KR20080036774A - Simulation method for calculating reflectivity and phase of multilayer system - Google Patents

Abstract

A method for simulating reflectivity and phase calculation of a multilayer system is provided to form a non-periodical multilayer thin film model, a defective multilayer thin film model including internal defect, and a multilayer thin film model considering diffusion between layers by increasing degree of freedom of an input file. Various models like a non-periodical multilayer thin film model, a defective multilayer thin film model including internal defect such as pores and foreign materials, and a multilayer thin film model considering diffusion between layers are formed by adjusting each structure factor of a multilayer thin film with an MRSP(Multilayer Reflectivity Simulation Program). Reflectivity and a phase of the multilayer thin film corresponding to the formed models are calculated based on a predetermined mathematical formula by using a small quantity of computing resources.

Description

Simulation method for calculating reflectivity and phase of multilayer system

1 is a diagram comparing the characteristics for MRSP and CXRO,

2 is an exemplary diagram showing an elementary frame of an MRSP implemented according to the present invention;

3A to 3C are exemplary views illustrating components of an input file and an output file.

4 is an exemplary view configured to explain the reflectivity of the multilayer thin film applied to the MRSP,

5A and 5B are graphs showing the results of optimizing the structural factors of the Mo / Si multilayer thin film using MRSP;

Figure 6 is a graph showing the result of comparing the reflectivity of the experimental value and the measured value using the MRSP.

The present invention relates to a method for simulating reflectance and phase calculation of a multilayer system,

More specifically, by using the MRSP (Multilayer Reflectivity Simulation Program), a simulation program that can freely adjust the thickness and physical properties of each layer to calculate the optical properties of the multilayer thin film, the reflectivity and phase of the multilayer thin film can be easily and quickly calculated. Reflective and phase calculation simulation method of a multilayer system.

In general, the simulation of optical properties of multilayer thin films is performed by simulation of optical properties of multilayer thin films with single structure factors and densities such as those published by The Center for X-Ray Optics (CXRO) under the US Lawrence Berkeley National Laboratory (LBNL). Possible programmatic methods are used.

However, such a program-based method has limitations such as the inability to individually control the thickness and physical properties of each layer. Therefore, the interdiffusion layer formed between the change in thickness of each layer and heterogeneous materials inevitably generated in the actual process. Since it is impossible to consider the effect of the back light on the optical properties of the multilayer thin film, there are many difficulties in the study of the actual multilayer thin film.

Therefore, the conventional method through the optical characteristics simulation program of the multilayer thin film as described above is limited in some efficiency, the problem of minimizing the reliability and satisfaction of practical use for the multi-layer system to be implemented by applying this method Are always implied.

The present invention has been made to solve the problems of the prior art as described above has the following object.

The present invention is to increase the degree of freedom of the input file significantly, unlike the conventional method, through which the defects including the aperiodic multilayer structure thin film model having different thickness of each layer and the internal defects composed of pores or foreign matter in the multilayer film ( It is an object of the present invention to provide a method for simulating reflectance and phase calculation of a multilayer structure system to freely form a multilayer structure thin film model in consideration of interlayer diffusion, in which a multi-layer thin film model and a mutual diffusion layer between a specific layer are generated.

It is another object of the present invention to calculate the reflectivity and phase of various types of multilayer thin films in a short time with a small amount of computing resources, thereby providing quantitative results on the optical properties of multilayer thin films of various fields applicable to optical materials. To provide a method for simulating the reflectivity and phase calculation of a multilayer system that can be easily secured.

Another object of the present invention is to improve the efficiency of the reflectivity and phase of the multi-layer thin film, such as to improve the efficiency, and to apply it to the application of nano-optical field difficult to apply experimentally, reliability of the use that can be implemented And to provide a method for simulating the reflectivity and phase calculation of the multilayer system to maximize the satisfaction.

Hereinafter, the present invention will be described in detail.

In describing the present invention, when it is determined that the detailed description of the related known function or configuration may unnecessarily obscure the subject matter of the present invention, the detailed description thereof will be omitted.

Terms to be described later are terms set in consideration of functions in the present invention, and may be changed according to a user's intention or custom such as an experimenter and a measurer, and a definition thereof should be made based on the contents throughout the present specification.

