CN107391834A - Optical thin-film structure analysis method based on quantum derivative genetic algorithm - Google Patents
Optical thin-film structure analysis method based on quantum derivative genetic algorithm Download PDFInfo
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Abstract
The invention discloses a kind of optical thin-film structure analysis method for being based on quantum derivative genetic algorithm (QIGA), it includes：(1) initial parameter value of the film characterization based on QIGA is inputted；(2) generation characterizes the initial quantum population of membrane structure parameter；(3) initial quantum population is observed；(4) judge whether to meet end condition, if so, then terminator, if it is not, then continuing；(5) Fitness analysis is carried out to the individual in quantum population, and preserves optimum individual；(6) quantum rotation door operation, filial generation is generated；(7) quantum variation operates, and updates filial generation；(8) quantum whole interference crossover operates, and updates filial generation；(9) elite retention strategy operates, and goes to step (4).The method of the present invention, with the high advantage of fast convergence rate and solving precision, solves the problems such as low efficiency present in the film grazing incidence X-ray reflectivity fitting solution based on traditional genetic algorithm, low precision in the GIXR fitting solution procedurees of film.
Description
Technical field
The present invention relates to a kind of optical thin-film structure analysis method for being based on quantum derivative genetic algorithm (QIGA), it is particularly
A kind of grazing incidence X-ray reflectivity spectrum (grazing incidence x-ray based on quantum derivative genetic algorithm
Reflectivity, GIXR) fitting solve film microstructure method, it is applied to single layer optical film and multilayer optical
The sign of film, belong to optical thin film representational field.
Background technology
Optical thin film is made up of layered medium, and a kind of optical medium material of light beam is propagated by interface.From 20th century
The thirties, diffusion pump started applied to optical system, and optical thin film is as optical media applications in optical system.Except it most
The functions such as basic reflection, antireflective and spectrum regulation and control, optical thin film also undertake polarization regulation and control, phase regulation and control in optical system
And the adjusting function such as photoelectricity, photo-thermal and optoacoustic.Nowadays, optical thin film be widely used in laser technology, photoelectron technology,
In the Modern Optics Technologies such as optical communication technique, light Display Technique and light storing technology.Especially emerging nano thin-film has uniqueness
Optics, electricity, magnetics, mechanics and gas-sensitive property, this causes it as functional material and structural material and also all had good
Development prospect.
The fast development of optical thin film has benefited from the development of thin film technique.Thin film technique mainly includes：Prepare, control, survey
Examination technology.The meaning of the wherein test of optical thin film is, passes through test, it is established that the contact of film both macro and micro, and then
The micro-parameter of element and the performance indications of element are obtained by analysis.Thus, optical thin film performance it is whether excellent often with
Its micro-parameter, such as geometric thickness, density, roughness have direct relation.How the structural parameters of accurate Characterization film, from
And it is that the optical thin film for designing and coating high quality establishes premise and basis also therefore has highly important meaning.At present,
Include applied to material and the instrument and method of surface measurement：Grazing incidence X-ray reflectivity spectrum (GIXR), transmission electron microscope
(TEM), rutherford backscattering spectrum, Auger electron spectroscopy, ellipsometer etc..Film or cycle wherein to nano grade membrane thickness is thick
Spend detection for nano level multilayer film frequently with method be TEM and GIXR.The former be it is a kind of can be directly to the microcosmic of film
The method characterized, but due to can be damaged while observation to film, it is not high plus accuracy of detection, so being commonly used for
The reference that multilayer film characterizes；One of the common method of the latter as test optical constant, advantage is that optical thin film will not be made
Into destruction, high-precision result can be obtained in the case where film layer information is less, and difficult point is that needs establish corresponding theory
Model, and to being had higher requirements for characterizing the derivation algorithm of membrane structure parameter.Therefore, selection is preferably fitted membrane structure
The derivation algorithm of parameter for nano grade membrane thickness film or nanometer-scale periodicity thickness multilayer film accurate Characterization have it is important
Meaning.
For being operated in the optical thin film of ultraviolet-extreme ultraviolet waveband, required blooming is in nanometer scale.
For example, the individual layer thickness of the optical thin film needed for deep ultraviolet band is only 20~30nm, and the multilayer film needed for extreme ultraviolet photolithographic
Periodic thickness is only nanometer scale.Realize above-mentioned optical thin film parameter fitting not only have in the foundation of theoretical model it is more high-leveled and difficult
Degree, the selection for derivation algorithm also have certain test, especially need to consider film in the fitting of multiplayer films in EUV
The diffusion layer of interlayer, result in increasing for multilayer film parameters, and search space increases severely.
Film fitting characterize frequently with algorithm have Levenberg-Marquart algorithms, climbing method, genetic algorithm etc..
Levenberg-Marquart algorithm the convergence speed is fast, but the probability for trying to achieve global extremum is small；Climbing method randomness is strong, it is difficult to
The iterative process carried out before is effectively utilized；Genetic algorithm (GA) uses binary coding, has ability of searching optimum strong, is
Optical thin film fitting characterizes conventional algorithm, but convergence rate is slow, easily precocious, it is difficult to which that degree of precision searches global optimum
Solution.
