CN103226241B - A kind of Optical system method for designing based on law of conservation of energy - Google Patents

Abstract

The invention provides an optical system analysis and design method based on the law of energy conservation, which belongs to the field of optical design, and solves the problem that the existing optical design software cannot make reasonable predictions on the imaging quality of the optical system with the optical film added. Estimation, leading to the problem that the optical system processed according to the design cannot be compatible with the optical film. From the perspective of energy modulation, this method takes strict electromagnetic field theory as the starting point, establishes an equivalent working interface, and combines the parameters of the bare optical system to construct an equivalent optical system with optical film added, and evaluates and analyzes the system. The invention overcomes the deficiency of existing optical design software in processing optical thin films, and equates complex physical optical processes in optical thin films into geometric optical processes, saving time and cost compared with existing optical software.

Description

A method for analyzing and designing optical systems based on the law of energy conservation

technical field

The invention relates to an optical system analysis and design method based on the law of energy conservation, which can be applied in the evaluation analysis and optimization design of the optical system, and belongs to the field of optical design.

Background technique

Extreme ultraviolet lithography (EUVL) uses 13.5nm extreme ultraviolet light (EUV) as the working wavelength. Almost all substances are opaque to this wavelength and have a refractive index close to 1. Therefore, the EUVL system must use a total reflection system and must be in The mirror surface is coated with Mo/Si reflectivity-enhancing optical film. The thickness of the existing Mo/Si film used in extreme ultraviolet lithography is about 300nm, which is much larger than its working wavelength. According to the strict electromagnetic field theory calculation, after the light energy enters a certain depth in the film, its energy will be completely reflected back to the In a vacuum environment (often referred to in the field of optics, the energy is reduced to 1/e ² of the initial energy), therefore, the optical film as an energy modulation mechanism must introduce aberrations into the system. In the optical design process, a set of feasible design schemes must consider the factors of subsequent processing and production. Optical thin films, as a key technology in extreme ultraviolet lithography technology, must be considered in the design process. The optical system after adding optical thin films must be considered. Make a reasonable assessment.

In the prior art, the processing of optical thin films by optical design software generally adopts the method of growing the thin film into the substrate (see CODEV, ZEMAX optical design software manual), that is, only the transmittance of the thin film introduced into the system and the value between [-π, π] phase difference, the base of the bare optical system is still used as the working surface when evaluating the image quality, so it is impossible to make a reasonable evaluation of the imaging quality of the optical system after adding the optical film, resulting in the optical system processed according to the design. Membrane compatibility issues.

Contents of the invention

The purpose of the present invention is to solve the problem that the existing optical design software cannot reasonably estimate the quality of the imaging system added with the optical film, resulting in the incompatibility of the optical system obtained by processing the optical film with the optical film. The optical system analysis and design method based on the law of energy conservation is used for the evaluation analysis and optimal design of the filmed optical system.

The invention provides a method for analyzing and designing an optical system based on the law of conservation of energy, the method comprising the following steps:

(1) Optimize the design of optical films in bare optical systems;

(2) Construct an equivalent working interface according to the structural parameters of the optical film and the bare optical system. The construction process is as follows:

Calculate the absorptivity R and transmittance T of the optical film;

When T<<R, according to the formula $R=\exp (-\frac{8\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\&Integral;}_0^{{\mathrm{D.}}^{,}}k(z,\mathrm{no}\left({\mathrm{\&theta;}}_i\right))\mathrm{dz})$ Obtain the effective incident depth D', in the formula, z is the coordinate that is perpendicular to the film surface downwards with the film surface as the origin, θ _i is the angle of incidence, and n(θ _i ) is the real part of the refractive index of the optical film material medium, k(z,n(θ _i )) is the extinction coefficient distribution of the optical film;

An equivalent working interface having the same energy modulation effect as the optical film is constructed between the surface of the optical film and the bottom surface of the optical film, and the vertical distance between the equivalent working interface and the surface of the optical film is D';

(3) Use the fitting algorithm to solve the system parameters that can represent the equivalent working interface and can be used by the optical design software to obtain the equivalent optical system;

(4) Evaluate the image quality of the equivalent optical system.

