CN106990528A - Multiplayer films in EUV characterized with good accuracy method based on double object genetic algorithm - Google Patents

Abstract

The invention discloses a kind of multiplayer films in EUV characterized with good accuracy method based on double object genetic algorithm, this method combines fitting by the non-dominated sorted genetic algorithm (NSGA II) of real coding to be applied to the grazing incidence X-ray reflectivity spectrums of EUV multilayer films with the experimental result of EUV reflectance spectrums.The grazing incidence X-ray reflectivity of EUV multilayer films is composed into the optimization aim with EUV reflectance spectrums as double object genetic algorithm, evolution obtains the non-dominant disaggregation close to Pareto forward positions, concentrate the remaining less excellent individual of the fitting of two fit objects further to optimize to non-domination solution using Levenberg Marquart algorithms, obtain two remaining minimum optimum structure parameters of fit object fitting.The present invention solves the problems, such as many solutions being fitted based on single goal during (grazing incidence X-ray reflectivity is composed or EUV reflectance spectrums) solves, and avoid by two fit objects simply plus with joint fitting solve when, influenced each other between target, or even seriously tend to one of target and cause the problem of multilayer film Microstructure characterization precision is not high.

Description

Multiplayer films in EUV characterized with good accuracy method based on double object genetic algorithm

Technical field

EUV needed for the multi-layer mirror used present invention relates particularly to one kind in extreme ultraviolet (EUV) photoetching technique The characterized with good accuracy method of multilayer film microstructure.

Background technology

EUV lithography technology is considered as to meet semiconductor industry demand, most promising Next Generation Lithography.But EUV wave bands, almost all of material is all opaque, and refractive index closely 1, so EUV optical systems can not be used Traditional refraction optical element, and reflective optical system must be used.Therefore, the multilayer film of EUV light high reflectances is realized Core optical element as EUV optical systems, meanwhile, EUV multilayer films also turn into EUV optical fields science and technology research and development focus with Core, by the common concern of domestic and international research team.

The material that EUV multilayer films obtain high reflectance is different with the optical wavelength difference that optical system is used, with light Wavelength is concentrated on exemplified by the exposure optical system of 13.5nm scopes, is gradually superimposed using molybdenum (Mo) layer and silicon (Si) layer more than multilayer film Mo/Si multilayer films, the multilayer film can realize 65%~68% reflectivity for the EUV light of vertical normal incidence.Although, The higher EUV multilayer films of reflectivity can be experimentally developed, but because EUV multilayer films are the complex bodies of a structure System, the characterized with good accuracy of its microstructure still suffers from higher difficulty, and only realize the microstructure of EUV multilayer films Characterized with good accuracy, could realize the preferred offer theoretical foundation of multilayer membrane process, and setting for complicated aperiodic EUV multilayer films Meter provides necessary theoretical calculation parameter.Research and analyse and show, the reason for EUV multilayer film Microstructure characterization difficulty is higher has three Aspect：(1) there is diffusion between multilayer film film layer, and the thickness of diffusion layer is only nm magnitudes.It is many by taking Mo/Si multilayer films as an example The Diffusion barrier layer of tunic is generally the MoSi for the generation that chemically reacted between Mo layers and Si layers₂Film, its thickness is between 1-3nm； (2) interface roughness between multilayer film film layer is difficult to carry out accurate Characterization, and interface roughness exists to 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 to carry out direct measurement.

To realize sign and the analysis of Mo/Si multilayer film microstructures, generally used in the context of detection of EUV multilayer films The fitting that method has grazing incidence X-ray reflectivity (GIXR) spectrum is solved, the fitting of EUV reflectance spectrums is solved and transmission electron microscope (TEM) detection method such as observation.In the above-mentioned methods, GIXR is a kind of lossless high-precision detecting method, but shortcoming is this The signal noise of detection is larger, and the parameter that the nonlinear fitting needed for theoretical model is solved is more, and the hard X that GIXR is used Ray is insensitive the physical characteristic of the diffusion layer multilayer film film layer；The noise of EUV reflectance spectrums is smaller, but waits periodic multilayer film Spectral reflectance curve it is relatively simple, it is difficult to pass through its fitting solve obtain multilayer film high-precision configuration parameter information；TEM side Although method directly can be observed to multilayer film film layer structure, this method is a kind of destructive detection method, and it characterizes essence Degree is not high, generally as the reference of multilayer film Microstructure characterization.

The content of the invention

To solve problem present in existing EUV multilayer films microstructure characterized with good accuracy, the invention provides a kind of base 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 spectrums of cycle EUV multilayer film, are solved and evolved by the fitting of double object genetic algorithm, obtain precision compared with The microstructural parameter of high multiplayer films in EUV, is solved in the past based on (GIXR or the EUV reflection of multilayer film of single testing result Spectrum) the sign precision that has it is not high the problem of.

