A method and apparatus for optical property modeling

Abstract

The present invention provides a method and apparatus for optical property modeling. The method includes dividing all microstructures in the periodic space into a plurality of thin slices in the z direction; obtaining each closed region projected by the thin slices of the same layer on the xy plane of the periodic space, and representing the boundaries of the respective closed regions as respective polygons; obtaining the x coordinates and y coordinates of the vertices of each polygon to form an x coordinate set and a y coordinate set, respectively forming candidate integral subintervals from the coordinates in the x coordinate set and the y coordinate set, obtaining a target integral subinterval from the candidate integral subintervals, and calculating the Fourier coefficients of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium according to the target integral subinterval, and finally realizing the optical property modeling of the periodic medium. According to the target integral subinterval, the present invention calculates the theoretical spectral data, which improves the efficiency of obtaining the theoretical spectral data while ensuring the accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of semiconductor manufacturing, and in particular, to a method and apparatus for optical property modeling. Background Art

[0002] In the fields of semiconductor manufacturing inspection, optical proximity correction of optical mask plates, optical scattering simulation calculation, etc., it is necessary to expand the two-dimensional Fourier coefficients of the dielectric constant of periodic media. Taking the semiconductor inspection field as an example, with the development of the semiconductor manufacturing industry, the device structure becomes more and more complex as the feature size shrinks. In order to ensure the reliability and consistency of manufacturing, strict process control is required for the manufacturing process. Among them, measuring the manufactured device is one of the core issues in process control. Optical Critical Dimension (OCD) measurement has the advantages of fast speed, low cost, and non-destructiveness, and has important applications in semiconductor manufacturing process control.

[0003] Currently, the Fourier coefficients of the dielectric constant ε(x, y) of periodic media are generally obtained by uniformly dividing the periodic space into grids, then using the dielectric constant at the center of each grid as the dielectric constant of this interval, and then performing a two-dimensional fast Fourier transform. To calculate the Toeplitz matrix of the dielectric constant ε(x, y) of periodic media, the intervals in the corresponding directions are generally uniformly divided along the X direction and the Y direction in the periodic space, then using the dielectric constant at the midpoint of each interval as the dielectric constant of this interval, and then performing integrals in the y direction and the x direction respectively, and performing a one-dimensional fast Fourier transform to obtain. However, this method has the problem that it is difficult to balance the calculation accuracy and efficiency, that is, when the number of divided intervals is large, the accuracy is high, but the calculation is time-consuming, while when the number of divided intervals is small, the calculation efficiency is improved, but the accuracy is low. Summary of the Invention

[0004] The purpose of the present invention is to provide a method, apparatus, and storage medium for optical property modeling, which improve the efficiency and accuracy of obtaining theoretical spectral data, so as to efficiently and accurately complete optical property modeling.

[0005] To achieve the above object, in a first aspect, the present invention provides an optical property modeling method, which includes: dividing the microstructures in a periodic medium into N thin slices in the z direction, where N is a positive integer; obtaining each closed region of the projection of the thin slices of the same layer on the xy plane of the periodic space, and representing the boundaries of the respective closed regions as respective polygons; obtaining the x coordinates and y coordinates of the vertices of each polygon to form the x coordinate set and the y coordinate set; respectively arranging the coordinates in the x coordinate set and the y coordinate set in descending or ascending order; in the sorted x coordinate set and y coordinate set, any two adjacent coordinates form a candidate integration sub-interval, and a target integration sub-interval is obtained based on the candidate integration sub-interval. According to the obtained target integration sub-interval in the x direction and the target integration sub-interval in the y direction, the Fourier coefficients of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium are calculated, and rigorous coupled wave analysis is performed using the Fourier coefficients of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium to achieve the optical property modeling of the periodic medium.

[0006] The beneficial effect of the optical property modeling method provided by the present invention is that by dividing all the microstructures in the periodic space into several thin slices in the z direction, and the thickness of the thin slices only needs to satisfy the uniform distribution of the medium in the z direction for the light scattering characteristics, then obtaining the closed regions of the projection of each thin slice on the xy plane of the periodic space, representing the boundaries of the closed regions as respective polygons, and obtaining the x coordinate set and y coordinate set of the vertices of all the polygons, and by arranging the coordinates in the sorted coordinate set in descending or ascending order, any two adjacent coordinates form a candidate integration sub-interval, and the target integration sub-interval is obtained from the candidate integration sub-interval, which improves the efficiency, and according to the target integration sub-interval, accurate theoretical spectral data is calculated, while ensuring the accuracy, the efficiency of obtaining the theoretical spectral data is improved, so that the optical property modeling can be completed efficiently and accurately.

[0007] Optionally, obtaining the target integration sub-interval based on the candidate integration sub-interval includes: determining the uniformity of the candidate integration sub-interval; if the candidate integration sub-interval is uniform, then using the candidate integration sub-interval as the target integration sub-interval; if the candidate integration sub-interval is non-uniform, then dividing the candidate integration sub-interval into two or more target integration sub-intervals.

[0008] Optionally, determining the uniformity of the candidate integration sub-interval includes: obtaining the length of the candidate integration sub-interval; determining the distribution uniformity of the microstructures within the candidate integration sub-interval. If the length of the candidate integration sub-interval is not less than a preset step size and the distribution of the microstructures within the candidate integration sub-interval is non-uniform, then the candidate integration sub-interval is non-uniform; otherwise, the candidate integration sub-interval is uniform.

[0009] Optionally, determining the distribution uniformity of the microstructures within the candidate integration sub-interval includes: determining whether the microstructures exist in the candidate integration sub-interval: selecting at least one coordinate from the candidate integration sub-interval, and drawing a line perpendicular to the candidate integration sub-interval with the coordinate; obtaining the number of intersection points of the line and the polygon; when the number of intersection points is greater than or equal to 1, then the microstructures exist in the candidate integration sub-interval; otherwise, the microstructures do not exist in the candidate integration sub-interval. The beneficial effect is that by determining whether the microstructures exist in the candidate integration sub-interval, the division of the candidate integration sub-interval without microstructures is avoided, improving the processing efficiency.

[0010] Optionally, determining the distribution uniformity of the microstructures within the candidate integration sub-interval includes: when the microstructures exist in the candidate integration sub-interval in the x direction, taking the x coordinates g d and g d+1 of the two vertices of the candidate integration sub-interval respectively to obtain the first reference boundary line x = g d and the second reference boundary line x = g d+1 , where d is a natural number;

[0011] obtaining the number h of the first boundary intersection points formed by the intersection of the first reference boundary line x = g d and the polygon, and the number k of the second boundary intersection points formed by the intersection of the second reference boundary line x = g d+1 and the polygon;

[0012] when h is not equal to k, the distribution of the microstructures within the candidate integration sub-interval is non-uniform;

[0013] or, when h is equal to k, obtaining the y values of the first boundary intersection points and the second boundary intersection points, and arranging the y values of the first boundary intersection points and the second boundary intersection points in ascending or descending order. The first boundary intersection points are denoted as (g d , α1), (g d , α2),..., (g d , αh), and the second boundary intersection points are denoted as (g d+1 , β1), (g d+1 , β2),..., (g d+1 , βk); taking (g d, α1) and (g d+1 , β1) form a line segment, (g d , α2) and (g d+1 , β2) form a line segment, and so on, until (g d , αh) and (g d+1 , βk) form a line segment, and calculate the absolute values of the slopes of all line segments;

