CN105785724B - A kind of optimization method of mask pattern, optimal focal plane position measuring method and system - Google Patents
A kind of optimization method of mask pattern, optimal focal plane position measuring method and system Download PDFInfo
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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
- G03F7/70058—Mask illumination systems
- G03F7/70125—Use of illumination settings tailored to particular mask patterns
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
- G03F7/70508—Data handling in all parts of the microlithographic apparatus, e.g. handling pattern data for addressable masks or data transfer to or from different components within the exposure apparatus
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70591—Testing optical components
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- General Physics & Mathematics (AREA)
- Preparing Plates And Mask In Photomechanical Process (AREA)
- Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)
Abstract
The present invention provides the optimization method and system of a kind of mask pattern, the object function for using is partially coherent light source lighting, slope of the corresponding graph position side-play amount of photoetching aerial image intensity distribution to defocusing amount under different defocusing amounts in predetermined focal depth range, the object function is based on optical patterning theory and combines optimization algorithm, with the evaluation function of the measurement sensitivity of the optimal focal plane position of projection objective system, obtain with lighting system match with optimization transmitance and phase mask pattern, the measurement sensitivity of the optimal focal plane position under the conditions of partially coherent light source lighting can be effectively improved.Meanwhile, the mask pattern obtained by the optimization method is based on phase-shift mask measuring principle, in the measurement for optimal focal plane position, it is not necessary to special measuring apparatus and the sensor of complexity, can effectively reduce measurement cost.
Description
Technical field
The present invention relates to etching system, more particularly to a kind of acquisition methods of mask pattern, the measurement of optimal focal plane position
Method and system.
Background technology
Litho machine is the visual plant in IC manufacturing, and the performance of litho machine determines device in IC manufacturing
Characteristic size.Projection objective system is core component in litho machine, and its major function is exposed by focusing on realization, so that
Mask pattern on mask plate is imaged onto on the object to be processed according to a certain percentage.
The depth of focus of the projection objective system of litho machine develops into 20nm in certain scope especially with photoetching technique
And following technology node, the depth of focus of litho machine is in below 60nm.And the size of depth of focus determines the size of imaging, in usual feelings
Under condition, can there is drift condition in actual imaging focal plane relative to optimal focal plane position, by detecting optimal focal plane position
The detection and control that can carry out focal plane position skew are put, and then improves photolithographic exposure quality and anti-aliasing degree.
In the prior art, a kind of optical grating construction based on phase-shift mask is disclosed, projection thing is measured by optical grating construction
The optimal focal plane position of mirror system, however, the method only can just be obtained under the less lighting system of partial coherence factor
Measurement sensitivity higher, and measurement sensitivity is poor under in the industry cycle widely used off-axis illumination mode, it is impossible to obtain satisfied
Measurement result.In some other method, with preferable sensitivity, but the biography of special measuring apparatus and complexity is but needed
Sensor system is completed, and testing cost is too high.
The content of the invention
In view of this, it is an object of the invention to provide a kind of measurement optimization method of optimal focal plane, measurement sensitivity
It is high and testing cost is low.
To achieve the above object, the present invention has following technical scheme：
A kind of optimization method of mask pattern, the mask pattern is used for the measurement of optimal focal plane position, including：
S01, there is provided the default transmitance and phase of the different zones on original mask image, original mask image correspondence
Phase-shift mask；
S02, sets up object function, obtains the target function value under default transmitance and phase, and the target function value is
Current goal functional value, wherein, object function is partially coherent light source lighting, photoetching under different defocusing amounts in predetermined focal depth range
Slope of the corresponding graph position side-play amount of aerial image intensity distribution to defocusing amount；
S03, with default transmitance and phase as starting point, optimized algorithm it is pre-conditioned under, using optimized algorithm
Transmitance and phase after being optimized；
S04, the target function value under the transmitance and phase after object function is optimized, the target function value is
Optimization object function value；
S05, according to current goal functional value and the difference of optimization object function value, it is determined that transmitance and phase after optimization
Whether be optimal mask pattern transmitance and phase parameter；
If it is not, the pre-conditioned of optimized algorithm is then reset, using the transmitance and phase after optimization as default
Cross rate and phase, and return to step S03.
Alternatively, the surface of light source of partially coherent light source is divided into multiple light sources point, the photoetching aerial image intensity distribution
It is the superposition of photoetching aerial image intensity distribution under each light source point.
Alternatively, the surface of light source of partially coherent light source is divided into the method for multiple light sources point and includes：
The circumscribed square of the surface of light source of partially coherent light source is taken, circumscribed square grid is divided into square sub-district
Domain, using the central point of each square subregion an as light source point.
Alternatively, optimized algorithm includes simulated annealing, genetic algorithm, ant group algorithm, gradient algorithm.
Alternatively, optimized algorithm is simulated annealing, according to current goal functional value and the difference of optimization object function value
Value, it is determined that whether the transmitance and phase after optimization are that the transmitance and phase parameter of optimal mask pattern includes：
Judge whether current goal functional value and the difference △ f of optimization object function value are not less than 0, if, it is determined that it is excellent
Transmitance and phase after change are the transmitance and phase of optimal mask pattern；
If △ f are less than 0, e is judged(△f/T0)Whether more than the random number between 0-1, if, it is determined that it is saturating after optimization
Cross rate and transmitance and phase parameter that phase is optimal mask pattern, T0It is the Current Temperatures of simulated annealing.
