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CN106990528B - High-precision characterization method of extreme ultraviolet multilayer films based on dual-objective genetic algorithm - Google Patents

High-precision characterization method of extreme ultraviolet multilayer films based on dual-objective genetic algorithm Download PDF

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CN106990528B
CN106990528B CN201710220536.8A CN201710220536A CN106990528B CN 106990528 B CN106990528 B CN 106990528B CN 201710220536 A CN201710220536 A CN 201710220536A CN 106990528 B CN106990528 B CN 106990528B
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匡尚奇
王名
王一名
孙秀平
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Changchun University of Science and Technology
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Abstract

The invention discloses a kind of multiplayer films in EUV characterized with good accuracy method based on double object genetic algorithm, this method combine fitting with the experimental result of EUV reflectance spectrum by the way that the non-dominated sorted genetic algorithm (NSGA-II) of real coding to be applied to the grazing incidence X-ray reflectivity spectrum of EUV multilayer film.Using the grazing incidence X-ray reflectivity of EUV multilayer film spectrum with EUV reflectance spectrum as the optimization aim of double object genetic algorithm, evolution obtains the non-dominant disaggregation close to the forward position Pareto, it concentrates the remaining lesser excellent individual of fitting of two fit objects to advanced optimize non-domination solution using Levenberg-Marquart algorithm, obtains two remaining the smallest optimum structure parameters of fit object fitting.The present invention solves the problems, such as the more solutions being fitted in (grazing incidence X-ray reflectivity spectrum or EUV reflectance spectrum) solution based on single goal, and it avoids two fit objects when simply summing it up joint fitting and solving, it influences each other between target, or even seriously tends to the problem that one of target causes multilayer film Microstructure characterization precision not high.

Description

Multiplayer films in EUV characterized with good accuracy method based on double object genetic algorithm
Technical field
Present invention relates particularly to EUV needed for one kind multi-layer mirror used in extreme ultraviolet (EUV) photoetching technique The characterized with good accuracy method of multilayer film microstructure.
Background technique
EUV lithography technology is considered as meeting semiconductor industry demand, most promising Next Generation Lithography.But EUV wave band, almost all of material is all opaque, and refractive index very close 1, so EUV optical system cannot use Traditional refraction optical element, and reflective optical system must be used.Therefore, the multilayer film of EUV light high reflectance is realized As the core optical element of EUV optical system, meanwhile, EUV multilayer film also become EUV optical field science and technology research and development hot spot with Core, the common concern by domestic and international research team.
EUV multilayer film obtains the material of high reflectance as optical wavelength used by optical system is different and different, with light Wavelength concentrates on for the exposure optical system of 13.5nm range, and multilayer film mostly uses molybdenum (Mo) layer and silicon (Si) layer to be gradually superimposed Mo/Si multilayer film, which can be realized the EUV light of vertical normal incidence 65%~68% reflectivity.Although The higher EUV multilayer film of reflectivity can be experimentally developed, but since EUV multilayer film is the more complicated body of structure System, there are still higher difficulty for the characterized with good accuracy of microstructure, and only realize the microstructure of EUV multilayer film Characterized with good accuracy is just able to achieve the theoretical foundation that preferably provides of multilayer film technique, and setting for complicated aperiodic EUV multilayer film Meter provides necessary theoretical calculation parameter.It researchs and analyses and shows that the higher reason of EUV multilayer film Microstructure characterization difficulty has three : (1) there is diffusion in aspect, and the thickness of diffusion layer is only nm magnitude between multilayer film film layer.It is more by taking Mo/Si multilayer film as an example The Diffusion barrier layer of tunic is generally the MoSi that generation is chemically reacted between Mo layers and Si layers2Film, thickness is between 1-3nm； (2) interface roughness between multilayer film film layer is difficult to carry out accurate Characterization, and interface roughness has the reflectivity of multilayer film Tremendous influence；(3) density of each film material of multilayer film determines the light refractive index for the material being coated with, and nm grades of thickness Density of film is difficult directly to be measured.
For the characterization and analysis for realizing Mo/Si multilayer film microstructure, generallyd use in the context of detection of EUV multilayer film Method has the fitting of grazing incidence X-ray reflectivity (GIXR) spectrum to solve, the fitting of EUV reflectance spectrum solves and transmission electron microscope (TEM) detection methods such as observation.In the above-mentioned methods, GIXR is a kind of lossless high-precision detecting method, but disadvantage is this The signal noise of detection is larger, and the parameter that nonlinear fitting needed for theoretical model solves is more, and hard X used by GIXR Ray is insensitive between the physical characteristic of the diffusion layer multilayer film film layer；The noise of EUV reflectance spectrum is smaller, but waits periodic multilayer films Spectral reflectance curve it is relatively simple, be difficult by its be fitted solve obtain multilayer film high-precision configuration parameter information；The side TEM Although method can directly be observed multilayer film film layer structure, this method is a kind of destructive detection method, and its characterization is smart Degree is not high, generally as the reference of multilayer film Microstructure characterization.
Summary of the invention
To solve the problems, such as existing EUV multilayer film microstructure characterized with good accuracy, the present invention provides a kind of bases In the multiplayer films in EUV characterized with good accuracy method of double object genetic algorithm, this method is based on double object genetic algorithm, joint etc. GIXR the and EUV reflectance spectrum of period EUV multilayer film is solved and is evolved by the fitting of double object genetic algorithm, obtain precision compared with The microstructural parameter of high multiplayer films in EUV solves in the past based on (GIXR or the EUV reflection of multilayer film of single testing result Spectrum) the not high problem of possessed characterization precision.