[0014] Select the maximum value from the absolute values of the slopes of all line segments. When the maximum value is greater than or equal to the first threshold, the distribution of the microstructures in the candidate integration sub-interval is uneven;

[0015] Otherwise, the distribution of the microstructures in the candidate integration sub-interval is uniform. The beneficial effect is that by obtaining the number h of the first boundary intersection points formed by the intersection of the first reference boundary line x = g d and the polygon, and the number k of the second boundary intersection points formed by the intersection of the second reference boundary line x = g d+1 and the polygon, determine whether the numbers of intersection points are equal. When the numbers of intersection points are not equal, determine that the candidate integration sub-interval is a non-uniform interval. When h is equal to k, connect the intersection points in sequence to form line segments, calculate the slopes of the line segments, take the maximum value of the absolute values of the slopes and compare it with the threshold. When the maximum value is greater than or equal to the set threshold, the candidate integration sub-interval is a non-uniform interval; otherwise, the candidate integration sub-interval is a uniform interval, so as to effectively and reliably obtain the candidate integration sub-intervals that need to be divided and the candidate integration sub-intervals that do not need to be divided.

[0016] Optionally, determining the uniformity of the distribution of the microstructures in the candidate integration sub-interval includes: when there are microstructures in the candidate integration sub-interval in the y direction, respectively use the y coordinates η q and η q +1 of the two vertices of the candidate integration sub-interval to obtain the third reference boundary line y = η q and the fourth reference boundary line y = η q +1 , where q is a natural number;

[0017] Obtain the number u of the third boundary intersection points formed by the intersection of the third reference boundary line y = η q and the polygon, and the number v of the fourth boundary intersection points formed by the intersection of the fourth reference boundary line y = η q +1 and the polygon;

[0018] When u is not equal to v, the distribution of the microstructures in the candidate integration sub-interval is uneven;

[0019] Or, when u is equal to v, obtain the y-values of the third boundary intersection point and the fourth boundary intersection point. The y-values of the third boundary intersection point and the fourth boundary intersection point are both arranged from small to large or from large to small. The third boundary intersection point is denoted as (σ1, η q ), (σ2, η q ), …, (σu, η q ), and the fourth boundary intersection point is denoted as (ω1, η q +1 ), (ω2, η q +1 ), …, (ωv, η q +1 ); form a line segment between (σ1, η q ) and (ω1, η q +1 ), form a line segment between (σ2, η q ) and (ω2, η q +1 ), and so on, until a line segment is formed between (σu, η q ) and (ωv, η q +1 ); calculate the reciprocals of the absolute values of the slopes of all line segments;

[0020] Select the maximum value from the reciprocals of the absolute values of the slopes of all line segments. When the maximum value is greater than or equal to the second threshold, the distribution of the microstructures in the candidate integration sub-interval is non-uniform;

[0021] Otherwise, the distribution of the microstructures in the candidate integration sub-interval is uniform. The beneficial effect is that the same method is also used for dividing the candidate integration sub-interval in the y direction, effectively and reliably obtaining the candidate integration sub-intervals that need to be divided and the candidate integration sub-intervals that do not need to be divided in the y direction, thereby improving the accuracy while avoiding dividing the uniform candidate integration sub-intervals with microstructures, thus ensuring the improvement of the optimization division efficiency and further improving the calculation efficiency.

[0022] In a second aspect, an embodiment of the present invention provides an optical property modeling device, which includes: a dividing unit for dividing the microstructure in the periodic medium into N layers of thin slices in the z direction; an obtaining module for obtaining each closed region projected by the thin slices of the same layer on the xy plane of the periodic space, and representing the boundaries of the closed regions as polygons; obtaining the x coordinates and y coordinates of the vertices of each polygon to form an x coordinate set and a y coordinate set; a processing unit connected to the obtaining module for respectively arranging the coordinates in the x coordinate set and the y coordinate set in descending or ascending order; in the arranged x coordinate set and y coordinate set, any two adjacent coordinates form a candidate integration sub-interval; the processing unit obtains a target integration sub-interval based on the candidate integration sub-interval. A calculating unit is connected to the processing unit and calculates the Fourier coefficients of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium based on the obtained target integration sub-interval in the x direction and the target integration sub-interval in the y direction; a modeling unit is connected to the calculating unit for performing rigorous coupled-wave analysis using the Fourier coefficients of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium to realize the optical property modeling of the periodic medium.

[0023] The beneficial effect of the optical property modeling device provided by the present invention is that: by optimizing the integration interval and the grid, the Fourier coefficients of the dielectric constant of the precise periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium are efficiently obtained, and then a high-precision theoretical spectrum is obtained with high efficiency, thereby improving the modeling efficiency and accuracy.

[0024] Optionally, when the processing unit obtains the target integration sub-interval based on the candidate integration sub-interval, it specifically is used for: determining the uniformity of the candidate integration sub-interval; if the candidate integration sub-interval is uniform, using the candidate integration sub-interval as the target integration sub-interval; if the candidate integration sub-interval is non-uniform, dividing the candidate integration sub-interval into two or more target integration sub-intervals. The beneficial effect is that: the uniformity of the candidate integration sub-interval is judged by this method, and the target integration sub-interval is obtained.

[0025] Optionally, when determining the uniformity of the candidate integration sub-interval, it specifically is used for: obtaining the length of the candidate integration sub-interval, determining the distribution uniformity of the microstructure in the candidate integration sub-interval, if the length of the candidate integration sub-interval is not less than a preset step length and the distribution of the microstructure in the candidate integration sub-interval is non-uniform, then the candidate integration sub-interval is non-uniform; otherwise, the candidate integration sub-interval is uniform. The beneficial effect is that: the uniformity of the candidate integration sub-interval is judged by this method, and the target integration sub-interval is obtained.

[0026] Optionally, when determining the uniformity of the distribution of the microstructures within the candidate integral sub-interval, it is specifically used for: determining whether there are microstructures in the candidate integral sub-interval: selecting at least one coordinate from the candidate integral sub-interval, and drawing a straight line perpendicular to the candidate integral sub-interval with the coordinate; obtaining the number of intersection points of the straight line and the polygon; when the number of intersection points is greater than or equal to 1, there are microstructures in the candidate integral sub-interval; otherwise, there are no microstructures in the candidate integral sub-interval. The beneficial effect is that by determining whether there are microstructures in the candidate integral sub-interval, the division of the candidate integral sub-intervals without microstructures is avoided, improving the processing efficiency and ensuring the calculation accuracy.

