CN114065592B - Optical property modeling method and device - Google Patents
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Abstract
本发明公开了一种光学特性建模方法和装置，该方法包括：将周期介质内的微结构在z方向上划分为N层薄片；针对同一层微结构的薄片，执行如下处理：获取所述薄片在周期空间xy平面上投影的各个封闭区域的几何信息；根据所述几何信息，对所述周期空间进行划分，得到x方向划分的目标积分子区间和y方向划分的目标积分子区间；计算周期介质的介电系数的傅里叶系数和周期介质的介电系数的托普利兹矩阵，以及进行严格耦合波分析，以实现周期介质的光学特性建模，该方法通过对积分区间的划分方法进行优化，从而高效地得到精确的周期介质的介电系数的傅里叶系数和介电系数的托普利兹矩阵。
The present invention discloses an optical property modeling method and device, which comprises: 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 geometric information of each closed area projected by the thin slice on the xy plane of the periodic space; dividing the periodic space according to the geometric information to obtain a target integral sub-interval divided in the x direction and a target 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, and performing strict coupled wave analysis to realize optical property modeling of the periodic medium. The method optimizes the division method of the integral interval, thereby efficiently obtaining the accurate Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient.
Description
Technical Field
The present invention relates to the field of semiconductor manufacturing technologies, and in particular, to a method and an apparatus for modeling optical characteristics.
Background
In the fields of semiconductor manufacturing detection, optical proximity correction of a photoetching mask plate, optical scattering simulation calculation and the like, the dielectric coefficient of a periodic medium needs to be subjected to two-dimensional Fourier coefficient expansion. Taking the semiconductor inspection field as an example, with the development of the semiconductor manufacturing industry, the device structure is more and more complex along with the shrinking feature size, and in order to ensure the requirements of reliability consistency of manufacturing, etc., more strict process control is required to be performed on the manufacturing process. Measurement of manufactured devices is one of the core problems in process control, and optical critical dimension (optical critical dimension, OCD) measurement techniques have the advantages of high speed, low cost, non-destructiveness and the like, and are important to be applied to advanced process control in semiconductor manufacturing. Optical critical dimension measurement technology is a model-based approach, so rapid and accurate modeling calculation is one of the core elements of optical critical dimension measurement.
Optical critical dimension measurement is supported by two key technologies, forward optical property modeling and reverse geometry extraction. In many forward optical characteristic modeling methods, the strict coupled wave analysis theory (RCWA) is widely applied to optical characteristic modeling of periodic media due to high modeling accuracy and wide application range. In the process of rigorous coupled wave analysis, a fourier coefficient of the dielectric constant of the periodic medium and a toeplitz matrix of the dielectric constant of the periodic medium need to be obtained.
In recent years, in order to ensure that critical dimensions (critical dimension, CD) are continuously reduced, semiconductor devices still maintain excellent performance, and the structural design is gradually changed from a simple planar structure to a complex three-dimensional structure. Three-dimensional structures mainly include multi-coating structures (multi-pattern), curved edge structures, and the like. The more complex the structure, the more outstanding the contradiction between the computational efficiency and the computational accuracy of the optical property modeling, the more time-consuming the prior art to obtain a theoretical spectrum with higher accuracy.
The method for solving the Fourier coefficient of the dielectric coefficient of the periodic medium provided in the prior art is to divide the periodic space into grids uniformly, then take the dielectric coefficient of the center of each grid as the dielectric coefficient of the grid, and then perform two-dimensional fast Fourier transform to obtain the Fourier coefficient of the dielectric coefficient. The toeplitz matrix for calculating the dielectric coefficient of the periodic medium is generally obtained by uniformly dividing intervals in corresponding directions along an X direction and a Y direction in a periodic space, taking the dielectric coefficient of the middle point of each interval as the dielectric coefficient of the interval, integrating the dielectric coefficients in the Y direction and the X direction respectively, and performing one-dimensional fast Fourier transform. The prior art has the problems that if the number of the divided integral intervals of the periodic space is large, the calculation accuracy can be improved, but the calculation time is consumed, so that the efficiency of the forward optical characteristic modeling is influenced, and if the number of the divided integral intervals of the periodic space is small, the calculation efficiency can be improved, but the calculation accuracy is low, so that the accuracy of the forward optical characteristic modeling is influenced.
Disclosure of Invention
The embodiment of the invention provides an optical characteristic modeling method and device, which optimize a dividing method of an integration interval based on geometric information of a microstructure, so that a Fourier coefficient of a dielectric coefficient of a precise periodic medium and a Toeplitz matrix of the dielectric coefficient of the periodic medium are obtained efficiently, and finally, the optical characteristic modeling is completed efficiently and precisely.
In a first aspect, the present invention provides a method of modeling optical properties, wherein the method comprises the steps of dividing a microstructure in a periodic medium into N layers of flakes in a z-direction, N being a positive integer;
For the sheet of the same layer microstructure, the following processing is performed:
Obtaining the geometric information of each closed area projected by the thin sheet on the xy plane of the periodic space;
and dividing the periodic space according to the geometric information to obtain a target integral interval divided in the x direction and a target integral interval divided in the y direction.
