CN105631193A - Hybrid genetic algorithm-based extreme ultraviolet multilayer film structure parameter inversion method - Google Patents

Abstract

The invention discloses a hybrid genetic algorithm-based extreme ultraviolet multilayer film structure parameter inversion method, belongs to the technical field of extreme ultraviolet lithography, and aims at solving the problem that the extreme ultraviolet multilayer film structure parameter determination in the prior art cannot have high efficiency and correctness at the same time. The inversion method comprises the following steps: calculating the reflectivity of a multilayer film under fixed wavelength and different grazing incident angles through optical constants and target structure parameters of the multilayer film so as to obtain a target grazing incident X-ray reflectance spectrum; and inversing the structure parameters of the multilayer film by adopting a genetic algorithm through the target grazing incident X-ray reflectance spectrum obtained in the step one, and continuing to inverse the structure parameters of the multilayer film by adopting a simplex algorithm so as to obtain the final structure parameters of the multilayer film, wherein the number of iterations of the genetic algorithm is 20-50 and the number of iterations of the simplex algorithm is 200-400. According to the method disclosed in the invention, the inversion of the structure parameters of the multilayer film is high in precision and relatively high in speed.

Description

Multiplayer films in EUV structural parameters inversion method based on genetic algorithm

Technical field

The invention belongs to extreme ultraviolet photolithographic technical field, be specifically related to a kind of multiplayer films in EUV structural parameters inversion method based on genetic algorithm.

Background technology

Extreme ultraviolet photolithographic (ExtremeUltravioletLithography, EUVL) technology is to use EUV wave band, and mainly 13.5nm wave band, carries out the micro-nano technology technology of photoetching. At present, EUVL technology has been able to realize the etching technics of 7nm live width, and possesses the probability reducing etching live width further. It is significant that this manufactures field at large scale integrated circuit, it is possible to the element realizing greater density is integrated, and less energy consumption.

Extreme ultraviolet photolithographic uses wavelength to be 10��14nm light source lighting, owing to nearly all known optical material all has strong absorption at this wave band, traditional refractive optical system cannot be adopted, so the illuminator of extreme ultraviolet etching system, mask and projection objective all adopt reflective designs, its reflective optical devices need to be coated with periodic multilayer film to improve reflectance. For improving the luminous flux of extreme ultraviolet etching system, require over coating process parameter optimization and improve the reflectance of each extreme ultraviolet multilayer film reflection mirror as far as possible, and be instruct process optimization to need the multiplayer films in EUV of deposition under each process conditions is carried out structural characterization.

Grazing incidence X-ray reflectivity spectrum is that multi-layer film structure is characterized the strongest means, compose inverting can obtain the structural parameters of multilayer film by the grazing incidence X-ray reflectivity of matching multilayer film, owing to the structural parameters of multilayer film are more and the data volume of grazing incidence X-ray reflectivity spectrum is bigger, although individually adopting Genetic Algorithm Fitting grazing incidence X-ray reflectivity spectrum can obtain globally optimal solution, but the iterative convergence speed of genetic algorithm is slower, operand plus genetic algorithm is big, and therefore the time needed for fit procedure is longer; Although and individually adopt simplex method matching grazing incidence X-ray reflectivity spectrum fast convergence rate, but refutation process is very easily absorbed in local minimum.

Summary of the invention

Present invention aim to address the defining method of multiplayer films in EUV structural parameters in prior art, it is impossible to the problem having both high efficiency and accuracy, it is provided that a kind of multiplayer films in EUV structural parameters inversion method based on genetic algorithm.

Based on the multiplayer films in EUV structural parameters inversion method of genetic algorithm, step is as follows:

Step one, by the optical constant of multilayer film and object construction parameter, calculate multilayer film reflectance under fixed wave length, different grazing angles, obtain target grazing incidence X-ray reflectivity spectrum;

Step 2, the target grazing incidence X-ray reflectivity spectrum obtained by step one, adopt the structural parameters of genetic inverse multilayer film, and the iterations of genetic algorithm is 20-50 time;

The structural parameters of the multilayer film that step 3, foundation step 2 obtain, adopt simplex algorithm to continue the structural parameters of INVERSION OF MULTI-LAYER film, and the iterations of simplex algorithm is 200-400 time;

Described step one is to step 3, and grazing incidence X-ray reflectivity spectrum is all obtained by recursive algorithm.

Further, the process of described step 2 and step 3 is:

With formula (1) for evaluation function, genetic algorithm is first adopted to find the structural parameters of the multilayer film making F value minimum in iterations, the structural parameters of the multilayer film obtained according to genetic algorithm again, adopt simplex algorithm to continually look for the structural parameters of the multilayer film minimum so that F value in iterations;

$F=\underset{i=1}{\overset{m}{\Σ}}|log10\left(R_c\right({\mathrm{\θ}}_i\left)\right)-log10\left(R_{goal}\right({\mathrm{\θ}}_i\left)\right)|---\left(1\right)$

In formula (1), m is integer, log10R_c(��_i) for calculating grazing incidence X-ray reflectivity spectrum, log10R_goai(��_i) compose for target grazing incidence X-ray reflectivity.

