Optical property modeling method and device

Abstract

The present invention discloses an optical property modeling method and device, which includes: dividing a microstructure in a periodic medium into N layers of thin slices in the z direction; performing the following processing for thin slices of the same layer of microstructure: obtaining each closed area of ​​the thin slice projected on the periodic space xy plane, and representing the boundaries of each closed area as each polygon; obtaining the x coordinate and y coordinate of each polygon vertex, and the line segment features of each polygon, dividing the periodic space according to the line segment features, and obtaining the integral sub-intervals divided in the x direction and the integral sub-intervals divided in the y direction; calculating the Fourier coefficients and Toeplitz matrix of the dielectric coefficient of the periodic medium based on the integral sub-intervals in the x and y directions, and performing strict coupled wave analysis to achieve optical property modeling of the periodic medium. The method optimizes the division method of the integral interval, and efficiently and accurately obtains the Fourier coefficients and Toeplitz matrix of the dielectric coefficient of the periodic medium.

Description

Technical Field

[0001] The present invention relates to the field of semiconductor manufacturing technology, and in particular to an optical property modeling method and device. Background Art

[0002] In the fields of semiconductor manufacturing inspection, optical proximity correction of photolithography masks, optical scattering simulation calculation, etc., it is necessary to expand the two-dimensional Fourier coefficients of the dielectric coefficients of periodic media. Taking the field of semiconductor inspection as an example, with the development of the semiconductor manufacturing industry, the device structure is becoming more and more complex as the feature size is reduced. In order to ensure the reliability and consistency of manufacturing, stricter process control is required for the manufacturing process. Measuring the manufactured devices is one of the core issues in process control.

[0003] Optical critical dimension measurement technology has the advantages of fast speed, low cost and non-destructiveness, and has important applications in advanced process control of semiconductor manufacturing. Optical critical dimension measurement technology is a model-based method, so fast and accurate modeling calculation is one of the core elements of optical critical dimension measurement.

[0004] Optical critical dimension measurement is supported by two key technologies, namely forward optical property modeling and reverse geometric parameter extraction. Among many forward optical property modeling methods, rigorous coupled wave analysis theory (RCWA) is widely used in the optical property modeling of periodic media due to its high modeling accuracy and wide applicability. In the process of rigorous coupled wave analysis, it is necessary to obtain the Fourier coefficients of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium.

[0005] In recent years, in order to ensure that semiconductor devices maintain excellent performance while the key dimensions continue to shrink, their structural design has gradually shifted from simple planar structures to complex three-dimensional structures. Three-dimensional structures mainly include multi-coatings, multi-patterns, and curved edge structures. The more complex the structure, the more prominent the contradiction between the computational efficiency and computational accuracy of optical property modeling, and the time required to obtain a high-precision theoretical spectrum using existing technologies has increased dramatically.

[0006] The Fourier coefficient solution method of the dielectric constant of the periodic medium provided in the prior art often divides the periodic space into grids uniformly, and then uses the dielectric constant of the center of each grid as the dielectric constant of the grid, and then performs a two-dimensional fast Fourier transform to obtain the Fourier coefficient of the dielectric constant. The Toeplitz matrix of the dielectric constant of the periodic medium is generally to uniformly divide the intervals in the corresponding directions along the X direction and the Y direction in the periodic space, and then uses the dielectric constant of the midpoint of each interval as the dielectric constant of the interval, and then integrates in the Y direction and the X direction respectively, and then performs a one-dimensional fast Fourier transform to obtain. The prior art has the following problems: if the periodic space is divided into more integral intervals, although the calculation accuracy can be improved, there is a problem of time-consuming calculation, which affects the efficiency of forward optical property modeling; and if the periodic space is divided into fewer integral intervals, although the calculation efficiency can be improved, there is a problem of low calculation accuracy, which affects the accuracy of forward optical property modeling. Summary of the invention

[0007] An embodiment of the present invention provides an optical property modeling method and device, which optimizes the method of dividing the integral interval based on the geometric information of the microstructure in the periodic medium, so as to efficiently obtain the accurate Fourier coefficients of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium.

[0008] In a first aspect, an embodiment of the present application provides an optical property modeling method, wherein the method comprises: dividing a microstructure in a periodic medium into N layers of thin slices in the z direction, where N is a positive integer; performing the following processing on thin slices of the same layer of microstructure: obtaining each closed area projected by the thin slice on the periodic space xy plane, and representing the boundaries of each closed area as each polygon; obtaining the x coordinate and y coordinate of each polygon vertex, and the line segment features of each polygon, wherein the line segment features include the slope of the line segment formed by two adjacent vertices on each polygon, the line segment features ... The invention relates to a method for obtaining a periodic space by dividing the periodic space into an integral sub-interval divided in the x-direction and an integral sub-interval divided in the y-direction according to the characteristics of the line segment or the length of the projection of the line segment on the x-axis and the y-axis respectively; dividing the periodic space according to the characteristics of the line segment to obtain the integral sub-interval divided in the x-direction and the integral sub-interval divided in the y-direction; calculating the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium based on the integral sub-interval divided in the x-direction and the integral sub-interval divided in the y-direction; and performing rigorous coupled wave analysis using the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium to realize optical property modeling of the periodic medium.

