CN113343492B - Optimization method, system and optical measurement method of theoretical spectrum data - Google Patents
Optimization method, system and optical measurement method of theoretical spectrum data Download PDFInfo
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Abstract
The invention provides an optimization method, a system and an optical measurement method of theoretical spectrum data, wherein the optimization method comprises the steps of 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; establishing a rank pair inequality comprising at least one adjustable parameter, taking the rank pair inequality as a constraint condition, and extracting a first optimized rank pair set from a convergence rank pair set; based on an RCWA algorithm, acquiring a first mean square error corresponding to a level pair set in a first optimization level pair set; comparing the first mean square error with a preset first threshold value, and extracting a second optimization level pair set; based on the RCWA algorithm, theoretical spectrum data corresponding to the second optimization level pair set is obtained. According to the invention, the convergence rank pair set is optimized through the rank pair inequality, and the number of the rank pairs in the second optimization rank pair set is small, so that the calculated amount can be reduced, and the efficiency of calculating theoretical spectrum data is 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 and optical 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 and an optical 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;
Establishing a rank pair inequality comprising at least one adjustable parameter, wherein the rank pair inequality is used as a constraint condition of the convergence rank pair set, and extracting a first optimization rank pair set from the convergence rank pair set by taking the rank pair inequality as the constraint condition;
based on an RCWA algorithm, acquiring a first mean square error corresponding to a rank pair set in the first optimization rank pair set; comparing the first mean square error with a preset first threshold value, and extracting a grade pair set corresponding to one first mean square error smaller than the first threshold value as a second optimized grade pair set;
based on the RCWA algorithm, theoretical spectrum data corresponding to the second 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 establishing a rank pair inequality comprising at least one adjustable parameter comprises:
establishing a first ratio of the order in the X direction to the truncated order, obtaining a first square term according to the square of the first ratio, establishing a second ratio of the order in the Y direction to the truncated order, and obtaining a second square term according to the square of the second ratio;
The order pair inequality is established based on the first square term, a second flat Fang Xiang, and at least one of the adjustable parameters.
Further, the establishing the rank pair inequality according to the first square term, the second square term, and at least one of the adjustable parameters includes:
and obtaining a first power according to the first square term and a positive adjustable exponent, obtaining a second power according to the second square term and the adjustable exponent, and establishing the order pair inequality according to the first power, the second power and the adjustable real number, wherein the adjustable exponent and the adjustable real number are both the adjustable parameters.
Further, the extracting the first optimized rank pair set from the converged rank pair set with the rank pair inequality as a constraint condition includes:
setting an initial value, a step length and a final value of at least one adjustable parameter, and changing the value of the adjustable parameter according to the initial value, the step length and the final value;
and extracting a grade pair set meeting grade pair inequality to form a first optimized grade pair set.
Further, the extracting a set of order pairs satisfying the order pair inequality, forming a first set of optimized order pairs includes:
and extracting the grade pair set meeting the grade pair inequality and removing the repeated grade pair set to form a first optimized grade pair set.
Further, the order pair inequality is
Wherein m and N are each a level in a X, Y direction, nx and Ny are each a truncated level set in a X, Y direction, and-N x ≤m≤N x ,-N y ≤n≤N y ；
Wherein, the gamma and the eta are adjustable parameters, the gamma is a positive real number, and the eta is a real number ranging from 0 to 2.
Further, based on an RCWA algorithm, third theoretical spectrum data corresponding to a rank pair set in the first optimization rank pair set is obtained, and a first mean square error corresponding to the rank pair set in the first optimization rank pair set is obtained according to the first theoretical spectrum data corresponding to the reference rank pair set and the third theoretical spectrum data; and comparing the first mean square error with a preset first threshold value, and extracting a grade pair set corresponding to the first mean square error which is smaller than the first threshold value and the largest first mean square error as a second optimized grade pair set.
According to a second aspect of the present invention, there is provided an optical measurement method comprising:
establishing a theoretical spectrum database corresponding to the sample model according to the method; 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.
According to a third 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, a first optimization module and a second optimization 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 first optimization module is used for establishing a rank pair inequality which comprises at least one adjustable parameter and is used for being used as a constraint condition of the convergence rank pair set, taking the rank pair inequality as the constraint condition, and extracting a first optimization rank pair set from the convergence rank pair set; the second optimization module is used for acquiring a first mean square error corresponding to the first optimization order pair set based on an RCWA algorithm; comparing the first mean square error with a preset first threshold value, and extracting a grade pair set corresponding to one first mean square error smaller than the first threshold value as a second optimized grade pair set; the spectrum calculation module is used for acquiring theoretical spectrum data corresponding to the second optimization level pair set based on an RCWA algorithm.
