Method and system for solving a Fraunhofer diffraction field of a mask pattern
By combining topological analysis and Bézier curve fitting with Green's theorem, the calculation of Fraunhofer diffraction field of mask pattern is transformed from two-dimensional surface integral to one-dimensional line integral, which solves the problem of low accuracy and efficiency in the calculation of lithographic mask pattern and realizes efficient and accurate lithography simulation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HUAZHONG UNIV OF SCI & TECH
- Filing Date
- 2026-02-28
- Publication Date
- 2026-06-16
AI Technical Summary
Existing technologies suffer from low accuracy and efficiency in calculating the Fraunhofer diffraction field of photolithographic mask patterns, and traditional methods introduce unavoidable sawtooth-like discrete errors and waste of computational resources.
Topological analysis is used to extract the boundary of the mask pattern, Bézier curve fitting is used to form the mask profile, and the two-dimensional surface integral of the Fraunhofer diffraction field is converted into a one-dimensional line integral along the profile curve. Dimensionality reduction calculation is then performed using Green's theorem.
It improves computational accuracy and efficiency, eliminates sawtooth discrete errors, reduces memory overhead, and enhances the convergence speed and solution quality of the reverse lithography algorithm.
Smart Images
Figure CN121746516B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of integrated circuit technology, and more specifically, relates to a method and system for solving the Fraunhofer diffraction field of a mask pattern. Background Technology
[0002] A photolithography system can be considered a low-pass filter system. Accurately and quickly assessing the degree to which the mask pattern is affected by the imaging effect of the photolithography system remains a constant challenge in computational photolithography. For Fraunhofer far-field imaging simulation, current techniques directly use fast FFT to simulate the mask pattern.
[0003] Traditional methods discretize the mask into a pixel matrix and calculate the spectrum using Fast Fourier Transform (FFT). Its computational complexity is O(n log n). ,in This refers to the grid resolution. As process nodes shrink, to ensure accuracy, The computational cost must increase exponentially, leading to a sharp rise in computational complexity. Lithography systems are essentially low-pass filters, with only the central low-frequency components participating in imaging (typically occupying only a tiny fraction of the spectrum). Full-image FFT calculations of the full frequency domain data truncate and discard most of the high-frequency components, resulting in significant computational waste. Pixelation representation introduces unavoidable staircase effects when processing curve masks or diagonal lines, causing sub-pixel-level simulation distortion. In gradient-based optimization tasks such as inverse lithography (ILT), binary pixel masks are non-differentiable. Existing techniques typically introduce a sigmoid function for continuous approximation, which not only increases computational overhead but also introduces physical discrepancies between the simulation model and the actual mask (hard truncation).
[0004] Therefore, a method for calculating the diffraction field of mask patterns that can solve the above problems is needed. Summary of the Invention
[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method and system for solving the Fraunhofer diffraction field of a mask pattern, which solves the problems of low calculation accuracy and efficiency in the diffraction field calculation process.
[0006] To achieve the above objectives, according to one aspect of the present invention, a method for solving the Fraunhofer diffraction field of a mask pattern is provided, the method comprising the following steps:
[0007] Topological analysis is performed on the mask pattern to extract its boundaries. The extracted boundaries are then fitted to obtain a mask contour formed by fitting multiple closed loops.
[0008] The two-dimensional surface integral of the Fraunhofer diffraction field of the mask pattern is converted into a one-dimensional line integral along the contour curve.
[0009] The diffraction field of each contour curve in each closed loop of the mask contour is calculated separately. The sum of the diffraction fields of all contour curves in all closed loops is the one-dimensional line integral diffraction field of the mask pattern along the contour curve, thereby obtaining the Fraunhofer diffraction field of the desired mask pattern.
[0010] More preferably, the fitting of the extracted boundary is performed using a piecewise Bézier curve.
[0011] More preferably, the dimensionality reduction adopts Green's formula.
[0012] More preferably, the formula for reducing the two-dimensional area integral of the Fraunhofer diffraction field of the mask pattern to a one-dimensional line integral along the contour curve is as follows:
[0013]
[0014] in, For the two-dimensional surface integral of the Fraunhofer diffraction field of the mask pattern, ( , (i) represents the spatial frequency coordinates of the obtained diffraction field, where i is the imaginary unit and e is the natural logarithm. Represents the integral of a closed profile. For all the curve contours of the mask, Input the spatial coordinates of the mask, Let be the differentials with respect to x and y, respectively. The input mask field.
