CN109164683B - Method and device for quickly determining light intensity distribution based on mask graphic processing - Google Patents

Method and device for quickly determining light intensity distribution based on mask graphic processing Download PDF

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CN109164683B
CN109164683B CN201811157255.3A CN201811157255A CN109164683B CN 109164683 B CN109164683 B CN 109164683B CN 201811157255 A CN201811157255 A CN 201811157255A CN 109164683 B CN109164683 B CN 109164683B
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CN109164683A (en
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阎江
梁文青
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Moyan Computational Science Suzhou Co ltd
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Moyan Computing Science Nanjing Co ltd
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    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
    • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
    • G03F7/70—Microphotolithographic exposure; Apparatus therefor
    • G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
    • G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
    • G03F7/70508—Data handling in all parts of the microlithographic apparatus, e.g. handling pattern data for addressable masks or data transfer to or from different components within the exposure apparatus
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
    • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
    • G03F7/70—Microphotolithographic exposure; Apparatus therefor
    • G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
    • G03F7/7055—Exposure light control in all parts of the microlithographic apparatus, e.g. pulse length control or light interruption
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods

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Abstract

The application discloses a method and a device for quickly determining light intensity distribution based on mask graphic processing. The method comprises the following steps: establishing a cross transfer function according to the light source function and the pupil function; performing singular value decomposition on the cross transfer function to obtain at least one frequency domain kernel function; determining at least one rectangle into which the mask graph is divided and characteristic information of each rectangle in the at least one rectangle; determining a rectangular projection coefficient corresponding to each rectangle and a kernel function projection coefficient corresponding to each frequency domain kernel function in at least one frequency domain kernel function; and determining the light intensity distribution at the position designated by the user according to the rectangular projection coefficients, the kernel function projection coefficients and the characteristic information of each rectangle. In the application, the light intensity distribution is rapidly determined through the kernel function projection coefficient and the rectangular projection coefficient. Because repeated rectangles exist in the rectangles divided by the mask graph, repeated calculation can be avoided when the rectangular projection coefficients are calculated, the calculation time is reduced, and the photoetching efficiency is improved.

Description

Method and device for quickly determining light intensity distribution based on mask graphic processing
Technical Field
The application belongs to the technical field of semiconductor lithography, and particularly relates to a method and a device for quickly determining light intensity distribution based on mask graph processing.
Background
With the promotion of relevant factors of industrial production technology, integrated circuit devices are smaller and smaller, the integration level of chips is higher and higher, and the manufacturing cost of devices related to intelligent equipment is reduced. In current social life, the use of smart devices makes integrated circuits relevant to the current life. In the industrial production of integrated circuits, the photolithography technique uses the principle of photochemical reaction to transfer a pre-designed mask pattern onto an imaging plane (wafer), which is an inevitable process.
Logic devices and memory devices in integrated circuit devices are different in manufacturing process flow due to the large differences in design. Integrated circuits are fabricated layer by means of so-called planar processes, which require more lithographic layers due to the complexity of the logic device design compared to the memory device design. The memory device has simple pattern, and the central area of the mask is a memory cell and is a regular one-dimensional pattern. The pattern of the logic device is complicated and is a complicated two-dimensional pattern. The lithography process transfers the reticle pattern from the mask to the imaging plane (wafer), and a complete set of lithography processes requires the execution of multiple processes, which is very costly. The real production can not optimize the technological parameters of the mask plate through industrial production. At this time, it is necessary to simulate the lithography process by calculating a lithography model, thereby optimizing and controlling the lithography, for example, increasing the lithography resolution. The lithography model includes: light source, mask, pupil and imaging plane. Wherein calculating the light intensity distribution on the imaging plane is an inevitable step in the lithography calculation.
In the related art, the calculation of the light intensity distribution on the imaging plane requires convolution operation of a mask function, and because the number of mask patterns is large, the amount of data for performing the convolution operation is large, and a large amount of calculation time is required. When the photolithography model is more and more complex, the calculation time required for photolithography is too long, which reduces the efficiency of photolithography.
Disclosure of Invention
The application provides a method and a device for quickly determining light intensity distribution based on mask graph processing, which can be used for solving the problems that in the related technology, due to the fact that the number of mask graphs is large, the data size of convolution operation is large, a large amount of calculation time is needed, and the photoetching efficiency is reduced.
