CN106951638A - The method for designing of wide angle extreme ultraviolet Mo/Si multilayer films based on quantum evolutionary algorithm - Google Patents
The method for designing of wide angle extreme ultraviolet Mo/Si multilayer films based on quantum evolutionary algorithm Download PDFInfo
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Abstract
The method for designing of wide angle extreme ultraviolet Mo/Si multilayer films based on quantum evolutionary algorithm belongs to multiplayer films in EUV research and development field, solves the problem of generally using big population scale present in Genetic Algorithm optimized design process, complicated calculating process and low solution efficiency in the design of wide angle multiplayer films in EUV.The following initial multiplayer films in EUV parameter value for 1) inputting quantum evolutionary algorithm of this method step;2) multilayer membrane system parameter is subjected to quantum coding, generates quantum chromosomes population;3) fitness of each multilayer membrane system is calculated, optimal film structure is selected;4) evolve and judge, meet Optimality Criteria, export optimal multilayer film film structure, algorithm stops;Otherwise continue to evolve;5) the multilayer membrane system rear steering the of quantum coding 3) step is updated by complementary variation and discrete crossover.This method is applied to the coatings optimization design of wide angle high reflectance multiplayer films in EUV, has the advantages that small population scale, fast convergence rate and solution efficiency are high.
Description
Technical field
The invention belongs to multiplayer films in EUV research and development field, and in particular to a kind of wide angle based on quantum evolutionary algorithm is high
The method for designing of reflectivity extreme ultraviolet Mo/Si multilayer films.
Background technology
In extreme ultraviolet (Extreme Ultraviolet) wave band, the refractive index of nearly all material close to 1 and with compared with
Strong absorption, so traditional through mode optical system can not be used, and uses the reflective optic based on multiplayer films in EUV
System.To realize high reflectance, reflection type optical element surface must be coated with the multilayer film that thickness reaches nanometer scale, so extremely purple
Outer multilayer film is important optical element in optical system, in extreme ultraviolet astronomy, extreme ultraviolet spectroscopy, extreme ultraviolet photolithographic skill
The research fields such as art, plasma diagnostics and synchrotron radiation have significant application value, and especially multiplayer films in EUV is extreme ultraviolet
The key technology and core reflective optical devices of photoetching technique.The cycle films such as the most use of traditional extreme ultraviolet Mo/Si multilayer films
System, but its interference pattern result in angle of reflection smaller bandwidth, generally [0 °, 9 °].Rather than wait the wide angle of cycle film structure
Multiplayer films in EUV can realize broad-angle-incident, and with higher reflectivity.What is particularly worth mentioning is that, it can expire
Need to meet the condition of large angle incidence with small reflector in the foot illuminator of extreme ultraviolet photolithographic, thus its research and development have it is important
Academic significance and actual application value.
The Film Design of multiplayer films in EUV is the primary and key issue of multiplayer films in EUV research and development.Current general algorithm
There are annealing algorithm and Nonlinear Least-Square Algorithm and genetic algorithm.Though annealing algorithm is less demanding to object function, realize
Come fairly simple, but its arithmetic speed is relatively low and is difficult to try to achieve the global pole figure of merit.Genetic algorithm (GA) is because with global search energy
Strong and strong applicability the advantage of power and as generally using algorithm, but because genetic algorithm is a kind of probability optimization algorithm, so
To obtain higher optimization efficiency and solving precision, often have the shortcomings that population scale is big and computational efficiency is low.
The content of the invention
In order to solve problems of the prior art, the invention provides a kind of wide angle based on quantum evolutionary algorithm
The method for designing of EUV Mo/Si multilayer films, solves the population rule in the design of wide angle multiplayer films in EUV in existing algorithm
Mould is big, convergence rate is slow and the problem of complicated calculating process.