And carrying out strict coupled wave analysis by utilizing the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium so as to realize the optical characteristic modeling of the periodic medium.
The optical characteristic modeling method has the beneficial effects that the microstructure in the periodic medium is divided into the slices and projected to the xy plane, and the division method of the integration interval can be optimized based on the geometric information of the closed area formed by the projection of the slice of the microstructure, so that the Fourier coefficient of the dielectric coefficient of the periodic medium and the toeplitz matrix of the dielectric coefficient are obtained efficiently, and the efficiency and the precision of the forward optical characteristic modeling are further improved.
In one possible embodiment, the acquiring the geometric information of each closed area projected by the sheet on the xy plane of the periodic space comprises acquiring each closed area projected by the sheet on the xy plane of the periodic space and representing the boundary of each closed area as each polygon, and acquiring the x coordinate and the y coordinate of each polygon vertex to form a set of x coordinates and a set of y coordinates.
In another possible embodiment, according to the geometric information, the periodic space is divided into a grid and a section to obtain a target integral section divided in the x direction and a target integral section divided in the y direction, wherein the method comprises the steps of arranging coordinates in the set of x coordinates and the set of y coordinates in a sequence from big to small or from small to big respectively, and forming candidate integral sections by any two adjacent coordinates in the set of x coordinates and the set of y coordinates after the sequence arrangement;
The method comprises the steps of determining whether a candidate integral interval is a non-uniform interval, obtaining the length of the candidate integral interval, dividing the candidate integral interval into a plurality of target integral intervals when the candidate integral interval is the non-uniform interval and the length of the candidate integral interval is larger than or equal to a preset step length, and taking the candidate integral interval as one target integral interval if the candidate integral interval is not the non-uniform interval.
In one possible embodiment, determining whether the candidate integral interval is a non-uniform interval includes obtaining a first reference boundary line and a second reference boundary line of the candidate integral interval constituted by the adjacent two coordinates in an x direction, the first reference boundary line and the second reference boundary line being non-coincident straight lines perpendicular to the candidate integral interval, and an intersection point of the first reference boundary line and the second reference boundary line with the candidate integral interval being not an end point of the candidate integral interval;
Acquiring the number h of first boundary intersections formed by the intersection of the first reference boundary line and the polygon and the number k of second boundary intersections formed by the intersection of the second reference boundary line and the polygon;
When h is not equal to k, the candidate integral interval is taken as a non-uniform interval, or when h is equal to k and is not equal to zero, the y coordinates (alpha 1, alpha 2,.. Alpha.h) of the first boundary intersection point and the y coordinates (beta 1, beta 2,.. Beta.k) of the second boundary intersection point are obtained, wherein the y coordinates of the h boundary intersection points and the y coordinates of the k boundary intersection points are all arranged in the order from large to small or from small to large, and when the h is equal to k and is equal to zero, the candidate integral interval is taken as the non-uniform interval, and the delta 1= |alpha 1-beta 1|+|alpha 2-beta 2|++ alpha h-beta k|is larger than or equal to a threshold value;
or when h is equal to k and not equal to zero, and Δ1= |α1- β1|+|α2- β2|++ α h- βk| is less than the threshold, treating the candidate integral subinterval as a uniform interval.
In the method, for any one candidate integral interval in the x direction, when the length of the candidate integral interval is smaller than a preset step length, the candidate integral interval is directly used as a target integral interval, no further division is performed, and the complexity of subsequent calculation can be reduced on the premise that the accuracy of the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium are not affected. And aiming at the candidate integral intervals which are larger than or equal to the preset step length, the candidate integral intervals can be further divided according to whether the integral intervals are uniform or not, so that the complexity of subsequent calculation is reduced, and the accuracy of the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium is improved.
In one possible embodiment, determining whether the candidate integral interval is a non-uniform interval includes obtaining a third reference boundary line and a fourth reference boundary line of the candidate integral interval constituted by the adjacent two coordinates in the y direction, the third reference boundary line and the fourth reference boundary line being non-coincident straight lines perpendicular to the candidate integral interval, and an intersection point of the third reference boundary line and the fourth reference boundary line with the candidate integral interval being not an end point of the candidate integral interval;
acquiring the number u of third boundary intersections formed by the intersection of the third reference boundary line and the polygon and the number v of fourth boundary intersections formed by the intersection of the fourth reference boundary line and the polygon;
When u is not equal to v, the candidate integral interval is taken as a non-uniform interval, or when u is equal to v and is not equal to zero, the x coordinates (sigma 1, sigma 2,., sigma u) of the third boundary intersection point and the x coordinates (omega 1, omega 2,., omega v) of the fourth boundary intersection point are obtained, wherein the x coordinates of the u boundary intersection points and the x coordinates of the v boundary intersection points are arranged in the order from large to small or from small to large, and delta 2= |sigma 1-omega 1|+|sigma 2-omega 2|++, the candidate integral interval is taken as the non-uniform interval, and when u is equal to v and is equal to zero, the candidate integral interval is taken as the uniform interval;
Or when u is equal to v and not equal to zero, and Δ2= |σ1- ω1|+|σ2- ω2|++.+ -. σu- ωv| is less than the set threshold, taking the candidate integrator subinterval as a uniform interval.