The technical proposal for solving the technical problem of the invention is as follows:
EUV multilayer film characterized with good accuracy method based on double object genetic algorithm, includes the following steps:
Step 1: the initial parameter value of the NSGA-II based on periods EUV multilayer film parametric solutions such as being suitable for, packet are inputted Include population scale N, the number of parameters of multilayer film microstructure based on four layer models, mutation probability pm, crossover probability pc, intersect Operator ηcWith mutation operator ηp, evolve algebra and each parameter of multilayer film microstructure based on four layer models search range；
Step 2: four layer models based on EUV multilayer film generate the initial parent population Q that NSGA-II evolves, and population Q can It is expressed as
Q=[a1,a2,a3,…,ai,…,aN-1,aN]。 (1)
By taking Mo/Si multilayer film as an example, the gene parameter of each individual is 8 in population, is expressed as follows
Wherein tsiFilm thickness, t for Si layersMoFilm thickness, t for Mo layersMo on SiFor Mo layers of thickness of diffusion layer, the t on Si layer For Mo/Si multilayer film average period thickness, σ be roughness between film layer, ρsiDensity, ρ for Si film layerMoFor Mo film layer Density, ρMoSi2The density of diffusion layer between Mo layers and Si layers (or between Si layers and Mo layers).Consider physics and the change of multilayer film Property is learned, waits the constraint condition of microstructural parameter in the period of periods Mo/Si multilayer film to be
Step 3: the fitness of each individual, fitness in the parent population of computational representation multilayer film microstructural parameter Including two, first fitness is the GIXR theoretical modeling result of individual and the degree of conformity of multilayer film experimental result, second Fitness is the degree of conformity of the theoretical modeling result of the EUV reflectance spectrum of individual and the experimental result of multilayer film.
Step 4: non-dominated ranking is carried out to the individual in the population of characterization multilayer film microstructural parameter, obtains population The dominated Sorting of middle individual, meanwhile, to non-dominant individual using the further sequence of crowding distance.
Step 5: using wheel match selection mechanism, crossover operation is carried out to the individual in population, characterization multilayer film is generated with this The progeny population of microstructural parameter.During crossover operation, it is desirable that operated to whole parameter genes of individual.
Step 6: Variation mechanism is used, the progeny population of characterization multilayer film microstructural parameter is further updated.It is making a variation In operation, only makes a variation to the single-gene of the individual of characterization multilayer film microstructural parameter, new filial generation is ultimately generated with this Population.
Step 7: the parent population and progeny population of characterization multilayer film microstructural parameter are merged, and use pair The individual merged in population is compared one by one than mechanism, for identical individual, retain first, and to it is another each and every one Body carries out new parameter gene assignment.
Step 8: the Bi-objective fitness of the merging population at individual of assessment characterization EUV multi-layer film structure parameter.
Step 9: non-dominated ranking is carried out to the merging population of characterization multilayer film microstructural parameter, to non-dominant individual Then calculate crowding distance.New parent population is filtered out by non-dominated ranking and crowding distance.Return step three, until Reach the evolutionary generation of requirement.
Step 10: by the evolution of NSGA-II, the experimental result for obtaining GIXR the and EUV reflectance spectrum of needle EUV multilayer film is made For the Bi-objective that fitting solves, optimization obtains the non-dominant disaggregation close to the forward position Pareto.
Step 11: residual according to the fitting of two experimental results to the individual of the non-domination solution concentration close to the forward position Pareto It is the sum of remaining to be assessed, select remaining lesser individual applications Levenberg-Marquart (LM) algorithm of total fitting to combine two Experimental result further progress optimizes and reduces total fitting remnants, and acquires multilayer according to the remaining the smallest individual of total fitting The microstructural parameter of film and the error of fitting of relevant parameter.
Compared with the prior art, the present invention is at least had the following beneficial effects:
(1) solution of previous EUV multilayer film microstructure, only with GIXR the or EUV reflectance spectrum work for waiting periodic multilayer films It is fitted for simple target, and the present invention is based on GIXR the and EUV reflectance spectrums that NSGA-II algorithm will wait periods EUV multilayer film Experimental result carries out joint fitting as Bi-objective and solves；
(2) present invention incorporates the strong point of the GIXR and EUV reflectance spectrum of period EUV multilayer film detection, the experiment knots of GIXR Fruit is more sensitive to the thicknesses of layers of multilayer film；The signal errors of EUV reflectance spectrum it is smaller and to the interface roughness of multilayer film and Surface layer roughness is more sensitive.So the characterization of the EUV multilayer film microstructure of degree of precision can be achieved in the present invention；
(3) under normal circumstances, the multi-layer film structure parametric inversion that the GIXR single goal based on period EUV multilayer film solves EUV reflectance spectrum and experimental result difference are very big；And the multilayer film that the EUV reflectance spectrum single goal based on period EUV multilayer film solves The GIXR of structural parameters inverting is equally very big with experimental result difference.In contrast, solved the present invention is based on NSGA-II fitting Multi-layer film structure parameter, GIXR the or EUV reflectance spectrum of inverting, which all has with experimental result, preferably to be met.
Detailed description of the invention
Fig. 1 is the membrane system schematic diagram of the period Mo/Si multilayer film of four layer models in exemplary embodiments of the present invention.Mo/Si is more Tunic was 60.5 periods, and membrane system is Sub [Si/MoSi2/Mo/MoSi2]60Si/SiO2/Air.Wherein 1 is ultra-smooth substrate；2 For Si film layer；3 be MoSi of the Mo film layer in Si film layer2Diffusion layer；4 be Mo layers；5 be MoSi of the Si film layer in Mo film layer2Expand Dissipate layer；6 be top layer Si film layer since the oxidation of environment is formed by SiO2Film layer.
