CN109634068A - Light source-mask batch optimization method that defocus low sensitivity, process window enhance - Google Patents

Light source-mask batch optimization method that defocus low sensitivity, process window enhance Download PDF

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CN109634068A
CN109634068A CN201910084372.XA CN201910084372A CN109634068A CN 109634068 A CN109634068 A CN 109634068A CN 201910084372 A CN201910084372 A CN 201910084372A CN 109634068 A CN109634068 A CN 109634068A
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light source
defocus
mask
optimization
matrix
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CN109634068B (en
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李艳秋
韦鹏志
李铁
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Beijing Institute of Technology BIT
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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
    • G03F7/705—Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions
    • 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
    • G03F7/70066—Size and form of the illuminated area in the mask plane, e.g. reticle masking blades or blinds
    • 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
    • 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
    • G03F7/70425—Imaging strategies, e.g. for increasing throughput or resolution, printing product fields larger than the image field or compensating lithography- or non-lithography errors, e.g. proximity correction, mix-and-match, stitching or double patterning
    • 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
    • G03F7/70425—Imaging strategies, e.g. for increasing throughput or resolution, printing product fields larger than the image field or compensating lithography- or non-lithography errors, e.g. proximity correction, mix-and-match, stitching or double patterning
    • G03F7/70433—Layout for increasing efficiency or for compensating imaging errors, e.g. layout of exposure fields for reducing focus errors; Use of mask features for increasing efficiency or for compensating imaging errors
    • 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
    • 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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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)

Abstract

The present invention proposes light source-mask batch optimization method of a kind of defocus low sensitivity, process window enhancing, process are as follows: selection primary light source, mask graph；Establish square that defocus high fidelity objective function is Euler's distance in targeted graphical photoresist corresponding with current light source figure and mask graph between imaging；Construct defocus low sensitivity penalty function itemWherein Idefocus(βi) it is defocus error βiAerial image, β is calculated by vector imaging model in placeiTo obey equally distributed random defocus variable；Calculate separately the weighting analytic gradient ▽ G of objective function and penalty function, i.e. ▽ G=▽ F+ ω ▽ Y；Light source, mask are updated and optimized by small lot gradient descent method.System after being optimized by this method obtains exposure figure more uniformly with consistent exposure figure within the scope of certain defocus error, compares conventional light source-photomask optimization method, have higher defocus robustness, bigger depth of focus and process window.

Description

Light source-mask batch optimization method that defocus low sensitivity, process window enhance
Technical field
The present invention relates to light source-mask batch optimization methods that a kind of defocus low sensitivity, process window enhance, and belong to collection Enhance technical field at circuit design, photoetching resolution.
Background technique
Photoetching process is the core process of super large-scale integration manufacturing field.The lithography system of industry mainstream at present Operation wavelength be 193nm.With moving down for technology node, it is necessary to introduce RET with improve photoetching at image quality Amount.Traditional RET such as light source-mask combined optimization technology (source mask optimization, letter Claim SMO) by optimization exposure light source and mask graph, optical approach effect (optical proximity can be corrected Effect, abbreviation OPE), image deformation, map migration caused by exposure technology error, image quality decline the problems such as.
However, traditional ideal photoetching SMO, such as the prior art (CN 102692814 B, 2013.09.11), Jin Jinzhen Nominal etching condition is optimized, i.e., only considers to correct the pattern error as caused by diffraction effect under best focal plane, not have Have specifically for the solution in the case of defocus.During actual exposure, such as crystal column surface out-of-flatness, photoresist are thick Degree, projection objective aberration, mask three-dismensional effect, fuel factor can all lead to focal shift, thus strong influence image quality and The fidelity of exposure figure.Therefore, focus deviation must control in focal depth range in exposure technology；Meanwhile with light Carving technology technology node moves down, and the marginal range of depth of focus will become smaller and smaller.Therefore, it is necessary to pass through SMO, optical adjacent Correct inverse lithographies technology (Inverse Lithography such as (Optical Proximity Correction, abbreviation OPC) Technology, abbreviation ILT) further relax the defocus error tolerance in practical photoetching process.