[0009] The beneficial effect of the optical property modeling method of the present invention is that: the above method does not need to divide the area where there is no microstructure, and divides the area where there is a microstructure according to the line segment characteristics, thereby reducing the number of divisions of the integral interval, improving the division accuracy of the integral interval, and improving processing efficiency and accuracy. At the same time, according to the line segment characteristics, division points are selected from the line segment in the x direction and the y direction to obtain the integral interval, and 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 then the Fourier coefficients of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium are used to perform strict coupled wave analysis to realize the optical property modeling of the periodic medium, which not only improves efficiency but also ensures accuracy.

[0010] In a possible embodiment, the periodic space is divided according to the line segment feature to obtain the integral sub-intervals divided in the x direction and the integral sub-intervals divided in the y direction, including: obtaining the division points in the x direction and the division points in the y direction on the line segment, respectively, and obtaining the x coordinates of the division points in the x direction and the y coordinates of the division points in the y direction; forming a set of x coordinates based on the x coordinates of the vertices of the polygons and the x coordinates of the division points in the x direction; forming a set of y coordinates based on the y coordinates of the vertices of the polygons and the y coordinates of the division points in the y direction; dividing the set of x coordinates and the set of y coordinates to obtain the integral sub-intervals divided in the x direction and the integral sub-intervals divided in the y direction. The beneficial effect is that according to the obtained x coordinates of the vertices of the division points in the x direction, and the y coordinates of the division points in the y direction and the vertices of the polygons, the acquisition of the integral sub-intervals can be determined by the geometric information of the microstructure in the periodic medium, which overcomes the defect of the prior art that the theoretical spectrum accuracy is improved by increasing the number of integral intervals (increasing the amount of calculation), and at the same time improves the accuracy and efficiency of optical property modeling.

[0011] In a possible embodiment, the set of x coordinates and the set of y coordinates are divided to obtain the integral sub-intervals divided in the x direction and the integral sub-intervals divided in the y direction, including: arranging the coordinates in the set of x coordinates and the set of y coordinates in order from large to small or from small to large; for the set of x coordinates after the order is arranged, any two adjacent x coordinates constitute the integral sub-interval divided in the x direction; for the set of y coordinates after the order is arranged, any two adjacent y coordinates constitute the integral sub-interval divided in the y direction. The beneficial effect is that by arranging the coordinates in the set of x coordinates and the set of y coordinates in order from large to small or from small to large, and any two adjacent x coordinates or y coordinates constitute the integral sub-interval.

[0012] In a possible embodiment, the division points in the x direction and the division points in the y direction are respectively obtained on the line segment, including: in the x direction, when the absolute value of the slope is less than a first threshold value and greater than a second threshold value, and the length of the projection of the line segment on the x-axis or the length of the line segment is not less than a preset value, at least one division point in the x direction is selected from the line segment between the two adjacent vertices, otherwise, the two adjacent vertices are used as the division points in the x direction of the line segment; in the y direction, when the absolute value of the slope is less than a third threshold value and greater than a fourth threshold value, and the length of the projection of the line segment on the y-axis or the length of the line segment is not less than a preset value, at least one division point in the y direction is selected from the line segment between the two adjacent vertices, otherwise, the two adjacent vertices are used as the division points in the y direction of the line segment. Its beneficial effects are: the first threshold is greater than the second threshold, the third threshold is greater than the fourth threshold, and whether the line segment is to be divided is determined by the threshold and the length of the line segment projection, so that line segments with too large a slope, too small a slope, or a small line segment length or line segment projection length are not divided, and the x-coordinate or y-coordinate of the vertex is directly obtained as the division point. Compared with the prior art, the periodic space is evenly divided in any case. The above method reduces unnecessary interval divisions, reduces the number of integral interval divisions without sacrificing calculation accuracy, and further improves processing efficiency and accuracy.

[0013] In a second aspect, an embodiment of the present application further provides an optical property modeling device, which includes a module / unit for executing any possible design method of the first aspect. These modules / units can be implemented by hardware, or by executing corresponding software implementations by hardware. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0015] Figure 1 (a) is a schematic diagram of uniform grid division in a periodic space in the prior art;

[0016] Figure 1 (b) is a schematic diagram of uniformly dividing the interval in the x direction in the prior art;

[0017] Figure 2 A schematic diagram of the three-dimensional structure of a microstructure in a periodic medium;

[0018] Figure 3 for Figure 2Schematic diagram of the mesostructure being layered into multiple flakes in the z direction;

[0019] Figure 4 A in the figure is a top view of a periodic medium;

[0020] Figure 4 B is Figure 4 Side view of the mesoperiodic medium in A;

[0021] Figure 5 A top view having a plurality of polygons in a periodic unit obtained by projecting any thin layer of another periodic medium in the z direction onto the xy plane of the periodic space;

[0022] Figure 6 A schematic diagram of the division of the integral sub-intervals of another periodic medium periodic unit in the x direction;

[0023] Figure 7 A is a flow chart of a method for obtaining a division point in the x direction from a line segment formed by two adjacent vertices of any polygon provided by an embodiment of the present invention;

[0024] Figure 7 B is a flowchart of another method for obtaining a division point in the x direction from a line segment formed by two adjacent vertices of any polygon provided by an embodiment of the present invention;

[0025] Figure 8 A schematic diagram of selecting at least one division point in the x direction on a line segment with a preset step length in an embodiment of the present invention;

[0026] Fig. 9 A schematic diagram of selecting at least one division point in the x direction on a line segment by using a bisection method in an embodiment of the present invention;

[0027] Fig.10 A schematic diagram of selecting at least one dividing point in the x direction on a line segment based on an empirical value in one embodiment of the present invention;

[0028] Fig.11 A schematic diagram of dividing a polygon into line segments with a preset step length in the x direction in another embodiment;

[0029] Fig.12 A in the figure shows a schematic diagram of a structure in which the microstructure is a prism;

[0030] Fig.12 B is Fig.12 A top view of a thin slice after microstructure delamination.