The technical proposal for solving the technical problem of the invention is as follows:
The method for designing of wide angle EUV Mo/Si multilayer films based on quantum evolutionary algorithm, this method comprises the following steps:
Step one:The initial multiplayer films in EUV parameter value based on quantum evolutionary algorithm is inputted, including:Quantum in population
Body number, quantum coding number of parameters, iterations, refinement number of times, ask general number of times, optimum individual number and optimum individual continuous
Number of crossings;
Step 2:Carry out quantum coding to multilayer membrane system parameter, generation quantum chromosomes generation population Q, population Q is represented
For
Q=[q1 q2 q3 q4 q5 q6 q7 q8 q9 q10] (1)
Step 3:The fitness of quantum individual in multilayer membrane system quantum chromosomes generation population Q is calculated, and is selected optimal
Quantum individual;
Step 4:Judge whether quantum chromosomes generation population Q meets optimization and require:If meeting optimization to require, algorithm
Stop, exporting optimal multilayer film film structure;If being unsatisfactory for optimization to require, step 5 is carried out;
Step 5:Quantum chromosomes generation population Q is updated by complementation variation and discrete crossover, formed under quantum chromosomes
Generation population Q ';Return to step three, and increase evolutionary generation.
The beneficial effects of the invention are as follows:
(1) gene code of quantum evolutionary algorithm has real number gene position and quantum probability gene position two parts to constitute, single
Individual chromosome can give expression to multiple quantum states, with certain computation capability.Therefore the wide angle based on quantum evolutionary algorithm
The method of degree multiplayer films in EUV design can realize the Optimizing Search problem that multi-parameter is realized with less population;
(2) search strategy of " refinement " and " asking general " is conjointly employed in the algorithm for design of wide angle multiplayer films in EUV
In, have global search and local search ability concurrently, and then possess higher solution efficiency and high solving precision;
(3) comparative analysis shows, the method for designing of the wide angle multiplayer films in EUV based on quantum evolutionary algorithm compared to
Film Design method based on Real Coding Genetic Algorithm is respectively provided with certain advantage in terms of optimization efficiency and solving precision;
(4) during multilayer film Film Design, it is contemplated that the diffusion in multilayer film between Mo films and Si tunics layer,
It is simulated as Mo/Si2 diffusion layers, makes the multilayer film theoretical reflectance rate that its design simulation goes out closer to experimental result.
Brief description of the drawings
The membrane system schematic diagram of the Mo/Si multilayer film with 49 cycle of Fig. 1 present invention based on four layer models.
The flow chart of the method for designing of wide angle EUV Mo/Si multilayer film of Fig. 2 present invention based on quantum evolutionary algorithm.
The optimal film of wide angle Mo/Si multilayer films based on coding quantum evolutionary algorithm (RQEA) in kind under Fig. 3 different parameters
The evaluation coefficient MF and the graph of a relation of evolutionary generation of system.
The wide angle Mo/Si multilayer films that the optimal Mo/Si multilayers membrane system of evolution based on RQEA is calculated under Fig. 4 different parameters
Reflectance spectrum.
The wide angle optimal membrane system of Mo/Si multilayer films based on Real Coding Genetic Algorithm (RGA) comments under Fig. 5 different parameters
Valency coefficient MF and evolutionary generation graph of a relation.
The wide angle Mo/Si multilayer films that the optimal Mo/Si multilayers membrane system of evolution based on RGA is calculated under Fig. 6 different parameters
Reflectance spectrum.
The evaluation coefficient MF of wide angle Mo/Si multilayer film optimal membrane systems of the Fig. 7 based on RQEA and RGA and the pass of evolutionary generation
The comparison diagram of system.
The wide angle Mo/Si multilayer films reflection that evolution optimal Mo/Si multilayer membrane systems of the Fig. 8 based on RQEA and RGA is calculated
Spectrum.
Table 1 is based on the obtained optimal wide angle high reflectance multilayer membrane systems of RQEA and the optimal Mo/Si obtained based on RGA
The contrast table of multilayer membrane system.
Embodiment
The present invention is described in further details with reference to the accompanying drawings and examples.