Further, in described step 2, the population number of genetic algorithm is 100, and crossover probability is 0.5, and mutation probability is 0.02.

Further, the wavelength of described grazing incidence X-ray reflectivity spectrum is fixed as 0.154nm.

Further, the excursion of described grazing angle is 0.2 ��-5 ��.

Compared with prior art, the invention have the benefit that

The multiplayer films in EUV structural parameters inversion method based on genetic algorithm of the present invention adopts genetic algorithm to carry out matching grazing incidence X-ray reflectivity spectrum, namely Genetic Algorithm Fitting grazing incidence X-ray reflectivity spectrum is first adopted, until iteration convergence to a certain extent after, the solution that genetic algorithm finds is near globally optimal solution, simplex method matching grazing incidence X-ray reflectivity is adopted to compose again, accelerate the speed of iteration convergence, the method has genetic algorithm global optimizing and the advantage of simplex method fast convergence rate concurrently, the structural parameters precision of INVERSION OF MULTI-LAYER film is high, speed, thus the process optimization for improving multiplayer films in EUV reflectance provides strong structural characterization means.

Accompanying drawing explanation

Fig. 1 is the present invention schematic diagram based on the multiplayer films in EUV structural parameters inversion method of genetic algorithm;

Fig. 2 is the structural representation of the multiplayer films in EUV of the present invention;

Fig. 3 is the target grazing incidence X-ray reflectivity spectrum of embodiment 1, comparative example 1 and comparative example 2;

Fig. 4 is the grazing incidence X-ray reflectivity spectrum contrast with target grazing incidence X-ray reflectivity spectrum of comparative example 1;

Fig. 5 is the grazing incidence X-ray reflectivity spectrum contrast with target grazing incidence X-ray reflectivity spectrum of comparative example 2;

Fig. 6 is the grazing incidence X-ray reflectivity spectrum contrast with target grazing incidence X-ray reflectivity spectrum of embodiment 1.

Detailed description of the invention

The present invention is further illustrated below in conjunction with accompanying drawing.

As it is shown in figure 1, when the structural parameters of multilayer film are known, it is possible to calculating the grazing incidence X-ray reflectivity spectrum of multilayer film, this is a forward problem; On the contrary, the present invention is based on the multiplayer films in EUV structural parameters inversion method of genetic algorithm, it is when the grazing incidence X-ray reflectivity of known multilayer film is composed, INVERSION OF MULTI-LAYER membrane structure parameter. The multi-layer film structure that the present invention is directed to is as in figure 2 it is shown, wall and absorbed layer by being periodically alternately deposited on substrate form. The structural parameters of the multilayer film of the present invention refer to absorber thickness d₁, space layer d₂, wall interface roughness �� on absorbed layer₁With wall interface roughness �� under absorbed layer₂��

Based on the multiplayer films in EUV structural parameters inversion method of genetic algorithm, step is as follows:

Step one, by the optical constant of multilayer film and object construction parameter, calculate multilayer film reflectance under fixed wave length, different grazing angles, obtain target reflection rate curve R_goai(��_i), target reflection rate curve is sought logarithm, obtains target grazing incidence X-ray reflectivity spectrum log10R_goai(��_i), target reflectivity curve negotiating recursive algorithm is determined, it may also be said to target grazing incidence X-ray reflectivity spectrum is determined by recursive algorithm;

Step 2, employing genetic algorithm are found and are made the structural parameters of the multilayer film that F value is minimum in evaluation function in 20-50 is for iterations, the structural parameters of the multilayer film obtained according to genetic algorithm again, simplex algorithm is adopted to continually look for making the structural parameters of the multilayer film that F value is minimum in evaluation function in 200-400 is for iterations, this optical constant is the structural parameters of final multilayer film, shown in evaluation function such as formula (1):

$F=\underset{i=1}{\overset{m}{\Σ}}|log10\left(R_c\right({\mathrm{\θ}}_i\left)\right)-log10\left(R_{goal}\right({\mathrm{\θ}}_i\left)\right)|---\left(1\right)$

In formula (1), m is integer, log10R_c(��_i) for calculating grazing incidence X-ray reflectivity spectrum, R_c(��_i) for calculating reflectance curve, calculate reflectance curve and determined by recursive algorithm, it may also be said to calculate grazing incidence X-ray reflectivity spectrum and determined by recursive algorithm.