In the method, aiming at any one candidate integral interval in the y direction, when the length of the candidate integral interval formed by two adjacent coordinates is smaller than a preset step length, the candidate integral interval is directly used as a target integral interval, no further division is performed, and the complexity of subsequent calculation can be reduced on the premise that the accuracy of the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium are not influenced. And aiming at the candidate integral intervals which are larger than or equal to the preset step length, the candidate integral intervals can be further divided according to whether the integral intervals are uniform or not, so that the complexity of subsequent calculation is reduced, and the accuracy of the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium is improved.
In a second aspect, embodiments of the present application also provide an optical property modeling apparatus comprising a module/unit performing the method of any one of the possible designs of the first aspect described above. These modules/units may be implemented by hardware, or may be implemented by hardware executing corresponding software.
The advantages of the second aspect described above may be seen from the description of the first aspect described above.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a method for dividing a grid in a periodic space and an integral interval in an x direction according to the prior art;
FIG. 2 is a schematic flow chart of an optical characteristic modeling method according to an embodiment of the present application;
FIG. 3 is a schematic view of a z-direction dividing sheet of a microstructure according to an embodiment of the present application;
FIG. 4 is a top view of a periodic space with multiple polygons of any one sheet in the z direction as projected on the xy plane according to one embodiment of the present application;
FIG. 5 is a schematic diagram of a method for partitioning candidate integral intervals according to an embodiment of the present application;
FIG. 6 is a schematic diagram of a method for determining whether an x-direction candidate integral interval is uniform according to an embodiment of the present application;
FIG. 7 is a schematic diagram of an x-direction candidate inter-sub-interval reference boundary according to an embodiment of the present application;
FIG. 8 is a schematic diagram illustrating a division of a target integral interval according to an embodiment of the present application;
FIG. 9 is a schematic diagram of a method for determining whether a candidate sub-interval in the y direction is uniform according to an embodiment of the present application;
Fig. 10 (a) is a side view of a microstructure of a prismatic table according to an embodiment of the present disclosure;
Fig. 10 (b) is a top view of a sheet of fig. 10 (a) with a microstructure of prismatically layered;
FIG. 11 (a) is a side view of an elliptical table with a microstructure according to an embodiment of the present application;
FIG. 11 (b) is a top view of a sheet of FIG. 11 (a) with one microstructure layered with elliptical tables;
FIG. 12 is a top view of a sheet with a microstructure layered with a rotating elliptical table;
FIG. 13 is a schematic diagram of an optical property modeling apparatus according to an embodiment of the present application;
fig. 14 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
In order to better understand the technical solutions in the embodiments of the present invention and make the above objects, features and advantages of the embodiments of the present invention more comprehensible, the following describes the technical solutions in the prior art and the embodiments of the present invention in further detail with reference to the accompanying drawings.
In the prior art, taking periodic medium into consideration to form periodic variation, the periodic space is generally uniformly divided into grids, as shown in figure 1, then the dielectric coefficient of the center of each grid is taken as the dielectric coefficient of the grid, two-dimensional fast Fourier transform is carried out to obtain the Fourier coefficient epsilon mn of the dielectric coefficient epsilon (x, y) of the periodic medium, in addition, the sections are uniformly divided along the x direction and the y direction in the periodic space, the dielectric coefficient of the middle point of each integration section is taken as the dielectric coefficient of the section, then the integration is carried out in the y direction and the x direction, and then one-dimensional fast Fourier transform is carried out to obtain the Toeplitz matrix of the dielectric coefficient epsilon (x, y) of the periodic medium. The method has the following problems that if the division intervals of the periodic space are more, the calculation accuracy of the Fourier coefficient of the dielectric coefficient of the periodic medium and the calculation accuracy of the Toeplitz matrix of the dielectric coefficient of the periodic medium can be improved, but the calculation time is time-consuming, and if the division intervals of the periodic space are less, the calculation efficiency can be improved, but the calculation accuracy of the Fourier coefficient of the dielectric coefficient of the periodic medium and the calculation accuracy of the Toeplitz matrix of the dielectric coefficient of the periodic medium is low, so that the efficiency of the forward optical characteristic modeling is influenced, and therefore, a high-efficiency and accurate calculation method of the Toeplitz matrix of the dielectric coefficient of the periodic medium is needed to be studied, so that the problem that the efficiency and the accuracy of the forward optical characteristic modeling cannot be achieved is solved.
Therefore, the optical characteristic modeling method provided by the invention optimizes the division of the integration interval based on the geometric information of the microstructure of the periodic medium in the periodic space, and obtains the optimized grid based on the division of the optimization interval instead of uniformly dividing the integration interval and the grid of the whole area in the periodic space, thereby further improving the Fourier coefficient epsilon mn of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic mediumAndAnd the calculation efficiency and precision of the model are improved.