The technical proposal for solving the technical problem of the invention is as follows：

EUV multilayer film characterized with good accuracy methods based on double object genetic algorithm, comprise the following steps：

Step one：Input the initial parameter value based on the NSGA-II suitable for waiting cycle EUV multilayer film parametric solution, bag Include population scale N, the number of parameters of multilayer film microstructure based on four layer models, mutation probability p_m, crossover probability p_c, intersect Operator η_cWith mutation operator η_p, the algebraically evolved and each parameter of multilayer film microstructure based on four layer models hunting zone；

Step 2：The initial parent population Q that four layer models generation NSGA-II based on EUV multilayer films evolves, population Q can It is expressed as

Q=[a₁,a₂,a₃,…,a_i,…,a_N-1,a_N]。 (1)

By taking Mo/Si multilayer films as an example, the gene parameter of each individual is 8 in population, and it is expressed as follows

Wherein t_siFor Si layers of thickness, t_MoFor Mo layers of thickness, t_{Mo on Si}For Mo layers of thickness of diffusion layer, the t on Si layers For Mo/Si multilayer films average period thickness, σ be roughness between film layer, ρ_siFor the density of Si film layers, ρ_MoFor Mo film layers Density, ρ_MoSi2For the 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, the constraints for waiting microstructural parameter in the cycle of cycle Mo/Si multilayer film is

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 modelings result of individual and the degree of conformity of multilayer film experimental result, second Fitness for individual EUV reflectance spectrums theoretical modeling result and multilayer film experimental result degree of conformity.

Step 4：The individual in population to characterizing multilayer film microstructural parameter carries out non-dominated ranking, obtains population Middle individual dominated Sorting, meanwhile, to non-dominant individual using the further sequence of crowding distance.

Step 5：Selection mechanism is matched using wheel, crossover operation is carried out to the individual in population, sign multilayer film is generated with this The progeny population of microstructural parameter.During crossover operation, it is desirable to which whole parameter genes to individual are operated.

Step 6：Using Variation mechanism, the progeny population for characterizing multilayer film microstructural parameter is further updated.In variation In operation, row variation only is entered to the individual single-gene for characterizing multilayer film microstructural parameter, new filial generation is ultimately generated with this Population.

Step 7：The parent population and progeny population for characterizing multilayer film microstructural parameter are merged, and use pair The individual merged in population is contrasted one by one than mechanism, for identical individual, reservation first, and to it is another each and every one Body carries out new parameter gene assignment.

Step 8：Assess the Bi-objective fitness for the merging population at individual for characterizing EUV multi-layer film structure parameters.

Step 9：Non-dominated ranking is carried out to the merging population for characterizing 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 to step three, until Reach the evolutionary generation of requirement.

Step 10：By NSGA-II evolution, the experimental result for obtaining GIXR the and EUV reflectance spectrums of pin EUV multilayer films is made The Bi-objective solved for fitting, optimization obtains the non-dominant disaggregation close to Pareto forward positions.

Step 11：It is residual according to the fitting of two experimental results to the individual of the non-domination solution concentration close to Pareto forward positions Remaining sum is estimated, and selection is always fitted remaining less individual applications Levenberg-Marquart (LM) algorithm and combines two Experimental result further optimizes and reduced total fitting remnants, and tries to achieve multilayer according to total remaining minimum individual of fitting The microstructural parameter of film and the error of fitting of relevant parameter.

Than prior art, the present invention at least has the advantages that：

(1) solution of EUV multilayer film microstructures in the past, makees only with GIXR or EUV reflectance spectrums of periodic multilayer film are waited It is fitted for simple target, and the present invention will wait GIXR the and EUV reflectance spectrums of cycle EUV multilayer film based on NSGA-II algorithms Experimental result carries out joint fitting as Bi-objective and solved；

(2) present invention incorporates the strong point that the GIXR and EUV reflectance spectrums of cycle EUV multilayer film are detected, GIXR experiment knot Fruit is more sensitive to the thicknesses of layers of multilayer film；The signal errors of EUV reflectance spectrums is smaller and interface roughness to multilayer film and Top layer roughness is more sensitive.So, the sign of the EUV multilayer film microstructures of the achievable degree of precision of the present invention；

(3) generally, the multi-layer film structure parametric inversion that the GIXR single goals based on cycle EUV multilayer film are solved EUV reflectance spectrums are very big with experimental result difference；And the multilayer film that the EUV reflectance spectrums single goal based on cycle EUV multilayer film is solved The GIXR of structural parameters inverting is equally very big with experimental result difference.By comparison, the present invention is fitted what is solved based on NSGA-II Multi-layer film structure parameter, GIXR the or EUV reflectance spectrums of inverting all have with experimental result preferably to be met.