[0031] Fig.13 A schematic diagram of an optical property modeling device provided in an embodiment of the present application;

[0032] Fig.14 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0033] In order to make the purpose, 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 in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. Unless otherwise defined, the technical terms or scientific terms used herein should be understood by people with general skills in the field to which the present invention belongs. "Including" and similar words used in this article mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0034] Figure 1 (a) is a schematic diagram of uniform grid division in a periodic space in the prior art. Figure 1 (b) is a schematic diagram of uniformly dividing intervals in the x direction in the prior art.

[0035] Reference Figure 1 ,like Figure 1 As shown in (a), the prior art divides the periodic space into grids uniformly, and then uses the dielectric coefficient of each grid center as the dielectric coefficient of the grid, and then performs a two-dimensional fast Fourier transform to obtain the Fourier coefficient ε of the dielectric coefficient of the periodic medium mn ,like Figure 1 As shown in (b), taking the x direction as an example, the prior art usually divides the interval in the x direction evenly, and then uses the dielectric constant of the midpoint of each interval as the dielectric constant of the interval, and then integrates in the y direction, and then performs a one-dimensional fast Fourier transform to obtain the Toeplitz matrix of ε(x, y) Do the same process in the y direction and get the Toeplitz matrix of ε(x, y) This method will bring about the problem of balancing calculation accuracy and efficiency when processing, that is, when there are many intervals or grids, the accuracy is high but it takes a lot of time, and when there are few intervals or grids, the efficiency is high but the accuracy is low.

[0036] In view of the problems existing in the prior art, the embodiments of the present invention refer to Figures 2 to 6 , providing a method for modeling optical properties.

[0037] Figure 2 A schematic diagram of the three-dimensional structure of the microstructure in a periodic medium. Figure 3 for Figure 2Schematic diagram of the mesostructure being layered into multiple flakes in the z direction. Figure 4 A is a top view of a periodic medium. Figure 4 B is Figure 4 A. Side view of the mesoperiodic medium.

[0038] Reference Figures 1 to 4 The periodic medium changes periodically in the x and y directions, and the periodic medium is usually not constant in the z direction. The microstructure of the periodic medium is divided into several thin slices in the z direction, and the light scattering characteristics of the thin slices in the z direction remain unchanged. In this way, the light scattering effect of the entire microstructure can be regarded as the light scattering effect of several superimposed thin slices with uniform distribution in the z direction.

[0039] The optical property modeling method of the present invention comprises: dividing the microstructure in the periodic medium into N layers of thin slices in the z direction, where N is a positive integer; performing the following processing for the thin slices of the same layer of microstructure: obtaining each closed area projected by the thin slice on the xy plane of the periodic space, and representing the boundaries of each closed area as each polygon; obtaining the x coordinate and y coordinate of each polygon vertex and the line segment features of each polygon, wherein the line segment features include the slope of the line segment formed by two adjacent vertices on each polygon, the length of the line segment or the length of the line segment projected on the x-axis and the y-axis respectively; dividing the periodic space according to the line segment features to obtain the integral sub-intervals divided in the x-direction and the integral sub-intervals divided in the y-direction; calculating the Fourier coefficients of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium based on the integral sub-intervals divided in the x-direction and the integral sub-intervals divided in the y-direction; and performing strict 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 property modeling of the periodic medium.

[0040] For the periodic space after any layer of thin film is projected on the xy plane of the periodic space, by dividing the intervals and grids in this way, it is possible to avoid excessive division of intervals and grids in areas where no graphics exist (projections of the thin film on the xy plane of the periodic space), as well as to avoid the increase in the amount of calculation caused by excessive division of intervals and grids. Moreover, by dividing the periodic space according to the slope of the line segment, the length of the line segment or the length of the projection of the line segment on the coordinate axis, it is possible to divide the area where graphics exist more accurately. The area where any layer of thin film is projected on the xy plane of the periodic space is determined by the geometric information of the microstructure of the periodic medium. Therefore, the above method optimizes the division of integral intervals in the periodic space based on the geometric information of the microstructure of the periodic medium, improves the calculation accuracy, and obtains the optimized grid based on the optimized integral interval, which is different from the prior art that uniformly divides the integral intervals and grids in the entire periodic space, thereby efficiently obtaining the accurate Fourier coefficient ε of the dielectric constant ε(x, y) of the periodic medium. mn 、Toeplitz matrix of dielectric constant ε(x, y) of periodic medium and This enables efficient and accurate modeling of forward optical properties.

[0041] In some specific embodiments of the present invention, a method for dividing a microstructure in a periodic medium into thin slices in the z direction is provided, such as Figure 3 As shown, it is divided into N layers of thin sheets, N is a positive integer, and the thickness of each thin sheet is small enough to satisfy the light scattering characteristics of each thin sheet in the z direction. In this way, the light scattering effect of the entire microstructure can be regarded as the light scattering effect of several thin sheets uniformly distributed in the z direction superimposed on each other. ε(x, y) is the dielectric constant of the periodic medium, which is a periodic function. The period of the periodic medium in the x direction is p x , the period in the y direction is p y , then ε(x, y)=ε(x+c*p x ,y+r*p y ), c and r are integers.