Alternatively, e is being judged(△f/T0)Whether more than also including after the random number between 0-1：If random less than described
Number, then judge whether to meet predetermined end condition, if so, then enter terminating Optimization Steps.
Additionally, the present invention also provides a kind of optimization system of mask pattern, the mask pattern is used for optimal focal plane position
The measurement put, it includes：
Original mask image provide unit, for provide the different zones on original mask image default transmitance and
Phase, original mask image correspondence phase-shift mask；
Object function sets up unit, for setting up object function, wherein, object function is partially coherent light source lighting, pre-
The graph position side-play amount in deep scope under different defocusing amounts corresponding to the distribution of photoetching aerial image intensity is focused to the oblique of defocusing amount
Rate；
Current goal functional value acquiring unit, for obtaining the target function value under default transmitance and phase, the mesh
Offer of tender numerical value is current goal functional value；
Optimization unit, for default transmitance and phase as starting point, optimized algorithm it is pre-conditioned under, utilize
Optimized algorithm optimized after transmitance and phase；
Optimization object function value acquiring unit, for by the mesh under the transmitance and phase after object function is optimized
Offer of tender numerical value, the target function value is optimization object function value；
Optimal mask pattern judging unit, for the difference according to current goal functional value and optimization object function value, really
Transmitance and phase after fixed optimization whether be optimal mask pattern transmitance and phase parameter；
It is pre-conditioned to reset unit, it is not the transmitance and phase of optimal mask pattern for the transmitance and phase after optimization
During the parameter of position, the pre-conditioned of optimized algorithm is reset, and using the transmitance and phase after optimization as default transmitance
And phase.
Alternatively, also including light source point division unit, for the surface of light source of partially coherent light source to be divided into multiple light sources
Point, the photoetching aerial image intensity is distributed as the superposition of photoetching aerial image intensity distribution under each light source point.
Alternatively, in light source point division unit, the circumscribed square of the surface of light source of partially coherent light source is taken, by circumscribed pros
Shape grid is divided into square subregion, using the central point of each square subregion an as light source point.
Alternatively, optimized algorithm includes simulated annealing, genetic algorithm, ant group algorithm, gradient algorithm.
Alternatively, optimized algorithm is simulated annealing, in optimal mask pattern judging unit, judges current goal function
Whether the difference △ f of value and optimization object function value are not less than 0, if, it is determined that transmitance and phase after optimization are optimal
The transmitance and phase of mask pattern；
If △ f are less than 0, e is judged(△f/T0)Whether more than the random number between 0-1, if, it is determined that it is saturating after optimization
Cross rate and transmitance and phase parameter that phase is optimal mask pattern, T0It is the Current Temperatures of simulated annealing.
Alternatively, also including terminating judging unit, for judging e(△f/T0)After less than the random number between 0-1, sentence
It is disconnected whether to meet predetermined end condition, if so, then enter to terminate optimizing.
Additionally, the present invention also provides a kind of optimal focal plane position measuring method, using the excellent of any of the above-described mask pattern
The transmitance and the corresponding mask pattern of phase parameter of the optimal mask pattern that change method is obtained carry out optimal focal plane position
Measurement.
The optimization method and system of mask pattern provided in an embodiment of the present invention, the object function for using is partially coherent light
In source lighting, predetermined focal depth range under different defocusing amounts the corresponding graph position side-play amount of photoetching aerial image intensity distribution to from
The slope of Jiao's amount, the object function is based on optical patterning theory and combines optimization algorithm, optimal with projection objective system
The evaluation function of the measurement sensitivity of focal plane position, obtains the transmitance and phase with optimization matched with lighting system
Mask pattern, the measurement sensitivity of the optimal focal plane position under the conditions of partially coherent light source lighting can be effectively improved.Together
When, the mask pattern obtained by the optimization method is based on phase-shift mask measuring principle, for optimal focal plane position
During measurement, it is not necessary to special measuring apparatus and the sensor of complexity, measurement cost can be effectively reduced.
Further, in the object function set up, the surface of light source of partially coherent light source is divided into multiple light sources point,
And then the photoetching aerial image intensity distribution under each light source point is overlapped as the photoetching aerial image intensity under light source lighting
Distribution, so as to effectively improve the position of the projection objective system optimal focal plane under the great photoetching vertical shaft lighting condition in partially coherent light source
The measurement sensitivity put.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
The accompanying drawing to be used needed for having technology description is briefly described, it should be apparent that, drawings in the following description are the present invention
Some embodiments, for those of ordinary skill in the art, on the premise of not paying creative work, can also basis
These accompanying drawings obtain other accompanying drawings.
