series expansion is performed on an optical characteristic parameter, and an RCWA algorithm is applied to calculate the theoretical spectral data, so that the calculation efficiency can be improved under the condition of ensuring the accuracy.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention provides an optimization method, a system, an electronic device and a measurement method of theoretical spectral data; and optimizing the set aiming at the convergence level obtained by using the RCWA algorithm during theoretical spectrum data calculation in optical critical dimension measurement, thereby improving the calculation efficiency of the theoretical spectrum data.
To achieve the above object, according to a first aspect of the present invention, there is provided a method for optimizing theoretical spectral data, the method comprising:
obtaining a sample model with a periodic structure in the direction X, Y;
obtaining a set of convergence order pairs of the sample model in the X, Y direction;
setting a convergence order pair which is not (0,0) and is axisymmetric or centrosymmetric in the X, Y direction as a convergence order pair group; based on RCWA algorithm, traversing the convergence level pair group in the convergence level pair set to obtain the mean square error removal of each convergence level pair in the convergence level pair group; comparing the removed mean square error with a first threshold value, and filtering all convergence level pairs corresponding to the removed mean square error smaller than the first threshold value to form an optimized level pair set;
and acquiring theoretical spectral data corresponding to the optimized level pair set based on the RCWA algorithm.
Further, the convergence level pair set is a level pair set obtained by performing convergence analysis on different optical characteristic parameters, and the optical characteristic parameters include a dielectric function, an electric field, and a magnetic field.
Further, the setting of the convergence order pair that is not (0,0) and is axisymmetric or centrosymmetric in the X, Y direction is a convergence order pair group, and includes:
setting a convergence level pair group: (m, n), (-m, n), (m, -n), and (-m, -n);
wherein m and n are not 0 at the same time, and-Nx is not less than m and not more than Nx, -Ny is not less than n and not more than Ny, and Nx and Ny are respectively the truncation orders set in the direction X, Y.
Further, the mean square error of each convergence level pair is the mean square error between theoretical spectral data of the convergence level pair set before and after the current convergence level pair in the convergence level pair group is removed or the current convergence level pair and any other one or more convergence level pairs in the convergence level pair group are simultaneously removed.
Further, the traversing the convergence level pair group in the convergence level pair set based on the RCWA algorithm to obtain a removed mean square error of each convergence level pair in the convergence level pair group includes:
acquiring convergence theoretical spectrum data corresponding to the convergence level pair set based on an RCWA algorithm;
traversing the convergence level pair group in the convergence level pair set, and removing the current convergence level pair in the convergence level pair group or simultaneously removing the current convergence level pair and any other one or more convergence level pairs in the convergence level pair group from the convergence level pair set, wherein the remaining convergence level pairs in the convergence level pair set form a removed level pair set;
based on RCWA algorithm, obtaining removal theoretical spectrum data corresponding to the removal level pair set;
and obtaining the mean square error removal of each convergence level pair in the convergence level pair group according to the convergence theoretical spectral data and the removal theoretical spectral data.
Further, when the current convergence level pair and any other one or more convergence level pairs in the convergence level pair group are removed simultaneously, the removed mean square error of any removed convergence level pair is calculated to obtain the removed mean square errors of all the removed convergence level pairs.
Further, the convergence level pair removed in the process of calculating the mean square error removal of the current convergence level pair is supplemented back to the convergence level pair set, and then the mean square error removal calculation of the next convergence level pair is performed.
According to a second aspect of the present invention there is provided a system for optimisation of theoretical spectral data using a method as described above, the system comprising: the device comprises an acquisition module, a convergence module, an optimization module and a calculation module; the acquisition module is used for acquiring a sample model with a periodic structure in the direction X, Y; the convergence module is used for acquiring a convergence order pair set of the sample model in the X, Y direction; the optimization module is used for setting a convergence level pair which is not (0,0) and is axisymmetric or centrosymmetric in the X, Y direction as a convergence level pair group; based on RCWA algorithm, traversing the convergence level pair group in the convergence level pair set to obtain the mean square error removal of each convergence level pair in the convergence level pair group; comparing the removed mean square error with a first threshold value, and filtering all convergence level pairs corresponding to the removed mean square error smaller than the first threshold value to form an optimized level pair set; the calculation module is used for acquiring theoretical spectrum data corresponding to the optimized level pair set based on an RCWA algorithm.
According to a third aspect of the present invention, there is provided an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the method as described above when executing the computer program.