[0015] More preferably, the formula for calculating the diffraction field of each profile curve in each closed loop is as follows:
[0016]
[0017] in, In the diffraction field coordinates The one-dimensional line integral of a contour curve in a mask pattern, where i is the imaginary unit. It is the natural logarithm. Indicates the line integral symbol, ( , Let ) represent the spatial frequency coordinates of the obtained diffraction field, s be the curve parameters, and ds be the derivative with respect to s. b represents the minimum and maximum values of s, respectively. The input mask field.
[0018] More preferably, the formula for calculating the one-dimensional line integral diffraction field of the mask pattern along the contour curve is as follows:
[0019]
[0020] in,( , () represents the frequency coordinates of the obtained diffraction field. In the diffraction field coordinates The one-dimensional line integral of the mask pattern along the contour curve is given by M, where M represents the mask pattern consisting of M closed regions. and Indicates the first A closed region is composed of Composed of segmented curves, This indicates that the first The transmittance of a closed region is ,, The summation symbol is used to represent the summation symbol. Indicates the integral sign, where s is the curve parameter. b represents the minimum and maximum values of s, respectively. This represents the coordinates of a point on the contour curve segment. and for coordinates for parameters The derivative of It is the differential of s.
[0021] More preferably, the fitting of the extracted boundary is performed using non-uniform rational B-splines, B-spline curves, Fourier descriptors, implicit function representations, higher-order polynomial fitting, or Hermitian splines; the dimensionality reduction is performed using Gaussian divergence theorem, Stokes' theorem, line integrals of complex functions, or boundary element method.
[0022] According to another aspect of the invention, a system for solving the Fraunhofer diffraction field of a mask pattern is provided, the system comprising an actuator for performing the above-described method for solving the Fraunhofer diffraction field of a mask pattern.
[0023] According to another aspect of the present invention, a computer storage medium is provided having a computer program stored thereon, the computer program being used to implement the above-described method for solving the Fraunhofer diffraction field of a mask pattern.
[0024] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:
[0025] 1. This invention abandons the traditional pixel grid representation and uses parametric curves (such as Bezier curves) to accurately describe the mask contour; it transforms the two-dimensional surface integral of the mask transmission function into a one-dimensional line integral along the contour, and then derives and solves the diffraction field; the analytical calculation based on parametric curves eliminates the "staircase effect", and can provide a theoretically accurate solution no matter how fine the simulation mesh is, which greatly improves the calculation accuracy and calculation efficiency.
[0026] 2. This invention uses Bézier curves to transform the countless sampling points of the mask Fraunhofer imaging problem into edge integration over the mask. Compared with the traditional FFT (Fast Fourier Transform) based method, it does not require high-resolution meshing of the mask, completely eliminating the aliasing effect. Especially when dealing with ultra-large-scale masks or non-orthogonal irregular patterns, this method significantly reduces memory overhead and greatly improves computational efficiency while ensuring computational accuracy.
[0027] 3. This invention transforms the two-dimensional surface integral of the mask transmission function into a one-dimensional line integral along the boundary Bézier curve using Green's formula. This reduces the computational complexity from being related to the "number of area pixels" to being related to the "number of contour control points." When processing photolithographic masks with sparse spectral characteristics, the computational speed can be improved by several orders of magnitude, and it naturally supports sparse sampling.
[0028] 4. The one-dimensional line integral of the diffraction field along the contour curve establishes a direct functional relationship between the spectrum and the coordinates of the control points. This relationship comes from the analytical representation of the mask contour, so it is smooth, continuous and differentiable. This allows the partial derivative with respect to the control point coordinates to be directly calculated during mask optimization without any manual approximation, which greatly improves the convergence speed and solution quality of the reverse lithography algorithm.
[0029] 5. In pursuit of accuracy, traditional FFT methods require extremely high sampling frequencies, resulting in a huge memory requirement for storing the mask matrix. This invention stores mask information using a series of Bezier control points, rather than storing high-resolution bitmaps. This achieves extremely high data compression, significantly reducing peak memory usage during full-chip simulation or large-scale multi-level optimization, making real-time simulation of ultra-complex masks possible on ordinary computing hardware. Attached Figure Description
[0030] Figure 1 This is a schematic diagram of the Bézier curve segment fitting boundary profile constructed according to a preferred embodiment of the present invention.