[0027] Optionally, when determining the uniformity of the distribution of the microstructures within the candidate integral sub-interval, it is specifically used for:

[0028] When there are microstructures in the candidate integral sub-interval in the x direction, the x coordinates g of the two vertices of the candidate integral sub-interval are respectively used d and g d+1 to obtain the first reference boundary line x = g d and the second reference boundary line x = g d+1 , where d is a natural number; obtaining the number h of the first boundary intersection points formed by the intersection of the first reference boundary line x = g d and the polygon, and the number k of the second boundary intersection points formed by the intersection of the second reference boundary line x = g d+1 and the polygon; when h is not equal to k, the distribution of the microstructures within the candidate integral sub-interval is uneven; or, when h is equal to k, obtaining the y values of the first boundary intersection point and the second boundary intersection point, and arranging the y values of the first boundary intersection point and the second boundary intersection point in ascending order or descending order, the first boundary intersection point is denoted as (g d , α1), (g d , α2),..., (g d , αh), and the second boundary intersection point is denoted as (g d+1 , β1), (g d+1 , β2),..., (g d+1 , βk); forming line segments from (g d , α1) and (g d+1 , β1), (g d , α2) and (g d+1 , β2) in sequence, and so on, until forming line segments from (g d , αh) and (g d+1 , βk), and calculating the absolute values of the slopes of all line segments.

[0029] Select the maximum value from the absolute values of the slopes of all line segments. When the maximum value is greater than or equal to the first threshold, the distribution of microstructures within the candidate integration sub-interval is non-uniform; otherwise, the distribution of microstructures within the candidate integration sub-interval is uniform. The beneficial effect is that: through the first reference boundary line x = g d The number h of the first boundary intersection points formed by intersecting with the polygon, and the second reference boundary line x = g d+1 The number k of the second boundary intersection points formed by intersecting with the polygon, determine whether the number of intersection points of the two straight lines is equal. When the number of intersection points is not equal, the candidate integration sub-interval is the non-uniform interval. When h is equal to k, connect the adjacent intersection points in sequence to form a line segment, calculate the slope of the line segment, take the maximum value of the absolute value of the slope and compare it with the threshold. When the maximum value is greater than or equal to the set threshold, the candidate integration sub-interval is the non-uniform interval; otherwise, the candidate integration sub-interval is the uniform interval, so as to effectively and reliably obtain the candidate integration sub-intervals that need to be divided and the candidate integration sub-intervals that do not need to be divided in the x direction.

[0030] Optionally, when determining the uniformity of the distribution of microstructures within the candidate integration sub-interval, it is specifically used for:

[0031] When there are microstructures in the candidate integration sub-interval in the y direction, respectively use the y coordinates η q and η q +1 of the two vertices of the candidate integration sub-interval to obtain the third reference boundary line y = η q and the fourth reference boundary line y = η q +1 , where q is a natural number;

[0032] Obtain the number u of the third boundary intersection points formed by the third reference boundary line y = η q intersecting with the polygon, and the number v of the fourth boundary intersection points formed by the fourth reference boundary line y = η q +1 intersecting with the polygon;

[0033] When u is not equal to v, the distribution of microstructures within the candidate integration sub-interval is non-uniform;

[0034] Or, when u is equal to v, obtain the y values of the third boundary intersection point and the fourth boundary intersection point. The y values of the third boundary intersection point and the fourth boundary intersection point are arranged from small to large or from large to small. The third boundary intersection point is denoted as (σ1, η q ), (σ2, η q ), …, (σu, η q ), and the fourth boundary intersection point is denoted as (ω1, η q +1 ), (ω2, η q +1 ), …, (ωv, η q +1 ); Denote (σ1, ηq ) forms a line segment with (ω1, η q +1 ), (σ2, η q ) forms a line segment with (ω2, η q +1 ), and so on, until (σu, η q ) forms a line segment with (ωv, η q +1 ), and calculate the reciprocal of the absolute value of the slope of all line segments;

[0035] Select the maximum value from the reciprocals of the absolute values of the slopes of all line segments. When the maximum value is greater than or equal to the second threshold, the distribution of the microstructures in the candidate integration sub-interval is non-uniform;

[0036] Otherwise, the distribution of the microstructures in the candidate integration sub-interval is uniform. The beneficial effect is that the same method is also used for dividing the candidate integration sub-intervals in the y direction, and the candidate integration sub-intervals that need to be divided and those that do not need to be divided can be effectively and reliably obtained in the y direction, thereby improving the accuracy while avoiding dividing the uniform candidate integration sub-intervals with microstructures, thus improving the efficiency of optimizing the divided intervals and further improving the calculation efficiency. Description of the Drawings

[0037] Figure 1 It is a schematic diagram of the uniformly divided grid in the periodic space provided by the prior art;

[0038] Figure 2 It is a schematic diagram of the uniform division of the integration interval (-p x / 2, p x / 2) in the x direction provided by the prior art;

[0039] Figure 3 It is a flowchart of the method for optical property modeling disclosed by the present invention;

[0040] Figure 4 It is a top view of the periodic space with multiple polygons obtained by projecting any thin slice in the xy plane in the z direction, disclosed by the present invention;

[0041] Figure 5 It is a flowchart of a method for determining the uniformity of any candidate integration sub-interval disclosed by the present invention;

[0042] Figure 6 It is a flowchart of the method for determining whether there are microstructures in the candidate integration sub-interval disclosed by the present invention;

[0043] Figure 7 It is a flowchart of the method for determining whether the distribution of microstructures in the candidate integration sub-interval in the x direction is uniform, disclosed by the present invention;

[0044] Figure 8Schematic diagram of connecting intersecting coordinate points into line segments disclosed by the present invention;

[0045] Figure 9 Schematic diagram of obtaining candidate integral subintervals in the x - direction according to the x - coordinate values of all vertices of a polygon;

[0046] Figure 10 Schematic diagram of target integral subintervals after dividing candidate integral subintervals in the x - direction;

[0047] Figure 11 Shows a side view of a frustum - shaped microstructure;

[0048] Figure 12 Top view of a thin slice after stratifying the microstructure;

[0049] Figure 13 Schematic diagram of the structure of the optical property modeling device disclosed by the present invention. Detailed implementation manners

[0050] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts belong to the scope of protection of the present invention. Unless otherwise defined, the technical terms or scientific terms used herein shall have the ordinary meanings understood by those of ordinary skill in the art in the field to which the present invention pertains. The words such as "including" used herein mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects.

[0051] Optical Critical Dimension (OCD) measurement technology is a modeling - based method. This measurement technology has two key technical supports, namely forward optical property modeling and reverse geometric parameter extraction. Among many forward optical property modeling methods, the Rigorous Coupled - Wave Analysis (RCWA) theory is widely used in the optical property modeling of periodic media due to its high modeling accuracy and wide application scope. Currently, referring to Figure 1 as shown, in order to obtain the Fourier coefficient ε mn of the dielectric coefficient of a periodic medium, generally, the periodic space is divided into grids, and then the dielectric coefficient at the center of each grid is used as the dielectric coefficient of the grid, and then two - dimensional fast Fourier transform is performed to obtain it. On the other hand, referring to Figure 2 as shown, in the x - direction, for the periodic interval (-p x / 2, p xA uniform division of (-p / 2, p / 2) is then performed, and the dielectric constant at the midpoint of each interval is used as the dielectric constant of that interval. Integration is carried out in the y-direction, and then a one-dimensional fast Fourier transform is performed to obtain the Toeplitz matrix of the dielectric constant ε(x, y) in the x-direction. mn, jl. Similarly, for the periodic interval (-p y / 2, p y / 2) in the y-direction, a uniform division is performed, and the dielectric constant at the midpoint of each interval is used as the dielectric constant of that interval. Integration is carried out in the x-direction, and finally a one-dimensional fast Fourier transform is performed to obtain the Toeplitz matrix of ε(x, y) in the y-direction. mn, jl. However, this method has the problem of being difficult to balance calculation accuracy and calculation efficiency, that is, when the number of divided intervals is large, the accuracy is high, but the calculation is time-consuming, and when the number of divided intervals is small, the calculation efficiency is improved, but the accuracy is low.