[0042] The shapes of the microstructures of the periodic medium are various, and the corresponding geometric structures are also various. There may be multiple microstructures in one periodic space. In some specific embodiments of the present invention, a method for obtaining a polygon is provided. Select any thin layer, such as Figure 5 As shown, Figure 5Any thin layer of another periodic medium in the z direction is projected on the xy plane of the periodic space to obtain a top view with multiple polygons in the periodic space. The shaded area in the figure is the projection of any thin layer of the microstructure. It can be seen from the figure that there are multiple polygons such as triangles, quadrilaterals and hexagons. For the same thin layer, all closed areas after the thin layer is projected are obtained, and the boundaries of each closed area are represented by polygons. For non-polygonal closed areas, they are approximated as polygons. For example, when the boundary line of the projected closed area is a curve, points are taken at a preset interval. The preset interval is determined by the relative size of the geometric information of the microstructure and the period length of the periodic space. The specific method is to select the starting point of the curve, and then take points along the curve in sequence at a preset interval until the end point of the curve to form a broken line. For complex periodic media, there are multiple microstructures in a periodic unit. At this time, the projection of any thin layer of the microstructure in a periodic unit has multiple closed areas. After obtaining the polygons corresponding to the multiple closed areas, each polygon is processed and analyzed one by one to obtain the line segment features of each polygon.

[0043] The prior art evenly divides the periodic space, and there is a problem of balancing the calculation accuracy and calculation efficiency of the theoretical spectrum, that is, more intervals and grid divisions improve the calculation accuracy, but the calculation is time-consuming, and more intervals and grid divisions improve the calculation efficiency, but the calculation accuracy is reduced. For periodic media including multiple microstructures with different geometric structures, the above-mentioned defects of the prior art are more obvious, that is, the more complex the microstructure in the periodic medium, the more prominent the contradiction between the calculation efficiency and calculation accuracy of the optical property modeling. The method provided by the embodiment of the present invention is used to divide the periodic space, the microstructure in the periodic medium is complex, and the division of the integral sub-intervals and grids can also accurately correspond to the geometric information of the microstructure in the periodic medium, and the geometric information of the microstructure in the periodic medium directly determines the theoretical spectrum. Therefore, the method provided by the embodiment of the present invention can simultaneously improve the accuracy and efficiency of obtaining the theoretical spectrum.

[0044] In addition, optionally, the periodic space is also projected as a polygon and the periodic space is taken as -p in the x direction. x / 2~p x / 2, the value in the y direction is -p y / 2~p y / 2, p x 、p y are the period lengths of the periodic space in the x and y directions respectively.

[0045] In some embodiments of the present invention, the periodic space is divided according to the line segment characteristics to obtain the integral sub-intervals divided in the x direction and the integral sub-intervals divided in the y direction, including: obtaining the division points in the x direction and the division points in the y direction on the line segment, respectively, and obtaining the x coordinates of the division points in the x direction and the y coordinates of the division points in the y direction; forming a set of x coordinates based on the x coordinates of the vertices of each polygon and the x coordinates of the division points in the x direction; forming a set of y coordinates based on the y coordinates of the vertices of each polygon and the y coordinates of the division points in the y direction; dividing the set of x coordinates and the set of y coordinates to obtain the integral sub-intervals divided in the x direction and the integral sub-intervals divided in the y direction. Optionally, the set of x coordinates may also include the x coordinates of the endpoints in the x direction of the periodic space - p x / 2 and p x / 2; the set of y coordinates can also include the y coordinates of the endpoints in the y direction of the periodic space -p y / 2 and p y / 2.

[0046] Further, in the above method, the set of x coordinates and the set of y coordinates are divided to obtain integral sub-intervals divided in the x direction and integral sub-intervals divided in the y direction, including: arranging the coordinates in the set of x coordinates and the set of y coordinates in order from large to small or from small to large, respectively; for the set of x coordinates after the sequential arrangement, any two adjacent x coordinates constitute the integral sub-interval divided in the x direction; for the set of y coordinates after the sequential arrangement, any two adjacent y coordinates constitute the integral sub-interval divided in the y direction.

[0047] Furthermore, in the above method, obtaining the set of x coordinates and the set of y coordinates also includes: performing deduplication processing on the x coordinates of each polygon vertex and the x coordinates of the division points in the x direction, and the y coordinates and the y coordinates of the division points in the y direction, and then arranging them from small to large or from large to small. Figure 6 As shown, Figure 6 This is a schematic diagram of the division of the integral sub-interval of another periodic medium periodic unit in the x direction. For example, by using the above method, the integral sub-interval divided in the x direction is (-p x / 2, t0), (t0, t1), (t1, t2), (t2, t3), (t3, t4), (t4, t5), (t5, p x / 2).

[0048] Furthermore, in the above method, the obtained integral sub-intervals divided in the x-direction and the integral sub-intervals divided in the y-direction are crisscrossed to obtain a grid based on the integral sub-intervals in the x-direction and the integral sub-intervals in the y-direction, thereby completing the grid division of the periodic space.