[0031] Figure 2 This is a schematic diagram of mask contour extraction constructed according to a preferred embodiment of the present invention, wherein (a) is the input mask pattern and (b) is the mask contour extracted by Bézier curve. Detailed Implementation
[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0033] A method for solving the Fraunhofer diffraction field of a mask pattern, the specific steps of which are as follows:
[0034] (1) Vectorization encoding of mask pattern
[0035] Topological analysis is performed on the input mask pattern to extract the closed boundary. The boundary is fitted using a piecewise Bézier curve to obtain the mask contour. The order of the Bézier curve (such as linear, quadratic, or cubic Bézier curve) is automatically selected based on the curvature change of the contour, as shown in formula (1).
[0036]
[0037] Where s is a parameter variable, and its value is usually between 1 and 2. between. This represents the point on the Bézier curve corresponding to the parameter s. Let be the i-th control point, and n be the order of the Bézier curve. For an n-order Bézier curve, it contains... One control point, This indicates a summation.
[0038] Thus, the mask pattern is parameterized as an ordered sequence of control points. This representation is mathematically continuous, completely eliminating the quantization error caused by pixelation.
[0039] like Figure 1 As shown, the blue lines from P0 to P3 represent the mask surface contour, and four points P0 to P3 are obtained by piecewise Bézier curve fitting.
[0040] For the mask shown in the left figure below, the contour of the curve and the control points of the Bézier curve are extracted through Bézier curve fitting encoding. For example... Figure 2 As shown, the red and blue dots are the control points of a series of Bézier curve segments obtained by fitting and encoding.
[0041] Ultimately, the mask pattern is encoded as a set of multiple closed loops, each represented by an ordered sequence of Bezier control points. This representation not only preserves the sub-pixel accuracy of the mask edges but also lays the foundation for subsequent analytical Fourier transforms.
[0042] This invention primarily uses the Bezier curve as the encoding basis. In practical applications, the following curves can also be used for boundary fitting, specifically:
[0043] (a) Non-uniform rational B-splines (NURBS): Compared with ordinary Bézier curves, NURBS can more accurately represent quadratic curves such as circular arcs and has better local controllability. It can directly replace Bézier control points for spectrum analysis derivation.
[0044] (b) B-splines: Control points are connected by piecewise polynomial basis functions. Although they are more complex in form, their derivative and integral properties are consistent with those of Bézier curves.
[0045] (c) Fourier Descriptors: The contour edges are represented as Fourier series expansions of the azimuth angles, and the corresponding mask spectrum is directly calculated using the harmonic properties in the frequency domain.
[0046] (d) Implicit function representation (such as level sets): Although level sets are usually used for pixelation, under certain conditions, pixel-free simulation can also be achieved by extracting the contour line analytical equations of the level sets and combining them with integral transformation.
[0047] (e) Higher-order polynomial fitting or Hermite splines: analytical curves constructed using edge point positions and derivative information, whose mathematical essence still belongs to parametric polynomial integrals.
[0048] It should also be emphasized that even if the Bézier curve is degenerated into a high-density polygonal line segment (Piecewise Linear), as long as Green's formula or a similar method is applied for frequency domain analytical transformation, it should still fall within the protection scope of this invention.
[0049] (2) Reduce the two-dimensional area integral of the mask transmission function to a one-dimensional line integral along the contour.
[0050] Taking deep ultraviolet lithography scalar imaging as an example, the near field of the mask It can be represented as ,in For the transmittance of the mask, the binary mask's It is 0 or a constant. The Fraunhofer diffraction field of the binary mask (i.e., the Fourier transform of the mask's near field) is:
[0051]
[0052] in, The two-dimensional surface integral of the Fraunhofer diffraction field of the mask pattern. Represents a two-dimensional area integral. This represents the spatial region enclosed by the mask outline, where i is the imaginary unit and e is the natural logarithm. Input the spatial coordinates of the mask, Let be the differentials with respect to x and y, respectively. The mask field is the input mask pattern; typically, the mask has a constant transmittance within each closed region. , The obtained diffraction field spatial frequency coordinates, i.e., spatial frequency, characterize the rate of change of the mask pattern grayscale (or phase) in space. In photolithography imaging simulation, the diffraction field needs to be discretized and sampled.