As shown in fig. 2, the present invention provides an optical characteristic modeling method, which includes the steps of:
s201, dividing the microstructure in the periodic medium into N layers of slices in the z direction, wherein N is a positive integer.
In the periodic space, the periodic medium may comprise several individual microstructures, each of which needs to be divided into a plurality of lamellae in the z-direction. Illustratively, assuming a side view of a microstructure as shown in the left-hand graph of fig. 3, which is not constant in the z-direction, the microstructure is divided into a plurality of layers of lamellae in the z-direction, and the thickness of the lamellae is sufficiently small, as shown in the right-hand graph of fig. 3, the light scattering properties of each layer of lamellae are uniformly constant in the z-direction, so that the light scattering effect of the entire microstructure can be regarded as a light scattering effect of a plurality of superimposed lamellae distributed uniformly in the z-direction.
S202, for the thin sheet with the same microstructure, acquiring the geometric information of each closed area projected by the thin sheet on the xy plane of the periodic space, and dividing the periodic space according to the geometric information to obtain a target integral interval divided in the x direction and a target integral interval divided in the y direction.
In addition, optionally, the periodic space is also used as a polygon during projection, and the periodic space is valued as-p x/2～px/2 in the x direction, and the periodic space is valued as-p y/2～py/2,px and p y in the y direction, which are respectively the period lengths of the periodic space in the x direction and the y direction.
S203, calculating Fourier coefficient epsilon mn of dielectric coefficient of periodic medium and Toeplitz matrix of dielectric coefficient of periodic mediumAnd
S204, performing strict coupled wave analysis by utilizing the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium so as to realize optical characteristic modeling of the periodic medium.
Specifically, a toeplitz matrix of dielectric coefficients of a periodic medium based on a fourier coefficient epsilon mn of the dielectric coefficients of the periodic mediumAndTheoretical spectra were calculated using a rigorous coupled wave analysis (rigorous coupled WAVE ANALYSIS, RCWA) theoretical algorithm.
In the above method, the calculation of the fourier coefficient of the dielectric function of the periodic medium and the toeplitz matrix of the dielectric coefficient of the periodic medium requires the division of the periodic space into grids and sections, respectively. Compared with the prior art, the grid and the interval are uniformly divided in the prior art, the geometric information of the microstructure in the periodic medium is not considered, the whole periodic space is directly uniformly divided, the geometric information of the microstructure is not changed or the periodic space corresponding to smaller change is uniformly divided, the calculated amount is increased, the periodic space corresponding to larger change of the geometric information of the microstructure is uniformly divided, if the dividing times are enough, the calculated amount is increased sharply, and if the dividing times are less, the calculating error is increased, and the accuracy of acquiring the theoretical spectrum is reduced. The embodiment of the invention optimizes the division of the grids and the intervals based on the geometric information of each closed area projected by the thin sheet on the xy plane of the periodic space, reduces the division quantity of the grids and the intervals, reduces the calculated amount and improves the calculation precision at the same time, thereby overcoming the defects of the prior art, and the geometric information of the closed areas is directly determined by the geometric information of the microstructure. Therefore, based on the target integral interval obtained by the method, the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium with high precision can be obtained more efficiently, and further the efficiency and the precision of calculating the theoretical spectrum are improved.
In a possible implementation manner, the geometric information of each closed area projected by the sheet on the xy plane of the periodic space can be obtained by obtaining each closed area projected by the sheet on the xy plane of the periodic space and representing the boundary of each closed area as each polygon, and obtaining the x coordinate and the y coordinate of each polygon vertex to form a set of x coordinates and a set of y coordinates.
In another possible implementation manner, the periodic space is divided according to the geometric information, where the coordinates in the set of x coordinates and the set of y coordinates are arranged in order from large to small or from small to large, and any two adjacent coordinates in the set of x coordinates and the set of y coordinates after the arrangement form a candidate integral interval, whether the candidate integral interval is a non-uniform interval is determined, the length of the candidate integral interval is obtained, and when the candidate integral interval is a non-uniform interval and the length of the candidate integral interval is greater than or equal to a preset step length, the candidate integral interval is divided into a plurality of target integral intervals, otherwise, the candidate integral interval is taken as a target integral interval.