The content of the invention
It is a primary object of the present invention to propose a kind of optical thin-film structure for being based on quantum derivative genetic algorithm (QIGA)
Analysis method, to overcome deficiency of the prior art.
To realize aforementioned invention purpose, the technical solution adopted by the present invention includes：
The embodiments of the invention provide a kind of optical thin-film structure analysis method based on quantum derivative genetic algorithm, and it is wrapped
Include following steps：Step 1：Input is applied to the fitting of film grazing incidence X-ray reflectivity spectrum, based on quantum derivative genetic algorithm
The initial parameter value of film microstructure analysis method, described initial parameter include：Quantum population scale N, chromosome number M,
The gene digit λ of each chromosome, evolutionary generation maximum of Tmax, quantum variation gene digit s, the full crossover probability P of quantumcWith
The span of each chromosome；
Step 2：Quantum coding is carried out to the microstructural parameter of optical thin film, generation characterizes the amount of optical thin-film structure
Sub- population
Q=[q1,q2,…,qi,…qN-1,qN],
Wherein arbitrarily quantum individual qiQuantum coding be
Step 3：Initial quantum population Q to characterizing optical thin-film structure0Measure and decode, obtain determining solution P0；
Step 4：Reach Evolution of Population algebraic maximum Tmax, if satisfied, then terminator, if not satisfied, then continue into
OK；
Step 5：The grazing incidence X-ray reflectivity spectrum of optical thin film is fitted, quantum individual is evaluated by fitting coefficient
Fitness, and screen and preserve optimal quantum individual；
Step 6：Quantum population Q is updated using Quantum rotating gate, filial generation Q ' is generated, filial generation Q ' is measured and decoded,
Obtain determining solution P ', continue to be fitted the grazing incidence X-ray reflectivity spectrum of optical thin film, quantum is evaluated by fitting coefficient
The fitness of body, and screen and preserve the optimum individual in quantum population；
Step 7：Mutation operation is carried out to quantum population, i.e. in order to each quantum individual s gene position of progress
Random selection, quantum non-gate operation is carried out to its quantum bit probability amplitude；
Step 8：With probability PcTo filial generation Q ' carry out classics quantum whole interference crossovers, if being intersected, filial generation Q ' is entered
Row measurement and decoding, obtain determining the fitness of each individual in solution P ', and evaluation quantum population, and screen and preserve optimal
Quantum individual, then quantum whole interference crossover is carried out, otherwise skip over；
Step 9：Filial generation Q ' is updated with elite retention strategy, filial generation Q ' is measured and decoded, obtains determining solution P ',
Step 4 is gone to afterwards.
Further, described optical thin film is monofilm or multilayer film.
Than prior art, the optical thin-film structure analysis method of the present invention based on QIGA has convergence rate
Fast and high solving precision advantage.
Brief description of the drawings
Fig. 1 is the side that a kind of GIXR fittings based on QIGA solve film microstructure in a typical embodiments of the invention
The flow chart of method.
Fig. 2 is the optimal evaluation for being fitted two Si monofilms GIXR in a typical embodiments of the invention based on GA and QIGA
Coefficient χ2With the collection of illustrative plates of the relation of evolutionary generation.
Fig. 3 a- Fig. 3 d are to be fitted two Si monofilms GIXR based on GA and QIGA in a typical embodiments of the invention to solve
The GIXR notional result and the comparison diagram of experimental result of obtained optimal film structure (100 generations of evolution) inverting.
Fig. 4 is to be fitted the cycle Mo/Si multilayer film GIXR such as two based on GA and QIGA in a typical embodiments of the invention
Optimal evaluation coefficient χ2With the collection of illustrative plates of the relation of evolutionary generation.
Fig. 5 a- Fig. 5 d are to be fitted two Mo/Si multilayer films GIXR based on GA and QIGA in a typical embodiments of the invention
Solve the GIXR notional result and the comparison diagram of experimental result of obtained optimal film structure (200 generations of evolution) inverting.
Specific embodiment
As it was previously stated, in view of the deficiencies in the prior art, inventor are able to through studying for a long period of time and largely putting into practice
Technical scheme is proposed, it is mainly that a kind of be fitted based on QIGA to the GIXR of single or multiple lift optical thin film is asked
Solution, the characterizing method of film microstructure is realized with this, and the characterizing method can effectively solve the method for solving based on traditional GA
The problem of existing convergence rate is slow, easily precocious low with solving precision.Technical scheme will be carried out as follows in detail
Explanation.
A kind of optical thin-film structure analysis method based on quantum derivative genetic algorithm provided in an embodiment of the present invention includes
Following steps：
Step 1：The initial parameter value for inputting the film characterization based on QIGA (is particularly suitable for GIXR fittings and is based on
The initial parameter value of QIGA film microstructure analysis method), initial parameter includes：Quantum population number scale N, quantum dye
Body number M, the gene position number λ needed for each quantum chromosomes, quantum evolution algebraic maximum Tmax, quantum variation gene digit
S, the full crossover probability P of quantumcWith the span of each quantum chromosomes.
