CN113343182B - Optimization method and system of theoretical spectrum data, electronic equipment and measurement method - Google Patents
Optimization method and system of theoretical spectrum data, 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 spectrum data, wherein the optimization method comprises the following steps: obtaining a sample model with a periodic structure in the X, Y direction; acquiring a convergence order pair set of the sample model in the X, Y direction; setting a convergence level pairing group; traversing a convergence level pair group in the convergence level pair set, and obtaining a removal mean square error of each convergence level pair in the convergence level pair group; comparing the removal mean square error with a first threshold value, and filtering all convergence order pairs which are smaller than the first threshold value and correspond to the removal mean square error to form an optimization order pair set; and acquiring theoretical spectrum data corresponding to the optimization level pair set. According to the method, the convergence grade pair with smaller mean square error is removed from the convergence grade pair set through the first threshold value filtering, and the number of the grade pairs of the optimized convergence grade pair set is smaller than that of the grade pairs in the original convergence grade pair set, so that the calculation efficiency of theoretical spectrum data is effectively improved.
Description
Technical Field
The present invention relates to the field of optical measurement; in particular, 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 measurement (Optical Critical Dimension, abbreviated as OCD) technique estimates specific morphological parameters of a sample by acquiring a scattering signal of a periodic structure of a specific region to be measured of the sample and a model of the sample, can meet the requirement of realizing rapid and accurate measurement in a new process and a new technique, has non-contact and non-destructive properties, and is widely applied to semiconductor manufacturing industry and optical measurement. The principle of the optical critical dimension measurement technology can be generally described as: firstly, a theoretical spectrum database corresponding to a morphology model of a sample is established, and then, a scattering signal of a periodic structure of a specific detected area of the sample is obtained to be matched with parameters of the theoretical spectrum database, so that specific morphology parameters of the sample are estimated. In creating a theoretical spectral database corresponding to the morphology model of the sample, the algorithm used to calculate the theoretical spectral data is a rigorous coupled wave analysis (Rigorous Coupled Wave Analysis, abbreviated as RCWA) algorithm. The RCWA algorithm is to substitute the dielectric function of the sample and the Fourier series expansion of the electromagnetic field of the sample area into Maxwell's equations, and solve the electric field of the incident area by using the continuous condition of the electromagnetic field, so as to obtain the reflection coefficient of the sample. 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 spectrum data of the sample.
Specifically, in the RCWA algorithm: for a sample model with a periodic structure in the X direction and the Y direction, fourier series expansion is generally performed on different optical characteristic parameters (such as a dielectric function, an electric field and a magnetic field) of the sample model in the X direction and the Y direction, the fourier series expansion is performed from negative infinity to positive infinity, the number of steps is required to be truncated in the actual application of the RCWA algorithm, and the maximum number of steps of truncation is called as the truncated number of steps, that is, the fourier series expansion is performed on the optical characteristic parameters only to the truncated number of steps in the actual application. And because of the X and Y directions, there are two cut-off orders; therefore:
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 cut-off level in the X direction is denoted as Nx, and the cut-off level in the Y direction is denoted as Ny.
Thus, a combination of one X-direction rank m and one Y-direction rank n is referred to as a rank pair, denoted (m, n). Since the X-direction rank has a plurality of values, and the Y-direction rank has a plurality of values, a plurality of combinations of the X-direction rank and the Y-direction rank are provided, and the different rank pair combinations form a rank pair set, and the rank pair set is a two-by-two combination of the X-direction rank and the Y-direction rank, and is expressed as: { (m, n) | -Nx.ltoreq.m.ltoreq.Nx, -Ny.ltoreq.Ny }, wherein the cut-off level in the X direction is denoted as Nx, and the cut-off level in the Y direction is denoted as Ny.
Based on the level pair set, carrying out Fourier series expansion on different optical characteristic parameters, and then applying an RCWA algorithm to calculate theoretical spectrum data; thus, one set of such order pairs corresponds to one theoretical spectral data. However, the calculation efficiency and the number of the level pairs corresponding to the fourier series are in a cubic inverse relation, so that when theoretical spectrum data are calculated: on the one hand, the more the number of the grade pairs corresponding to the Fourier series is, the higher the accuracy of calculating theoretical spectrum data by the RCWA algorithm is, but the larger the calculated amount of calculating the theoretical spectrum data by the RCWA algorithm is, the lower the calculation efficiency is; on the other hand, the smaller the number of pairs of the fourier series, the higher the calculation efficiency, but the accuracy of calculating theoretical spectral data by the RCWA algorithm is lowered. Therefore, before theoretical spectrum data are calculated, the convergence analysis is carried out on the grade pair set corresponding to the Fourier series expansion of different optical characteristic parameters, so as to obtain a convergence grade pair set.
The purpose of the convergence analysis is to obtain a convergence order pair set, and theoretical spectrum data is calculated by using the convergence order pair set, so that the calculation efficiency can be improved under the condition of ensuring the accuracy. The approach to convergence analysis is:
Setting a first level threshold Nxr (positive integer) of the truncated level Nx in the X direction and a second level threshold Nyr (positive integer) of the truncated 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 the combination of the level m in the X direction and the level n in the Y direction, and acquiring first theoretical spectrum data corresponding to the reference level pair set based on an RCWA algorithm;
changing the truncated order Nx in the X direction and the truncated order Ny in the Y direction according to a set starting point and a set step length, so that the truncated orders Nx and Ny are respectively increased to a first order threshold Nxr and a second order threshold Nyr, obtaining an original order pair set corresponding to one truncated order Nx and Ny based on the combination of the orders m in the X direction and the orders n in the Y direction, and obtaining second theoretical spectrum data corresponding to one original order pair set based on an RCWA algorithm;
and calculating a mean square error MSE between the first theoretical spectrum data and the second theoretical spectrum data, sequentially comparing the mean square error MSE with a preset MSE threshold value, and extracting one original grade pair set corresponding to the first mean square error MSE smaller than the MSE threshold value as a convergence grade pair set.