In detail, the shapes of the microstructures are various, the corresponding geometries are also various, and the non-polygonal geometry can be approximated as a polygon, and the polygon has a plurality of vertices. For complex periodic media, there are multiple microstructures in one periodic unit, and fig. 4 is a plan view of one periodic unit obtained by projecting any sheet in the z direction on the xy plane, where it can be seen that there are multiple polygons such as triangles, quadrilaterals, and hexagons. in this example, the vertex coordinates of the triangle, the vertex coordinates of the quadrilateral point, and the vertex coordinates of the hexagonal point may be sequentially obtained, and then, based on the vertex coordinates of the triangle, The quadrilateral point vertex coordinates and the hexagonal point vertex coordinates construct a set of x coordinates of all vertices and a set of y coordinates of all vertices, alternatively, the x coordinate set may further include endpoint x coordinates-p x/2 and p x/2;y coordinates in the x direction of the periodic space and endpoint y coordinates-p y/2 and p y/2 in the y direction of the periodic space. Optionally, in constructing the set of x coordinates and the set of y coordinates, deduplication may also be performed, as well as a sort process from large to small or from small to large. Taking the order from small to large as an example, the set of x coordinates for all polygon vertices is denoted as { -p x/2,g0,g1,…,gτ,px/2 }, and-p x/2<g0<g1<…<gτ<px/2, τ is a natural number, the set of y coordinates for all polygon vertices is denoted as { -p y/2,η0,η1,…,ηζ,py/2 }, and-p y/2<η0<η1<…<ηζ<py/2, ζ is a natural number. And dividing the set of coordinates in the y direction into a plurality of target integral intervals based on the coordinates in the set of coordinates in the y direction to obtain a plurality of target integral intervals in the y direction. In the method, aiming at any one candidate integral interval in the x direction and the y direction, when the length of the candidate integral interval formed by two adjacent coordinates is smaller than a preset step length, the candidate integral interval is directly used as a target integral interval, no further division is performed, and the complexity of subsequent calculation can be reduced on the premise that the accuracy of the toeplitz matrix of the dielectric coefficient of the periodic medium and the dielectric coefficient of the periodic medium is not influenced. For candidate integral intervals larger than or equal to the preset step length, whether the integral intervals are further divided or not can be judged according to whether the integral intervals are uniform or not, so that accuracy and calculation efficiency of calculating the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium are improved.
Wherein the candidate integral intervals are uniform if the distribution of the periodic medium in the candidate integral intervals is uniform or the candidate integral intervals do not have the polygon, and the candidate integral intervals are non-uniform if the distribution of the periodic medium in the candidate integral intervals is non-uniform. Specifically, it may be determined whether the candidate integral intervals are uniform as follows. For a candidate integral interval in the x direction, the number of first boundary intersections formed by intersecting all polygon boundaries in the candidate integral interval with a first reference boundary line of the candidate integral interval is the same as the number of second boundary intersections formed by intersecting the polygon boundaries with a second reference boundary line of the candidate integral interval, and the sum of absolute values of differences of corresponding y values of all polygon boundaries in the candidate integral interval with the second boundary intersection line is smaller than a threshold value, the candidate integral interval is uniform, otherwise, the candidate integral interval is non-uniform, wherein the first reference boundary line and the second reference boundary line are lines which are perpendicular to the non-coincident line of the candidate integral interval, and the intersections of the first reference boundary line and the second reference boundary line with the candidate integral interval are not endpoints of the candidate integral interval, and for a candidate integral interval in the y direction, the number of intersections formed by intersecting all polygon boundaries in the candidate integral interval with a third reference boundary line of the candidate integral interval and the fourth reference boundary line of the candidate integral interval is the same as the fourth reference boundary line of the candidate integral interval, and the intersection of the fourth reference boundary line of the candidate integral interval is the uniform, otherwise, the first reference boundary line is the non-coincident line of the fourth reference boundary line is the non-uniform, and the non-coincident line of the fourth reference boundary line is the non-coincident line of the candidate boundary line of the fourth boundary line is the non-uniform, and the fourth reference boundary line is the intersection of the candidate boundary line of the intersection of the candidate boundary line is the intersection of the intersection line of the fourth boundary line.
Taking the example of obtaining candidate integral intervals in the x direction as an example, fig. 5 shows that a period unit includes a plurality of microstructures, and x coordinate values of all vertices of a polygon corresponding to each microstructure are obtained to obtain a schematic diagram of the candidate integral intervals in the x direction. The polygon in the middle of fig. 5 is obtained by polygon processing of a graph with a projection boundary of the microstructure thin layer as a curve. Arranging the x coordinate values of all the vertexes from large to small or from small to large, and forming candidate integral intervals according to any two adjacent coordinates in the coordinate set arranged in sequence, wherein the candidate integral intervals are as shown in figure 5 (-px/2,g0),(g0,g1),(g1,g2)……(g12,g13),(g13,g14),(g14,px/2).
The present embodiment provides a method flow for determining whether candidate integral intervals are uniform, which includes the following steps, as shown in fig. 6.
S601, a first reference boundary line and a second reference boundary line of any candidate integral interval in the x direction are obtained. Illustratively, the two x-coordinates of the candidate subinterval are g γ' and g γ'+1,gγ'<gγ'+1, respectively, and a first straight line expressed by x=g γ' +δ1 and a second straight line expressed by x=g γ'+1 - δ2 are respectively used as the first reference boundary line and the second reference boundary line of the candidate subinterval.
Wherein γ' is a natural number, 0< δ 1<g γ'+1-gγ',0<δ2<gγ'+1-gγ', and g γ'+δ1≠gγ'+1 - δ2.
S602, the number h of first boundary intersections formed by the first reference boundary line intersecting the polygon and the number k of second boundary intersections formed by the second reference boundary line intersecting the polygon are obtained.
S603, judging whether h is equal to k, if yes, executing S604, otherwise executing S608.
