CN105446087A - Extreme ultraviolet wave band optical constant inversion method based on genetic algorithm - Google Patents

Extreme ultraviolet wave band optical constant inversion method based on genetic algorithm Download PDF

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Publication number
CN105446087A
CN105446087A CN201510962173.6A CN201510962173A CN105446087A CN 105446087 A CN105446087 A CN 105446087A CN 201510962173 A CN201510962173 A CN 201510962173A CN 105446087 A CN105446087 A CN 105446087A
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China
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optical constant
extreme ultraviolet
genetic algorithm
monofilm
inversion method
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喻波
姚舜
金春水
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Priority to CN201510962173.6A priority Critical patent/CN105446087A/en
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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
    • G03F7/20—Exposure; Apparatus therefor
    • G03F7/2002—Exposure; Apparatus therefor with visible light or UV light, through an original having an opaque pattern on a transparent support, e.g. film printing, projection printing; by reflection of visible or UV light from an original such as a printed image
    • G03F7/2008—Exposure; Apparatus therefor with visible light or UV light, through an original having an opaque pattern on a transparent support, e.g. film printing, projection printing; by reflection of visible or UV light from an original such as a printed image characterised by the reflectors, diffusers, light or heat filtering means or anti-reflective means used
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B1/00—Optical elements characterised by the material of which they are made; Optical coatings for optical elements
    • G02B1/10—Optical coatings produced by application to, or surface treatment of, optical elements
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B5/00—Optical elements other than lenses
    • G02B5/08—Mirrors
    • G02B5/0816—Multilayer mirrors, i.e. having two or more reflecting layers

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)
  • Investigating Or Analysing Materials By Optical Means (AREA)
  • Exposure Of Semiconductors, Excluding Electron Or Ion Beam Exposure (AREA)

Abstract

An extreme ultraviolet wave band optical constant inversion method based on a genetic algorithm belongs to the technical field of extreme ultraviolet photolithography, solving the problem in the prior art that the inversion method of the optical constant of the single film is liable to run into the local minimum. The method of the invention comprises steps as follows: calculating the reflectivity of the single film at fixed wave length at different grazing incidence angles through the object optical constant and object film thickness of the single film, obtaining an object reflectivity curve, carrying out inversion to the film thickness and the object optical constant of the single film through the obtained object reflectivity curve and the genetic algorithm, wherein the reflectivity curve of the single film is determined by a recursive algorithm. The method improves stability of the inversion process, prevents the inversion process from running into the local minimum. The errors of the optical constant and the object optical constant obtained by inversion method are very few; the inversion precision of the optical constant is high; therefore the basis for optimizing the technology of improving the reflectivity of the extreme ultraviolet multilayer film is provided.

