CN109270802A - A kind of fast acquiring method and device of crystal column surface light distribution - Google Patents

A kind of fast acquiring method and device of crystal column surface light distribution Download PDF

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CN109270802A
CN109270802A CN201811157236.0A CN201811157236A CN109270802A CN 109270802 A CN109270802 A CN 109270802A CN 201811157236 A CN201811157236 A CN 201811157236A CN 109270802 A CN109270802 A CN 109270802A
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CN109270802B (en
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阎江
梁文青
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Moyan Computing Science (nanjing) Co Ltd
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    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
    • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
    • G03F7/70—Microphotolithographic exposure; Apparatus therefor
    • G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
    • G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
    • G03F7/70508—Data handling in all parts of the microlithographic apparatus, e.g. handling pattern data for addressable masks or data transfer to or from different components within the exposure apparatus
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms

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Abstract

This application discloses the fast acquiring methods and device of a kind of crystal column surface light distribution, by by the light source function on frequency domain and the pupil function on frequency domain, it is projected on Fourier-Bessel orthogonal basis function respectively, obtains the frequency domain projection coefficient of light source function and the frequency domain projection coefficient of pupil function.Then according to the transformation relation between Fourier-Bessel orthogonal basis function and Circle-Bessel orthogonal basis function, the spatial domain projection coefficient of light source function and the spatial domain projection coefficient of pupil function are obtained.Then, first group of pre-calculated data collection is obtained, and according to first group of pre-calculated data collection, obtains and intersects transmission function.Then, according to the spatial domain projection coefficient of the second of acquisition group of pre-calculated data collection, intersection transmission function, first group of pre-calculated data collection, the spatial domain projection coefficient of light source function and pupil function, the projection coefficient of kernel function is obtained.Finally, obtaining the light distribution of crystal column surface according to the projection coefficient of kernel function and acquired third group pre-calculated data collection.

Description

A kind of fast acquiring method and device of crystal column surface light distribution
Technical field
This application involves technical field of lithography more particularly to a kind of fast acquiring methods and dress of crystal column surface light distribution It sets.
Background technique
Photoetching process utilizes photochemical reaction principle, and the figure being pre-designed on mask is transferred to crystal column surface, It is an important process step in IC manufacturing.Photo-etching technological process is realized by lithography model, shown in Figure 1 Structural schematic diagram, lithography model specifically include that light source, collector lens, mask, projection pupil, projecting lens and wafer.Knot Lithography model is closed, photo-etching technological process includes: that the light issued from each light source becomes directional light after collector lens, this is parallel Illumination is mapped on mask, makes the pattern on mask, by projection pupil and projecting lens, is imaged on the wafer surface, Therefore crystal column surface is also known as imaging plane.Wherein, light source is a series of mutually incoherent point light source groups at projection pupil is used for The frequency range for the light that can pass through is limited, light source forms light distribution on imaging plane.
As the pattern of light source and mask in lithography system is increasingly sophisticated, in actual photo-etching technological process, Due to the diffraction and interference phenomenon of light, optical proximity effect can be generated, this optical proximity effect will lead on imaging plane There is a certain error for pattern on pattern and mask, and this error will directly affect the performance of final integrated circuit.Currently, By calculate photoetching can the light distribution on crystal column surface calculated, to minimize pattern and mask on imaging plane The error of upper pattern.In calculating photoetching, the calculation method of initially use crystal column surface light distribution is, with Hopkins public affairs Based on formula, the calculating of light distribution is carried out according to the ideal function of light source function, pupil function and mask, Lithography model is described by intersecting transmitting (Transmission Cross Coefficient, TCC) function in Hopkins formula In optical delivery property, TCC function is the four-dimensional convolution function operation about light source function and pupil function, due to the function It is related to four-dimensional operation, therefore, if directly calculating the light distribution of crystal column surface by Hopkins formula, it will generate suitable Big computational complexity and runing time.
In view of the above-mentioned problems, the prior art has developed a kind of fast algorithm again, the process of this fast algorithm is: by light source Function and pupil function are projected on the basic function of Bessel functional dependence, obtain TCC function by the operation to projection coefficient, On this basis, it is decomposed for TCC function, the ideal function for decomposing resulting kernel function and mask is subjected to convolution, The light distribution of crystal column surface is calculated.When any technological parameter in lithography model changes, such as on mask Figure when changing, re-execute above-mentioned calculation process, the light distribution of crystal column surface can be calculated.This algorithm is kept away The four-dimensional crossing operation for having exempted from TCC function, can accelerate the calculating speed of crystal column surface light distribution.
But applicant has found in research process of the invention, the crystal column surface light distribution that the prior art provides In quick calculation method, when any technological parameter in lithography model changes, mask is especially being replaced each time When, the process for re-executing above-mentioned algorithm is required, the light distribution of crystal column surface is recalculated.Mask need to frequently changed In the case where, the calculating time of this algorithm will be significantly greatly increased, and especially reach several hundred a GB, mask in the graphic file of mask In the higher situation of ideal function complexity of version, in the calculation method that above-mentioned technology provides, for crystal column surface light distribution Calculating speed be unable to satisfy process requirements.
Summary of the invention
In order to solve the crystal column surface light distribution provided in the prior art quick calculation method calculating speed, can not Meet the problem of technique requires, the application discloses a kind of quick obtaining of crystal column surface light distribution by following each embodiment Method and device.
The application's in a first aspect, disclosing a kind of fast acquiring method of crystal column surface light distribution, the method packet It includes:
By the light source function on frequency domain and the pupil function on frequency domain, Fourier-Bessel orthogonal basis is projected to respectively On function, and obtain the frequency domain projection coefficient of the light source function and the frequency domain projection coefficient of the pupil function, wherein institute Stating Fourier-Bessel orthogonal basis function is one group of basic function on frequency domain；
According between Fourier-Bessel orthogonal basis function and Circle-Bessel orthogonal basis function transformation relation, The frequency domain projection coefficient of the light source function and the frequency domain projection coefficient of the pupil function obtain the light source letter in spatial domain The spatial domain throwing of number, the pupil function in spatial domain, the spatial domain projection coefficient of the light source function and the pupil function Shadow coefficient, wherein the Circle-Bessel orthogonal basis function is one group of basic function in spatial domain；
According to the Circle-Bessel orthogonal basis function, first group of pre-calculated data collection is obtained, and according to described first Group pre-calculated data collection, the light source function in the spatial domain and the pupil function in the spatial domain, obtain in spatial domain Intersection transmission function；
According to the Circle-Bessel orthogonal basis function, second group of pre-calculated data collection is obtained, and according to described first Group pre-calculated data collection, second group of pre-calculated data collection, the intersection transmission function, the spatial domain of the light source function are thrown The spatial domain projection coefficient of shadow coefficient and the pupil function, obtains the projection coefficient of kernel function；
The graph function of mask is obtained, and according to the graph function of the mask, obtains third group pre-calculated data Collection；
According to the projection coefficient of the kernel function and the third group pre-calculated data collection, the light intensity of crystal column surface is obtained Distribution.
Optionally, described by the light source function on frequency domain and the pupil function on frequency domain, Fourier- is projected to respectively On Bessel orthogonal basis function, and obtain the frequency domain projection of the frequency domain projection coefficient and the pupil function of the light source function Coefficient, comprising:
It, will be on the light source Function Projective to Fourier-Bessel orthogonal basis function on frequency domain by following formula:
Wherein,Indicate that the light source function on frequency domain, (f, g) indicate position table of the light source in frequency domain orthogonal coordinates Show, (r, θ) is that position of the light source on Frequency Domain Polar indicates, (f, g) etc. in (r, θ) and orthogonal coordinates in polar coordinates Valence,For the frequency domain projection coefficient of the light source function, Fns() indicates that Fourier-Bessel orthogonal basis function, ∑ () indicate Summation operation in mathematical operation；
By following formula, the pupil function on frequency domain is projected on Fourier-Bessel orthogonal basis function:
Wherein,Indicate the pupil function on frequency domain,For the frequency domain projection coefficient of the pupil function；
By following formula, the frequency domain projection coefficient of the light source function is obtained:
Wherein,For the frequency domain projection coefficient of the light source function, Jn'(λns) be the primal Bessel function derivative, λnsIndicate s-th of zero root of n rank Bessel function,Indicate FnsThe conjugate complex number of (), ∫ ∫ () indicate double product partite transport It calculates；
By following formula, the frequency domain projection coefficient of the pupil function is obtained:
Wherein,For the frequency domain projection coefficient of the pupil function.