[0049] In some embodiments of the present invention, the division points in the x direction and the division points in the y direction are respectively obtained on the line segment, including: in the x direction, when the absolute value of the slope is less than a first threshold value and greater than a second threshold value, and the length of the projection of the line segment formed by the two adjacent vertices on the x-axis or the length of the line segment is not less than a preset value, at least one division point in the x direction is selected from the line segment between the two adjacent vertices, otherwise, the two adjacent vertices are used as the division points in the x direction of the line segment; in the y direction, when the absolute value of the slope is less than a third threshold value and greater than a fourth threshold value, and the length of the projection of the line segment formed by the two adjacent vertices on the y-axis or the length of the line segment is not less than a preset value, at least one division point in the y direction is selected from the line segment between the two adjacent vertices, otherwise, the two adjacent vertices are used as the division points in the y direction of the line segment; wherein the first threshold value>the second threshold value, the third threshold value>the fourth threshold value, the line segment between the two adjacent vertices does not include the two adjacent vertices, and the vertices are the endpoints of the line segment. Further, the x coordinates of the division points in the x direction are obtained according to the obtained division points in the x direction, and the y coordinates of the division points in the y direction are obtained according to the division points in the y direction.

[0050] In some specific embodiments of the present invention, the first threshold and the second threshold can be two reciprocal values, and the second threshold can be tan1°-tan15°. The third threshold can be equal to the first threshold, or different from the first threshold; the fourth threshold can be equal to the second threshold, or different from the second threshold. The length of the projection of the line segment on the x-axis is the difference between the x-coordinates of the two vertices corresponding to the line segment, and the length of the projection of the line segment on the y-axis is the difference between the y-coordinates of the two vertices corresponding to the line segment; the preset value can be 0.01-5nm.

[0051] The above embodiment avoids selecting division points for the part between the vertices of a line segment that is close to the horizontal or vertical line segment, and also avoids selecting division points for the part between the vertices of a line segment whose length is small enough and whose projection length on the coordinate axis is small enough. The geometric information of the microstructure corresponding to the line segment between the vertices for which no division points are selected has little or no change. At the same time, for the line segment corresponding to the line segment with a large change in the geometric information of the microstructure, division points are selected for the part between the vertices of the line segment, and based on the coordinates of all division points and the coordinates of the vertices, the integration interval and grid are divided based on the geometric information of the microstructure, thereby improving the calculation accuracy and efficiency.

[0052] Figure 7 A is a flow chart of a method for obtaining division points in the x direction from a line segment formed by two adjacent vertices of any polygon provided by an embodiment of the present invention.

[0053] In some specific embodiments of the present invention, referring to Figure 7 In step A, the following steps are included:

[0054] S1. Get the coordinate values ​​(x, y) of all vertices of the polygon;

[0055] S2. Get the length of the line segment formed by every two adjacent vertices on the polygon projected in the x direction.

[0056] Determine whether the length of the projection is less than the preset value, if so, execute S4, if not, execute S3;

[0057] S3, obtaining the absolute value of the slope of the line segment, and determining whether the absolute value of the slope of the line segment is greater than the second threshold and less than the first threshold, if so, executing S5, if not, executing S4;

[0058] S4, taking the two adjacent vertices as the dividing points of the line segment in the x direction;

[0059] S5. Select at least one dividing point in the x direction from the line segment between the two adjacent vertices.

[0060] Figure 7 B is a flowchart of another method for obtaining division points in the x direction from a line segment formed by two adjacent vertices of any polygon provided by an embodiment of the present invention.

[0061] Optional, see Figure 7 In B, the step of determining the length of the line segment projection in the x direction is set after the step of determining the slope of the line segment. The specific steps are as follows:

[0062] S'1. Get the coordinate values ​​(x, y) of all vertices of the polygon;

[0063] S'2, obtain the absolute value of the slope of the line segment formed by every two adjacent vertices on the polygon, and determine whether the absolute value of the slope of the line segment is greater than the second threshold and less than the first threshold. If so, execute S'3; if not, execute S'4;

[0064] S'3, obtaining the length of the projection of the line segment in the x direction, and determining whether the projection length is less than the preset value, if so, executing S'4, if not, executing S'5;

[0065] S'4, taking the two adjacent vertices as the dividing points of the line segment in the x direction;

[0066] S'5. Select at least one dividing point in the x direction from the line segment between the two adjacent vertices.

[0067] Optionally, for the above steps S1-S5 or S'1-S'5, the length of the line segment projection in the x direction may be replaced by the length of the line segment. In addition, based on the above steps S1-S5 or S'1-S'5, the division points of all line segments in the y direction may be obtained similarly.

[0068] In some embodiments of the present invention, obtaining at least one division point in the x direction from the line segment between the two adjacent vertices includes: selecting at least one division point in the x direction from the line segment according to a preset step size, a binary method, or an empirical value as a reference; selecting at least one division point in the y direction from the line segment between the two adjacent vertices includes: selecting at least one division point in the y direction from the line segment according to a preset step size, a binary method, or an empirical value as a reference.

[0069] Figure 8 It is a schematic diagram of selecting at least one x-direction dividing point of the line segment with a preset step size in an embodiment of the present invention.

[0070] In some specific embodiments of the present invention, referring to Figure 8 , taking at least one x-direction dividing point of line segment Q2 as an example, the preset step size is 1nm, the x-coordinate values ​​of the two vertices of line segment Q2 are 2 and 5, and the length of line segment Q2 projected on the x-axis is 3nm, then the line segment Q2 is divided into three equal parts, and the x-coordinate values ​​of the dividing points are 3 and 4.

[0071] Fig. 9 The figure is a schematic diagram of selecting at least one dividing point in the x direction on a line segment by using the bisection method in an embodiment of the present invention.