Fig. 2 is that NSGA-II algorithm is based in exemplary embodiments of the present invention, anti-with the GIXR of period Mo/Si multilayer film and EUV The experimental result of spectrum is penetrated as fitting Bi-objective, solves the flow chart of multilayer film microstructural parameter.
Fig. 3 a is that GIXR the and EUV reflectance spectrum in exemplary embodiments of the present invention with period Mo/Si multilayer film is the double of fitting Target is based on NSGA-II algorithm, after 50,100,300 and 500 generations of evolving, the non-domination solution forward position of Bi-objective；And respectively Using GIXR and EUV reflectance spectrum as single goal, using the optimum individual obtained after GA 500 generations of evolution.
Fig. 3 b is based on NSGA-II algorithm in exemplary embodiments of the present invention, before the non-domination solution obtained after the evolution of 500 generations Solution in edge and non-domination solution forward position is remaining to total fitting of fitting Bi-objective.
Fig. 4 is in invention exemplary embodiments for the remaining lesser excellent individual application of total fitting of Bi-objective Levenberg-Marquart algorithm is combined that Bi-objective advanced optimizes as a result, wherein overall be fitted remaining the smallest individual quilt It is considered as optimal solution.
Fig. 5 a- Fig. 5 d be respectively in exemplary embodiments of the present invention with GIXR be fitting simple target, optimize acquisition GIXR the and EUV reflectance spectrum of multi-layer film structure parametric inversion；And using the multilayer film parameters of GIXR single object optimization as initial value, The inverting of multi-layer film structure parameter institute is obtained using the joint GIXR and EUVR reflectance spectrum fitting of Levenberg-Marquart algorithm The fitting of accordingly result and accordingly result is remaining.
Fig. 6 a- Fig. 6 d is the GIXR of the parametric inversion based on the optimum individual in Fig. 4 in exemplary embodiments of the present invention respectively It is remaining with EUV reflectance spectrum and corresponding fitting.
Specific embodiment
As previously mentioned, it is extremely purple based on double object genetic algorithm that the invention proposes a kind of in view of the deficiencies in the prior art Outer multilayer film characterized with good accuracy method, non-dominated sorted genetic algorithm NSGA-II (IEEE of this method based on real coding Transactions on Evolutionary Computation, 6,182 (2002)), combine the glancing incidence X of EUV multilayer film Reflectance spectrum (GIXR) and EUV reflectance spectrum are fitted solution to multilayer film microstructure, realize the high-precision of multilayer film microstructure Degree characterization.
Specifically, a kind of EUV multilayer film high-precision table based on double object genetic algorithm provided in an embodiment of the present invention Sign method includes the following steps:
Step 1: the initial parameter value of the NSGA-II based on periods EUV multilayer film parametric solutions such as being suitable for, packet are inputted Include population scale N, the number of parameters of multilayer film microstructure based on four layer models, mutation probability pm, crossover probability pc, intersect Operator ηcWith mutation operator ηp, evolve algebra j and the multilayer film microstructure based on four layer models each parameter search model It encloses；
Step 2: four layer models based on EUV multilayer film, which generate, is suitable for the initial parent population Q that NSGA-II evolves, kind Group Q is represented by
Q=[a1,a2,a3,…,ai,…,aN-1,aN]。 (1)
By taking Mo/Si multilayer film as an example, individual gene parameter is in population
Wherein tSiFilm thickness, t for Si layersMoFilm thickness, t for Mo layersMo on SiFor Mo layers of thickness of diffusion layer, the t on Si layer For Mo/Si multilayer film average period thickness, σ be interface roughness, ρ between film layerSiDensity, ρ for Si film layerMoFor Mo film The density of layer, ρMoSi2The density of diffusion layer between Mo layers and Si layers (or between Si layers and Mo layers)；
Step 3: the fitness of each individual in the parent population of computational representation EUV multilayer film microstructural parameter adapts to Degree includes two, wherein first fitness is the GIXR theoretical modeling result of individual and meeting for EUV multilayer film experimental result Degree, and second fitness is the theoretical modeling result of EUV reflectance spectrum and meeting for the experimental result of EUV multilayer film of individual Degree；
Step 4: non-dominated ranking is carried out to the individual in the population of characterization EUV multilayer film microstructural parameter, is planted Individual dominated Sorting in group, meanwhile, to non-dominant individual using the further sequence of crowding distance；
Step 5: using wheel match selection mechanism, carrying out crossover operation to the individual in population, and it is more to generate characterization EUV with this The progeny population of tunic microstructural parameter, during crossover operation, it is desirable that whole parameter genes of individual are operated；
Step 6: Variation mechanism is used, the progeny population of characterization multilayer film microstructural parameter is further updated；
Step 7: the parent population and progeny population of characterization EUV multilayer film microstructural parameter are merged；
Step 8: the Bi-objective fitness of the merging population at individual of assessment characterization EUV multi-layer film structure parameter；
Step 9: non-dominated ranking is carried out to the merging population of characterization EUV multilayer film microstructural parameter, to non-dominant Body then calculates crowding distance, and new parent population is filtered out by non-dominated ranking and crowding distance, return step three, Evolutionary generation until reaching requirement.