S604, it is determined whether h and k are equal to zero, if not, S605 is executed, and if yes, S607 is executed.
S605, acquiring y coordinates (α1, α2,..alpha.h) of the first boundary intersection point and y coordinates (β1, β2,..beta.k) of the second boundary intersection point, wherein the y coordinates of the h boundary intersection points and the y coordinates of the k boundary intersection points are all arranged in order from large to small or from small to large, and Δ1= |α1- β1|+|α2- β2|++, and Δ1+|αh- βk|.
Alternatively, if the periodic space is also a polygon during the projection of the slice, in this step, it is determined whether h and k are equal to 2, that is, if h and k are equal to 2, the candidate integral sub-section is a uniform section, and if not, S605 is executed.
Illustratively, the periodic space at the time of sheet projection is taken as one polygon, as shown in fig. 7, the first reference boundary line x=g γ' +δ1 intersects the polygon to form the y coordinates of four boundary intersections α1, α2, α3, and α4, and the second reference boundary line x=g γ'+1 —δ2 intersects the polygon to form the y coordinates of four boundary intersections β1, β2, β3, and β4. Alternatively, when the projection time does not perform the polygon processing on the periodic space, the first reference boundary line x=g γ' +δ1 and the second reference boundary line=g γ'+1 —δ2 in fig. 7 intersect the polygon to form two boundary intersections.
S606, it is determined whether Δ1 is smaller than a threshold, if yes, S607 is executed, and if no, S608 is executed.
For example, the threshold may be one percent of the x-direction period length p x or one thousandth of p x.
And S607, taking the candidate integral sub-interval as a uniform interval.
And S608, taking the candidate integral sub-interval as a non-uniform interval.
Further, when the candidate integral intervals in the x direction are non-uniform intervals, the candidate integral intervals can be divided according to a preset step length (according to experience of 0.1-5 nm), the candidate integral intervals can be divided by a dichotomy, the candidate integral intervals can be continuously divided by other dividing methods, and the dividing of each candidate integral interval is completed one by analogy, so that the target integral intervals in the x direction are obtained. Illustratively, fig. 8 shows a schematic diagram of a target integral interval obtained by dividing the candidate integral interval in the x-direction shown in fig. 5. As shown in FIG. 8, compared with the prior art that the periodic space is uniformly divided, the obtained target integral intervals are directly determined by the geometric information of the projected closed area of the microstructure sheet in the periodic medium by adopting the method of the embodiment of the invention, the number of the obtained target integral intervals is reduced, the calculated amount is reduced, the obtained target integral intervals can reflect the change of the geometric information of the microstructure in the periodic medium, the accuracy of obtaining the theoretical spectrum is further improved, the defect that the calculation efficiency and the calculation accuracy in the prior art cannot be achieved is overcome, and in addition, the more complex the microstructure in the periodic medium, the more obvious the effect of the embodiment of the invention on the improvement of the calculation efficiency and the calculation accuracy is.
As shown in fig. 9, the present embodiment provides a determining method for determining whether the candidate integral intervals in the y direction are uniform, which includes the following steps.
S901, a third reference boundary line and a fourth reference boundary line of any candidate integral interval in the y direction are acquired. Illustratively, the two y coordinates of the candidate subinterval are η e' and η e'+1,ηe'<ηe'+1, respectively, and a third straight line denoted by y=η e' +δ1 'and a fourth straight line denoted by y=η e'+1 - δ2' are respectively used as the third reference boundary line and the fourth reference boundary line of the candidate subinterval.
Where e ' is a natural number, 0< δ1' < η e'+1-ηe',0<δ2'<ηe'+1-ηe', and η e'+δ1'≠ηe'+1 - δ2'.
S902, the number u of third boundary intersection points formed by the intersection of the third reference boundary line and the polygon and the number v of fourth boundary intersection points formed by the intersection of the fourth reference boundary line and the polygon are obtained.
S903, judging whether u is equal to v, if so, executing S904, otherwise, executing S908.
S904, it is determined whether u and v are equal to zero, if not, S905 is executed, and if yes, S907 is executed.
S905, acquiring the x-coordinates (σ1, σ2,..once, σu) of the third boundary intersection point and the x-coordinates (ω1, ω2,..once, ωv) of the fourth boundary intersection point, wherein the x-coordinates of the u boundary intersection points and the x-coordinates of the v boundary intersection points are all arranged in the order from large to small or from small to large, and Δ2= |σ1- ω1|+|σ2- ω2|++,.+ - |σu- ωv|.
Alternatively, if the periodic space is also a polygon during the slice projection, in this step, it is determined whether u and v are equal to 2, that is, if u and v are equal to 2, the candidate integral sub-section is a uniform section, and if not, S905 is performed.
S906, it is determined whether Δ2 is smaller than a set threshold, if yes, S907 is executed, and if no, S908 is executed.
Illustratively, the set threshold may be one percent of the y-direction period length p y or one thousandth of the y-direction period length p y.
And S907, taking the candidate integral sub-interval as a uniform interval.
And S908, taking the candidate integral sub-interval as a non-uniform interval.