Brief description of the drawings

Fig. 1 is the membrane system schematic diagram of the cycle Mo/Si multilayer film of four layer models in exemplary embodiments of the present invention.Mo/Si is more Tunic was 60.5 cycles, and its membrane system is Sub [Si/MoSi₂/Mo/MoSi₂]₆₀Si/SiO₂/Air.Wherein 1 is ultra-smooth substrate；2 For Si film layers；3 be MoSi of the Mo film layers in Si film layers₂Diffusion layer；4 be Mo layers；5 be MoSi of the Si film layers in Mo film layers₂Expand Dissipate layer；6 SiO formed by top layer Si film layer due to the oxidation of environment₂Film layer.

Fig. 2 is that NSGA-II algorithms are based in exemplary embodiments of the present invention, anti-with the GIXR and EUV of cycle Mo/Si multilayer film It is fitting Bi-objective to penetrate the experimental result of spectrum, solves the flow chart of multilayer film microstructural parameter.

Fig. 3 a are using GIXR the and EUV reflectance spectrums of cycle Mo/Si multilayer film as the double of fitting in exemplary embodiments of the present invention Target, based on NSGA-II algorithms, 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 spectrums as single goal, using the optimum individual obtained after GA 500 generations of evolution.

Fig. 3 b are that NSGA-II algorithms are based in exemplary embodiments of the present invention, before the non-domination solution obtained after being evolved through 500 generations Total fitting of the solution to being fitted Bi-objective in edge and non-domination solution forward position is remaining.

Fig. 4 is the remaining less excellent individual application of total fitting for Bi-objective in invention exemplary embodiments The result that Levenberg-Marquart algorithms joint Bi-objective further optimizes, wherein the remaining minimum individual quilt of overall fitting It is considered as optimal solution.

Fig. 5 a- Fig. 5 d be respectively in exemplary embodiments of the present invention using GIXR as the simple target of fitting, what optimization was obtained GIXR the and EUV reflectance spectrums of multi-layer film structure parametric inversion；And using the multilayer film parameters of GIXR single object optimizations as initial value, Combine the fitting of GIXR and EUVR reflectance spectrums using Levenberg-Marquart algorithms and obtain the inverting of multi-layer film structure parameter institute The fitting of accordingly result and accordingly result is remaining.

Fig. 6 a- Fig. 6 d are 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 spectrums and corresponding fitting.

Embodiment

As it was previously stated, in view of the deficiencies in the prior art, the present invention proposes a kind of extremely purple based on double object genetic algorithm 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 films Reflectance spectrum (GIXR) and EUV reflectance spectrums are fitted solution to multilayer film microstructure, realize the high-precision of multilayer film microstructure Degree is characterized.

Specifically, the high-precision table of a kind of EUV multilayer films based on double object genetic algorithm provided in an embodiment of the present invention The method of levying comprises the following steps：

Step one：Input the initial parameter value based on the NSGA-II suitable for waiting cycle EUV multilayer film parametric solution, bag Include population scale N, the number of parameters of multilayer film microstructure based on four layer models, mutation probability p_m, crossover probability p_c, intersect Operator η_cWith mutation operator η_p, the algebraically j that evolves and multilayer film microstructure based on four layer models each parameter search model Enclose；

Step 2：Four layer models generation based on EUV multilayer films is applied to the initial parent population Q that NSGA-II evolves, and plants Group Q is represented by

Q=[a₁,a₂,a₃,…,a_i,…,a_N-1,a_N]。 (1)

By taking Mo/Si multilayer films as an example, individual gene parameter is in population

Wherein t_SiFor Si layers of thickness, t_MoFor Mo layers of thickness, t_{Mo on Si}For Mo layers of thickness of diffusion layer, the t on Si layers For Mo/Si multilayer films average period thickness, σ be interface roughness, ρ between film layer_SiFor the density of Si film layers, ρ_MoFor Mo films The density of layer, ρ_MoSi2For the density of diffusion layer between Mo layers and Si layers (or between Si layers and Mo layers)；

Step 3：The fitness of each individual, is adapted in the parent population of computational representation EUV multilayer film microstructural parameters Degree includes two, wherein first fitness is the GIXR theoretical modelings result of individual and meeting for EUV multilayer film experimental results Degree, and the theoretical modeling result of EUV reflectance spectrum and the meeting of the experimental result of EUV multilayer film of second fitness for individual Degree；

Step 4：The individual in population to characterizing EUV multilayer film microstructural parameters carries out non-dominated ranking, is planted Individual dominated Sorting in group, meanwhile, to non-dominant individual using the further sequence of crowding distance；