In a first aspect, the present application provides a method for rapidly determining a light intensity distribution based on reticle graphic processing, the method comprising:
establishing a cross transfer function according to the light source function and the pupil function;
performing singular value decomposition on the cross transfer function to obtain at least one frequency domain kernel function;
determining at least one rectangle into which the reticle pattern is divided, and feature information of each rectangle of the at least one rectangle, wherein the feature information comprises: the length of the rectangle, the width of the rectangle and the coordinates of the center of the rectangle;
determining a rectangular projection coefficient corresponding to each rectangle and a kernel function projection coefficient corresponding to each frequency domain kernel function in the at least one frequency domain kernel function;
and determining the light intensity distribution at the position designated by the user according to the rectangular projection coefficients, the kernel function projection coefficients and the characteristic information of each rectangle.
Optionally, the determining the rectangular projection coefficient corresponding to each rectangle and the kernel function projection coefficient corresponding to each frequency domain kernel function of the at least one frequency domain kernel function includes:
calculating the rectangular projection coefficient according to the following relation
Figure BDA0001819189070000021
Wherein, αnsFor the rectangular projection coefficients, h represents the length of the rectangle, w represents the width of the rectangle, JnRepresenting a first class of n-th order Bessel functions, λnsThe s-th zero-root, f, representing a first class of n-th order Bessel functionsjAnd gjCoordinates representing frequency domain discrete sampling points;
calculating the kernel function projection coefficient corresponding to each frequency domain kernel function according to the following relational expression
Figure BDA0001819189070000022
Wherein,
Figure BDA0001819189070000023
projection coefficient phi corresponding to the kth frequency domain kernel function in the at least one frequency domain kernel functionk(fj,gj) Representing a k-th one of the at least one frequency-domain kernel at (f)j,gj) Value of above, JmRepresenting a first class of m-th order Bessel functions, λmtRepresenting the t-th zero-root of the first class of m-th order bezier functions.
Optionally, the determining, according to the rectangular projection coefficients, the kernel function projection coefficients and the feature information of each rectangle, the light intensity distribution at the position specified by the user includes:
determining the light intensity distribution at the user-specified position according to the following relation
Figure BDA0001819189070000024
Where I (x, y) represents the light intensity distribution at the user-specified position (x, y), αnsFor the said rectangular projection coefficients, the rectangular projection coefficients,
Figure BDA0001819189070000025
for the kernel function projection coefficient corresponding to the kth frequency domain kernel function of the at least one frequency domain kernel function, Δ x and Δ y represent the coordinates of the center of the rectangle, Cn+m,q(x, y) represents the orthogonal basis function of the zero-q roots of order n + m on the spatial domain, γn+m,qCoefficients are projected as the product of the basis functions.
Optionally, before determining the light intensity distribution at the user-specified position according to the rectangular projection coefficients, the kernel function projection coefficients and the feature information of each rectangle, the method further includes:
determining the projection coefficient of the product of the basis functions according to the following relation
Figure BDA0001819189070000026
Wherein, FBns(fj,gj) The Fourier Bessel basis function representing the zero-root of the nth order s is in (f)j,gj) Value of, FBmt(fj,gj) The Fourier Bessel basis function representing the mth order t zero is at (f)j,gj) The value of (a) is greater than (b),
Figure BDA0001819189070000027
the conjugate function of the Fourier Bessel basis function representing the zero-root of order q of n + m is represented by (f)j,gj) The value of (c) above.
In a second aspect, the present application provides a device for rapidly determining a light intensity distribution based on reticle graphic processing, the device comprising:
the function establishing module is used for establishing a cross transfer function according to the light source function and the pupil function;
the function decomposition module is used for carrying out singular value decomposition on the cross transfer function to obtain at least one frequency domain kernel function;
a rectangle determination module, configured to determine at least one rectangle into which the reticle pattern is divided, and feature information of each rectangle of the at least one rectangle, where the feature information includes: the length of the rectangle, the width of the rectangle and the coordinates of the center of the rectangle;
a projection determination module, configured to determine a rectangular projection coefficient corresponding to each rectangle and a kernel function projection coefficient corresponding to each frequency domain kernel function in the at least one frequency domain kernel function;
and the light intensity determining module is used for determining the light intensity distribution at the position designated by the user according to the rectangular projection coefficient, the kernel function projection coefficient and the characteristic information of each rectangle.
According to the scheme provided by the application, the light intensity distribution on the specified position of a user can be quickly determined by determining the kernel function projection coefficient corresponding to the kernel function of the frequency domain and the rectangular projection coefficient corresponding to the rectangle divided by the mask graph. Repeated rectangles can appear in rectangles divided by the mask graph, and rectangular projection coefficients are also equal for rectangles with equal length and width, so that repeated calculation can be avoided when the rectangular projection coefficients are determined, the calculation time is reduced, and the photoetching efficiency is further improved.