Optionally, the Fourier-Bessel orthogonal basis function is one group of basic function on frequency domain, is described in polar coordinates On, the expression formula of the Fourier-Bessel orthogonal basis function are as follows:
Fns(f, g)=Fns(r, θ)=Jn(λnsr)exp(inθ)；
Wherein, Fns() indicates Fourier-Bessel orthogonal basis function, Jn(λnsIt r) is the primal Bessel function, λnsFor S-th of zero root of n rank Bessel function, (f, g) in (r, θ) and orthogonal coordinates in polar coordinates are of equal value.
Optionally, described according between Fourier-Bessel orthogonal basis function and Circle-Bessel orthogonal basis function Transformation relation, the frequency domain projection coefficient of the light source function and the frequency domain projection coefficient of the pupil function, obtain space Light source function on domain, the pupil function in spatial domain, the light source function spatial domain projection coefficient and the pupil letter Several spatial domain projection coefficients, comprising:
By following formula, the spatial domain projection system of the light source function and the light source function in the spatial domain is obtained Number:
Wherein, the light source function on γ () representation space domain, (x, y) indicate position of the light source in spatial domain orthogonal coordinates It indicates,The position for being light source on spatial domain polar coordinates indicates, in polar coordinatesWith in orthogonal coordinates (x, Y) of equal value, κnsFor the spatial domain projection coefficient of the light source function, Cns() indicates Circle-Bessel orthogonal basis function, Kns Fourier transformation is carried out between the Fourier-Bessel orthogonal basis function and the Circle-Bessel orthogonal basis function When Fourier Transform Coefficients, the Fourier-Bessel orthogonal basis function and the Circle-Bessel orthogonal basis function Between transformation relation be Fourier transformation relationship；
By following formula, the spatial domain projection system of the pupil function and the pupil function in the spatial domain is obtained Number:
Wherein, the pupil function on h () representation space domain, μnsFor the spatial domain projection coefficient of the pupil function.
Optionally, the Circle-Bessel orthogonal basis function is one group of basic function in spatial domain, the Circle- The expression formula of Bessel orthogonal basis function are as follows:
Wherein, Cns() indicates Circle-Bessel orthogonal basis function, J'n(λns) it is leading for the primal Bessel function Number, λnsFor s-th of zero root of n rank Bessel function, and in polar coordinatesIt is of equal value with (x, y) in orthogonal coordinates；
By following formula, it is orthogonal with the Circle-Bessel to obtain the Fourier-Bessel orthogonal basis function Fourier transformation relationship between basic function:
Wherein, Fns() indicates Fourier-Bessel orthogonal basis function, Cns() indicates Circle-Bessel orthogonal basis letter Number,Indicate Fourier transformation, KnsFor Fourier Transform Coefficients；
By following formula, the Fourier Transform Coefficients are obtained:
Optionally, described that first group of pre-calculated data collection is obtained according to the Circle-Bessel orthogonal basis function, and According to the light source function in first group of pre-calculated data collection, the spatial domain and the pupil function in the spatial domain, Obtain the intersection transmission function in spatial domain, comprising:
First group of pre-calculated data collection is obtained by the following formula:
Wherein, αmt,pqFor each group of Circle-Bessel orthogonal basis function Cns() corresponding projection coefficient, and αmt,pq∈ Data1, Data1 indicate that first group of pre-calculated data collection, n, m, p respectively indicate in Circle-Bessel orthogonal basis function The order of corresponding the primal Bessel function, and n, m, p ∈ [0,32], s, t, q are respectively the first kind Bessel letter of corresponding rank The corresponding zero root of number, and s, t, q ∈ [1,60], Cns()、Cmt() and Cpq() indicates Circle-Bessel orthogonal basis function,For the CmtThe conjugate complex number of (), (x1,y1) and (x2,y2) respectively indicate the two o'clock of light source in spatial domain；
According to first group of pre-calculated data collection Data1, basis function decomposition formula, the basis function decomposition formula are obtained For a Circle-Bessel orthogonal basis function to be decomposed into two Circle-Bessel orthogonal basis functions, the basic function Decomposition formula are as follows:
Wherein,For the CpqThe conjugate complex number of ()；
According to the basis function decomposition formula, by following formula, the light source function in the spatial domain is decomposed:
Wherein, the light source function on γ () representation space domain, κnsFor the spatial domain projection coefficient of the light source function；
According to the pupil function in the decomposition result and the spatial domain of the light source function in the spatial domain, by with Lower formula obtains the intersection transmission function in the spatial domain:
Wherein, TCC (x1,y1；x2,y2) indicating the intersection transmission function, n, n' and n " they are corresponding first kind Bessel letter Several ranks, s, s' and s " are the corresponding zero root of corresponding the primal Bessel function.
Optionally, described that second group of pre-calculated data collection is obtained according to the Circle-Bessel orthogonal basis function, and According to first group of pre-calculated data collection, second group of pre-calculated data collection, the intersection transmission function, the light source letter The spatial domain projection coefficient of several spatial domain projection coefficient and the pupil function, obtains the projection coefficient of kernel function, comprising:
Second group of pre-calculated data collection is obtained by the following formula:
Wherein, bpqFor different Circle-Bessel orthogonal basis function Cns()CmtThe corresponding projection coefficient of () product, and bpq∈ Data2, Data2 indicate second group of pre-calculated data collection, Cns()、Cmt() and Cpq() indicates Circle- Bessel orthogonal basis function；
According to second group of pre-calculated data collection Data2, the product of two Circle-Bessel orthogonal basis functions is thrown On shadow to a Circle-Bessel orthogonal basis function, the projection result of the basis function product are as follows:
Cns(x,y)Cmt(x, y)=∑pqbpqCpq(x,y)；
According to second group of pre-calculated data collection Data2, the projection result and the intersection of the basis function product Transmission function obtains kernel function by following formula:
φi'(x, y)=∑nsβnsCns(x,y)；
Wherein, φi'(x, y) is the kernel function, and i' is the index of the kernel function, βnsFor the projection of the kernel function Coefficient, Cns() indicates Circle-Bessel orthogonal basis function；
By following formula, the projection coefficient of the kernel function is obtained:
βns=f (κns,μn's',μn”s”,αmt,pq,bpq)；
Wherein, f () indicates the multiplication cross operation in mathematical operation, κnsSystem is projected for the spatial domain of the light source function Number, μn's'And μn”s”When indicating the Circle-Bessel orthogonal basis function of corresponding different rank, the space of the pupil function Domain projection coefficient, αmt,pq∈ Data1, bpq∈Data2。
Optionally, the graph function for obtaining mask, and according to the graph function of the mask, obtain third group Pre-calculated data collection, comprising:
The graph function of the mask is obtained by following formula according to the linear combination of mask graph:
Wherein, M (x, y) indicates that the graph function of the mask, rect indicate the rectangle in the mask graph, Trap indicates the right-angled trapezium in the mask graph, and V indicates the V-arrangement in the mask graph, Mrect(x, y) indicates institute State the ideal function of rectangle in mask graph, Mtrap(x, y) indicates the ideal function of right-angled trapezium in the mask graph, MV(x, y) indicates the ideal function of V-arrangement in the mask graph, ci=± 1, cj=± 1, ck=± 1, i is the mask The index of rectangle in figure, j are the index of right-angled trapezium in the mask graph, and k is the finger of V-arrangement in the mask graph Mark；
The third group pre-calculated data collection is obtained by following formula according to the graph function of the mask:
Wherein,Data3 indicates the third Group pre-calculated data collection, Cns() indicates the Circle-Bessel orthogonal basis function,Indicate the convolution fortune in mathematical operation It calculates.
Optionally, the projection coefficient and the third group pre-calculated data collection according to the kernel function obtains brilliant The light distribution of circular surfaces, comprising:
Wherein, I (x, y) indicates the light distribution of the crystal column surface, βnsFor the projection coefficient of the kernel function, i' is institute The index of kernel function is stated,Data3 indicates described the Three groups of pre-calculated data collection.