Description

Based on the extreme ultraviolet waveband optical constant inversion method of genetic algorithm
Technical field
The invention belongs to extreme ultraviolet photolithographic technical field, be specifically related to a kind of extreme ultraviolet waveband optical constant inversion method based on genetic algorithm.
Background technology
Extreme ultraviolet photolithographic (ExtremeUltravioletLithography, EUVL) technology uses EUV wave band, and mainly 13.5nm wave band, carries out the micro-nano technology technology of photoetching.At present, EUVL technology can realize the etching technics of 7nm live width, and possesses the possibility reducing etching live width further.It is significant that this manufactures field at large scale integrated circuit, and the element that can realize larger density is integrated, and lower energy consumption.
Extreme ultraviolet photolithographic uses wavelength to be 10-14nm light illumination, because nearly all known optical material all has strong absorption at this wave band, traditional refractive optical system cannot be adopted, so the illuminator of extreme ultraviolet etching system, mask and projection objective all adopt reflective designs, its reflective optical devices need be coated with periodic multilayer film to improve reflectivity.For improving the luminous flux of extreme ultraviolet etching system, need the reflectivity being improved each extreme ultraviolet multilayer film reflection mirror by coating process parameter optimization as far as possible, and first the prerequisite of process optimization is want the extreme ultraviolet waveband optical constant of Accurate Measurement film material.
The extreme ultraviolet waveband optical constant of film material is generally obtained by the extreme ultraviolet waveband reflectivity curve of matching monofilm, because the thickness of monofilm and optical constant exist certain correlativity, therefore the thickness of monofilm is obtained by the extreme ultraviolet waveband reflectivity curve of matching monofilm and optical constant exists Multiple solution, if adopt local search of algorithm of the prior art to determine optical constant and thickness, refutation process is very easily absorbed in local minimum, is difficult to the extreme ultraviolet waveband optical constant of Accurate Measurement film material.
Genetic algorithm is a kind of random search algorithm based on natural population's Genetic evolution mechanism, has the feature of global optimizing, namely can find root quickly and accurately by the minimum of entirety, and depend on starting condition not too much, and computational accuracy is high.But in prior art, yet there are no the method based on genetic algorithm determination extreme ultraviolet waveband optical constant.
Summary of the invention
The inversion method that the object of the invention is the optical constant solving monofilm in prior art is very easily absorbed in the problem of local minimum, provides a kind of extreme ultraviolet waveband optical constant inversion method based on genetic algorithm.
It is as follows that the present invention solves the problems of the technologies described above the technical scheme taked.
Based on the extreme ultraviolet waveband optical constant inversion method of genetic algorithm, step is as follows:
Step one, by the objective optics constant of monofilm and target film thickness, calculate the reflectivity of monofilm under fixed wave length, different grazing angles, obtain target reflectivity curve;
Step 2, the target reflectivity curve obtained by step one, adopt thickness and the optical constant of genetic inverse monofilm;
In described step one and step 2, the reflectance curve of monofilm is all determined by recursive algorithm.
Further, the process of described step 2 is: with formula (1) for evaluation function, and adopt genetic algorithm to find the optical constant and thickness that make F value minimum, this optical constant is the optical constant of monofilm;
F = Σ i = 1 m | R c ( θ i ) - R g o a l ( θ i ) | - - - ( 1 )
In formula (1), m is integer, R c(θ i) be computational reflect rate curve, R goai(θ i) be target reflectivity curve.
Further, in described step 2, the population number of genetic algorithm is 100, and crossover probability is 0.5, and mutation probability is 0.02, and number of iterations was 500 generations.
Further, the variation range of the grazing angle of described reflectance curve is 2.5 °-85 °.
Further, the wavelength of described reflectance curve is fixed as 13.5nm.
Further, the thickness of described monofilm is 10-90nm.
Compared with prior art, beneficial effect of the present invention is:
Extreme ultraviolet waveband optical constant inversion method based on genetic algorithm of the present invention, by adopting global optimizing algorithm---the reflectance curve that genetic algorithm carrys out matching extreme ultraviolet waveband obtains the optical constant of monofilm, improve the stability of refutation process, avoid refutation process and be absorbed in local minimum, the optical constant obtained by the method inverting and objective optics constant error very little, optical constant inversion accuracy is high, thus is that the process optimization improving multiplayer films in EUV reflectivity provides foundation.
Accompanying drawing explanation
Fig. 1 is the schematic diagram of the extreme ultraviolet waveband optical constant inversion method that the present invention is based on genetic algorithm;
Fig. 2 is the target reflectivity curve of the embodiment of the present invention 1 and comparative example 1;
Fig. 3 is the simplicial method matching reflectance curve of comparative example 1 of the present invention and the contrast of target reflectivity curve;
Fig. 4 is the Genetic Algorithm Fitting reflectance curve of the embodiment of the present invention 1 and the contrast of target reflectivity curve.
Embodiment
The present invention is further illustrated below in conjunction with accompanying drawing.
As shown in Figure 1, if the thickness of known monofilm and optical constant just can by reflectivity computation model calculate extreme ultraviolet monofilm reflectance curve, this is a forward process; Contrary, the present invention is based on the extreme ultraviolet waveband optical constant inversion method of genetic algorithm, is when known extreme ultraviolet monofilm reflectance curve, the thickness of inverting extreme ultraviolet monofilm and optical constant.The optical constant of extreme ultraviolet monofilm of the present invention refers to refractive index n and the extinction coefficient ξ of monofilm.Wherein, wavelength is generally fixed as 13.5nm, and the variation range of grazing angle is 2.5 °-85 °.
The step of the extreme ultraviolet waveband optical constant inversion method based on genetic algorithm of the present invention is as follows:
Step one, by the objective optics constant of known monofilm and target film thickness, calculate the reflectivity of monofilm under fixed wave length, different grazing angles, obtain target reflectivity curve R goai(θ i), and target reflectivity curve negotiating recursive algorithm is determined;
Step 2, adopt genetic algorithm to find to make thickness that in evaluation function, F value is minimum and optical constant, this optical constant is the optical constant of monofilm at extreme ultraviolet waveband, and evaluation function is such as formula shown in (1):
F = Σ i = 1 m | R c ( θ i ) - R g o a l ( θ i ) | - - - ( 1 )
In formula (1), m is integer, R c(θ i) be computational reflect rate curve, and computational reflect rate curve is determined by recursive algorithm, m is natural number;
For making algorithm iteration speed of convergence the fastest, the Selecting parameter of genetic algorithm is as follows: population number is 100, and crossover probability is 0.5, and mutation probability is 0.02, and algebraically was 500 generations, also according to actual conditions, can select other parameters.
In said method, recursive algorithm is those skilled in the art's well-known algorithms, and detailed process is:
Through type (2) calculates the Fresnel reflection coefficient F of jth layer and jth+1 interface layer j, j+1;
F j , j + 1 = k j - k j + 1 k j + k j + 1 - - - ( 2 )
In formula (2),
k j = 2 π λ ( N j 2 - cos 2 θ ) 1 / 2
k j + 1 = 2 π λ ( N j + 1 2 - cos 2 θ ) 1 / 2
N jfor the complex index of refraction of jth tunic, N j=n j+ i ξ j, n jfor the refractive index of jth tunic, ξ jfor the extinction coefficient of jth tunic, N j+1for the complex index of refraction of jth+1 tunic, N j+1=n j+1+ i ξ j+1, n j+1for the refractive index of jth+1 tunic, ξ j+1for the extinction coefficient of jth+1 tunic, by that analogy; θ is grazing angle; I is unit imaginary number;
Then through type (3) calculates different boundary reflection rate;
R j , j + 1 = α j 2 R j + 1 , j + 2 + F j , j + 1 1 + R j + 1 , j + 2 F j , j + 1 - - - ( 3 )
In formula (3), R j, j+1for film system is by the end of the reflection coefficient at a jth interface; R j+1, j+2for film system is by the end of the reflection coefficient at jth+1 interface, by that analogy; α j=exp (-ik jd j), d jfor the thickness of jth layer;
No matter recursive procedure, for calculate the top one deck gradually from substrate, is monofilm or multilayer film, and all available through type (3) calculates the reflectivity of film.Known monofilm thickness and optical constant, just can calculate to obtain reflectance curve by formula (3).On the contrary, known reflectivity curve also inverting can obtain optical constant.
The present invention is further illustrated below in conjunction with comparative example and embodiment.
Comparative example 1
For molybdenum monofilm, first by the optical constant n=0.9216 of molybdenum in database at 13.5nm place, ξ=0.006365 is as the objective optics constant of refutation process, the target reflectivity curve that the extreme ultraviolet reflectance curve calculated with molybdenum monofilm thickness d=20nm is refutation process, result is as shown in Figure 2; Then adopting simplicial method inverting to obtain optical constant is n=0.9302, ξ=0.006721, thickness d=20.5nm, and corresponding reflectance curve and the contrast of target reflectivity curve are as shown in Figure 3.
Embodiment 1
For molybdenum monofilm, first by the optical constant n=0.9216 of molybdenum in database at 13.5nm place, ξ=0.006365 is as the objective optics constant of refutation process, the target reflectivity curve that the extreme ultraviolet reflectance curve calculated with molybdenum monofilm thickness d=20nm is refutation process, result is as shown in Figure 2; Then adopting genetic inverse to obtain optical constant is n=0.9235, ξ=0.006416, thickness d=20.1nm, and corresponding reflectance curve and the contrast of target reflectivity curve are as shown in Figure 4.
Composition graphs 2-4 can find out, the error of the optical constant that embodiment 1 inverting obtains and objective optics constant will much smaller than comparative example 1, illustrate the optical constant that inverting of the present invention obtains and objective optics constant error very little, optical constant inversion accuracy is high, thus is that the process optimization improving multiplayer films in EUV reflectivity provides foundation.