Fig. 1 shows the flow chart of the optimization method of mask pattern according to embodiments of the present invention；
Fig. 2 shows that the cross section structure of the original mask image employed in optimization method according to embodiments of the present invention shows
It is intended to；
Fig. 3 shows the phase distribution schematic diagram in each region of the original mask image of Fig. 2；
Fig. 4 shows that the coherent source employed in the optimization method of the embodiment of the present invention carries out the structure after rasterizing
Schematic diagram；
Fig. 5 shows the original mask image corresponding photoetching of difference defocusing amount in whole focal depth range in an embodiment
Aerial image intensity distribution schematic diagram；
Fig. 6 shows the phase distribution schematic diagram of the mask pattern that the original mask image of Fig. 5 is obtained after optimization；
Fig. 7 shows the mask pattern of the optimized rear optimization for obtaining of the original mask image of Fig. 5 in whole focal depth range
The corresponding photoetching aerial image intensity distribution schematic diagram of interior different defocusing amounts；
Fig. 8 shows the structural representation of the optimization system of mask pattern according to embodiments of the present invention.
Specific embodiment
To enable the above objects, features and advantages of the present invention more obvious understandable, below in conjunction with the accompanying drawings to the present invention
Specific embodiment be described in detail.
Many details are elaborated in the following description in order to fully understand the present invention, but the present invention can be with
Other manner described here is different from using other to implement, those skilled in the art can be without prejudice to intension of the present invention
In the case of do similar popularization, therefore the present invention is not limited by following public specific embodiment.
A kind of optimization method of mask pattern is proposed in the present invention, and the mask pattern is used for optimal focal plane position
Measurement, with reference to shown in Fig. 1, the method includes：
S01, there is provided the different zones on original mask image correspond to default transmitance and phase, and original mask image is
Phase-shift mask；
S02, sets up object function, obtains the target function value under default transmitance and phase, and the target function value is
Current goal functional value, wherein, object function is partially coherent light source lighting, photoetching under different defocusing amounts in predetermined focal depth range
Slope of the corresponding graph position side-play amount of aerial image intensity distribution to defocusing amount；
S03, with default transmitance and phase as starting point, optimized algorithm it is pre-conditioned under, using optimized algorithm
Transmitance and phase after being optimized；
S04, the target function value under the transmitance and phase after object function is optimized, the target function value is
Optimization object function value；
S05, according to current goal functional value and the difference of optimization object function value, it is determined that transmitance and phase after optimization
Whether be optimal mask pattern transmitance and phase parameter；
It is default transmission with transmitance and phase after optimization if it is not, then resetting the pre-conditioned of optimized algorithm
Rate and phase, and return to step S03.
The optimization method can realize in simulation algorithm, for example can in matlab using simulated annealing come real
It is existing, the transmitance and phase parameter of optimal mask pattern are obtained after the optimization, optimal mask pattern will be used for optimal focal plane
The measurement of position.
In the present invention, the object function for using is different defocusing amounts in partially coherent light source lighting, predetermined focal depth range
, to the slope of defocusing amount, the object function is with optical patterning for the corresponding graph position side-play amount of lower photoetching aerial image intensity distribution
Based on theory and optimization algorithm is combined, with the evaluation letter of the measurement sensitivity of the optimal focal plane position of projection objective system
Number, obtain with lighting system match with optimization transmitance and phase mask pattern, part phase can be effectively improved
The measurement sensitivity of the optimal focal plane position under dry light source lighting condition.Meanwhile, the mask figure that is obtained by the optimization method
Shape is based on phase-shift mask measuring principle, in the measurement for optimal focal plane position, it is not necessary to special measuring apparatus and
Complicated sensor, can effectively reduce measurement cost.
In order to be better understood from technical scheme and technique effect, below with reference to flow chart to specific implementation
Example is described in detail.
S01, there is provided the default transmitance and phase of the different zones on original mask image, original mask image correspondence
Phase-shift mask.
In the present invention, it is that mask pattern is obtained by the optimization method of emulation, original mask image can be non-physical
The mask pattern of presence, but the relevant parameter of mask pattern, in embodiments of the present invention, original mask image corresponds to interdependent
Mask, thereon in the presence of multiple different regions, each different zones is correspondingly arranged default transmitance and phase.
In a specific embodiment, the corresponding entity mask pattern of original mask image can be the mask figure of two
Shape, referring to figs. 2 and 3 shown, entity mask pattern includes shading layer and the photic zone, the first phase shift layer and that connect successively
This four different regions of two phase shift layers, shading layer can be the multiple alternatively non-transparent regions with one fixed width, and shading layer can be with
Realized by metal material, metal material is, for example, crome metal, and the transmitance and phase of shading layer are all 0；Photic zone, the first phase
Moving layer and the second phase shift layer can realize that light transmissive material for example can be by the opening of the different depth on light transmissive material
The mask substrate of quartz plate, photic zone can be the surface region for not covering alternatively non-transparent material quartz plate, and its transmitance is 1, phase
Position is 0；First phase shift layer can be the opening on quartz plate with the first depth, and depth for example can beFirst phase
The transmitance for moving layer is 1, and phase is 90 °；Second phase shift layer can be the opening on quartz plate with the second depth, and depth is for example
Can beThe transmitance of the second phase shift layer is 1, and for 180 ° wherein, λ is that the light for inciding the test mask exists to phase
Wavelength in vacuum, n is the refractive index of printing opacity layer material, and k is positive integer.For the mask pattern of the entity, in simulation algorithm
In, can be expressed with the default transmitance of the different zones on original mask image and phase, can be by the original mask
Figure mask functionTo express, the mould correspondence transmitance of mask function,Value corresponding phase, light blocking area
It is correspondingIt is worth for π/4, it is necessary to illustrate, is 0 for its transmitance of light blocking area, phase value herein is to ensure mask
The term amplitude of function is that transmitance is 0, and the phase value is not embodied on mask pattern really, and transparent area is correspondingIt is 0 to be worth,
First phase-shifted region is correspondingIt is pi/2 to be worth, and the second phase-shifted region is correspondingIt is π to be worth.