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In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flow diagram illustrating a method for rapid determination of a light intensity distribution based on reticle graphic processing in accordance with an exemplary embodiment;
FIG. 2 is a schematic diagram illustrating a frequency domain light source and a spatial domain light source in accordance with an exemplary embodiment;
FIG. 3 is a schematic view of a reticle pattern shown in accordance with an exemplary embodiment;
FIG. 4 is a diagram illustrating a light intensity distribution according to an exemplary embodiment;
FIG. 5 is a block diagram illustrating a rapid determination of light intensity distribution based on reticle graphic processing in accordance with an exemplary embodiment.
Detailed Description
In order to make the technical solutions in the embodiments of the present application better understood and make the above objects, features and advantages of the embodiments of the present application more comprehensible, the technical solutions in the embodiments of the present application are described in further detail below with reference to the accompanying drawings.
In the method provided by the embodiment of the application, the execution main body of each step may be a terminal. The terminal is used for photoetching calculation in the photoetching process, and further, photoetching is optimized and controlled.
FIG. 1 is a flow chart illustrating a method for rapid determination of a light intensity distribution based on reticle graphic processing in accordance with an exemplary embodiment. The method may include several steps as follows.
Step 101, establishing a cross transfer function according to the light source function and the pupil function.
When the terminal determines the light intensity distribution of the photoetching model, a light source function and a pupil function are determined. When light emitted by the light source passes through the pupil, part of the light cannot pass through the pupil. The light source function and the pupil function are determined by the light source and the pupil, and if the light source is different, the light source function is also different; pupil functions are different if the pupils are different. Thus, the source function and the pupil function may be predetermined according to the source and pupil actually used in the lithographic process.
After determining the light source function and the pupil function, the terminal establishes a Cross transfer function (TCC) according to the light source function and the pupil function.
Optionally, the terminal establishes the cross transfer function according to the following relation:
TCC(x1,y1；x2,y2)＝J(x1-x2,y1-y2)H(x1,y1)H*(-x2,-y2)
where J (x, y) denotes a light source function on the spatial domain, and H (x, y) denotes a pupil function on the spatial domain. (x)1,y1) And (x)2,y2) Respectively representing two coordinate points in space, TCC (x)1,y1；x2,y2) Representing the cross transfer function to be established by the terminal.
Alternatively, the light source function represents a circular ring light source in the frequency domain, and the light source function J (x, y) in the spatial domain is a response of the light source function in the frequency domain in space. Wherein, the light source function in the frequency domain and the response in the space are realized by fast Fourier transform. Illustratively, as shown in fig. 2, the annular light source 201 has an inner diameter of 0.4 and an outer diameter of 0.6, representing a light source function in the spatial domain, and the light source 202 represents a light source in the frequency domain.
The pupil function H (x, y) in the spatial domain is the spatial response of the pupil function in the frequency domain. Wherein the pupil function in the frequency domain and its spatial response are implemented by a fast fourier transform. The pupil function represents a circular function in the frequency domain, and its radius is 1.
And 102, performing singular value decomposition on the cross transfer function to obtain at least one frequency domain kernel function.
The cross transfer function established by the terminal can be expressed as a matrix with the size of n × n × n × n, namely a cross transfer matrix2×n2And then performing matrix decomposition on the two-dimensional matrix. Since the cross transfer matrix is a positive definite matrix, the terminal can perform singular value decomposition on the cross transfer matrix. Through singular value decomposition, the terminal obtains at least one spatial domain kernel function, which is shown in the following relation:
Figure BDA0001819189070000041
wherein phi isk(x, y) represents a k-th spatial-domain kernel of the at least one spatial-domain kernel. And the terminal determines a frequency domain kernel function corresponding to each spatial domain kernel function in the at least one spatial domain kernel function through Fourier transform to obtain the at least one frequency domain kernel function. A kth frequency domain kernel of the at least one frequency domain kernel is represented as Φk(f,g)。
Step 103, determining at least one rectangle into which the reticle pattern is divided, and characteristic information of each rectangle in the at least one rectangle.
The mask graph is a two-dimensional simple polygon and only comprises right-angle line segments. Thus, the reticle pattern may be divided into at least one rectangle. In the embodiment of the application, the division of the mask graph can be performed in advance by technicians, or can be performed by a terminal according to the vertex information of the mask graph. It should be noted that, in the lithography model, the reticle pattern is also referred to as a lithography pattern or a lithography pattern on the reticle.
