CN109164683A - Light distribution fast determination method and device based on mask graph processing - Google Patents
Light distribution fast determination method and device based on mask graph processing Download PDFInfo
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- CN109164683A CN109164683A CN201811157255.3A CN201811157255A CN109164683A CN 109164683 A CN109164683 A CN 109164683A CN 201811157255 A CN201811157255 A CN 201811157255A CN 109164683 A CN109164683 A CN 109164683A
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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
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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
- G03F7/7055—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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- G—PHYSICS
- 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
Abstract
This application discloses a kind of light distribution fast determination methods and device based on mask graph processing.This method comprises: establishing according to light source function and pupil function and intersecting transmission function；Singular value decomposition is carried out to transmission function is intersected, obtains at least one frequency domain kernel function；Determine the characteristic information of each rectangle at least one rectangle and at least one rectangle that mask graph is divided into；Determine each corresponding kernel function projection coefficient of frequency domain kernel function in the corresponding rectangular projection coefficient of each rectangle and at least one frequency domain kernel function；According to rectangular projection coefficient, the characteristic information of kernel function projection coefficient and each rectangle determines the light distribution in specified location in user.In the application, by kernel function projection coefficient and rectangular projection coefficient, light distribution is quickly determined.Exist in the rectangle divided due to mask graph and repeat rectangle, it can be avoided and compute repeatedly when calculating rectangular projection coefficient, reduce and calculate the time, improve photoetching efficiency.
Description
Technical field
The application belongs to technical field of semiconductor lithography, in particular to a kind of light distribution based on mask graph processing
Fast determination method and device.
Background technique
With the promotion of industrial production technology correlative factor, integrated circuit device is smaller and smaller, and the integrated level of chip is more next
It is higher, so that the relevant device manufacturing cost of smart machine reduces.And in current social life, smart machine use so that
Integrated circuit with live now it is closely bound up.In the industrial production of integrated circuit, photoetching technique utilizes photochemical reaction principle
Prior design is transferred on an imaging plane (wafer) in mask graph, is one of inevitable technique.
Logical device and memory device in integrated circuit device, since there are biggish difference, the works of manufacture for its design
There is also differences for skill process.Integrated circuit is prepared in layer by so-called planar technology, due to logical device
It is more complicated relative to memory device design structure, thus need more lithography layers.The graphics Web publishing of memory device is simple,
Exposure mask central area is storage unit, is the one-dimensional pattern of rule.The graphics Web publishing of logical device is complicated, for complicated two dimension
Figure.Mask graph is transferred on imaging plane (wafer) by photoetching process from mask, and the photoetching process of complete set needs
The execution of multiple working procedure expends huge.True production can not pass through industrial production Optimizing Process Parameters to mask.
At this time, it may be necessary to simulate photoetching process by calculating lithography model, and then optimize and control photoetching, such as increases photoetching and differentiate
Rate.Lithography model includes: light source, mask, pupil and imaging plane.Wherein, the light distribution calculated on imaging plane is photoetching
An inevitable step in calculating.
In the related art, the light distribution calculated on imaging plane needs the convolution algorithm to mask function, due to covering
Template figure enormous amount causes the data volume for carrying out convolution algorithm huge, needs largely to calculate the time.When lithography model is got over
When coming more complicated, calculating overlong time needed for carrying out photoetching reduces the efficiency for carrying out photoetching.
Summary of the invention
The application provides a kind of light distribution fast determination method and device based on mask graph processing, can be used for solving
Certainly in the related technology, due to mask graph enormous amount, cause the data volume for carrying out convolution algorithm huge, need largely to count
Evaluation time reduces the problem of carrying out photoetching efficiency.
In a first aspect, the application provides a kind of light distribution fast determination method based on mask graph processing, it is described
Method includes:
According to light source function and pupil function, establishes and intersect transmission function；
Singular value decomposition is carried out to the intersection transmission function, obtains at least one frequency domain kernel function；
Determine the spy of each rectangle at least one rectangle and at least one described rectangle that mask graph is divided into
Reference breath, the characteristic information include: the length of rectangle, the width of rectangle and the coordinate of rectangular centre；
It determines each in the corresponding rectangular projection coefficient of each rectangle and at least one described frequency domain kernel function
The corresponding kernel function projection coefficient of frequency domain kernel function；
According to the rectangular projection coefficient, the characteristic information of the kernel function projection coefficient and each rectangle is determined
Light distribution in specified location in user.