According to a fourth aspect of the present invention, there is provided a measurement method comprising:
applying a theoretical spectral database corresponding to the sample model according to the method described above; the theoretical spectrum database comprises the appearance parameters of the sample model and theoretical spectrum data corresponding to the appearance parameters;
obtaining measurement spectrum data of a corresponding measurement area of a sample to be measured;
and determining the appearance parameters of the corresponding measurement area of the sample to be measured according to the measurement spectrum data and the theoretical spectrum database.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
according to the method for optimizing the theoretical spectral data, the original level pair set is subjected to convergence analysis, and then the mean square error is removed for optimization. In the invention, the convergence level pairs with symmetry are extracted from the convergence level pair set to form a convergence level pair group, the mean square error removal of each convergence level pair is calculated, and the symmetry of the convergence level pairs can be utilized according to conditions to reduce the calculated amount and improve the calculation efficiency of theoretical spectral data; in addition, a convergence level pair with a smaller mean square error is removed through the first threshold filtering, namely a secondary convergence level pair is removed, the remaining convergence level pairs form an optimization level pair set, the mean square errors of theoretical spectral data and convergence spectral data corresponding to the optimized convergence level pair set are ensured to be the same as the magnitude of the first threshold, and the number of the level pairs of the optimized convergence level pair set is less than that of the level pairs in the original convergence level pair set, so that the calculation efficiency of the theoretical spectral data can be improved on the premise of keeping the magnitude of the mean square error.
Drawings
FIG. 1 is a flow chart of a method of optimizing theoretical spectral data implemented in accordance with the present invention;
FIG. 2 is a flow chart of a method of optimizing theoretical spectral data to obtain a set of convergence level pairs, implemented in accordance with the present invention;
FIG. 3 is a flow chart of an optimization method for obtaining a set of optimization level pairs for a theoretical spectral data optimization method implemented in accordance with the present invention;
FIG. 4 is an exemplary diagram of the use of a sample model in a method of optimization of theoretical spectral data, implemented in accordance with the present invention;
fig. 5 is a graph of a convergence level pair distribution corresponding to a set of 11 × 11 level thresholds in a theoretical spectral data optimization method implemented according to the present invention;
FIG. 6 is a rank pair distribution graph of a set of optimized rank pairs for a first threshold of 0.01 in a method of optimizing theoretical spectral data, implemented in accordance with the present invention;
fig. 7 is a rank pair distribution diagram of a set of optimized rank pairs when a first threshold is set to 1 in an optimization method of theoretical spectral data implemented in accordance with the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
It should be noted that in the functional equations of the present invention, the symbol "·" is an operation symbol representing the multiplication of two constants or vectors before and after, and "/" is an operation symbol representing the division of two constants or vectors before and after, and all the functional equations of the present invention follow the mathematical operation of addition, subtraction, multiplication and division.
It should be noted that the term "first \ second" referred to in the present invention is only used for distinguishing similar objects, and does not represent a specific ordering for the objects, and it should be understood that "first \ second" may be interchanged in a specific order or sequence, if allowed. It should be understood that "first \ second" distinct objects may be interchanged under appropriate circumstances such that embodiments of the invention described herein may be practiced in sequences other than those described or illustrated herein.
Referring to fig. 1, a schematic flow chart of a theoretical spectrum data optimization method provided by the present invention is shown. According to a particular embodiment, the method comprises:
s101: obtaining a sample model with a periodic structure in the direction X, Y;
in the present embodiment, the X direction and the Y direction are two directions perpendicular to each other; specifically, in the two-dimensional structure sample model, the X direction and the Y direction may be set as two directions perpendicular on the plane of the two-dimensional structure sample model; in the three-dimensional structure sample model, the X direction and the Y direction may be set to two directions perpendicular to a certain structure plane in the three-dimensional structure sample model. For example, as shown in the three-dimensional structure sample of fig. 4, the X (X coordinate) direction corresponds to the horizontal spatial position of the sample, and the Y (Y coordinate) direction corresponds to the vertical spatial position of the sample.
In this embodiment, the periodic structure means that the sample has a grating structure, and the grating structure includes a plurality of light-transmitting areas and a plurality of light-opaque areas arranged according to a predetermined rule. For the two-dimensional grating structure, the two-dimensional grating structure can be a long grating structure and a circular grating structure; the long grating structure is a line structure formed by a plurality of opaque areas which are parallel to each other, specifically, the distance between lines is equal, and the line density of the common long grating is 25,50,100,125 and 250 lines/mm; the circular grating structure is a centripetal stripe structure formed by a plurality of opaque regions with equal grating pitch angles, specifically, the distances among all the lines are equal, if the diameter of the common circular grating is 70mm, the density of the lines is 100-768 lines/circle, and if the diameter of the common circular grating is 110mm, the density of the lines is 600-1024 lines/circle.
S102: acquiring a convergence order pair set of the sample model in the direction X, Y;
in this embodiment, the convergence order pair set is a set of order pairs obtained by performing convergence analysis on different optical characteristic parameters, which include a dielectric function, an electric field, and a magnetic field.