[0052] In view of the existing problems, an embodiment of the present invention provides a method for optical property modeling. Referring to Figure 3 as shown, the method includes:

[0053] S301: Divide the microstructures in the periodic medium into N thin slices in the z-direction, where N is a positive integer.

[0054] In this step, all the microstructures in the periodic space are divided into N thin slices in the z-direction. The thickness of each thin slice only needs to satisfy the uniform distribution of the medium in the z-direction for the light scattering characteristics, so that the light scattering effect of the entire microstructure can be regarded as the light scattering effects of several uniformly distributed thin slices stacked together in the z-direction.

[0055] S302: Obtain the closed regions of the projections of the thin slices of the same layer on the xy plane of the periodic space, and represent the boundaries of the closed regions as polygons; then obtain the x-coordinates and y-coordinates of the vertices of each polygon to form the x-coordinate set and the y-coordinate set.

[0056] In this step, in order to ensure that the graphs formed by the sides in each closed region are all polygons, geometric figures with less than three sides are taken as polygons by taking points at a preset interval along the sides, ensuring the point-taking analysis of all figures and further improving the accuracy of the calculated theoretical spectral data. Among them, the size of the preset interval is determined according to the shape and size of the microstructures.

[0057] In addition, optionally, when projecting, the periodic space is also regarded as a polygon, and the periodic space takes values in the x-direction from -p x / 2 to p x / 2, and takes values in the y-direction from -p y / 2 to p y / 2, p x 、py are the periodic lengths of the periodic space in the x - direction and y - direction respectively.

[0058] S303: Arrange the coordinates in the x - coordinate set and the y - coordinate set respectively in descending or ascending order; in the sorted x - coordinate set and y - coordinate set, any two adjacent coordinates form a candidate integration sub - interval.

[0059] In this step, exemplarily, combined with Figure 4 as shown in Figure 4 is a top - view of a periodic space with multiple polygons obtained by projecting any thin slice in the z - direction onto the xy - plane. Obtain the coordinates of all polygon vertices and construct the x - coordinate set of all vertices and the y - coordinate set of all vertices. Optionally, the x - coordinate set may also include the x - coordinates of the endpoints - p x / 2 and p x / 2 in the x - direction of the periodic space; the y - coordinate set may also include the y - coordinates of the endpoints - p y / 2 and p y / 2 in the y - direction of the periodic space. Optionally, during the process of constructing the x - coordinate set and the y - coordinate set of all vertices, duplicate x - coordinates and y - coordinates can also be removed, and sorting processing can be performed in descending or ascending order. Exemplarily, taking the ascending order as an example, arrange the x - coordinates in ascending order, {-p x / 2, g0, g1, g2,..., g b , p x / 2}, and - p x / 2 < g0 < g1 < … < < p x / 2 and arrange the y - coordinates in ascending order, {-p y / 2, η0, η1, η2, …, η c , p y / 2}, and - p y / 2 < η0 < η1 < … < η c < p y / 2, and combine any two adjacent x - coordinates into candidate integration sub - intervals in the x - direction (-p x / 2, g0), (g0, g1), (g1, g2),...., (g b-1 , g b ), (g b , p x / 2), and combine any two adjacent y - coordinates into candidate integration sub - intervals in the y - direction (-p y / 2, η0), (η0, η1), (η1, η2),...., (η c-1 , η c ), (ηc , p y / 2).

[0060] S304: Obtain the target integral sub - interval based on the candidate integral sub - interval.

[0061] S305: Based on the obtained target integral sub - interval in the x - direction and the target integral sub - interval in the y - direction, calculate the Fourier coefficients of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium.

[0062] In this step, calculate the Toeplitz matrix of the dielectric constant ε(x, y) of the periodic medium according to the target integral sub - interval in the x - direction and the target integral sub - interval in the y - direction mn, jl and mn, jl and the Fourier coefficients of the dielectric constant ε(x, y) of the periodic medium , and use the rigorous coupled - wave analysis algorithm to calculate the theoretical spectral data.

[0063] Specifically, the expansion of ε(x, y) is , where is the imaginary unit, m, n are integers. For the calculation formula is:

[0064]

[0065] For the Toeplitz matrix of ε(x, y) mn, jl and mn, jl the calculation formulas are respectively:

[0066] ;

[0067] ;

[0068] where i is the imaginary unit , is the period length in the x - direction, is the period length in the y - direction, , .

[0069] The orders m, j in the x - direction can take integers from - Nx to Nx, and the orders n, l in the y - direction can take values from - Ny to Ny. Nx is the truncation order in the x - direction, and Ny is the truncation order in the y - direction.

[0070] S306: Use the Fourier coefficients of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium to perform rigorous coupled - wave analysis to realize the optical property modeling of the periodic medium.

[0071] Compared with the prior art which divides all intervals in the periodic space, the method of this embodiment obtains initial candidate integral sub-intervals based on the projection of each layer of thin slices, and obtains target integral sub-intervals based on the candidate integral sub-intervals, so that the number of target integral sub-intervals obtained by this method is reduced, and it can also reflect the change of the microstructural geometric information in the periodic medium, improving the efficiency and accuracy. Moreover, according to the target integral sub-intervals, theoretical spectral data is calculated, which improves the efficiency of obtaining the theoretical spectral data while ensuring the accuracy, so that the optical property modeling can be completed efficiently and accurately.

[0072] In some embodiments, for any candidate integral sub-interval, if the candidate integral sub-interval is uniform, then the candidate integral sub-interval is used as the target integral sub-interval; if the candidate integral sub-interval is non-uniform, then the candidate integral sub-interval is divided into two or more target integral sub-intervals. Further, some embodiments of the present invention also disclose how to determine the uniformity of the candidate integral sub-intervals. Obtain the length of the candidate integral sub-interval, and the length of the candidate integral sub-interval is the absolute value of the difference between the coordinate values of the endpoints of the candidate integral sub-interval. If the length of the candidate integral sub-interval is greater than or equal to the preset step size and the microstructure distribution within the candidate integral sub-interval is non-uniform, then the candidate integral sub-interval is non-uniform. Otherwise, the candidate integral sub-interval is uniform. Among them, the value range of the preset step size is generally 0.1 - 5 nm.

[0073] Exemplarily, in combination with Figure 5 as shown Figure 5 is a flowchart of a method for determining the uniformity of any candidate integral sub-interval, and this method includes:

[0074] S501: Judge whether the interval length of the candidate integral sub-interval is less than the preset step size.