Optionally, the determination each corresponding rectangular projection coefficient of rectangle and at least one described frequency-domain kernel
Each corresponding kernel function projection coefficient of frequency domain kernel function in function, comprising:
The rectangular projection coefficient is calculated according to following relational expression
Wherein, αnsFor the rectangular projection coefficient, h indicates the length of the rectangle, and w indicates the width of the rectangle, JnIt indicates
First kind n rank Bessel function, λnsIndicate s-th of zero root of first kind n rank Bessel function, fjAnd gjIt indicates that frequency domain is discrete to adopt
The coordinate of sampling point；
Each corresponding kernel function projection coefficient of frequency domain kernel function is calculated according to following relational expression
Wherein,For the corresponding kernel function projection of k-th of frequency domain kernel function at least one described frequency domain kernel function system
Number, Φk(fj,gj) indicate that k-th of frequency domain kernel function is in (f at least one described frequency domain kernel functionj,gj) on value, JmIt indicates
First kind m rank Bessel function, λmtIndicate t-th of zero root of first kind m rank Bessel function.
Optionally, described according to the rectangular projection coefficient, the spy of the kernel function projection coefficient and each rectangle
Reference breath, determines the light distribution in specified location in user, comprising:
The light distribution in the specified location in user is determined according to following relational expression
Wherein, I (x, y) indicates the light distribution on specified location in user (x, y), αnsFor the rectangular projection coefficient,
For the corresponding kernel function projection coefficient of k-th of frequency domain kernel function at least one described frequency domain kernel function, Δ x and Δ y indicate institute
State the coordinate of rectangular centre, Cn+m,qThe orthogonal basis function of n+m rank q zero root on (x, y) representation space domain, γn+m,qFor basic function
Product projection coefficient.
Optionally, described according to the rectangular projection coefficient, the spy of the kernel function projection coefficient and each rectangle
Reference breath, before determining the light distribution in specified location in user, further includes:
The basis function product projection coefficient is determined according to following relational expression
Wherein, FBns(fj,gj) indicate Fourier's Bezier basic function of n rank s zero root in (fj,gj) on value, FBmt(fj,
gj) indicate Fourier's Bezier basic function of m rank t zero root in (fj,gj) on value,Indicate n+m rank q zero root
Fourier's Bezier basic function conjugate function in (fj,gj) on value.
Second aspect, the application provides a kind of quick determining device of light distribution based on mask graph processing, special
Sign is that described device includes:
Function establishes module, for establishing and intersecting transmission function according to light source function and pupil function；
Function decomposition module obtains at least one frequency-domain kernel for carrying out singular value decomposition to the intersection transmission function
Function；
Rectangle determining module, for determine at least one rectangle that mask graph is divided into and it is described at least one
The characteristic information of each rectangle in rectangle, the characteristic information include: the length of rectangle, the width of rectangle and the coordinate of rectangular centre；
Project determining module, for determine the corresponding rectangular projection coefficient of each rectangle and it is described at least one
Each corresponding kernel function projection coefficient of frequency domain kernel function in frequency domain kernel function；
Light intensity determining module, for according to the rectangular projection coefficient, the kernel function projection coefficient and each square
The characteristic information of shape determines the light distribution in specified location in user.
Scheme provided by the present application, by determining that the corresponding kernel function projection coefficient of frequency domain kernel function and mask graph are drawn
The corresponding rectangular projection coefficient of rectangle divided, can quickly determine the light distribution in specified location in user.Due to mask
It will appear repetition rectangle in the rectangle that figure is divided into, and for the long rectangle equal with width, rectangular projection coefficient is also equal, because
This, can be avoided when determining rectangular projection coefficient and compute repeatedly, and reduces and calculates the time, and then improves the efficiency of photoetching.