In this embodiment, referring to fig. 2, the step S102 specifically includes:
s201: setting a first-level threshold Nxr (positive integer) of a truncation level Nx in the X direction and a second-level threshold Nyr (positive integer) of a truncation level Ny in the Y direction, generating a reference level pair set corresponding to the first-level threshold Nxr and the second-level threshold Nyr based on pairwise combination of a level m in the X direction and a level n in the Y direction, and acquiring first theoretical spectral data corresponding to the reference level pair set based on an RCWA algorithm;
in this embodiment, a three-dimensional rectangular coordinate system XYZ is established, and a fourier series expansion of the dielectric function ∈ (x, y) is:
wherein the content of the first and second substances,
Similarly, the Fourier series expansion of the electric and magnetic fields is:
wherein j is an imaginary unit, ε0Is dielectric constant in vacuum, mu0Is magnetic permeability in vacuum, Sxmn、Symn、SzmnThe components of the diffraction orders of the amplitude of the electric field in the x, y and z directions, Uxmn、Uymn、UzmnThe components of the diffraction orders of the amplitude of the magnetic field in the x-direction, the y-direction and the z-direction, kxm,kynThe wavevector components in the X and Y directions for each diffraction order.
In the above formula, m is the order in the X direction, and n is the order in the Y direction, it can be seen that in the above fourier series expansion, there are many expansion terms determined by different order pairs, and in actual calculation, the more expansion terms in the expansion, the larger the calculation amount, and the lower the calculation efficiency, so we need to reduce the number of expansion terms on the premise of ensuring the calculation accuracy, i.e. optimize the order pair set, so that the number of order pairs included in the order pair set is as small as possible, and at the same time, the calculation accuracy can be ensured. Therefore, before calculation, convergence analysis is carried out on a level pair set of a dielectric function, an electric field and a magnetic field subjected to Fourier series expansion, and a reference level pair set is generated on the basis of pairwise combination by setting a first level threshold Nxr in the X direction and a second level threshold Nyr in the Y direction; and calculating the set by using an RCWA algorithm based on the reference level to obtain first theoretical spectral data.
S202: changing the truncation level Nx in the X direction and the truncation level Ny in the Y direction according to a set starting point and a set step length to enable the truncation level Nx and Ny to be respectively increased to a first level threshold Nxr and a second level threshold Nyr, obtaining an original level pair set corresponding to a group of truncation level Nx and Ny based on pairwise combination of the level m in the X direction and the level n in the Y direction, and obtaining second theoretical spectral data corresponding to the original level pair set based on an RCWA algorithm;
in the present embodiment, the X-direction cutoff order Nx and the Y-direction cutoff order Ny are increased from the starting point (for example, 0) to the X-direction first-order threshold Nxr and the Y-direction second-order threshold Nyr in a set step size (for example, the same step size and both 1), an original-order pair set is generated based on the combinations of the two, and second theoretical spectral data is calculated by the RCWA algorithm based on the original-order pair set.
S203: calculating a second Mean Square Error (MSE) between the first theoretical spectral data and the second theoretical spectral data2Determining said second mean square error MSE2Sequentially with a second threshold MSEy2Comparing, extracting the first MSE smaller than the second threshold valuey2Second mean square error MSE of2The corresponding original level pair set is a convergence level pair set.
In this embodiment, the RCWA algorithm is applied to calculate a second mean square error MSE between first theoretical spectral data obtained by the reference level pair set and second theoretical spectral data obtained by the original level pair set2. Setting a second threshold MSE according to the condition of the hardware equipmenty2In general, the larger the truncation order, the more order pairs in the set of original order pairs, the second theoretical spectral data and the second theoretical spectral data of the first theoretical spectral dataMean square error MSE2The smaller, during the increase of the truncation orders Nx and Ny, the first is made smaller than a second threshold value MSEy2Second mean square error MSE of2The corresponding original order pair set is called a convergence order pair set, but the efficiency of computing theoretical spectral data by applying the RCWA algorithm based on the expansion of the convergence order pair set by the fourier series is low, so the convergence order pair set needs to be optimized.
Specifically, the second threshold MSEy2The threshold is set according to hardware conditions of the OCD measuring device, and the value range is, for example, 1e-7 to 1.
S103: setting a convergence order pair which is not (0,0) and is axisymmetric or centrosymmetric in the X, Y direction as a convergence order pair group; based on RCWA algorithm, traversing the convergence level pair group in the convergence level pair set, and obtaining the removed mean square error (also called first mean square error MSE) of each convergence level pair in the convergence level pair group1) (ii) a Comparing the removed mean square error with a first threshold value, and filtering all convergence level pairs corresponding to the removed mean square error smaller than the first threshold value to form an optimized level pair set;
in the prior art, a convergence level pair set is obtained based on a pairwise combination rule according to the truncation level in the X direction and the truncation level in the Y direction, that is, step S102. In this embodiment, in order to improve the efficiency of calculating theoretical spectral data, the convergence level pair set needs to be optimized first, that is, the level pairs in the convergence level pair set are screened, and the secondary level pairs in the convergence level pair set are removed, so that the convergence level pair corresponding to the convergence level pair set when the mean square error is smaller than the first threshold value is filtered (i.e., removed) in the convergence level pair set, and the remaining convergence level pairs form an optimized level pair set.