Step 5：Selection mechanism is matched using wheel, crossover operation is carried out to the individual in population, it is more to generate sign EUV with this The progeny population of tunic microstructural parameter, during crossover operation, it is desirable to which whole parameter genes to individual are operated；

Step 6：Using Variation mechanism, the progeny population for characterizing multilayer film microstructural parameter is further updated；

Step 7：The parent population and progeny population for characterizing EUV multilayer film microstructural parameters are merged；

Step 8：Assess the Bi-objective fitness for the merging population at individual for characterizing EUV multi-layer film structure parameters；

Step 9：Non-dominated ranking is carried out to the merging population for characterizing EUV multilayer film microstructural parameters, to non-dominant Body then calculates crowding distance, and filters out by non-dominated ranking and crowding distance new parent population, return to step three, Evolutionary generation until reaching requirement.

Step 10：By NSGA-II evolution, the experimental result for obtaining GIXR the and EUV reflectance spectrums of pin EUV multilayer films is made The Bi-objective solved for fitting, optimization obtains the non-dominant disaggregation close to Pareto forward positions；

Step 11：It is residual according to the fitting of two experimental results to the individual of the non-domination solution concentration close to Pareto forward positions Remaining sum is estimated, and the remaining less individual applications Levenberg-Marquart algorithms of selection joint fitting combine two realities Test result further to optimize, the total optimal solution for being fitted remaining minimum individual for fitting of selection, and then try to achieve the micro- of EUV multilayer films See the error of structural parameters and relevant parameter.

Further, during the step one, population scale N is 50-200, and population scale preferably is 100； Mutation probability p_mFor 0.1-1.0, preferably mutation probability 0.1；Crossover probability p_cFor 0.1-1.0, preferably crossover probability is 0.9；Intersect Operator η_cFor 1-50, crossover operator preferably is 2；Mutation operator η_pFor 1-50, mutation operator preferably is 2；The algebraically j of evolution For 300-500, algebraically j preferably is 500.

Further, during the step 2, it is considered to the physics and chemical property of multilayer film, cycle Mo/Si is waited The constraints of microstructural parameter is in the multilayer film cycle

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 results,For theory Evaluation coefficient of the inversion result with respect to EUV multilayer film GIXR experimental results；R_cAnd R_mRespectively theoretical modeling and experiment are measured EUV reflectivity；I_cAnd I_mThe grazing incidence X-ray reflectivity light intensity that respectively theoretical modeling and experiment are measured, and σ_mFor corresponding experimental point Measurement error standard deviation.

Further, during the step 6, in mutation operation, only to characterizing 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 contrast Mechanism is contrasted the individual merged in population one by one, for identical individual, is retained first, and to another individual Enter row stochastic gene parameter assignment.

Further, the EUV multilayer films include any combination or two or more in Mo/Si, Rh/Si, Ni/C, Ru/C The EUV multilayer films that combined and alternatively is constituted, and not limited to this.

The present invention is described in further detail with example below in conjunction with the accompanying drawings.

NSGA-II is applied among cycle Mo/Si multilayer film Microstructure characterization by the embodiment of the present invention, by the cycle GIXR the and EUV reflectance spectrums joint fitting of Mo/Si multilayer films is solved, and obtains the characterized with good accuracy of multilayer film microstructural parameter, Solve the problems, such as the problem of the simple target fitting solving precision caused by many solutions is relatively low.In order that the multilayer of theoretical simulation Film microstructure more conforms to reality, and four layer models are used in the single cycle of multilayer film, that is, considers Mo film layers and Si film layers Between material phase counterdiffusion, and by diffusion layer with MoSi₂Film layer is simulated, and concrete structure is as shown in Figure 1.The present invention's In embodiment, Mo/Si multilayer films totally 60.5 cycles.In theoretical simulation process, Si and Mo atomic scattering factor parameter are come Lawrence Berkeley National Laboratory databases are come from, and using the complex refractivity index n of following formula calculating material =(1- δ)-i β, wherein

Wherein r_e、N_A, M and ρ be respectively the classical radius of electronics, Avogadro constant number, material relative atomic mass and material Density, while X_iFor corresponding atomic ratio, and f ' and f " is the atomic scattering factor provided in database.

The method that cycle Mo/Si multilayer film microstructural parameter is solved based on Bi-objective is further illustrated with reference to Fig. 2, specifically Implementation steps are as follows：

Step one：Input is applied to wait the NSGA-II of cycle EUV multilayer film parametric solution initial parameter value.Wherein wrap Include population scale N, mutation probability p_m, crossover probability p_c, crossover operator η_cWith mutation operator η_p, the algebraically 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 scope of each parameter.Wherein, population scale N is 50- 200, population scale preferably is 100；Mutation probability p_mFor 0.1-1.0, preferably mutation probability 0.1；Crossover probability p_cFor 0.1- 1.0, preferably crossover probability is 0.9；Crossover operator η_cFor 1-50, crossover operator preferably is 2；Mutation operator η_pFor 1-50, preferably Mutation operator be 2；The algebraically j of evolution is 300-500, and algebraically j preferably is 500.