S02, sets up object function, obtains the target function value under default transmitance and phase, and the target function value is
Current goal functional value, wherein, object function is partially coherent light source lighting, photoetching under different defocusing amounts in predetermined focal depth range
Slope of the corresponding graph position side-play amount of aerial image intensity distribution to defocusing amount.
In the embodiment of the present invention, be analog portion illumination of coherent light source condition and the optimization method that carries out, partially coherent
Light source lighting can realize that the object function of structure is to be shone in partially coherent light source by setting light source form and coherence factor
Under the conditions of bright, the corresponding graph position side-play amount pair of photoetching aerial image intensity distribution under different defocusing amounts in predetermined focal depth range
The slope of defocusing amount.
Wherein, defocusing amount d is the optimal focal plane position and real space picture into image position of the projection objective system of litho machine
The measures of dispersion put, in defocusing amount d=0, then corresponds to optimal focal plane position.In a lithography system, due to control, environment etc. because
The presence of element, causes the position in actual imaging surface positional deviation ideal image face, so that defocusing amount d is produced, defocusing amount d meetings
So that the phase of light propagated in etching system changes, it is considered to the phase place change of the light that the defocusing amount is produced, can be with
The Electric Field Distribution at the location of the real image plane under partially coherent light source lighting being informed in, and then, can obtain under the defocusing amount
The corresponding graph position side-play amount of photoetching aerial image intensity distribution, image pattern position offset, the graph position
Side-play amount then reflects the degree of correlation of the graph position side-play amount to defocusing amount with respect to the slope of defocusing amount, for different transmitances and phase
The mask pattern of position, i.e., different mask pattern then corresponds to different slope values, i.e. target function value, is made with the slope value
The mask pattern of optimization is obtained for the evaluation function of the measurement sensitivity of optimal focal plane position, has been taken into full account and has been photo-etched into
As theoretical, the measurement sensitivity of the optimal focal plane position of projection objective system under the conditions of off-axis illumination can be effectively improved.
In more excellent embodiment, with reference to shown in Fig. 4, for partially coherent light source, its surface of light source 110 can be divided into
Multiple light sources point 130, above-mentioned photoetching aerial image intensity distribution is then folding that photoetching aerial image intensity under each light source point is distributed
Plus, to effectively improve the measurement sensitivity of the projection objective system optimal focal plane position under the conditions of photoetching off-axis illumination.Namely
Say, divided by the surface of light source 110 where the source region 100 by coherent source, so as to 100 points turn to by source region
Light source point 130, the illuminant characterization of source region 100 can be expressed by the illuminant characterization of 120 points of each light source, and for light
The light source point of the non-light source region part on source face 110, illuminant characterization is expressed as 0, and non-light source region is the glazing of surface of light source 110
Region outside source region 100.
The object function constructed by embodiment, described in detail below in the Realization of Simulation for a better understanding of the present invention
Build the process of object function.
First, original mask image grid is turned into multiple subregions, the transmitance and phase of original mask image are used
Mask function M represents,
Preferably, according to the physical size and pixel size of original mask image, can be by original mask image rasterizing
It is N*N sub-regions, N is positive integer, each sub-regions are an element in simulation calculation matrix, grid turns to N*N
Subregion is more convenient for simulation calculation.
Then, the surface of light source of partially coherent light source is divided into multiple light sources point, with reference to shown in Fig. 4.
Specifically, as shown in figure 4, surface of light source is divided into Ns*Ns sub-regions 120, can be for just per sub-regions 120
Square region, the central point (x per sub-regions 120s,ys) regard the light source point 130 of the subregion as, so as to by 110 strokes of surface of light source
It is divided into multiple light sources point 130, each light source point 130 is a sampled point, and the illuminant characterization per sub-regions is then with the sub-district
Central point (the x in domains,ys) place the intensity of light source and polarization state represent that expression formula is Ei(xs,ys), for the non-light on surface of light source
Light source point at source region, Ei(xs,ys) it is 0.
When rasterizing is carried out, can be carried out using the steps：
Take the circumscribed square of the surface of light source 110 of partially coherent light source.
Circumscribed square grid is divided into square subregion 120, by the central point of each square subregion 120
130 used as a light source point.
The each edge of circumscribed square can be divided into Ns sections, so as to circumscribed square grid is being turned into Ns*Ns just
Square subregion, light source point of its central point as the subregion can be taken per sub-regions.For institute in etching system
There are various shapes in the surface of light source of the partially coherent light source of use, can carry out rasterizing using the method, simply obtain
In light source dot matrix, the number at different light source point coordinates not for 0 is different.
Then, object function is obtained.