The mean square error of each convergence level pair is the mean square error between theoretical spectral data of the convergence level pair set before and after the current convergence level pair in the convergence level pair group is removed, or the current convergence level pair (namely, the convergence level pair) and any one or more convergence level pairs in the convergence level pair group (namely, the convergence level pairs except the convergence level pair in the convergence level pair group) are simultaneously removed.
In this embodiment, the convergence level pair group that is axisymmetric or centrosymmetric in the direction X, Y includes (m, n), (-m, n), (m, -n), and (-m, -n), and the removed mean square error of a convergence level pair (m, n) is defined as the mean square error between the theoretical spectral data of the convergence level pair set and the theoretical spectral data of the original convergence level pair set, that is, when the removed mean square error of a convergence level pair (m, n) is calculated, the convergence level pair (m, n) needs to be removed, and only the convergence level pair (m, n), it is also possible to remove not only the convergence order pair (m, n) but also any one or more of other convergence order pairs (-m, n), (m, -n) and (-m, -n), where m is the order in the X direction, n is the order in the Y direction, and m and n cannot be 0 at the same time.
Specifically, the traversing a convergence level pair group in the convergence level pair set based on the RCWA algorithm to obtain a removed mean square error of each convergence level pair in the convergence level pair group (m, n), (-m, n), (m, -n), and (-m, -n), includes:
acquiring convergence theoretical spectrum data corresponding to the convergence level pair set based on an RCWA algorithm;
traversing the convergence level pair group in the convergence level pair set, and removing the current convergence level pair in the convergence level pair group or simultaneously removing the current convergence level pair and any other one or more convergence level pairs in the convergence level pair group from the convergence level pair set, wherein the remaining convergence level pairs in the convergence level pair set form a removed level pair set;
based on RCWA algorithm, obtaining removal theoretical spectrum data corresponding to the removal level pair set;
and obtaining the mean square error removal of each convergence level pair in the convergence level pair group according to the convergence theoretical spectral data and the removal theoretical spectral data.
It should be noted that the symmetry of the convergence order pair can be used as appropriate to reduce the amount of calculation and improve the calculation efficiency of the theoretical spectral data. Specifically, when one convergence level pair in the convergence level pair group is removed to form a removal level pair set, symmetry of the convergence level pair is not considered, and for traversal, the value ranges of m and n need to be set to-Nx ≦ m ≦ Nx ≦ Ny ≦ n ≦ Ny, and the calculation amount is large, wherein Nx is the truncation level in the X direction and Ny is the truncation level in the Y direction; when the current convergence level pair and any one or more other convergence level pairs in the convergence level pair group are removed simultaneously, the removed mean square error of any removed convergence level pair is calculated to obtain the removed mean square error of all the removed convergence level pairs, all m and n in the above value range (-Nx is less than or equal to m and less than or equal to Nx, -Ny is less than or equal to n and less than or equal to Ny) can be avoided being traversed, the traversal range of m and/or n can be narrowed by utilizing the symmetry of the convergence level pairs, and only the removed mean square error of partial convergence level pairs is calculated (according to the set traversal direction and the traversal range), so that the calculation amount can be reduced, and the calculation efficiency of theoretical spectral data can be improved.
In addition, the convergence level pair removed in the process of calculating the mean square error removal of the current convergence level pair is supplemented back to the convergence level pair set, and then the mean square error removal calculation of the next convergence level pair is performed, so that the convergence level pair sets used in the calculation of each mean square error removal are the same.
More specifically, in the case of calculating the removed mean square error of all the non- (0,0) convergence level pairs in the convergence level pair set, it is preferable to select a scheme for calculating the removed mean square error of the convergence level pair (m, n) by simultaneously removing the four level pairs of the convergence level pair set (m, n), (-m, n), (m, -n), and (-m, -n), because this scheme greatly utilizes the symmetry between the level pairs, and the removed mean square error of the level pair (-m, n), (m, -n), or (-m, -n) can be obtained by calculating the removed mean square error of the level pair (m, n), thereby reducing the number of times of calculating the removed mean square error of the level pair. Referring to fig. 3, in the specific step of the scheme, in step S103, an optimized level pair set is obtained according to removal of a mean square error, and the step S103 specifically includes:
s301: setting a convergence level pair group: (m, n), (-m, n), (m, -n), and (-m, -n).
Wherein m and n are not 0 at the same time, and-Nx is not less than m and not more than Nx, -Ny is not less than n and not more than Ny, and Nx and Ny are respectively the truncation orders set in the direction X, Y.
S302: acquiring convergence theoretical spectrum data corresponding to the convergence level pair set based on an RCWA algorithm; traversing the convergence level pair group in the convergence level pair set, and removing four convergence level pairs in the convergence level pair set, wherein the remaining convergence level pairs in the convergence level pair set form a removed level pair set; based on RCWA algorithm, obtaining removal theoretical spectrum data corresponding to the removal level pair set; and obtaining the mean square error removal of each convergence level pair in the convergence level pair group according to the convergence theoretical spectral data and the removal theoretical spectral data.