[0075] In this step, the candidate integral sub-interval includes the candidate integral sub-interval in the x direction and the candidate integral sub-interval in the y direction, and the candidate integral sub-interval in the x direction and the candidate integral sub-interval in the y direction are respectively compared with the preset step size. When the interval length of the integral sub-interval is less than the preset step size, go to S505, and when the interval length of the integral sub-interval is greater than or equal to the preset step size, go to S502.

[0076] S502: Judge whether there is a microstructure in the candidate integral sub-interval.

[0077] In this step, at least one coordinate is selected from the candidate integral sub-intervals, a straight line perpendicular to the candidate integral sub-interval is drawn with this coordinate, and the number of intersection points of this straight line and the polygon is obtained. When the number of intersection points is greater than or equal to 1, there is a microstructure in the candidate integral sub-interval, and S503 is entered. If the number of intersection points is 0, there is no microstructure in the candidate integral sub-interval, and S505 is entered.

[0078] Optionally, if the periodic space is also regarded as a polygon during the thin-film projection, when the number of intersection points mentioned in the above step is greater than or equal to 3, there is a microstructure in the candidate integral sub-interval. If the number of intersection points is 2, there is no microstructure in the candidate integral sub-interval.

[0079] S503: Determine whether the distribution of the microstructure is uniform.

[0080] In this step, when the microstructure is uniformly distributed within the candidate integral sub-interval, S505 is entered. When the microstructure is non-uniformly distributed within the candidate integral sub-interval, S504 is entered.

[0081] S504: The candidate integral sub-interval is a non-uniform interval.

[0082] S505: The candidate integral sub-interval is a uniform interval.

[0083] It should be noted that some embodiments also provide a method for determining whether there is a microstructure in the candidate integral sub-interval. Refer to Figure 6 as shown Figure 6 is a flowchart of the method for determining whether there is a microstructure in the candidate integral sub-interval. The method includes: taking the candidate integral sub-interval (g d-1， g d ) in the x direction as an example, selecting the points between this candidate integral sub-interval , g d-1 < <g d , drawing a straight line passing through and perpendicular to this candidate integral sub-interval with x = as the judgment boundary, and obtaining the number of intersection points of this judgment boundary and the polygon. Determine whether the number of intersection points is 0. In this step, if the number of intersection points is 0, there is no microstructure in this candidate integral sub-interval. If there are intersection points, there is a microstructure in this candidate integral sub-interval. Optionally, if the periodic space is also regarded as a polygon during the thin-film projection, in the above method for determining whether there is a microstructure in the candidate integral sub-interval, determine whether the number of intersection points is 2. If the number of intersection points is 2, there is no microstructure in the candidate integral sub-interval. If the number of intersection points is greater than 2, there is a microstructure in this candidate integral sub-interval.

[0084] In addition, some embodiments also provide a method for determining whether the distribution of microstructures within a candidate integration sub-interval is uniform. Refer to Figure 7 as shown. Figure 7 FIG. Figure 7 is a flowchart of a method for determining whether the distribution of microstructures within a candidate integration sub-interval in the x direction is uniform. Assume that the candidate integration sub-interval is (g d , g d+1 ). The method includes:

[0085] S701: Use the first straight line represented by x = g d and the second straight line represented by x = g d+1 as the first reference boundary line and the second reference boundary line of the candidate integration sub-interval respectively. Obtain the numbers of the first boundary intersection point and the second boundary intersection point formed by the intersection of the first reference boundary line and the second reference boundary line with the polygon, and denote them as h and k respectively.

[0086] S702: Determine whether h and k are equal.

[0087] In this step, if h is not equal to k, go to S707; if h is equal to k, go to S703.

[0088] S703: Obtain the y values of the first boundary intersection point and the second boundary intersection point, and arrange them in ascending order or descending order. Taking the ascending order as an example, denote them as (g d , α1), (g d , α2),..., (g d , αh), α1 < α2 < … < αh, (g d+1 , β1), (g d+1 , β2),..., (g d+1 , βk), β1 < β2 < … < βk, and go to S704.

[0089] In this step, that is, obtain the intersection points of the first reference boundary line and the second reference boundary line with the polygon within the candidate integration sub-interval.

[0090] S704: Connect the points (g d , α1) and (g d+1 , β1), the points (g d , α2) and (g d+1 , β2), …, the points (g d , αh) and (g d+1 , βk) to form line segments, calculate the absolute value of the slope of each line segment, and obtain the maximum value of the absolute values of the slopes of all line segments , and go to S705.

[0091] In this step, as shown in Figure 8 , the point (gd , (g, α1) and (g d+1 , β1) are connected to form a line segment, and the slope of this line segment is represented by the ratio of the difference in the y - coordinates to the difference in the x - coordinates. Then, calculate the point (g d , α2) and (g d+1 , β2), and connect to form the slope of the line segment.

[0092] S705: Determine whether it is less than a preset threshold.

[0093] When is less than the preset threshold, enter S706; when is greater than or equal to the preset threshold, enter S707.

[0094] S706: The distribution of the micro - structures in this candidate integration sub - interval is uniform.

[0095] S707: The distribution of the micro - structures in this candidate integration sub - interval is non - uniform.

[0096] It should be noted that when is less than the preset threshold, the distribution of the micro - structures in this candidate integration sub - interval is uniform, then this candidate integration sub - interval is uniform, and there is no need to divide this candidate integration sub - interval. If is greater than or equal to the preset threshold, the distribution of the micro - structures in this candidate integration sub - interval is non - uniform, then this candidate integration sub - interval is non - uniform, and it is necessary to divide this candidate integration sub - interval.

[0097] In addition, when judging whether the distribution of the micro - structures in the candidate integration sub - interval is uniform in the y - direction, is the maximum value of the reciprocals of the absolute values of all line segment slopes.

[0098] Specifically, represent two adjacent y - coordinates as η q and η q +1 respectively. Use the third straight line represented by y = η q and the fourth straight line represented by y = η q +1 as the third reference boundary line and the fourth reference boundary line of the candidate integration sub - interval respectively, where q is a natural number; obtain the number of intersection points u formed by the intersection of the third straight line and the polygon, and the number of intersection points v formed by the intersection of the fourth straight line and the polygon;

[0099] When u is not equal to v, the distribution of the micro - structures in the candidate integration sub - interval is non - uniform;

[0100] Or, when u is equal to v, obtain the coordinate set of the u intersection points {(σ1, η q ), (σ2, η q ), …, (σu, η q)}, and the coordinate set of the v intersection points {(ω1, η q +1 ), (ω2, η q +1 ), …, (ωv, η q +1 )}, where the u intersection point coordinates and the x-value coordinates of the v intersection points are arranged in descending or ascending order; form a line segment between (σ1, η q ) and (ω1, η q +1 ), form a line segment between (σ2, η q ) and (ω2, η q +1 ), and so on, until a line segment is formed between (σu, η q ) and (ωv, η q +1 ), and calculate the reciprocal of the absolute value of the slope of all line segments;

[0101] Select the maximum value from the reciprocals of the absolute values of the slopes of all line segments. When the maximum value is greater than or equal to the set threshold, the distribution of the microstructures in the candidate integration sub-interval is non-uniform; otherwise, the distribution of the microstructures in the candidate integration sub-interval is uniform.

