CN109212913A - Light distribution acquisition methods and device based on non-homogeneous calculating - Google Patents
Light distribution acquisition methods and device based on non-homogeneous calculating Download PDFInfo
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- 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
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Abstract
This application discloses a kind of light distribution acquisition methods and device based on non-homogeneous calculating, this method comprises: obtaining the light source sampling matrix and pupil sampling matrix based on intersecting area to light source function and pupil function progress uniform sampling on frequency domain；Non-homogeneous inverse Fourier transform is carried out to light source sampling matrix and pupil sampling matrix, obtains intersecting transfer matrix；Determine the frequency domain kernel function for intersecting transfer matrix；Establish the sampling matrix of the mask function on frequency domain and the sampling matrix of frequency domain kernel function；The light distribution in specified location in user is obtained by non-homogeneous inverse Fourier transform according to the sampling matrix of the sampling matrix of the mask function on frequency domain and frequency domain kernel function.In the application, due to using the method for sampling based on intersecting area, computational accuracy is improved, meanwhile using non-homogeneous inverse Fourier transform, under identical sampling density, the calculation amount to light distribution can be reduced, so as to shorten duration is calculated, improve the efficiency for carrying out photoetching to photoresist.
Description
Technical field
The application belongs to technical field of semiconductor lithography, in particular to a kind of light distribution based on non-homogeneous calculating obtains
Method and device.
Background technique
Smart machine and present inseparable, the smart phone of life, smart home and intelligent wearable device are generally and each
People is related.The operation of smart machine is more the operation of chip rearward quietly.Currently, with smart machine function and correlation
Performance requirement it is higher and higher, the requirement for chip is also increasing.As chip production manufacturer uses the variation of technology, production
The integrated level of the development of equipment, material and technique, chip is higher and higher, and transistor size is multiplied on unit area, finally
So that the performance of smart machine is higher and higher, and opposite production cost is lower and lower.In the production process of chip, photoetching technique
It is that figure of the prior design on mask is transferred to one using photochemical reaction principle for the key technology in chip production
On substrate (photoresist), so that etching and ion implanting are possibly realized.Light, which is radiated on mask, occurs diffraction, different diffraction
The light of grade converges in photoresist surface, this process is a two-phonon process；Image on photoresist excites chemical reaction, through drying
Photoresist is caused locally to dissolve in developer solution after roasting.When carrying out photoetching, need first to calculate lithography model, and then according to photoetching mould
Type controls photoetching process.It calculates lithography model and refers to that terminal describes two-phonon process with mathematical formulae by calculating, so as to control
It makes and optimizes photoetching.
In the related art, lithography model mainly includes light source, mask, pupil and photoresist, wherein light source and pupil
It is typically defined on frequency domain, and mask and imaging plane then show that photoetching is thus calculated in spatial domain to need to use Fourier
Transformation.When determining the light distribution in lithography model on photoresist, Fast Fourier Transform (FFT) (Fast Fourier is generallyd use
Transformation, FFT) method calculated.FFT is effective realization of discrete Fourier transform.Based on the discrete of sampling
Fourier, sampling density have larger impact to model accuracy, and sampling density is higher, and computational accuracy is also higher, required calculating
Duration is also longer.Since FFT is confined on equally distributed orthogonal grid, frequency domain sample and spatial domain sampling are couplings, are led
Cause sampling density limited.In order to guarantee that certain calculation accuracy meets production needs, it is necessary to improve sampling density, lead to light distribution
Calculation amount increase, calculate duration it is also elongated.
Light distribution is calculated using FFT in the related technology above-mentioned, in order to guarantee computational accuracy, when calculating improves sampling
Density causes the calculation amount of light distribution to increase, to increase calculating duration, reduces the effect that photoetching is carried out to photoresist
Rate.
Summary of the invention
The application provides a kind of light distribution acquisition methods and device based on non-homogeneous calculating, can be used for solving related skill
In art, in order to guarantee computational accuracy, sampling density is improved, causes the calculation amount of light distribution to increase, thus when increasing calculating
It is long, reduce the problem of efficiency of photoetching is carried out to photoresist.
In a first aspect, the application provides a kind of light distribution acquisition methods based on non-homogeneous calculating, which comprises
To the light source function and pupil function progress uniform sampling on frequency domain, the light source sampling square based on intersecting area is obtained
Battle array and pupil sampling matrix；
Non-homogeneous inverse Fourier transform is carried out to the light source sampling matrix and the pupil sampling matrix, obtains intersecting biography
Pass matrix；
Determine the frequency domain kernel function for intersecting transfer matrix；
Establish the sampling matrix of the mask function on frequency domain and the sampling matrix of the frequency domain kernel function, the mask function
Indicate the geometry of mask；
According to the sampling matrix of the sampling matrix of the mask function on the frequency domain and the frequency domain kernel function, by non-equal
Even inverse Fourier transform obtains the light distribution in specified location in user.