In step S302, sequentially traversing other convergence level points in the X or Y direction in a preset traversal direction with any convergence level point (i.e., a value of m or n) in the X or Y direction as a starting point; the preset traversal direction may be traversal from the maximum convergence level Nx, Ny to the negative direction, or traversal from the minimum convergence level-Nx, -Ny to the positive direction, or traversal to the positive/negative direction based on any point. For example, taking the X direction as an example: the convergence order m in the X direction may be sequentially extracted from Nx to-Nx with Nx as a starting point; the convergence order m in the X direction can also be extracted from-Nx to Nx in sequence by taking-Nx as a starting point; or taking 0 as a starting point, sequentially extracting convergence orders m in the X direction from 0 to Nx and then from-Nx to 0. Specifically, when the convergence level pair (m, n) is traversed in four quadrants corresponding to the levels m and n in the direction X, Y, the traversal direction may sequentially traverse other convergence level pairs in all the quadrants in a preset traversal direction with any one of the convergence level pairs in any one of the quadrants as a starting point; for example: all convergence level pair traversals can be sequentially performed through the second quadrant, the third quadrant and the fourth quadrant by taking (Nx, 0) of the first quadrant as a starting point.
It should be noted that, the (0,0) level pair is excluded when the convergence level pair group is defined, the (0,0) level pair is not encountered during traversal, and the removed mean square error of the (0,0) level pair does not need to be calculated, so that the first quadrant, the second quadrant, the third quadrant, and the fourth quadrant described above do not include the (0,0) level pair.
Specifically, traversing the convergence level pair group in the convergence level pair set, sequentially extracting the convergence level m in the X direction from 0 to Nx, and sequentially extracting the convergence level n in the Y direction from 0 to Ny.
And obtaining the removed mean square error corresponding to the convergence level pair (-m, n), (m, -n), (-m, -n) according to the same removed mean square error of each convergence level pair in the convergence level pair group. In this embodiment, the scheme of simultaneously removing four level pairs, namely, level pair (m, n), (-m, n), (m, -n) and (-m, -n), to calculate the mean square error removal of the level pair (m, n) is optimal because the scheme greatly utilizes the symmetry between the level pairs, and can reduce the traversal range of m and n, for example, the level m in the X direction traverses from 0 to Nx, and the level n in the Y direction traverses from 0 to Ny, because the mean square error removal of the four level pairs, namely, (m, n), (-m, n), (m, -n) and (-m, -n), is the same, the mean square error removal of the level pair can be calculated, thereby reducing the number of mean square error removal times of the level pair, and improving the calculation efficiency of theoretical spectral data.
More specifically, the convergence order pair (-m, n) is an order pair in which the convergence order pair (m, n) is symmetric with respect to the y-axis, the convergence order pair (m, -n) is an order pair in which the convergence order pair (m, n) is symmetric with respect to the x-axis, and the convergence order pair (-m, -n) is an order pair in which the convergence order pair (m, n) is symmetric with respect to the order pair (0, 0); while the order pair (0,0) does not remove the mean square error because it is necessary in calculating the theoretical spectral data. When one of the convergence orders m or n is 0, 2 repeated convergence order pairs appear, and in this case, only the removed mean square error of 2 unrepeated convergence order pairs in the convergence order pair group needs to be calculated.
More specifically, when neither m nor n is 0, removing a convergence level pair group (m, n), (-m, n), (m, -n), (-m, -n) in the convergence level pair set to form a removed level pair set;
when m is 0 and n is not 0, the convergence order pair group includes: (0, n), (0, n) and (0, -n), only the removed mean square error of the (0, n) and (0, -n) convergence level pairs is needed to be calculated, and the convergence level pair groups (0, n), (0, -n) are removed from the convergence level pair set to form a removed level pair set;
when n is 0 and m is not 0, the convergence order pair group includes: (m,0), (-m,0), (m,0) and (-m,0), only the removed mean square error of the (m,0) and (-m,0) convergence level pair needs to be calculated, and the convergence level pair group (m,0), (-m,0) is removed from the convergence level pair set to form a removed level pair set.
In step S302 of this embodiment, a removal level pair set corresponding to each convergence level pair in the convergence level pair group is sequentially obtained according to a set traversal direction and a set traversal range, so as to form L removal level pair sets; based on RCWA algorithm, sequentially acquiring L pieces of theoretical spectrum data for removal; obtaining a mean square error removal value of each convergence level pair in the convergence level pair group according to the convergence theoretical spectral data and each removal theoretical spectral data; wherein L is (Nx +1) (Ny +1) -1. Specifically, the convergence level pairs in the convergence level pair group removed by the current calculation are complemented back to the original convergence level pair set, and then the next level pair is calculated, so that the convergence level pair sets used in calculating each removed mean square error are the same.