Illustratively, as shown in FIG. 3, the reticle pattern 301 is a two-dimensional polygon comprising a plurality of right-angled line segments. The terminal divides the reticle graph 301 according to the vertex information of the reticle graph to obtain a divided reticle graph 302, wherein the divided reticle graph 302 comprises a plurality of rectangles, such as a rectangle 303 and a rectangle 304 shown in FIG. 3.
The terminal determines at least one rectangle into which the mask pattern is divided and the characteristic information of each rectangle in the at least one rectangle, namely the terminal determines each rectangle in the divided mask pattern and the characteristic information of each rectangle. The characteristic information includes: the length of the rectangle, the width of the rectangle, and the coordinates of the center of the rectangle.
Alternatively, the reticle pattern is divided into at least one rectangle, and the mask function representing the reticle pattern is represented by a rectangular function representing the divided rectangle. The following relationship is shown:
Figure BDA0001819189070000051
M(xy) is a mask function over the spatial domain,
Figure BDA0001819189070000052
is a rectangular function on the ith rectangular space domain in the at least one rectangle. Accordingly, the terminal determines the mask function in the frequency domain by fourier transform, as shown by the following relation:
Figure BDA0001819189070000053
m (f, g) is the mask function in the frequency domain, Δ x and Δ y are the coordinates of the center of the rectangle, h is the length of the rectangle, w is the width of the rectangle, i represents the imaginary unit of the complex number, and the sinc function is
Figure BDA0001819189070000054
The response in the frequency domain is shown by the following relation:
Figure BDA0001819189070000055
the terminal may represent the mask function in the spatial and frequency domains by at least one rectangle into which the reticle pattern is divided.
And 104, determining a rectangular projection coefficient corresponding to each rectangle and a kernel function projection coefficient corresponding to each frequency domain kernel function in at least one frequency domain kernel function.
After the at least one frequency domain kernel function is obtained and the characteristic information of each rectangle is determined, the terminal determines a rectangular projection coefficient corresponding to each rectangle and a kernel function projection coefficient corresponding to each frequency domain kernel function. The rectangular projection coefficient and the kernel function projection coefficient are projection coefficients obtained by projecting a rectangular function in a frequency domain, namely a sinc function and a frequency domain kernel function, to a Fourier Bessel basis function by using numerical integration operation at a terminal. Each rectangle corresponds to a rectangular projection coefficient, and each frequency domain kernel corresponds to a kernel projection coefficient. The rectangular projection coefficients corresponding to the rectangles having the same length and width are equal.
Optionally, the terminal calculates the rectangular projection coefficient by the following relation:
Figure BDA0001819189070000056
wherein, αnsIs a rectangular projection coefficient, h represents the length of the rectangle, w represents the width of the rectangle, JnRepresenting a first class of n-th order Bessel functions, λnsThe s-th zero-root, f, representing a first class of n-th order Bessel functionsjAnd gjRepresenting the coordinates of the frequency domain discrete sample points. Since each rectangle corresponds to a rectangular projection coefficient, the terminal needs to determine the rectangular projection coefficients with the same number as the rectangles for at least one rectangle into which the reticle pattern is divided. However, as can be seen from the above-mentioned relational expression, when calculating the rectangular projection coefficients, the difference between different rectangles is the length and width of the rectangle, i.e., the value of the sinc function. Since the reticle pattern is a two-dimensional simple polygon, a repeated rectangle, that is, a rectangle having the same length and width, appears in the rectangle into which the reticle pattern is divided. For rectangles of equal length and width, the values of the sinc function are also equal, and their corresponding rectangular projection coefficients are also equal. Therefore, when the terminal determines the rectangular projection coefficient corresponding to each rectangle, the calculation is only needed once for the rectangles with the same length and width, repeated calculation is not needed, and the calculation time is saved.
Optionally, the terminal calculates a kernel function projection coefficient corresponding to each frequency domain kernel function according to the following relation:
Figure BDA0001819189070000057
wherein,
Figure BDA0001819189070000058
for a kernel projection coefficient, phi, corresponding to the kth frequency-domain kernel of the at least one frequency-domain kernelk(fj,gj) Representing a k-th one of the at least one frequency-domain kernel at (f)j,gj) Value of above, JmRepresenting a first class of m-th order Bessel functions, λmtRepresenting the t-th zero-root of the first class of m-th order bezier functions.