First, the reflectivity and phase calculation simulation method of the multilayer system to be implemented according to the present invention by controlling the structural factors of the multilayer thin film using the MRSP (Multilayer Reflectivity Simulation Program) individually, the thickness of each layer having a different periodicity Implement various models such as thin-film models and multi-layer thin-film models that consider interlayer diffusion, in which a multi-layered thin film model with internal defects consisting of pores or debris in a multi-layer film and interdiffusion layers between specific layers are considered. In addition, the reflectivity and phase of the multilayer thin film for the various models described above are executed to be calculated by a small amount of computing resources.

Therefore, the structure factors of the multilayer thin film using the MRSP are individually adjusted to quantitatively analyze the results of reflectivity and phase, and the MRSP is used for the Mo / Si multilayer thin film for the extreme ultraviolet exposure process. It will perform structure factor optimization.

In addition, the MRSP is used to predict the structural factors of the Mo / Si multilayer thin film for the extreme ultraviolet exposure process, and the structure of each layer is determined based on the result of measuring the reflectivity of the mask for the extreme ultraviolet light exposure process. The traceback is performed to predict the average structural factor of the mask.

EXAMPLE

With reference to a preferred embodiment for achieving the present invention described above will be described in detail.

First, the present invention is to calculate the reflectivity and phase of the multilayer thin film using the MRSP (Multilayer Reflectivity Simulation Program), which is a simulation program capable of calculating the optical properties of the multilayer thin film by freely adjusting the thickness and physical properties of each layer.

Accordingly, the present invention has developed an MRSP that maximizes the degree of freedom of input file configuration by focusing on the user's convenience in order to calculate the reflectance and phase of the multilayer structure thin film that can be applied to the basic science fields related to optical materials. It is made using Visual C ++ MFC on Windows operating system and can be divided into input file and output file in the form of general-purpose text file.

Figure 1 shows a comparison of the characteristics of the MRSP and CXRO, through which it can be seen that the execution through the MRSP is significantly superior to the execution through the CXRO.

2 shows a basic frame of an MRSP according to the present invention. The user can set a range of wavelength values to be viewed, determine how many steps to calculate the wavelength range, and also determine an initial frame. The angle of the beam incident on the surface and the polarization form of the incident beam can be selected.

3A and 3B illustrate components of an input file and an output file. The input file and the output file of the program according to the present invention are formed in a text format.

That is, as shown in FIG. 3A, the left column of the input file represents a material constituting each layer, and each material is input by being divided into a format of 'material name.ndb'.

In addition, as shown in FIG. 3C, the 'ndb' file is a sequence of the corresponding energy (eV), refractive index (n), and loss factor (k) from the left side, and all refractive index information is related to the x-ray data of CXRO. Referring to the base, the right column of the input pile is the thickness of the material constituting each layer and input in terms of metric units. Also, the stacking order of the multilayered thin film structure consists of the upper side of the input pile and the bottom side of the input pile. It means.

In addition, as shown in FIG. 3B, the output file represents a wavelength value in which the first column is divided into specific steps from the left, the second column is calculated reflectivity, and the third column is calculated phase value (degree). ).

Figure 4 is an exemplary view configured to explain the reflectivity of the multilayer thin film applied to the MRSP, the order of each layer in the multilayer thin film is the first layer deposited on the substrate, the layer on the surface of the thin film is determined as the final layer .

The reflectivity (R _sub ) in the substrate is assumed to be '0' because the reflected light source is all absorbed by the substrate itself because the thickness of the substrate is very large compared to the thickness of the deposited thin film, and the reflectance (R _sub ) is initial value. By using the relationship between reflectance (R _N , R _{N +1} ) between two adjacent layers, the reflectivity (R _Air ) from the first layer to the final layer was calculated. This is defined as a Fresnel equation and reflectance can be calculated by calculating the relative magnitude of the incident electric field and the reflected electric field when electromagnetic waves are incident and reflected on the multilayer thin film.