More specifically, the removed mean square error of the convergence level pair may measure the importance of the convergence level pair, and the greater the removed mean square error, the greater the importance of the convergence level pair. If only one convergence level pair is removed when the mean square error is removed in calculation, and the symmetry of the convergence level pair is not utilized, the number of convergence level pairs contained in the level pair set with the X-direction truncation level Nx and the Y-direction truncation level Ny is (2Nx +1) (2Ny +1), and since the mean square error is not removed by the convergence level pair (0,0), the mean square error removal frequency of each convergence level pair is calculated to be (2Nx +1) (2Ny +1) -1. However, in this embodiment, the symmetry of the convergence order pair is used, so that the calculation amount can be reduced, and the calculation efficiency of the theoretical spectral data can be improved. Specifically, the removed mean square error of the convergence level pair (m, n), (-m, n), (m, -n) and (-m, -n) is calculated under the condition of removing the four convergence level pairs, and the number of the convergence level pairs required to be calculated is (Nx +1) (Ny +1) -1 because the removed mean square errors of the four convergence level pairs (m, n), (-m, n), (m, -n), (-m, -n) and (n) are calculated in the same way, so the removed mean square errors of the four convergence level pairs (m, n), (-m, n), (m, -n), (-m, -n) are the same.
More specifically, for the convergence level pair (m, n), (-m, n), (m, -n) and (-m, -n) are removed from the convergence level pair set, then the remaining convergence level pair set is used to perform Fourier expansion on different optical characteristic parameters and the RCWA algorithm is used to calculate and remove theoretical spectral data, then the mean square error with the theoretical spectral data of the original convergence level pair set is calculated, i.e. the removed mean square error of the level pair (m, n), and then the removed mean square errors of the corresponding convergence level pair (-m, n), (m, -n) and (-m, -n) are obtained according to the convergence level pair (m, n), (-m, n), (m, -n) and (-m, -n) being the same, and after the calculation is finished, the convergence level pairs (m, n), (-m, n), (m, -n) and (-m, -n) removed in the calculation process are supplemented back to the original convergence level pair set, the mean square error removal calculation of the next convergence level pair is carried out, and the mean square error removal of all the convergence level pairs is obtained after the whole traversal process is finished.
S303: and comparing the removed mean square error with a first threshold value, and filtering all convergence level pairs corresponding to the removed mean square error smaller than the first threshold value to form an optimized level pair set.
In step S303, the hardware device determines the first threshold MSEy1Filtering out and removing MSE with mean square error smaller than first threshold valuey1Corresponding convergence level pairs, the remaining set of convergence level pairs forming an optimized level pair set. At this time, the mean square error of the theoretical spectral data and the converged spectral data corresponding to the optimization level pair set is equal to the first threshold MSEy1Are of the same order. The number of the order pairs of the optimized order pair set is less than that of the order pairs in the original convergence order pair set, so that the calculation amount can be reduced and the calculation effect can be improved on the premise of keeping the magnitude of Mean Square Error (MSE)And (4) rate.
More specifically, the first threshold MSEy1The threshold is determined according to hardware conditions of the OCD measuring device, and the value range is, for example, 1e-7 to 1. Preferably, the first threshold value MSEy1And a second threshold value MSEy2The values of (A) are the same.
S104: and acquiring theoretical spectral data corresponding to the optimized level pair set based on the RCWA algorithm.
In the embodiment, based on the RCWA algorithm, the dielectric function of the sample model medium, the fourier series expansion of the electric field and the magnetic field are substituted into the maxwell equation set, the electric field in the incident region is solved by using the continuous condition of the electromagnetic field, so that the reflection coefficient of the sample is obtained, each wavelength point is traversed, the RCWA algorithm is used for calculating the reflection coefficient of the sample corresponding to the wavelength point, and thus the theoretical spectral data of the sample is obtained.
According to another specific embodiment of the present invention, there is provided a method for optimizing theoretical spectral data, the method including:
s101': a sample having a periodic structure in both the X and Y directions is provided. Referring to fig. 4, fig. 4 provides a block diagram of a sample model, the lowest layer is a substrate, on which a thin film layer is arranged, then a Y-direction grating is arranged, and the top is an X-direction grating.
S102': setting the first-level threshold Nxr in the X direction and the second-level threshold Nyr in the Y direction as 11, generating a reference-level pair set based on pairwise combination, wherein the reference-level pair set is known as a set of 11 × 11, assuming that convergence analysis is performed, then obtaining Nx and Ny corresponding to the convergence-level pair set, and the convergence-level pair set distribution map is shown in fig. 5. The horizontal axis coordinate represents convergence level m in the X direction, the vertical axis coordinate represents convergence level n in the Y direction, each square represents a convergence level pair (m, n), the number of squares is the number of convergence level pairs included in the convergence level pair set, and 121 squares can be seen.