Step 2：Quantum coding is carried out to the microstructural parameter of optical thin film, generation characterizes optical thin-film structure parameter
Quantum population Q, the population is represented by
Q=[q1, q2..., qN-1, qN]
Wherein arbitrarily quantum individual qiQuantum coding be
Step 3：To initial population Q0Measure and decode, obtain determining solution P0。
Step 4：The judgement of end condition.Reach quantum population evolutionary generation maximum of Tmax, if satisfied, then terminating journey
Sequence；If not satisfied, then continue.
Step 5：The grazing incidence X-ray reflectivity spectrum of film is fitted, the suitable of quantum individual is evaluated by fitting coefficient
Response, and screen and preserve optimum individual in quantum population.
Step 6：Quantum rotation updates.Using Quantum rotating gate Population Regeneration Q, filial generation Q ' is generated, filial generation Q ' is surveyed
Amount and decoding, obtain determining solution P '.The grazing incidence X-ray reflectivity spectrum of film is fitted, quantum is evaluated by fitting coefficient
The fitness of individual, and screen and preserve optimal quantum individual.
Step 7：Quantum variation operates.Row variation is entered to each quantum individual in quantum population, i.e., chooses individual at random
Middle s gene position, quantum non-gate operation is carried out to its quantum bit probability amplitude.
Step 8：Quantum whole interference crossover operates.With probability Pc=0.04 pair of filial generation carries out classical quantum whole interference crossover
Operation.A uniform random number r ∈ (0,1) is generated, if r<Pc, then this operation is carried out, i.e., filial generation Q ' is measured
And decoding, obtain determining the fitness of each individual in solution P ', and evaluation quantum population, and screen and preserve optimal quantum
Body, then quantum whole interference crossover is carried out, otherwise skip over this step.
Step 9：Filial generation Q ' is updated with elite retention strategy, filial generation Q ' is measured and decoded, obtains determining solution P ',
Step 4 is gone to afterwards.
Further, in two the embodiment of the present invention the step of, arbitrarily quantum bit gene meets
In initialization procedure, the quantum bit gene position of each individual is entered as in quantum population
Further, in five the embodiment of the present invention the step of, the evaluation function of quantum individual adaptation degree is
Wherein χ2For the evaluation coefficient of quantum individual, m counts for experimental data, IK, calc.For the theoretical reflectance of kth data point
Intensity, and IK, meas.For the experiment reflected intensity of kth data point.
Further, in five the embodiment of the present invention the step of, using the reason of Fresnel coefficient method calculating optical film
By reflected intensity.Further, in step 6 of the embodiment of the present invention, using Quantum rotating gate to each individual in quantum population
All gene positions carry out rotation renewal, Quantum rotating gate is
Wherein θIj, kFor the anglec of rotation of k-th of gene position in j-th of chromosome of i-th of quantum individual, its value is expressed as
θij,k=s (αij,k,βij,k)·Δθij,k, wherein s (αij,k,βij,k) determined by inquiring about table 1 below, to control the side of rotation
To；And Δ θij,kThe size of rotation is controlled, its numerical value is
Δθij,k=(θij,k)min+fiJ, k×[(θij,k)max-(θij,k)min]
Wherein (θij,k)min=0.001 π be search angle range intervals minimum value, (θij,k)max=0.05 π is angle of aspect
Spend the maximum of range intervals, while fij,kFor
Wherein choromelens is the chromogene length of current quantum individual, and A enters for the two of i-th of quantum individual
System determines solution pi, B is that the binary system of current optimum individual determines solution pbest, and Ham (A, B) is piAnd pbestMiddle relevant position
The number differed.Further, in six the embodiment of the present invention the step of, using the quantum gene position of Quantum rotating gateIt is updated, is updated to
WhereinQuantum gene position after being updated for Quantum rotating gate.
Further, in seven the embodiment of the present invention the step of, s gene position ginseng is selected at random from each quantum individual
Operated with quantum non-gate
WhereinTo choose k-th of gene position in j-th of chromosome in i-th of quantum individual,For quantum variation
Gene position afterwards.
Further, in seven the embodiment of the present invention the step of, after the quantum non-gate operation is completed, according to such as
Under evaluation function the fitness of new filial generation quantum individual is assessed,
Wherein χ2For the evaluation coefficient of quantum individual, m counts for experimental data, Ik,calc.For the theoretical reflectance of kth data point
Intensity, and Ik,meas.For the experiment reflected intensity of kth data point, and preserve optimal quantum individual.
Further, in eight the embodiment of the present invention the step of, with probability PcIt is complete that=0.04 pair of filial generation carries out classical quantum
Crossover operation is disturbed, a uniform random number r ∈ (0,1) is generated, if r<Pc, then this operation is carried out, i.e., to filial generation Q '
Measure and decode, obtain determining the fitness of each individual in solution P ', and evaluation quantum population, and screen and preserve most
Excellent quantum individual, then quantum whole interference crossover is carried out, otherwise skip over this step.