Optionally, after the terminal determines the rectangular projection coefficient corresponding to each rectangle and the kernel function projection coefficient corresponding to each frequency domain kernel function in the at least one frequency domain kernel function, the terminal determines the mask function and the frequency domain kernel function after projection according to the following relations:
Figure BDA0001819189070000061
Figure BDA0001819189070000062
FBns(f, g) Fourier Bessel basis function, FB, representing zero s of order nmt(f, g) represents the Fourier Bessel basis function of the mth order t zero root.
And 105, determining the light intensity distribution at the position designated by the user according to the rectangular projection coefficients, the kernel function projection coefficients and the characteristic information of each rectangle.
After the terminal determines the rectangular projection coefficient corresponding to each rectangle and the kernel function projection coefficient corresponding to each frequency domain kernel function in the at least one frequency domain kernel function, the terminal determines the light intensity distribution at the position specified by the user according to the rectangular projection coefficient, the kernel function projection coefficient and the characteristic information of each rectangle.
The terminal determines the light intensity distribution at the designated position of the user according to the following relation
Figure BDA0001819189070000063
I (x, y) represents the light intensity distribution at the user-specified position (x, y), Cn+m,q(x, y) represents the orthogonal basis function of the zero-q roots of order n + m on the spatial domain, γn+m,qCoefficients are projected as the product of the basis functions. Wherein, Cn+m,qAnd (x, y) and the Fourier Bessel basis function of the zeroth order q of n + mth are Fourier transform. Gamma rayn+m,qIs to project the product of Fourier Bessel basis functions onto FourierProjection coefficients obtained on Bessel basis functions.
Illustratively, as shown in FIG. 4, the resulting light intensity distribution at the imaging plane is shown. Wherein different colors in different regions indicate different light intensities, and the color of the region 401 is different from that of the region 402, and the light intensity is also different.
Optionally, the basis function product projection coefficient γ is determined according to the following relationn+m,q
Figure BDA0001819189070000064
Wherein, FBns(fj,gj) The Fourier Bessel basis function representing the zero-root of the nth order s is in (f)j,gj) Value of, FBmt(fj,gj) The Fourier Bessel basis function representing the mth order t zero is at (f)j,gj) The value of (a) is greater than (b),
Figure BDA0001819189070000065
the conjugate function of the Fourier Bessel basis function representing the zero-root of order q of n + m is represented by (f)j,gj) The value of (c) above. Since the Fourier Bessel basis function is irrelevant to the light source function, the pupil function and the mask function in the process of calculating photoetching, the light intensity distribution can be predetermined or set before the light intensity distribution is determined, and the calculation time is saved.
Optionally, after determining the projected mask function and the frequency domain kernel function, the terminal calculates the field strength by using the projected mask function and the frequency domain kernel function, and performs inverse fourier transform on the field strength to finally determine the analytic expression of the light intensity distribution at the position specified by the user. The terminal determines the field intensity corresponding to each frequency domain kernel function according to the following relational expression:
Figure BDA0001819189070000071
according to the field intensity of the relational expression technology, the Fourier Bessel basis function FB is actually calculatedns(f, g) and FBmtMultiplication of (f, g), of Fourier Bessel basis functionsThe product is projected onto the Fourier Bessel basis function as shown in the following relation:
Figure BDA0001819189070000072
Bn+m,q(f, g) represents the Fourier Bessel basis function of the zeroth q order of n + mth. Wherein n, m, s, t and q can be set according to practical experience. Therefore, the terminal determines the field strength corresponding to each frequency domain kernel function as shown in the following relation:
Figure BDA0001819189070000073
after the field intensity corresponding to each frequency domain kernel function is determined, the light intensity distribution at the position designated by the user is determined according to the following relational expression:
Figure BDA0001819189070000074
F-1representing an inverse fourier transform. Orthogonal basis function C due to zero root of order q of n + m on spatial domainn+m,q(x, y) is Fourier transformed with the Fourier Bessel basis function of zero-n + mth order q, so F-1[Ek(f,g)]Is Cn+m,q(x, y) are combined linearly, the following relationship is obtained:
Figure BDA0001819189070000075
the terminal finally determines the analytical formula of the light intensity distribution at the position designated by the user as follows:
Figure BDA0001819189070000076
in the method provided by the embodiment of the application, the light intensity distribution at the position designated by a user can be quickly determined by determining the kernel function projection coefficient corresponding to the frequency domain kernel function and the rectangular projection coefficient corresponding to the rectangle divided by the mask graph. Repeated rectangles can appear in rectangles divided by the mask graph, and rectangular projection coefficients are also equal for rectangles with equal length and width, so that repeated calculation can be avoided when the rectangular projection coefficients are determined, the calculation time is reduced, and the photoetching efficiency is further improved.