In the second aspect of the application, a kind of quick obtaining device of crystal column surface light distribution, described device packet are disclosed It includes:
Projection module, for being projected to respectively by the light source function on frequency domain and the pupil function on frequency domain On Fourier-Bessel orthogonal basis function, and obtain the frequency domain projection coefficient and the pupil function of the light source function Frequency domain projection coefficient, wherein the Fourier-Bessel orthogonal basis function is one group of basic function on frequency domain；
Conversion module, for according to Fourier-Bessel orthogonal basis function and Circle-Bessel orthogonal basis function it Between transformation relation, the frequency domain projection coefficient of the light source function and the frequency domain projection coefficient of the pupil function, obtain empty Between the light source function on domain, the pupil function in spatial domain, the light source function spatial domain projection coefficient and the pupil The spatial domain projection coefficient of function, wherein the Circle-Bessel orthogonal basis function is one group of basic function in spatial domain；
First group of pre-calculated data collection obtains module, for according to the Circle-Bessel orthogonal basis function, obtaining the One group of pre-calculated data collection, and according to light source function in first group of pre-calculated data collection, the spatial domain and described Pupil function in spatial domain obtains the intersection transmission function in spatial domain；
Second group of pre-calculated data collection obtains module, for according to the Circle-Bessel orthogonal basis function, obtaining the Two groups of pre-calculated data collection, and according to first group of pre-calculated data collection, second group of pre-calculated data collection, the intersection The spatial domain projection coefficient of transmission function, the spatial domain projection coefficient of the light source function and the pupil function obtains core The projection coefficient of function；
Third group pre-calculated data collection obtains module, for obtaining the graph function of mask, and according to the mask Graph function, obtain third group pre-calculated data collection；
Light distribution obtains module, for the projection coefficient and the third group pre-calculated data according to the kernel function Collection, obtains the light distribution of crystal column surface.
According to the above-mentioned technical solution, this application discloses a kind of fast acquiring method of crystal column surface light distribution and Device, by the way that it is orthogonal to project to Fourier-Bessel respectively by the light source function on frequency domain and the pupil function on frequency domain On basic function, the frequency domain projection coefficient of the light source function and the frequency domain projection coefficient of the pupil function are obtained.Then, root According to the transformation relation between Fourier-Bessel orthogonal basis function and Circle-Bessel orthogonal basis function, the light is obtained The spatial domain projection coefficient of source function and the spatial domain projection coefficient of the pupil function.Then, first group of precomputation is obtained Data set, and according to first group of pre-calculated data collection, it obtains and intersects transmission function.Then, pre- according to the second of acquisition group Calculate data set, the spatial domain projection system for intersecting transmission function, first group of pre-calculated data collection, the light source function The spatial domain projection coefficient of the several and described pupil function, obtains the projection coefficient of kernel function.Then, according to acquired mask Graph function, obtain third group pre-calculated data collection.Finally, according to the projection coefficient of the kernel function and the third group Pre-calculated data collection obtains the light distribution of crystal column surface.
By a kind of fast acquiring method of crystal column surface light distribution disclosed in the present application, crystal column surface will be finally calculated The formula of light distribution, the operation being reduced between the projection coefficient of kernel function and the third group pre-calculated data collection, can According to the actual process condition of production, the light distribution of quick obtaining crystal column surface.Wherein, the projection coefficient of the kernel function is light The spatial domain projection coefficient of source function, the spatial domain projection coefficient of pupil function, first group of pre-calculated data collection and second group Pre-calculated data collection multiplication cross as a result, first group of pre-calculated data collection is each group of precalculated Circle- The corresponding projection coefficient of Bessel orthogonal basis function, second group of pre-calculated data collection are precalculated different Circle- The corresponding projection coefficient of Bessel orthogonal basis function product.When any technological parameter in lithography model changes, i.e. light Corresponding change occurs for the spatial domain projection coefficient of source function and the spatial domain projection coefficient of pupil function, at this point, not having to again Execute entire calculation process, it is only necessary to which the variation for considering corresponding two projection coefficients in multiplication cross operation just can be counted quickly Calculate the projection coefficient of kernel function.In addition, the third group pre-calculated data collection obtained in the application can characterize arbitrary mask Domain shape regardless of what shape the figure of mask is, can be transferred through the third group of the application foundation in the actual production process Pre-calculated data collection is described, that is to say, that the third group pre-calculated data collection established in the application is equivalent to a table Lattice contain the characteristic manner of the mask pattern of arbitrary shape in this table, that is, contain the mask with arbitrary shape The graph function of version, and the graph function of the mask with arbitrary shape has further corresponded to the size of light distribution. When carrying out the calculating of crystal column surface light distribution, if replacement mask or technological parameter are changed, without holding again The entire calculation process of row, it is only necessary to according to the spatial domain projection coefficient of the spatial domain projection coefficient of light source function and pupil function Variation, carries out corresponding crossing operation, obtains the projection coefficient of kernel function, then according to the figure of actual mask version, by looking into Table is looked into and takes third group pre-calculated data collection, corresponding mask layout shape function, and then the light of quick obtaining crystal column surface are obtained It is strong to be distributed, in actual process production, a kind of fast acquiring method and device energy of crystal column surface light distribution disclosed in the present application Enough meet technique requirement.
Detailed description of the invention
In order to illustrate more clearly of the technical solution of the application, letter will be made to attached drawing needed in the embodiment below Singly introduce, it should be apparent that, for those of ordinary skills, without creative efforts, also Other drawings may be obtained according to these drawings without any creative labor.
Fig. 1 is lithography model structural schematic diagram disclosed in the prior art；
Fig. 2 is a kind of workflow schematic diagram of the fast acquiring method of crystal column surface light distribution disclosed in the present application；
Fig. 3 is Fourier-Bessel in a kind of fast acquiring method of crystal column surface light distribution disclosed in the present application The schematic diagram of orthogonal basis function；
Fig. 4 is in a kind of fast acquiring method of crystal column surface light distribution disclosed in the present application, and Circle-Bessel is just Hand over the schematic diagram of basic function；
Fig. 5 is in a kind of fast acquiring method of crystal column surface light distribution disclosed in the present application, and mask graph divides Schematic diagram；
Fig. 6 is in a kind of fast acquiring method of crystal column surface light distribution disclosed in the present application, and rectangle characterization is simple more The schematic diagram of side shape；
Fig. 7 is that third group is estimated to count in a kind of fast acquiring method of crystal column surface light distribution disclosed in the present application Schematic diagram is established according to the data of concentration rectangular graph；
Fig. 8 is that third group is estimated to count in a kind of fast acquiring method of crystal column surface light distribution disclosed in the present application According to the schematic diagram of collection；
Fig. 9 is four class right angled triangles in a kind of fast acquiring method of crystal column surface light distribution disclosed in the present application Schematic diagram；
Figure 10 is to be expected in a kind of fast acquiring method of crystal column surface light distribution disclosed in the present application using third group It calculates data set and calculates light intensity schematic diagram；
Figure 11 is in a kind of fast acquiring method of crystal column surface light distribution disclosed in the present application, and mask is in wafer table The outline drawing of face light distribution.
Specific embodiment
In order to solve the crystal column surface light distribution provided in the prior art quick calculation method calculating speed, can not Meet the problem of technique requires, the application discloses a kind of quick obtaining of crystal column surface light distribution by following each embodiment Method and device.
The application first embodiment discloses a kind of fast acquiring method of crystal column surface light distribution, shown in Figure 2 Workflow schematic diagram, which comprises
Light source function on frequency domain and the pupil function on frequency domain are projected to Fourier- by step S11 respectively On Bessel orthogonal basis function, and obtain the frequency domain projection of the frequency domain projection coefficient and the pupil function of the light source function Coefficient, wherein Fourier-Bessel (Fourier-Bezier) orthogonal basis function is one group of basic function on frequency domain.
As an example, the light source in the embodiment of the present application is simple annular light source, internal diameter σin=0.2, outer diameter σout =0.6, function of the light source on frequency domain are as follows:
Wherein, (f, g) is that position of the light source in frequency domain orthogonal coordinates indicates, f indicates light source in frequency domain orthogonal coordinates Abscissa size, g indicates ordinate size of the light source in frequency domain orthogonal coordinates.
Pupil function are as follows:
Step S12, according to the change between Fourier-Bessel orthogonal basis function and Circle-Bessel orthogonal basis function The frequency domain projection coefficient of relationship, the frequency domain projection coefficient of the light source function and the pupil function is changed, is obtained in spatial domain Light source function, the pupil function in spatial domain, the spatial domain projection coefficient of the light source function and the pupil function Spatial domain projection coefficient, wherein the Circle-Bessel orthogonal basis function is one group of basic function in spatial domain.
Step S13 obtains first group of pre-calculated data collection according to the Circle-Bessel orthogonal basis function, and according to First group of pre-calculated data collection, the light source function in the spatial domain and the pupil function in the spatial domain obtain Intersection transmission function in spatial domain.
Step S14 obtains second group of pre-calculated data collection according to the Circle-Bessel orthogonal basis function, and according to First group of pre-calculated data collection, described intersects transmission function, the light source function at second group of pre-calculated data collection The spatial domain projection coefficient of spatial domain projection coefficient and the pupil function, obtains the projection coefficient of kernel function.
Step S15 obtains the graph function of mask, and according to the graph function of the mask, it is pre- to obtain third group Calculate data set.