Step 10: by the evolution of NSGA-II, the experimental result for obtaining GIXR the and EUV reflectance spectrum of needle EUV multilayer film is made For the Bi-objective that fitting solves, optimization obtains the non-dominant disaggregation close to the forward position Pareto；
Step 11: residual according to the fitting of two experimental results to the individual of the non-domination solution concentration close to the forward position Pareto The sum of remaining to be assessed, the remaining lesser individual applications Levenberg-Marquart algorithm of selection joint fitting combines two realities It tests result to advanced optimize, selects always to be fitted remaining the smallest individual as the optimal solution of fitting, and then acquire the micro- of EUV multilayer film See the error of structural parameters and relevant parameter.
Further, during the step 1, population scale N is 50-200, and preferred population scale is 100； Mutation probability pmFor 0.1-1.0, preferably mutation probability 0.1；Crossover probability pcFor 0.1-1.0, preferably crossover probability is 0.9；Intersect Operator ηcFor 1-50, preferred crossover operator is 2；Mutation operator ηpFor 1-50, preferred mutation operator is 2；The algebra j of evolution It is 500 for 300-500, preferred algebra j.
Further, during the step 2, consider the physics and chemical property of multilayer film, wait periods Mo/Si The constraint condition of microstructural parameter is in the multilayer film period
Further, during the step 3, the evaluation function of Bi-objective fitness is
WhereinEvaluation coefficient for theoretical inversion result with respect to EUV multilayer film EUV reflectance spectrum experimental result,For theory Evaluation coefficient of the inversion result with respect to EUV multilayer film GIXR experimental result；RcAnd RmRespectively theoretical modeling and experiment measure EUV reflectivity；IcAnd ImThe respectively grazing incidence X-ray reflectivity light intensity of theoretical modeling and experiment measurement, and σmFor corresponding experimental point Measurement error standard deviation.
Further, during the step 6, in mutation operation, only to characterization multilayer film microstructural parameter Individual single-gene carry out mutation operation.
Further, during the step 6, during being merged for population and progeny population, using comparison Mechanism compares the individual merged in population one by one, for identical individual, retains first, and to another individual Into row stochastic gene parameter assignment.
Further, the EUV multilayer film includes any combination or two or more in Mo/Si, Rh/Si, Ni/C, Ru/C The EUV multilayer film that combined and alternatively is constituted, and it is without being limited thereto.
The present invention is described in further detail with example with reference to the accompanying drawing.
NSGA-II is applied among period Mo/Si multilayer film Microstructure characterization by the embodiment of the present invention, by the period GIXR the and EUV reflectance spectrum joint fitting of Mo/Si multilayer film solves, and obtains the characterized with good accuracy of multilayer film microstructural parameter, Solves the problems, such as the lower problem of the fitting of the simple target caused by more solutions solving precision.In order to make the multilayer of theoretical simulation Film microstructure is more in line with reality, and four layer models, i.e. consideration Mo film layer and Si film layer are used in the single cycle of multilayer film Between material phase counterdiffusion, and by diffusion layer with MoSi2Film layer is simulated, and specific structure is as shown in Figure 1.Of the invention In embodiment, Mo/Si multilayer film totally 60.5 periods.In theoretical simulation process, the atomic scattering factor parameter of Si and Mo are come Derived from Lawrence Berkeley National Laboratory database, and using the complex refractivity index n of following formula calculating material =(1- δ)-i β, wherein
Wherein re、NA, M and ρ be respectively electronics classics radius, Avogadro constant number, material relative atomic mass and material Density, while XiFor corresponding atomic ratio, and f ' and f " is the atomic scattering factor provided in database.
The method that period Mo/Si multilayer film microstructural parameter is solved based on Bi-objective is further illustrated in conjunction with Fig. 2, specifically Implementation steps are as follows:
Step 1: input is suitable for waiting the initial parameter value of the NSGA-II of periods EUV multilayer film parametric solution.Wherein wrap Include population scale N, mutation probability pm, crossover probability pc, crossover operator ηcWith mutation operator ηp, the algebra k that evolves, and be based on The number of parameters of the multilayer film microstructure of four layer models and the chess game optimization range of each parameter.Wherein, population scale N is 50- 200, preferred population scale is 100；Mutation probability pmFor 0.1-1.0, preferably mutation probability 0.1；Crossover probability pcFor 0.1- 1.0, preferably crossover probability is 0.9；Crossover operator ηcFor 1-50, preferred crossover operator is 2；Mutation operator ηpFor 1-50, preferably Mutation operator be 2；The algebra j of evolution is 300-500, and preferred algebra j is 500.