Based on the above steps, when the candidate integral intervals in the y direction are non-uniform intervals, the candidate integral intervals can be divided according to a preset step length (according to experience of 0.1-5 nm), the candidate integral intervals can be divided by a dichotomy method, the candidate integral intervals can be continuously divided by other dividing methods, and the dividing of each candidate integral interval is completed one by analogy, so that the target integral intervals in the y direction are obtained.
In a possible embodiment, based on the target integral interval in the x direction and the target integral interval in the y direction, a grid consisting of the target integral interval in the x direction and the target integral interval in the y direction is obtained, assuming that c 1,c2,…,cφ are respectively recorded, phi grids are counted in total, the target integral interval obtained in the x direction is recorded as (-px/2,t0),(t0,t1),(t1,t2),…,(tγ-1,tγ),(tγ,px/2),y, and the target integral interval obtained in the x direction is recorded as (-py/2,s0),(s0,s1),(s1,s2),…,(se-1,se),(se,py/2)., and the toeplitz matrix of dielectric coefficient epsilon (x, y) of the periodic medium is obtained jl Toeplitz matrix of dielectric constant epsilon (x, y) of periodic medium satisfying the following formula one jl The following formula two is satisfied.
The fourier coefficient of the dielectric coefficient epsilon (x, y) of the periodic medium satisfies the following equation three:
where i is the imaginary unit P x is the x-direction period, p y is the y-direction period, m and j are the x-direction orders, n and l are the y-direction orders ,kx＝2π/px,-px/2、t0、t1、t2、…、tγ-1、tγ、px/2, respectively, the x-coordinate ;ky＝2π/py,-py/2、s0、s1、s2、…、se-1、se、py/2 of the target integral interval in the x-direction is the y-coordinate of the target integral interval in the y-direction,Representative gridX-coordinate and y-coordinate of the center point of (c),Representative gridIs defined by the area of the (c),Is the number of grids, m, n, j and l are integers, gamma and e are natural numbers,Is a positive integer.
In order to verify the model established by the method, the microstructure in the periodic medium is respectively a prismatic table, an elliptical table and a rotary elliptical table for verification.
Scene one
Fig. 10 (a) shows a side view of a microstructure as a pyramid, fig. 10 (b) shows a top view of one sheet after the microstructure is layered as a pyramid, and the gray area in fig. 10 (b) is a projection of the microstructure sheet on the xy plane of the periodic space, the most peripheral dotted line box represents the periodic space, and the vertical dotted line straight line shows the division of the target integral interval in the x direction. The microstructure shown in FIG. 10 (a) is assumed to have the characteristics of TCD_x of 60nm, TCD_Y of 30nm, BCD_x of 80nm, BCD_Y of 50nm, height of 100nm, and number of layers of 10. After modeling the optical characteristics according to the above method, theoretical spectral calculation results are compared with the following table 1. In the prior art, the integration interval is uniformly divided, 256 intervals are uniformly divided in the X direction and the Y direction, and 3 target integration subintervals are respectively divided in the X direction and the Y direction by adopting the method, so that the calculated amount of the Theplitz matrix for solving the dielectric coefficient of the periodic medium and the dielectric coefficient of the periodic medium is greatly reduced, the calculation efficiency of the theoretical spectrum is further improved, 58 seconds are consumed for acquiring the theoretical spectrum in the prior art, 46 seconds are consumed for acquiring the theoretical spectrum in the application, and meanwhile, the precision of the theoretical spectrum obtained by the method is improved by one order of magnitude compared with the precision of the theoretical spectrum obtained by the prior art, and therefore, the theoretical spectrum with higher precision is obtained in less time by adopting the method, and the calculation efficiency and the calculation precision of the theoretical spectrum are improved.
TABLE 1
Scene two
Fig. 11 (a) shows a side view of an elliptical table with a microstructure, fig. 11 (b) shows a top view of a sheet with a layered microstructure, fig. 11 (b) shows a projection of the microstructure sheet on the xy plane of the periodic space, the most peripheral dotted line box represents the periodic space, and the vertical dotted line straight line shows the division of the target integral interval. The microstructure shown in FIG. 11 (a) is assumed to be an elliptical table and has the characteristics of an elliptical table upper elliptical x-axis radius of 40nm, an elliptical table upper elliptical Y-axis radius of 30nm, an elliptical table lower elliptical x-axis radius of 60nm, an elliptical table lower elliptical Y-axis radius of 50nm, an elliptical table height of 100nm, and a number of layers of 10. After modeling the optical characteristics according to the above method, the theoretical spectral calculation results are shown in table 2. In the prior art, the integration interval is uniformly divided into 256 intervals in the X and Y directions, and the method is adopted to divide 87 target integration intervals in the X and 67 target integration intervals in the Y direction, so that the calculated amount of the Theplitz matrix for solving the dielectric coefficient of the periodic medium and the dielectric coefficient of the periodic medium is greatly reduced, the calculation efficiency of the theoretical spectrum is further improved, 172 seconds are consumed for acquiring the theoretical spectrum in the prior art, 160 seconds are consumed for acquiring the theoretical spectrum in the application, and meanwhile, the precision of the theoretical spectrum obtained by the method is improved by one order of magnitude compared with the precision of the theoretical spectrum obtained by the prior art, so that the theoretical spectrum with higher precision is obtained in less time by adopting the method, and the calculation efficiency and the calculation precision of the theoretical spectrum are improved.