Specifically, as described above, the first theoretical spectrum data corresponding to the reference order pair set is calculated by using the RCWA algorithm, the X-direction truncated order Nx and the Y-direction truncated order Ny are gradually increased from a set starting point (for example, 0) to the first order threshold Nxr and the second order threshold Nyr respectively (for example, the X-direction and the Y-direction are gradually increased according to a step size of 1), one original order pair set corresponding to the X-direction truncated order Nx and the Y-direction truncated order Ny is generated based on the two combinations, the RCWA algorithm is applied, the mean square error MSE of the second theoretical spectrum data corresponding to the original order pair set and the first theoretical spectrum data is calculated, the MSE threshold is obtained according to the condition of the hardware device, in general, the larger the truncated order Nx and the Ny is, the more the number of order pairs in the original order pair set is, the smaller the MSE is, and in the process of increasing the truncated order Nx and Ny, the one original order pair set corresponding to the MSE error smaller than the MSE threshold is called the original order pair set. Typically, the convergence level pair set can be found without increasing to the first and second level thresholds Nxr, nyr.
In the prior art, a convergence order pair set can be obtained based on convergence analysis, theoretical spectrum data is calculated based on the convergence order pair set, namely, a fourier series item corresponding to the convergence order pair set is reserved when fourier series expansion is carried out on optical characteristic parameters, and the theoretical spectrum data is calculated by applying an RCWA algorithm, so that the calculation efficiency can be improved under the condition of ensuring the accuracy, but the calculation efficiency of the theoretical spectrum data is lower, and therefore, the convergence order pair set needs to be optimized.
Disclosure of Invention
Aiming at the defects or improvement demands of the prior art, the invention provides an optimization method, a system, electronic equipment and a measurement method of theoretical spectrum data; and optimizing the collection aiming at the convergence level acquired by using the RCWA algorithm when calculating the theoretical spectrum data in the 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 of optimizing theoretical spectral data, the method comprising:
obtaining a sample model with a periodic structure in the X, Y direction;
acquiring a convergence order pair set 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; traversing the convergence grade pair group in the convergence grade pair set based on an RCWA algorithm to obtain a removal mean square error of each convergence grade pair in the convergence grade pair group; comparing the mean square error removal with a first threshold value, and filtering all convergence level pairs corresponding to the mean square error removal smaller than the first threshold value to form an optimization level pair set;
based on the RCWA algorithm, theoretical spectrum data corresponding to the optimization level pair set is obtained.
Further, the convergence order pair set is an order pair set obtained by performing convergence analysis on different optical characteristic parameters, and the optical characteristic parameters comprise a dielectric function, an electric field and a magnetic field.
Further, the set of convergence order pairs that are not (0, 0) and are axisymmetric or centrosymmetric in the X, Y direction is a convergence order pair group, comprising:
setting a convergence level pairing group: (m, n), (-m, n), (m, -n) and (-m, -n);
wherein, m and n are not equal to 0 at the same time, 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 cut-off orders set in the X, Y direction.
Further, the mean square error removal of each convergence order pair is mean square error removal of the current convergence order pair in the convergence order pair group or simultaneous removal of the current convergence order pair and theoretical spectrum data of the convergence order pair set before and after any one or more convergence order pairs in the convergence order pair group.
Further, traversing the convergence level pair group in the convergence level pair set based on the RCWA algorithm to obtain a mean square error removal of each convergence level pair in the convergence level pair group, including:
based on an RCWA algorithm, acquiring convergence theoretical spectrum data corresponding to the convergence order pair set;
traversing the convergence grade pair group in the convergence grade pair set, removing the current convergence grade pair in the convergence grade pair group or simultaneously removing the current convergence grade pair and any one or more convergence grade pairs in the convergence grade pair group, wherein the rest convergence grade pairs in the convergence grade pair set form a removal grade pair set;
based on an RCWA algorithm, obtaining removal theoretical spectrum data corresponding to the removal level pair set;
And obtaining the removal mean square error of each convergence order pair in the convergence order pair group according to the convergence theoretical spectrum data and the removal theoretical spectrum data.
Further, when the current convergence order pair and any one or more convergence order pairs in the convergence order pair group are removed at the same time, the removal mean square error of any one of the removed convergence order pairs is calculated to obtain the removal mean square error of all the removed convergence order pairs.
Further, the convergence order pair removed in the current calculation process of removing the mean square error of the convergence order pair is complemented back to the convergence order pair set, and then calculation of removing the mean square error of the next convergence order pair is carried out.
According to a second aspect of the present invention there is provided a system for optimisation of theoretical spectroscopic data, using a method as described above, the system comprising: the system 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 X, Y direction; 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 convergence order pairs which are not (0, 0) and are axisymmetric or centrosymmetric in the X, Y direction as convergence order pair groups; traversing the convergence grade pair group in the convergence grade pair set based on an RCWA algorithm, and obtaining a removal mean square error of each convergence grade pair in the convergence grade pair group; comparing the mean square error removal with a first threshold value, and filtering all convergence level pairs corresponding to the mean square error removal smaller than the first threshold value to form an optimization level pair set; the calculation module is used for acquiring theoretical spectrum data corresponding to the optimization level pair set based on the 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 the computer program is executed.