Step 2: Mo/Si multilayer film microstructural parameter of the characterization based on four layer models, and be suitable for NSGA-II and calculate The initialization of the population Q of method.Population Q is represented by
Q=[a1,a2,a3,…,ai,…,aN-1,aN], (2)
By taking Mo/Si multilayer film as an example, the gene parameter of each individual is 8 in population, is expressed as follows
Wherein Si layers of film thickness tSi, Mo layers of film thickness tMo, the Mo layers of thickness of diffusion layer t on Si layerMo on Si, Mo/Si it is more Tunic average period thickness t, roughness σ, Si film layer between film layer density psi, Mo film layer density pMo, Mo layers and Si layers Between (or between Si layers and Mo layers) diffusion layer density pMoSi2.Consider physics, chemical property and the experiment experience of multilayer film, week The constraint condition of microstructural parameter in a cycle of phase multilayer film is
Step 3: the fitness of each individual, fitness in the parent population of computational representation multilayer film microstructural parameter It is the EUV reflectance spectrum and multilayer film experimental result of the parameter theory simulation according to individual characterization including two: first fitness Degree of conformity；Second fitness is the GIXR of parameter theory simulation and meeting for multilayer film experimental result according to individual characterization Degree.The evaluation function of two degrees of conformity is respectively
WhereinFor the evaluation coefficient of the relatively more tunic EUV reflectance spectrum experimental result of theoretical inversion result,It is theoretical anti- Drill the evaluation coefficient of the relatively more tunic GIXR experimental result of result, RcAnd RmThe respectively EUV reflection of theoretical modeling and experiment measurement Rate；IcAnd ImThe respectively grazing incidence X-ray reflectivity intensity of theoretical modeling and experiment measurement, and σmFor the measurement of corresponding experimental point The standard deviation of error.In (5) formula, theoretical reflectance rate RcWith reflected intensity IcIt is all made of in the present invention based on Fresnel coefficient Method is calculated, and the reflection coefficient in multilayer film between jth layer and+1 layer of jth is
For s polarised light, qj=njcosθj；And for p-polarization light,The reflected amplitude of jth layer is
WhereinFor interface roughness between film layer, in the present invention using Nevot the and Croce factor come Reflection coefficient in (6) formula is modified, can be obtained
In above-mentioned (6) formula into (8) formula, λ is the optical wavelength of incident light, nj、θj、tjAnd σjJth layer respectively in multilayer film Refractive index, incidence angle, film thickness and interface roughness.Simultaneously in (5) formula,That is φiFor glancing incidence angles. For the Mo/Si multilayer film being coated in ultra-smooth substrate, it is believed that substrate is the medium of infinite thickness, therefore enables r0=0, and then adopt The reflected amplitude r of multilayer film top layer (multilayer film is m layers total) is calculated with the recursive iteration method based on (7) formulam.Multilayer as a result, The reflectivity of film top layer is
R=| rm|2。 (9)
It is emphasized that the reflectivity in the calculating process of the EUV reflectance spectrum of Mo/Si multilayer film is in the present invention with wave Long λ is independent variable, and in the calculating process of the GIXR of multilayer film, reflectivity is with grazing angle φiFor independent variable, and GIXR Reflected intensity is
I=I0·R+Ibackground。 (10)
I in above formula0For incident intensity, IbackgroundFor background intensity.
Step 4: it is non-that two evaluation function values progress are based on to the individual in the population of characterization multilayer film microstructural parameter Dominated Sorting.To dominated Sorting individual in population, and for non-dominant individual using the further sequence of crowding distance.
Step 5: using wheel match selection mechanism, crossover operation is carried out to the individual parameter in population, generates characterization EUV The progeny population of multilayer film microstructural parameter.In crossover operation in the present invention, it is desirable that individual characterization structural parameters Full gene carries out the crossover operation between two individuals.
Step 6: mutation operation is used, the progeny population of characterization multilayer film microstructural parameter is further updated.It is making a variation In operation, only makes a variation to a gene for characterizing multilayer film microstructural parameter in individual, filial generation is updated further with this Population is
Q '=[a '1,a′2,a′3,…,a′i,…,a′N-1,a′N]。 (11)
Step 7: the parent population and progeny population of characterization multilayer film microstructural parameter are merged.Merge laggard Row contrast operation, will merge each of population body and other individuals carry out gene pairs ratio.For identical individual, protect It stays first, and carrying out new gene assignment to another.Then merging population is
Q ∪ Q '=[a1,a2,a3,…,ai,…,aN-1,aN,a′1,a′2,a′3,…,a′i,…,a′N-1,a′N]。 (12)
Step 8: the Bi-objective fitness of the merging population at individual of assessment characterization EUV multi-layer film structure parameter.
Step 9: non-dominated ranking is carried out to the merging population of characterization multilayer film microstructural parameter, to non-dominant individual Then calculate crowding distance.New parent population is filtered out by non-dominated ranking and crowding distance.Return step three, until Reach the evolutionary generation of requirement.
Step 10: by the evolution of NSGA-II, the experimental result for obtaining GIXR the and EUV reflectance spectrum of needle EUV multilayer film is made For the Bi-objective that fitting solves, optimization obtains the non-dominant disaggregation close to the forward position Pareto.
Step 11: residual according to the fitting of two experimental results to the individual of the non-domination solution concentration close to the forward position Pareto The sum of remaining to be assessed, the remaining lesser individual applications Levenberg-Marquart algorithm of selection joint fitting combines two realities It tests result to advanced optimize, selects always to be fitted remaining the smallest individual as the optimal solution of fitting, and obtain the microcosmic knot of multilayer film The error of structure parameter and relevant parameter.Wherein combine the evaluation system of two experimental results based on Levenberg-Marquart algorithm Number is the sum of the evaluation coefficient of two targets in (5) formula, as