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, the convergence grade pair set is optimized through the grade pair inequality, the grade pair inequality is used as a constraint condition, the first optimization grade pair set is extracted from the convergence grade pair set, then the RCWA algorithm is applied to the first optimization grade pair set to calculate the first mean square error of the spectrum corresponding to the first optimization grade pair set and the spectrum of the reference grade pair set, the grade pair set corresponding to the first mean square error smaller than the first threshold value is extracted to be the second optimization grade pair set, namely the optimized grade pair set, theoretical spectrum data are obtained according to the second optimization grade pair set, and the calculated amount can be effectively reduced and the efficiency of calculating the theoretical spectrum data is improved because the number of grade pairs in the second optimization grade pair set is smaller than that in the original convergence grade pair set.
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 a method of optimizing theoretical spectral data in accordance with the present invention for obtaining a set of second optimization order pairs;
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 graph of a second mean square error between first theoretical spectral data and second theoretical spectral data and X-direction and Y-direction cutoff orders in a theoretical spectral data optimization method implemented in accordance with the present invention;
FIG. 6 is a distribution diagram of the first optimized rank pairs of a theoretical spectroscopic data optimization method implemented in accordance with the present invention;
fig. 7 is a graph of a first mean square error and a rank versus inequality between first theoretical spectral data and third theoretical spectral data for an optimization method of theoretical spectral data implemented in accordance with 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 direction and the Y direction;
in this embodiment, the X direction and the Y direction are two directions perpendicular to each other; specifically, in a two-dimensional structure sample, the X direction and the Y direction may be set to two directions perpendicular to the plane of the two-dimensional structure sample; in the three-dimensional structure sample, the X-direction and the Y-direction may be set to two directions perpendicular to the cross section in the three-dimensional structure sample. 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 or 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 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, the liquid crystal display device comprises a liquid crystal display device,
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 preset 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 RCWA algorithm is applied to calculate the second mean square error MSE between the first theoretical spectral data obtained from the reference level pair set and the second theoretical spectral data obtained from the original level 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 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 the theoretical spectrum 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 Is set according to the hardware condition of the OCD measuring device, and the value range is 1e-7 to 1.
S103: establishing a rank pair inequality comprising at least one adjustable parameter, wherein the rank pair inequality is used as a constraint condition of the convergence rank pair set, and extracting a first optimization rank pair set from the convergence rank pair set by taking the rank pair inequality as the constraint condition;
in this embodiment, the establishing a rank pair inequality including at least one adjustable parameter includes: establishing a first ratio of the order in the X direction to the truncated order, obtaining a first square term according to the square of the first ratio, establishing a second ratio of the order in the Y direction to the truncated order, and obtaining a second square term according to the square of the second ratio; the order pair inequality is established based on the first square term, a second flat Fang Xiang, and at least one of the adjustable parameters.
Specifically, the first square term, the second square term, and at least one of the adjustable parameters establish the rank pair inequality comprising: and obtaining a first power according to the first square term and a positive adjustable exponent gamma, obtaining a second power according to the second square term and the adjustable exponent, and establishing the order pair inequality according to the first power, the second power and an adjustable real number eta, wherein the adjustable exponent gamma and the adjustable real number eta are both the adjustable parameters.
More specifically, the first ratio of the order m in the X direction to the truncated order Nx isThe square of said first ratio yields a first square term +.>According to said first square term->And a positive adjustable exponent gamma to a first power +.>The second ratio of the order n in the Y direction to the truncated order Ny is +.>The square of the second ratio obtains a second square term of +.>According to said second square item->And a positive adjustable index gamma to a second power
In this embodiment, the order pair inequality is
Wherein m and N are each a level in a X, Y direction, nx and Ny are each a truncated level set in a X, Y direction, and-N x ≤m≤N x ,-N y ≤n≤N y ；
Wherein, the gamma and eta are respectively adjustable parameters, gamma is positive real number, eta is real number, and eta is more than or equal to 0 and less than or equal to 2.