Existing SMO, OPC method for improving focusing performance is as follows, pertinent literature (IEEE Transactions on Image Processing, 2011,20:2856-2864) in ILT optimization architecture using defocus correction term improve a fixed 100nm from The fidelity of exposure figure under focal plane, but cannot be guaranteed the global fidelity under other focal planes.Pertinent literature (J OPTICS-UK, 2010,12:45601-45609) a kind of statistic optimization based on random defocus variable is proposed, it can compensate for Global fidelity of the optimization system under different defocus error variable quantities, to expand depth of focus.
However, above-mentioned optimization method be difficult to directly improve under different focal planes the uniformity of exposure figure with it is consistent Property, therefore the compensation ability of defocus error is limited, the robustness of optimization system focus point offset is relatively low.Meanwhile The above method uses gradient descent method (gradient descent, abbreviation GD) or stochastic gradient descent method (stochastic Gradient descent, abbreviation SGD) method optimizes, and for a wide range of, the defocus training set of large sample size, this method is complete Office's search capability is restricted, and the performance of optimization is weaker.
Summary of the invention
The purpose of the present invention is provide one kind under defocus problem condition inevitable during considering actual exposure Defocus low sensitivity, process window enhancing light source-mask batch optimization method, this method can be in effective compensation lithography system Uncertain defocus error.Realize that technical solution of the invention is as follows:
A kind of defocus low sensitivity, process window enhancing light source-mask batch optimization method, detailed process are as follows:
Step 1: initialization light source figure and mask graph；
Step 2: constitution optimization objective function G:
If F is imaging fidelity function, it is defined as targeted graphical photoetching corresponding with current light source figure and mask graph Square of Euler's distance in glue between imaging, i.e.,WhereinFor each pixel of targeted graphical Pixel value, Z (βi) indicate to be calculated current light source figure and the corresponding photoresist of mask graph by vector imaging model in defocusing amount βi When imaging, wherein βiTo obey equally distributed random defocus variable, i.e. βi∈ U (- α, α), εβi{ } is mathematic expectaion, Two norms of representing matrix.
Structure imaging result is to the low sensitivity item penalty function of defocusWherein Idefocus(βi) it is that current light source figure and mask graph are calculated using vector imaging model in corresponding defocusing amount βiUnder space Picture；
Optimization object function G is configured to the weighted sum of F and Y, i.e. G=F+ ω Y, wherein ω is weight coefficient；
Step 3: being based on the optimization object function G, light source and mask are carried out using small lot gradient descent method excellent Change.
Further, the detailed process of step 1 of the present invention are as follows:
Light source is initialized size as N by step 101S×NSLight source figure J, by mask graph M be initialized as size be N The targeted graphical of × NWherein NSIt is integer with N；
The pixel value of light emitting region is 1 in step 102, setting primary light source figure J, and the pixel value of light emitting region is not 0； It is sized as NS×NSLight source matrix of variables Ωs: as J (xs,ysWhen)=1,As J (xs,ysWhen)=0,Wherein J (xs,ys) indicate each pixel (x on light source figures,ys) pixel value；Initial mask figure is set The transmissivity of shape M transmission region is 1, and the transmissivity of light is 0；It is sized the mask matrix of variables Ω for N × NM: when When M (x, y)=1,As M (x, y)=0,Wherein M (x, y) is indicated on mask graph The transmitance of each pixel (x, y)；Enable initial binary mask graph Mb=M.
Further, the detailed process of step 3 of the present invention are as follows:
A series of defocus error factor-betas are randomly generated in step 301i,βi+1,…,βi+lbatch-1, lbatchIt is small lot gradient Random sample number in descent method in a wheel iteration, calculating target function G is for light source matrix of variables ΩsGradient matrix ▽ Ga(Ωs), wherein a=i, i+1 ... i+lbatch-1；Utilize normalized steepest descent method, batch updating light source variable square Battle array ΩsForWhereinOptimize step-length for preset light source, obtains corresponding current Ωs Light source figure J,
Step 302 utilizes normalized steepest descent method, batch updating mask matrix of variables ΩMForWhereinFor preset photomask optimization step-length, corresponding current Ω is obtainedM's Mask graph M,Update the binary mask figure M of corresponding current Mb,T under normal circumstancesmIt is taken as 0.5；
Step 303 calculates current light source figure J and binary mask figure MbThe value of corresponding objective function G；When the value is small In predetermined threshold δ D or more new light sources matrix of variables ΩsWith mask matrix of variables ΩMNumber reach predetermined upper limit value KSMWhen, into Enter step 304, otherwise return step 301；
Step 304 terminates optimization, and by current light source figure J and binary mask figure MbIt is determined as optimized Light source figure and mask graph.