과 E_{j +1}을 각각 반사된 빔과 투과된 빔의 전기장 진폭이라 하며, 맥스윌(Maxwell) 방정식에서 계면에서의 전기장과 자기장 성분은 각각 연속적이어야 하므로 σ분극(polarization)과 같은 경우 E_j와

의 진폭은 j번째 층과 j+1번째 층의 절반에서 계산될 수 있으며, j+1번째 층과 j번째 층의 관계식은 하기와 같다.Therefore, E _j is referred to as the electric field amplitude of the j-th layer incident beam having a refractive index of n _j ,

And as the electric field amplitude of E _{j + 1} respectively, the reflected beam and the transmitted beam, and if the electric field and the magnetic field component in the Max interface in Wiltshire (Maxwell) equation, so each must be continuous, such as σ polarization (polarization) and E _j

The amplitude of can be calculated in half of the j th layer and the j + 1 th layer, and the relationship between the j + 1 th layer and the j th layer is as follows.

(Equation 1)

(Equation 2)

(Equation 3)

(Equation 4)

Θ _j is the incident angle at the interface between the j th layer and the j + 1 th layer, and θ is the incident angle of the beam incident upon vacuum.

Equation 1 and Equation 2 can be combined to obtain Equation 5 below.

(Eq. 5)

Here, F _j represented in Equation 5 is represented by Equation 6 below.

(Equation 6)

Π polarization is represented by the following equation.

(Eq. 7)

Using the reflectivity of the substrate assumed as '0' above as an initial value, the relationship between the first layer and the second layer is obtained through the relational expression of the reflection coefficients (R _j , R _{j +1} ) between two adjacent layers, and the final layer is sequentially The reflection coefficient R ₀ can be calculated, and since R is a complex number, the total reflectivity can be obtained as shown in Equation 8 below.

(Eq. 8)

In Equation 8, I ₀ (θ) is the intensity of the beam incident on the surface at the angle of θ, and I (θ) is the intensity of the reflected beam.

By utilizing the MRSP implemented in accordance with the present invention, structural factor optimization of the Mo / Si multilayer thin film can be performed.

In other words, in addition to the selection of the constituent material in the Mo / Si multilayer mask for the extreme ultraviolet exposure process, the structural factor of the thin film is the most important factor that determines the optical properties of the reflective mask, and the thickness of the absorber material (high atomic number, Mo) When d _h and the thickness of the spacer material (low atomic number, Si) is d _l , the main structural factors of the multilayer thin film are as follows.

d-spacing: d _h + d _l

γ: d _h / d-spacing

N: total number of cycles

Therefore, in order to extract the structural factors of the optimized Mo / Si multilayer thin film, the angle of incidence is fixed to 90 degrees, and the Mo / Si multilayer thin film model is fabricated for the change of various structural factors. Was predicted.

For this purpose, the reflectivity calculation was performed centering on three structural factors, d-spacing, γ, and N, which have the greatest influence on the optical characteristics of the mask.

In general, the period of the whole cycle changes d-spacing at intervals of 0.2 nm in the range of 6 to 8 nm when N is fixed at 40, and at intervals of 0.1 to 0.9 at intervals of 0.1 to 0.9 at constant d-spacing values, respectively. 5A and 5B show the results of calculating the reflectivity at the time of vertical incidence and reflection at each structural factor when changed.

As shown in FIGS. 5A and 5B, when d is 6.2 to 7.4 and γ is 0.4, a relatively high theoretical reflectance of 74% or more can be seen.

In addition, the structural factors of the Mo / Si multilayer thin film for the extreme ultraviolet exposure process can be predicted by utilizing the MRSP implemented according to the present invention.

That is, the actual reflectivity of the fabricated Mo / Si multilayer thin film was actually measured by the EUV beam. As a result, it was found that the maximum reflectance was 61.36% at the wavelength of 13.08 nm.

Based on the experimental results, it is possible to trace back and analyze the average state of the structural factors of the multilayer thin film using MRSP.

Therefore, since the density of the Mo and Si layers is a structural factor included in the atomic scattering factor associated with the refractive index, the change in density of each layer is a factor directly related to the optical properties, and each layer is deposited by an actual sputtering process. In this case, the density can be reduced compared to the theoretical value.