Step 2：The Mo/Si multilayer film microstructural parameters based on four layer models are characterized, and are calculated suitable for NSGA-II The population Q of method initialization.Population Q is represented by

Q=[a₁,a₂,a₃,…,a_i,…,a_N-1,a_N], (2)

By taking Mo/Si multilayer films as an example, the gene parameter of each individual is 8 in population, and it is expressed as follows

Wherein Si layers of thickness t_Si, Mo layers of thickness t_Mo, the Mo layers of thickness of diffusion layer t on Si layers_{Mo on Si}, Mo/Si it is many Tunic average period thickness t, the density p of roughness σ, Si film layer between film layer_si, Mo film layers density p_Mo, Mo layers and Si layers Between (or between Si layers and Mo layers) diffusion layer density p_MoSi2.Consider physics, chemical property and the experiment experience of multilayer film, week The constraints 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 Including two：First fitness is the EUV reflectance spectrums and multilayer film experimental result of the parameter theory simulation characterized according to individual Degree of conformity；Second fitness is the GIXR of parameter theory simulation and meeting for multilayer film experimental result characterized according to individual Degree.The evaluation function of two degrees of conformity is respectively

WhereinFor the evaluation coefficient of theoretical inversion result opposing layers film EUV reflectance spectrum experimental results,It is anti-for theory Drill the evaluation coefficient of result opposing layers film GIXR experimental results, R_cAnd R_mThe respectively EUV reflections of theoretical modeling and experiment measurement Rate；I_cAnd I_mThe grazing incidence X-ray reflectivity intensity that respectively theoretical modeling and experiment are measured, and σ_mFor the measurement of corresponding experimental point The standard deviation of error.In (5) formula, theoretical reflectance rate R_cWith reflected intensity I_cIn the present invention using based on Fresnel coefficient Method is calculated, and the reflectance factor in multilayer film between+1 layer of jth layer and jth is

For s polarised lights, q_j=n_jcosθ_j；And for p-polarization light,Jth layer reflected amplitude be

WhereinFor interface roughness between film layer, in the present invention using Nevot the and Croce factors come Reflectance factor in (6) formula is modified, can be obtained

In above-mentioned (6) formula into (8) formula, λ is the optical wavelength of incident light, n_j、θ_j、t_jAnd σ_jJth layer respectively in multilayer film Refractive index, incidence angle, thickness and interface roughness.Simultaneously in (5) formula,That is φ_iFor glancing incidence angles. For the Mo/Si multilayer films being coated with ultra-smooth substrate, it is believed that substrate is the medium of infinite thickness, therefore makes r₀=0, and then adopt The reflected amplitude r of the multilayer film the superiors (multilayer film is common m layers) is calculated with the recursive iteration method based on (7) formula_m.Thus, multilayer The reflectivity of the film the superiors is

R=| r_m|²。 (9)

It is emphasized that in the present invention, the reflectivity in the calculating process of the EUV reflectance spectrums of Mo/Si multilayer films is with ripple Long λ is independent variable, and in the GIXR of multilayer film calculating process, reflectivity is with grazing angle φ_iFor independent variable, and GIXR Reflected intensity is

I=I₀·R+I_background。 (10)

I in above formula₀For incident intensity, I_backgroundFor background intensity.

Step 4：It is non-that the individual in population to characterizing multilayer film microstructural parameter is based on two evaluation function values progress Dominated Sorting.To dominated Sorting individual in population, and for non-dominant individual using the further sequence of crowding distance.

Step 5：Selection mechanism is matched using wheel, crossover operation is carried out to the individual parameter in population, generation characterizes EUV The progeny population of multilayer film microstructural parameter.In crossover operation in the present invention, it is desirable to characterize structural parameters to individual Full gene carries out the crossover operation between two individuals.

Step 6：Using mutation operation, the progeny population for characterizing multilayer film microstructural parameter is further updated.In variation In operation, row variation only is entered to the gene that multilayer film microstructural parameter is characterized in individual, filial generation is further updated 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 for characterizing multilayer film microstructural parameter are merged.Merge laggard The each individual merged in population and other individuals are carried out gene pairs ratio by row contrast operation.For identical individual, protect Stay first, and the gene assignment new to another progress.Then merging population is

Q ∪ Q '=[a₁,a₂,a₃,…,a_i,…,a_N-1,a_N,a′₁,a′₂,a′₃,…,a′_i,…,a′_N-1,a′_N]。 (12)

Step 8：Assess the Bi-objective fitness for the merging population at individual for characterizing EUV multi-layer film structure parameters.