Step S16 obtains wafer table according to the projection coefficient of the kernel function and the third group pre-calculated data collection The light distribution in face.
As shown from the above technical solution, this application discloses a kind of fast acquiring methods of crystal column surface light distribution, lead to It crosses the light source function on frequency domain and the pupil function on frequency domain, projects to Fourier-Bessel orthogonal basis function respectively On, obtain the frequency domain projection coefficient of the light source function and the frequency domain projection coefficient of the pupil function.Then, according to Transformation relation between Fourier-Bessel orthogonal basis function and Circle-Bessel orthogonal basis function obtains the light source The spatial domain projection coefficient of function and the spatial domain projection coefficient of the pupil function.Then, first group is obtained to expect to count According to collection, and according to first group of pre-calculated data collection, obtains and intersect transmission function.Then, estimated according to the second of acquisition group Calculate the spatial domain projection coefficient of data set, the intersection transmission function, first group of pre-calculated data collection, the light source function And the spatial domain projection coefficient of the pupil function, obtain the projection coefficient of kernel function.Then, according to acquired mask Graph function obtains third group pre-calculated data collection.Finally, pre- according to the projection coefficient of the kernel function and the third group Data set is calculated, the light distribution of crystal column surface is obtained.
By a kind of fast acquiring method of crystal column surface light distribution disclosed in the present application, crystal column surface will be finally calculated The formula of light distribution, the operation being reduced between the projection coefficient of kernel function and the third group pre-calculated data collection, can According to the actual process condition of production, the light distribution of quick obtaining crystal column surface.Wherein, the projection coefficient of the kernel function is light The spatial domain projection coefficient of source function, the spatial domain projection coefficient of pupil function, first group of pre-calculated data collection and second group Pre-calculated data collection multiplication cross as a result, first group of pre-calculated data collection is each group of precalculated Circle- The corresponding projection coefficient of Bessel orthogonal basis function, second group of pre-calculated data collection are precalculated different Circle- The corresponding projection coefficient of Bessel orthogonal basis function product.When any technological parameter in lithography model changes, i.e. light Corresponding change occurs for the spatial domain projection coefficient of source function and the spatial domain projection coefficient of pupil function, at this point, not having to again Execute entire calculation process, it is only necessary to which the variation for considering corresponding two projection coefficients in multiplication cross operation just can be counted quickly Calculate the projection coefficient of kernel function.In addition, the third group pre-calculated data collection obtained in the application can characterize arbitrary mask Domain shape regardless of what shape the figure of mask is, can be transferred through the third group of the application foundation in the actual production process Pre-calculated data collection is described, that is to say, that the third group pre-calculated data collection established in the application is equivalent to a table Lattice contain the characteristic manner of the mask pattern of arbitrary shape in this table, that is, contain the mask with arbitrary shape The graph function of version, and the graph function of the mask with arbitrary shape can further correspond to the big of light distribution It is small.When carrying out the calculating of crystal column surface light distribution, if replacement mask or technological parameter are changed, weight is not had to Newly execute entire calculation process, it is only necessary to which system is projected according to the spatial domain of the spatial domain projection coefficient of light source function and pupil function Several variations carries out corresponding crossing operation, obtains the projection coefficient of kernel function, then according to the figure of actual mask version, leads to It crosses and tables look-up, that is, look into and take third group pre-calculated data collection, obtain corresponding mask layout shape function, and then quick obtaining crystal column surface Light distribution, actual process production in, a kind of fast acquiring method and dress of crystal column surface light distribution disclosed in the present application It sets and can satisfy technique requirement.
Further, described by the light source function on frequency domain and the pupil function on frequency domain, it projects to respectively On Fourier-Bessel orthogonal basis function, and obtain the frequency domain projection coefficient and the pupil function of the light source function Frequency domain projection coefficient, comprising:
It, will be on the light source Function Projective to Fourier-Bessel orthogonal basis function on frequency domain by following formula:
Wherein,Indicate that the light source function on frequency domain, (f, g) indicate that position of the light source in frequency domain orthogonal coordinates indicates, F indicates abscissa size of the light source in frequency domain orthogonal coordinates, and g indicates ordinate size of the light source in frequency domain orthogonal coordinates, (r, θ) is that position of the light source on Frequency Domain Polar indicates, r indicates polar diameter size of the light source in Frequency Domain Polar, and θ indicates light Polar angle size of the source in Frequency Domain Polar, (f, g) in (r, θ) and orthogonal coordinates in polar coordinates is of equal value,For the light The frequency domain projection coefficient of source function, Fns() indicates that Fourier-Bessel orthogonal basis function, ∑ () indicate asking in mathematical operation And operation.
By following formula, the pupil function on frequency domain is projected on Fourier-Bessel orthogonal basis function:
Wherein,Indicate the pupil function on frequency domain,For the frequency domain projection coefficient of the pupil function.
By following formula, the frequency domain projection coefficient of the light source function is obtained:
Wherein,For the frequency domain projection coefficient of the light source function, Jn'(λns) be the primal Bessel function derivative, λnsIndicate s-th of zero root of n rank Bessel function,Indicate FnsThe conjugate complex number of (), ∫ ∫ () indicate double product partite transport It calculates.
By following formula, the frequency domain projection coefficient of the pupil function is obtained:
Wherein,For the frequency domain projection coefficient of the pupil function.
Further, referring to Fig. 3, the Fourier-Bessel orthogonal basis function is one group of basic function on frequency domain, is retouched It states on polar coordinates, the expression formula of the Fourier-Bessel orthogonal basis function are as follows:
Fns(f, g)=Fns(r, θ)=Jn(λnsr)exp(inθ)；
Wherein, Fns() indicates Fourier-Bessel orthogonal basis function, Jn(λnsIt r) is the primal Bessel function, λnsFor S-th of zero root of n rank Bessel function, (f, g) in (r, θ) and orthogonal coordinates in polar coordinates is of equal value, and exp (in θ) indicates e (in θ) power, i indicate imaginary number, n indicate the primal Bessel function rank, θ indicate polar coordinates in angle.Cross in Fig. 3 Coordinate is the r in Fourier-Bessel orthogonal basis function, and ordinate is the θ in Fourier-Bessel orthogonal basis function, figure In when showing n=0, s is respectively the figure of 1,2,3,4,5 five groups of Fourier-Bessel orthogonal basis functions, each group of n, s Corresponding one group of Fourier-Bessel orthogonal basis function Fns()。
In conjunction with Fourier-Bessel orthogonal basis function and the light source function, the frequency domain of the light source function projects system Number can be indicated by following formula:
Wherein, the integral result of the integral part the primal Bessel function easy to use in above-mentioned formula indicates:
Wherein, J0(λ0sR) 0 in indicates the order of the primal Bessel function, λ0sFor 0 rank the primal Bessel function S-th of zero root.
In conjunction with Fourier-Bessel orthogonal basis function and the pupil function, the frequency domain of the pupil function projects system Number can be indicated by following formula:
Further, it is described according to Fourier-Bessel orthogonal basis function and Circle-Bessel orthogonal basis function it Between transformation relation, the frequency domain projection coefficient of the light source function and the frequency domain projection coefficient of the pupil function, obtain empty Between the light source function on domain, the pupil function in spatial domain, the light source function spatial domain projection coefficient and the pupil The spatial domain projection coefficient of function, comprising:
By following formula, the spatial domain projection system of the light source function and the light source function in the spatial domain is obtained Number:
Wherein, the light source function on γ () representation space domain, (x, y) indicate position of the light source in spatial domain orthogonal coordinates It indicates, x indicates abscissa size of the light source in spatial domain orthogonal coordinates, and y indicates that light source is vertical in spatial domain orthogonal coordinates Coordinate size,The position for being light source on spatial domain polar coordinates indicates that ρ indicates cross of the light source on spatial domain polar coordinates Coordinate size,Ordinate size of the light source on spatial domain polar coordinates is indicated, in polar coordinatesIn orthogonal coordinates (x, y) it is of equal value, κnsFor the spatial domain projection coefficient of the light source function, Cns() indicates Circle-Bessel orthogonal basis letter Number, KnsIt is carried out in Fu between the Fourier-Bessel orthogonal basis function and the Circle-Bessel orthogonal basis function Fourier Transform Coefficients when leaf transformation, the Fourier-Bessel orthogonal basis function are orthogonal with the Circle-Bessel Transformation relation between basic function is Fourier transformation relationship.
By following formula, the spatial domain projection system of the pupil function and the pupil function in the spatial domain is obtained Number:
Wherein, the pupil function on h () representation space domain, μnsFor the spatial domain projection coefficient of the pupil function.