Further, described optical thin film is monofilm.
Further, described optical thin film is multilayer film.
In the aforementioned characteristic method of the present invention, the parameter information of optical thin film is encoded using quantum bit, using this method
Coding allows a chromosome to represent the superposition of multiple states, so as to possess more preferable diversity spy than traditional genetic algorithm
Sign.
In the aforementioned characteristic method of the present invention, quantum volume is carried out to chromosome using quantum derivative genetic algorithm (QIGA)
Code, and chromogene is updated using Quantum rotating gate, quantum variation and quantum crossover operation will reduce solving result
It is absorbed in the possibility of local optimum.
In the aforementioned characteristic method of the present invention, the anglec of rotation of quantum door chooses dynamic rotary angle, and the value of the anglec of rotation is by needing
Hamming distance between the individual and optimum individual of evolution determines that the dynamic adjustment of the anglec of rotation will influence convergence rate, in practice it has proved that,
The convergence rate of dynamic rotary angle strategy is better than fixed anglec of rotation strategy.
The method that the fittings of the GIXR based on QIGA of the present invention characterize optical thin film microstructure has that solution efficiency is fast, intends
Close the advantages of precision is high and solving precision is high.
The present invention is described in further details with reference to the accompanying drawings and examples.
The GIXR that QIGA is applied to nanoscale monofilm and waits cycle EUV multilayer film is fitted by the present invention, is verified with this
Feasibilities and advantage of the QIGA in optical thin film Microstructure characterization, and then improve the optical thin film based on GIXR and characterize efficiency
And precision.For example, in some typical embodiments of the present invention, QIGA is applied to based on Si monofilms and waits the cycle extremely purple
During the GIXR of outer Mo/Si multilayer films fitting solves, with this embodiment checking sight method in monofilm and multilayer film microstructure
Characterize the feasibility of application.Meanwhile by and QIGA accordingly result and the Si monofilms based on GA and etc. cycle extreme ultraviolet Mo/
The GIXR of Si multilayer films fitting characterization result is analyzed, and verifies QIGA among the GIXR fittings of film solve with this
Feasibility and advantage.
Refer to the GIXR that Fig. 1 shows a kind of optical thin film based on QIGA in the typical embodiments of the present invention
Fitting solves analysis method, and it is comprised the following specific steps that：
Step 1：Input the initial parameter value of optical thin film (also abbreviation film as follows) structural analysis based on QIGA.Its
Include, quantum population scale N, quantum chromosomes number M, the gene position number λ needed for each quantum chromosomes, evolutionary generation is most
Big value Tmax, quantum variation gene digit s, the full crossover probability P of quantumcWith the span of each quantum chromosomes；
Step 2：Characterize the initialization of the quantum population of optical thin-film structure.The microstructural parameter of optical thin film is entered
Row quantum coding, generation characterize the quantum population Q of optical thin-film structure parameter, and the population is expressed as
Q=[q1, q2,…,qi,…,qN-1, qN], (1)
Wherein i-th of quantum individual qiQuantum coding be
Wherein arbitrarily quantum bit gene meets
In initialization procedure, the equal assignment of quantum bit gene position of each quantum individual (also abbreviation quantum individual as follows)
For
Step 3：To initial population Q0Measure and decode, obtain determining solution.A random number r ∈ (0,1) is generated,
IfThen the determination solution of the gene position is 0；Otherwise it is 1 to determine solution, and then obtains determining solution P0For
P0=[p1,p2,…,pi,…,pN-1,pN] (5)
Wherein any individual piBe encoded to
pi=[ai1,1,ai1,2,…,ai1,λ-1,ai1,λ,…,aij,1,aij,2,…,aij,λ-1,aij,λ,…,aiM,1,aiM,2,…,
aiM,λ-1,aiM,λ]
(6)
Wherein aij,k1 or 0 are taken according to measurement result, then binary coding is converted into the decimal system.
Step 4：The judgement of end condition.Reach quantum population evolutionary generation maximum of Tmax, if satisfied, then terminating journey
Sequence；If not satisfied, then continue；
Step 5：Individual adaptation degree is assessed in quantum population, and preserves optimum individual.Solution P will be determined by binary system
Coding and decoding is decimal system parameter, and the fitness of quantum individual is assessed according to following evaluation function,
Wherein χ2For the evaluation coefficient of quantum individual, m counts for experimental data, Ik,calc.For the theoretical reflectance of kth data point
Intensity, and Ik,meas.For the experiment reflected intensity of kth data point.In the present invention, film is calculated using Fresnel coefficient method
Theoretical reflectance intensity.In the process, the present invention calculates theoretical reflected intensity, corresponding atomic scattering using Fresnel coefficient method
Factor data can be derived from document (Henke B L, Gullikson E M, Davis J C.X-Ray Interactions:
Photoabsorption, Scattering, Transmission, and Reflection at E=0-30000eV, Z=1-
92.Atomic Data&Nuclear Data Tables,1993,54(2):181-342)。
Step 6：Quantum rotation updates.Using Quantum rotating gate Population Regeneration Q, filial generation Q ' is generated, filial generation Q ' is surveyed
Amount and decoding, obtain determining solution P '.The grazing incidence X-ray reflectivity spectrum of film is fitted, quantum is evaluated by fitting coefficient
The fitness of individual, and screen and preserve optimal quantum individual.Wherein, to all gene position implementation amounts of each individual in population
Cervical orifice of uterus rotation renewal, Quantum rotating gate are
θ in above formulaij,kIndividual for i-th of quantum, the anglec of rotation of k-th of gene position, its value are expressed as in j-th of chromosome
θij,k=s (αij,k,βij,k)·Δθij,k, wherein s (αij,k,βij,k) direction rotated is controlled, determined by inquiry table 1.