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 morphological parameters of the sample model and theoretical spectrum data corresponding to the morphological parameters;
obtaining measurement spectrum data of a measurement area corresponding to a sample to be measured;
and determining the morphological parameters of the measurement region corresponding to the sample to be measured according to the measured spectrum data and the theoretical spectrum database.
In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:
according to the optimization method of theoretical spectrum data, after convergence analysis is carried out on the collection of the original level pair, the optimization is carried out by removing the mean square error. According to the method, the convergence order pairs with symmetry are extracted from the convergence order pair set to form the convergence order pair group, the mean square error removal of each convergence order pair is calculated, and the symmetry of the convergence order pairs can be utilized according to the situation so as to reduce the calculated amount and improve the calculation efficiency of theoretical spectrum data; in addition, the convergence order pair with smaller mean square error is removed through the first threshold value filtering, namely secondary convergence order pairs are removed, the rest convergence order pairs form an optimized order pair set, meanwhile, the fact that the mean square error of theoretical spectrum data corresponding to the optimized convergence order pair set and the convergence spectrum data is the same as the magnitude of the first threshold value is guaranteed, the number of the optimized convergence order pair set is smaller than that of the original convergence order pair set, and therefore the calculation efficiency of the theoretical spectrum data can be improved on the premise that the magnitude of the mean square error is maintained.
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 for optimizing theoretical spectral data in accordance with the present invention for obtaining a collection of converging level pairs;
FIG. 3 is a flow chart of an acquisition optimization order pair set for a theoretical spectroscopic 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 optimizing theoretical spectroscopic data implemented in accordance with the present invention;
FIG. 5 is a chart of a convergence level pair set corresponding to a set 11×11 level threshold in a method for optimizing theoretical spectral data according to the present invention;
FIG. 6 is a plot of the optimized rank pairs of the set of rank pairs for a first threshold of 0.01 in a method for optimizing theoretical spectral data implemented in accordance with the present invention;
fig. 7 is a distribution of the number of optimization pairs of the set of number of optimization pairs when the first threshold is set to 1 in a method for optimizing theoretical spectral data according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
It should be noted that, in the function equations related to the present invention, the symbol "·" is a sign indicating multiplication of the front and rear constants or vectors, and "/" is a sign indicating division of the front and rear constants or vectors, and all the function equations in the present invention follow a mathematical add-subtract multiplication-division algorithm.
It should be noted that the term "first/second" related to the present invention is merely to distinguish similar objects, and does not represent a specific order for the objects, and it should be understood that "first/second" may interchange a specific order or precedence where allowed. It is to be understood that the "first\second" distinguishing aspects may be interchanged where appropriate to enable embodiments of the invention described herein to be implemented in sequences other than those described or illustrated herein.
Referring to fig. 1, a flow chart of a theoretical spectrum data optimizing method provided by the invention is shown. According to a specific embodiment, the method comprises:
S101: obtaining a sample model with a periodic structure in the X, Y direction;
in this 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 to two directions perpendicular to 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 structural plane in the three-dimensional structure sample model. For example, as shown in fig. 4, a three-dimensional structure sample, 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 including a plurality of light-transmitting regions and a plurality of light-impermeable regions arranged according to a predetermined rule. For a two-dimensional grating structure, it may be a long grating structure and a round 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 line distances are equal, and the line density of the common long grating is 25,50,100,125,250 lines/mm; the circular grating structure is a centripetal stripe structure formed by a plurality of opaque areas with equal grating angles, specifically, the distances among all the lines are equal, if the diameter of a common circular grating is 70mm, the line density is 100-768 lines/week, and if the diameter is 110mm, the line density is 600-1024 lines/week.
S102: acquiring a convergence order pair set of the sample model in the X, Y direction;
in this embodiment, the convergence order pair set is an order pair set obtained by performing convergence analysis on different optical characteristic parameters, where the optical characteristic parameters 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 order threshold Nxr (positive integer) of the truncated order Nx in the X direction and a second order threshold Nyr (positive integer) of the truncated order Ny in the Y direction, generating a reference order pair set corresponding to the first order threshold Nxr and the second order threshold Nyr based on the combination of the order m in the X direction and the order n in the Y direction, and acquiring first theoretical spectrum data corresponding to the reference order pair set based on an RCWA algorithm;
in this embodiment, a three-dimensional rectangular coordinate system XYZ is established, and the fourier series expansion of the dielectric function epsilon (x, y) is:
wherein,
Λ x ,Λ y is the period of the sample in the X and Y directions.
Likewise, the fourier series expansion of the electric and magnetic fields is:
wherein j is an imaginary unit, ε 0 Is the dielectric constant in vacuum, mu 0 Is permeability in vacuum, S xmn 、S ymn 、S zmn The components of the diffraction orders in the x-direction, y-direction and z-direction, respectively, of the amplitude of the electric field, U xmn 、U ymn 、U zmn The components of the diffraction orders in the x-direction, y-direction and z-direction, k, respectively, of the amplitude of the magnetic field xm ,k yn Wave vector components in the X-direction and the Y-direction 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 fourier series expansion, there are many expansion items determined by different order pairs, in actual calculation, the more expansion items in the expansion are, the larger the calculation amount is, and the lower the calculation efficiency is, so we need to reduce the number of expansion items on the premise of ensuring the calculation accuracy, that is, optimize the order pair set, so that the number of order pairs contained in the order pair set is as small as possible, and meanwhile, the calculation accuracy can be ensured. Therefore, before calculation, the convergence analysis is carried out on the level pair sets of the dielectric function, the electric field and the magnetic field by carrying out Fourier series expansion, and the reference level pair sets are generated based on the combination of two pairs 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 order to obtain first theoretical spectrum data.