Further, referring to fig. 4, the Circle-Bessel orthogonal basis function is one group of basic function in spatial domain, institute State the expression formula of Circle-Bessel orthogonal basis function are as follows:
Wherein, Cns() indicates Circle-Bessel orthogonal basis function, J'n(λns) it is leading for the primal Bessel function Number, λnsFor s-th of zero root of n rank Bessel function, and in polar coordinatesOf equal value, Fig. 4 with (x, y) in orthogonal coordinates In abscissa correspond to the ρ in Circle-Bessel orthogonal basis function, ordinate corresponds to Circle-Bessel orthogonal basis function InWhen showing n=0 in figure, s is respectively the figure of 1,2,3,4,5 five groups of Circle-Bessel orthogonal basis functions, Each group of n, s correspond to one group of Circle-Bessel orthogonal basis function Cns()。
By following formula, it is orthogonal with the Circle-Bessel to obtain the Fourier-Bessel orthogonal basis function Fourier transformation relationship between basic function:
Wherein, Fns() indicates Fourier-Bessel orthogonal basis function, Cns() indicates Circle-Bessel orthogonal basis letter Number,Indicate Fourier transformation, KnsFor Fourier Transform Coefficients.
By following formula, the Fourier Transform Coefficients are obtained:
Light source function gamma (x, y) in spatial domain and the pupil function h (x, y) in spatial domain pass through frequency domain glazing respectively Source functionWith pupil function on frequency domainFourier transformation obtained by, the spatial domain projection coefficient of light source function with Relationship between frequency domain projection coefficient meets:Likewise, the spatial domain projection coefficient and frequency domain of pupil function Relationship between projection coefficient meets:
It is further, described that first group of pre-calculated data collection is obtained according to the Circle-Bessel orthogonal basis function, And according to the light source function in first group of pre-calculated data collection, the spatial domain and the pupil letter in the spatial domain Number obtains the intersection transmission function in spatial domain, comprising:
First group of pre-calculated data collection is obtained by the following formula:
Wherein, αmt,pqFor each group of Circle-Bessel orthogonal basis function Cns() corresponding projection coefficient, and αmt,pq∈ Data1, Data1 indicate that first group of pre-calculated data collection, n, m, p respectively indicate in Circle-Bessel orthogonal basis function The order of corresponding the primal Bessel function, and n, m, p ∈ [0,32], s, t, q are respectively the first kind Bessel letter of corresponding rank The corresponding zero root of number, and s, t, q ∈ [1,60], Cns()、Cmt() and Cpq() indicates Circle-Bessel orthogonal basis function,For the CmtThe conjugate complex number of (), (x1,y1) and (x2,y2) respectively indicate the position table of the two o'clock of light source in spatial domain Show.
Pass through precalculated above-mentioned multiple groups Circle-Bessel orthogonal basis function Cns() corresponding projection coefficient αmt,pq, First group of pre-calculated data collection is formed after saving, so that when carrying out light distribution calculating, first group of pre-calculated data Collection participates in calculating as known quantity, also, first group of pre-calculated data collection is to be directed in lithography system to have invariance Data precalculated, when the technological parameter of lithography model changes, first group of pre-calculated data collection is not It can change, in actual process production, the calculating of final light distribution is directly participated in using precalculated data set, Greatly improve the speed of crystal column surface light distribution calculating.As an example, utilizing HDF5 lattice in embodiments herein Formula file stores first group of pre-calculated data collection Data1, and co-exists in 1920 texts in first group of pre-calculated data collection Data1 Part, respectively corresponds different Circle-Bessel orthogonal basis functions, and each file is respectively present 1920*1920 data.
According to first group of pre-calculated data collection Data1, basis function decomposition formula is obtained, described first group expects to count It is essentially the variables separation of Circle-Bessel orthogonal basis function according to collection Data1, the basis function decomposition formula is used for one A Circle-Bessel orthogonal basis function is decomposed into two Circle-Bessel orthogonal basis functions, the basis function decomposition formula Are as follows:
Wherein,For the CpqThe conjugate complex number of ().
According to the basis function decomposition formula, in conjunction with the light source function in above-mentioned acquired spatial domain:By following formula, the light source function in the spatial domain is decomposed:
Wherein, the light source function on γ () representation space domain, κnsFor the spatial domain projection coefficient of the light source function.
According to the pupil function in the decomposition result and the spatial domain of the light source function in the spatial domain, by with Lower formula obtains the intersection transmission function in the spatial domain:
Wherein, TCC (x1,y1；x2,y2) indicating the intersection transmission function, n, n' and n " they are corresponding first kind Bessel letter Several ranks, s, s' and s " are the corresponding zero root of corresponding the primal Bessel function.
It is further, described that second group of pre-calculated data collection is obtained according to the Circle-Bessel orthogonal basis function, And according to first group of pre-calculated data collection, second group of pre-calculated data collection, the intersection transmission function, the light source The spatial domain projection coefficient of function and the spatial domain projection coefficient of the pupil function, obtain the projection coefficient of kernel function, packet It includes:
Second group of pre-calculated data collection is obtained by the following formula:
Wherein, bpqFor different Circle-Bessel orthogonal basis function Cns()CmtThe corresponding projection coefficient of () product, and bpq∈ Data2, Data2 indicate second group of pre-calculated data collection, Cns()、Cmt() and Cpq() indicates Circle- Bessel orthogonal basis function.
Similarly with first group of pre-calculated data collection, the second pre-calculated data collection is by precalculating and saving Above-mentioned different Circle-Bessel orthogonal basis function Cns()CmtThe corresponding projection coefficient b of () productpqIt is formed by.Into When row light distribution calculates, second group of pre-calculated data collection participates in calculating as known quantity, also, described second group estimated It calculates data set to be precalculated again for the data in lithography system with invariance, when the technique of lithography model is joined When number changes, second group of pre-calculated data collection can't change, and in actual process production, utilize preparatory meter Good data set directly participates in the calculating of final light distribution, can greatly improve the speed of crystal column surface light distribution calculating Degree.As an example, in the embodiment of the present application, stored in second group of pre-calculated data Data2 using HDF5 formatted file, and the Two groups of pre-calculated data Data2 co-exist in 1920*1920 file, respectively correspond different Circle-Bessel orthogonal basis letters Number product, each file are respectively present 1920 data, and the data volume is identical as Data1 data volume.
According to second group of pre-calculated data collection Data2, the product of two Circle-Bessel orthogonal basis functions is thrown On shadow to a Circle-Bessel orthogonal basis function, the projection result of the basis function product are as follows:
Cns(x,y)Cmt(x, y)=∑pqbpqCpq(x,y)；
According to second group of pre-calculated data collection Data2, the projection result and the intersection of the basis function product Transmission function, the intersection transmission function are on above-mentioned decomposition texture and spatial domain according to the light source function in spatial domain Intersection transmission function in spatial domain acquired in pupil function, in conjunction with another expression formula for intersecting transmission function:Can from intersect transmission function in decomposite required kernel function, by with Lower formula obtains kernel function:
φi'(x, y)=∑nsβnsCns(x,y)；
Wherein, φi'(x, y) is the kernel function, and i' is the index of the kernel function, indicates i-th ' a kernel function, βnsFor The projection coefficient of the kernel function, Cns() indicates Circle-Bessel orthogonal basis function.
By following formula, the projection coefficient of the kernel function is obtained:
βns=f (κns,μn's',μn”s”,αmt,pq,bpq)；
Wherein, f () indicates the multiplication cross operation in mathematical operation, κnsSystem is projected for the spatial domain of the light source function Number, μn's'And μn”s”When indicating the Circle-Bessel orthogonal basis function of corresponding different rank, the space of the pupil function Domain projection coefficient, αmt,pq∈ Data1, bpq∈Data2。
It can be said that the projection coefficient of the kernel function is the space of the spatial domain projection coefficient of light source function, pupil function The result of domain projection coefficient, first group of pre-calculated data collection and second group of pre-calculated data collection multiplication cross.Wherein, first group Pre-calculated data collection be the precalculated corresponding projection coefficient of each group of Circle-Bessel orthogonal basis function, second group Pre-calculated data collection is the precalculated different corresponding projection coefficients of Circle-Bessel orthogonal basis function product, by There is invariance in first group of pre-calculated data collection and second group of pre-calculated data collection, when the technological parameter hair in lithography model When changing, it can only be related to the variation of light source function and pupil function, that is to say, that there was only the spatial domain of light source function at this time Projection coefficient, pupil function spatial domain projection coefficient can generate corresponding change according to the variation of technological parameter, at this moment calculate The projection coefficient of kernel function, it is only necessary to the corresponding data in multiplication cross is changed, the projection coefficient of kernel function just can be quickly obtained, In actual process production, the final calculating speed for being directed to crystal column surface light distribution can be effectively improved, meets technique requirement.