TABLE 2
Scene three
The parameters of the rotating elliptical table are assumed to have the characteristics of 40nm of the x-axis radius of the ellipse on the elliptical table, 30nm of the Y-axis radius of the ellipse on the elliptical table, 60nm of the x-axis radius of the ellipse under the elliptical table, 50nm of the Y-axis radius of the ellipse under the elliptical table, 30 degrees of the rotation angle of the elliptical table, 100nm of the elliptical table height and 10 layering numbers. Fig. 12 is a top view of a sheet after the microstructure of the rotating elliptical table is layered, the gray area is the projection of the microstructure sheet on the xy plane of the periodic space, the most peripheral dotted line box represents the periodic space, and the vertical dotted line straight line represents the division of the integration interval. After modeling the optical characteristics according to the above method, the theoretical spectral calculation results are shown in table 3. In the prior art, the integration interval is uniformly divided into 128 intervals in the X and Y directions, and the method is adopted to divide 101 target integration intervals in the X and 77 target integration intervals in the Y direction, so that the calculated amount of the Theplitz matrix for solving the dielectric coefficient of the periodic medium and the dielectric coefficient of the periodic medium is greatly reduced, the calculation efficiency of the theoretical spectrum is further improved, 176 seconds are consumed for acquiring the theoretical spectrum in the prior art, 160 seconds are consumed for acquiring the theoretical spectrum in the application, and meanwhile, the precision of the theoretical spectrum obtained by the method is improved by one order of magnitude compared with the precision of the theoretical spectrum obtained by the prior art, therefore, the theoretical spectrum with higher precision is obtained in less time by adopting the method, and the calculation efficiency and the calculation precision of the theoretical spectrum are improved.
TABLE 3 Table 3
Based on the above-described optical characteristic modeling method, in some embodiments of the present application, an optical characteristic modeling apparatus is disclosed in an embodiment of the present application, and as shown in fig. 13, the apparatus 1300 is used to implement the method described in each of the above method embodiments, and includes a dividing unit 1301, a calculating unit 1302, and a modeling unit 1303.
The dividing unit 1301 is configured to divide the microstructure in the periodic medium into N layers of slices in the z direction, and perform, for slices of the same layer of microstructure, processing to obtain geometric information of each closed region projected by the slice on the xy plane of the periodic space, and divide the periodic space according to the geometric information to obtain a target integral interval divided in the x direction and a target integral interval divided in the y direction.
A calculation unit 1302 for calculating a fourier coefficient of the dielectric coefficient of the periodic medium and a toprilz matrix of the dielectric coefficient of the periodic medium.
And the modeling unit 1303 is used for performing rigorous coupled wave analysis by utilizing the Fourier coefficient of the dielectric coefficient of the periodic medium and the Toeplitz matrix of the dielectric coefficient of the periodic medium so as to realize optical characteristic modeling of the periodic medium.
All relevant contents of each step related to the above method embodiment may be cited to the functional descriptions of the corresponding functional modules, which are not described herein.
In other embodiments of the application, an electronic device 1400 is disclosed, as shown in FIG. 14, which may include one or more processors 1401, memory 1402, display 1403, one or more applications (not shown), and one or more computer programs 1404, all of which may be connected via one or more communication buses 1405. Wherein the one or more computer programs 1404 are stored in the memory 1402 and configured to be executed by the one or more processors 1401, the one or more computer programs 1404 comprising instructions.
The application also provides a computer readable medium having stored thereon a computer program which, when executed by a computer, implements the method of the above-described method embodiments. Specific effects can be added to the above embodiments.
The application also provides a computer program product which, when executed by a computer, implements the method of the above-described method embodiments. Specific effects can be added to the above embodiments.
From the foregoing description of the embodiments, it will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-described division of functional modules is illustrated, and in practical application, the above-described functional allocation may be implemented by different functional modules according to needs, i.e. the internal structure of the apparatus is divided into different functional modules to implement all or part of the functions described above. The specific working processes of the above-described systems, devices and units may refer to the corresponding processes in the foregoing method embodiments, which are not described herein.
The functional units in the embodiments of the present application may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit. The integrated units may be implemented in hardware or in software functional units.
The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the embodiments of the present application may be essentially or a part contributing to the prior art or all or part of the technical solution may be embodied in the form of a software product stored in a storage medium, including several instructions for causing a computer device (which may 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 the embodiments of the present application. The storage medium includes various media capable of storing program codes such as flash memory, removable hard disk, read-only memory, random access memory, magnetic disk or optical disk.
The foregoing is merely a specific implementation of the embodiment of the present application, but the protection scope of the embodiment of the present application is not limited to this, and any changes or substitutions within the technical scope disclosed in the embodiment of the present application should be covered in the protection scope of the embodiment 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.
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