[0053] Using Green's formula (3), the surface integral in (2) can be converted into a one-dimensional diffraction field line integral, i.e., formula (11).
[0054]
[0055] Q and P are functions, and the region... It is a closed region. express edge, Input the spatial coordinates of the mask, Let be the differentials with respect to x and y, respectively. For all the curve contours of the mask, This represents the spatial region enclosed by the mask outline. Integral representation of closed contour This represents a two-dimensional area integral.
[0056] The specific derivation process is as follows:
[0057] For formula (3), it is only necessary to find a specific set of functions P and Q that satisfy... This allows the area integral to be converted into the marginal integral.
[0058] Not difficult to obtain, and When such conditions are met, for the region Inside, take it here ,Right now .
[0059] Calculate separately ,
[0060]
[0061]
[0062] in Input the spatial coordinates of the mask, , To find the partial derivatives with respect to x and y respectively, ( , () represents the frequency coordinates of the obtained diffraction field. For the input mask field, Let i be the natural logarithm, and i be the imaginary unit.
[0063] Therefore, the integrand on the left side of Green's formula
[0064]
[0065] in , To find the partial derivatives with respect to x and y respectively, let P and Q be functions. For the spatial coordinates of the input mask, ( , () represents the frequency coordinates of the obtained diffraction field. For the input mask field, Let i be the natural logarithm, and i be the imaginary unit.
[0066] That is
[0067]
[0068] in For the spatial coordinates of the input mask, ( , () represents the frequency coordinates of the obtained diffraction field. For the input mask field, Let i be the natural logarithm, and i be the imaginary unit. These are the differentials with respect to x and y, respectively.
[0069] Substitute the result into Green's theorem
[0070]
[0071] in,( , () represents the frequency coordinates of the obtained diffraction field. Input the spatial coordinates of the mask, Let be the differentials with respect to x and y, respectively. For the input mask field, Let i be the natural logarithm, and i be the imaginary unit. Represents a two-dimensional area integral. Represents the integral of a closed profile. For all the curve contours of the mask, It represents the spatial region enclosed by the mask outline.
[0072] Right now
[0073]
[0074] in,( , () represents the frequency coordinates of the obtained diffraction field. Input the spatial coordinates of the mask, Let be the differentials with respect to x and y, respectively. For the input mask field, Let i be the natural logarithm, and i be the imaginary unit. Represents a two-dimensional area integral. Represents the integral of a closed profile. For all the curve contours of the mask, It represents the spatial region enclosed by the mask outline.
[0075] for( , When ) equals 0, a meaningless situation occurs, which, according to the physical meaning of Fraunhofer diffraction fields, is ( , A value of 0 corresponds to the area of the mask region, so it is necessary to find a new value that satisfies the condition. , This place makes but:
[0076]
[0077] in Input the spatial coordinates of the mask, , To find the partial derivatives with respect to x and y respectively, let P' and Q' be functions. In this case, Green's theorem is:
[0078]
[0079] in, Input the spatial coordinates of the mask, Let be the differentials with respect to x and y, respectively. Represents the integral of a closed profile. Represents a two-dimensional area integral. For all the curve contours of the mask, dA represents the spatial region enclosed by the mask outline, where A is the area of the region and dA represents the derivative of the area.
[0080] In summary, formula (11) is derived.
[0081]
[0082] in, The two-dimensional surface integral of the Fraunhofer diffraction field of the mask pattern. , ), where \(\xi\) and \(\eta\) are the spatial frequency coordinates of the resulting diffraction field, \(i\) is the imaginary unit, and \(e\) is the base of the natural logarithm. denotes a closed contour integral. represents all the curve contours of the mask. are the spatial coordinates of the input mask. denote the partial derivatives with respect to \(x\) and \(y\) respectively. is the input mask field. Usually, each closed region of the mask has a constant transmittance, which is generally taken as , where \(0 < T < 1\) or \(0\) represents the transmissive region and the non - transmissive region respectively.
[0083] According to the definition of the Fourier transform, the mask spectrum is the integral of the mask transmittance function over a two - dimensional region. According to Green's theorem, if the function is constant within a closed region, the two - dimensional area integral over this region can be accurately transformed into a line integral along the edge contour of this region.