In the present embodiment, the rank pair inequality isThe deduction process is specifically as follows:
as a result of: -N x ≤m≤N x ,-N y ≤n≤N y
So that:
squaring to obtain:
in order to narrow the range of values of m, n, we perform γ (γ is a positive real number) to the power, to obtain:
so that:
in order to further reduce the value range of m and n, 2 on the right side of the inequality can be changed into an adjustable parameter eta (0 is more than or equal to eta is less than or equal to 2), so that the following is obtained:
in the prior art, according to the truncated level in the X direction and the truncated level in the Y direction, a convergence level pair set is obtained based on the combination of two pairs, i.e. step S102. The patent obtains the order pairs meeting the order pair inequality based on the order pair inequality, and forms an optimized order pair set. In the order pair inequality, nx is the cut-off order in the X direction. Ny is the cut-off order in the Y direction. m is the order of x direction, and the value range is-Nx to Nx. n is the order of y direction, and the value range is-Ny to Ny. Gamma, eta are adjustable parameters. The effect of this order pair inequality is that a series of order pairs (m, n) corresponding to a group of γ and η can be obtained from this order pair inequality, i.e. a set of order pairs is formed, since γ and η are adjustable, a plurality of sets of order pairs can be obtained, and then the plurality of sets of order pairs form a first set of optimized order pairs (which is a set of elements, i.e. a set of sets) of order pairs.
In this embodiment, the extracting the first optimized rank pair set from the converged rank pair set using the rank pair inequality as a constraint condition includes:
setting an initial value, a step length and a final value of at least one adjustable parameter, and changing the value of the adjustable parameter according to the initial value, the step length and the final value;
and extracting a grade pair set meeting grade pair inequality to form a first optimized grade pair set.
In this embodiment, changing the value of the adjustable parameter according to the initial value, the step length and the final value is specifically to sequentially change the value of the adjustable parameter η and/or γ in the order pair inequality from small to large, so as to obtain the order pair inequality; the changing mode of eta and/or gamma comprises the following steps:
setting the eta value as a fixed positive real number in 0 to 2, wherein the gamma is sequentially increased to a gamma final value from a gamma initial value by a gamma step length, and acquiring a corresponding order pair inequality group;
preferably, said η is 1;
preferably, the initial value of γ, the step length of γ, and the final value of γ are set according to the sample model, respectively;
more preferably, the initial value of γ is 0.1, the step size of γ is 0.1, and the final value of γ is 20; or alternatively
Setting the gamma value as a fixed positive real number, for example, 1, wherein eta is sequentially increased to eta final value from eta initial value by eta step length, and obtaining a corresponding order pair inequality group;
Preferably, the η initial value, the η step size and the η final value are each set according to the sample model;
more preferably, the initial value of η is 0.1, the step size of η is 0.1 and the final value of η is 2; or alternatively
Setting eta and gamma to respectively start from respective initial values, and sequentially increasing to respective final values by respective step sizes to obtain corresponding order pair inequality groups;
wherein, the initial value of gamma and the initial value of eta can be the same or different, the step length of gamma and the step length of eta can be the same or different, and the final value of gamma and the final value of eta can be the same or different;
preferably, the initial value of γ, the step length of γ, the final value of γ, the initial value of η, the step length of η and the final value of η are set according to the sample model respectively;
more preferably, the initial value of γ is 0.1, the step size of γ is 0.1, the final value of γ is 20, the initial value of η is 0.1, the step size of η is 0.1, and the final value of η is 2.
Specifically, according to the above level pair inequality, nx and Ny take truncated levels of convergence in the X direction and the Y direction, respectively, without loss of generality, for example: let η=1, but η may be other real numbers from 0 to 2 in special cases; starting from 0.1, increasing gamma with a step size of 0.1 until the trend of the set of the level pairs corresponding to the level pair inequality corresponding to gamma is gradually unchanged, wherein gamma is generally enough to 20, and can be larger in special cases; alternatively, γ=1 may be fixed, η may be gradually increased from small to small, and γ and η may be gradually increased from small to small, respectively, for the purpose of obtaining a series of step pair inequalities, thereby obtaining a series of step pair sets; as described above, each gamma, eta fixed value corresponds to a rank pair inequality, a rank pair set can be obtained according to a rank pair inequality, and a plurality of rank pair sets satisfying the rank pair inequality are extracted, namely, a first optimized rank pair set is formed.