Step 9：Non-dominated ranking is carried out to the merging population for characterizing 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 to step three, until Reach the evolutionary generation of requirement.

Step 10：By NSGA-II evolution, the experimental result for obtaining GIXR the and EUV reflectance spectrums of pin EUV multilayer films is made The Bi-objective solved for fitting, optimization obtains the non-dominant disaggregation close to Pareto forward positions.

Step 11：It is residual according to the fitting of two experimental results to the individual of the non-domination solution concentration close to Pareto forward positions Remaining sum is estimated, and the remaining less individual applications Levenberg-Marquart algorithms of selection joint fitting combine two realities Test result further to optimize, the total optimal solution for being fitted remaining minimum individual for fitting of selection, 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 algorithms Number is the evaluation coefficient sum of two targets in (5) formula, is

It is feasibility and high precision of the checking present invention in terms of EUV multilayer film microstructural parameter solutions, difference pin GIXR the and EUV reflectance spectrums of the cycle Mo/Si multilayer film of experiment test are intended based on the joint that NSGA-II algorithms carry out Bi-objective Close, accordingly result is shown in Fig. 3 a- Fig. 3 b.In fig. 3 a, Mo/Si multilayer films theoretical modeling EUV reflectance spectrums and experimental result meet The evaluation coefficient of degreeAnd the evaluation coefficient of the degree of conformity of theoretical modeling GIXR and experimental resultWhile drilling with evolution And then be gradually reduced, i.e., the non-domination solution forward position of Bi-objective is in successive optimization.The EUV reflections with multilayer film are given in Fig. 3 a Spectrum or the solving-optimizing result that GIXR is single goal, as a result show, the fitting of simple target, which is solved, can realize experimental result 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 Bi-objective fitting based on NSGA-II algorithms can realize two experimental results, while two fitting knots There is no reciprocal influence between fruit.When evolving to for 500 generation, optimal individual is fitted in non-domination solution forward position to EUV reflectance spectrums Corresponding fitting it is remaining remaining close to the fitting using EUV reflectance spectrums as the optimum solution of single goal；And it is right in non-domination solution forward position The optimal individual corresponding fitting of GIXR fittings is remaining remaining close to the fitting using GIXR as the optimum solution of single goal, this explanation Non-domination solution forward position is close to the Pareto forward positions (the optimal non-domination solution forward position of Bi-objective) of two fit objects.In order to dock Further progress is preferred for the individual that the non-domination solution in nearly Pareto forward positions is concentrated, and Fig. 3 b give every in assessment non-domination solution forward position The remaining sum of fitting of each and every one body acupuncture to two experimental results.It can be found that existing always in non-domination solution forward position from Fig. 3 b It is fitted remaining less excellent individual.In order to further optimize to the remaining less excellent individual of total fitting, that is, reduce its total Fitting it is remaining, the present invention use Levenberg-Marquart algorithms to be first compared with the parameter of excellent individual using total fitting remnants Initial value joint GIXR and EUV reflectance spectrums further optimize, and optimum results are shown in Fig. 4.In Fig. 4, Levenberg- is passed through The remaining further reduction of total fitting of the Marquart algorithms to excellent individual, and can be relatively easy to obtain total fitting remnants χ²Minimum individual, the individual parameter is the multilayer film optimum structure parameter that present invention fitting is solved.In order to embody the present invention Outstanding advantage in terms of the microcosmic result parameter sign of multilayer film, by optimum results and the single goal fitting result of the present invention and The single goal using GIXR of document report is fitted optimal parameter as initial value, using Levenberg-Marquart algorithms to (13) Result (S.N.Yakunin, I.A.Makhotkin, et.al.Combined EUV the reflectance and that formula is optimized X-ray reflectivity data analysis of periodic multilayer structures,Optics Express, Vol.213079,20076-20086.) it is analyzed, concrete outcome is shown in Fig. 5 a- Fig. 5 d.In fig 5 a, with The GIXR of Mo/Si multilayer films is simple target, and the best fit of GIXR testing results is realized (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 goals fitting anti- The EUV reflectance spectrums (dotted line in Fig. 5 c) and the deviation of experimental result drilled are very big.Use Yakunin et al. report with GIXR's Single goal fitting optimum parameter value is initial value, total fitting remnants is carried out using Levenberg-Marquart algorithms excellent Change, really can be with reverse simulation degree (solid line in Fig. 5 c) of the larger raising multilayer film parameters to EUV reflectance spectrums, but accordingly Cost be that the fitting remnants of GIXR results are greatly improved (Fig. 5 b are shown in solid).Trace it to its cause and be, Levenberg- Required precision of the optimization of Marquart algorithms to initial value is higher, it is possible to achieve efficient local search optimization, it is impossible to real Existing global optimization, and GIXR the and EUV reflectance spectrums of multilayer film have many solutions, and cause optimization to be absorbed in local optimum Solution.