Object function is that under partially coherent light source lighting, photoetching aerial image is strong under different defocusing amounts in predetermined focal depth range
Slope of the graph position side-play amount corresponding to distribution to defocusing amount is spent, that is, under partially coherent light source, with graph position
Side-play amount is object function to the susceptibility of defocusing amount, and graph position side-play amount can by photoetching aerial image intensity be distributed come
Obtain, it is related to defocusing amount and illuminant characterization.The specific derivation of equation is as follows：
For defocusing amount d, can cause that the phase of the light propagated in etching system changes, the change δ of phase is as follows
It is shown：
Wherein,It is wave number, nwIt is the refractive index of optical projection system image space medium, (α ', β ', γ ') it is emergent ray
Direction cosines.δ is the scalar matrix of N × N, in matrix each element representation by certain is put on pupil light wave in light
Phase place change in etching system, this phase place change is caused by defocus.
When defocusing amount d is 0, chip is at the position of ideal image face, the Electric Field Distribution such as following formula institute on wafer position
Show：
Wherein, nwIt is the refractive index of optical projection system image space medium, R is the reduction magnification of projection objective system, generally 4, F-1{ } represents inverse Fourier transform.⊙ represents homography element multiplication.Low-pass filter function U is the scalar matrix of N × N, is represented
To the limited acceptance ability of diffraction spectrum, i.e., the value inside pupil is 1 to the numerical aperture of optical projection system, and the value outside pupil is
0, specifically it is expressed as follows：
Wherein, (f, g) is normalized world coordinates on entrance pupil.V is a vector matrix of N × N, and each element is
The matrix of one 3 × 3：
When defocusing amount d is not 0, it is contemplated that propagate light in the etching system caused by non-ideal lithography system defocusing amount d
The phase changing capacity δ of line, then the Electric Field Distribution in non-ideal lithography system on wafer position be expressed as below：
Due to Ei(xs,ys) in element value it is unrelated with mask coordinate, so the Electric Field Distribution of wafer position can also be write as：
Wherein,Represent convolution,It is the vector matrix of N × N, each matrix element
Element is 3 × 1 vector (vx',vy',vz')T, wherein vx',vy',vz' it is the function of α ' and β '.
Then Ewafer(αs,βs) three components in global coordinate system are
Wherein,P=x, y, z.Vp' it is the scalar matrix of N × N, by vector matrix V' each elements
Single coordinate components composition.
Then, the expression formula for photoetching aerial image intensity distribution under different defocusing amounts is as follows：
Wherein,Represent to matrix modulus and squared.The photoetching aerial image intensity is distributed, i.e., at wafer position
Imaging results intensity distribution i.e. at imaging surface, the formula expresses the imaging results intensity under different light source points under different defocusing amounts
Distribution, is the imaging results distribution at ideal image position if d=0.
By the formula so that d=0, different light source point (x are calculated respectivelys,ys) under ideal image position at imaging knot
Fruit intensity distribution, then, according to Abbe (Abbe) principle, is overlapped to the imaging results intensity under each light source point, then can be with
Obtain the photoetching aerial image intensity distribution I at ideal image positionbf(x,y,z)。
By the formula so that d is different values, different light source point (x are calculated respectivelys,ys) under different defocusing amount positions at
Imaging results intensity distribution, then, similarly, according to Abbe principles, the imaging results intensity under each light source point is folded
Plus, then can obtain the photoetching aerial image intensity distribution I at different defocusing amount positionsdef(x,y,z)。
According to Abbe principles, the expression formula of photoetching aerial image intensity distribution is as follows at the different defocusing amount positions after superposition：
Wherein, NsIt is the quantity of the light source point of partially coherent light source.Defocusing amount d in above formula is set to 0, you can managed
Imaging results intensity distribution I at imagination facebf(x,y,z)。
In specific calculating, predetermined focal depth range can be set, according to certain step change defocusing amount, at one
In specific embodiment, focal depth range is, for example, -100nm to 100nm, and step-length is 5nm, obtains each light source under different defocusing amounts
Photoetching aerial image intensity distribution after point imaging results distribution superposition, different defocusing amount includes the ideal situation and d of d=0
It is the situation of other values.
And then, according to the definition of map migration amount, map migration amount is the actual imaging position and ideal position of figure
Measures of dispersion, solution meets equationX coordinate value, the as photoetching aerial image intensity is distributed corresponding figure
Shaped position side-play amount.And graph position side-play amount when graph position side-play amount and d are not 0 when passing through d=0 obtains difference
Map migration amount under defocusing amount to the slope of defocusing amount, the slope can by the numerical differentiation to graph position side-play amount come
Obtain.
By the object function of above-mentioned foundation, first, the target function value under default transmitance and phase is obtained, also
It is to obtain the corresponding slope value of object function under the mask function M under default transmitance and phase, obtains original mask image
Susceptibility of the graph position side-play amount relative to defocusing amount.For the ease of description, the target function value is denoted as current goal function
Value fcur。
Then, in S03, with default transmitance and phase as starting point, optimized algorithm it is pre-conditioned under, using excellent
Change transmitance and phase after algorithm is optimized.
Optimized by optimized algorithm, optimized algorithm for example can be simulated annealing, genetic algorithm, ant group algorithm
Or gradient algorithm etc., by these optimized algorithms, algorithm condition, transmitance and phase that acquisition more optimizes can be set.
In a specific embodiment, optimized using the optimized algorithm of simulated annealing, in the optimized algorithm
In, pre-conditioned, the initial temperature T of optimized algorithm is first set020 DEG C are set to, final temperature is set to 0.00005 DEG C, decay
Coefficient TξIt is 0.97, markovian length is 5000.