Further, it when the polygon of mask plate patterns only includes Manhattan line segment and diagonal line segment, is easy The polygon is divided into the combination of polygon and isosceles right triangle that simple right angle indicates, wherein Manhattan line Section is a kind of geometry term of use in geometry metric space.It include 3 figures, leftmost figure in Fig. 5 referring to Fig. 5 For the mask graph that the embodiment of the present application uses, in the leftmost figure, there are diagonal line segments at two, i.e., with two circles Enclose the position marked.The figure of intermediate figure and rightmost is respectively to divide the schematic diagram of diagonal line segment at above-mentioned two.? In intermediate figure, on position labelled in circle, biggish graph block subtracts triangle, forms first of Far Left figure The figure that circle marks.In the figure of rightmost, after draw above shape block accordingly subtracts two following triangles, formed most Figure labelled in second circle of left panels.It by the above process, can be by the original figure of leftmost mask It is decomposed into a polygon and three isosceles orthogonals only containing Manhattan line segment.
The graph function for obtaining mask, and according to the graph function of the mask, obtain the precomputation of third group Data set, comprising:
The mask graph completed is divided, the polygon only containing Manhattan line segment at this time can be complete by one group Figure (rectangle, right-angled trapezium, V-arrangement) is described using linear combination operation.As an example, in the embodiment of the present application, ginseng See Fig. 6,1/4 infinite planar of shadow representation in figure, by the plus and minus calculation (linear combination) of infinite planar, by the Polygons Representation For the alternating signed magnitude arithmetic(al) of vertex correlation rectangle, that is to say, that, can equivalent description left side using the calculating process of geometric figure Polygon.Basic function of the three kinds of fundamental figures (rectangle, right-angled trapezium, V-arrangement) provided by the present application as mask graph, and And these three fundamental figures have invariance, any mask graph is all characterized by the linear operation of these three figures.
The graph function of the mask is obtained by following formula according to the linear combination of mask graph:
Wherein, M (x, y) indicates that the graph function of the mask, rect indicate the rectangle in the mask graph, Trap indicates the right-angled trapezium in the mask graph, and V indicates the V-arrangement in the mask graph, Mrect(x, y) indicates institute State the ideal function of rectangle in mask graph, Mtrap(x, y) indicates the ideal function of right-angled trapezium in the mask graph, MV(x, y) indicates the ideal function of V-arrangement in the mask graph, ci=± 1, cj=± 1, ck=± 1, i is the mask The index of rectangle in figure indicates that i-th of rectangle, j are the index of right-angled trapezium in the mask graph, and j-th of expression straight Angle is trapezoidal, and k is the index of V-arrangement in the mask graph, indicates k-th of V-arrangement.
Since three kinds of fundamental figures have invariance, the graph function of acquired mask also has invariance Matter, therefore the third group pre-calculated data collection is obtained by following formula according to the graph function of the mask:
Wherein,Data3 indicates the third Group pre-calculated data collection, Cns() indicates the Circle-Bessel orthogonal basis function,Indicate the convolution fortune in mathematical operation It calculates.Store third group pre-calculated data collection Data3 using HDF5 formatted file, in third group pre-calculated data collection Data3 about Circle-Bessel orthogonal basis function includes 1920 data files altogether.At this point, the third group pre-calculated data collection also has There is invariance, also, third group pre-calculated data collection can characterize the graph function of any mask, that is to say, that third Group pre-calculated data collection is equivalent to a table, and the graph function of the mask of arbitrary shape is contained in this table, and And the graph function of the mask of the arbitrary shape has further corresponded to the size of light distribution, is finally calculating crystal column surface When light distribution, corresponding kernel function projection coefficient only need to be calculated, in conjunction with third group pre-calculated data collection, uses the side tabled look-up Formula, just can quick obtaining crystal column surface light distribution.
As an example, Circle-Bessel orthogonal basis function C in the embodiment of the present applicationns() is about origin symmetry, and letter Number energy concentrates on λn,s+4It is interior, it may be assumed that
Thus, the embodiment of the present application calculates above-mentioned third group pre-calculated data collection, C using the method for convolution mask02(x,y) Corresponding convolution mask is as shown in the leftmost figure of Fig. 7, (x, y) ∈ [- λ06,λ06], convolution mask is one in effective range λn,s+4Interior sampling matrix, the size of matrix are N × N.Rectangular graph is respectively 2 for length and width as shown in the figure among Fig. 7 λ06Rectangle, and the lower-left point of rectangle is located at origin, thus corresponding ideal function:
The ideal function of rectangular graph is one in 2 λ of effective rangen,s+4Interior sampling matrix, the size of matrix be 2N × 2N.Coordinates computed position (x in the embodiment of the present application0,y0) pre-calculated dataFor the portion of convolution mask matrix Point element and are as follows:
Convolution mask center is moved to (x0,y0), the convolution of the coordinate position be convolution mask effective coverage with The sum of the element of rectangular graph effective coverage lap, as shown in the figure of Fig. 7 rightmost.
Referring to Fig. 8, according to the invariance of Circle-Bessel orthogonal basis function and above-mentioned three kinds of fundamental figures, third Group pre-calculated data collection Data3 are as follows:Wherein, the graph function of the mask are as follows:
Fig. 8 illustrates third group pre-calculated data collection, above 3 figures of a row be three kinds of basic geometric figures, wherein Mrect(x, y) indicates the ideal function of rectangle in the mask graph；Mtrap(x, y) indicates right angle in the mask graph Trapezoidal ideal function.MV(x, y) indicates the ideal function of V-arrangement in the mask graph.3 figures of a row are phase below Answer geometric figure about some Circle-Bessel orthogonal basis function Cns(the volume of third group pre-calculated data collection corresponding to () Product) image, whereinIndicate that third group pre-calculated data concentrates the estimated of rectangle Data element is calculated,Indicate that third group pre-calculated data concentrates the estimated of right-angled trapezium Data element is calculated,Indicate that third group pre-calculated data concentrates the pre-calculated data of V-arrangement Element, C0,10(x, y) is one group of Circle-Bessel orthogonal basis function, and the n in the Circle-Bessel orthogonal basis function For 0, s 10.
In addition, showing 4 seed types of isosceles right triangle referring to Fig. 9, in figure, there is only two in the embodiment of the present application Class isosceles right triangle, the i.e. two class isosceles right triangles occurred in Fig. 5 at most deposit complicated mask graph In 4 class isosceles right triangles, i.e. 4 classes shown in Fig. 9, the two class triangles occurred in Fig. 4 correspond to wherein two in Fig. 9 Kind triangular type.
Further, the projection coefficient and the third group pre-calculated data collection according to the kernel function obtains The light distribution of crystal column surface, comprising:
Wherein, I (x, y) indicates the light distribution of the crystal column surface, βnsFor the projection coefficient of the kernel function, i' is institute The index of kernel function is stated,Data3 indicates described the Three groups of pre-calculated data collection.By the calculation formula of crystal column surface light distribution it is found that calculating the final step of light distribution only The operation between the projection coefficient and third group pre-calculated data collection of kernel function is contained, third group pre-calculated data collection is pre- It first calculates, and there is the function of similar table, the graph function of the mask of arbitrary shape is contained in this table, Therefore the light distribution for calculating crystal column surface is finally reduced to the calculating of kernel function projection coefficient, estimated further combined with third group Tabling look-up for data set is calculated, crystal column surface light distribution just can be obtained.And in the calculating of kernel function projection coefficient, first group is pre- Calculate data set and second group of pre-calculated data collection be all it is computed in advance, need to only be obtained corresponding according to technological parameter The spatial domain projection coefficient of the spatial domain projection coefficient of light source function, pupil function, can quickly calculate the throwing of kernel function Shadow coefficient, therefore the present processes are capable of the light distribution of quick obtaining crystal column surface.Moreover, being obtained in the embodiment of the present application The calculating data of third group pre-calculated data collection, the corresponding convolution mask matrix of Circle-Bessel orthogonal basis function greatly may be used It can be repeated application, the calculating speed of crystal column surface light distribution at this time is sufficient for technique requirement.
Referring to Figure 10, the process of row's graphical display triangle geometry operation above in figure, corresponding in Fig. 6 about using The calculating process of geometric figure, the content of the polygon on the left of equivalent description.Intermediate row's figure is to pass through third group precomputation Data set uses example, third group pre-calculated data collection in black shade corresponding diagram 8, figure below using one of look-up table To use third group pre-calculated data to use sample result figure by look-up method, it can be seen from fig. 10 that specifying at first Mask pattern, i.e., a triangle in the upper left corner in figure using the precomputation of third group by disclosed method After the tabling look-up of data set, corresponding light distribution is finally quickly obtained, i.e., nethermost width figure.Figure 11 is to pass through the application A kind of fast acquiring method of disclosed crystal column surface light distribution, wheel of the acquired mask in crystal column surface light distribution Wide schematic diagram.