For feasibility and high precision of the verifying present invention in terms of EUV multilayer film microstructural parameter solution, difference needle The joint for carrying out Bi-objective based on NSGA-II algorithm to GIXR the and EUV reflectance spectrum of the period Mo/Si multilayer film of experiment test is quasi- It closes, accordingly result is shown in Fig. 3 a- Fig. 3 b.In fig. 3 a, Mo/Si multilayer film theoretical modeling EUV reflectance spectrum and experimental result meet The evaluation coefficient of degreeAnd the evaluation coefficient of the degree of conformity of theoretical modeling GIXR and experimental resultDrilling with evolution simultaneously And then be gradually reduced, i.e., the non-domination solution forward position of Bi-objective is in successive optimization.The EUV reflection with multilayer film is given in Fig. 3 a Spectrum or GIXR are the solving optimization result of single goal, the results showed that, experimental result may be implemented in the fitting solution of simple target Best fit, but inverting is carried out to another experimental result with identical parameter, the result and experimental result deviation of simulation are very big. Fitting optimization while two experimental results, while two fitting knots may be implemented in Bi-objective fitting based on NSGA-II algorithm There is no reciprocal influence between fruit.When evolving to for 500 generation, optimal individual is fitted to EUV reflectance spectrum in non-domination solution forward position Corresponding fitting remnants have been approached it is remaining by the fitting of the optimum solution of single goal of EUV reflectance spectrum；And it is right in non-domination solution forward position The corresponding fitting remnants that GIXR is fitted optimal individual have been approached, this explanation remaining by the fitting of the optimum solution of single goal of GIXR Non-domination solution forward position has been approached the forward position Pareto (the best non-domination solution forward position of Bi-objective) of two fit objects.In order to dock The individual further progress that the non-domination solution in the nearly forward position Pareto is concentrated is preferred, and Fig. 3 b gives every in assessment non-domination solution forward position Fitting remnants the sum of of each and every one body acupuncture to two experimental results.From in Fig. 3 b it can be found that existing in non-domination solution forward position total The remaining lesser excellent individual of fitting.In order to advanced optimize to the remaining lesser excellent individual of total fitting, that is, it is total to reduce it Fitting it is remaining, the present invention use Levenberg-Marquart algorithm with total fitting it is remaining compared with the parameter of excellent individual be first Initial value joint GIXR and EUV reflectance spectrum advanced optimizes, and optimum results are shown in Fig. 4.In Fig. 4, pass through Levenberg- Marquart algorithm is remaining to total fitting of excellent individual to be further decreased, and can be relatively easy to obtain total fitting remnants χ2The smallest individual, the individual parameter are the multilayer film optimum structure parameter that present invention fitting solves.In order to embody the present invention Outstanding advantage in terms of the microcosmic result parameter characterization of multilayer film, by optimum results of the invention and single goal fitting result and It is reported in the literature that optimal parameter is fitted as initial value, using Levenberg-Marquart algorithm to (13) using the single goal of GIXR Result (S.N.Yakunin, I.A.Makhotkin, et.al.Combined EUV the reflectance and that formula optimizes X-ray reflectivity data analysis of periodic multilayer structures,Optics Express, Vol.213079,20076-20086.) it compares and analyzes, concrete outcome is shown in Fig. 5 a- Fig. 5 d.In fig 5 a, with The GIXR of Mo/Si multilayer film is simple target, realizes the best fit of GIXR testing result (in Fig. 5 a using genetic algorithm Dotted line) and corresponding minimum fitting remnants (dotted line in Fig. 5 b), but apply the optimum parameter value of GIXR single goal fitting anti- The EUV reflectance spectrum (dotted line in Fig. 5 c) and the deviation of experimental result drilled are very big.Use Yakunin et al. report with GIXR's It is initial value that single goal, which is fitted optimum parameter value, is carried out using Levenberg-Marquart algorithm to total fitting remnants excellent Change, biggish can improve multilayer film parameters really to the reverse simulation degree (solid line in Fig. 5 c) of EUV reflectance spectrum, but accordingly Cost be that the fitting remnants of GIXR result greatly improve (Fig. 5 b is shown in solid).The reason is that Levenberg- The optimization of Marquart algorithm is higher to the required precision of initial value, and efficient local search optimization, Wu Fashi may be implemented Existing global optimization, and GIXR the and EUV reflectance spectrum of multilayer film there are problems that solving more, and optimization is caused to fall into local optimum Solution.
It can be obtained based on the present invention Bi-objective fitting optimization method obtained based on NSGA-II algorithm close The non-dominant disaggregation in the forward position Pareto has been completed the large range of global search for double fit objects, has utilized Levenberg-Marquart algorithm can get high-precision multilayer to the further optimization for lowering fitting remnants of excellent individual Film microstructural parameter characterization, accordingly result are shown in Fig. 6 a- Fig. 6 d.It is respectively to be based on present invention knot obtained in Fig. 6 a and Fig. 6 b Fitting remnants comparative analysis in the multilayer film GIXR of structure parameter institute inverting and corresponding fitting remnants and Fig. 5 b shows to be based on Although the fitting of Bi-objective fitting algorithm multilayer film parameters obtained is remaining remaining slightly larger than the fitting based on GIXR single goal, But it is substantially better than and is fitted optimum parameter value as initial value, by Levenberg-Marquart algorithm pair using using the single goal of GIXR The fitting of total obtained parameter of the remaining optimization method of fitting is remaining.Meanwhile based on present invention structural parameters inverting obtained EUV reflectance spectrum (Fig. 6 c) and its be fitted remaining (Fig. 6 d) be significantly less than above-mentioned previously reported method for solving fitting it is remaining. 1 is mutually shown in Table with above method multi-layer film structure parameter obtained based on the present invention.It can see from table 1, it is mono- using GIXR The error of the parameter of the multilayer film of target fitting is maximum, and the fitting optimum parameter value of the single goal based on GIXR is initial value The parameter error that Levenberg-Marquart algorithm obtains is close with based on the obtained parameter error precision of the present invention, institute There is the remaining and higher characterization essence of the smallest fitting with the fitting result of the multilayer film parameters obtained based on solution required by the present invention Degree, and solve the problems, such as more solutions in multilayer film characterization problems.
1. period of table Mo/Si multilayer film fitting result
The characterized with good accuracy method of EUV multilayer film microstructure given by the present invention is applicable not only to the embodiment of the present invention The structural characterization of the Mo/Si multilayer film discussed applies also for what Rh/Si, Ni/C, Ru/C etc. were alternately made of two kinds of materials The characterization of the microstructure of EUV multilayer film.
It should be appreciated that the above is only a specific embodiment of the invention, it is noted that for the general of the art For logical technical staff, various improvements and modifications may be made without departing from the principle of the present invention, these improve and Retouching also should be regarded as protection scope of the present invention.