Detailed description of the invention
In order to more clearly explain the technical solutions in the embodiments of the present application, make required in being described below to embodiment
Attached drawing is briefly described, it should be apparent that, the drawings in the following description are only some examples of the present application, for
For those of ordinary skill in the art, without creative efforts, it can also be obtained according to these attached drawings other
Attached drawing.
Fig. 1 is that a kind of light distribution based on mask graph processing shown according to an exemplary embodiment quickly determines
The flow chart of method；
Fig. 2 is the schematic diagram of a kind of frequency domain light source and spatial domain light source shown according to an exemplary embodiment；
Fig. 3 is a kind of schematic diagram of mask graph shown according to an exemplary embodiment；
Fig. 4 is a kind of schematic diagram of light distribution shown according to an exemplary embodiment；
Fig. 5 is that a kind of light distribution based on mask graph processing shown according to an exemplary embodiment quickly determines
The block diagram of device.
Specific embodiment
In order to make those skilled in the art more fully understand the technical solution in the embodiment of the present application, and keep the application real
The above objects, features, and advantages for applying example can be more obvious and easy to understand, with reference to the accompanying drawing to the technology in the embodiment of the present application
Scheme is described in further detail.
The executing subject of method provided by the embodiments of the present application, each step can be terminal.The terminal is used for photoetching process
In photoetching calculate, and then optimize and control photoetching.
Fig. 1 is that a kind of light distribution based on mask graph processing shown according to an exemplary embodiment quickly determines
The flow chart of method.This method may include the following steps.
Step 101, it according to light source function and pupil function, establishes and intersects transmission function.
When terminal determines the light distribution of lithography model, light source function and pupil function are first determined.The light that light source issues
When line passes through pupil, there is some light that can not pass through pupil.Light source function and pupil function are determined that light source is not by light source and pupil
Together, then light source function is also different；Pupil is different, then pupil function is also different.Therefore, light source function and pupil function can bases
The light source and pupil actually used in photoetching process predefines.
After determining light source function and pupil function, terminal is established according to light source function and pupil function and intersects transmitting letter
Number (Transmission Cross Coefficient, TCC).
Optionally, terminal intersects transmission function according to following relation reality:
TCC(x1,y1；x2,y2)=J (x1-x2,y1-y2)H(x1,y1)H*(-x2,-y2)
Wherein, the light source function on J (x, y) representation space domain, the pupil function on H (x, y) representation space domain.(x1,y1)
(x2,y2) respectively indicate spatially two coordinate points, TCC (x1,y1；x2,y2) indicate the terminal intersection to be established transmitting letter
Number.
Optionally, the annulus light source on light source function representation frequency domain, the light source function J (x, y) in spatial domain are on frequency domain
The response spatially of light source function.Wherein, the light source function on frequency domain and its response spatially pass through fast Fourier
Transformation is realized.Illustratively, as shown in Fig. 2, the internal diameter of annulus light source 201 is 0.4, outer diameter 0.6, the light on representation space domain
Source function, light source 202 indicate the light source on frequency domain.
Pupil function H (x, y) in spatial domain is the response of pupil function spatially on frequency domain.Wherein, on frequency domain
Pupil function and its response spatially pass through Fast Fourier Transform (FFT) realization.Pupil function indicates the circular function on frequency domain,
Its radius is 1.
Step 102, to transmission function progress singular value decomposition is intersected, at least one frequency domain kernel function is obtained.
It is n × n × n × n matrix that the intersection transmission function that terminal is established, which can be expressed as a size, that is, intersects and pass
Pass matrix.The intersection transfer matrix is four-matrix, which is n by terminal2×n2Two-dimensional matrix, then it is carried out
Matrix decomposition.Because above-mentioned intersection transfer matrix is positive definite matrix, terminal can carry out singular value decomposition to it.Pass through surprise
Different value is decomposed, and terminal obtains at least one spatial domain kernel function, shown in following relational expression:
Wherein, φk(x, y) indicates k-th of spatial domain kernel function at least one spatial domain kernel function.Terminal passes through Fu
In leaf transformation, determine the corresponding frequency domain kernel function of each spatial domain kernel function at least one spatial domain kernel function, obtain to
A few frequency domain kernel function.K-th of frequency-domain kernel function representation at least one frequency domain kernel function is Φk(f,g)。
Step 103, each rectangle at least one rectangle and at least one rectangle that mask graph is divided into is determined
Characteristic information.