In order to further reduce the amount of computation and improve the computation efficiency, in this embodiment, the extracting the set of order pairs satisfying the order pair inequality, and forming the first optimized set of order pairs includes:
and extracting the grade pair set meeting the grade pair inequality and removing the repeated grade pair set to form a first optimized grade pair set.
Specifically, the order pair sets obtained through some adjustable parameters gamma and/or eta are identical or repeated, so that the repeated order pair sets exist in the first optimized order pair set, the repeated order pair sets are removed through comparison, the non-repeated order pair sets are obtained, and the first optimized order pair set is obtained according to the removed repeated order pair sets.
S104: based on RCWA algorithm, obtaining a first mean square error MSE corresponding to the rank pair set in the first optimization rank pair set 1 The method comprises the steps of carrying out a first treatment on the surface of the The first mean square error MSE 1 With a preset first threshold MSE y1 Comparing, extracting less than the first threshold MSE y1 Is a first mean square error MSE 1 The corresponding level pair set is a second optimized level pair set;
Acquiring third theoretical spectrum data corresponding to a rank pair set in the first optimized rank pair set based on an RCWA algorithm, and acquiring a first mean square error MSE corresponding to the rank pair set in the first optimized rank pair set according to the first theoretical spectrum data corresponding to a reference rank pair set and the third theoretical spectrum data 1 。
In order to improve the calculation efficiency, in this embodiment, the first mean square error is compared with a preset first threshold MSE y1 Comparing, extracting less than the first threshold MSE y1 And the largest first mean square error MSE 1 The corresponding secondary pair set is a second optimized secondary pair set, and the number of secondary pairs included in the second optimized secondary pair set is minimum.
In this embodiment, the first mean square error MSE is sequentially obtained from the small number to the large number of the rank pairs of the rank pair set in the first optimized rank pair set 1 At this time, the first one smaller than the first threshold MSE is extracted y1 Is the first mean square error MSE of (2) 1 The corresponding level pair set (namely the largest first mean square error) is the second optimized level pair set, so that the process of traversing all level pair sets in the first optimized level pair set can be avoided, and the calculation efficiency is highest. Furthermore, if the first mean square error MSE is acquired sequentially from large to small 1 Then the last one smaller than said first threshold MSE is extracted y1 Is the first mean square error MSE of (2) 1 The corresponding set of rank pairs (i.e., the largest first mean square error) is the second optimized set of rank pairs, but its computational efficiency is not as lowTo a large computational height.
In this embodiment, as shown in fig. 3, the specific steps in step S104 include:
s401: acquiring third theoretical spectrum data corresponding to the grade pair set in the first optimized grade pair set based on an RCWA algorithm;
s402: sequentially acquiring a first mean square error MSE from small to large according to the first theoretical spectrum data and the third theoretical spectrum data and the number of the grade pairs of the grade pair set in the first optimized grade pair set 1 The first mean square error MSE is calculated 1 With a preset first threshold MSE y1 Comparing, extracting a first MSE less than the first threshold MSE y1 Is the first mean square error MSE of (2) 1 The corresponding set of level pairs is a second set of optimized level pairs.
Taking as an example that gamma and/or eta increase, the number of the corresponding first optimized rank pairs in the rank pair set is increased, so that the first mean square error MSE corresponding to the rank pair set 1 Is gradually reduced. Then compare the first mean square error MSE 1 With a first threshold MSE y1 Obtain a first MSE less than a first threshold value y1 Is the first mean square error MSE of (2) 1 The corresponding set of the order pairs is called a second optimized order pair set, and because the number of the order pairs in the second optimized order pair set is smaller than the number of the order pairs in the convergence order pair set in the prior art, the calculation amount can be effectively reduced, the efficiency of calculating theoretical spectrum data can be improved, and the method can meet the condition that the MSE is smaller than the first threshold value y1 Is not limited.
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.
S105: based on the RCWA algorithm, theoretical spectrum data corresponding to the second optimization level pair set is obtained.