Optionally, the light source function is J (f, g), and the pupil function is K (f, g), wherein (f, g) is indicated on frequency domain
Coordinate；
The light source function and pupil function on frequency domain carries out uniform sampling, obtains the light source based on intersecting area and adopts
Sample matrix and pupil sampling matrix, comprising:
The first sampled point set is established on frequency domain；
According to the first sampled point set, the light source function and the pupil function are sampled, obtained described
Light source sampling matrix J [n]=[J (fi,gj)] and pupil sampling matrix K [n]=[K (fi,gj)], wherein J (fi,gj) table
Show the element of light source sampling matrix the i-th row jth column, and J (fi,gj) corresponding functional value is that sampling area and light source are effective
The intersecting area of computational domain, K (fi,gj) indicate the element that pupil sampling matrix the i-th row jth arranges.
Optionally, described that non-homogeneous Fourier's inversion is carried out to the light source sampling matrix and the pupil sampling matrix
It changes, obtains intersecting transfer matrix, comprising:
It is calculated according to following relational expression and intersects transmission function
J (x'-x ", y'-y ")=INUFFT [J [n]]
K (x', y')=INUFFT [K [n]]
t(x',y'；X ", y ")=j (x'-x ", y'-y ") k (x', y') k*(-x”,-y”)
Wherein, t (x', y'；X ", y ") it is the intersection transmission function, k*(- x " ,-y ") is the conjugation letter of k (x', y')
Number, (x', y') and (x ", y ") are the coordinate points in spatial domain, and J [n] is the light source sampling matrix, and K [n] is that the pupil is adopted
Sample matrix, INUFFT [] indicate non-homogeneous inverse Fourier transform；
Determine that the intersection transfer matrix is T=[t (x', y'；x",y")].
Optionally, the determination frequency domain kernel function for intersecting transfer matrix, comprising:
Projection matrix is calculated according to following relational expression
T=[t (x', y'；x",y")]
B=[bj(x',y')]
P=bTb*
Wherein, P is the projection matrix, bj(x, y) is the orthogonal basis function in spatial domain, b=[bj(x', y')] for institute
State the matrix of orthogonal basis function, bj(x', y') is the element in the matrix of the orthogonal basis function, JnFor n-th order first kind shellfish plug
That function, λnsFor s-th of zero root of n-th order Bessel function；
Eigenvalues Decomposition is carried out to the projection matrix, determines the eigenvectors matrix U and characteristic value of the projection matrix
Matrix Λ, wherein P=U Λ U*；
The frequency domain kernel function for intersecting transmission function is calculated according to following relational expression
Ψ (f, g)=∑ γiuijBj(f,g)
Wherein, γiFor the element of the i-th row of the eigenvalue matrix, uijFor the i-th row jth of described eigenvector matrix
The element of column, Bj(f, g) is the orthogonal basis function on frequency domain, and in the orthogonal basis function on the frequency domain and the spatial domain
Fourier transformation, Ψ (f, g) are the frequency domain kernel function for intersecting transmission function to orthogonal basis function each other.
Optionally, the sampling matrix of the sampling matrix for establishing the mask function on frequency domain and the frequency domain kernel function,
Include:
According to following the second sampled point of relation reality set
Wherein, second sampling point set is combined into { (fi,gj), w and h are the period of the mask function；
The sampling matrix of the mask function on the frequency domain is calculated according to the second sampled point set and following relational expression
With the sampling matrix of the frequency domain kernel function
M [n]=[M (fi,gj)]
Ψ [n]=[Ψ (fi,gj)]
Wherein, M [n] is the sampling matrix of the mask function on the frequency domain, and Ψ [n] is the sampling of the frequency domain kernel function
Matrix.
Optionally, described according to the sampling matrix of the mask function on the frequency domain and the sampling square of the frequency domain kernel function
Battle array obtains the light distribution in specified location in user by non-homogeneous inverse Fourier transform, comprising:
The light distribution is calculated according to following relational expression
I (x, y)=∑ | INUFFT [Ψ (fi,gj)M(fi,gj)]|2
Wherein, (x, y) is the coordinate of the designated position, and I (x, y) is the light distribution on the designated position.
Second aspect, the application provide a kind of light distribution acquisition device based on non-homogeneous calculating, and described device includes:
Matrix sampling module, for obtaining based on phase to the light source function and pupil function progress uniform sampling on frequency domain
The light source sampling matrix and pupil sampling matrix of cross surface product；
Matrix computing module, for carrying out non-homogeneous Fourier to the light source sampling matrix and the pupil sampling matrix
Inverse transformation obtains intersecting transfer matrix；
Function determination module, for determining the frequency domain kernel function for intersecting transfer matrix；
The matrix sampling module, be also used to establish the mask function on frequency domain sampling matrix and the frequency domain kernel function
Sampling matrix, the mask function indicates the geometry of mask；
Light intensity acquisition module, for according to the sampling matrix of the mask function on the frequency domain and the frequency domain kernel function
Sampling matrix obtains the light distribution in specified location in user by non-homogeneous inverse Fourier transform.