[0102] Refer to Figure 9 and Figure 10 shown, Figure 9 is a schematic diagram of obtaining the candidate integration sub-interval in the x direction according to the x coordinate values of all vertices of the polygon, where the candidate integration sub-interval (-p x / 2, g0), (g 14 , p x / 2) is uniform, Figure 10 is a schematic diagram of the target integration sub-interval after dividing the candidate integration sub-interval in the x direction, that is, obtaining the target integration sub-interval (-p x / 2, t0), (t0, t1), (t1, t2), …, ( , ), ( , p x / 2) in the x direction. Compared with the prior art that uniformly divides the periodic space, the division method of the embodiment of the present invention avoids dividing the areas without microstructures and areas with microstructure distributions, thereby avoiding dividing all the integration sub-intervals, improving the accuracy while improving the processing efficiency. In addition, when the microstructures in the periodic medium are more complex, for the method of uniformly dividing the periodic space in the prior art, the time consumption for obtaining a high-precision theoretical spectrum increases sharply, while the method provided by the embodiment of the present invention can obtain a higher-precision theoretical spectrum and avoid the sharp increase in calculation time consumption.

[0103] According to the obtained target integration sub-interval, calculate

[0104]

[0105] Similarly, based on the target integral sub-intervals in the y direction, it can be efficiently and accurately calculated that .

[0106]

[0107] Based on the division of the integral intervals in the x and y directions, grids are obtained and denoted as c1, c2, …, c φ , with a total of φ.

[0108]

[0109] where i is the imaginary unit , is the period length in the x direction, is the period length in the y direction, m and j are the orders in the x direction, n and l are the orders in the y direction, , , t0, t1, t2, …, , , are respectively the x coordinates of the target integral sub-intervals in the x direction; , , s0, s1, s2, …, s e-1 , s e , are respectively the y coordinates of the target integral sub-intervals in the y direction, , , representing the x coordinate and y coordinate of the center point of the grid , representing the grid 's area, m, n, j, and l are integers, and e are natural numbers, and φ is a positive integer.

[0110] To verify the model established by the above method, a frustum is used for verification below. Figure 11 Fig. shows the side view of a frustum as the microstructure, Figure 12 Fig. is the top view of a thin slice after the microstructure is layered, Figure 12 The gray area in Fig. is the projection of the microstructure thin slice in the xy plane of the periodic space. The outermost dotted square represents the periodic space, and the vertical dotted lines show the division of the target integral sub-intervals. Assume Figure 11The parameters of the frustum shown have the following characteristics: TCD_x: 60 nm, frustum TCD_Y: 30 nm, frustum BCD_x: 30 nm, frustum BCD_Y: 50 nm, frustum height: 100 nm, number of layers: 10. After optical property modeling is performed according to the above method, the theoretical spectrum calculation results are compared in Table 1 below. The prior art evenly divides the integration interval, evenly dividing 256 intervals in both the X and Y directions, while the method of this application divides 3 target integration sub-intervals in the X and Y directions respectively. Thus, the computational amount of the Fourier coefficients of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium is greatly reduced, thereby improving the calculation efficiency of the theoretical spectrum. It takes 58 seconds for the prior art to obtain the theoretical spectrum, and it takes 46 seconds for this application to obtain the theoretical spectrum. At the same time, the accuracy of the theoretical spectrum obtained by the method of this application is improved by one order of magnitude compared with the accuracy of the theoretical spectrum obtained by the prior art. Thus, it can be seen that the method of this application obtains a theoretical spectrum with higher accuracy in less time, while improving the calculation efficiency and calculation accuracy of the theoretical spectrum.

[0111] Table 1

[0112]

[0113] In another embodiment disclosed in the present invention, an optical property modeling device is provided. Referring to Figure 13 as shown, the device includes: a dividing unit 1301 for dividing the microstructures in the periodic medium into N thin slices in the z direction, where N is a positive integer; an obtaining module 1302 connected to the dividing unit 1301 for obtaining each closed region projected by the thin slices of the same layer on the xy plane of the periodic space, and representing the boundaries of each closed region as each polygon; obtaining the x coordinates and y coordinates of each polygon vertex to form a set of x coordinates and a set of y coordinates; a processing unit 1303 connected to the obtaining module 1302 for respectively arranging the coordinates in the set of x coordinates and the set of y coordinates in ascending or descending order; in the sorted set of x coordinates and the set of y coordinates, any two adjacent coordinates respectively form a candidate integration sub-interval; the processing unit 1303 obtains a target integration sub-interval based on the candidate integration sub-interval; a calculating unit 1304 is connected to the processing unit 1303, and calculates the Fourier coefficients of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium according to the obtained target integration sub-interval in the x direction and the target integration sub-interval in the y direction; a modeling unit 1305 is connected to the calculating unit 1304 for performing rigorous coupled wave analysis using the Fourier coefficients of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium to realize optical property modeling of the periodic medium.

[0114] In this embodiment, by optimizing the integration interval and the grid, the Fourier coefficients of the periodic medium dielectric constant and the Toeplitz matrix of the periodic medium dielectric constant are efficiently obtained, thereby improving the modeling efficiency and accuracy.

[0115] Optionally, when the processing unit 1303 obtains the target integration sub-interval based on the candidate integration sub-interval, it is specifically configured to: determine the uniformity of the candidate integration sub-interval; if the candidate integration sub-interval is uniform, use the candidate integration sub-interval as the target integration sub-interval; if the candidate integration sub-interval is non-uniform, divide the candidate integration sub-interval into two or more target integration sub-intervals.

[0116] Optionally, determining the uniformity of the candidate integration sub-interval includes: obtaining the length of the candidate integration sub-interval, determining the distribution uniformity of the microstructures within the candidate integration sub-interval, if the length of the candidate integration sub-interval is not less than the preset step size and the distribution of the microstructures within the candidate integration sub-interval is non-uniform, then the candidate integration sub-interval is non-uniform; otherwise, the candidate integration sub-interval is uniform.

[0117] Optionally, when the processing unit 1303 determines the distribution uniformity of the microstructures within the candidate integration sub-interval, it includes: determining whether there are microstructures in the candidate integration sub-interval, selecting at least one coordinate from the candidate integration sub-interval, and drawing a straight line perpendicular to the candidate integration sub-interval direction with this coordinate; obtaining the number of intersection points of the straight line and the polygon; when the number of intersection points is greater than or equal to 1, then there are microstructures in the candidate integration sub-interval; otherwise, there are no microstructures in the candidate integration sub-interval.

[0118] When the processing unit 1303 determines whether the candidate integration sub-interval with microstructures in the x-direction is uniform, it includes: when there are microstructures in the candidate integration sub-interval in the x-direction, respectively using the x-coordinates g d and g d+1 to obtain the first reference boundary line x = g d and the second reference boundary line x = g d+1 , where d is a natural number, obtaining the number h of the first boundary intersection points formed by the intersection of the first reference boundary line x = g d and the polygon, and the number k of the second boundary intersection points formed by the intersection of the second reference boundary line x = g d+1 and the polygon;

[0119] When h is not equal to k, the distribution of the microstructures within the candidate integration sub-interval is non-uniform, or, when h is equal to k, obtaining the y-values of the first boundary intersection point and the second boundary intersection point, the y-values of the first boundary intersection point and the second boundary intersection point are arranged from small to large or from large to small, and the first boundary intersection point is denoted as (gd , α1), (g d , α2),..., (g d , αh), and the second boundary intersection points are denoted as (g d+1 , β1), (g d+1 , β2),..., (g d+1 , βk); form a line segment between (g d , α1) and (g d+1 , β1), form a line segment between (g d , α2) and (g d+1 , β2), and so on, until a line segment is formed between (g d , αh) and (g d+1 , βk), and calculate the absolute values of the slopes of all line segments; select the maximum value from the absolute values of the slopes of all line segments. When the maximum value is greater than or equal to the first threshold, the distribution of microstructures in the candidate integration sub-interval is non-uniform; otherwise, the candidate integration sub-interval is a uniform interval.