FIG. 5 is a block diagram illustrating a rapid determination of light intensity distribution based on reticle graphic processing in accordance with an exemplary embodiment. The apparatus has functionality to implement the above-described method examples. The apparatus may include: a function building module 501, a function decomposition module 502, a rectangle determination module 503, a projection determination module 504 and a light intensity determination module 505.
A function establishing module 501, configured to establish a cross transfer function according to the light source function and the pupil function.
A function decomposition module 502, configured to perform singular value decomposition on the cross transfer function to obtain at least one frequency domain kernel function.
A rectangle determination module 503, configured to determine at least one rectangle into which the reticle pattern is divided, and feature information of each rectangle of the at least one rectangle, where the feature information includes: the length of the rectangle, the width of the rectangle, and the coordinates of the center of the rectangle.
A projection determining module 504, configured to determine a rectangular projection coefficient corresponding to each of the rectangles and a kernel function projection coefficient corresponding to each of the at least one frequency domain kernel functions.
And the light intensity determining module 505 is configured to determine the light intensity distribution at the position specified by the user according to the rectangular projection coefficients, the kernel function projection coefficients and the feature information of each rectangle.
In the device provided by the embodiment of the application, the light intensity distribution at the position designated by a user can be quickly determined by determining the kernel function projection coefficient corresponding to the frequency domain kernel function and the rectangular projection coefficient corresponding to the rectangle divided by the mask graph. Repeated rectangles can appear in rectangles divided by the mask graph, and rectangular projection coefficients are also equal for rectangles with equal length and width, so that repeated calculation can be avoided when the rectangular projection coefficients are determined, the calculation time is reduced, and the photoetching efficiency is further improved.
Optionally, the projection determining module 504 is specifically configured to:
calculating the rectangular projection coefficient according to the following relation
Figure BDA0001819189070000081
Wherein, αnsFor the rectangular projection coefficients, h represents the length of the rectangle, w represents the width of the rectangle, JnRepresenting a first class of n-th order Bessel functions, λnsThe s-th zero-root, f, representing a first class of n-th order Bessel functionsjAnd gjCoordinates representing frequency domain discrete sampling points;
calculating the kernel function projection coefficient corresponding to each frequency domain kernel function according to the following relational expression
Figure BDA0001819189070000082
Wherein,
Figure BDA0001819189070000083
projection coefficient phi corresponding to the kth frequency domain kernel function in the at least one frequency domain kernel functionk(fj,gj) Representing a k-th one of the at least one frequency-domain kernel at (f)j,gj) Value of above, JmRepresenting a first class of m-th order Bessel functions, λmtRepresenting the t-th zero-root of the first class of m-th order bezier functions.
Optionally, the light intensity determining module 505 is specifically configured to:
determining the light intensity distribution at the user-specified position according to the following relation
Figure BDA0001819189070000084
Where I (x, y) represents the light intensity distribution at the user-specified position (x, y), αnsFor the said rectangular projection coefficients, the rectangular projection coefficients,
Figure BDA0001819189070000085
for the kernel function projection coefficient corresponding to the kth frequency domain kernel function of the at least one frequency domain kernel function, Δ x and Δ y represent the coordinates of the center of the rectangle, Cn+m,q(x, y) represents the orthogonal basis function of the zero-q roots of order n + m on the spatial domain, γn+m,qCoefficients are projected as the product of the basis functions.
Optionally, the light intensity determination module 505 is further configured to:
determining the projection coefficient of the product of the basis functions according to the following relation
Figure BDA0001819189070000086
Wherein, FBns(fj,gj) The Fourier Bessel basis function representing the zero-root of the nth order s is in (f)j,gj) Value of, FBmt(fj,gj) The Fourier Bessel basis function representing the mth order t zero is at (f)j,gj) The value of (a) is greater than (b),
Figure BDA0001819189070000091
the conjugate function of the Fourier Bessel basis function representing the zero-root of order q of n + m is represented by (f)j,gj) The value of (c) above.