Scheme provided by the present application, by based on intersecting area light source sampling matrix and pupil sampling matrix carry out it is non-
Uniform inverse Fourier transform obtains intersecting transfer matrix, and then determines the frequency domain kernel function for intersecting transfer matrix, finally according to frequency
The sampling matrix of mask function on domain and the sampling matrix of frequency domain kernel function are obtained and are used using non-homogeneous inverse Fourier transform
Light distribution on the designated position of family.Since the method for sampling based on intersecting area of use improves sampling precision, in turn
Computational accuracy is improved, meanwhile, using non-homogeneous inverse Fourier transform, under identical sampling density, calculation amount is smaller, calculates
Duration is shorter.Therefore, in the case where guaranteeing that certain calculation accuracy is needed to meet production, the light to lithography model can be reduced
The calculation amount being distributed by force improves the efficiency that photoetching is carried out to photoresist so as to shorten calculating duration.
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 a kind of stream of light distribution acquisition methods based on non-homogeneous calculating shown according to an exemplary embodiment
Cheng Tu；
Fig. 2 is a kind of schematic diagram of sampled value based on intersecting area shown according to an exemplary embodiment；
Fig. 3 is the schematic diagram of the sampling of a kind of pair of light source and pupil sampling shown according to an exemplary embodiment；
Fig. 4 is a kind of schematic diagram of sampling point distributions on one-dimensional shown according to an exemplary embodiment；
Fig. 5 is the schematic diagram of the geometric figure of a variety of masks shown according to an exemplary embodiment；
Fig. 6 is a kind of schematic diagram for covering light distribution shown according to an exemplary embodiment；
Fig. 7 is a kind of calculation of light distribution acquisition methods based on non-homogeneous calculating shown according to an exemplary embodiment
Method flow chart；
Fig. 8 is a kind of frame of light distribution acquisition device based on non-homogeneous calculating shown according to an exemplary embodiment
Figure.
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 for calculating photoetching
The related data of lithography model in the process, and photoetching is carried out according to lithography model.
Fig. 1 is a kind of light distribution acquisition methods based on non-homogeneous calculating shown according to an exemplary embodiment.It should
Method may include the following steps.
Step 101, to the light source function and pupil function progress uniform sampling on frequency domain, the light based on intersecting area is obtained
Source sampling matrix and pupil sampling matrix.
When terminal calculates 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, having some light that can not then indicate by pupil, pupil function can be by the light of the pupil.Light source letter
Several and pupil function is determined that light source is different, then light source function is also different by light source and pupil；Pupil is different, then pupil function
It is different.Therefore, light source function and pupil function can be predefined according to the light source and pupil actually used.
After determining light source function and pupil function, terminal carries out light source function and pupil function in conventional coordinates equal
Even sampling obtains the light source sampling matrix and pupil sampling matrix based on intersecting area.At this point, light source function and pupil function are
In frequency domain coordinates system.
Optionally, light source function is J (f, g), and pupil function is K (f, g), wherein (f, g) representative function is on frequency domain
Coordinate, i.e. J (f, g) and K (f, g) are the functions on frequency domain.The frequency limited of light source function and pupil function is a round letter
Number, radius is the highest frequency allowed through lens.When carrying out uniform sampling to light source function and pupil function, first in frequency domain
On establish the first sampled point set.The collection is combined into the uniform sampling point set for carrying out uniform sampling, including multiple sampled points.Terminal
According to the first sampled point set, light source function and pupil function are sampled, obtain light source sampling matrix J [n]=[J (fi,
gj)] and pupil sampling matrix K [n]=[K (fi,gj)], wherein J (fi,gj) indicate the member that light source sampling matrix the i-th row jth arranges
Element, K (fi,gj) indicate the element that pupil sampling matrix the i-th row jth arranges.(fi,gj) indicate the first sampled point set in sampling
Point corresponds to the square that a geometric center is the point, then the sampled value of the sampled point is its corresponding square and circle
Function corresponds to the intersecting area of geometric figure.Uniform sampling is carried out to light source function and pupil function, is by based on intersection
The long-pending method of sampling obtains sampled value, i.e. J (fi,gj) corresponding functional value be sampling area and the effective computational domain of light source intersection
Area.Illustratively, as shown in Fig. 2, it illustrates the schematic diagram of the sampled value based on intersecting area, the sampling of sampled point 201
The area for the sampling area 202 that value is square, and the sampling area 204 that the sampled value of sampled point 203 is square and circle
The effective computational domain 205 of light source intersection 206 area.By the method for sampling based on intersecting area, obtain based on phase
The light source sampling matrix and pupil sampling matrix of cross surface product.Wherein, the element in matrix be the corresponding sampled value of sampled point, i.e., on
State intersecting area.
Illustratively, using the light source function of quadrupole light source and ideal pupil function, pass through adopting based on intersecting area
Quadrat method, and f is normalized to highest sample frequencymax=gmax=1.With reference to Fig. 3, sampled it illustrates light source sampling and pupil
Schematic diagram.Wherein, the left side is light source sampling, and the right is pupil sampling.
Since terminal uses the method for sampling based on intersecting area, in identical calculating duration, sampling essence is improved
Degree, and then improve computational accuracy.Therefore, it under identical computational accuracy, is reduced using the method for sampling based on intersecting area
Calculating duration.