[0120] Optionally, when the processing unit 1303 determines whether a candidate integration sub-interval with microstructures in the y-direction is uniform, it includes: when there are microstructures in the candidate integration sub-interval in the y-direction, respectively use the y-coordinates η q and η q +1 of the two vertices of the candidate integration sub-interval to obtain the third reference boundary line y = η q and the fourth reference boundary line y = η q +1 , where q is a natural number, and q is a natural number; obtain the number u of the third boundary intersection points formed by the intersection of the third reference boundary line y = η q and the polygon, and the number v of the fourth boundary intersection points formed by the intersection of the fourth reference boundary line y = η q +1 and the polygon;

[0121] When u is not equal to v, the distribution of microstructures in the candidate integration sub-interval is non-uniform;

[0122] Or, when u is equal to v, obtain the y-values of the third boundary intersection points and the fourth boundary intersection points. The y-values of the third boundary intersection points and the fourth boundary intersection points are arranged from small to large or from large to small. The third boundary intersection points are denoted as (σ1, η q ), (σ2, η q ), …, (σu, η q ), and the fourth boundary intersection points are denoted as (ω1, η q +1 ), (ω2, η q +1 ), …, (ωv, η q +1 ); form a line segment between (σ1, η q ) and (ω1, η q +1 ), (σ2, ηq ) forms a line segment with (ω2, η q +1 ), and so on, until (σu, η q ) forms a line segment with (ωv, η q +1 ), and calculate the reciprocal of the absolute value of the slope of all line segments;

[0123] Select the maximum value from the reciprocals of the absolute values of the slopes of all line segments. When the maximum value is greater than or equal to the second threshold, the distribution of the microstructures in the candidate integration sub-interval is uneven;

[0124] Otherwise, the distribution of the microstructures in the candidate integration sub-interval is uniform.

[0125] In still another embodiment disclosed in the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the above method steps are implemented, and the above method is run by executing the computer program.

[0126] As described above, it is only the specific implementation manners of the embodiments of the present application, but the protection scope of the embodiments of the present application is not limited thereto. Any changes or substitutions within the technical scope disclosed in the embodiments of the present application should be covered within the protection scope of the embodiments of the present application. Therefore, the protection scope of the embodiments of the present application shall be subject to the protection scope of the claims.

Claims

1. An optical property modeling method, characterized in that including: dividing the microstructure in the periodic medium into N thin slices in the z direction, where N is a positive integer; obtaining each closed region of the projection of the thin slice of the same layer on the xy plane of the periodic space, and representing the boundaries of the respective closed regions as respective polygons; obtaining the x coordinates and y coordinates of the vertices of each polygon to form an x coordinate set and a y coordinate set; sorting the coordinates in the x coordinate set and the y coordinate set respectively in descending or ascending order; in the sorted x coordinate set and y coordinate set, any two adjacent coordinates respectively form a candidate integration subinterval; obtaining a target integration subinterval based on the candidate integration subinterval; calculating the Fourier coefficients of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium according to the obtained target integration subinterval in the x direction and the target integration subinterval in the y direction; performing rigorous coupled-wave analysis using the Fourier coefficients of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium to realize the optical characteristic modeling of the periodic medium; wherein, obtaining a target integration subinterval based on the candidate integration subinterval includes: determining the uniformity of the candidate integration subinterval; if the candidate integration subinterval is uniform, taking the candidate integration subinterval as the target integration subinterval; if the candidate integration subinterval is non-uniform, dividing the candidate integration subinterval into two or more target integration subintervals.

2. The method according to claim 1, characterized in that, The determining the uniformity of the candidate integration subinterval includes: obtaining the length of the candidate integration subinterval; determining the distribution uniformity of the microstructure within the candidate integration subinterval; if the length of the candidate integration subinterval is not less than a preset step size and the distribution of the microstructure within the candidate integration subinterval is non-uniform, then the candidate integration subinterval is non-uniform; otherwise, the candidate integration subinterval is uniform.

3. The method according to claim 2, wherein The determining the distribution uniformity of the microstructure within the candidate integration subinterval includes: judging whether the microstructure exists in the candidate integration subinterval: selecting at least one coordinate from the candidate integration subinterval, and drawing a line perpendicular to the candidate integration subinterval with the coordinate; obtaining the number of intersections of the line and the polygon; when the number of intersections is greater than or equal to 1, then the microstructure exists in the candidate integration subinterval; otherwise, the microstructure does not exist in the candidate integration subinterval.

4. The method according to claim 3, characterized in that, The determining the distribution uniformity of the microstructure within the candidate integration subinterval includes: When there are microstructures in the candidate integration sub-intervals in the x direction, the x coordinates g d and g d+1 of the two vertices of the candidate integration sub-intervals are used to obtain the first reference boundary line x = g d and the second reference boundary line x = g d+1 , where d is a natural number; Obtain the first reference boundary line \(x = g\) d The number \(h\) of the first boundary intersection points formed by intersecting with the polygon, and the second reference boundary line \(x = g\) d+1 The number \(k\) of the second boundary intersection points formed by intersecting with the polygon; when h is not equal to k, then the distribution of the microstructure within the candidate integration subinterval is non-uniform; Alternatively, when h is equal to k, obtain the y-values of the first boundary intersection point and the second boundary intersection point. The y-values of the first boundary intersection point and the second boundary intersection point are arranged from small to large or from large to small. The first boundary intersection point is denoted as (g d , α1), (g d , α2),..., (g d , αh), and the second boundary intersection point is denoted as (g d+1 , β1), (g d+1 , β2),..., (g d+1 , βk); form line segments by connecting (g d , α1) and (g d+1 , β1), (g d , α2) and (g d+1 , β2), and so on, until connecting (g d , αh) and (g d+1 , βk), and calculate the absolute values of the slopes of all line segments; selecting the maximum value from the absolute values of the slopes of all line segments, when the maximum value is greater than or equal to a first threshold, then the distribution of the microstructure within the candidate integration subinterval is non-uniform; otherwise, the distribution of the microstructure within the candidate integration subinterval is uniform.