Further, defocus error factor-beta is randomly generated in the present inventioniMethod are as follows: selection suitably choose suitable defocus Error range, wherein being limited to ± a up and down, one group for being uniformly distributed U (- α, α) using computer random generation obedience is trained at random Collect β={ βi}。
Beneficial effect
First, compared with traditional SMO method, the present invention will introduce defocus muting sensitive sense in the objective function of SMO and penalize letter Number Y realizes optimization system focusing to effectively constrain the uniformity and consistency of exposure figure under different defocusing amounts Point offset muting sensitive sense, effectively raises technique robustness and process window.Therefore, the light source and cover that the present invention optimizes Mould not only has both high anti-aliasing degree and high uniformity under different focal planes, and further expands photoetching Process window relaxes error margin, so as to more effectively reduce influence of the extreme exposures condition to optical patterning.
Second, the present invention establishes on the basis of vector imaging model, it is contemplated that the polarization characteristic of light can accurately describe to surpass Propagation, focusing and the imaging process of light under big NA situation.
Third, the present invention has been firstly introduced small lot gradient descent method and has solved SMO multi-objective optimization question, for big model It encloses, a large amount of defocusing amount training set β={ βi, compared with stochastic gradient descent method, which achieves more preferably convergence effect Fruit effectively reduces optimization system to the susceptibility of defocus, technique robustness is improved, compared with traditional gradient descent method With better effect of optimization and optimization efficiency.
Detailed description of the invention
Fig. 1 is overview flow chart of the invention.
Fig. 2 is this multiple target light source-photomask optimization method flow diagram.
Fig. 3 is that traditional technology optimizes the schematic diagram being imaged in light source, mask and its corresponding photoresist.
The signal that Fig. 4 is light source figure after the optimization of this improved technology, is imaged in mask graph and its corresponding photoresist Figure (is not introduced into susceptibility constraint).
The signal that Fig. 5 is light source figure after the optimization of this improved technology, is imaged in mask graph and its corresponding photoresist Figure (introduces susceptibility constraint).
Fig. 6 compared changing by corresponding pattern error after traditional technology and the technology of the present invention optimization with defocusing amount bent Line.
Fig. 7 compared through corresponding process window after traditional technology and the technology of the present invention optimization.
Fig. 8 compared figure after being optimized the multi-objective problem using small lot gradient descent method and stochastic gradient descent method and miss Difference is with defocusing amount change curve.
Fig. 9 compared corresponding after utilizing small lot gradient descent method and stochastic gradient descent method to optimize the multi-objective problem Process window.
Specific embodiment
Further the present invention is described in detail with reference to the accompanying drawing.
The principle of the present invention: it is imaged in the relevant technologies (CN 102692814 B, 2013.09.11)-based on Abbe vector On the basis of mixed type light source-photomask optimization algorithm of model, the present invention devises while including that defocus fidelity and defocus are low The novel optimization object function that susceptibility is penalized.Meanwhile using normalized small lot for the first time during light source-photomask optimization Gradient descent method has fully considered influence of the uncertain defocus error of lithography system to imaging, so that the light source that optimization obtains Preferable uniform exposure figure can be obtained within the scope of certain defocus error with mask, effectively improve depth of focus.
Embodiment 1:
As shown in Figure 1, light source-mask batch optimization method of a kind of defocus low sensitivity, process window enhancing, specific mistake Journey are as follows:
Step 1: initialization light source figure and mask graph；
Step 2, constitution optimization objective function G:
If F is imaging fidelity function, it is defined as targeted graphical photoetching corresponding with current light source figure and mask graph Square of Euler's distance in glue between imaging, i.e.,WhereinFor target photoetching offset plate figure, Z (βi) indicate to be calculated current light source figure and the corresponding photoresist of mask graph by vector imaging model in defocusing amount βiWhen at Picture；Wherein, βiTo obey equally distributed random defocus variable,For mathematic expectaion,Two norms of representing matrix.