It can obtain close based on the fitting optimization method of the Bi-objective based on NSGA-II algorithms that the present invention is obtained The non-dominant disaggregation in Pareto forward positions, has completed the large range of global search for double fit objects, has utilized Further attenuating of the Levenberg-Marquart algorithms to excellent individual, which is fitted remaining optimization, can obtain high-precision multilayer Film microstructural parameter is characterized, and accordingly result is shown in Fig. 6 a- Fig. 6 d.It is respectively the knot obtained based on the present invention in Fig. 6 a and Fig. 6 b The multilayer film GIXR of structure parameter institute inverting and corresponding fitting are remaining, and the remaining comparative analysis of fitting in Fig. 5 b shows, is based on Although the fitting for the multilayer film parameters that Bi-objective fitting algorithm is obtained is remaining remaining slightly larger than the fitting based on GIXR single goals, But it is substantially better than and is fitted optimum parameter value as initial value using using GIXR single goal, by Levenberg-Marquart algorithm pair The fitting that the remaining optimization method of total fitting obtains parameter is remaining.Meanwhile, the structural parameters inverting obtained based on the present invention EUV reflectance spectrums (Fig. 6 c) and its fitting remaining (Fig. 6 d) be significantly less than above-mentioned previously reported method for solving fitting it is remaining. Based on the present invention 1 is mutually shown in Table with the multi-layer film structure parameter that the above method is obtained.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 algorithms are obtained based on the parameter error precision obtained by the present invention with being close, institute There is the remaining and higher sign essence of minimum 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 many solutions in multilayer film characterization problems.

1. cycle of table Mo/Si multilayer films fitting result

The characterized with good accuracy method of EUV multilayer film microstructures given by the present invention is applicable not only to the embodiment of the present invention The structural characterization of the Mo/Si multilayer films discussed, applies also for what Rh/Si, Ni/C, Ru/C etc. were alternately made up of two kinds of materials The sign of the microstructure of EUV multilayer films.

It should be appreciated that described above is only the embodiment of the present invention, it is noted that for the general of the art For logical technical staff, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improve and Retouching also should be regarded as protection scope of the present invention.

Claims (8)

1. the multiplayer films in EUV characterized with good accuracy method based on double object genetic algorithm, it is characterised in that this method is included such as Lower step：

Step one：The initial parameter value based on the NSGA-II suitable for waiting cycle EUV multilayer film parametric solution is inputted, including is planted Group scale N, the number of parameters of multilayer film microstructure based on four layer models, mutation probability p_m, crossover probability p_c, crossover operator η_cWith mutation operator η_p, the algebraically j that evolves and multilayer film microstructure based on four layer models each parameter search scope；

Step 2：Four layer models generation based on EUV multilayer films is applied to initial parent population Q, population Q that NSGA-II evolves It is represented by Q=[a₁,a₂,a₃,…,a_i,…,a_N-1,a_N]。 (1)

By taking Mo/Si multilayer films as an example, individual gene parameter is in population

Wherein t_SiFor Si layers of thickness, t_MoFor Mo layers of thickness, t_{Mo on Si}It is for Mo layers of thickness of diffusion layer, the t on Si layers Mo/Si multilayer films average period thickness, σ be film layer between interface roughness, ρ_SiFor the density of Si film layers, ρ_MoFor Mo film layers Density, ρ_MoSi2For the density of diffusion layer between Mo layers and Si layers (or between Si layers and Mo layers)；

Step 3：The fitness of each individual, fitness bag in the parent population of computational representation EUV multilayer film microstructural parameters Two are included, wherein first fitness is the GIXR theoretical modelings result of individual and the degree of conformity of EUV multilayer film experimental results, and Second fitness is the degree of conformity of the theoretical modeling result and the experimental result of EUV multilayer films of the EUV reflectance spectrums of individual；

Step 4：The individual in population to characterizing EUV multilayer film microstructural parameters carries out non-dominated ranking, obtains in population The dominated Sorting of individual, meanwhile, to non-dominant individual using the further sequence of crowding distance；

Step 5：Selection mechanism is matched using wheel, crossover operation is carried out to the individual in population, sign EUV multilayer films are generated with this The progeny population of microstructural parameter, during crossover operation, it is desirable to which whole parameter genes to individual are operated；

Step 6：Using Variation mechanism, the progeny population for characterizing multilayer film microstructural parameter is further updated；

Step 7：The parent population and progeny population for characterizing EUV multilayer film microstructural parameters are merged；

Step 8：Assess the Bi-objective fitness for the merging population at individual for characterizing EUV multi-layer film structure parameters；

Step 9：Non-dominated ranking is carried out to the merging population for characterizing EUV multilayer film microstructural parameters, to non-dominant individual then Calculate crowding distance, and filter out by non-dominated ranking and crowding distance new parent population, return to step three, until Reach the evolutionary generation of requirement.