The present invention by Real-coded quantum evolutionary algorithm be applied to wide angle high reflectance Mo/Si multilayer films design it
In, demonstrate feasibility of the quantum evolutionary algorithm in complicated multilayer film Film Design.In order that the theoretical mould of Mo/Si multilayer films
Intend close to experimental result, using the MoSi considered between Mo film layers and Si film layers2Four layer models of diffusion layer, as shown in figure 1, and
Mo/Si multilayer films totally 49 cycles.Due to the diffusion layer MoSi between Mo and Si2Film layer is very thin, can be approximately considered diffusion layer
Physical thickness and chemical property are constant, while the general Mo layers of MoSi on Si layers2Thickness of diffusion layer is compared with Si layers on Mo layers
MoSi2Thickness is spread, so both thickness of order is closely 1.0nm and 0.5nm respectively.Meanwhile, Si, Mo and MoSi2Density use
Volume density numerical value, corresponding atomic scattering factor data are derived from document (B.L.Henke, E.M.Gullikson, and
J.C.Davis,At.Data Nucl.Data Tables 54,(1993))。
The wide angle high reflectance extreme ultraviolet Mo/Si multilayer films based on quantum evolutionary algorithm are further illustrated with reference to Fig. 2
Method for designing, specific implementation step is as follows:
Step one:Input the initial multiplayer films in EUV parameter value of quantum evolutionary algorithm.The population scale N models of use
Enclose, i.e., the number of quantum individual is 5-10 in population, population scale preferably is 10, the real number gene position of each quantum chromosomes
The number of parameter is 98, and 49 cycles of corresponding Mo/Si multilayer films, iterations scope is 1000-3000, preferably iteration time
Number is 2000.In complementary mutation process, " refinement " number of times m1Scope be 2-10, preferably " refinement " number of times be 8;" asking general " is secondary
Number m2Scope is 2-10, and preferably " asking general ", number of times is 2, and " refinement " number of times m1The number of times m that generally higher than " asks general "2(i.e. m1>m2)。
During discrete crossover, the fitst water individual number s of selection scope is 2-6, and fitst water number of individuals preferably is 4, each
The continuous number of crossings m of excellent individual3Scope is 2-10, and preferably continuous number of crossings is 4.
Step 2:Characterize the quantum population initialization of multilayer membrane system.To characterizing the chromosome of multilayer membrane system using amount
Son coding, the population Q of generation quantum chromosomes is expressed as
Q=[q1q2q3q4q5q6q7q8q9q10](1)
In step 2, the chromosome for characterizing multilayer membrane system uses quantum coding, and the quantum coding of each parameter is by reality
Number part and quantum probability width two parts are constituted, and the quantum chromosomes of i-th of individual are
Wherein tSiAnd tMoThe thicknesses of layers of Si layers and Mo layers is represented respectively, and the corresponding probability amplitude of quantum bit of chromosome is
[cosθj,isinθj,i]T。
Step 3:The fitness of each multilayer film film structure is calculated, and selects optimal film layer structure.The evaluation letter of use
Number is
Wherein MF is the evaluation coefficient of individual, and θ is incidence angle, R0(θ) is target reflectivity curve, and R (θ) is according to a certain
The reflection spectrum curve for the wide angle multiplayer films in EUV that individual is calculated.Reflectivity is calculated using Fresnel coefficient method.It is right
In s polarised lights, reflectance factor is
And for p-polarization light, reflectance factor is
The reflected amplitude r of jth layerjFor
WhereinThe interface roughness of multilayer film is considered using the Debye-Waller factors, so reflection system
Number is modified to
Wherein, λ represents the wavelength of incident light, nj、θj、tj、σjThe complex refractivity index, incidence angle, film of jth tunic are represented respectively
Thickness degree and interface roughness.It is generally acknowledged that the substrate of multilayer film is Semi-infinite Medium, therefore R0=0, by being shaken to reflectivity
Width is iterated calculating, the reflectivity R=of the superiors' film layer (N layers) | rN|2.Incident extreme ultraviolet optical wavelength is 13.5nm,
The scope of incidence angle θ is [0 °, 18 °], target reflectivity R0(θ) ≡ 50%.
Step 4:Judge whether quantum chromosomes generation population Q meets optimization and require:If meeting optimization to require, algorithm
Stop, exporting optimal multilayer film film structure;If being unsatisfactory for optimization to require, step 5 is carried out;
Step 5:The quantum chromosomes generation kind encoded for multilayer membrane system is updated by complementary variation and discrete crossover
Group Q, forms quantum chromosomes two generations population Q2;Return to step three.