Structure imaging result is to the sensitivity terms penalty function of errorWherein Idefocus(βi) it is that current light source figure and mask graph are calculated using vector imaging model in corresponding defocusing amount βiUnder space Picture；
Optimization object function G is configured to the weighted sum of F and Y, i.e. G=F+ ω Y, wherein ω is weight coefficient；
Step 3: being based on the optimization object function G, light source and mask are optimized using small lot descent method.
The present invention passes through the anti-aliasing degree and characteristic size (Critical under constraint different focal planes variation Dimension, abbreviation CD) uniformity, the susceptibility of practical lithography system focus point offset is reduced, to improve technique robust Property, process window is further increased, the tolerance of lithography system is relaxed.Since the multi-objective optimization question considers greatly simultaneously Range, the random defocus error of large sample size, therefore the algorithm for introducing the decline of small lot gradient is solved, and the overall situation is improved Search capability and optimization performance.
Embodiment 2:
As shown in Fig. 2, the present embodiment establishes the multiple target light source for defocus muting sensitive sense-mask batch optimization method, Specific steps are as follows:
It (1), is N by light source initialization sizeS×NSLight source figure J, by mask graph M be initialized as size be N × N Targeted graphicalWherein NSIt is integer with N.
(2), the pixel value that light emitting region on primary light source figure J is arranged is 1, and the pixel value of light emitting region is not 0；Setting Size is NS×NSLight source matrix of variables Ωs: as J (xs,ysWhen)=1,As J (xs,ysWhen)=0,Wherein J (xs,ys) indicate each pixel (x on light source figures,ys) pixel value；Initial mask figure is set The transmissivity of shape M transmission region is 1, and the transmissivity of light is 0；It is sized the mask matrix of variables Ω for N × NM: when When M (x, y)=1,As M (x, y)=0,Wherein M (x, y) is indicated on mask graph The transmitance of each pixel (x, y)；Enable initial binary mask graph Mb=M.
(3), constitution optimization objective function G；If F is imaging fidelity function, it is defined as targeted graphical and current light source figure Square of Euler's distance in shape and the corresponding photoresist of mask graph between imaging, i.e.,WhereinFor target photoetching offset plate figure, Z (βi) indicate defocus error βiThe photoetching offset plate figure at place；Sensitivity of the structure imaging result to defocus Spending item penalty function isWherein Idefocus(βi) it is defocus error βiMould is imaged by vector in place Aerial image, β is calculated in typeiIt is the stochastic variable for indicating defocus error.The weighted sum for being F and Y by objective function, i.e. G =F+ ω Y, wherein ω is weight coefficient.
With reference to the prior art (CN 102692814 B, 2013.09.11), in the ideal case, it is imaged using Abbe vector Model calculates aerial image corresponding to current light source and mask are as follows:
Wherein,| | indicate that last calculated result I is to each element modulus in matrix The scalar matrix (if all elements in a matrix are scalar, being called scalar matrix) that one size is N × N, table Show current light source and the corresponding aerial image intensity distribution of mask.For light source point J (xs,ys) corresponding to mask diffraction matrices, According to Thelma Hopkins approximation, each point is defined as on mask to light source point J (xs,ys) light path, it may be assumed that
Wherein, NA indicates that the object-side numerical aperture of optical projection system, pixel indicate the side length of all subregion on mask graph.
Indicating convolution, ⊙ indicates that the corresponding element of two matrixes is directly multiplied,Table Show inverse fourier transform, nwIndicating the refractive index of lithography system image space immersion liquid, R is the reduction magnification of preferred view system, Generally 4；V′pBy vector matrix (if the element in a matrix is vector or matrix, being called vector matrix)In each element p-component composition；P herein indicates the polarization direction of light, embodies imaging model Vectorial property.The specific calculating process of V ' has a detailed description in the prior art (CN102692814B, 2013.09.11), this Place repeats no more.
The above aerial image intensity is calculated according to vector imaging model in the ideal case.For being missed containing defocus Poor βiSystem can equally be calculated comprising β according to the vector imaging model after popularizationiAerial image intensity expression formula, give Its corresponding aerial image intensity expression formula out:
Wherein, ε is direction cosines of the lithography system emergent pupil along the direction of propagation.