Step 102, non-homogeneous inverse Fourier transform is carried out to light source sampling matrix and pupil sampling matrix, obtains intersecting biography
Pass matrix.
Above-mentioned light source sampling matrix and the corresponding sampled point of pupil sampling matrix are the sampled points on frequency domain, therefore, eventually
End carries out non-homogeneous inverse Fourier transform to light source sampling matrix and pupil sampling matrix, and then obtains the biography of the intersection in spatial domain
Pass matrix.Coupled relation is not present in the sampled point of sampled point and frequency domain in spatial domain, and is spatially sampled as nonuniform sampling,
More in close center sampling, sampled point then samples more sparse further away from center.Referring to FIG. 4, it illustrates on one-dimensional
Sampling point distributions.Wherein, it closer to center 401, samples more intensive.
Since coupled relation is not present in the sampled point of sampled point and frequency domain in spatial domain, spatial domain and frequency domain are avoided
Coupled relation reduces extra calculating process, and then shortens calculating duration.
Optionally, terminal is calculated according to following relational expression intersects transmission function:
J (x'-x ", y'-y ")=INUFFT [J [n]]
K (x', y')=INUFFT [K [n]]
t(x',y'；X ", y ")=j (x'-x ", y'-y ") k (x', y') k*(-x”,-y”)
Wherein, t (x', y'；X ", y') ' it is to intersect transmission function, k*(- x " ,-y ") is the conjugate function of k (x ", y "),
(x', y') and (x ", y ") is the coordinate points in spatial domain.Wherein INUFFT [] indicates non-homogeneous inverse Fourier transform.INUFFT
[] specific calculation relational expression are as follows:
H (x, y)=∫ ∫ H (f, g) e-i(fx+gy)Dfdg=INUFFT [H (f, g)]
Wherein, h (x, y) is the function in spatial domain, then H (f, g) corresponds to frequency domain.
Terminal determines that intersecting transfer matrix is T=[t (x', y' after obtaining intersecting transmission function；x",y")].
Step 103, the frequency domain kernel function for intersecting transfer matrix is determined.
After terminal determines intersection transfer matrix, the intersection transmission function in spatial domain is determined, then close to transmission function is intersected
Eigenvalues Decomposition is carried out in the projection matrix of orthogonal basis function, spatial domain kernel function is obtained and finally utilizes Fu of orthogonal basis function
In leaf transformation, determine frequency domain kernel function.
Firstly, terminal calculates projection matrix according to following relational expression:
T=[t (x', y'；x",y")]
B=[bj(x',y')]
P=bTb*
P is projection matrix, bj(x, y) is the orthogonal basis function in spatial domain, b=[bj(x', y')] it is orthogonal basis function
Matrix, bj(x', y') is the element in the matrix of orthogonal basis function, JnFor n-th order Bessel function of the first kind, λnsFor n-th order
S-th of zero root of Bessel function.Wherein, relational expression P=bTb*Be by terminal will intersect transmission function project to it is above-mentioned orthogonal
What basic function obtained.Terminal projects intersection transmission function in orthogonal basis function and obtains following relational expression:
The matrix of the relational expression is expressed as T=bPb*, by matrix operation rule it is found that P=bTb*。
Terminal carries out Eigenvalues Decomposition after obtaining projection matrix, to projection matrix, determines the feature vector of projection matrix
Matrix and eigenvalue matrix.Projection matrix P=U Λ U*, Λ is characterized value matrix, and U is characterized vector matrix, U*For feature vector
The complex conjugate of matrix.From the above-mentioned calculating for projecting intersection transmission function in orthogonal basis function: T=bPb*, will obtain in turn
Relational expression: T=bU Λ U*b*.Wherein, intersect the spatial domain kernel function of transmission function are as follows: Φ (x, y)=bU.Therefore, terminal according to
Following relational expression calculates the spatial domain kernel function for intersecting transmission function:
Φ (x, y)=∑ γiuijbj(x,y)
Wherein, γiIt is characterized the element of the i-th row in value matrix Λ, uijThe member that the i-th row jth arranges in eigenvectors matrix U
Element.Since the orthogonal basis function on orthogonal basis function and spatial domain on frequency domain is a pair of of Fourier transformation, intersects transmission function
Frequency domain kernel function and to intersect the spatial domain kernel function of transmission function be a pair of of Fourier transformation, therefore, terminal is determined to intersect and be passed
The frequency domain kernel function of delivery function.
Finally, terminal calculates the frequency domain kernel function for intersecting transmission function according to following relational expression:
Ψ (f, g)=∑ γiuijBj(f,g)
Wherein, Bj(f, g) is the orthogonal basis function on frequency domain, and Ψ (f, g) is the frequency domain kernel function for intersecting transmission function.
Step 104, the sampling matrix of the mask function on frequency domain and the sampling matrix of frequency domain kernel function are established.