In this embodiment, based on the RCWA algorithm, the dielectric function of the sample model medium, the electric field, and the fourier series expansion of the electromagnetic 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': setting a first-level sub-threshold Nxr in the X direction and a second-level sub-threshold Nyr in the Y direction to be 11, generating a reference level pair set based on combination of two pairs, knowing that the reference level pair set is a set of 11X 11, and acquiring first theoretical spectrum data corresponding to the reference level pair set based on an RCWA algorithm; gradually increasing the X-direction cutting-off orders Nx and Y-direction cutting-off orders Ny from 0*0 to corresponding order thresholds respectively to obtain corresponding original order pair sets, and obtaining second theoretical spectrum data corresponding to the original order pair sets based on an RCWA algorithm; and calculates a second mean square error MSE between the first theoretical spectral data of the reference level pair set and the second theoretical spectral data of the original level pair set 2 The method comprises the steps of carrying out a first treatment on the surface of the Determining a second threshold MSE from hardware y2 For 5, extract the first MSE less than the second threshold MSE y2 Is the second mean square error MSE of (2) 2 As can be seen from fig. 5, when Nx is 5 and Ny is 5, the corresponding original pair set is a convergence pair set, and is smaller than the second threshold MSE for the first time y2 A corresponding set of converging level pairs can be obtained, see in particular fig. 5.
S103': in order to inequalityExtracting a first optimization level pair set from the convergence level pair set as a constraint condition;
wherein m and N are each a level in a X, Y direction, nx and Ny are each a truncated level set in a X, Y direction, and-N x ≤m≤N x ,-N y ≤n≤N y ；
In this embodiment, γ is set to increase from 0.1 by a step size of 0.1 up to 20, where γ is 200 in total, so there are 200 pairs of pairs (together forming the first optimized pair set), but there are 9 pairs of pairs that are repeated and not repeated, and the 9 pairs of pairs are plotted as 9 pairs of pairs, as in fig. 6, the horizontal axis represents the m-direction of the order, the vertical axis represents the n-direction of the order, each block represents a pair of pairs, gray represents the converging pair satisfying the pair of pairs inequality, black represents the converging pair not satisfying the pair inequality, the set of all gray blocks is a pair of pairs, and the number of gray blocks is the number of pairs contained in the pair of pairs. By deduplication, 9 non-duplicate sets of rank pairs in fig. 6 were obtained, γ= 0.10,0.30,0.40,0.50,0.70,0.80,1.00,1.60, 11.50,9 non-duplicate sets of rank pairs, respectively, forming a first optimized set of rank pairs. Here, the "gamma" indicated in the figure is "γ".
S104': obtaining a first mean square error MSE between third theoretical spectral data corresponding to a first optimized level pair set (with 9 non-repeated level pair sets) and first theoretical spectral data of a reference level pair set in the upper graph 1 As shown in fig. 7, the horizontal axis represents γ.
Determining a first threshold MSE from hardware y1 5, the first is less than the first threshold MSE y1 In this example, the first optimized rank pair set corresponding to γ=0.5, i.e., the second optimized rank pair set; the second optimized set of pairs is shown in fig. 6 and 7, and the number of gray squares represents the number of pairs contained in the set of pairs, so the number of pairs corresponding to γ=0.5 is 61, and the number of converging pairs of the original 5*5 (Nx is 5 and ny is 5) is allThe number of blocks is 121 in total, and obviously the number of the grade pair sets corresponding to gamma=0.5 is smaller, so the grade pair set corresponding to gamma=0.5 is a second optimized grade pair set.
S105': and (3) based on the fact that the grade pair set corresponding to gamma=0.5 is a second optimized grade pair set, carrying out Fourier series expansion on the dielectric function, the electric field and the magnetic field, and calculating theoretical spectrum data by applying an RCWA algorithm.
The present invention provides an optical measurement method based on the above embodiment, including:
s106: establishing a theoretical spectrum database corresponding to the sample model according to the optimization method of the theoretical spectrum data; the theoretical spectrum database comprises morphological parameters of the sample model and theoretical spectrum data corresponding to the morphological parameters;
s107: obtaining measurement spectrum data of a measurement area corresponding to a sample to be measured;
s108: 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 device comprises an acquisition module, a convergence module, a first optimization module, a second optimization module and a spectrum 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 first optimization module is used for establishing a rank pair inequality which comprises at least one adjustable parameter and is used for being used as a constraint condition of the convergence rank pair set, taking the rank pair inequality as the constraint condition, and extracting a first optimization rank pair set from the convergence rank pair set; the second optimization module is used for acquiring a first mean square error corresponding to the first optimization order pair set based on an RCWA algorithm; the first mean square error is compared with a preset first threshold MSE y1 Comparing, extracting less than the first threshold MSE y1 The first mean square error corresponding rank pair set is a second optimized rank pair set; light sourceThe spectrum calculation module is used for calculating theoretical spectrum data corresponding to the second optimization level pair set based on an 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.