S103': calculating the corresponding removed mean square error for each convergence level pair, the calculation result being shown in the block of fig. 5, according to a first threshold MSEy1Is carried out according to the situationDiscussion:
if the first threshold value MSE is sety1Is 0.01, as shown in FIG. 6, the white square indicates that the removed mean square error is less than the first threshold MSEy1And the convergence level pairs filtered out, the grey squares representing the remaining level pairs. The set of gray squares in fig. 6 represents the optimized set of convergence level pairs, i.e., the optimized set of level pairs. As shown in fig. 6, the number of gray squares is 93, and the number of original squares is 121, that is, the number of convergence level pairs included in the optimization level pair set is 23% less than the number of convergence level pairs included in the convergence level pair set, thereby improving the efficiency of the RCWA algorithm in calculating theoretical spectral data. The mean square error MSE between the theoretical spectral data calculated by the optimized optimization level pair set and the convergence theoretical spectral data calculated by the convergence level pair set is 0.0287379, which proves that the order of the mean square error MSE between the theoretical spectral data calculated by the optimized optimization level pair set and the convergence theoretical spectral data calculated by the convergence level pair set and the first threshold MSE are the order of magnitude of the mean square error MSE between the theoretical spectral data calculated by the optimized optimization level pair set and the convergence theoretical spectral data calculated by the convergence level pair set and the first threshold MSEy1As such, it has proven feasible to compute the set with the optimized optimization order.
If the first threshold value MSE is sety11, as shown in FIG. 7, the white square indicates that the removed mean square error is less than the first threshold MSEy1And the convergence level pairs are filtered out, and the gray squares represent the level pairs that are not removed. The set of gray squares in fig. 7 represents the optimized set of convergence level pairs, i.e., the optimized set of level pairs. As shown in fig. 7, the number of gray squares is 45, and the number of original squares is 121, that is, the number of convergence level pairs included in the optimization level pair set is 63% less than the number of convergence level pairs included in the convergence level pair set, thereby improving the efficiency of the RCWA algorithm in calculating theoretical spectral data. The mean square error MSE between the theoretical spectral data calculated using the optimized set of optimization level pairs and the convergence theoretical spectral data calculated using the set of convergence level pairs, obtained using the RCWA algorithm, is 1.21516, and it can be similarly demonstrated that the mean square error MSE between the theoretical spectral data corresponding to the optimized set of optimization level pairs and the convergence theoretical spectral data corresponding to the set of convergence level pairs is 1.21516The order of the MSE and the first threshold MSEy1As such, it has proven feasible to compute the set with the optimized optimization order.
S104': and performing Fourier series expansion on the dielectric function, the electric field and the magnetic field based on the optimized level pair set, and calculating theoretical spectral data by applying an RCWA algorithm.
The present invention provides a measurement method based on the above embodiment, including:
s105': establishing a theoretical spectrum database corresponding to the sample model by using the method according to the steps S101-S104; the theoretical spectrum database comprises the appearance parameters of the sample model and theoretical spectrum data corresponding to the appearance parameters;
s106': obtaining measurement spectrum data of a corresponding measurement area of a sample to be measured;
s107': and determining the appearance parameters of the corresponding measurement area of the sample to be measured according to the measurement spectrum data and the theoretical spectrum database.
The present invention provides a theoretical spectral data optimization system based on the above embodiment, the system includes: the device comprises an acquisition module, a convergence module, an optimization module and a calculation module; the acquisition module is used for acquiring a sample model with a periodic structure in the direction X, Y; the convergence module is used for acquiring a convergence order pair set of the sample model in the X, Y direction; the optimization module is used for setting a convergence level pair which is not (0,0) and is axisymmetric or centrosymmetric in the X, Y direction as a convergence level pair group; based on RCWA algorithm, traversing the convergence level pair group in the convergence level pair set to obtain the mean square error removal of each convergence level pair in the convergence level pair group; comparing the removed mean square error with a first threshold value, and filtering all convergence level pairs corresponding to the removed mean square error smaller than the first threshold value to form an optimized level pair set; the calculation module is used for acquiring theoretical spectrum data corresponding to the optimized level pair set based on an RCWA algorithm.
The present invention further provides a computer-readable storage medium on which a computer program is stored, which, when being executed by a processor, implements the method as described above.
The present invention also provides a measurement method based on the above embodiment, including:
s1: establishing a theoretical spectrum database corresponding to the sample model by applying the optimization method of the theoretical spectrum data; the theoretical spectrum database comprises the appearance parameters of the sample model and theoretical spectrum data corresponding to the appearance parameters;
s2: obtaining measurement spectrum data of a corresponding measurement area of a sample to be measured;
s3: and determining the appearance parameters of the corresponding measurement area of the sample to be measured according to the measurement spectrum data and the theoretical spectrum database.