Then, in step S04, the target function value under the transmitance and phase after object function is optimized should
Target function value is optimization object function value.
By the object function of above-mentioned foundation, the target under the transmitance and phase of the optimization obtained in previous step is obtained
Functional value, that is, the corresponding slope value of object function under the mask function M under the transmitance and phase of optimization is obtained, obtain excellent
The susceptibility of the graph position side-play amount relative to defocusing amount of the mask pattern of change, for the ease of description, target function value note
It is optimization object function value fref。
Then, in step S05, according to current goal functional value and the difference of optimization object function value, it is determined that after optimization
Transmitance and phase whether be optimal mask pattern transmitance and phase.
According to current goal functional value fcurWith optimization object function value frefDifference △ f come determine optimized algorithm optimize
The transmitance and phase for obtaining afterwards whether be optimal mask pattern transmitance and phase, wherein, △ f=fref-fcur, according to institute
The optimized algorithm of use is different, can also be different according to the method that difference carries out optimal mask pattern determination.
In the present embodiment, optimized algorithm uses simulated annealing, at this according to current goal functional value and optimization mesh
The difference of offer of tender numerical value, it is determined that optimization after transmitance and phase whether be optimal mask pattern transmitance and phase parameter
In step, specifically include：
First, it is determined that whether the difference △ f of current goal functional value and optimization object function value are not less than 0, if so, then true
Transmitance after fixed optimization and transmitance and phase that phase is optimal mask pattern.
If △ f are less than 0, e is then judged(△f/T0)Whether more than the random number between 0-1, if, it is determined that after optimization
Transmitance and transmitance and phase parameter that phase is optimal mask pattern, T0 is the Current Temperatures of simulated annealing.
After it is determined that transmitance and phase after optimization are optimal mask pattern, then terminate the optimization method, then, if
Mask pattern before settled is by the mask pattern after optimization, the corresponding transmitance of data mask figure, phase and optimization
Target function value, the mask pattern after the optimization can be used for the measurement of optimal focal plane position.
For by it is above-mentioned judge to determine optimization after transmitance and phase as optimal mask pattern after, can be again
Set optimized algorithm it is pre-conditioned, it usually needs reset it is pre-conditioned in partial condition, such as in simulated annealing
In can reset initial temperature T0And attenuation coefficient TξDeng, and repeat step S03-S05, new pre-conditioned lower heavy
Newly optimize and judge, to export optimal mask pattern.
In order to avoid optimization cannot convergent situation, i.e., cannot obtain suitable optimal mask pattern, judging e(△f/T0)
After the size of the random number between 0-1, if less than described random number, continuing to determine whether to meet predetermined termination bar
Part, if so, then enter terminating Optimization Steps, stops the optimization method, and predetermined end condition can be according to different optimized algorithms
To determine, in simulated annealing, predetermined end condition can be Current Temperatures T0＜ TfOr optimization number of times is more than predetermined value
Deng.
The optimization method of the above-mentioned mask pattern to the embodiment of the present invention is described in detail, using above-mentioned optimization
The transmitance and mask pattern corresponding to phase parameter of the optimal mask pattern that method is obtained, can be carried out optimal in etching system
The measurement of focal plane position.
The technique effect of optimization method for a better understanding of the present invention, below by a simulation result for instantiation
It is described in detail.In the specific embodiment, with reference to shown in Fig. 2, the substrate 301 of the original mask image is quartz
Plate, the region that metallic chromium layer is covered in substrate 301 is light blocking area 302, and transparent area 303 is not to cover metallic chromium layer and expose base
The region at bottom 301, the first phase shift layer 304 and the open area that the second phase shift layer 305 is that depth is different in substrate 301；Printing opacity
Area 303 is connected with the first phase shift layer 304, and the phase difference of their transmitted light is 90 °；First phase shift layer 304 and the second phase shift layer
305 are connected, and the phase difference of their transmitted light is 180 °.Light blocking area 302, transparent area 302, the first phase shift layer 304 and the second phase
Moving the width ratio of layer 305 is：4：1：2：1, the width of the second phase shift layer 305 is 41nm, and the opening of the first phase shift layer 304 depth isSecond phase shift layer 305 opening depth beλ is the aerial wavelength of incident light, and n is the transparency carrier
Refractive index, k is positive integer.
It is the partially coherent light source of the present embodiment use with reference to shown in Fig. 4, the partially coherent light source is drawn by by surface of light source
It is divided into multiple light sources point.With reference to shown in Fig. 5, the A in wherein Fig. 5 be under the light source lighting system original mask image whole
The corresponding photoetching aerial image intensity distribution of different defocusing amount in focal depth range, B be under specific threshold photoetching aerial image intensity whole
, i.e., be converted into for the continuously distributed photoetching aerial image intensity in A by specific threshold value by two Distribution values in individual focal depth range
Two Distribution values, can see from B figures, not shown between the position offset and defocusing amount of original mask image obvious
Linear relationship, the original mask image is not suitable for the detection of the optimal focal plane position under the partially coherent light source lighting.