[0072] In some specific embodiments of the present invention, referring to Fig. 9 , take obtaining at least one x-direction dividing point of line segment Q2 as an example, and take bisection twice as an example, first obtain the x-coordinate values ​​of the two vertices of line segment Q2: the x-coordinate value of vertex e1 is 2, the x-coordinate value of vertex e5 is 5, the x-coordinate value of the midpoint e3 of the first bisection is 3.5, and the x-coordinate value of the two midpoints of the second bisection: the x-coordinate value of e2 is 2.75, and the x-coordinate value of e4 is 4.25.

[0073] Fig.10 It is a schematic diagram of selecting at least one division point in the x direction on a line segment based on an empirical value in an embodiment of the present invention.

[0074] In some specific embodiments of the present invention, referring to Fig.10, take at least one x-direction dividing point of line segment Q2 as an example, the empirical value is tan20°, the slope of line segment Q2 is tan60°, the number of divisions is tan60° / tan20°=4.75, rounded to 5, then divide it into five equal parts, the x-coordinate values ​​of the two vertices of line segment Q2 are 2 and 5, and the x-coordinate values ​​of the dividing points are: 2.6, 3.2, 3.8, 4.4.

[0075] In some embodiments of the present invention, the Toeplitz matrix of the dielectric constant of the periodic medium satisfies the following formula:

[0076]

[0077]

[0078] The Fourier coefficient of the dielectric constant of a periodic medium satisfies the following formula:

[0079]

[0080] Where i is the imaginary unit p x is the period in the x direction, p y is the period in the y direction, m and j are the orders in the x direction, n and l are the orders in the y direction, k x =2π / p x , -p x / 2, t0, t1, t2, …, t u-1 ,t u 、p x / 2 are the x-coordinates of the target integral subintervals in the x-direction; k y =2π / py, -p y / 2, s0, s1, s2, …, s e-1 、s e 、p y / 2 are the y coordinates of the target integral subinterval in the y direction, Representative Grid The x- and y-coordinates of the center point, Representative Grid is the area of ​​the grid, and φ is the number of grids obtained by dividing the integration interval in the x-direction and the y-direction.

[0081] Fig.11 It is a schematic diagram of dividing the line segments of the polygon with a preset step size in the x direction in another embodiment.

[0082] In some embodiments of the present invention, referring to Fig.11 , taking the x direction as an example, the integral interval in the x direction within one period of the periodic medium is expressed as (-p x / 2, t0), (t0, t1), (t1, t2), ..., (t u-1 , t u ), (t u , p x / 2), specifically, the left and right figures are both rectangles, and the slopes of the sides of the figures are less than or equal to the second threshold or greater than or equal to the first threshold, so the line segments of the left and right figures are not divided, the middle figure is an irregular polygon, and the line segments formed by the sides of the irregular polygon are q1, q2, q3, ..., q11, q12, respectively. Since the length of the projection of the line segments q1 and q7 in the x direction is less than the preset value, the line segments q1 and q7 are not divided; the length of the projection of the line segments q2, q3, q5, q6, q8, q9, q11, q12 in the x direction is greater than the preset value, and the slope is less than the first threshold and greater than the second threshold, then the line segments q2, q3, q5, q6, q8, q9, q11, q12 are divided according to the preset step size; the absolute value of the slope of the line segments q4 and q10 is less than the second threshold, and they are not divided; the optimized integral subinterval is recorded as (-p x / 2, t0), (t0, t1), (t1, t2), ..., (t 19 , t 20 ), (t 20 , p x / 2). The above embodiment shows the advantages of the present invention for the interval division in the x direction of the periodic space. Based on the projection of a thin layer divided in the z direction on the xy plane of the periodic space, the polygons corresponding to all closed areas are obtained, and the interval division in the x direction is completed according to the slope of the line segment of each polygon, the length of the line segment projection in the x direction or the length of the line segment. The method avoids the problem of the prior art for intervals such as (-p x / 2, t0), (t0, t1), (t1, t2), (t 20 , p x / 2) and other intervals, thus reducing the number of interval divisions. At the same time, this method can obtain more accurate interval divisions than the prior art uniform divisions, such as (t2, t3), (t3, t4), ..., (t 17 , t 18 ) can accurately reflect the changes in the geometric information of the microstructure, that is, the division of the above embodiment can achieve higher calculation accuracy and efficiency.

[0083] In order to verify the model established by the above method, the microstructure in the periodic medium is used as a prism for verification.

[0084] Fig.12 A in the figure shows a schematic diagram of a microstructure that is a prism. Fig.12 B is Fig.12A top view of a thin slice after microstructure stratification. Fig.12 The gray area in B is the projection of a thin slice on the periodic space xy plane after the microstructure is layered. The outermost dotted box represents the periodic space, and the vertical dotted line shows the target integral sub-interval divided in the x direction. Fig.12 The parameters of the prism of the microstructure shown in A have the following characteristics: TCD_x: 60nm, prism TCD_Y: 30nm, prism BCD_x: 80nm, prism BCD_Y: 50nm, prism height: 100nm, number of layers: 10. After the optical property modeling is performed according to the above method, the theoretical spectrum calculation results are compared as shown in the following table. The prior art divides the integral interval uniformly, and 256 intervals are evenly divided in the X and Y directions, while the method of the present application divides 3 target integral sub-intervals in the X and Y directions respectively, thereby greatly reducing the amount of calculation for solving the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium, thereby improving the calculation efficiency of the theoretical spectrum. The prior art takes 58 seconds to obtain the theoretical spectrum, and the present application takes 46 seconds to obtain the theoretical spectrum. At the same time, the accuracy of the theoretical spectrum obtained by the method of the present application is improved by one order of magnitude compared with the accuracy of the theoretical spectrum obtained by the prior art. It can be seen that the method of the present application uses less time to obtain a more accurate theoretical spectrum, while improving the calculation efficiency and accuracy of the theoretical spectrum.