The specific theoretical spectral data optimization method is the same as that described above, and is therefore described in detail. It should be understood that any process or method descriptions of methods, structures, or steps described herein that are in a block diagram or otherwise may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps in the process, and that the scope of embodiments of the present invention includes additional implementations in which functions may be executed out of order from that shown or discussed, including in substantially the same way or in an opposite order depending on the functionality involved, as would be understood by those reasonably skilled in the art of embodiments of the present invention.
It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present invention may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (10)
1. A method of optimizing theoretical spectral data, the method comprising:
obtaining a sample model with a periodic structure in the direction X, Y;
obtaining a set of convergence order pairs of the sample model in the X, Y direction;
setting a convergence order pair which is not (0,0) and is axisymmetric or centrosymmetric in the X, Y direction as a convergence order pair group; based on RCWA algorithm, traversing the convergence level pair group in the convergence level pair set to obtain the mean square error removal of each convergence level pair in the convergence level pair group; comparing the removed mean square error with a first threshold value, and filtering all convergence level pairs corresponding to the removed mean square error smaller than the first threshold value to form an optimized level pair set;
and acquiring theoretical spectral data corresponding to the optimized level pair set based on the RCWA algorithm.
2. The method of claim 1, wherein the collection of converging pairs is a collection of converging pairs obtained by convergence analysis of different optical parameters, the optical parameters including dielectric function, electric field, and magnetic field.
3. The method for optimizing theoretical spectral data according to claim 1, wherein said setting of the pair of convergence orders that is not (0,0) and is axisymmetric or centrosymmetric in the X, Y direction is a convergence order pair group, comprising:
setting a convergence level pair group: (m, n), (-m, n), (m, -n), and (-m, -n);
wherein m and n are not 0 at the same time, and-Nx is not less than m and not more than Nx, -Ny is not less than n and not more than Ny, and Nx and Ny are respectively the truncation orders set in the direction X, Y.
4. The method for optimizing theoretical spectral data according to claim 1, wherein the mean square error removal of each convergence level pair is a mean square error between the theoretical spectral data of the convergence level pair set before and after removing the current convergence level pair in the convergence level pair group or simultaneously removing the current convergence level pair and any other one or more convergence level pairs in the convergence level pair group.
5. The method for optimizing theoretical spectral data according to claim 4, wherein the step of traversing the convergence level pair group in the convergence level pair set based on the RCWA algorithm to obtain a removed mean square error of each convergence level pair in the convergence level pair group comprises:
acquiring convergence theoretical spectrum data corresponding to the convergence level pair set based on an RCWA algorithm;
traversing the convergence level pair group in the convergence level pair set, and removing the current convergence level pair in the convergence level pair group or simultaneously removing the current convergence level pair and any other one or more convergence level pairs in the convergence level pair group from the convergence level pair set, wherein the remaining convergence level pairs in the convergence level pair set form a removed level pair set;
based on RCWA algorithm, obtaining removal theoretical spectrum data corresponding to the removal level pair set;
and obtaining the mean square error removal of each convergence level pair in the convergence level pair group according to the convergence theoretical spectral data and the removal theoretical spectral data.
6. The method for optimizing theoretical spectral data according to claim 4, wherein when removing the current convergence level pair and any other one or more convergence level pairs in the convergence level pair group at the same time, the removed mean square error of any removed convergence level pair is calculated to obtain the removed mean square errors of all the removed convergence level pairs.
7. The method of claim 1, wherein the removed mean square error of the convergence level pair is calculated after the convergence level pair removed in the mean square error removal calculation process is added back to the convergence level pair set.
8. A system for optimizing theoretical spectral data, wherein the method of claims 1-7 is applied, the system comprising: the device comprises an acquisition module, a convergence module, an optimization module and a calculation module; the acquisition module is used for acquiring a sample model with a periodic structure in the direction X, Y; the convergence module is used for acquiring a convergence order pair set of the sample model in the X, Y direction; the optimization module is used for setting a convergence level pair which is not (0,0) and is axisymmetric or centrosymmetric in the X, Y direction as a convergence level pair group; based on RCWA algorithm, traversing the convergence level pair group in the convergence level pair set to obtain the mean square error removal of each convergence level pair in the convergence level pair group; comparing the removed mean square error with a first threshold value, and filtering all convergence level pairs corresponding to the removed mean square error smaller than the first threshold value to form an optimized level pair set; the calculation module is used for acquiring theoretical spectrum data corresponding to the optimized level pair set based on an RCWA algorithm.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the steps of the method according to any of claims 1 to 7 are implemented when the computer program is executed by the processor.
10. A method of measurement, comprising:
applying the method according to claims 1-7 to build a theoretical spectral database corresponding to the sample model; the theoretical spectrum database comprises the appearance parameters of the sample model and theoretical spectrum data corresponding to the appearance parameters;
obtaining measurement spectrum data of a corresponding measurement area of a sample to be measured;
and determining the appearance parameters of the corresponding measurement area of the sample to be measured according to the measurement spectrum data and the theoretical spectrum database.
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