S202: changing the truncated order Nx in the X direction and the truncated order Ny in the Y direction according to a set starting point and a set step length, so that the truncated orders Nx and Ny are respectively increased to a first order threshold Nxr and a second order threshold Nyr, obtaining an original order pair set corresponding to one truncated order Nx and Ny based on the combination of the orders m in the X direction and the orders n in the Y direction, and obtaining second theoretical spectrum data corresponding to one original order 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 start point (for example, 0) by a set step length (for example, the step length is the same and both are 1) to the first order threshold Nxr in the X-direction and the second order threshold Nyr in the Y-direction, an original order pair set is generated based on the combination of two pairs, and the second theoretical spectrum 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 data 2 The second mean square error MSE is calculated 2 Sequentially with a second threshold MSE y2 Comparing, extracting a first MSE less than the second threshold MSE y2 Is the second mean square error MSE of (2) 2 The corresponding one of the original level pair sets is a convergence level pair set.
In this embodiment, the reference order is calculated by applying the RCWA algorithmSecond mean square error MSE between first theoretical spectral data obtained from the pair set and second theoretical spectral data obtained from the original order pair set 2 . Setting a second threshold MSE according to the condition of the hardware equipment y2 In general, the larger the truncated order, the more order pairs in the original set of order pairs, the second mean square error MSE of the second theoretical spectral data and the first theoretical spectral data 2 The smaller, during the increase of the truncated orders Nx and Ny, the first one is smaller than the second threshold MSE y2 Is the second mean square error MSE of (2) 2 The corresponding one of the sets of original order pairs is called a convergence order pair set, but it is still inefficient to apply the RCWA algorithm to calculate theoretical spectral data based on the expansion of the fourier series of the convergence order pair set, so that the convergence order pair set needs to be optimized.
Specifically, the second threshold MSE y2 The threshold value is set according to the hardware condition of the OCD measuring device, and the value range is 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; traversing the convergence order pair group in the convergence order pair set based on an RCWA algorithm to obtain a removed mean square error (also referred to as a first mean square error MSE) of each convergence order pair in the convergence order pair group 1 ) The method comprises the steps of carrying out a first treatment on the surface of the Comparing the mean square error removal with a first threshold value, and filtering all convergence level pairs corresponding to the mean square error removal smaller than the first threshold value to form an optimization level pair set;
in the prior art, a convergence level pair set is obtained based on a pairwise combination rule according to the truncated level in the X direction and the truncated level in the Y direction, i.e., step S102. In this embodiment, in order to improve the efficiency of calculating the theoretical spectrum data, the convergence rank pair set needs to be optimized first, that is, the rank pairs therein need to be screened, and the secondary rank pairs therein need to be removed, so that in this embodiment, the convergence rank pair set is filtered (that is, removed) to remove the convergence rank pair corresponding to the mean square error smaller than the first threshold value, and the remaining convergence rank pairs form an optimized rank pair set.
The mean square error removal of each convergence order pair is mean square error between theoretical spectrum data of the convergence order pair set before and after removing the current convergence order pair in the convergence order pair group or removing the current convergence order pair (i.e. the convergence order pair) and any one or more convergence order pairs in the convergence order pair group (i.e. the convergence order pairs except the convergence order pair).
In this embodiment, the convergent order pair group axially symmetric or centrosymmetrically in the X, Y direction includes (m, n), (-m, n), (m, -n) and (-m, -n), and the removal mean square error of one convergent order pair (m, n) is defined as removal of the convergent order pair (m, n) or removal of any one or more of the convergent order pairs (-m, n), (m, -n) and (-m, -n) simultaneously with the removal of the convergent order pair (m, n), that is, the removal of the convergent order pair (m, n) is required when calculating the removal mean square error of one convergent order pair (m, n), and the removal of not only the convergent order pair (m, n) but also any one or more of the other convergent order pairs (-m, n), (m, -n) and (-m, -n) is required, wherein m is not the Y order in the X direction and n is not required.
Specifically, the traversing the convergence order pair group in the convergence order pair set based on the RCWA algorithm, to obtain a mean square error removal of each convergence order pair in the convergence order pair group (m, n), (-m, n), (m, -n) and (-m, -n), includes:
based on an RCWA algorithm, acquiring convergence theoretical spectrum data corresponding to the convergence order pair set;
traversing the convergence grade pair group in the convergence grade pair set, removing the current convergence grade pair in the convergence grade pair group or simultaneously removing the current convergence grade pair and any one or more convergence grade pairs in the convergence grade pair group, wherein the rest convergence grade pairs in the convergence grade pair set form a removal grade pair set;
based on an RCWA algorithm, obtaining removal theoretical spectrum data corresponding to the removal level pair set;
and obtaining the removal mean square error of each convergence order pair in the convergence order pair group according to the convergence theoretical spectrum data and the removal theoretical spectrum data.