In the complementary mutation process of step 5, a base in the chromosome only constituted every time to multilayer membrane system thickness
Because carrying out Gaussian mutation, remaining gene keeps constant, and uses Quantum rotating gateThe quantum for updating quantum chromosomes is general
Rate width
Wherein For the anglec of rotation of Quantum rotating gate, θ 0 is initial rotation
Corner (θ0=0.01 π),It is object function in Searching pointI-th dimension variable gradient absolute value average, sgn () is
Sign function, to control the direction of rotation, and then ensures convergence of algorithm.θ0、WithThree's collective effect is controlled
The size of the anglec of rotation, with the convergence rate of this control algolithm.In the process, | αt j,i|2Reduce with the increase of algebraically, realize
Small range search to thickness parameter neighbour's solution domain, i.e. " refinement " process of thickness;And | βt j,i|2Gradually increase, realize and thickness is joined
" asking general " process of the extensive search, i.e. thickness of number solution space.During the discrete crossover of step 5, selected in population
S excellent individual, each excellent individual carries out discrete crossover, i.e., continuous p with other individuals at randomm=0.5 probability exchanges two
The gene position of male parent, the more new individual if the sign multilayer membrane system filial generation quantum individual of generation is due to parent individuality, otherwise not
It is updated.
For the checking wide angle multiplayer films in EUV method for designing based on Real-coded quantum evolutionary algorithm of the invention
Feasibility and advantage, by the efficiency and precision of the wide angle Mo/Si multilayer film Film Designs based on quantum evolutionary algorithm with being based on
Genetic algorithm (K.Deb and R.B.Agrawal. " Simulated binary crossover for continuous
Search space " in Complex Syst.Apr, 1995.vol.9.pp.115-148.) multilager design efficiency and essence
Degree is analyzed.In the wide angle multiplayer films in EUV design of the genetic algorithm based on real coding, the reason of multilayer film
Four layer models are equally based on by simulation, 49 multilayer film cycle 98 thicknesses of layers parameters of correspondence are optimized, thicknesses of layers
The region of search is [1.5nm, 4.5nm].While the mesh of the solution of the multilayer membrane system and quantum evolutionary algorithm of genetic algorithm for solving
(incident optical wavelength is fixed as 13.5nm to mark, and incidence angle θ is [0 °, 18 °], target reflectivity R0(θ)=50%) it is complete
Identical.But two kinds of algorithms it is different be genetic algorithm population scale N=100, crossover probability be Pc and mutation probability
It is respectively 0.1 and 0.9 for Pm.
Influence of the evolution parameter value to multilayer film solution efficiency in Real-coded quantum evolutionary algorithm is analyzed, there is provided multigroup
Evolution parameter value optimizes solution, and comparative result is shown in Fig. 3.By the evolution result in Fig. 3 based on Different Evolutionary parameter and
Fig. 4 is analyzed based on the reflectance spectrum that optimal solution under different parameters is calculated to be shown, in the number of times m of " refinement "1It is larger,
" asking general " number of times m2It is smaller, and in the case that the excellent individual number s that selects is larger, the efficiency that multilayer film is solved is higher and seek
Excellent precision is higher, and with the increase of evolutionary generation, the characteristic is also by the more obvious of performance, and this explanation is calculated in quantum evolution
The raising for promoting the evolution pressure of excellent individual efficiency of evolution is increased in method, while the reflection platform of the reflectance spectrum calculated
Also it is more smooth.Given in Fig. 5 and Fig. 6 under multigroup evolution parameter, wide angle multilager design based on genetic algorithm is asked
The reflectance spectrum that evolution situation and optimal solution are calculated is solved, comparative analysis shows, the crossover operator η in genetic algorithmcAnd variation
Operator ηmConcrete numerical value same efficiency of evolution and solving precision to algorithm and the reflectance spectrum that is finally inversed by have important shadow
Ring, and being stepped up with evolutionary generation, the influence of evolution parameter also all the more obvious.