Therefore, the actual measurement result when the layer density is 80% and the d-spacing increases by 4.15% through various combinations of the d-spacing and the layer density measured in the layer density range up to 80% based on the theoretical 100% It can be seen that the wavelength of 13.08 nm, which is exactly the same as.

In addition to the foregoing experiments, consideration of the interdiffusion layer (MoSi ₂ ) generated at the interface between layers and the surface oxide layer (SiO ₂ ) generated by oxidation of the Si layer, which is a surface layer, is essential, and structural differences between the Mo and Si layers are essential. Due to the difference in surface density, the thickness of the interdiffusion layer generated between layers has a certain ratio.

When the Mo layer on the Si layer (Mo on Si) is about 1.5 times the thickness difference of the interdiffusion layer occurs compared to the Si layer on the Mo layer (Si on Mo) and the surface oxide layer is about the Si layer It is produced with a thickness of 2 nm.

In actual experimental equipment, Mo on Si was measured at ~ 1.2 nm and Si on Mo at ~ 0.8 nm, and the information on d-spacing and density changes from previous experiments was comprehensively applied. Reflectivity is calculated and compared with the actual measurement results are shown in FIG.

As a result, a very close value with an error rate of about 2.3% was obtained with a maximum reflectance of 63.67% at 13.08 nm, which is the same wavelength as the measured value, from the final calculated result. In the process, it is possible to provide quantitative information on the average structural factors of the finally produced multilayer thin film.

Finally, various modifications can be made to the implementation of the method for simulating the reflectivity and phase calculation of the multilayer system implementing the present invention and can take various forms.

It is to be understood, however, that the present invention is not limited to the specific forms referred to in the above description, but rather includes all modifications, equivalents and substitutions within the spirit and scope of the invention as defined by the appended claims. It should be understood to do.

As described above, there is an effect of forming a multi-layered model of various forms through the reflectance and phase calculation simulation method of the present invention, a multi-layered system, and the effect that the optical properties of the formed model is accurately calculated.

In addition, the present invention makes it possible to quickly calculate the reflectivity and phase of various types of multilayer thin films with a small amount of computing resources in a short time so that the quantitative results of the optical properties of the multilayer thin films in various fields that can be applied as optical materials are easily obtained. The effect is secured.

In addition, the present invention can be applied to the extreme ultraviolet exposure process technology, one of the next-generation nano-device fabrication technology, in particular to find the optimized structure of the multi-layered thin film used as the mask for the extreme ultraviolet light exposure process or compare with the actual measured reflectivity Through it is possible to trace back the average structural factors of the multilayer thin film.

In addition, the present invention improves the efficiency and the like, such that the reflectivity and phase of the multilayer thin film can be easily and quickly calculated, and thus the reliability and satisfaction of the use can be extended and applied to the nano-optical field that is difficult to apply experimentally by applying the same. There are several effects that are maximized.

Claims (9)

Individually adjust the structural factors of multilayer thin films using the MRSP (Multilayer Reflectivity Simulation Program), a non-periodic multilayer thin film model with different thickness of each layer, and a defective multilayer including internal defects composed of pores or foreign substances in the multilayer film And to form various models such as a multi-layer thin film model in which inter-diffusion between layers of a structural thin film model and a specific layer is generated, and Reflectance and phase calculation of the multilayer thin film for the various models described above is performed by a small amount of computing resources. The method of claim 1, The reflectivity and phase of the multilayer thin film is a reflection and phase calculation simulation method of the multilayer structure system, characterized in that it is carried out to calculate through the following equation. ①

②

③

④

E _j is the electric field amplitude of the j-th layer incident beam with an index of refraction of n _j ,

And the electric field amplitude, the electric field and magnetic field components at the interface of the reflected beam, the E _{j +1,} respectively, and the transmitted beam, so each must be continuous if: σ polarization (polarization) and E _j

The amplitude of is calculated from half of j-th layer and j + 1th layer, and is a relation between j + 1th layer and jth layer, θ _j is the incident angle at the interface between jth layer and j + 1th layer, θ is vacuum When the incident angle of the incident beam The method of claim 2, Using the above equations, the following equations are obtained, using the reflectivity of the substrate as an initial value, and using the relationship between the reflection coefficients (R _j , R _{j +1} ) between two adjacent layers. Reflecting, calculating the coefficient of reflection (R ₀ ) to the final layer in turn, and calculating the total reflectivity. ⑤