It should be noted that, the symmetry of the convergence order pair may be utilized according to circumstances to reduce the calculation amount and improve the calculation efficiency of the theoretical spectrum data. Specifically, when one convergence order pair in the convergence order pair group is removed to form a removal order pair set, symmetry of the convergence order pair is not considered, in order to realize traversal, a value range of m and n needs to be set to be-nx.ltoreq.m.ltoreq.nx, -ny.ltoreq.n.ltoreq.ny, the calculated amount is large, wherein Nx is a truncated order in the X direction, and Ny is a truncated order in the Y direction; when the current convergence order pair and any one or more other convergence order pairs in the convergence order pair group are removed at the same time, the removal mean square error of any one of the removed convergence order pairs is calculated to obtain the removal mean square error of all the removed convergence order pairs, so that all m and n in the above value range (-Nx < m < Nx, -Ny < n < Ny) can be avoided from being traversed, the symmetry of the convergence order pairs can be utilized, the traversing range of m and/or n can be reduced, and only the removal mean square error of part of the convergence order pairs (according to the set traversing direction and traversing range) can be calculated, thereby reducing the calculated amount and improving the calculation efficiency of theoretical spectrum data.
In addition, the convergence order pair removed in the calculation process of removing the mean square error of the current convergence order pair is complemented back to the convergence order pair set, and then calculation of removing the mean square error of the next convergence order pair is carried out, so that the convergence order pair set used in calculation of each removal of the mean square error is the same.
More specifically, in the case of calculating the mean square error removal of all non (0, 0) pairs in the convergence order pair set, a scheme of calculating the mean square error removal of the convergence order pair by simultaneously removing the four pairs in the convergence order pair group (m, n), (-m, n), (m, -n) and (-m, -n) is optimal because the scheme greatly utilizes symmetry between the pairs, and the mean square error removal of the (-m, n), (m, -n) or (-m, -n) pairs can be obtained by calculating the mean square error removal of the (m, n) pairs, thereby reducing the number of times of mean square error removal of the calculated pairs. Referring to fig. 3, step S103 obtains an optimized rank pair set according to the removal of the mean square error, where step S103 specifically includes:
s301: setting a convergence level pairing group: (m, n), (-m, n), (m, -n) and (-m, -n).
Wherein, m and n are not equal to 0 at the same time, 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 cut-off orders set in the X, Y direction.
S302: based on an RCWA algorithm, acquiring convergence theoretical spectrum data corresponding to the convergence order pair set; traversing the convergence grade pair group in the convergence grade pair set, removing four convergence grade pairs in the convergence grade pair group in the convergence grade pair set, and forming a removal grade pair set by the rest convergence grade pairs in the convergence grade pair set; based on an RCWA algorithm, obtaining removal theoretical spectrum data corresponding to the removal level pair set; and obtaining the removal mean square error of each convergence order pair in the convergence order pair group according to the convergence theoretical spectrum data and the removal theoretical spectrum data.
In step S302 of this embodiment, taking any convergence-level point (i.e. a value of m or n) in the X or Y direction as a starting point, sequentially traversing other convergence-level points in the X or Y direction in a preset traversing direction; the preset traversing direction can be traversing from the largest convergent orders Nx and Ny to the negative direction, or traversing from the smallest convergent orders Nx and Ny to the positive direction, or traversing 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 can be sequentially extracted from Nx to-Nx with Nx as a starting point; the convergence order m in the X direction can be sequentially extracted from-Nx to Nx by taking-Nx as a starting point; or sequentially extracting convergence orders m in the X direction from 0 to Nx and from-Nx to 0 with 0 as a starting point. Specifically, the convergence level pairs (m, n) are traversed in four quadrants corresponding to the levels m and n in the X, Y direction at the same time, and the traversing direction can sequentially traverse other convergence level pairs on all quadrants in a preset traversing direction by taking any convergence level pair of any quadrant as a starting point; for example: all convergence level pairs can be traversed by taking (Nx, 0) of the first quadrant as a starting point and sequentially passing through the second quadrant, the third quadrant and the fourth quadrant.
It should be noted that, the above-mentioned convergence level pair group is defined by excluding the (0, 0) level pair, and the (0, 0) level pair is not encountered during traversal, and the mean square error of the (0, 0) level pair is not required 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, the convergence order m in the X direction is sequentially extracted from 0 to Nx, and the convergence order n in the Y direction is sequentially extracted from 0 to Ny.
And obtaining the removal mean square error corresponding to the convergence grade pair (-m, n), (m-n) and (-m-n) according to the same removal mean square error of each convergence grade pair in the convergence grade pair group. In this embodiment, the scheme of simultaneously removing four pairs of the orders (m, n), (-m, n), (m, -n) and (-m, -n) to calculate the mean square error of the pairs of the orders (m, n) is optimal, because the scheme greatly utilizes symmetry between the pairs of the orders, can narrow the traversing range of m and n, for example, the X-direction order m traverses from 0 to Nx, the Y-direction order n traverses from 0 to Ny, and since the mean square error of the four pairs of the orders (m, n), (-m, n), (m, -n) and (-m, -n) is the same, the mean square error of the order (m, n) is calculated, thereby reducing the number of times of calculating the mean square error of the order pair of the order, and improving the calculation efficiency of theoretical spectrum data.
More specifically, the converging rank pair (-m, n) is a rank pair of which converging rank pair (m, n) is symmetrical about the y-axis, converging rank pair (m, -n) is a rank pair of which converging rank pair (m, n) is symmetrical about the x-axis, converging rank pair (-m, -n) is a rank pair of which converging rank pair (m, n) is symmetrical about the rank pair (0, 0); and the rank pair (0, 0) does not remove the mean square error because it is necessary in the process of calculating theoretical spectral data. When one of the convergence levels m or n is 0, 2 repeated convergence level pairs will occur, in which case only the mean square error removal of 2 non-repeated convergence level pairs in the convergence level pair group need be calculated.