Claims (6)

1., based on the extreme ultraviolet waveband optical constant inversion method of genetic algorithm, it is characterized in that, step is as follows:
Step one, by the objective optics constant of monofilm and target film thickness, calculate the reflectivity of monofilm under fixed wave length, different grazing angles, obtain target reflectivity curve;
Step 2, the target reflectivity curve obtained by step one, adopt thickness and the optical constant of genetic inverse monofilm;
In described step one and step 2, the reflectance curve of monofilm is all determined by recursive algorithm.
2. the extreme ultraviolet waveband optical constant inversion method based on genetic algorithm according to claim 1, it is characterized in that, the process of described step 2 is:
With formula (1) for evaluation function, adopt genetic algorithm to find the optical constant and thickness that make F value minimum, this optical constant is the optical constant of monofilm;
F = Σ i = 1 m | R c ( θ i ) - R g o a l ( θ i ) | - - - ( 1 )
In formula (1), m is integer, R c(θ i) be computational reflect rate curve, R goai(θ i) be target reflectivity curve.
3. the extreme ultraviolet waveband optical constant inversion method based on genetic algorithm according to claim 1, is characterized in that, in described step 2, the population number of genetic algorithm is 100, and crossover probability is 0.5, and mutation probability is 0.02, and number of iterations was 500 generations.
4. the extreme ultraviolet waveband optical constant inversion method based on genetic algorithm according to claim 1, is characterized in that, the variation range of the grazing angle of described reflectance curve is 2.5 °-85 °.
5. the extreme ultraviolet waveband optical constant inversion method based on genetic algorithm according to claim 1, it is characterized in that, the wavelength of described reflectance curve is fixed as 13.5nm.
6. the extreme ultraviolet waveband optical constant inversion method based on genetic algorithm according to claim 1, is characterized in that, the thickness of described monofilm is 10-90nm.
CN201510962173.6A 2015-12-21 2015-12-21 Extreme ultraviolet wave band optical constant inversion method based on genetic algorithm Pending CN105446087A (en)

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Cited By (1)

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CN105929468A (en) * 2016-07-06 2016-09-07 宁波万维显示科技有限公司 Anti-reflection glass design method, device, and stereoscopic display apparatus

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