It should be noted that, when the apparatus provided in the foregoing embodiment implements the functions thereof, only the division of the above functional modules is illustrated, and in practical applications, the above functions may be distributed by different functional modules according to actual needs, that is, the content structure of the device is divided into different functional modules, so as to complete all or part of the functions described above. In addition, the apparatus and method embodiments provided by the above embodiments belong to the same concept, and specific implementation processes thereof are described in the method embodiments for details, which are not described herein again.
In addition, the present application further provides a computer storage medium, wherein the computer storage medium may store a program, and the program may include some or all of the steps of the embodiments of the method for rapid determination of a light intensity distribution based on reticle graphic processing provided by the present application when executed. The storage medium may be a magnetic disk, an optical disk, a Read-only Memory (ROM), a Random Access Memory (RAM), or the like.
In the above embodiments, all or part may be implemented by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer program product.
The computer program product includes one or more computer instructions. When the computer program is loaded and executed by a computer, the procedures or functions according to the above-described embodiments of the present application are wholly or partially generated. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device.
The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another computer readable storage medium, for example, from one network node, computer, server, or data center to another site, computer, or server by wire or wirelessly.
Further, in the description of the present application, "a plurality" means two or more than two unless otherwise specified. In addition, in order to facilitate clear description of technical solutions of the embodiments of the present application, in the embodiments of the present application, terms such as "first" and "second" are used to distinguish the same items or similar items having substantially the same functions and actions. Those skilled in the art will appreciate that the terms "first," "second," etc. do not denote any order or quantity, nor do the terms "first," "second," etc. denote any order or importance.
The above-described embodiments of the present application do not limit the scope of the present application.

Claims (8)

1. A method for quickly determining light intensity distribution based on mask plate graphic processing is characterized by comprising the following steps:
establishing a cross transfer function according to the light source function and the pupil function;
performing singular value decomposition on the cross transfer function to obtain at least one frequency domain kernel function;
determining at least one rectangle into which the reticle pattern is divided, and feature information of each rectangle of the at least one rectangle, wherein the feature information comprises: the length of the rectangle, the width of the rectangle and the coordinates of the center of the rectangle;
determining a rectangular projection coefficient corresponding to each rectangle and a kernel function projection coefficient corresponding to each frequency domain kernel function in the at least one frequency domain kernel function, wherein the rectangular projection coefficient and the kernel function projection coefficient refer to projection coefficients obtained by projecting a rectangular function on a frequency domain, namely a sinc function and a frequency domain kernel function, to a Fourier Bessel basis function by using numerical integration operation at a terminal;
and determining the light intensity distribution at the position designated by the user according to the rectangular projection coefficients, the kernel function projection coefficients and the characteristic information of each rectangle.
2. The method of claim 1, wherein determining the rectangular projection coefficients corresponding to each of the rectangles and the kernel function projection coefficients corresponding to each of the at least one frequency domain kernel functions comprises:
calculating the rectangular projection coefficient according to the following relation
Figure FDA0002460939430000011
Wherein, αnsFor the rectangular projection coefficients, h represents the length of the rectangle, w represents the width of the rectangle, JnRepresenting a first class of n-th order Bessel functions, λnsThe s-th zero-root, f, representing a first class of n-th order Bessel functionsjAnd gjCoordinates representing frequency domain discrete sampling points;
calculating the kernel function projection coefficient corresponding to each frequency domain kernel function according to the following relational expression
Figure FDA0002460939430000012
Wherein,
Figure FDA0002460939430000013
projection coefficient phi corresponding to the kth frequency domain kernel function in the at least one frequency domain kernel functionk(fj,gj) Representing a k-th one of the at least one frequency-domain kernel at (f)j,gj) Value of above, JmRepresenting a first class of m-th order Bessel functions, λmtRepresenting the t-th zero-root of the first class of m-th order bezier functions.
3. The method of claim 1, wherein determining the light intensity distribution at the user-specified position according to the rectangular projection coefficients, the kernel function projection coefficients and the feature information of each rectangle comprises:
determining the light intensity distribution at the user-specified position according to the following relation
Figure FDA0002460939430000014
Where I (x, y) represents the light intensity distribution at the user-specified position (x, y), αnsFor the said rectangular projection coefficients, the rectangular projection coefficients,
Figure FDA0002460939430000015
for the kernel function projection coefficient corresponding to the kth frequency domain kernel function of the at least one frequency domain kernel function, Δ x and Δ y represent the coordinates of the center of the rectangle, Cn+m,q(x, y) represents the orthogonal basis function of the zero-q roots of order n + m on the spatial domain, γn+m,qProjecting coefficients, gamma, for the product of the basis functionsn+m,qThe projection coefficient is obtained by projecting the product of the fourier bessel basis function onto the fourier bessel basis function.