Claims (8)

1.基于双目标遗传算法的极紫外多层膜高精度表征方法，其特征在于，该方法包括如下步骤：1. the EUV multilayer film high-precision characterization method based on dual-target genetic algorithm, is characterized in that, the method comprises the steps: 步骤一：输入基于适用于等周期极紫外多层膜参数求解的NSGA-II的初始参数值，包括种群规模N、基于四层模型的多层膜微观结构的参数个数、变异概率pm、交叉概率pc、交叉算子ηc和变异算子ηp、进化的代数j以及基于四层模型的多层膜微观结构的各参数搜索范围；Step 1: Input the initial parameter values based on NSGA-II, which is suitable for solving the parameters of the constant-period EUV multilayer film, including the population size N, the number of parameters of the multilayer film microstructure based on the four-layer model, the variation probability p m , Crossover probability p c , crossover operator η c and mutation operator η p , evolutionary algebra j and the search range of each parameter of the multilayer film microstructure based on the four-layer model; 步骤二：基于极紫外多层膜的四层模型生成适用于NSGA-II进化的初始父代种群Q，种群Q可表示为Step 2: Generate the initial parent population Q suitable for NSGA-II evolution based on the four-layer model of EUV multilayer film, and the population Q can be expressed as Q＝[a1,a2,a3,…,ai,…,aN-1,aN] (1)Q=[a 1 ,a 2 ,a 3 ,...,a i ,...,a N-1 ,a N ] (1) 以Mo/Si多层膜为例，种群中个体的基因参数为Taking the Mo/Si multilayer film as an example, the genetic parameters of the individuals in the population are 其中tSi为Si层的膜厚、tMo为Mo层的膜厚、tMoonSi为Mo层在Si层上的扩散层厚度、t为Mo/Si多层膜的平均周期厚度、σ为膜层间的界面粗糙度、ρSi为Si膜层的密度、ρMo为Mo膜层的密度、ρMoSi2为Mo层和Si层之间扩散层的密度；where t Si is the film thickness of the Si layer, t Mo is the film thickness of the Mo layer, t MoonSi is the thickness of the diffusion layer of the Mo layer on the Si layer, t is the average period thickness of the Mo/Si multilayer film, and σ is the film thickness The interface roughness between the two, ρ Si is the density of the Si film layer, ρ Mo is the density of the Mo film layer, ρ MoSi2 is the density of the diffusion layer between the Mo layer and the Si layer; 步骤三：计算表征极紫外多层膜微观结构参数的父代种群中每个个体的适应度，适应度包括两个，其中第一个适应度为个体的GIXR理论模拟结果与极紫外多层膜实验结果的符合度，而第二个适应度为个体的EUV反射谱的理论模拟结果与极紫外多层膜的实验结果的符合度；Step 3: Calculate the fitness of each individual in the parent population that characterizes the microstructural parameters of the EUV multilayer film. The fitness includes two, the first fitness is the individual's GIXR theoretical simulation result and the EUV multilayer film. The degree of agreement of the experimental results, and the second fitness is the degree of agreement between the theoretical simulation results of the individual EUV reflectance spectrum and the experimental results of the EUV multilayer film; 步骤四：对表征极紫外多层膜微观结构参数的种群中的个体进行非支配排序，得到种群中个体的支配排序，同时，对非支配个体采用拥挤度距离进一步排序；Step 4: Perform non-dominated sorting on the individuals in the population representing the microstructural parameters of the EUV multilayer film to obtain the dominant ranking of the individuals in the population, and at the same time, further sort the non-dominated individuals by crowding degree distance; 步骤五：采用轮赛选择机制，对种群中的个体进行交叉操作，以此生成表征极紫外多层膜微观结构参数的子代种群，在交叉操作过程中，要求对个体的全部参数基因进行操作；Step 5: Use the round-robin selection mechanism to perform crossover operations on the individuals in the population, so as to generate a progeny population representing the microstructural parameters of the EUV multilayer film. During the crossover operation, all parameter genes of the individuals are required to be operated. ; 步骤六：采用变异机制，进一步更新表征多层膜微观结构参数的子代种群；Step 6: Use the mutation mechanism to further update the progeny population that characterizes the microstructural parameters of the multilayer film; 步骤七：对表征极紫外多层膜微观结构参数的父代种群和子代种群进行合并；Step 7: Merge the parent and child populations that characterize the microstructural parameters of the EUV multilayer film; 步骤八：评估表征极紫外多层膜结构参数的合并种群个体的双目标适应度；Step 8: Evaluate the dual-objective fitness of the combined population individuals characterizing the structural parameters of the EUV multilayer film; 步骤九：对表征极紫外多层膜微观结构参数的合并种群进行非支配排序，对非支配个体则计算拥挤度距离，并通过非支配排序和拥挤度距离筛选出新的父代种群，返回步骤三，直到达到要求的进化代数；Step 9: Perform non-dominated sorting on the combined population representing the microstructural parameters of the EUV multilayer film, calculate the crowding degree distance for the non-dominated individuals, and screen out the new parent population through the non-dominated sorting and crowding degree distance, and return to step Three, until the required evolutionary algebra is reached; 步骤十：通过NSGA-II的进化，获得针极紫外多层膜的GIXR和EUV反射谱的实验结果作为拟合求解的双目标，优化获得接近Pareto前沿的非支配解集；Step 10: Through the evolution of NSGA-II, the experimental results of the GIXR and EUV reflectance spectra of the needle extreme ultraviolet multilayer film are obtained as the dual objectives of the fitting solution, and the non-dominated solution set close to the Pareto front is obtained by optimization; 步骤十一：对接近Pareto前沿的非支配解集中的个体依据两个实验结果的拟合残余之和进行评估，选择联合拟合残余较小的个体应用Levenberg-Marquart算法联合两个实验结果进一步优化，选择总拟合残余最小的个体为拟合的最优解，进而求得极紫外多层膜的微观结构参数和相应参数的误差。