Wherein, for making algorithm iteration convergence rate the fastest, the parameter of genetic algorithm selects as follows: population number is 100, crossover probability is 0.5, mutation probability is 0.02, owing to the iterative convergence speed of genetic algorithm is slower, operand plus genetic algorithm is big, therefore the time needed for fit procedure is longer, for this, the iterations of genetic algorithm is defined as 20-50 generation, now iteration convergence to a certain extent after, the solution that genetic algorithm finds is near globally optimal solution, then simplex algorithm matching grazing incidence X-ray reflectivity is adopted to compose again, the iterations of simplex algorithm is 200-400 generation.

In said method, recursive algorithm is those skilled in the art's well-known algorithms, and detailed process is:

Through type (1) calculates the Fresnel reflection coefficient F of jth layer and jth+1 interface layer_j,j+1;

$F_{j,j+1}=\frac{k_j-k_{j+1}}{k_j+k_{j+1}}---\left(1\right)$

In formula (1),

$k_j=\frac{2\mathrm{\π}}{\mathrm{\λ}}{(N_j^2-{\cos }^2\mathrm{\θ})}^{1/2}$

$k_{j+1}=\frac{2\mathrm{\π}}{\mathrm{\λ}}{(N_{j+1}^2-{\cos }^2\mathrm{\θ})}^{1/2}$

N_jFor the complex refractivity index of jth tunic, N_j=n_j+i��_j, n_jFor the refractive index of jth tunic, ��_jFor the extinction coefficient of jth tunic, N_j+1For the complex refractivity index of jth+1 tunic, N_j+1=n_j+1+i��_j+1, n_j+1For the refractive index of jth+1 tunic, ��_j+1For the extinction coefficient of jth+1 tunic, by that analogy; �� is grazing angle; I is unit imaginary number;

Then pass through formula (2) and calculate different interfaces reflectance;

$R_{j,j+1}={\mathrm{\α}}_j^2\frac{R_{j+1,j+2}+F_{j,j+1}}{1+R_{j+1,j+2}+F_{j,j+1}}\exp (k_j{k}_{j+1}{{\mathrm{\σ}}_j}^2/2)---\left(3\right)$

In formula (3), R_j,j+1For the film system reflection coefficient by the end of jth interface; R_j+1,j+2For the film system reflection coefficient by the end of+1 interface of jth, by that analogy; ��_j=exp (-ik_jd_j), d_jFor the thickness of jth layer, ��_jInterface roughness for jth interface;

No matter recursive procedure, for calculating topmost one layer gradually from substrate, is monofilm or multilayer film, and all available through type (3) calculates the reflectance of thin film, reflectance is being asked logarithm, is namely obtaining grazing incidence X-ray reflectivity rate. Known multi-layer film structure parameter, i.e. multilayer film absorber thickness d₁, space layer d₂, interface roughness �� between two retes₁And ��₂, it is possible to calculated to obtain grazing incidence X-ray reflectivity spectrum by formula (1). On the contrary, known grazing incidence X-ray reflectivity spectrum inverting can also obtain multi-layer film structure parameter.

The present invention is further illustrated below in conjunction with comparative example and embodiment.

Comparative example 1

For Mo/Si multilayer film, the Mo/Si multilayer film optical constant at wavelength 0.154nm place is provided by data base, the refractive index n of Mo_Mo=0.99997127, extinction coefficient ��_MoThe refractive index n of=1.8853960e-06, Si_Si=0.99999289, extinction coefficient are ��_Si=1.6199057e-07; Mo/Si multilayer film object construction parameter is d₁=4.2, d₂=2.8, ��₁=0.4, ��₂=0.3, this object construction parameter the target grazing incidence X-ray reflectivity spectrum that grazing incidence X-ray reflectivity spectrum is multilayer film calculated, as shown in Figure 3. Being composed by target grazing incidence X-ray reflectivity, adopt genetic inverse multilayer film object construction parameter, iteration 200 times, the structural parameters obtaining multilayer film are d₁=4.2003, d₂=2.7995, ��₁=0.4003, ��₂=0.2993, corresponding reflectance spectrum and the contrast of target reflectance spectra are as shown in Figure 4.

From fig. 4, it can be seen that the structural parameters that genetic inverse obtains are almost substantially identical with object construction parameter, but the calculating time of 200 generation genetic algorithms is 1000 minutes, consuming time long.