Terminal is after determining the frequency domain kernel function for intersecting transfer matrix, respectively to the mask function and frequency-domain kernel on frequency domain
Function carries out uniform sampling, the sampling matrix of the mask function on frequency domain and the sampling matrix of frequency domain kernel function is established, after being used for
It is continuous to calculate light distribution.Wherein, mask function indicates the geometry of mask.Illustratively, as shown in figure 5, it illustrates more
The geometric figure of kind mask.For establishing the sampling matrix of mask function, terminal can use the fast Fourier side of polygon
The foundation of method progress sampling matrix.
Optionally, the sampling matrix of the sampling matrix of the mask function on frequency domain and frequency domain kernel function in order to obtain, terminal
First establish the second sampled point set { (fi,gj)}.Wherein, the sampled point (f in the second sampled point seti,gj) according to following relationship
Formula is established:
Wherein, w and h is the period of mask function.Terminal calculates frequency further according to the second sampled point set and following relational expression
The sampling matrix of mask function on domain and the sampling matrix of frequency domain kernel function:
M [n]=[M (fi,gj)]
Ψ [n]=[Ψ (fi,gj)]
Wherein, M [n] is the sampling matrix of the mask function on frequency domain, and Ψ [n] is the sampling matrix of frequency domain kernel function.Ψ
(fi,gj) it is the element that the i-th row jth arranges in the sampling matrix of frequency domain kernel function, M (fi,gj) adopting for the mask function on frequency domain
The element that the i-th row jth arranges in sample matrix.Also, M (fi,gj) it is sampled point (fi,gj) the corresponding mask function on frequency domain
In value.xiAnd yiFor the coordinate of the mask function in spatial domain.
Step 105, according to the sampling matrix of the sampling matrix of the mask function on frequency domain and frequency domain kernel function, by non-equal
Even inverse Fourier transform obtains the light distribution in specified location in user.
For terminal after the sampling matrix of the sampling matrix and frequency domain kernel function that get the mask function on frequency domain, utilization is non-
Uniform inverse Fourier transform obtains the light distribution in specified location in user.Illustratively, as shown in fig. 6, it illustrates 4 kinds
The schematic diagram of mask and its corresponding light distribution.Wherein, light distribution is corresponding with the geometry of mask.Such as mask
The curve 602 of 601 corresponding light distribution is corresponding with the geometry of mask 601.
Optionally, terminal calculates light distribution according to following relational expression:
I (x, y)=∑ | INUFFT [Ψ (fi,gj)M(fi,gj)]|2, wherein (x, y) is the coordinate of specified location in user,
Then I (x, y) is the light distribution in specified location in user.
It is the light intensity in computed user locations by non-homogeneous inverse Fourier transform in the relevant calculation of lithography model
Distribution, the light distribution without calculating entire photoresist plane intersect at the mode that FFT calculates light distribution, reduce and obtain
Calculating needed for taking the light distribution of inoperative position.Therefore, under identical sampling density, the meter of non-homogeneous inverse Fourier transform
Calculation amount is smaller, and it is shorter to calculate duration.Further, since using the method for sampling based on intersecting area, spatial domain and frequency are avoided
Therefore the coupled relation in domain under identical sampling density, reduces the calculating duration of terminal.
Optionally, as shown in fig. 7, it illustrates the algorithm flows of the light distribution acquisition methods based on non-homogeneous calculating
Figure.As shown, Polygon FFT refers to the fast Fourier method of polygon, EVD refers to Eigenvalues Decomposition operation, m (x,
Y) mask function on representation space domain.
In method provided by the embodiments of the present application, by based on intersecting area light source sampling matrix and pupil sample
Matrix carries out non-homogeneous inverse Fourier transform, obtains intersecting transfer matrix, and then determine the frequency domain kernel function for intersecting transfer matrix,
Finally according to the sampling matrix of the sampling matrix of the mask function on frequency domain and frequency domain kernel function, non-homogeneous Fourier's inversion is utilized
It changes, calculates the light distribution in specified location in user.Since the method for sampling based on intersecting area of use improves sampling
Precision, and then computational accuracy is improved, meanwhile, using non-homogeneous inverse Fourier transform, under identical sampling density, calculation amount
It is smaller, it is shorter to calculate duration.Therefore, in the case where guaranteeing that certain calculation accuracy is needed to meet production, can reduce to light
The calculation amount of the light distribution of die sinking type improves the efficiency that photoetching is carried out to photoresist so as to shorten calculating duration.
Fig. 8 is a kind of frame of light distribution acquisition device based on non-homogeneous calculating shown according to an exemplary embodiment
Figure.The device, which has, realizes the exemplary function of the above method.The apparatus may include: matrix sampling module 801, matrix calculate mould
Block 802, function determination module 803 and light intensity acquisition module 804.
Matrix sampling module 801, for being based on to the light source function and pupil function progress uniform sampling on frequency domain
The light source sampling matrix and pupil sampling matrix of intersecting area.
Matrix computing module 802, for carrying out non-homogeneous Fu to the light source sampling matrix and the pupil sampling matrix
In leaf inverse transformation, obtain intersect transfer matrix.
Function determination module 803, for determining the frequency domain kernel function for intersecting transfer matrix.