And the mask pattern by above-mentioned original mask image after being optimized after optimized algorithm optimization, with reference to figure
Shown in 6, Fig. 6 is the phase and transmitance distribution schematic diagram of the mask pattern obtained after optimizing, a region for identical color
Represent a phase and transmitance.With reference to shown in Fig. 7, the A in Fig. 7 is the mask pattern optimized under the partially coherent light source whole
The corresponding photoetching aerial image intensity distribution of different defocusing amount in individual focal depth range, B is that photoetching aerial image intensity exists under specific threshold
Two Distribution values in whole focal depth range, from B figures it can be seen that, its map migration amount with defocusing amount linear change, by right
Map migration amount in figure carries out linear fit, and the slope that can obtain linear relationship between defocusing amount and map migration amount is about
0.3501.It can be seen that, the mask graph has preferable detection sensitivity under the conditions of off-axis illumination, also demonstrates involved by the present invention
And the correctness and validity of optimization method.
The optimization method to the mask pattern of the embodiment of the present invention is described in detail above, additionally, the present invention is also
There is provided the optimization system for realizing the above method, with reference to shown in Fig. 8, including：
Original mask image provides unit 200, the default transmission for providing the different zones on original mask image
Rate and phase, original mask image correspondence phase-shift mask；
Object function sets up unit 210, for setting up object function, wherein, object function be partially coherent light source lighting,
Graph position side-play amount in predetermined focal depth range under different defocusing amounts corresponding to the distribution of photoetching aerial image intensity is to defocusing amount
Slope；
Current goal functional value acquiring unit 220, for obtaining the target function value under default transmitance and phase, should
Target function value is current goal functional value；
Optimization unit 230, for default transmitance and phase as starting point, optimized algorithm it is pre-conditioned under,
Transmitance and phase after being optimized using optimized algorithm；
Optimization object function value acquiring unit 240, for by under the transmitance and phase after object function is optimized
Target function value, the target function value be optimization object function value；
Optimal mask pattern judging unit 250, for the difference according to current goal functional value and optimization object function value,
It is determined that optimization after transmitance and phase whether be optimal mask pattern transmitance and phase parameter；
It is pre-conditioned to reset unit 260, it is not the transmitance of optimal mask pattern for the transmitance and phase after optimization
During with phase parameter, the pre-conditioned of optimized algorithm is reset, and using the transmitance and phase after optimization as default
Cross rate and phase.
Further, also including light source point division unit, for the surface of light source of partially coherent light source to be divided into multiple light
Source point, the photoetching aerial image intensity is distributed as the superposition of photoetching aerial image intensity distribution under each light source point.
Further, in light source point division unit, take the circumscribed square of the surface of light source of partially coherent light source, by it is circumscribed just
Square grid is divided into square subregion, using the central point of each square subregion an as light source point.
Further, optimized algorithm includes simulated annealing, genetic algorithm, ant group algorithm, gradient algorithm.
Further, optimized algorithm is simulated annealing, in optimal mask pattern judging unit 250, judges current mesh
Whether the difference △ f of offer of tender numerical value and optimization object function value are not less than 0, if, it is determined that transmitance and phase after optimization
It is the transmitance and phase of optimal mask pattern；
If △ f are less than 0, e is judged(△f/T0)Whether more than the random number between 0-1, if, it is determined that it is saturating after optimization
Cross rate and transmitance and phase parameter that phase is optimal mask pattern, T0 is the initial temperature of simulated annealing.
Further, also including terminating judging unit, for judging e(△f/T0)After less than the random number between 0-1,
Judge whether to meet predetermined end condition, if so, then enter to terminate optimizing.
Each embodiment in this specification is described by the way of progressive, identical similar portion between each embodiment
Divide mutually referring to what each embodiment was stressed is the difference with other embodiment.Especially for system reality
Apply for example, because it is substantially similar to embodiment of the method, so describing fairly simple, related part is referring to embodiment of the method
Part explanation.
The above is only the preferred embodiment of the present invention, although the present invention is disclosed as above, so with preferred embodiment
And it is not limited to the present invention.Any those of ordinary skill in the art, are not departing from technical solution of the present invention ambit
Under, many possible variations and modification are all made to technical solution of the present invention using the methods and techniques content of the disclosure above,
Or it is revised as the Equivalent embodiments of equivalent variations.Therefore, every content without departing from technical solution of the present invention, according to of the invention
Technical spirit still falls within the technology of the present invention side to any simple modification, equivalent variation and modification made for any of the above embodiments
In the range of case protection.
Claims (13)
1. a kind of optimization method of mask pattern, the mask pattern is used for the measurement of optimal focal plane position, it is characterised in that
Including：
S01, there is provided the default transmitance and phase of the different zones on original mask image, original mask image correspondence phase shift
Mask；
S02, sets up object function, obtains the target function value under default transmitance and phase, and the target function value is current
Target function value, wherein, object function is partially coherent light source lighting, photoetching space under different defocusing amounts in predetermined focal depth range
The slope of graph position side-play amount as corresponding to intensity distribution to defocusing amount；
S03, with default transmitance and phase as starting point, optimized algorithm it is pre-conditioned under, using optimized algorithm obtain
Transmitance and phase after optimization；
S04, the target function value under the transmitance and phase after object function is optimized, the target function value is optimization
Target function value；
S05, according to current goal functional value and the difference of optimization object function value, it is determined that transmitance and phase after optimization whether
It is the transmitance and phase parameter of optimal mask pattern；
If it is not, the pre-conditioned of optimized algorithm is then reset, using the transmitance and phase after optimization as default transmitance
And phase, and return to step S03.