Mask graph is two-dimensional simple polygon, and only includes right angle line segment.Therefore, mask graph can be drawn
It is divided at least one rectangle.In the embodiment of the present application, the division of mask graph can be divided in advance by technical staff,
It can also be divided by terminal according to the vertex information of mask graph.It should be noted that in lithography model, mask
Figure is also known as the litho pattern or litho pattern covered in version.
It is exemplary, as shown in figure 3, mask graph 301 is two-dimensional polygon, it include multiple right angle line segments.Terminal root
It is divided according to the vertex information of mask graph 301, the mask after the division of mask graph 302. after being divided
Domain shape 302 is by including multiple rectangles, for example, rectangle shown in Fig. 3 303 and rectangle 304.
Terminal determines the spy of each rectangle at least one rectangle and at least one rectangle that mask graph is divided into
Reference breath, i.e. terminal determine each of the mask graph after dividing rectangle and the characteristic information of each rectangle.It is special
Reference breath includes: the length of rectangle, the width of rectangle and the coordinate of rectangular centre.
Optionally, mask graph is divided at least one rectangle, then it represents that the mask function of mask graph is by table
Show that the rectangular function for the rectangle that division obtains indicates.Shown in following relational expression:
M (x, y) is the mask function in spatial domain,For first of rectangular space at least one above-mentioned rectangle
Rectangular function on domain.Correspondingly, terminal changes the mask function determined on frequency domain by Fourier, shown in following relational expression:
M (f, g) is the mask function on frequency domain, and Δ x and Δ y are the coordinate of rectangular centre, and h is the length of rectangle, and w is rectangle
Width, i indicates the imaginary unit of plural number, and sinc function isResponse on frequency domain, shown in following relational expression:
The mask at least one rectangle representation space domain and frequency domain that terminal can be divided by mask graph
Function.
Step 104, it determines each in the corresponding rectangular projection coefficient of each rectangle and at least one frequency domain kernel function
The corresponding kernel function projection coefficient of frequency domain kernel function.
After obtaining at least one above-mentioned frequency domain kernel function, and the characteristic information of determining each rectangle, terminal determines every
A corresponding rectangular projection coefficient of rectangle and the corresponding kernel function projection coefficient of each frequency domain kernel function.Wherein, square
Shape projection coefficient and kernel function projection coefficient refer to that terminal utilizes numerical integration operation by the rectangular function on frequency domain i.e. sinc letter
The projection coefficient that several and frequency-domain kernel Function Projective is obtained to Fourier's Bezier basic function.Each rectangle corresponds to a rectangle
Projection coefficient, each frequency domain kernel function correspond to a kernel function projection coefficient.Also, corresponding to as broad as long rectangle
Rectangular projection coefficient is equal.
Optionally, terminal calculates rectangular projection coefficient by following relational expression:
Wherein, αnsFor rectangular projection coefficient, h indicates the length of rectangle, and w indicates the width of rectangle, JnIndicate the match of first kind n rank shellfish
That function, λnsIndicate s-th of zero root of first kind n rank Bessel function, fjAnd gjIndicate the coordinate of frequency domain discrete sampling point.By
A rectangular projection coefficient is corresponded in each rectangle, therefore at least one rectangle that mask graph is divided into,
Terminal is it needs to be determined that rectangular projection coefficient identical with the quantity of rectangle.But by above-mentioned relation formula it is found that calculating rectangular projection
When coefficient, the difference between different rectangles is the length and width of rectangle, the i.e. value of sinc function.Since mask graph is two
Therefore the simple polygon of dimension will appear repetition rectangle in the rectangle being divided by mask graph, that is, it is equal with width length occur
Rectangle.For the long rectangle equal with width, the value of sinc function is also equal, their corresponding rectangular projection coefficients are also equal.
So terminal is when determining the corresponding rectangular projection coefficient of each rectangle, for the long rectangle equal with width, one need to be calculated
It is secondary, without being computed repeatedly, saves and calculate the time.