[0084] Although the above embodiments use Green's theorem to achieve the conversion from a two - dimensional spatial domain area integral to a one - dimensional edge line integral, in practical applications, the following methods can also be used for dimensionality reduction:
[0085] (a) The 2D form of Gauss's Divergence Theorem: By defining a specific vector field (whose divergence is equal to the complex transmittance function of the mask), the flux integral within the region is converted into a flux integral along the closed curve using the divergence theorem.
[0086] (b) Stokes' Theorem: From the perspective of simplifying in the complex plane or three - dimensional manifolds, the integral of the mask function is converted into an edge curl integral through exterior differential forms.
[0087] (c) Line integral of complex functions (Cauchy integral formula and its corollaries): If the mask edge is characterized as an analytic curve in the complex plane, the region integral can be converted into an edge path integral based on complex variables using the properties of analytic functions.
[0088] (d) Conversion of the Boundary Element Method (BEM) concept: Using the Green's function as the weight function, the governing equation (such as the source - term integral of the wave equation) is converted into an integral equation that only contains boundary variables.
[0089] The above methods are consistent with the Bessel - Green framework adopted in this invention in terms of physical mechanism, and the convergence and accuracy gain of their calculation results both stem from the core idea of "converting from surface to line and analytically representing" proposed in this invention.
[0090] (3) Bessel contour analytic integral:
[0091] The integral of the above contour line is decomposed into several segments of Bézier curve paths. Bézier curves have an analytical expression in polynomial form, and their frequency domain components (…) The Fourier integral term under () can be used to derive analytical solutions or efficient numerical approximations. To obtain the mapping relationship from the "Bézier curve control points" to the "Fraunhofer diffraction field," a section of a Bézier curve is used as an example for derivation. The obtained one-dimensional diffraction field line integral is denoted as... .
[0092] Taking a third-order Bézier curve as an example, the coordinates of each point on the curve are: According to formula (1), the coordinates of the points on the curve profile are obtained as follows:
[0093]
[0094] Among them, on the curve segment This represents the coordinates of a point on the contour curve segment. and These are the control points of the Bézier curve. coordinates and Coordinates, i.e., control points coordinates , The summation symbol is used, taking a third-order Bézier curve as an example, so it ranges from 0 to 3, obtained from formula (12). coordinates for parameters derivative and :
[0095]
[0096] in, and Indicates the curve segment The derivative of the coordinates with respect to the parameter s, and These are the control points of the Bézier curve. coordinates and Coordinates, i.e., control points coordinates , The summation symbol is used, and in the case of a third-order Bézier curve, it ranges from 0 to 3.
[0097] Obtained through substitution , Substituting into formula (5), we get:
[0098] Mapping relationship of a contour line in a closed region:
[0099]
[0100] in This represents the mask integral of the curve segment within the contour. , () represents the spatial frequency coordinates of the obtained diffraction field. Let be the natural logarithm, i be the imaginary unit, and s be the curve parameter, which here takes the value of . , Indicates the integral symbol, This represents the coordinates of a point on the contour curve segment. This indicates that the point is relative to The derivative value, i.e., the tangent value, For the input mask field, It is the differential of s.
[0101] As can be seen from the transformation relationship of formula (5), formula (8) is the mapping relationship from the "Bézier curve control point" to the "François diffraction field".
[0102] For a closed contour, it can be divided into several contour segments. These contour segments correspond to a series of control points. As long as the first control point and the last control point coincide, the closed contour can be obtained.
[0103] Let the mask pattern consist of M closed regions, where the first region is... A closed region is composed of Segment curve Composition, and the transmittance of the closed region is That is, within this closed area Therefore, we have:
[0104]
[0105] in,( , () represents the frequency coordinates of the obtained diffraction field. In the diffraction field coordinates The one-dimensional line integral of the mask pattern along the contour curve is given by M, where M represents the mask pattern consisting of M closed regions. and Indicates the first A closed region is composed of Composed of segmented curves, This indicates that the first The transmittance of a closed region is , The summation symbol is used to represent the summation symbol. This indicates the integral sign, and s is the curve parameter, which here takes the value of , This represents the coordinates of a point on the contour curve segment. and for coordinates for parameters The derivative of It is the differential of s.