2. method according to claim 1, it is characterised in that the surface of light source of partially coherent light source is divided into multiple light sources
Point, the photoetching aerial image intensity is distributed as the superposition of photoetching aerial image intensity distribution under each light source point.
3. method according to claim 2, it is characterised in that the surface of light source of partially coherent light source is divided into multiple light sources
The method of point includes：
The circumscribed square of the surface of light source of partially coherent light source is taken, circumscribed square grid is divided into square subregion, will
The central point of each square subregion is used as a light source point.
4. method according to claim 1, it is characterised in that optimized algorithm includes simulated annealing, genetic algorithm, ant
Group's algorithm, gradient algorithm.
5. method according to claim 1, it is characterised in that optimized algorithm is simulated annealing, according to current goal
The difference of functional value and optimization object function value, it is determined that optimization after transmitance and phase whether be optimal mask pattern transmission
Rate and phase parameter include：
Judge whether current goal functional value and the difference DELTA f of optimization object function value are not less than 0, if, it is determined that after optimization
Transmitance and transmitance and phase that phase is optimal mask pattern；
If Δ f is less than 0, e is judged(Δf/T0)Whether more than the random number between 0-1, if, it is determined that the transmitance after optimization
With the transmitance and phase parameter that phase is optimal mask pattern, T0It is the Current Temperatures of simulated annealing.
6. method according to claim 5, it is characterised in that judging e(Δf/T0)Whether more than the random number between 0-1
Also include afterwards：If being less than the random number, judge whether to meet predetermined end condition, if so, then enter terminating optimization step
Suddenly.
7. a kind of optimization system of mask pattern, the mask pattern is used for the measurement of optimal focal plane position, it is characterised in that
Including：
Original mask image provides unit, default transmitance and phase for providing the different zones on original mask image
Position, original mask image correspondence phase-shift mask；
Object function sets up unit, for setting up object function, wherein, object function is partially coherent light source lighting, focuses in advance
Slope of the corresponding graph position side-play amount of photoetching aerial image intensity distribution to defocusing amount under different defocusing amounts in deep scope；
Current goal functional value acquiring unit, for obtaining the target function value under default transmitance and phase, the target letter
Numerical value is current goal functional value；
Optimization unit, for default transmitance and phase as starting point, optimized algorithm it is pre-conditioned under, using optimization
Algorithm optimized after transmitance and phase；
Optimization object function value acquiring unit, for by the target letter under the transmitance and phase after object function is optimized
Numerical value, the target function value is optimization object function value；
Optimal mask pattern judging unit, for the difference according to current goal functional value and optimization object function value, determines excellent
Transmitance and phase after change whether be optimal mask pattern transmitance and phase parameter；
It is pre-conditioned to reset unit, it is not transmitance and the phase ginseng of optimal mask pattern for the transmitance and phase after optimization
During number, the pre-conditioned of optimized algorithm is reset, and using the transmitance and phase after optimization as default transmitance and phase
Position.
8. system according to claim 7, it is characterised in that also including light source point division unit, for by partially coherent
The surface of light source of light source is divided into multiple light sources point, and photoetching aerial image is strong under the photoetching aerial image intensity is distributed as each light source point
Spend the superposition of distribution.
9. system according to claim 8, it is characterised in that in light source point division unit, take the light of partially coherent light source
The circumscribed square in source face, square subregion is divided into by circumscribed square grid, by the center of each square subregion
O'clock as a light source point.
10. system according to claim 7, it is characterised in that optimized algorithm include simulated annealing, genetic algorithm,
Ant group algorithm, gradient algorithm.
11. systems according to claim 7, it is characterised in that optimized algorithm is simulated annealing, optimal mask pattern
In judging unit, judge whether current goal functional value and the difference DELTA f of optimization object function value are not less than 0, if, it is determined that
Transmitance and phase after optimization are the transmitance and phase of optimal mask pattern；
If Δ f is less than 0, e is judged(Δf/T0)Whether more than the random number between 0-1, if, it is determined that the transmitance after optimization
With the transmitance and phase parameter that phase is optimal mask pattern, T0It is the Current Temperatures of simulated annealing.
12. systems according to claim 11, it is characterised in that also including terminating judging unit, for judging e(Δf/T0)After less than the random number between 0-1, judge whether to meet predetermined end condition, if so, then enter to terminate optimizing.
13. a kind of optimal focal plane position measuring methods, it is characterised in that using as any one of claim 1-6
The transmitance and the corresponding mask pattern of phase parameter of the optimal mask pattern that the optimization method of mask pattern is obtained are carried out most preferably
The measurement of focal plane position.
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| TWI766127B (en) * | 2018-11-19 | 2022-06-01 | 聯華電子股份有限公司 | Method for optimizing focal parameters of lithographic process |
| CN113325662A (en) * | 2020-02-28 | 2021-08-31 | 中芯国际集成电路制造(上海)有限公司 | Auxiliary pattern configuration method, mask and forming method thereof and related equipment |
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