⑥

⑦

⑧

Equation ⑤ is obtained by combining Equations ① and ②, π polarization is represented by Equation ⑦, and total reflectivity can be obtained by Equation ⑧, where R is a complex number and I ₀ (θ) is θ angle at the surface. The intensity of the incident beam, I (θ), is the intensity of the reflected beam The method of claim 1, Reflectance and phase calculation simulation method of the multilayer system, characterized in that the adjustment of the structural factors of the multilayer thin film using the MRSP to the quantitative analysis of the results of reflectivity and phase. The method of claim 1, Reflectance and phase calculation simulation method of a multilayer structure system, characterized in that by using the MRSP structure optimization of the Mo / Si multilayer thin film for extreme ultraviolet light exposure process. The method of claim 5, Reflecting and phase calculation simulation method of the multilayer structure system, characterized in that for performing the prediction of the structural factors of the Mo / Si multilayer thin film for the extreme ultraviolet exposure process using the MRSP. The method of claim 6, Reflectance and phase calculation simulation method of the multilayer structure system characterized in that the traceback of the structure of each layer based on the result of measuring the reflectivity of the mask for the extreme ultraviolet exposure process to predict the average structural factors of the mask . Individually adjust the structural factors of multilayer thin films using the MRSP (Multilayer Reflectivity Simulation Program), a non-periodic multilayer thin film model with different thickness of each layer, and a defective multilayer including internal defects composed of pores or foreign substances in the multilayer film It is implemented to form various models such as a structured thin film model and a multi-layered thin film model in which interdiffusion layers are generated, in which interdiffusion layers are generated, and a small amount of computing of reflectivity and phase of the multilayer thin film for the various models described above. To calculate by resource, Individually adjust the structural factors of the multilayer thin film using the MRSP to quantitatively analyze the results of reflectance and phase, and optimize the structural factors of the Mo / Si multilayer thin film for the extreme ultraviolet exposure process by using the MRSP. By using the MRSP to predict the structural factors of the Mo / Si multilayer thin film for the extreme ultraviolet exposure process, and based on the result of measuring the reflectivity of the mask for the extreme ultraviolet light exposure process Reflectance and phase calculation simulation method of a multilayer system, characterized in that it is executed to trace back to predict the average structural factor of the mask. Individually adjust the structure factors of multilayer thin films using the MRSP (Multilayer Reflectivity Simulation Program), a non-periodic multi-layer thin film model with different thickness of each layer, and a defective multilayer including internal defects composed of pores or foreign substances in the multilayer film It is implemented to form various models such as a structured thin film model and a multi-layered thin film model in which interdiffusion layers are generated, in which interdiffusion layers are generated, and a small amount of computing of reflectivity and phase of the multilayer thin film for the various models described above. To calculate by resource, The reflectivity and phase of the multilayer thin film are performed to be calculated by the following equations, and the first layer is obtained through the relational expression of the reflection coefficients (R _j , R _{j + 1} ) between two adjacent layers, using the reflectivity of the substrate as an initial value. Reflectivity and phase calculation simulation method for calculating the reflection coefficient (R ₀ ) to the final layer in turn, and calculating the total reflectivity. ①

②

③

④

Where E _j is the electric field amplitude of the j-th layer incident beam with a refractive index of n _j ,

And the electric field amplitude, the electric field and magnetic field components at the interface of the reflected beam, the E _{j +1,} respectively, and the transmitted beam, so each must be continuous if: σ polarization (polarization) and E _j

The amplitude of is calculated from half of j-th layer and j + 1th layer, and is a relation between j + 1th layer and jth layer, θ _j is the incident angle at the interface between jth layer and j + 1th layer, θ is vacuum When the incident angle of the incident beam ⑤

⑥

⑦

⑧

Equation ⑤ is obtained by combining Equations ① and ②, π polarization is represented by Equation ⑦, and total reflectivity can be obtained by Equation ⑧, where R is a complex number and I ₀ (θ) is θ angle at the surface. The intensity of the incident beam, I (θ), is the intensity of the reflected beam

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