On the basis studied respectively to the wide angle multilager design based on quantum evolutionary algorithm and based on genetic algorithm
On, the optimal evolutionary process based on two kinds of algorithms is further analyzed, comparing result refers to Fig. 7.Pass through Fig. 7 pair
Than analysis shows, the design of the wide angle Mo/Si multilayer films based on quantum evolutionary algorithm solves quality and is substantially better than based on heredity
The optimizing quality of algorithm, and have the advantages that fast convergence rate and solution efficiency are high.It is worth noting that, based on quantum evolution
The population number N=10 used in the programming of algorithm is much smaller than the population number N=100 that genetic algorithm is used, while also remote small
The parameter to be optimized in Film Design is total (parameter of Mo and Si thicknesses of layers totally 98), and this has fully demonstrated quantum and entered
Change algorithm have can with Small Population carry out multi-parameters optimization solution advantage, and this be traditional genetic algorithm can not be by comparison
, and small also imply that of population scale reduces computation complexity, simplifies calculating process.By based on quantum evolutionary algorithm
The comparative analysis of the design and the Evolutionary Design based on genetic algorithm of wide angle Mo/Si multilayer films shows, because quantum evolution is calculated
Genes of individuals coding employs quantum coding in method, and quantum coding is made up of real coding and quantum probability width, quantum probability width
Updated by Quantum rotating gate realization, and then control the Evolutionary direction and the size of variation of real part, embodiment during this
The superimposed characteristics of quantum state, thus with certain computation capability.So, the wide angle based on quantum evolutionary algorithm
The design of Mo/Si multilayer films under conditions of with Small Population scale, can carry out the search and optimization of multi-parameter, and obtain more
Preferable optimization efficiency and solving precision.
To based on the Real-coded quantum evolutionary algorithm under different parameters and Real Coding Genetic Algorithm evolution it is optimal
Solution calculates reflectance spectrum, refers to Fig. 8.Being subject to analysis to the result of calculation in Fig. 8 can obtain, the wide angle pole based on two kinds of algorithms
The film structure that ultraviolet multilager design method is designed is all ideal, may be implemented in incidence angle for 0 ° -18 ° when, reach
50% or so reflectivity, while it can be seen that the reflection of the reflectance spectrum calculated based on Real-coded quantum evolutionary algorithm is put down
Platform is also more smooth, embody quantum evolutionary algorithm applied to the feasibility in the Film Design of wide angle multiplayer films in EUV with
Superiority.Membrane system to the optimal solution of the wide angle multiplayer films in EUV design based on quantum evolutionary algorithm and genetic algorithm is carried out
Analysis, accordingly result refers to table 1.It is analyzed and is shown by the result to table 1, is obtained most based on two kinds of algorithm designs
Excellent wide angle multiplayer films in EUV film structure is entirely different, so the multilayer film Film Design knot based on quantum evolutionary algorithm
Fruit provides another alternative Film Design result for the plated film development of wide angle Mo/Si multilayer films.
Table 1 is based on the obtained optimal wide angle high reflectance multilayer membrane systems of RQEA and the optimal Mo/Si obtained based on RGA
The contrast table of multilayer membrane system
Claims (7)
1. the method for designing of the wide angle extreme ultraviolet Mo/Si multilayer films based on quantum evolutionary algorithm, it is characterised in that this method bag
Include following steps:
Step one:The initial multiplayer films in EUV parameter value based on quantum evolutionary algorithm is inputted, including:Quantum individual in population
Number, quantum coding number of parameters, iterations, refinement number of times, general number of times, optimum individual number and optimum individual is asked continuously to intersect
Number of times;
Step 2:Carry out quantum coding to multilayer membrane system parameter, generation quantum chromosomes generation population Q, population Q is expressed as
Q=[q1 q2 q3 q4 q5 q6 q7 q8 q9 q10]
Step 3:The fitness of quantum individual in multilayer membrane system quantum chromosomes generation population Q is calculated, and selects optimal amount
Sub- individual;
Step 4:Judge whether quantum chromosomes generation population Q meets optimization and require:If meeting optimization to require, algorithm stops,
Export optimal multilayer film film structure;If being unsatisfactory for optimization to require, step 5 is carried out;
Step 5:Quantum chromosomes generation population Q is updated by complementation variation and discrete crossover, quantum chromosomes are formed of future generation
Population Q ';Return to step three, and increase evolutionary generation.
2. the method for designing of the wide angle extreme ultraviolet Mo/Si multilayer films according to claim 1 based on quantum evolutionary algorithm,
Characterized in that, during the step one, quantum individual number N scopes is 5-20 in the population used;Each gene position
Number of parameters is 98, and iterations scope is 1000-3000 times, refinement number of times m1Scope be 2-10, seek general number of times m2Scope is
2-10, m1>m2;Optimal quantum individual number s scopes are 2-6, the continuous number of crossings m of optimum individual3Scope is 2-10.