In table 1, pij,kK-th of gene position in j-th of chromosome of binary system solution is corresponded to for i-th of quantum individual,
(pbest)j,kFor k-th of gene position in j-th of chromosome of the optimal corresponding binary system solution of quantum individual of current search.χi 2And χ2 best
The evaluation coefficient of the individual and optimal quantum individual of i-th of quantum.Δθij,kThe size of rotation is controlled, its numerical value is
Δθij,k=(θij,k)min+fij,k×[(θij,k)max-(θij,k)min]
(9)
(θ in above formulaij,k)min=0.001 π is the minimum value of search angle range intervals；(θij,k)max=0.05 π is search
The maximum in angular range section.Meanwhile f in above formulaij,kFor
Wherein choromelens is the chromogene length of current quantum individual, and A enters for the two of i-th of quantum individual
System determines solution pi, B is that the binary system of current optimum individual determines solution pbest, and Ham (A, B) is piAnd pbestMiddle relevant position
The number differed.Based on the Quantum rotating gate in (8) formula to quantum gene positionIt is updated, is updated to
WhereinQuantum gene position after being updated for Quantum rotating gate.
Rotation renewal is carried out to each individual each gene position in quantum population, and then generates progeny population.Antithetical phrase
In generation, is measured and decodes, and then each individual fitness is assessed based on (7) formula, and updates optimum individual with this.
Table 1.s (αij,k,βij,k) inquiry table
Step 7：Quantum variation operates.Row variation is entered to each quantum individual in population, i.e., chooses s in individual at random
Individual gene position, quantum non-gate operation is carried out to its quantum bit probability amplitude
WhereinTo choose k-th of gene position in j-th of chromosome in i-th of quantum individual,For quantum variation
Gene position afterwards.
Step 8：Quantum whole interference crossover operates.With probability Pc=0.04 pair of filial generation carries out classical quantum whole interference crossover
Operation, a uniform random number r ∈ (0,1) is generated, if r<Pc, then this operation is carried out, i.e., filial generation Q ' is measured
And decoding, obtain determining the fitness of each individual in solution P ', and evaluation quantum population, and screen and preserve optimal quantum
Body, then quantum whole interference crossover is carried out, otherwise skip over this step.
Step 9：Filial generation Q ' is updated with elite retention strategy, filial generation Q ' is measured and decoded, obtains determining solution P ',
Step 4 is gone to afterwards.
In order to which the feasibility of the fitting derivation algorithm to the above-mentioned film GIXR based on QIGA is verified with high efficiency,
The present invention the typical embodiments by the GIXR of Si monofilms and Mo/Si multilayer films fitting solve exemplified by, and by its result with
The result that solution is fitted based on GA is analyzed.Relevant parameter is used by GA, population scale N=100, dye
Colour solid number is M=6, and evolutionary generation is respectively 100 or 200 to monofilm and multilayer film, mutation probability Pm=0.01, crossover probability
Pc=0.5.
In the present invention, Si monofilms are coated with respectively using magnetron sputtering coating system and wait cycle Mo/Si multilayer film each
Two film samples, and application PANalytical Powder X-ray diffractometers are carried out to the grazing incidence X-ray reflectivity of film
Measure (GIXR), X-ray diffractometer uses wavelength to be detected for 0.154nm hard X ray, corresponding monofilm and multilayer film
Shown in test result as Fig. 3 a- Fig. 3 d and Fig. 5 a- Fig. 5 d.Illustrated in more detail below in conjunction with embodiment 1-2.
Si monofilm GIXR of the embodiment 1 based on QIGA fitting solves
Quantum population scale N=100, quantum chromosomes number M=6, gene position number λ needed for each quantum chromosomes=
20, evolutionary generation maximum of Tmax=100, quantum variation gene position s=2, the full crossover probability P of quantumc=0.04 and each quantum
The span (being shown in Table 2) of chromosome.The quantum population of the sign Si monofilms of generation is
Q=[q1,q2,…,qi,…,q99,q100]
Wherein i-th of individual is
Above-mentioned 6 chromosome represents respectively, the geometric thickness of Si film layers, the density of Si film layers, the roughness of Si film layers, table
Face SiO2The geometric thickness of oxide layer, SiO2The density of film layer, and surface oxide layer SiO2Roughness.In order to preferably right
GIXR than the Si monofilms based on QIGA and GA is fitted solution efficiency, and Fig. 2 gives the optimal plan of two Si individual layer membrane samples
Relation of the evaluation coefficient with evolutionary generation is closed, it is clear that GIXR solution efficiency and fitting precision are higher from figure,
Especially for Si monofilms 2.