The matrix sampling module 801, be also used to establish the mask function on frequency domain sampling matrix and the frequency-domain kernel
The sampling matrix of function, the mask function indicate the geometry of mask.
Light intensity acquisition module 804, for the sampling matrix and the frequency-domain kernel letter according to the mask function on the frequency domain
Several sampling matrixs obtains the light distribution in specified location in user by non-homogeneous inverse Fourier transform.
In device provided by the embodiments of the present application, by based on intersecting area light source sampling matrix and pupil sample
Matrix carries out non-homogeneous inverse Fourier transform, obtains intersecting transfer matrix, and then determine the frequency domain kernel function for intersecting transfer matrix,
Finally according to the sampling matrix of the sampling matrix of the mask function on frequency domain and frequency domain kernel function, non-homogeneous Fourier's inversion is utilized
It changes, obtains the light distribution in specified location in user.Since the method for sampling based on intersecting area of use improves sampling
Precision, and then computational accuracy is improved, meanwhile, using non-homogeneous inverse Fourier transform, under identical sampling density, calculation amount
It is smaller, it is shorter to calculate duration.Therefore, in the case where guaranteeing that certain calculation accuracy is needed to meet production, can reduce to light
The calculation amount of the light distribution of die sinking type improves the efficiency that photoetching is carried out to photoresist so as to shorten calculating duration.
Optionally, the light source function is J (f, g), and the pupil function is K (f, g), wherein (f, g) is indicated on frequency domain
Coordinate.The matrix sampling module 801, is specifically used for:
The first sampled point set is established on frequency domain；
According to the first sampled point set, the light source function and the pupil function are sampled, obtained described
Light source sampling matrix J [n]=[J (fi,gj)] and pupil sampling matrix K [n]=[K (fi,gj)], wherein J (fi,gj) table
Show the element of light source sampling matrix the i-th row jth column, and J (fi,gj) corresponding functional value is that sampling area and light source are effective
The intersecting area of computational domain, K (fi,gj) indicate the element that pupil sampling matrix the i-th row jth arranges.
Optionally, the matrix computing module 802, is specifically used for:
It is calculated according to following relational expression and intersects transmission function
J (x'-x ", y'-y ")=INUFFT [J [n]]
K (x', y')=INUFFT [K [n]]
t(x',y'；X ", y ")=j (x'-x ", y'-y ") k (x', y') k*(-x”,-y”)
Wherein, t (x', y'；X ", y ") it is the intersection transmission function, k*(- x " ,-y ") is the conjugation letter of k (x', y')
Number, (x', y') and (x ", y ") are the coordinate points in spatial domain, and J [n] is the light source sampling matrix, and K [n] is that the pupil is adopted
Sample matrix, INUFFT [] indicate non-homogeneous inverse Fourier transform；
Determine that the intersection transfer matrix is T=[t (x', y'；x",y")].
Optionally, the function determination module 803, is specifically used for:
Projection matrix is calculated according to following relational expression
T=[t (x', y'；x",y")]
B=[bj(x',y')]
P=bTb*
Wherein, P is the projection matrix, bj(x, y) is the orthogonal basis function in spatial domain, b=[bj(x', y')] for institute
State the matrix of orthogonal basis function, bj(x', y') is the element in the matrix of the orthogonal basis function, JnFor n-th order first kind shellfish plug
That function, λnsFor s-th of zero root of n-th order Bessel function；
Eigenvalues Decomposition is carried out to the projection matrix, determines the eigenvectors matrix U and characteristic value of the projection matrix
Matrix Λ, wherein P=U Λ U*；
The frequency domain kernel function for intersecting transmission function is calculated according to following relational expression
Ψ (f, g)=∑ γiuijBj(f,g)
Wherein, γiFor the element of the i-th row of the eigenvalue matrix, uijFor the i-th row jth of described eigenvector matrix
The element of column, Bj(f, g) is the orthogonal basis function on frequency domain, and in the orthogonal basis function on the frequency domain and the spatial domain
Fourier transformation, Ψ (f, g) are the frequency domain kernel function for intersecting transmission function to orthogonal basis function each other.
Optionally, device according to claim 10, which is characterized in that the matrix sampling module 801 is specific to use
In:
According to following the second sampled point of relation reality set
Wherein, second sampling point set is combined into { (fi,gj), w and h are the period of the mask function；
The sampling matrix of the mask function on the frequency domain is calculated according to the second sampled point set and following relational expression
With the sampling matrix of the frequency domain kernel function
M [n]=[M (fi,gj)]
Ψ [n]=[Ψ (fi,gj)]
Wherein, M [n] is the sampling matrix of the mask function on the frequency domain, and Ψ [n] is the sampling of the frequency domain kernel function
Matrix.
Optionally, the light intensity acquisition module 804, is specifically used for:
The light distribution is calculated according to following relational expression
I (x, y)=∑ | INUFFT [Ψ (fi,gj)M(fi,gj)]|2
Wherein, (x, y) is the coordinate of the designated position, and I (x, y) is the light distribution on the designated position.