[0085]

[0086] Fig.13 A schematic diagram of an optical property modeling device provided in an embodiment of the present application.

[0087] Based on the above optical property modeling method, in some embodiments of the present application, the present application embodiment discloses an optical property modeling device, such as Fig.13 As shown, the device 13 is used to implement the methods recorded in the above method embodiments, and includes: a division unit 1301, a calculation unit 1302 and a modeling unit 1303.

[0088] The division unit 1301 is used to divide the microstructure in the periodic medium into N layers of thin slices in the z direction, where N is a positive integer; for the thin slices of the same layer of microstructure, the following processing is performed: each closed area of ​​the thin slice projected on the xy plane of the periodic space is obtained, and the boundaries of each closed area are represented as each polygon; the x coordinate and y coordinate of each polygon vertex and the line segment features of each polygon are obtained, and the line segment features include the slope of the line segment formed by two adjacent vertices on each polygon, the length of the line segment or the length of the line segment projected on the x-axis and the y-axis respectively; the periodic space is divided according to the line segment features to obtain the integral sub-intervals divided in the x-direction and the integral sub-intervals divided in the y-direction;

[0089] A calculation unit 1302 is used to calculate the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium based on the integral sub-intervals divided in the x direction and the integral sub-intervals divided in the y direction;

[0090] The modeling unit 1303 is used to perform rigorous coupled wave analysis using the Fourier coefficient of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium to achieve optical property modeling of the periodic medium.

[0091] All relevant contents of each step involved in the above method embodiment can be referred to the functional description of the corresponding functional module, and will not be repeated here.

[0092] Fig.14 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application.

[0093] In other embodiments of the present application, the present application discloses an electronic device, such as Fig.14 As shown, the electronic device 14 may include: one or more processors 1401; a memory 1402; a display 1403; one or more applications (not shown); and one or more computer programs 1404, and the above components may be connected via one or more communication buses 1405. The one or more computer programs 1404 are stored in the above memory 1402 and are configured to be executed by the one or more processors 1401, and the one or more computer programs 1404 include instructions.

[0094] The present invention also provides a computer readable medium on which a computer program is stored, and when the computer program is executed by a computer, the method described in the above method embodiment is implemented. The specific effects can be referred to in the above embodiment.

[0095] The present invention also provides a computer program product, which implements the method described in the above method embodiment when executed by a computer. The specific effects can be found in the above embodiment.

[0096] Through the description of the above implementation methods, technicians in the relevant field can clearly understand that for the convenience and simplicity of description, only the division of the above functional modules is used as an example. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device is divided into different functional modules to complete all or part of the functions described above. The specific working process of the system, device and unit described above can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0097] Each functional unit in each embodiment of the present application can be integrated into a processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The above integrated unit can be implemented in the form of hardware or in the form of software functional units.

[0098] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiment of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as flash memory, mobile hard disk, read-only memory, random access memory, disk or optical disk.

[0099] The above is only a specific implementation of the embodiment of the present application, but the protection scope of the embodiment of the present application is not limited thereto, and any changes or replacements within the technical scope disclosed in the embodiment of the present application should be included in the protection scope of the embodiment of the present application. Therefore, the protection scope of the embodiment of the present application should be based on the protection scope of the claims.

Claims

1. An optical property modeling method, characterized in that: The method includes: The microstructure in the periodic medium is divided into N thin slices in the z direction, where N is a positive integer; For the slices of the same microstructure, the following processing is performed: Acquire each closed area projected by the sheet on the periodic space xy plane, and represent the boundaries of each closed area as each polygon; acquire the x-coordinate and y-coordinate of each polygon vertex, and the line segment features of each polygon, wherein the line segment features include the slope of the line segment formed by two adjacent vertices on each polygon, the length of the line segment, or the length of the line segment projected on the x-axis and the y-axis respectively; According to the line segment characteristics, the periodic space is divided to obtain integral sub-intervals divided in the x direction and integral sub-intervals divided in the y direction; Based on the integral sub-intervals divided in the x direction and the integral sub-intervals divided 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; A rigorous coupled wave analysis is performed using the Fourier coefficient of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium to achieve optical property modeling of the periodic medium.

2. The method according to claim 1, characterized in that According to the line segment feature, the periodic space is divided to obtain integral sub-intervals divided in the x direction and integral sub-intervals divided in the y direction, including: Obtaining a division point in the x direction and a division point in the y direction on the line segment, and obtaining an x ​​coordinate of the division point in the x direction and a y coordinate of the division point in the y direction; Based on the x coordinates of the vertices of the polygons and the x coordinates of the division points in the x direction, a set of x coordinates is formed; based on the y coordinates of the vertices of the polygons and the y coordinates of the division points in the y direction, a set of y coordinates is formed; The set of x-coordinates and the set of y-coordinates are divided to obtain integral sub-intervals divided in the x-direction and integral sub-intervals divided in the y-direction.