5. The method according to claim 3 or 4, characterized in that, The determining the distribution uniformity of the microstructure within the candidate integration subinterval includes: When there are microstructures in the candidate integral sub-interval in the y direction, the y coordinates η q and η q +1 of the two vertices of the candidate integral sub-interval are respectively used to obtain the third reference boundary line y = η q and the fourth reference boundary line y = η q +1 , where q is a natural number; Obtain the third reference boundary line y = η q The number of third boundary intersection points u formed by intersecting with the polygon, and the fourth reference boundary line y = η q +1 The number of fourth boundary intersection points v formed by intersecting with the polygon; when u is not equal to v, then the distribution of the microstructure within the candidate integration subinterval is non-uniform; Or, when u is equal to v, obtain the y-values of the third boundary intersection point and the fourth boundary intersection point. The y-values of the third boundary intersection point and the fourth boundary intersection point are arranged from small to large or from large to small. The third boundary intersection point is denoted as (σ1, η q ), (σ2, η q ), …, (σu, η q ), and the fourth boundary intersection point is denoted as (ω1, η q +1 ), (ω2, η q +1 ), …, (ωv, η q +1 ); form a line segment between (σ1, η q ) and (ω1, η q +1 ), form a line segment between (σ2, η q ) and (ω2, η q +1 ), and so on, until a line segment is formed between (σu, η q ) and (ωv, η q +1 ); calculate the reciprocals of the absolute values of the slopes of all line segments; Select the maximum value from the reciprocals of the absolute values of the slopes of all line segments. When the maximum value is greater than or equal to the second threshold, the distribution of the microstructures in the candidate integration sub-interval is non-uniform; Otherwise, the distribution of the microstructures in the candidate integration sub-interval is uniform.

6. An optical property modeling device, characterized in that, The device includes: A dividing unit for dividing the microstructures in the periodic medium into N thin slices in the z direction, where N is a positive integer; An obtaining module connected to the dividing unit for obtaining the respective closed regions projected by the thin slices of the same layer on the xy plane of the periodic space, and representing the boundaries of the respective closed regions as respective polygons; obtaining the x coordinates and y coordinates of the vertices of each polygon to form an x coordinate set and a y coordinate set; A processing unit connected to the obtaining module for respectively arranging the coordinates in the x coordinate set and the y coordinate set in descending or ascending order; in the sorted x coordinate set and y coordinate set, any two adjacent coordinates respectively form a candidate integration sub-interval; The processing unit obtains a target integration sub-interval based on the candidate integration sub-interval; A calculating unit connected to the processing unit for calculating the Fourier coefficients of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium according to the obtained target integration sub-interval in the x direction and the target integration sub-interval in the y direction; A modeling unit connected to the calculating unit for performing rigorous coupled-wave analysis using the Fourier coefficients of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium to realize the optical property modeling of the periodic medium; Wherein, when the processing unit obtains the target integration sub-interval based on the candidate integration sub-interval, it specifically is used for: Determine the uniformity of the candidate integration sub-interval; If the candidate integration sub-interval is uniform, then use this candidate integration sub-interval as the target integration sub-interval; if the candidate integration sub-interval is non-uniform, then divide this candidate integration sub-interval into two or more target integration sub-intervals.

7. The device according to claim 6, characterized in that, When determining the uniformity of the candidate integration sub-interval, it specifically is used for: Obtain the length of the candidate integration sub-interval; Determine the distribution uniformity of the microstructures in the candidate integration sub-interval; If the length of the candidate integration sub-interval is not less than the preset step size and the distribution of the microstructures in the candidate integration sub-interval is non-uniform, then this candidate integration sub-interval is non-uniform; otherwise, this candidate integration sub-interval is uniform.

8. The device according to claim 7, characterized in that, When determining the distribution uniformity of the microstructures in the candidate integration sub-interval, it specifically is used for: Judge whether there are the microstructures in the candidate integration sub-interval: Select at least one coordinate from the candidate integration sub-interval, and draw a straight line perpendicular to the candidate integration sub-interval with this coordinate; obtain the number of intersections of the straight line and the polygon; When the number of intersections is greater than or equal to 1, then there are microstructures in the candidate integration sub-interval; otherwise, there are no microstructures in the candidate integration sub-interval.

9. The device according to claim 8, characterized in that, When determining the distribution uniformity of the microstructures in the candidate integration sub-interval, it specifically is used for: When there are microstructures in the candidate integration sub-interval in the x direction, the x coordinates g of the two vertices of the candidate integration sub-interval are respectively used d and g d+1 to obtain the first reference boundary line x = g d and the second reference boundary line x = g d+1 , where d is a natural number; Obtain the first reference boundary line \(x = g\) d The number \(h\) of the first boundary intersection points formed by intersecting with the polygon, and the second reference boundary line \(x = g\) d+1 The number \(k\) of the second boundary intersection points formed by intersecting with the polygon; When h is not equal to k, the distribution of the microstructures within the candidate integration sub-interval is non-uniform; Or, when h is equal to k, obtain the y-values of the first boundary intersection point and the second boundary intersection point. The y-values of the first boundary intersection point and the second boundary intersection point are both arranged from small to large or from large to small. The first boundary intersection point is denoted as (g d , α1), (g d , α2),..., (g d , αh), and the second boundary intersection point is denoted as (g d+1 , β1), (g d+1 , β2),..., (g d+1 , βk); form a line segment between (g d , α1) and (g d+1 , β1), form a line segment between (g d , α2) and (g d+1 , β2), and so on, until a line segment is formed between (g d , αh) and (g d+1 , βk), and calculate the absolute values of the slopes of all line segments; Select the maximum value from the absolute values of the slopes of all the line segments. When the maximum value is greater than or equal to the first threshold, the distribution of the microstructures within the candidate integration sub-interval is non-uniform; Otherwise, the distribution of the microstructures within the candidate integration sub-interval is uniform.

10. The device according to claim 8 or 9, characterized in that When determining the uniformity of the distribution of the microstructures within the candidate integration sub-interval, it is specifically used for: When there are microstructures in the candidate integral sub-interval in the y direction, the y coordinates η q and η q +1 of the two vertices of the candidate integral sub-interval are respectively used to obtain the third reference boundary line y = η q and the fourth reference boundary line y = η q +1 , where q is a natural number; Obtain the third reference boundary line y = η q The number u of third boundary intersection points formed by intersecting with the polygon, and the fourth reference boundary line y = η q +1 The number v of fourth boundary intersection points formed by intersecting with the polygon; When u is not equal to v, the distribution of the microstructures within the candidate integration sub-interval is non-uniform; Alternatively, when u is equal to v, obtain the y-values of the third boundary intersection point and the fourth boundary intersection point. The y-values of the third boundary intersection point and the fourth boundary intersection point are arranged from small to large or from large to small. Denote the third boundary intersection point as (σ1, η q ), (σ2, η q ), …, (σu, η q ), and denote the fourth boundary intersection point as (ω1, η q +1 ), (ω2, η q +1 ), …, (ωv, η q +1 ); form a line segment between (σ1, η q ) and (ω1, η q +1 ), form a line segment between (σ2, η q ) and (ω2, η q +1 ), and so on, until a line segment is formed between (σu, η q ) and (ωv, η q +1 ); calculate the reciprocals of the absolute values of the slopes of all line segments; Select the maximum value from the reciprocals of the absolute values of the slopes of all the line segments. When the maximum value is greater than or equal to the second threshold, the distribution of the microstructures within the candidate integration sub-interval is non-uniform; Otherwise, the distribution of the microstructures within the candidate integration sub-interval is uniform.

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