Following is the application Installation practice, can be used for executing the application embodiment of the method.It is real for the application device Undisclosed details in example is applied, the application embodiment of the method is please referred to.
Correspondingly, another embodiment of the application discloses a kind of quick obtaining device of crystal column surface light distribution, the dress It sets and includes:
Projection module, for being projected to respectively by the light source function on frequency domain and the pupil function on frequency domain On Fourier-Bessel orthogonal basis function, and obtain the frequency domain projection coefficient and the pupil function of the light source function Frequency domain projection coefficient, wherein the Fourier-Bessel orthogonal basis function is one group of basic function on frequency domain.
Conversion module, for according to Fourier-Bessel orthogonal basis function and Circle-Bessel orthogonal basis function it Between transformation relation, the frequency domain projection coefficient of the light source function and the frequency domain projection coefficient of the pupil function, obtain empty Between the light source function on domain, the pupil function in spatial domain, the light source function spatial domain projection coefficient and the pupil The spatial domain projection coefficient of function, wherein the Circle-Bessel orthogonal basis function is one group of basic function in spatial domain.
First group of pre-calculated data collection obtains module, for according to the Circle-Bessel orthogonal basis function, obtaining the One group of pre-calculated data collection, and according to light source function in first group of pre-calculated data collection, the spatial domain and described Pupil function in spatial domain obtains the intersection transmission function in spatial domain.
Second group of pre-calculated data collection obtains module, for according to the Circle-Bessel orthogonal basis function, obtaining the Two groups of pre-calculated data collection, and according to first group of pre-calculated data collection, second group of pre-calculated data collection, the intersection The spatial domain projection coefficient of transmission function, the spatial domain projection coefficient of the light source function and the pupil function obtains core The projection coefficient of function.
Third group pre-calculated data collection obtains module, for obtaining the graph function of mask, and according to the mask Graph function, obtain third group pre-calculated data collection.
Light distribution obtains module, for the projection coefficient and the third group pre-calculated data according to the kernel function Collection, obtains the light distribution of crystal column surface.
Combine detailed description and exemplary example that the application is described in detail above, but these explanations are simultaneously It should not be understood as the limitation to the application.It will be appreciated by those skilled in the art that without departing from the application spirit and scope, A variety of equivalent substitution, modification or improvements can be carried out to technical scheme and embodiments thereof, these each fall within the application In the range of.The protection scope of the application is determined by the appended claims.

Claims (10)

1. a kind of fast acquiring method of crystal column surface light distribution characterized by comprising
By the light source function on frequency domain and the pupil function on frequency domain, Fourier-Bessel orthogonal basis function is projected to respectively On, and obtain the frequency domain projection coefficient of the light source function and the frequency domain projection coefficient of the pupil function, wherein it is described Fourier-Bessel orthogonal basis function is one group of basic function on frequency domain；
According to the transformation relation, described between Fourier-Bessel orthogonal basis function and Circle-Bessel orthogonal basis function The frequency domain projection coefficient of light source function and the frequency domain projection coefficient of the pupil function, obtain spatial domain on light source function, The spatial domain projection coefficient of pupil function, the light source function in spatial domain and the spatial domain of the pupil function project system Number, wherein the Circle-Bessel orthogonal basis function is one group of basic function in spatial domain；
According to the Circle-Bessel orthogonal basis function, first group of pre-calculated data collection is obtained, and pre- according to described first group Data set, the light source function in the spatial domain and the pupil function in the spatial domain are calculated, the friendship in spatial domain is obtained Pitch transmission function；
According to the Circle-Bessel orthogonal basis function, second group of pre-calculated data collection is obtained, and pre- according to described first group Calculate data set, second group of pre-calculated data collection, the intersection transmission function, the spatial domain of light source function projection system The spatial domain projection coefficient of the several and described pupil function, obtains the projection coefficient of kernel function；
The graph function of mask is obtained, and according to the graph function of the mask, obtains third group pre-calculated data collection；
According to the projection coefficient of the kernel function and the third group pre-calculated data collection, the light intensity point of crystal column surface is obtained Cloth.
2. the method according to claim 1, wherein described by the light source function on frequency domain and the light on frequency domain Pupil function is projected to respectively on Fourier-Bessel orthogonal basis function, and obtains the frequency domain projection coefficient of the light source function And the frequency domain projection coefficient of the pupil function, comprising:
It, will be on the light source Function Projective to Fourier-Bessel orthogonal basis function on frequency domain by following formula:
Wherein,Indicate that the light source function on frequency domain, (f, g) indicate that position of the light source in frequency domain orthogonal coordinates indicates, (r, It is θ) that position of the light source on Frequency Domain Polar indicates, (f, g) in (r, θ) and orthogonal coordinates in polar coordinates is of equal value,For The frequency domain projection coefficient of the light source function, Fns() indicates that Fourier-Bessel orthogonal basis function, ∑ () indicate mathematical operation In summation operation；
By following formula, the pupil function on frequency domain is projected on Fourier-Bessel orthogonal basis function:
Wherein,Indicate the pupil function on frequency domain,For the frequency domain projection coefficient of the pupil function；
By following formula, the frequency domain projection coefficient of the light source function is obtained:
Wherein,For the frequency domain projection coefficient of the light source function, Jn'(λns) be the primal Bessel function derivative, λnsTable Show s-th of zero root of n rank Bessel function,Indicate FnsThe conjugate complex number of (), ∫ ∫ () indicate double integral operation；
By following formula, the frequency domain projection coefficient of the pupil function is obtained:
Wherein,For the frequency domain projection coefficient of the pupil function.
3. according to the method described in claim 2, it is characterized in that, the Fourier-Bessel orthogonal basis function is on frequency domain One group of basic function, describe on polar coordinates, the expression formula of the Fourier-Bessel orthogonal basis function are as follows:
Fns(f, g)=Fns(r, θ)=Jn(λnsr)exp(inθ)；
Wherein, Fns() indicates Fourier-Bessel orthogonal basis function, Jn(λnsIt r) is the primal Bessel function, λnsFor n rank S-th of zero root of Bessel function, (f, g) in (r, θ) and orthogonal coordinates in polar coordinates are of equal value.
4. according to the method described in claim 2, it is characterized in that, it is described according to Fourier-Bessel orthogonal basis function with The frequency domain projection coefficient and the pupil of transformation relation, the light source function between Circle-Bessel orthogonal basis function The frequency domain projection coefficient of function obtains the sky of the light source function in spatial domain, the pupil function in spatial domain, the light source function Between the spatial domain projection coefficient of domain projection coefficient and the pupil function, comprising:
By following formula, the spatial domain projection coefficient of the light source function and the light source function in the spatial domain is obtained:
Wherein, the light source function on γ () representation space domain, (x, y) indicate position table of the light source in spatial domain orthogonal coordinates Show,The position for being light source on spatial domain polar coordinates indicates, in polar coordinatesWith (x, y) in orthogonal coordinates Equivalence, κnsFor the spatial domain projection coefficient of the light source function, Cns() indicates Circle-Bessel orthogonal basis function, KnsFor When carrying out Fourier transformation between the Fourier-Bessel orthogonal basis function and the Circle-Bessel orthogonal basis function Fourier Transform Coefficients, the Fourier-Bessel orthogonal basis function and the Circle-Bessel orthogonal basis function it Between transformation relation be Fourier transformation relationship；
By following formula, the spatial domain projection coefficient of the pupil function and the pupil function in the spatial domain is obtained:
Wherein, the pupil function on h () representation space domain, μnsFor the spatial domain projection coefficient of the pupil function.