Optionally, terminal calculates each corresponding kernel function projection coefficient of frequency domain kernel function according to following relational expression:
Wherein,For the corresponding kernel function projection coefficient of k-th of frequency domain kernel function, Φ at least one frequency domain kernel functionk
(fj,gj) indicate that k-th of frequency domain kernel function is in (f at least one frequency domain kernel functionj,gj) on value, JmIndicate first kind m rank shellfish
Sai Er function, λmtIndicate t-th of zero root of first kind m rank Bessel function.
Optionally, terminal determines every in the corresponding rectangular projection coefficient of each rectangle and at least one frequency domain kernel function
After a corresponding kernel function projection coefficient of frequency domain kernel function, the mask function and frequency after projection are determined according to following relational expression
Domain kernel function:
FBns(f, g) indicates Fourier's Bezier basic function of n rank s zero root, FBmt(f, g) is indicated in Fu of m rank t zero root
Leaf Bezier basic function.
Step 105, according to rectangular projection coefficient, the characteristic information of kernel function projection coefficient and each rectangle determines user
Light distribution on designated position.
Terminal determines each frequency domain in the corresponding rectangular projection coefficient of each rectangle and at least one frequency domain kernel function
After the corresponding kernel function projection coefficient of kernel function, according to rectangular projection coefficient, kernel function projection coefficient and each rectangle
Characteristic information determines the light distribution in specified location in user.
Terminal determines the light distribution in specified location in user according to following relational expression
I (x, y) indicates the light distribution on specified location in user (x, y), Cn+m,qN+m rank q on (x, y) representation space domain
The orthogonal basis function of zero root, γn+m,qFor basis function product projection coefficient.Wherein, Cn+m,qIn Fu of (x, y) and n+m rank q zero root
Leaf Bezier basic function Fourier transformation each other.γn+m,qIt is that the product of Fourier's Bezier basic function is projected into Fourier shellfish
The projection coefficient obtained on Sai Er basic function.
Illustratively, as shown in figure 4, it illustrates the light distribution finally on imaging plane.Wherein, different zones
Different colours illustrate different light intensity, and region 401 is different from the color in region 402, and light intensity is also different.
Optionally, basis function product projection coefficient γ is determined according to following relational expressionn+m,q
Wherein, FBns(fj,gj) indicate Fourier's Bezier basic function of n rank s zero root in (fj,gj) on value, FBmt(fj,
gj) indicate Fourier's Bezier basic function of m rank t zero root in (fj,gj) on value,Indicate n+m rank q zero root
Fourier's Bezier basic function conjugate function in (fj,gj) on value.Due to Fourier's Bezier basic function and calculate photoetching
When light source function, pupil function and mask function it is unrelated, therefore, can predefine or set before determining light distribution
It sets, saves and calculate the time.
Optionally, after determining mask function and the frequency domain kernel function after projection, terminal utilizes the mask function after projection
Field strength is calculated with frequency domain kernel function, carries out inverse Fourier transform, the final light determined in specified location in user further according to field strength
The analytic expression being distributed by force.Wherein, terminal determines the corresponding field strength of each frequency domain kernel function according to following relational expression:
According to the relational expression technology field strength, really calculating Fourier's Bezier basic function FBns(f, g) and FBmt(f,g)
Product, the product of Fourier's Bezier basic function is projected on Fourier's Bezier basic function, shown in following relational expression:
Bn+m,qFourier's Bezier basic function of (f, g) expression n+m rank q zero root.Wherein, n, m, s, t and q can be according to realities
The setting of border experience.Therefore, terminal determines shown in the corresponding following relational expression of field strength of each frequency domain kernel function:
After determining the corresponding field strength of each frequency domain kernel function, the light in specified location in user is determined according to following relational expression
Strong distribution:
F-1Indicate inverse Fourier transform.Due to the orthogonal basis function C of the n+m rank q zero root in spatial domainn+m,q(x, y) and n+
Fourier's Bezier basic function Fourier transformation, therefore F each other of m rank q zero root-1[Ek(f, g)] it is Cn+m,qLinear group of (x, y)
It closes, then obtains following relational expression:
Terminal finally determines the analytic expression of the light distribution in specified location in user are as follows:
In method provided by the embodiments of the present application, by determining the corresponding kernel function projection coefficient of frequency domain kernel function and covering
The corresponding rectangular projection coefficient of rectangle that template figure divides, can quickly determine the light distribution in specified location in user.