Step 11: Evaluate the individuals in the non-dominated solution set close to the Pareto front according to the sum of the fitting residuals of the two experimental results, select the individual with the smaller joint fitting residual, and apply the Levenberg-Marquart algorithm to combine the two experimental results for further optimization , the individual with the smallest total fitting residual is selected as the optimal solution of fitting, and then the microstructural parameters of EUV multilayer films and the errors of corresponding parameters are obtained. 2.根据权利要求1所述的基于双目标遗传算法的极紫外多层膜高精度表征方法，其特征在于，在所述步骤一的过程中，种群规模N为50-200；变异概率pm为0.1-1.0；交叉概率pc为0.1-1.0；交叉算子ηc为1-50；变异算子ηp为1-50；进化的代数j为300-500。2. The method for high-precision characterization of EUV multilayer films based on a dual-target genetic algorithm according to claim 1, wherein in the process of step 1, the population size N is 50-200; the mutation probability p m is 0.1-1.0; the crossover probability p c is 0.1-1.0; the crossover operator η c is 1-50; the mutation operator η p is 1-50; the evolutionary algebra j is 300-500. 3.根据权利要求2所述的基于双目标遗传算法的极紫外多层膜高精度表征方法，其特征在于，在所述步骤一的过程中，种群规模N为100；变异概率pm为0.1；交叉概率pc为0.9；交叉算子ηc为2；变异算子ηp为2；进化的代数j为500。3. The method for high-precision characterization of EUV multilayer films based on a dual-target genetic algorithm according to claim 2, wherein in the process of step 1, the population size N is 100; the mutation probability p m is 0.1 The crossover probability p c is 0.9; the crossover operator η c is 2; the mutation operator η p is 2; the evolutionary algebra j is 500. 4.根据权利要求1所述的基于双目标遗传算法的极紫外多层膜高精度表征方法，其特征在于，在所述步骤二的过程中，考虑多层膜的物理和化学性质，等周期Mo/Si多层膜周期内微观结构参数的约束条件为4. The method for high-precision characterization of EUV multilayer films based on a dual-target genetic algorithm according to claim 1, wherein in the process of the second step, the physical and chemical properties of the multilayer films are considered, and the periodic The constraints on the microstructural parameters of Mo/Si multilayer films in the period are as follows: 5.根据权利要求1所述的基于双目标遗传算法的极紫外多层膜高精度表征方法，其特征在于，在所述步骤三的过程中，双目标适应度的评价函数为5. the high-precision characterization method of EUV multilayer film based on dual-objective genetic algorithm according to claim 1, is characterized in that, in the process of described step 3, the evaluation function of dual-objective fitness is 其中为理论反演结果相对极紫外多层膜EUV反射谱实验结果的评价系数，为理论反演结果相对极紫外多层膜GIXR实验结果的评价系数；Rc和Rm分别为理论模拟和实验测量的EUV反射率；Ic和Im分别为理论模拟和实验测量的掠入射X射线反射强度，而σm为相应实验点的测量误差的标准差。in is the evaluation coefficient of the theoretical inversion results relative to the experimental results of EUV reflectance spectra of EUV multilayer films, are the evaluation coefficients of the theoretical inversion results relative to the GIXR experimental results of EUV multilayer films; R c and R m are the EUV reflectivity of theoretical simulation and experimental measurement, respectively; I c and I m are the grazing incidence of theoretical simulation and experimental measurement, respectively X-ray reflection intensity, and σ m is the standard deviation of the measurement error at the corresponding experimental point. 6.根据权利要求1所述的基于双目标遗传算法的极紫外多层膜高精度表征方法，其特征在于，在所述步骤六的过程中，在变异操作中，仅对表征多层膜微观结构参数的个体的单基因进行变异操作。6. The method for high-precision characterization of EUV multilayer films based on a dual-target genetic algorithm according to claim 1, characterized in that, in the process of step 6, in the mutation operation, only the microscopic characterization of multilayer films is performed. Individual genes of structural parameters were subjected to mutation operations. 7.根据权利要求1所述的基于双目标遗传算法的极紫外多层膜高精度表征方法，其特征在于，在所述步骤六的过程中，代种群和子代种群进行合并过程中，采用对比机制将合并种群中的个体逐一进行对比，对于完全相同的个体，保留其一，而对另一个个体进行随机的基因参数赋值。7. The method for high-precision characterization of EUV multilayer films based on dual-target genetic algorithm according to claim 1, characterized in that, in the process of the step 6, in the process of merging the generation population and the descendant population, using contrast The mechanism compares the individuals in the merged population one by one, retains one of the identical individuals, and assigns random gene parameter assignments to the other individual. 8.根据权利要求1所述的基于双目标遗传算法的极紫外多层膜高精度表征方法，其特征在于：所述极紫外多层膜包括Mo/Si、Rh/Si、Ni/C、Ru/C中的任一组合或两个以上组合交替构成的极紫外多层膜。8. The high-precision characterization method for EUV multilayer films based on dual-target genetic algorithm according to claim 1, wherein the EUV multilayer films comprise Mo/Si, Rh/Si, Ni/C, Ru An extreme ultraviolet multilayer film composed of any combination or two or more combinations of /C alternately.
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