5. according to the method described in claim 4, it is characterized in that, the Circle-Bessel orthogonal basis function is spatial domain On one group of basic function, the expression formula of the Circle-Bessel orthogonal basis function are as follows:
Wherein, Cns() indicates Circle-Bessel orthogonal basis function, J'n(λns) be the primal Bessel function derivative, λns For s-th of zero root of n rank Bessel function, and in polar coordinatesIt is of equal value with (x, y) in orthogonal coordinates；
By following formula, the Fourier-Bessel orthogonal basis function and the Circle-Bessel orthogonal basis letter are obtained Fourier transformation relationship between number:
Wherein, Fns() indicates Fourier-Bessel orthogonal basis function, Cns() indicates Circle-Bessel orthogonal basis function,Indicate Fourier transformation, KnsFor Fourier Transform Coefficients；
By following formula, the Fourier Transform Coefficients are obtained:
6. according to the method described in claim 4, it is characterized in that, described according to the Circle-Bessel orthogonal basis function, Obtain first group of pre-calculated data collection, and according to the light source function in first group of pre-calculated data collection, the spatial domain with And the pupil function in the spatial domain, obtain the intersection transmission function in spatial domain, comprising:
First group of pre-calculated data collection is obtained by the following formula:
Wherein, αmt,pqFor each group of Circle-Bessel orthogonal basis function Cns() corresponding projection coefficient, and αmt,pq∈ Data1, Data1 indicate that first group of pre-calculated data collection, n, m, p respectively indicate in Circle-Bessel orthogonal basis function The order of corresponding the primal Bessel function, and n, m, p ∈ [0,32], s, t, q are respectively the first kind Bessel letter of corresponding rank The corresponding zero root of number, and s, t, q ∈ [1,60], Cns()、Cmt() and Cpq() indicates Circle-Bessel orthogonal basis function,For the CmtThe conjugate complex number of (), (x1,y1) and (x2,y2) respectively indicate the two o'clock of spatial domain light source；
According to first group of pre-calculated data collection Data1, basis function decomposition formula is obtained, the basis function decomposition formula is used for One Circle-Bessel orthogonal basis function is decomposed into two Circle-Bessel orthogonal basis functions, the basis function decomposition Formula are as follows:
Wherein,For the CpqThe conjugate complex number of ()；
According to the basis function decomposition formula, by following formula, the light source function in the spatial domain is decomposed:
Wherein, the light source function on γ () representation space domain, κnsFor the spatial domain projection coefficient of the light source function；
According to the pupil function in the decomposition result and the spatial domain of the light source function in the spatial domain, pass through following public affairs Formula obtains the intersection transmission function in the spatial domain:
Wherein, TCC (x1,y1；x2,y2) indicating the intersection transmission function, n, n' and n " they are corresponding the primal Bessel function Rank, s, s' and s " are the corresponding zero root of corresponding the primal Bessel function.
7. according to the method described in claim 6, it is characterized in that, described according to the Circle-Bessel orthogonal basis function, Second group of pre-calculated data collection is obtained, and according to first group of pre-calculated data collection, second group of pre-calculated data collection, institute It states and intersects transmission function, the spatial domain projection coefficient of the light source function and the spatial domain projection coefficient of the pupil function, Obtain the projection coefficient of kernel function, comprising:
Second group of pre-calculated data collection is obtained by the following formula:
Wherein, bpqFor different Circle-Bessel orthogonal basis function Cns()CmtThe corresponding projection coefficient of () product, and bpq∈ Data2, Data2 indicate second group of pre-calculated data collection, Cns()、Cmt() and Cpq() is indicating Circle-Bessel just Hand over basic function；
According to second group of pre-calculated data collection Data2, the product of two Circle-Bessel orthogonal basis functions is projected to On one Circle-Bessel orthogonal basis function, the projection result of the basis function product are as follows:
Cns(x,y)Cmt(x, y)=∑pqbpqCpq(x,y)；
It is transmitted according to second group of pre-calculated data collection Data2, the projection result of the basis function product and the intersection Function obtains kernel function by following formula:
φi'(x, y)=∑nsβnsCns(x,y)；
Wherein, φi'(x, y) is the kernel function, and i' is the index of the kernel function, βnsFor the projection coefficient of the kernel function, Cns() indicates Circle-Bessel orthogonal basis function；
By following formula, the projection coefficient of the kernel function is obtained:
βns=f (κns,μn's',μn”s”,αmt,pq,bpq)；
Wherein, f () indicates the multiplication cross operation in mathematical operation, κnsFor the spatial domain projection coefficient of the light source function, μn's'And μn”s”When indicating the Circle-Bessel orthogonal basis function of corresponding different rank, the spatial domain of the pupil function is thrown Shadow coefficient, αmt,pq∈ Data1, bpq∈Data2。
8. the method according to the description of claim 7 is characterized in that the graph function for obtaining mask, and according to described The graph function of mask obtains third group pre-calculated data collection, comprising:
The graph function of the mask is obtained by following formula according to the linear combination of mask graph:
Wherein, M (x, y) indicates that the graph function of the mask, rect indicate the rectangle in the mask graph, trap table Show the right-angled trapezium in the mask graph, V indicates the V-arrangement in the mask graph, Mrect(x, y) indicates the mask The ideal function of rectangle, M in domain shapetrap(x, y) indicates the ideal function of right-angled trapezium in the mask graph, MV(x,y) Indicate the ideal function of V-arrangement in the mask graph, ci=± 1, cj=± 1, ck=± 1, i is in the mask graph The index of rectangle, j are the index of right-angled trapezium in the mask graph, and k is the index of V-arrangement in the mask graph；
The third group pre-calculated data collection is obtained by following formula according to the graph function of the mask:
Wherein,Data3 indicates that the third group is pre- Calculate data set, Cns() indicates the Circle-Bessel orthogonal basis function,Indicate the convolution algorithm in mathematical operation.
9. according to the method described in claim 8, it is characterized in that, the projection coefficient according to the kernel function and described Third group pre-calculated data collection, obtains the light distribution of crystal column surface, comprising:
Wherein, I (x, y) indicates the light distribution of the crystal column surface, βnsFor the projection coefficient of the kernel function, i' is the core The index of function,Data3 indicates the third group Pre-calculated data collection.
10. a kind of quick obtaining device of crystal column surface light distribution characterized by comprising
Projection module, for projecting to Fourier- respectively for the light source function on frequency domain and the pupil function on frequency domain On Bessel orthogonal basis function, and obtain the frequency domain projection of the frequency domain projection coefficient and the pupil function of the light source function Coefficient, wherein the Fourier-Bessel orthogonal basis function is one group of basic function on frequency domain；
Conversion module, for according between Fourier-Bessel orthogonal basis function and Circle-Bessel orthogonal basis function The frequency domain projection coefficient of transformation relation, the frequency domain projection coefficient of the light source function and the pupil function obtains spatial domain On light source function, the pupil function in spatial domain, the light source function spatial domain projection coefficient and the pupil function Spatial domain projection coefficient, wherein the Circle-Bessel orthogonal basis function is one group of basic function in spatial domain；
First group of pre-calculated data collection obtains module, for obtaining first group according to the Circle-Bessel orthogonal basis function Pre-calculated data collection, and according in first group of pre-calculated data collection, the spatial domain light source function and the space Pupil function on domain obtains the intersection transmission function in spatial domain；
Second group of pre-calculated data collection obtains module, for obtaining second group according to the Circle-Bessel orthogonal basis function Pre-calculated data collection, and transmitted according to first group of pre-calculated data collection, second group of pre-calculated data collection, the intersection The spatial domain projection coefficient of function, the spatial domain projection coefficient of the light source function and the pupil function obtains kernel function Projection coefficient；
Third group pre-calculated data collection obtains module, for obtaining the graph function of mask, and according to the figure of the mask Shape function obtains third group pre-calculated data collection；
Light distribution obtains module, for the projection coefficient and the third group pre-calculated data collection according to the kernel function, Obtain the light distribution of crystal column surface.
CN201811157236.0A 2018-09-30 2018-09-30 Method and device for quickly acquiring light intensity distribution on surface of wafer Active CN109270802B (en)

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Publication number Priority date Publication date Assignee Title
CN103926803A (en) * 2014-04-21 2014-07-16 中国科学院上海光学精密机械研究所 Method for describing lithography machine illuminating light source
CN107479335A (en) * 2017-09-13 2017-12-15 苏州珂晶达电子有限公司 The optical imagery quick calculation method decomposed based on light source interaural crosscorrelation function
CN107621757A (en) * 2017-09-13 2018-01-23 苏州珂晶达电子有限公司 A kind of intersection transmission function quick decomposition method based on indicator function
CN107644131A (en) * 2017-09-13 2018-01-30 苏州珂晶达电子有限公司 Intersection transmission function quick decomposition method based on polar coordinates sampling

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103926803A (en) * 2014-04-21 2014-07-16 中国科学院上海光学精密机械研究所 Method for describing lithography machine illuminating light source
CN107479335A (en) * 2017-09-13 2017-12-15 苏州珂晶达电子有限公司 The optical imagery quick calculation method decomposed based on light source interaural crosscorrelation function
CN107621757A (en) * 2017-09-13 2018-01-23 苏州珂晶达电子有限公司 A kind of intersection transmission function quick decomposition method based on indicator function
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