It will appear repetition rectangle in the rectangle being divided into due to mask graph, and for the long rectangle equal with width, rectangular projection system
Number is also equal, therefore, can be avoided and computes repeatedly when determining rectangular projection coefficient, reduces and calculates the time, and then improves photoetching
Efficiency.
Fig. 5 is that a kind of light distribution based on mask graph processing shown according to an exemplary embodiment quickly determines
The block diagram of device.The device, which has, realizes the exemplary function of the above method.The apparatus may include: function establishes module 501, letter
Number decomposing module 502, rectangle determining module 503 project determining module 504 and light intensity determining module 505.
Function establishes module 501, for establishing and intersecting transmission function according to light source function and pupil function.
Function decomposition module 502 obtains at least one frequency domain for carrying out singular value decomposition to the intersection transmission function
Kernel function.
Rectangle determining module 503, for determining at least one rectangle and described at least one that mask graph is divided into
The characteristic information of each rectangle in a rectangle, the characteristic information include: the length of rectangle, the width of rectangle and the seat of rectangular centre
Mark.
Project determining module 504, for determine the corresponding rectangular projection coefficient of each rectangle and it is described at least
Each corresponding kernel function projection coefficient of frequency domain kernel function in one frequency domain kernel function.
Light intensity determining module 505, for according to the rectangular projection coefficient, the kernel function projection coefficient and described each
The characteristic information of rectangle determines the light distribution in specified location in user.
In device provided by the embodiments of the present application, by determining the corresponding kernel function projection coefficient of frequency domain kernel function and covering
The corresponding rectangular projection coefficient of rectangle that template figure divides, can quickly determine the light distribution in specified location in user.
It will appear repetition rectangle in the rectangle being divided into due to mask graph, and for the long rectangle equal with width, rectangular projection system
Number is also equal, therefore, can be avoided and computes repeatedly when determining rectangular projection coefficient, reduces and calculates the time, and then improves photoetching
Efficiency.
Optionally, the projection determining module 504, is specifically used for:
The rectangular projection coefficient is calculated according to following relational expression
Wherein, αnsFor the rectangular projection coefficient, h indicates the length of the rectangle, and w indicates the width of the rectangle, JnIt indicates
First kind n rank Bessel function, λnsIndicate s-th of zero root of first kind n rank Bessel function, fjAnd gjIt indicates that frequency domain is discrete to adopt
The coordinate of sampling point；
Each corresponding kernel function projection coefficient of frequency domain kernel function is calculated according to following relational expression
Wherein,For the corresponding kernel function projection of k-th of frequency domain kernel function at least one described frequency domain kernel function system
Number, Φk(fj,gj) indicate that k-th of frequency domain kernel function is in (f at least one described frequency domain kernel functionj,gj) on value, JmIt indicates
First kind m rank Bessel function, λmtIndicate t-th of zero root of first kind m rank Bessel function.
Optionally, the light intensity determining module 505, is specifically used for:
The light distribution in the specified location in user is determined according to following relational expression
Wherein, I (x, y) indicates the light distribution on specified location in user (x, y), αnsFor the rectangular projection coefficient,
For the corresponding kernel function projection coefficient of k-th of frequency domain kernel function at least one described frequency domain kernel function, Δ x and Δ y indicate institute
State the coordinate of rectangular centre, Cn+m,qThe orthogonal basis function of n+m rank q zero root on (x, y) representation space domain, γn+m,qFor basic function
Product projection coefficient.
Optionally, the light intensity determining module 505, is also used to:
The basis function product projection coefficient is determined according to following relational expression
Wherein, FBns(fj,gj) indicate Fourier's Bezier basic function of n rank s zero root in (fj,gj) on value, FBmt(fj,
gj) indicate Fourier's Bezier basic function of m rank t zero root in (fj,gj) on value,Indicate n+m rank q zero root
Fourier's Bezier basic function conjugate function in (fj,gj) on value.