Comparative example 2

For Mo/Si multilayer film, the Mo/Si multilayer film optical constant at wavelength 0.154nm place is provided by data base, the refractive index n of Mo_Mo=0.99997127, extinction coefficient ��_MoThe refractive index n of=1.8853960e-06, Si_Si=0.99999289, extinction coefficient are ��_Si=1.6199057e-07; Mo/Si multilayer film object construction parameter is d₁=4.2, d₂=2.8, ��₁=0.4, ��₂=0.3, this object construction parameter the target grazing incidence X-ray reflectivity spectrum that grazing incidence X-ray reflectivity spectrum is multilayer film calculated, as shown in Figure 3. Being composed by target grazing incidence X-ray reflectivity, adopt genetic inverse multilayer film object construction parameter, iteration 20 times, the structural parameters obtaining reflectance coating are d₁=4.2406, d₂=2.7589, ��₁=0.4003, ��₂=0.2993, corresponding reflectance spectrum and the contrast of target reflectance spectra are as shown in Figure 5.

From fig. 5, it can be seen that due to 20 the not convergences of genetic algorithm iteration, the structural parameters that therefore inverting obtains have certain error compared with object construction parameter, and corresponding reflectance spectrum and target reflectance spectra have certain difference.

Embodiment 1

For Mo/Si multilayer film, the Mo/Si multilayer film optical constant at wavelength 0.154nm place is provided by data base, the refractive index n of Mo_Mo=0.99997127, extinction coefficient ��_MoThe refractive index n of=1.8853960e-06, Si_Si=0.99999289, extinction coefficient are ��_Si=1.6199057e-07; Mo/Si multilayer film object construction parameter is d₁=4.2, d₂=2.8, ��₁=0.4, ��₂=0.3, this object construction parameter the target grazing incidence X-ray reflectivity spectrum that grazing incidence X-ray reflectivity spectrum is multilayer film calculated, as shown in Figure 3. Composed by target grazing incidence X-ray reflectivity, adopt genetic inverse multilayer film object construction parameter, iteration 20 times, then adopt simplex algorithm to continue inverting object construction parameter, iteration 200 times, obtain d₁=4.1999, d₂=2.8000, ��₁=0.4000, ��₂=0.2999, corresponding reflectance spectrum and the contrast of target reflectance spectra are as shown in Figure 6.

As can be seen from Figure 6, the structural parameters that genetic algorithm inverting obtains almost fit like a glove with object construction parameter, it is 106 minutes that 20 generation genetic algorithms add the calculating time of 200 iteration of simplex algorithm, and the calculating time of 200 independent generation genetic algorithms is 1000 minutes (comparative example 1), the former far fewer than the latter required time, and the former obtained result is slightly better than the latter on the contrary, the structural parameters precision of the multilayer film that the inversion method of this explanation present invention obtains is high, speed.

Claims (5)

1. based on the multiplayer films in EUV structural parameters inversion method of genetic algorithm, it is characterised in that step is as follows:

Step one, by the optical constant of multilayer film and object construction parameter, calculate multilayer film reflectance under fixed wave length, different grazing angles, obtain target grazing incidence X-ray reflectivity spectrum;

Step 2, the target grazing incidence X-ray reflectivity spectrum obtained by step one, adopt the structural parameters of genetic inverse multilayer film, and the iterations of described genetic algorithm is 20-50 time;

The structural parameters of the multilayer film that step 3, foundation step 2 obtain, adopt simplex algorithm to continue the structural parameters of INVERSION OF MULTI-LAYER film, and the iterations of described simplex algorithm is 200-400 time;

Described step one is to step 3, and grazing incidence X-ray reflectivity spectrum is all obtained by recursive algorithm.

2. the multiplayer films in EUV structural parameters inversion method based on genetic algorithm according to claim 1, it is characterised in that the process of described step 2 and step 3 is:

With formula (1) for evaluation function, genetic algorithm is first adopted to find the structural parameters of the multilayer film making F value minimum in iterations, the structural parameters of the multilayer film obtained according to genetic algorithm again, adopt simplex algorithm to continually look for the structural parameters of the multilayer film minimum so that F value in iterations;

$F=\underset{i=1}{\overset{m}{\Σ}}|log10\left(R_c\right({\mathrm{\θ}}_i\left)\right)-log10\left(R_{goal}\right({\mathrm{\θ}}_i\left)\right)|---\left(1\right)$

In formula (1), m is integer, log10R_c(��_i) for calculating grazing incidence X-ray reflectivity spectrum, log10R_goai(��_i) compose for target grazing incidence X-ray reflectivity.

3. the multiplayer films in EUV structural parameters inversion method based on genetic algorithm according to claim 1, it is characterised in that in described step 2, the population number of genetic algorithm is 100, and crossover probability is 0.5, and mutation probability is 0.02.

4. the multiplayer films in EUV structural parameters inversion method based on genetic algorithm according to claim 1, it is characterised in that the wavelength of described grazing incidence X-ray reflectivity spectrum is fixed as 0.154nm.

5. the multiplayer films in EUV structural parameters inversion method based on genetic algorithm according to claim 1, it is characterised in that the excursion of described grazing angle is 0.2 ��-5 ��.