Fig. 3 a- Fig. 3 d give the optimal film layer structure parameter of Si monofilms based on GA and QIGA acquisitions and (evolve 100
Generation) theoretical inverting GIXR and experimental results contrast.Specifically, Fig. 3 a are to be fitted Si monofilms 1 based on GA
GIXR solves to obtain the contrast of the notional result and experimental result of membrane structure parametric inversion；Fig. 3 b are mono- based on QIGA fittings Si
The GIXR of tunic 1 solves to obtain the contrast of the notional result and experimental result of membrane structure parametric inversion；Fig. 3 c are to be intended based on GA
The GIXR for closing Si monofilms 2 solves to obtain the contrast of the notional result and experimental result of membrane structure parametric inversion；Fig. 3 d are base
Solve to obtain the contrast of the notional result and experimental result of membrane structure parametric inversion in the GIXR of QIGA fitting Si monofilms 2.
Analysis shows are carried out to Fig. 3 a- Fig. 3 d, because QIGA has higher fitting precision, so the optimal film layer ginseng according to its solution
Number invertings GIXR be fitted with experimental result it is more preferable, corresponding parameters of film and based on GA solution parameters of film refer to table
2。
Table 2
Mo/Si multilayer film GIXR of the embodiment 2 based on QIGA fitting solves
Quantum population scale N=100, quantum chromosomes number M=11, the gene position number λ needed for each quantum chromosomes
=20, evolutionary generation maximum of Tmax=200, quantum variation gene position s=2, the full crossover probability P of quantumc=0.04 measures with each
The span (being shown in Table 3) of daughter chromosome.The quantum population of the sign Mo/Si multilayer films of generation is
Q=[q1,q2,…,qi,…,q99,q100]
Wherein i-th of individual is
Above-mentioned 11 chromosome represents respectively, the geometric thickness of Si film layers, the density of Si film layers, and the geometry of Mo film layers is thick
Degree, the density of Mo film layers, the geometric thickness of diffusion layers of the Mo on Si, thickness of diffusion layer of the Si on Mo, MoSi2Diffusion layer
Density, multi-layer film surface SiO2The geometric thickness of oxide layer, SiO2The density of film layer, SiO2The surface roughness of film layer.
The optimum individual that the GIXR fittings that Fig. 4 gives two Mo/Si multilayer membrane samples based on QIGA and GA solve
Evaluation coefficient is with the relation of evolutionary generation, and what can be apparent from from Fig. 4 sees, the plan based on GA is compared in the fitting based on QIGA
Closing optimization has higher efficiency, and after being optimized to for 200 generation, QIGA optimal fitting precision is far above GA fitting precision.With
Fig. 4 is corresponding, and Fig. 5 a- Fig. 5 d sets forth two multilayer membrane samples, and the fitting based on QIGA and GA is solved and carried out to 200
Dai Shi, the theoretical modeling GIXR results of optimal multilayer film parametric inversion and the contrast of measured result that two kinds of algorithms obtain.Specifically
For, Fig. 5 a are that the GIXR that Mo/Si multilayer films 1 are fitted based on GA solves to obtain the notional result and reality of membrane structure parametric inversion
Test the contrast of result.Fig. 5 b are that the GIXR that Mo/Si multilayer films 1 are fitted based on QIGA solves to obtain the reason of membrane structure parametric inversion
By the contrast of result and experimental result.Fig. 5 c are that the GIXR that Mo/Si multilayer films 2 are fitted based on GA solves to obtain membrane structure parameter
The contrast of the notional result and experimental result of inverting.Fig. 5 d be based on QIGA be fitted Mo/Si multilayer films 2 GIXR solve to obtain it is thin
The contrast of the notional result and experimental result of membrane structure parameter inverting.It is based on it is clear that the fitting result based on QIGA is compared
GA fitting result meet with experimental result it is more preferable, be worth mentioning when, evolve 200 generation when, fitting within based on GA is certain
Can not also truly reaction experiment result in degree.Table 3 is referred to based on the QIGA and GA multi-layer film structure parameters obtained.
From the point of view of the phenetic analysis result of comprehensive foregoing Si monofilms and Mo/Si multilayer films, the GIXR of base GA film plan
The convergence rate of conjunction analysis is slow and solving precision is low.GA solving precision is low show certain evolutionary generation after, in population most
Excellent individual evaluation coefficient is difficult to drop to a more satisfactory numerical value, so that the GIXR collection of illustrative plates of theoretical inverting is tied with experiment
Fruit difference is larger.