Step 10：By NSGA-II evolution, the experimental result for obtaining GIXR the and EUV reflectance spectrums of pin EUV multilayer films is used as plan The Bi-objective solved is closed, optimization obtains the non-dominant disaggregation close to Pareto forward positions；

Step 11：The individual concentrated to the non-domination solution close to Pareto forward positions is according to the fitting remnants' of two experimental results Be estimated, the remaining less individual applications Levenberg-Marquart algorithms of selection joint fitting combine two experiment knots Fruit further optimization, selects the remaining minimum individual of total fitting to be the optimal solution of fitting, and then try to achieve the microcosmic knot of EUV multilayer films The error of structure parameter and relevant parameter.

2. the EUV multilayer film characterized with good accuracy methods according to claim 1 based on double object genetic algorithm, its feature exists During the step one, population scale N is 50-200；Mutation probability p_mFor 0.1-1.0；Crossover probability p_cFor 0.1- 1.0；Crossover operator η_cFor 1-50；Mutation operator η_pFor 1-50；The algebraically j of evolution is 300-500.

3. the EUV multilayer film characterized with good accuracy methods according to claim 2 based on double object genetic algorithm, its feature exists During the step one, population scale N is 100；Mutation probability p_mFor 0.1；Crossover probability p_cFor 0.9；Intersect and calculate Sub- η_cFor 2；Mutation operator η_pFor 2；The algebraically j of evolution is 500.

4. the EUV multilayer film characterized with good accuracy methods according to claim 1 based on double object genetic algorithm, its feature exists During the step 2, it is considered to the physics and chemical property of multilayer film, wait micro- in the multilayer film cycle in cycle Mo/Si See structural parameters constraints be

$\left\{\begin{array}{c}{t}_{SionMo}=t-t_{Si}-t_{Mo}-t_{MoonSi}\\ t_{SionMo}\≥0.\ln m\\ t_{MoonSi}\≥t_{SionMo}\\ t_{Si}\≥t_{{\mathrm{SiO}}_2}\end{array}\right.---\left(3\right).$

5. the EUV multilayer film characterized with good accuracy methods according to claim 1 based on double object genetic algorithm, its feature exists During the step 3, the evaluation function of Bi-objective fitness is

$\left\{\begin{array}{c}{\mathrm{\χ}}_1^2=\underset{i=1}{\overset{N_{npts-1}}{\Σ}}{\left(\frac{R_c\left({\mathrm{\λ}}_i\right)-R_m\left({\mathrm{\λ}}_i\right)}{{\mathrm{\σ}}_m\left({\mathrm{\λ}}_i\right)}\right)}^2\\ {\mathrm{\χ}}_2^2=\underset{i=1}{\overset{N_{npts-2}}{\Σ}}{\left(\frac{I_c\left({\mathrm{\φ}}_i\right)-I_m\left({\mathrm{\φ}}_i\right)}{{\mathrm{\σ}}_m\left({\mathrm{\φ}}_i\right)}\right)}^2\end{array}\right.,---\left(4\right)$

WhereinEvaluation coefficient for theoretical inversion result with respect to EUV multilayer film EUV reflectance spectrum experimental results,For theoretical inverting As a result with respect to the evaluation coefficient of EUV multilayer film GIXR experimental results；R_cAnd R_mRespectively theoretical modeling and the EUV of experiment measurement is anti- Penetrate rate；I_cAnd I_mThe grazing incidence X-ray reflectivity intensity that respectively theoretical modeling and experiment are measured, and σ_mFor the survey of corresponding experimental point Measure the standard deviation of error.

6. the EUV multilayer film characterized with good accuracy methods according to claim 1 based on double object genetic algorithm, its feature exists In, during the step 6, in mutation operation, the individual single-gene only to characterizing multilayer film microstructural parameter Carry out mutation operation.

7. the EUV multilayer film characterized with good accuracy methods according to claim 1 based on double object genetic algorithm, its feature exists During the step 6, during being merged for population and progeny population, population will be merged using contrast mechanism In individual contrasted one by one, for identical individual, reservation to another individual first, and enter row stochastic gene Parameter assignment.

8. the EUV multilayer film characterized with good accuracy methods according to claim 1 based on double object genetic algorithm, its feature exists In：What any combination or two or more combined and alternatively that the EUV multilayer films include in Mo/Si, Rh/Si, Ni/C, Ru/C were constituted EUV multilayer films.