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 in each embodiment of the light distribution acquisition methods provided by the present application based on non-homogeneous calculating when executing
Some or all of step.The storage medium can for magnetic disk, CD, read-only memory (Read-Only Memory,
) or random access memory (Random Access Memory, RAM) etc. ROM.
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 (12)
1. a kind of light distribution acquisition methods based on non-homogeneous calculating, which is characterized in that the described method includes:
To on frequency domain light source function and pupil function carry out uniform sampling, obtain light source sampling matrix based on intersecting area and
Pupil sampling matrix；
Non-homogeneous inverse Fourier transform is carried out to the light source sampling matrix and the pupil sampling matrix, obtains intersecting transmitting square
Battle array；
Determine the frequency domain kernel function for intersecting transfer matrix；
The sampling matrix of the mask function on frequency domain and the sampling matrix of the frequency domain kernel function are established, the mask function indicates
The geometry of mask；
According to the sampling matrix of the sampling matrix of the mask function on the frequency domain and the frequency domain kernel function, pass through non-homogeneous Fu
In leaf inverse transformation, obtain specified location in user on light distribution.
2. the pupil function is K the method according to claim 1, wherein the light source function is J (f, g)
(f, g), wherein (f, g) indicates the coordinate on frequency domain；
The light source function and pupil function on frequency domain carries out uniform sampling, obtains the light source sampling square based on intersecting area
Battle array and pupil sampling matrix, comprising:
The first sampled point set is established on frequency domain；
According to the first sampled point set, the light source function and the pupil function are sampled, the light source is obtained
Sampling matrix J [n]=[J (fi,gj)] and pupil sampling matrix K [n]=[K (fi,gj)], wherein J (fi,gj) indicate institute
State the element of light source sampling matrix the i-th row jth column, and J (fi,gj) corresponding functional value is that sampling area is effectively calculated with light source
The intersecting area in domain, K (fi,gj) indicate the element that pupil sampling matrix the i-th row jth arranges.
3. the method according to claim 1, wherein described sample the light source sampling matrix and the pupil
Matrix carries out non-homogeneous inverse Fourier transform, obtains intersecting transfer matrix, comprising:
It is calculated according to following relational expression and intersects transmission function
J (x'-x ", y'-y ")=INUFFT [J [n]]
K (x', y')=INUFFT [K [n]]
t(x',y'；X ", y ")=j (x'-x ", y'-y ") k (x', y') k*(-x”,-y”)
Wherein, t (x', y'；X ", y ") it is the intersection transmission function, k*(- x " ,-y ") is the conjugate function of k (x', y'), (x',
Y') and (x ", y ") is the coordinate points in spatial domain, and J [n] is the light source sampling matrix, and K [n] is the pupil sampling matrix,
INUFFT [] indicates non-homogeneous inverse Fourier transform；
Determine that the intersection transfer matrix is T=[t (x', y'；x",y")].
4. according to the method described in claim 3, it is characterized in that, the determination frequency-domain kernel letter for intersecting transfer matrix
Number, comprising:
Projection matrix is calculated according to following relational expression
T=[t (x', y'；x",y")]
B=[bj(x',y')]
P=bTb*
Wherein, P is the projection matrix, bj(x, y) is the orthogonal basis function in spatial domain, b=[bj(x', y')] be it is described just
Hand over the matrix of basic function, bj(x', y') is the element in the matrix of the orthogonal basis function, JnFor n-th order first kind Bezier letter
Number, λnsFor s-th of zero root of n-th order Bessel function；
Eigenvalues Decomposition is carried out to the projection matrix, determines the eigenvectors matrix U and eigenvalue matrix of the projection matrix
Λ, wherein P=U Λ U*；
The frequency domain kernel function for intersecting transmission function is calculated according to following relational expression
Ψ (f, g)=∑ γiuijBj(f,g)
Wherein, γiFor the element of the i-th row of the eigenvalue matrix, uijFor described eigenvector matrix the i-th row jth arrange
Element, Bj(f, g) is the orthogonal basis function on frequency domain, and the orthogonal basis function on the frequency domain is orthogonal in the spatial domain
Fourier transformation, Ψ (f, g) are the frequency domain kernel function for intersecting transmission function to basic function each other.
5. according to the method described in claim 4, it is characterized in that, the sampling matrix for establishing the mask function on frequency domain and
The sampling matrix of the frequency domain kernel function, comprising:
According to following the second sampled point of relation reality set
Wherein, second sampling point set is combined into { (fi,gj), w and h are the period of the mask function；
Sampling matrix and the institute of the mask function on the frequency domain are calculated according to the second sampled point set and following relational expression
State the sampling matrix of frequency domain kernel function
M [n]=[M (fi,gj)]
Ψ [n]=[Ψ (fi,gj)]
Wherein, M [n] is the sampling matrix of the mask function on the frequency domain, and Ψ [n] is the sampling square of the frequency domain kernel function
Battle array.