It should be noted that device provided by the above embodiment is when realizing its function, only with above-mentioned each functional module
Division progress for example, in practical application, can be according to actual needs and by above-mentioned function distribution by different function moulds
Block is completed, i.e., the content structure of equipment is divided into different functional modules, to complete all or part of function described above
Energy.In addition, apparatus and method embodiment provided by the above embodiment belongs to same design, specific implementation process is detailed in method reality
Example is applied, which is not described herein again.
In addition, the application also provides a kind of computer storage medium, wherein the computer storage medium can be stored with journey
Sequence, the program may include that the application provides each reality of the light distribution fast determination method handled based on mask graph when executing
Some or all of apply in example step.The storage medium can be magnetic disk, CD, read-only memory (Read-Only
Memory, ROM) or random access memory (Random Access Memory, RAM) etc..
In the above-described embodiments, it can be realized fully or partially through software, hardware, firmware or any combination thereof.
When implemented in software, it can entirely or partly realize in the form of a computer program product.
The computer program product includes one or more computer instructions.The calculating is loaded and executed in computer
When machine program, entirely or partly generate according to process or function described in the above-mentioned each embodiment of the application.The computer
It can be general purpose computer, special purpose computer, computer network or other programmable devices.
The computer instruction may be stored in a computer readable storage medium, or from a computer-readable storage
Medium is transmitted to another computer readable storage medium, for example, the computer instruction can be from a network node, calculating
Machine, server or data center are transmitted by wired or wireless way to another website, computer or server.
In addition, unless otherwise indicated, " multiple " refer to two or more in the description of the present application.In addition, in order to
Convenient for clearly describing the technical solution of the embodiment of the present application, in embodiments herein, the words such as " first ", " second " are used
Sample distinguishes function and the essentially identical identical entry of effect or similar item.It will be appreciated by those skilled in the art that " first ",
Printed words such as " second " are not defined quantity and execution order, and the printed words such as " first ", " second " also do not limit one
Fixed difference.
Above-described the application embodiment does not constitute the restriction to the application protection scope.
Claims (8)
1. a kind of light distribution fast determination method based on mask graph processing, which is characterized in that the described method includes:
According to light source function and pupil function, establishes and intersect transmission function；
Singular value decomposition is carried out to the intersection transmission function, obtains at least one frequency domain kernel function；
Determine the feature letter of each rectangle at least one rectangle and at least one described rectangle that mask graph is divided into
Breath, the characteristic information include: the length of rectangle, the width of rectangle and the coordinate of rectangular centre；
Determine each frequency domain in the corresponding rectangular projection coefficient of each rectangle and at least one described frequency domain kernel function
The corresponding kernel function projection coefficient of kernel function；
According to the rectangular projection coefficient, the characteristic information of the kernel function projection coefficient and each rectangle determines user
Light distribution on designated position.
2. the method according to claim 1, wherein the determination each corresponding rectangle of rectangle is thrown
Each corresponding kernel function projection coefficient of frequency domain kernel function in shadow coefficient and at least one described frequency domain kernel function, comprising:
The rectangular projection coefficient is calculated according to following relational expression
Wherein, αnsFor the rectangular projection coefficient, h indicates the length of the rectangle, and w indicates the width of the rectangle, JnIndicate first
Class n rank Bessel function, λnsIndicate s-th of zero root of first kind n rank Bessel function, fjAnd gjIndicate frequency domain discrete sampling point
Coordinate；
Each corresponding kernel function projection coefficient of frequency domain kernel function is calculated according to following relational expression
Wherein,For the corresponding kernel function projection coefficient of k-th of frequency domain kernel function at least one described frequency domain kernel function, Φk
(fj,gj) indicate that k-th of frequency domain kernel function is in (f at least one described frequency domain kernel functionj,gj) on value, JmIndicate first kind m
Rank Bessel function, λmtIndicate t-th of zero root of first kind m rank Bessel function.