3. the method for designing of the wide angle extreme ultraviolet Mo/Si multilayer films according to claim 1 based on quantum evolutionary algorithm,
Characterized in that, during the step 2, to the quantum coding of multilayer membrane system chromosome, the dye of any i-th of individual
Colour solid is
Wherein tSiAnd tMoThe thicknesses of layers of Si layers and Mo layers is represented respectively, and the probability amplitude of the quantum bit of chromosome is [cos θj,i
sinθj,i]T, θ is incidence angle.
4. the method for designing of the wide angle extreme ultraviolet Mo/Si multilayer films according to claim 1 based on quantum evolutionary algorithm,
Characterized in that, in the step 3, the fitness of quantum individual is judged by evaluation function.
5. the method for designing of the wide angle extreme ultraviolet Mo/Si multilayer films according to claim 1 based on quantum evolutionary algorithm,
Characterized in that, in the complementary mutation process of the step 5, every time only to one in the chromosome of correspondence multilayer membrane system
Real number gene position carries out Gaussian mutation, and uses Quantum rotating gateChromosome probability amplitude is updated, i.e.,
Wherein For the anglec of rotation of Quantum rotating gate, θ0For initial rotation angle
(θ0=0.01 π),It is object function in Searching pointI-th dimension variable gradient absolute value average, sgn () be symbol
Function, the direction to control rotation, | αt j,i|2Reduce with the increase of algebraically, | βt j,i|2Gradually increase.
6. the method for designing of the wide angle extreme ultraviolet Mo/Si multilayer films according to claim 1 based on quantum evolutionary algorithm,
Characterized in that, during the discrete crossover of the step 5, the gene position of two male parents, generation are exchanged with pm=0.5 probability
New generation quantum chromosomes population Q.
7. the method for designing of the wide angle extreme ultraviolet Mo/Si multilayer films according to claim 1 based on quantum evolutionary algorithm,
Characterized in that, the multilayer film film structure of four layer models of diffusion layer is sub/ [MoSi between Mo layers and Si layers2/Mo/
MoSi2/Si]49/air。
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CN107391925A (en) * | 2017-07-19 | 2017-11-24 | 长春理工大学 | Optical thin film characterizing method based on cloud model quantum evolutionary algorithm |
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CN107861241A (en) * | 2017-10-10 | 2018-03-30 | 长春理工大学 | The discretization Film Design method of broadband EUV multilayer films based on EA |
CN109373918A (en) * | 2018-12-18 | 2019-02-22 | 哈尔滨工业大学 | A kind of high effective optical measurement method for two-dimensional material measured film thickness |
CN110850520A (en) * | 2019-12-03 | 2020-02-28 | 中国科学院长春光学精密机械与物理研究所 | Preparation method of extreme ultraviolet band ultra-wideband multilayer film |
CN114202117A (en) * | 2021-12-07 | 2022-03-18 | 北京量子信息科学研究院 | Data processing method, data processing device, computer equipment and storage medium |
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CN107391925A (en) * | 2017-07-19 | 2017-11-24 | 长春理工大学 | Optical thin film characterizing method based on cloud model quantum evolutionary algorithm |
CN107678158A (en) * | 2017-10-10 | 2018-02-09 | 长春理工大学 | The discretization Film Design method of broadband EUV multilayer films based on QIGA |
CN107861241A (en) * | 2017-10-10 | 2018-03-30 | 长春理工大学 | The discretization Film Design method of broadband EUV multilayer films based on EA |
CN107678158B (en) * | 2017-10-10 | 2020-02-07 | 长春理工大学 | Discrete membrane system design method of broadband EUV (extreme ultraviolet) multilayer membrane based on QIGA (quality enhancement factor) |
CN107861241B (en) * | 2017-10-10 | 2020-04-03 | 长春理工大学 | EA-based discretization film system design method for broadband EUV multilayer film |
CN109373918A (en) * | 2018-12-18 | 2019-02-22 | 哈尔滨工业大学 | A kind of high effective optical measurement method for two-dimensional material measured film thickness |
CN110850520A (en) * | 2019-12-03 | 2020-02-28 | 中国科学院长春光学精密机械与物理研究所 | Preparation method of extreme ultraviolet band ultra-wideband multilayer film |
CN114202117A (en) * | 2021-12-07 | 2022-03-18 | 北京量子信息科学研究院 | Data processing method, data processing device, computer equipment and storage medium |
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