4. The method of claim 3, wherein before determining the light intensity distribution at the user-specified position based on the rectangular projection coefficients, the kernel function projection coefficients and the feature information of each rectangle, the method further comprises:
determining the projection coefficient of the product of the basis functions according to the following relation
Figure FDA0002460939430000021
Wherein, FBns(fj,gj) The Fourier Bessel basis function representing the zero-root of the nth order s is in (f)j,gj) Value of, FBmt(fj,gj) The Fourier Bessel basis function representing the mth order t zero is at (f)j,gj) The value of (a) is greater than (b),
Figure FDA0002460939430000022
the conjugate function of the Fourier Bessel basis function representing the zero-root of order q of n + m is represented by (f)j,gj) The value of (c) above.
5. A rapid determination device of light intensity distribution based on mask plate graphic processing is characterized in that the device comprises:
the function establishing module is used for establishing a cross transfer function according to the light source function and the pupil function;
the function decomposition module is used for carrying out singular value decomposition on the cross transfer function to obtain at least one frequency domain kernel function;
a rectangle determination module, configured to determine at least one rectangle into which the reticle pattern is divided, and feature information of each rectangle of the at least one rectangle, where the feature information includes: the length of the rectangle, the width of the rectangle and the coordinates of the center of the rectangle;
the projection determining module is configured to determine a rectangular projection coefficient corresponding to each rectangle and a kernel function projection coefficient corresponding to each frequency domain kernel function in the at least one frequency domain kernel function, where the rectangular projection coefficient and the kernel function projection coefficient are projection coefficients obtained by projecting a sine function and a frequency domain kernel function, which are rectangular functions in a frequency domain, to a fourier bessel basis function by using a numerical integration operation at a terminal;
and the light intensity determining module is used for determining the light intensity distribution at the position designated by the user according to the rectangular projection coefficient, the kernel function projection coefficient and the characteristic information of each rectangle.
6. The apparatus of claim 5, wherein the projection determination module is specifically configured to:
calculating the rectangular projection coefficient according to the following relation
Figure FDA0002460939430000023
Wherein, αnsFor the rectangular projection coefficients, h represents the length of the rectangle, w represents the width of the rectangle, JnRepresenting a first class of n-th order Bessel functions, λnsThe s-th zero-root, f, representing a first class of n-th order Bessel functionsjAnd gjCoordinates representing frequency domain discrete sampling points;
calculating the kernel function projection coefficient corresponding to each frequency domain kernel function according to the following relational expression
Figure FDA0002460939430000031
Wherein,
Figure FDA0002460939430000032
projection coefficient phi corresponding to the kth frequency domain kernel function in the at least one frequency domain kernel functionk(fj,gj) Representing a k-th one of the at least one frequency-domain kernel at (f)j,gj) Value of above, JmRepresenting a first class of m-th order Bessel functions, λmtRepresenting the t-th zero-root of the first class of m-th order bezier functions.
7. The apparatus of claim 5, wherein the light intensity determination module is specifically configured to:
determining the light intensity distribution at the user-specified position according to the following relation
Figure FDA0002460939430000033
Where I (x, y) represents the light intensity distribution at the user-specified position (x, y), αnsFor the said rectangular projection coefficients, the rectangular projection coefficients,
Figure FDA0002460939430000034
for the kernel function projection coefficient corresponding to the kth frequency domain kernel function of the at least one frequency domain kernel function, Δ x and Δ y represent the coordinates of the center of the rectangle, Cn+m,q(x, y) represents the orthogonal basis function of the zero-q roots of order n + m on the spatial domain, γn+m,qProjecting coefficients, gamma, for the product of the basis functionsn+m,qThe projection coefficient is obtained by projecting the product of the fourier bessel basis function onto the fourier bessel basis function.
8. The apparatus of claim 7, wherein the light intensity determination module is further configured to:
determining the projection coefficient of the product of the basis functions according to the following relation
Figure FDA0002460939430000035
Wherein, FBns(fj,gj) The Fourier Bessel basis function representing the zero-root of the nth order s is in (f)j,gj) Value of, FBmt(fj,gj) The Fourier Bessel basis function representing the mth order t zero is at (f)j,gj) The value of (a) is greater than (b),
Figure FDA0002460939430000036
representing zero roots of order q of n + mThe conjugate function of the Fourier Bessel basis function is at (f)j,gj) The value of (c) above.
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