[0106] (4) Full-frequency domain analytical calculation:
[0107] For each spatial frequency sampling point, the pre-derived Bessel segment integral formula is directly applied, and the total spectrum of the mask is obtained by accumulating the contributions of all boundary segments. During the calculation, the filtering effect of spatial resolution in lithographic imaging can be directly considered, and only the center segment is calculated. , Frequency points within the specified frequency range can avoid wasting computing resources.
[0108] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for solving the Fraunhofer diffraction field of a mask pattern, characterized in that, The method includes the following steps: Topological analysis is performed on the mask pattern to extract its boundaries. The extracted boundaries are then fitted to obtain a mask contour formed by fitting multiple closed loops. The two-dimensional area integral of the Fraunhofer diffraction field of the mask pattern is reduced to a one-dimensional line integral along the contour curve; The diffraction field of each contour curve in each closed loop of the mask contour is calculated separately. The sum of the diffraction fields of all contour curves in all closed loops is the one-dimensional line integral diffraction field of the mask pattern along the contour curve, thereby obtaining the Fraunhofer diffraction field of the desired mask pattern.
2. The method for solving the Fraunhofer diffraction field of a mask pattern as described in claim 1, characterized in that, The extracted boundary is fitted using a piecewise Bézier curve.
3. The method for solving the Fraunhofer diffraction field of a mask pattern as described in claim 2, characterized in that, The dimensionality reduction is achieved using Green's formula.
4. The method for solving the Fraunhofer diffraction field of a mask pattern as described in claim 3, characterized in that, The formula for reducing the two-dimensional area integral of the Fraunhofer diffraction field of the mask pattern to a one-dimensional line integral along the contour curve is as follows: in, For the two-dimensional surface integral of the Fraunhofer diffraction field of the mask pattern, ( , (i) represents the spatial frequency coordinates of the obtained diffraction field, where i is the imaginary unit and e is the natural logarithm. Represents the integral of a closed profile. For all the curve contours of the mask, Input the spatial coordinates of the mask, Let be the differentials with respect to x and y, respectively. The input mask field.
5. The method for solving the Fraunhofer diffraction field of a mask pattern as described in claim 4, characterized in that, The formula for calculating the diffraction field of each profile curve in each closed loop is as follows: in, In the diffraction field coordinates The one-dimensional line integral of a contour curve in a mask pattern, where i is the imaginary unit. It is the natural logarithm. Indicates the line integral symbol, ( , Let ) represent the spatial frequency coordinates of the obtained diffraction field, s be the curve parameters, and ds be the derivative with respect to s. b represents the minimum and maximum values of s, respectively. For the input mask field, This represents the coordinates of a point on the contour curve segment. and for coordinates for parameters The derivative of .
6. The method for solving the Fraunhofer diffraction field of a mask pattern as described in claim 5, characterized in that, The formula for calculating the one-dimensional line integral diffraction field of the mask pattern along the contour curve is as follows: in,( , () represents the frequency coordinates of the obtained diffraction field. In the diffraction field coordinates The one-dimensional line integral of the mask pattern along the contour curve is given by M, where M represents the mask pattern consisting of M closed regions. and Indicates the first A closed region is composed of Composed of segmented curves, This indicates that the first The transmittance of a closed region is , The summation symbol is used to represent the summation symbol. Indicates the integral sign, where s is the curve parameter. b represents the minimum and maximum values of s, respectively. This represents the coordinates of a point on the contour curve segment. and for coordinates for parameters The derivative of It is the differential of s.
7. The method for solving the Fraunhofer diffraction field of a mask pattern as described in claim 1, characterized in that, The extraction boundary is fitted using non-uniform rational B-splines, B-spline curves, Fourier descriptors, implicit function representations, higher-order polynomial fitting, or Hermitian splines; the dimensionality reduction is achieved using Gaussian divergence theorem, Stokes' theorem, line integrals of complex functions, or the boundary element method.
8. A system for solving the Fraunhofer diffraction field of a mask pattern, characterized in that, The system includes an actuator for performing a method for solving the Fraunhofer diffraction field of a mask pattern as described in any one of claims 1-7.
9. A computer storage medium having a computer program stored thereon, characterized in that, The computer program is used to implement the method for solving the Fraunhofer diffraction field of a mask pattern as described in any one of claims 1-7.