More specifically, when neither of the m and n is 0, removing the converging level pair group (m, n), (-m, n), (m, -n), (-m, -n) from the converging 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), the mean square error removal of (0, n) and (0, -n) convergent order pairs only needs to be calculated, and convergent order pair groups (0, n), (0, -n) are removed from the convergent order pair set to form a removal order 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) the mean square error removal of the (m, 0) and (-m, 0) converging order pairs only needs to be calculated, and the converging order pair group (m, 0), (-m, 0) is removed from the converging order pair set to form a removing order 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 traversal range, so as to form L removal level pair sets; based on an RCWA algorithm, sequentially acquiring L pieces of theoretical spectral data for removal; obtaining the removal mean square error of each convergence order pair in the convergence order pair group according to the convergence theoretical spectrum data and each removal theoretical spectrum data; wherein, L is (nx+1) (Ny+1) -1. Specifically, the convergence order pairs in the convergence order pair group removed in the calculation are complemented to the original convergence order pair set, and then the calculation of the next order pair is performed, so that the convergence order pair sets used in calculating each removal of the mean square error are the same.
More specifically, the removal of the mean square error for a converging rank pair may measure the importance of the converging rank pair, the greater the removal of the mean square error, the greater the importance of the converging rank pair. If only one convergence order pair is removed when the mean square error is calculated and the symmetry of the convergence order pair is not utilized, then the X-direction truncated order is Nx, the Y-direction truncated order is Ny, the number of convergence order pairs included in the set of order pairs is (2nx+1) (2ny+1), and since the convergence order pair (0, 0) does not remove the mean square error, the number of mean square error removal times for each convergence order pair is calculated to be (2nx+1) (2ny+1) -1. However, in this embodiment, the symmetry of the convergence order pair is utilized, so that the calculation amount can be reduced, and the calculation efficiency of the theoretical spectrum data can be improved. Specifically, the mean square error removal of the convergence order pair (m, n) is calculated with the four pairs of convergence order pairs (m, n), (-m, n), (m, -n) and (-m, -n) removed, and since the mean square error removal calculation method of the four pairs of convergence order pairs is the same, the mean square error removal of the four pairs of convergence order pairs (m, n), (-m, n), (m, -n) and (-m, -n) is the same, and therefore the number of convergence order pairs to be calculated is (nx+1) (ny+1) -1.
More specifically, for the convergence order pair (m, n), (-m, n), (m, -n) and (-m, -n) are removed from the convergence order pair set, then the rest convergence order pair set is used for carrying out Fourier expansion on different optical characteristic parameters and calculating removal theoretical spectrum data by using RCWA algorithm, then the mean square error of theoretical spectrum data of the original convergence order pair set is calculated, namely the removal mean square error of the order pair (m, n), then the removal mean square error of the next convergence order pair (m, n), (-m, n), (m, -n) and (-m, -n) is the same according to the removal mean square error of the convergence order pair (m, n), (m, -n) and (-m, -n), the removal mean square error of the corresponding convergence order pair (-m, -n) is obtained, after calculation is finished, the convergence order pair removed in the calculation process is carried out, the next convergence order pair removal mean square error is carried out, and the whole calculation process is completed, and then all the mean square error is removed.
S303: and comparing the mean square error removal with a first threshold value, and filtering all convergence grade pairs corresponding to the mean square error removal smaller than the first threshold value to form an optimization grade pair set.
In step S303 of the present embodiment, the hardware device determines a first threshold MSE y1 Filtering out a mean square error less than a first threshold MSE y1 Corresponding convergence level pairs, the remaining set of convergence level pairs being formed as a set of optimization level pairs. At this time, the mean square error of the theoretical spectrum data and the convergent spectrum data corresponding to the optimization order pair set is equal to the first threshold MSE y1 Is the same magnitude. The number of the order pairs of the optimized order pair set is smaller than that of the original convergence order pair set, so that the calculation amount can be reduced and the calculation efficiency can be improved on the premise of keeping the magnitude of the mean square error MSE.
More specifically, a first threshold MSE y1 The threshold value is determined according to the hardware condition of the OCD measuring device, and the value range is 1e-7 to 1. Preferably, the first threshold MSE y1 And a second threshold MSE y2 The values of (2) are the same.
S104: based on the RCWA algorithm, theoretical spectrum data corresponding to the optimization level pair set is obtained.
In this 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 maxwell's equations, the electric field of the incident region is solved by using the continuous condition of the electromagnetic field, so as to obtain the reflection coefficient of the sample, each wavelength point is traversed, and the reflection coefficient of the sample corresponding to the wavelength point is calculated by using the RCWA algorithm, so as to obtain the theoretical spectrum data of the sample.
According to another specific embodiment of the present invention, there is provided a method for optimizing theoretical spectral data, the method comprising:
s101': a sample having a periodic structure in both the X-direction and the Y-direction is provided. Referring to fig. 4, fig. 4 provides a block diagram of a sample model, where the lowest layer is a substrate, on which is a thin film layer, and on which is a Y-direction grating, and on top of which is an X-direction grating.