6. according to the method described in claim 5, it is characterized in that, the sampling square according to the mask function on the frequency domain
The sampling matrix of battle array and the frequency domain kernel function obtains the light intensity in specified location in user by non-homogeneous inverse Fourier transform
Distribution, comprising:
The light distribution is calculated according to following relational expression
I (x, y)=∑ | INUFFT [Ψ (fi,gj)M(fi,gj)]|2
Wherein, (x, y) is the coordinate of the designated position, and I (x, y) is the light distribution on the designated position.
7. a kind of light distribution acquisition device based on non-homogeneous calculating, which is characterized in that described device includes:
Matrix sampling module, for obtaining based on intersection to the light source function and pupil function progress uniform sampling on frequency domain
Long-pending light source sampling matrix and pupil sampling matrix；
Matrix computing module, for carrying out non-homogeneous Fourier's inversion to the light source sampling matrix and the pupil sampling matrix
It changes, obtains intersecting transfer matrix；
Function determination module, for determining the frequency domain kernel function for intersecting transfer matrix；
The matrix sampling module is also used to establish the sampling matrix of the mask function on frequency domain and adopting for the frequency domain kernel function
Sample matrix, the mask function indicate the geometry of mask；
Light intensity acquisition module, for according to the sampling matrix of the mask function on the frequency domain and the sampling of the frequency domain kernel function
Matrix obtains the light distribution in specified location in user by non-homogeneous inverse Fourier transform.
8. device according to claim 7, which is characterized in that the light source function is J (f, g), and the pupil function is K
(f, g), wherein (f, g) indicates the coordinate on frequency domain；
The matrix sampling module, is specifically used for:
The first sampled point set is established on frequency domain；
According to the first sampled point set, the light source function and the pupil function are sampled, the light source is obtained
Sampling matrix J [n]=[J (fi,gj)] and pupil sampling matrix K [n]=[K (fi,gj)], wherein J (fi,gj) indicate institute
State the element of light source sampling matrix the i-th row jth column, and J (fi,gj) corresponding functional value is that sampling area is effectively calculated with light source
The intersecting area in domain, K (fi,gj) indicate the element that pupil sampling matrix the i-th row jth arranges.
9. device according to claim 7, which is characterized in that the matrix computing module is specifically used for:
It is calculated according to following relational expression and intersects transmission function
J (x'-x ", y'-y ")=INUFFT [J [n]]
K (x', y')=INUFFT [K [n]]
t(x',y'；X ", y ")=j (x'-x ", y'-y ") k (x', y') k*(-x”,-y”)
Wherein, t (x', y'；X ", y ") it is the intersection transmission function, k*(- x " ,-y ") is the conjugate function of k (x', y'), (x',
Y') and (x ", y ") is the coordinate points in spatial domain, and J [n] is the light source sampling matrix, and K [n] is the pupil sampling matrix,
INUFFT [] indicates non-homogeneous inverse Fourier transform；
Determine that the intersection transfer matrix is T=[t (x', y'；x",y")].
10. device according to claim 9, which is characterized in that the function determination module is specifically used for:
Projection matrix is calculated according to following relational expression
T=[t (x', y'；x",y")]
B=[bj(x',y')]
P=bTb*
Wherein, P is the projection matrix, bj(x, y) is the orthogonal basis function in spatial domain, b=[bj(x', y')] be it is described just
Hand over the matrix of basic function, bj(x', y') is the element in the matrix of the orthogonal basis function, JnFor n-th order first kind Bezier letter
Number, λnsFor s-th of zero root of n-th order Bessel function；
Eigenvalues Decomposition is carried out to the projection matrix, determines the eigenvectors matrix U and eigenvalue matrix of the projection matrix
Λ, wherein P=U Λ U*；
The frequency domain kernel function for intersecting transmission function is calculated according to following relational expression
Ψ (f, g)=∑ γiuijBj(f,g)
Wherein, γiFor the element of the i-th row of the eigenvalue matrix, uijFor described eigenvector matrix the i-th row jth arrange
Element, Bj(f, g) is the orthogonal basis function on frequency domain, and the orthogonal basis function on the frequency domain is orthogonal in the spatial domain
Fourier transformation, Ψ (f, g) are the frequency domain kernel function for intersecting transmission function to basic function each other.
11. device according to claim 10, which is characterized in that the matrix sampling module is specifically used for:
According to following the second sampled point of relation reality set
Wherein, second sampling point set is combined into { (fi,gj), w and h are the period of the mask function；
Sampling matrix and the institute of the mask function on the frequency domain are calculated according to the second sampled point set and following relational expression
State the sampling matrix of frequency domain kernel function
M [n]=[M (fi,gj)]
Ψ [n]=[Ψ (fi,gj)]
Wherein, M [n] is the sampling matrix of the mask function on the frequency domain, and Ψ [n] is the sampling square of the frequency domain kernel function
Battle array.
12. device according to claim 11, which is characterized in that the light intensity acquisition module is specifically used for:
The light distribution is calculated according to following relational expression
I (x, y)=∑ | INUFFT [Ψ (fi,gj)M(fi,gj)]|2
Wherein, (x, y) is the coordinate of the designated position, and I (x, y) is the light distribution on the designated position.
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