By comparison, the efficiency that the GIXR of the film based on QIGA fitting solves is very high, after certain evolutionary generation,
The evaluation coefficient of optimum individual in quantum population is rapidly decreased to relatively low desired quantity, and this explanation is based on QIGA, film ginseng
Number chess game optimizations to global optimum, and the GIXR collection of illustrative plates of its inverting meet with experimental result it is fine.The above results are analyzed, its
Reason may is that the film analysis method of (1) based on QIGA employs quantum bit coding, quantum bit coding on coding
Different from traditional binary strings genetic algorithm coded system, a quantum bit can not only represent 0 and 1 two states, but
Represent the linear superposition of 0 state and 1 state, so that the diversity of population is expanded；(2) renewal of quantum population is mainly depended on
In Quantum rotating gate, and the dynamic rotary angle strategy that the present invention uses makes evolution towards optimal optical thin-film structure individual evolution
The size of the anglec of rotation is adjusted while direction, convergence rate and enhancing local optimal searching ability are improved with this；(3) quantum variation and amount
The operation that son intersects inhibits population to be absorbed in local optimum, ensures that fitting solution searches global optimum.In summary point
Analysis, QIGA is applied to, based in film GIXR fitting solution procedurees, have obvious feasibility and prominent advantage, fully exhibition
Application value of the quantum algorithm in terms of film microstructure sign is showed.
Table 3
It should be appreciated that the above is only the concrete application example of the present invention, any limit is not formed to protection scope of the present invention
System.All technical schemes formed using equivalent transformation or equivalent replacement, all fall within rights protection scope of the present invention.
Claims (10)
1. a kind of optical thin-film structure analysis method based on quantum derivative genetic algorithm, it is characterised in that comprise the following steps：
Step 1：Input is microcosmic suitable for the fitting of film grazing incidence X-ray reflectivity spectrum, the film based on quantum derivative genetic algorithm
The initial parameter value of structure analysis method, initial parameter therein include：Quantum population scale N, chromosome number M, each dyeing
The gene digit λ of body, evolutionary generation maximum of Tmax, quantum variation gene digit s, the full crossover probability P of quantumcWith each dyeing
The span of body；
Step 2：Quantum coding is carried out to the microstructural parameter of optical thin film, generation characterizes the quantum kind of optical thin-film structure
Group
Q=[q1,q2,…,qi,…qN-1,qN],
Wherein arbitrarily quantum individual qiQuantum coding be
<mrow>
<msub>
<mi>q</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<mn>...</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>...</mn>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
<mo>,</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
<mo>,</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
<mo>,</mo>
<mi>&lambda;</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
<mo>,</mo>
<mi>&lambda;</mi>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mn>...</mn>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<mn>...</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>...</mn>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>&lambda;</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>&lambda;</mi>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mn>...</mn>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>M</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>M</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>M</mi>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>M</mi>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<mn>...</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>...</mn>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>M</mi>
<mo>,</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>M</mi>
<mo>,</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
<mo>|</mo>
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>M</mi>
<mo>,</mo>
<mi>&lambda;</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>M</mi>
<mo>,</mo>
<mi>&lambda;</mi>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mo>;</mo>
</mrow>
Step 3：Initial quantum population Q to characterizing optical thin-film structure0Measure and decode, obtain determining solution P0；
Step 4：Reach Evolution of Population number maximum of Tmax, if satisfied, then terminator, if not satisfied, then continuing；
Step 5：The grazing incidence X-ray reflectivity spectrum of optical thin film is fitted, the suitable of quantum individual is evaluated by fitting coefficient
Response, and screen and preserve optimal quantum individual；
Step 6：Quantum population Q is updated using Quantum rotating gate, filial generation Q ' is generated, filial generation Q ' is measured and decoded, is obtained
It is determined that solution P ', continues to be fitted the grazing incidence X-ray reflectivity spectrum of optical thin film, quantum individual is evaluated by fitting coefficient
Fitness, and screen and preserve the optimum individual in quantum population；
Step 7：Mutation operation is carried out to quantum population, i.e. in order to the random of each quantum individual s gene position of progress
Selection, quantum non-gate operation is carried out to its quantum bit probability amplitude；
Step 8：With probability PcTo filial generation Q ' carry out quantum whole interference crossovers, if being intersected, filial generation Q ' is measured and
Decoding, obtains determining the fitness of each individual in solution P ', and evaluation quantum population, and screens and preserve optimal quantum
Body, then quantum whole interference crossover is carried out, otherwise skip over；
Step 9：Filial generation Q ' is updated with elite retention strategy, filial generation Q ' is measured and decoded, obtains determining solution P ', afterwards
Go to step 4.