3. The method according to claim 2, characterized in that The set of x coordinates and the set of y coordinates are divided to obtain integral subintervals divided in the x direction and integral subintervals divided in the y direction, including: Arrange the coordinates in the set of x coordinates and the set of y coordinates in order from large to small or from small to large respectively; For the set of x-coordinates arranged in sequence, any two adjacent x-coordinates constitute an integral sub-interval divided in the x-direction; For the set of y coordinates arranged in sequence, any two adjacent y coordinates constitute an integral sub-interval divided in the y direction.

4. The method according to claim 2, characterized in that: Obtaining a division point in the x direction and a division point in the y direction on the line segment respectively, including: In the x-direction, when the absolute value of the slope is less than a first threshold value and greater than a second threshold value, and the length of the projection of the line segment on the x-axis or the length of the line segment is not less than a preset value, at least one division point in the x-direction is selected from the line segment between the two adjacent vertices, otherwise, the two adjacent vertices are used as the division points in the x-direction of the line segment; In the y direction, when the absolute value of the slope is less than the third threshold and greater than the fourth threshold, and the length of the projection of the line segment on the y axis or the length of the line segment is not less than a preset value, at least one y-direction dividing point is selected from the line segment between the two adjacent vertices; otherwise, the two adjacent vertices are used as the y-direction dividing points of the line segment.

5. The method according to claim 4, characterized in that Selecting at least one division point in the x direction from the line segment between the two adjacent vertices includes: Select at least one dividing point in the x direction from the line segment according to a preset step size, a dichotomy method or an empirical value; Selecting at least one division point in the y direction from the line segment between the two adjacent vertices includes: At least one dividing point in the y direction is selected from the line segment according to a preset step size, a dichotomy method or an empirical value.

6. An optical property modeling device, characterized in that: The device includes: A division unit, used to divide the microstructure in the periodic medium into N thin slices in the z direction, where N is a positive integer; For the slices of the same microstructure, the following processing is performed: Acquire each closed area projected by the sheet on the periodic space xy plane, and represent the boundaries of each closed area as each polygon; acquire the x-coordinate and y-coordinate of each polygon vertex, and the line segment features of each polygon, wherein the line segment features include the slope of the line segment formed by two adjacent vertices on each polygon, the length of the line segment, or the length of the line segment projected on the x-axis and the y-axis respectively; According to the line segment characteristics, the periodic space is divided to obtain integral sub-intervals divided in the x direction and integral sub-intervals divided in the y direction; A calculation unit, used for calculating the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium based on the integral sub-interval divided in the x direction and the integral sub-interval divided in the y direction; The modeling unit is used to perform rigorous coupled wave analysis using the Fourier coefficient of the dielectric constant of the periodic medium and the Toeplitz matrix of the dielectric constant of the periodic medium to achieve optical property modeling of the periodic medium.

7. The optical characteristic modeling device according to claim 6, characterized in that: The division unit divides the periodic space according to the line segment feature to obtain the integral sub-intervals divided in the x direction and the integral sub-intervals divided in the y direction, which is specifically used for: Obtaining a division point in the x direction and a division point in the y direction on the line segment, and obtaining an x ​​coordinate of the division point in the x direction and a y coordinate of the division point in the y direction; Based on the x-coordinates of the vertices of the polygons and the x-coordinates of the division points in the x-direction, forming a set of x-coordinates; Based on the y coordinates of the vertices of the polygons and the y coordinates of the division points in the y direction, forming a set of y coordinates; The set of x-coordinates and the set of y-coordinates are divided to obtain integral sub-intervals divided in the x-direction and integral sub-intervals divided in the y-direction.

8. The optical characteristic modeling device according to claim 7, characterized in that: The division unit divides the set of x coordinates and the set of y coordinates to obtain integral sub-intervals divided in the x direction and integral sub-intervals divided in the y direction, specifically for: Arrange the coordinates in the set of x coordinates and the set of y coordinates in order from large to small or from small to large respectively; For the set of x-coordinates arranged in sequence, any two adjacent x-coordinates constitute an integral sub-interval divided in the x-direction; For the set of y coordinates arranged in sequence, any two adjacent y coordinates constitute an integral sub-interval divided in the y direction.

9. The optical characteristic modeling device according to claim 7, characterized in that: The division unit obtains the division points in the x direction and the division points in the y direction on the line segment respectively, specifically for: In the x-direction, when the absolute value of the slope is less than a first threshold value and greater than a second threshold value, and the length of the projection of the line segment on the x-axis or the length of the line segment is not less than a preset value, at least one division point in the x-direction is selected from the line segment between the two adjacent vertices, otherwise, the two adjacent vertices are used as the division points in the x-direction of the line segment; In the y direction, when the absolute value of the slope is less than the third threshold and greater than the fourth threshold, and the length of the projection of the line segment on the y axis or the length of the line segment is not less than a preset value, at least one y-direction dividing point is selected from the line segment between the two adjacent vertices; otherwise, the two adjacent vertices are used as the y-direction dividing points of the line segment.

10. The optical characteristic modeling device according to claim 7, characterized in that: The division unit selects at least one division point in the x direction from the line segment between the two adjacent vertices, specifically for: Select at least one dividing point in the x direction from the line segment according to a preset step size, a dichotomy method or an empirical value; Selecting at least one division point in the y direction from the line segment between the two adjacent vertices includes: At least one dividing point in the y direction is selected from the line segment according to a preset step size, a dichotomy method or an empirical value.

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