S102': the first-order threshold Nxr in the X direction and the second-order threshold Nyr in the Y direction are set to 11, and a reference-order pair set is generated based on the combination of the first-order threshold Nxr and the second-order threshold Nyr in the Y direction, and it is known that the reference-order pair set is a set of 11×11, and the Nx and Ny corresponding to the convergence-order pair set obtained after the convergence analysis are assumed to be 5, and the convergence-order pair set distribution diagram is shown in fig. 5. Wherein, the horizontal axis coordinate represents the convergence order m in the X direction, the vertical axis coordinate represents the convergence order n in the Y direction, each square block represents one convergence order pair (m, n), the number of the square blocks is the number of the convergence order pairs contained in the convergence order pair set, and 121 square blocks can be seen.
S103': calculating the corresponding mean square error of each convergence order pair, the calculation results being shown in the block of FIG. 5, according to a first threshold MSE y1 The setting cases of (a) are discussed:
if a first threshold MSE is set y1 At 0.01, as shown in FIG. 6, a white square indicates that the mean square error removed is less than the first threshold MSE y1 And the filtered out converging level pairs, the grey squares represent the remaining level pairs. The set of gray squares in fig. 6 represents the optimized convergence level pair set, i.e., the optimized level pair set. As shown in fig. 6, the number of gray squares is 93, and the original number of squares is 121, that is, the number of convergence order pairs contained in the optimization order pair set is 23% less than the number of convergence order pairs contained in the convergence order pair set, so that the efficiency of calculating theoretical spectrum data by the RCWA algorithm is improved. Obtained using the RCWA algorithm, the mean square error mse= 0.0287379 between the theoretical spectral data calculated with the optimized optimization order pair set and the converging theoretical spectral data calculated with the converging order pair set, which demonstrates the order of magnitude of the mean square error MSE of the theoretical spectral data calculated with the optimized optimization order pair set and the converging theoretical spectral data calculated with the converging order pair set and the first threshold MSE y1 As such, it has proven feasible to aggregate with optimized optimization levels.
If a first threshold MSE is set y1 1, as shown in FIG. 7, the white square indicates that the mean square error is less than the first threshold MSE y1 And the filtered out pairs of converging orders, the grey squares represent the pairs of orders that have not been removed. The set of gray squares in fig. 7 represents the optimized convergence level pair set, i.e., the optimized level pair set. As shown in FIG. 7, the number of gray squares is 45, the original number of squares is 121, i.e. the number of convergence order pairs contained in the optimization order pair set is 63% less than the number of convergence order pairs contained in the convergence order pair set, thereby improving the efficiency of the RCWA algorithm in calculating theoretical spectral dataThe rate. Using the RCWA algorithm, the mean square error mse= 1.21516 between the theoretical spectral data calculated with the optimized set of optimization order pairs and the converging theoretical spectral data calculated with the converging order pair, can also prove that the magnitude of the mean square error MSE of the theoretical spectral data corresponding with the optimized set of second optimization order pairs and the converging theoretical spectral data corresponding with the converging order pair is equal to the first threshold MSE y1 As such, it has proven feasible to aggregate with optimized optimization levels.
S104': based on the optimization order pair set, fourier series expansion is carried out on the dielectric function, the electric field and the magnetic field, and the RCWA algorithm is applied to calculate theoretical spectrum data.
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 morphological parameters of the sample model and theoretical spectrum data corresponding to the morphological parameters;
s106': obtaining measurement spectrum data of a measurement area corresponding to a sample to be measured;
s107': and determining the morphological parameters of the measurement region corresponding to the sample to be measured according to the measured spectrum data and the theoretical spectrum database.
The invention provides an optimization system of theoretical spectrum data based on the embodiment, which comprises: the system 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 X, Y direction; 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 convergence order pairs which are not (0, 0) and are axisymmetric or centrosymmetric in the X, Y direction as convergence order pair groups; traversing the convergence grade pair group in the convergence grade pair set based on an RCWA algorithm, and obtaining a removal mean square error of each convergence grade pair in the convergence grade pair group; comparing the mean square error removal with a first threshold value, and filtering all convergence level pairs corresponding to the mean square error removal smaller than the first threshold value to form an optimization level pair set; the calculation module is used for acquiring theoretical spectrum data corresponding to the optimization level pair set based on the RCWA algorithm.
The present invention also provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a method as described above.
The invention also provides a measuring method based on the embodiment, which comprises the following steps:
s1: establishing a theoretical spectrum database corresponding to the sample model by applying the optimization method of theoretical spectrum data; the theoretical spectrum database comprises morphological parameters of the sample model and theoretical spectrum data corresponding to the morphological parameters;
s2: obtaining measurement spectrum data of a measurement area corresponding to a sample to be measured;
s3: and determining the morphological parameters of the measurement region corresponding to the sample to be measured according to the measured spectrum data and the theoretical spectrum database.
The optimization method of the specific theoretical spectrum data is the same as the above, and therefore will be described again. It should be appreciated that any process or method description in a method, block diagram, or otherwise described herein 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 of the process, and that embodiments of the present invention include additional implementations in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the embodiments of the present invention.
It is to be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
Those of ordinary skill in the art will appreciate that all or a portion of the steps carried out in the method of the above-described embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, and where the program, when executed, includes one or a combination of the steps of the method embodiments.
In addition, each functional unit in the embodiments of the present invention may be integrated in one processing module, or each unit may exist alone physically, or two or more units may be integrated in one module. The integrated modules may be implemented in hardware or in software functional modules. The integrated modules may also be stored in a computer readable storage medium if implemented in the form of software functional modules and sold or used as a stand-alone product.