Using sigmoid function come approximate description photoresist effect, Wherein, a indicates the slope of photoresist approximate model, trIndicate the threshold value of photoresist approximate model.Therefore, according to aerial image intensity Idefocus(βi) calculate imaging in light source figure and the corresponding photoresist of mask graph are as follows:
In addition, also containing aerial image intensity to defocusing amount β in optimization object function of the inventioniSusceptibility penalty function, This is given below embodies form:
Wherein, Re expression takes real part, and Im expression takes imaginary part；
Wherein
According to above-mentioned calculating process, fidelity function will be imaged and be added with the imaging sensitivity function after weighting, can obtain To the value of objective function G.
(4), defocus error is randomly generatedWith this condition, target letter under corresponding defocusing amount is calculated Number G is for light source matrix of variables ΩsGradient matrix
Gradient matrix ▽ Ga(Ωs) it is objective function G to matrix of variables ΩsIn each element ask obtained by partial derivative, wherein a =i, i+1 ... i+lbatch-1；Although JsumIt is J (xs,ys) function, but constant is assumed in the present invention, this Kind is assumed to can simplify calculating, and is conducive to the stability of optimization.
According to step (3) it is found that gradient matrix ▽ Ga(Ωs)=▽ Fa(Ωs)+ω▽Ya(Ωs)；Gradient is presented below Matrix ▽ Ga(Ωs) expression.
F is to Ωs(xs,ys) partial derivative can calculate are as follows:
Y is calculated belowiTo Ωs(xs,ys) partial derivative, first simplify Yi:
This simplification is the calculation amount in order to reduce circulation summation；It is also to have physical significance that this, which simplifies result, is equivalent to The aerial image intensity generated to the single polarization direction of each light source point is to square summation again after wavefront differentiation.
Therefore,
It is the Fourier transform property in order to utilize convolution that summation, which is rewritten as convolution, in above formula, to accelerate to calculate speed Degree.Then according to chain rule for differentiation,
Utilize normalized small lot gradient descent method, more new light sources matrix of variables ΩsFor WhereinOptimize step-length for preset light source, obtains corresponding current ΩsLight source figure J,Meaning of this replacement is by optimization object from J (xs,ys) ∈ [0,1] is converted into Ωs(xs,ys) ∈ (- ∞ ,+∞), thus make it is constrained optimization be changed into unconfined optimization, reduce optimization difficulty.|||| It indicates to extract square root again after square summation by element each in matrix, therefore deserves to be called and state more new algorithm as under normalized steepest Drop method.Compared with traditional steepest descent method, normalized steepest descent method utilizes normalization of the objective function to Optimal Parameters Gradient value instruct the update of Optimal Parameters, so that different target function is to optimization in the case of eliminating different trained sampled points Difference between the gradient value of parameter improves optimization stability of the invention.
(5), objective function G is calculated under corresponding defocusing amount to mask matrix of variables ΩMGradient matrixGradient matrix ▽ Ga(ΩM) it is objective function G to matrix of variables ΩMIn Each element is asked obtained by partial derivative.
According to step (3) it is found that gradient matrix ▽ Ga(ΩM)=▽ Fa(ΩM)+ω▽Ya(ΩM), expression.
In the present invention, ▽ Fa(ΩM) can calculate are as follows:
Wherein,*Expression takes conjugate operation, and ο is indicated matrix in horizontal and vertical upper rotation 180 degree.
▽ Y is calculated belowi(ΩM), i.e.,It is convenient to write, by ΩM(x, y) is denoted as mkl, this notation may be used also To distinguish (x, y) coordinate in mask plane and image planes；At this point,
Wherein,This amount occurred in the calculation formula of light source gradient.
Utilize normalized small lot gradient descent method, more new mask matrix of variables ΩMFor WhereinFor preset photomask optimization step-length, corresponding current Ω is obtainedMMask graph M,Update the binary mask figure M of corresponding current Mb,One As in the case of tmIt is taken as 0.5.
(6), current light source figure J and binary mask figure M is calculatedbThe value of corresponding objective function G；When the value is less than in advance Determine threshold value δ D or more new light sources matrix of variables ΩsWith mask matrix of variables ΩMNumber reach predetermined upper limit value KSMWhen, enter (7), (4) otherwise are returned to.
(7), optimization is terminated, and by current light source figure J and binary mask figure MbIt is determined as optimized light source Figure and mask graph.