2. optical thin-film structure analysis method according to claim 1, it is characterised in that：In described step two, appoint
Quantum bit gene of anticipating meets
<mrow>
<msubsup>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<mn>1</mn>
</mrow>
In initialization procedure, the quantum bit gene position of each individual is entered as in quantum population
<mrow>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</msqrt>
<mo>.</mo>
</mrow>
3. optical thin-film structure analysis method according to claim 1, it is characterised in that：In described step five, amount
The evaluation function of individual adaptation degree is in sub- population
<mrow>
<msup>
<mi>&chi;</mi>
<mn>2</mn>
</msup>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>I</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>m</mi>
<mi>e</mi>
<mi>a</mi>
<mi>s</mi>
<mo>.</mo>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>c</mi>
<mi>a</mi>
<mi>l</mi>
<mi>c</mi>
<mo>.</mo>
</mrow>
</msub>
</mrow>
<msub>
<mi>I</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>m</mi>
<mi>e</mi>
<mi>a</mi>
<mi>s</mi>
<mo>.</mo>
</mrow>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
Wherein χ2For the evaluation coefficient of quantum individual, m counts for experimental data, Ik,calc.Theoretical reflectance for kth data point is strong
Degree, and Ik,meas.For the experiment reflected intensity of kth data point.
4. optical thin-film structure analysis method according to claim 3, it is characterised in that：In described step five, adopt
With the theoretical reflectance intensity of Fresnel coefficient method calculating optical film.
5. optical thin-film structure analysis method according to claim 1, it is characterised in that：In described step six, adopt
Rotation renewal is carried out to all gene positions of each individual in quantum population with Quantum rotating gate, Quantum rotating gate is
<mrow>
<mi>U</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>cos&theta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>sin&theta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>sin&theta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>cos&theta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein θij,kFor the anglec of rotation of k-th of gene position in j-th of chromosome of i-th of quantum individual, its value is expressed as θij,k=
s(αij,k,βij,k)·Δθij,k, wherein s (αij,k,βij,k) determined by tabling look-up, to control the direction of rotation, Δ θij,kControl
The size of rotation, its numerical value are
Δθij,k=(θij,k)min+fij,k×[(θij,k)max-(θij,k)min]
Wherein (θij,k)min=0.001 π be search angle range intervals minimum value, (θij,k)max=0.05 π is search angle model
Enclose the maximum in section, while fij,kFor
<mrow>
<msub>
<mi>f</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>H</mi>
<mi>a</mi>
<mi>m</mi>
<mrow>
<mo>(</mo>
<mi>A</mi>
<mo>,</mo>
<mi>B</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>c</mi>
<mi>h</mi>
<mi>o</mi>
<mi>r</mi>
<mi>m</mi>
<mi>e</mi>
<mi>l</mi>
<mi>e</mi>
<mi>n</mi>
<mi>s</mi>
</mrow>
</mfrac>
</mrow>
Wherein choromelens is the chromogene length of current quantum individual, and A is that the binary system of i-th of quantum individual is true
Surely p is solvedi, B is that the binary system of current optimum individual determines solution pbest, and Ham (A, B) is piAnd pbestMiddle relevant position is different
Binary-coded number.
6. optical thin-film structure analysis method according to claim 5, it is characterised in that：, should in described step six
With the quantum gene position of Quantum rotating gateIt is updated, is updated to
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mi>U</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
WhereinQuantum gene position after being updated for Quantum rotating gate.
7. optical thin-film structure analysis method according to claim 1, it is characterised in that：In described step seven, from
S gene position is selected in each quantum individual at random and participates in quantum non-gate operation
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
WhereinTo choose k-th of gene position in j-th of chromosome in i-th of quantum individual,After quantum variation
Gene position.
8. optical thin-film structure analysis method according to claim 7, it is characterised in that：In described step seven,
After completing the quantum non-gate operation, fitness individual in new filial generation quantum population is entered according to following evaluation function
Row is assessed
<mrow>
<msup>
<mi>&chi;</mi>
<mn>2</mn>
</msup>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>I</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>m</mi>
<mi>e</mi>
<mi>a</mi>
<mi>s</mi>
<mo>.</mo>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>c</mi>
<mi>a</mi>
<mi>l</mi>
<mi>c</mi>
<mo>.</mo>
</mrow>
</msub>
</mrow>
<msub>
<mi>I</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>m</mi>
<mi>e</mi>
<mi>a</mi>
<mi>s</mi>
<mo>.</mo>
</mrow>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
Wherein χ2For the evaluation coefficient of quantum individual, m counts for experimental data, Ik,calc.Theoretical reflectance for kth data point is strong
Degree, and Ik,meas.For the experiment reflected intensity of kth data point, and screen and preserve the optimum individual in quantum population.
9. optical thin-film structure analysis method according to claim 1, it is characterised in that：In described step eight, with
Probability Pc=0.04 pair of filial generation carries out classical quantum whole interference crossover operation, generates a uniform random number r ∈ (0,1),
If r<Pc, then this operation is carried out, i.e., filial generation Q ' is measured and decoded, obtains determining solution P ', and evaluation quantum population
In each individual fitness, and screen and preserve optimal quantum individual, then carry out classical quantum whole interference crossover, otherwise skip over
This step.
10. the optical thin-film structure analysis method according to any one of claim 1-9, it is characterised in that：Described light
It is monofilm or multilayer film to learn film.
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