The above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, or the like.
Although embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives, and variations may be made in the above embodiments by those skilled in the art without departing from the spirit and principles of the invention. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (9)
1. A method of optimizing theoretical spectral data, the method comprising:
obtaining a sample model with a periodic structure in the X, Y direction;
acquiring a convergence order pair set of the sample model in the X, Y direction; the convergence order pair set is obtained by carrying out convergence analysis on different optical characteristic parameters;
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; traversing the convergence grade pair group in the convergence grade pair set based on an RCWA algorithm to obtain a removal mean square error of each convergence grade pair in the convergence grade pair group; comparing the mean square error removal with a first threshold value, and filtering all convergence level pairs corresponding to the mean square error removal smaller than the first threshold value to form an optimization level pair set; the value range of the first threshold value is 1e-7 to 1;
Based on an RCWA algorithm, acquiring theoretical spectrum data corresponding to the optimization level pair set;
the mean square error removing of each convergence level pair is to remove the current convergence level pair in the convergence level pair group or remove the mean square error between the theoretical spectrum data of the convergence level pair set before and after the current convergence level pair or any one or more convergence level pairs in the convergence level pair group.
2. The method of optimizing theoretical spectral data of claim 1, wherein the optical characteristic parameters include dielectric functions, electric fields, and magnetic fields.
3. The method of optimizing theoretical spectral data according to claim 1, wherein the set of converging order pairs that are not (0, 0) and are axisymmetric or centrosymmetric in the X, Y direction is a converging order pair group, comprising:
setting a convergence level pairing group: (m, n), (-m, n), (m, -n) and (-m, -n);
wherein, m and n are not equal to 0 at the same time, 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 cut-off orders set in the X, Y direction.
4. The method for optimizing theoretical spectral data according to claim 1, wherein traversing the set of convergence order pairs in the set of convergence order pairs based on the RCWA algorithm, obtaining a mean square error removal for each convergence order pair in the set of convergence order pairs, comprises:
Based on an RCWA algorithm, acquiring convergence theoretical spectrum data corresponding to the convergence order pair set;
traversing the convergence grade pair group in the convergence grade pair set, removing the current convergence grade pair in the convergence grade pair group or simultaneously removing the current convergence grade pair and any one or more convergence grade pairs in the convergence grade pair group, wherein the rest convergence grade pairs in the convergence grade pair set form a removal grade pair set;
based on an RCWA algorithm, obtaining removal theoretical spectrum data corresponding to the removal level pair set;
and obtaining the removal mean square error of each convergence order pair in the convergence order pair group according to the convergence theoretical spectrum data and the removal theoretical spectrum data.
5. The method according to claim 1, wherein when the current convergence order pair and any one or more other convergence order pairs in the convergence order pair group are removed at the same time, the removal mean square error of any one of the removed convergence order pairs is calculated to obtain the removal mean square error of all the removed convergence order pairs.
6. The method according to claim 1, wherein the convergence order pair removed in the calculation of the removal mean square error of the current convergence order pair is complemented to the convergence order pair set, and then the calculation of the removal mean square error of the next convergence order pair is performed.
7. An optimization system of theoretical spectral data, characterized in that it applies the method of any one of claims 1-6, said system comprising: the system 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 X, Y direction; 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 convergence order pairs which are not (0, 0) and are axisymmetric or centrosymmetric in the X, Y direction as convergence order pair groups; traversing the convergence grade pair group in the convergence grade pair set based on an RCWA algorithm, and obtaining a removal mean square error of each convergence grade pair in the convergence grade pair group; comparing the mean square error removal with a first threshold value, and filtering all convergence level pairs corresponding to the mean square error removal smaller than the first threshold value to form an optimization level pair set; the calculation module is used for acquiring theoretical spectrum data corresponding to the optimization level pair set based on the RCWA algorithm.
8. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any one of claims 1-6 when the computer program is executed.
9. A method of measurement, comprising:
-establishing a theoretical spectroscopic database corresponding to the sample model using the method according to any one of claims 1-6; the theoretical spectrum database comprises morphological parameters of the sample model and theoretical spectrum data corresponding to the morphological parameters;
obtaining measurement spectrum data of a measurement area corresponding to a sample to be measured;
and determining the morphological parameters of the measurement region corresponding to the sample to be measured according to the measured spectrum data and the theoretical spectrum database.
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| 一维亚波长光栅等效折射率描述光栅光谱特性的有效性研究;桑田;蔡托;刘晓春;蔡绍洪;;激光与光电子学进展;20111010(第10期);56-62 * |
| 严格耦合波分析建模算法及其在光学散射测量中的应用研究;马园;中国优秀硕士学位论文全文数据库，基础科学;20130715(第2013年第07期);1-58 * |
| 严格耦合波法模拟周期性材料的反射特性;贾玉歆;中国优秀硕士学位论文全文数据库，基础科学;20180215(第2018年第02期);1-51 * |
| 光栅耦合器的衍射场研究;吴少强;中国优秀硕士学位论文全文数据库，基础科学;20190515(第2019年第05期);1-93 * |
| 周期结构材料中的衍射电磁波的场模拟算法研究;刘博;中国优秀硕士学位论文全文数据库，工程科技Ⅰ辑;20120415(第2012年第04期);1-75 * |
| 基于严格耦合波分析（RCWA）方法的相位光栅衍射特性研究;朱媛媛;中国优秀硕士学位论文全文数据库，基础科学;20210115(第2021年第01期);1-74 * |
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