3. the method according to claim 1, wherein described according to the rectangular projection coefficient, the kernel function
The characteristic information of projection coefficient and each rectangle, determines the light distribution in specified location in user, comprising:
The light distribution in the specified location in user is determined according to following relational expression
Wherein, I (x, y) indicates the light distribution on specified location in user (x, y), αnsFor the rectangular projection coefficient,For institute
The corresponding kernel function projection coefficient of k-th of frequency domain kernel function at least one frequency domain kernel function is stated, Δ x and Δ y indicate the square
The coordinate at shape center, Cn+m,qThe orthogonal basis function of n+m rank q zero root on (x, y) representation space domain, γn+m,qFor basis function product
Projection coefficient.
4. according to the method described in claim 3, it is characterized in that, described according to the rectangular projection coefficient, the kernel function
The characteristic information of projection coefficient and each rectangle, before determining the light distribution in specified location in user, further includes:
The basis function product projection coefficient is determined according to following relational expression
Wherein, FBns(fj,gj) indicate Fourier's Bezier basic function of n rank s zero root in (fj,gj) on value, FBmt(fj,gj) table
Show Fourier's Bezier basic function of m rank t zero root in (fj,gj) on value,Indicate Fu of n+m rank q zero root
In leaf Bezier basic function conjugate function in (fj,gj) on value.
5. a kind of quick determining device of light distribution based on mask graph processing, which is characterized in that described device includes:
Function establishes module, for establishing and intersecting transmission function according to light source function and pupil function；
Function decomposition module obtains at least one frequency domain kernel function for carrying out singular value decomposition to the intersection transmission function；
Rectangle determining module, for determining at least one rectangle and at least one described rectangle that mask graph is divided into
In each rectangle characteristic information, the characteristic information includes: the length of rectangle, the width of rectangle and the coordinate of rectangular centre；
Determining module is projected, for determining the corresponding rectangular projection coefficient of each rectangle and at least one described frequency domain
Each corresponding kernel function projection coefficient of frequency domain kernel function in kernel function；
Light intensity determining module, for according to the rectangular projection coefficient, the kernel function projection coefficient and each rectangle
Characteristic information determines the light distribution in specified location in user.
6. device according to claim 5, which is characterized in that the projection determining module is specifically used for:
The rectangular projection coefficient is calculated according to following relational expression
Wherein, αnsFor the rectangular projection coefficient, h indicates the length of the rectangle, and w indicates the width of the rectangle, JnIndicate first
Class n rank Bessel function, λnsIndicate s-th of zero root of first kind n rank Bessel function, fjAnd gjIndicate frequency domain discrete sampling point
Coordinate；
Each corresponding kernel function projection coefficient of frequency domain kernel function is calculated according to following relational expression
Wherein,For the corresponding kernel function projection coefficient of k-th of frequency domain kernel function at least one described frequency domain kernel function, Φk
(fj,gj) indicate that k-th of frequency domain kernel function is in (f at least one described frequency domain kernel functionj,gj) on value, JmIndicate first kind m
Rank Bessel function, λmtIndicate t-th of zero root of first kind m rank Bessel function.
7. device according to claim 5, which is characterized in that the light intensity determining module is specifically used for:
The light distribution in the specified location in user is determined according to following relational expression
Wherein, I (x, y) indicates the light distribution on specified location in user (x, y), αnsFor the rectangular projection coefficient,For institute
The corresponding kernel function projection coefficient of k-th of frequency domain kernel function at least one frequency domain kernel function is stated, Δ x and Δ y indicate the square
The coordinate at shape center, Cn+m,qThe orthogonal basis function of n+m rank q zero root on (x, y) representation space domain, γn+m,qFor basis function product
Projection coefficient.
8. device according to claim 7, which is characterized in that the light intensity determining module is also used to:
The basis function product projection coefficient is determined according to following relational expression
Wherein, FBns(fj,gj) indicate Fourier's Bezier basic function of n rank s zero root in (fj,gj) on value, FBmt(fj,gj) table
Show Fourier's Bezier basic function of m rank t zero root in (fj,gj) on value,Indicate Fu of n+m rank q zero root
In leaf Bezier basic function conjugate function in (fj,gj) on value.
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