Embodiment of the invention:
If Fig. 3 is that the relevant technologies (CN 102692814 B, 2013.09.11) (lower referred to as initial SMO) (optimization only exists Carried out under nominal etching condition) optimization after light source figure, mask graph and its corresponding photoresist picture in defocus.Institute It is shown as the schematic diagram being imaged in primary light source, initial mask and its corresponding photoresist.In Fig. 3,301 be the light source after optimization Figure, different colors represent the different normalized intensity distribution of light source.302 be the mask graph after optimization, while being also mesh It marks on a map shape, white represents transmission region, and black represents light, characteristic size 45nm.In the case where defocus 90nm, After 303 is are used as mask as light source, 302 using 301, lithography system is imaged in the photoresist.Compare target exposure pattern 304 It can be seen that exposure figure has had larger distortion in defocus, pattern error is the 2882 (fidelities of definition imaging here Spend value of the function F as pattern error).
It is illustrated in figure 4 when weighting repeated factor ω=0 (is called and improved SMO) to this SMO technology in the following text and (does not introduce susceptibility about Beam), light source figure, mask graph and its imaging of the corresponding photoresist in defocus after optimization.It should be noted that every One group of weight factor is the source mask after corresponding one group of optimization.In Fig. 4,401 be using the light source figure after improvement SMO optimization Shape；402 be using the mask graph after improvement SMO optimization；In the case where defocus 90nm, 403 for using 401 as light sources, 402, as after mask, are imaged in the photoresist of lithography system, it is seen that 303 are obviously reduced before distortion relatively, and figure misses Difference is only 1884.
It is illustrated in figure 5 and improves SMO calculating (i.e. introducing susceptibility constraint) in weight factor ω=0.1, after optimization Light source figure, mask graph and its imaging of the corresponding photoresist in defocus.In Fig. 5,501 be excellent using SMO is improved Light source figure after change；502 be using the mask graph after improvement SMO optimization；In the case where defocus 90nm, 503 be use It after 501 are used as mask as light source, 502, is imaged in the photoresist of lithography system, it is seen that 303 and 403 have before distortion relatively Further to reduce, pattern error is only 1399.
If Fig. 6 compared initial SMO, improvement SMO (0nm, 100nm) within the scope of certain defocus error, exposure figure is missed The change curve of difference.More initial SMO, correlation curve slope, respectively be improve SMO (ω=0.1) < improve SMO (ω=0) < just Beginning SMO, therefore SMO is improved to defocus error with lower susceptibility, exposure figure is within the scope of certain defocus error There are better uniformity and consistency.In addition, when introducing defocus low sensitivity penalty function item (when ω ≠ 0), exposure figure Uniformity under different defocusing amounts has further improvement.On the other hand, under same defocusing amount, pattern error is to change respectively Into SMO (ω=0.1) < improvement SMO (ω=0) < initial SMO.Demonstrate that the method increase the overall situations under different focal planes Fidelity can effectively inhibit in actual exposure system random, uncertain focal shift.
Such as the process window that Fig. 7 compared initial SMO, improve SMO, process window, which is sized, is respectively, initial SMO < improve SMO (ω=0) < improve SMO (ω=0.1), it was demonstrated that multiple target light source-photomask optimization of the present invention is obviously improved The process window of photoetching, to further relax the error margin during actual exposure.In addition, introducing the sense of defocus muting sensitive When spending penalty function item, due to the raising of exposure figure uniformity under different defocusing amounts, so that optimization system robustness is changed It is kind, to further increase process window (comparing result when ω=0 and ω=0.1).
As Fig. 8 compared the change curve for the exposure figure error that modified SMO is optimized using algorithms of different.Its In, the present invention solves the multi-objective optimization question using the algorithm of small lot gradient decline.Compared to stochastic gradient descent method, lead to Small lot gradient descent method is crossed with bigger defocus robustness.Equally, Fig. 9 compared modified SMO and be utilized respectively in small batches The process window that amount gradient, stochastic gradient optimize.Wherein, the system obtained after the optimization of small lot gradient descent method Process window is bigger.To demonstrate since the sample range of defocusing amount is larger, and number of samples is more, for the multiple target Optimization problem can further increase ability of searching optimum using small lot gradient algorithm, promote optimization precision.