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 (10)
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;
establishing a rank pair inequality comprising at least one adjustable parameter, wherein the rank pair inequality is used as a constraint condition of the convergence rank pair set, and extracting a first optimization rank pair set from the convergence rank pair set by taking the rank pair inequality as the constraint condition;
based on an RCWA algorithm, acquiring a first mean square error corresponding to a rank pair set in the first optimization rank pair set; comparing the first mean square error with a preset first threshold value, and extracting a grade pair set corresponding to one first mean square error smaller than the first threshold value as a second optimized grade pair set;
based on the RCWA algorithm, theoretical spectrum data corresponding to the second optimization level pair set is obtained.
2. The method of optimizing theoretical spectroscopic data of claim 1, wherein the convergence order pair set is an order pair set obtained by performing convergence analysis on different optical characteristic parameters including a dielectric function, an electric field, and a magnetic field.
3. The method of optimizing theoretical spectral data of claim 1, wherein said establishing a rank-versus-inequality comprising at least one adjustable parameter comprises:
establishing a first ratio of the order in the X direction to the truncated order, obtaining a first square term according to the square of the first ratio, establishing a second ratio of the order in the Y direction to the truncated order, and obtaining a second square term according to the square of the second ratio;
the order pair inequality is established based on the first square term, a second flat Fang Xiang, and at least one of the adjustable parameters.
4. A method of optimizing theoretical spectral data according to claim 3, wherein said establishing said order pair inequality based on said first square term, second square term, and at least one of said adjustable parameters comprises:
and obtaining a first power according to the first square term and a positive adjustable exponent, obtaining a second power according to the second square term and the adjustable exponent, and establishing the order pair inequality according to the first power, the second power and the adjustable real number, wherein the adjustable exponent and the adjustable real number are both the adjustable parameters.
5. The method of optimizing theoretical spectral data of any of claims 1-4, wherein said extracting a first set of optimized rank pairs from said set of converging rank pairs, subject to a rank pair inequality, comprises:
Setting an initial value, a step length and a final value of at least one adjustable parameter, and changing the value of the adjustable parameter according to the initial value, the step length and the final value;
and extracting a grade pair set meeting grade pair inequality to form a first optimized grade pair set.
6. The method of claim 5, wherein the extracting a set of order pairs that satisfy the order pair inequality to form a first set of optimized order pairs comprises:
and extracting the grade pair set meeting the grade pair inequality and removing the repeated grade pair set to form a first optimized grade pair set.
7. The method of optimizing theoretical spectral data of claim 1, wherein the order pair inequality is
Wherein m and N are each a level in a X, Y direction, nx and Ny are each a truncated level set in a X, Y direction, and-N x ≤m≤N x ,-N y ≤n≤N y ；
Wherein, the gamma and the eta are adjustable parameters, the gamma is a positive real number, and the eta is a real number ranging from 0 to 2.
8. The optimization method of theoretical spectrum data according to claim 1, wherein third theoretical spectrum data corresponding to a level pair set in the first optimization level pair set is obtained based on an RCWA algorithm, and a first mean square error corresponding to the level pair set in the first optimization level pair set is obtained according to the first theoretical spectrum data corresponding to a reference level pair set and the third theoretical spectrum data; and comparing the first mean square error with a preset first threshold value, and extracting a grade pair set corresponding to the first mean square error which is smaller than the first threshold value and the largest first mean square error as a second optimized grade pair set.
9. An optical measurement method, comprising:
establishing a theoretical spectral database corresponding to the sample model according to the method of any one of claims 1-8; 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.
10. An optimization system of theoretical spectral data, characterized in that it applies the method of any one of claims 1-8, said system comprising: the device comprises an acquisition module, a convergence module, a first optimization module, a second optimization module and a spectrum 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 first optimization module is used for establishing a rank pair inequality which comprises at least one adjustable parameter and is used for being used as a constraint condition of the convergence rank pair set, taking the rank pair inequality as the constraint condition, and extracting a first optimization rank pair set from the convergence rank pair set; the second optimization module is used for acquiring a first mean square error corresponding to the first optimization order pair set based on an RCWA algorithm; comparing the first mean square error with a preset first threshold value, and extracting a grade pair set corresponding to one first mean square error smaller than the first threshold value as a second optimized grade pair set; the spectrum calculation module is used for acquiring theoretical spectrum data corresponding to the second optimization level pair set based on an RCWA algorithm.
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