As the above analysis, due to focal shift band in this light source-photomask optimization method energy effective compensation lithography system The distortion come.It can be improved global fidelity of the exposure system within the scope of certain defocus, to effectively expand depth of focus.Together When, the introducing of defocus low sensitivity penalty function further ensure that under different focal planes the uniformity of exposure figure with it is consistent Property, it further reduced the susceptibility of optimization system focus point offset, to improve process window and technique robustness.Due to Defocus is constantly present during actual exposure, therefore under comparable conditions, and modified SMO is better than initial SMO method, more It can adapt to the focus point offset problem as caused by many factors in practical lithography system.
Although being described in conjunction with the accompanying a specific embodiment of the invention, it will be apparent to those skilled in the art that Without departing from the principles of the invention, several deformations, replacement can also be made and improved, these also should be regarded as belonging to the present invention Protection scope.

Claims (5)

1. light source-mask batch optimization method of a kind of defocus low sensitivity, process window enhancing, which is characterized in that specific mistake Journey are as follows:
Step 1: initialization light source figure and mask graph；
Step 2: constitution optimization objective function G:
If F is imaging fidelity function, it is defined as in targeted graphical photoresist corresponding with current light source figure and mask graph Square of Euler's distance between imaging；
Low sensitivity penalty function item of the structure imaging result to defocus errorWherein Idefocus(βi) it is that current light source figure and mask graph are calculated using vector imaging model in defocus error βiFor corresponding space Picture, βiIndicate random defocus variable,For mathematic expectaion；
Optimization object function G is configured to the weighted sum of F and Y, i.e. G=F+ ω Y, wherein ω is weight coefficient；
Step 3: being based on the optimization object function G, light source and mask are optimized using small lot gradient descent method.
2. light source-mask batch optimization method that a kind of defocus low sensitivity, process window enhance according to claim 1, It is characterized in that, the detailed process of the step 1 are as follows:
Light source is initialized size as N by step 101S×NSLight source figure J, by mask graph M be initialized as size be N × N Targeted graphicalWherein NSIt is integer with N；
The pixel value of light emitting region is 1 in step 102, setting primary light source figure J, and the pixel value of light emitting region is not 0；Setting Size is NS×NSLight source matrix of variables Ωs, as J (xs,ysWhen)=1,As J (xs,ysWhen)=0,Wherein J (xs,ys) indicate each pixel (x on light source figures,ys) pixel value；Initial mask figure is set The transmissivity of shape M transmission region is 1, and the transmissivity of light is 0；It is sized the mask matrix of variables Ω for N × NM, when When M (x, y)=1,As M (x, y)=0,Wherein M (x, y) is indicated on mask graph The transmitance of each pixel (x, y)；Enable initial binary mask graph Mb=M.
3. light source-mask batch optimization method that a kind of defocus low sensitivity, process window enhance according to claim 2, It is characterized in that, the detailed process of the step 3 are as follows:
A series of defocus error factors are randomly generated in step 301lbatchIt is small lot gradient descent method In one wheel iteration in random sample number, calculating target function G is for light source matrix of variables ΩsGradient matrixWherein a=i, i+1 ... i+lbatch-1；Utilize normalized steepest descent method, batch updating light source variable Matrix ΩsForWhereinOptimize step-length for preset light source, obtains corresponding current ΩsLight source figure J,
Step 302 utilizes normalized steepest descent method, batch updating mask matrix of variables ΩMForWhereinFor preset photomask optimization step-length, corresponding current Ω is obtainedM's Mask graph M,Update the binary mask figure M of corresponding current Mb,tmFor parameter preset；
Step 303 calculates current light source figure J and binary mask figure MbThe value of corresponding objective function G；When the value is less than in advance Determine threshold value δ D or more new light sources matrix of variables ΩsWith mask matrix of variables ΩMNumber reach predetermined upper limit value KSMWhen, into step Rapid 304, otherwise return step 301；
Step 304 terminates optimization, and by current light source figure J and binary mask figure MbIt is determined as optimized light source figure Shape and mask graph.
4. light source-mask batch optimization method that a kind of defocus low sensitivity, process window enhance according to claim 3, It is characterized in that, described be randomly generated defocus error factor-betaiMethod are as follows: choose suitable error range, wherein up and down be limited to ± A is generated using computer and is obeyed one group of random defocus training set β={ β for being uniformly distributed U (- α, α)i}。
5. light source-mask batch optimization method that a kind of defocus low sensitivity, process window enhance according to claim 3, It is characterized in that, tmIt is taken as 0.5.
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