In the technical solution of the present invention, step (1) optimizes the specific process of designing the optical film in the bare optical system as follows: according to the structural parameters of the bare optical system, the distribution of the incident angle of light along with the effective illumination area of the mirror is solved, and then through the average incident angle distribution and The performance of optical thin films requires optimizing the structural parameters of optical thin films.

In the technical solution of the present invention, the specific process of the image quality evaluation described in step (4) is: input the system parameters obtained in step (3) into the optical design software, if the requirements are directly met, the design is ended, and it is called the bare optical system and the optical system. The compatibility of the film is excellent. If the requirements cannot be met, the image distance will be used as the optimization variable to optimize the equivalent optical system for the first time. If the requirements are met, the design will be terminated. It is said that the bare optical system has good compatibility with the optical film. Requirements, the equivalent optical system is re-optimized with the structural parameters in the equivalent optical system as variables. If the requirements are met, the design is terminated, and the compatibility between the bare optical system and the optical film is said to be qualified. If the requirements are not met, the bare optical system is called Compatibility with optical film is unqualified, redesign.

The beneficial effects of the present invention are:

(1) For the extreme ultraviolet light system, through strict electromagnetic field theory calculation, after the light energy is incident to a certain depth in the film, its energy will all be reflected back to the vacuum environment. Incidence depth, combined with optical film, mirror substrate and other factors to construct a virtual surface, which is equivalent to the real working surface of the optical system after adding optical film, called the equivalent working interface;

(2) An equivalent working interface is built in the optical system analysis and design method of the present invention, and the physical optical process of the modulation of the light energy by the thin film is converted into a more intuitive geometric optical process, thereby realizing the integration with existing optical design software The combination of the coating optical system makes a more comprehensive and reliable evaluation of the performance of the coating optical system, overcomes the weakness of the existing analysis method that can only analyze the relative phase shift and transmittance of [-π, π] introduced by the optical film, and is more intuitive. More clearly explain the effect of optical film on the optical system, and quickly complete the evaluation analysis and optimal design of the coating optical system;

(3) The optical system analysis and design method of the present invention is applicable to extreme ultraviolet lithography reflective systems whose optical film thickness is much larger than the operating wavelength of the system, and is also applicable to other coated optical systems, such as refractive systems, reflective systems or catadioptric systems .

Description of drawings

Fig. 1 is a schematic diagram of a coated optical element formed after adding an optical film on an optical substrate;

Figure 2 is the effect diagram obtained according to the equivalent working interface after the light is incident on the coated optical element;

Figure 3 is a flow chart of optical system analysis and design using equivalent working interface.

In the figure: 11, optical substrate, 12, first film layer, 13, second film layer, 14, bottom surface of optical film, 15, surface of optical film, 21, incident light, 22, light returning to vacuum environment, 23, etc. Effective working interface, 24, reflected light, 25, transmitted light, 26, a tiny area with an illumination area of S.

Detailed ways

Fig. 1 and Fig. 2 are the core schematic diagrams of the present invention. Combining Fig. 1 and Fig. 2, the construction principle of the equivalent working interface in the analysis and design of the optical system of the present invention is explained.

1 is a schematic diagram of a coated optical element formed after adding an optical film on an optical substrate 11. The optical film is generally a multilayer film system, which is formed by alternating arrangement of the first film layer 12 and the second film layer 13. The first film layer 12 and the second film layer 13 are made of two materials with different refractive indices, 14 is the bottom surface of the optical film, which is coplanar with the surface of the optical substrate 11, and 15 is the surface of the optical film.

Figure 2 is the effect diagram obtained according to the equivalent working interface after the light is incident on the coated optical element; from the perspective of energy modulation, assuming that the equivalent working interface of the coated optical element is 23, then, whether it is For reflective elements, the additional thickness D is the distance between the equivalent working interface 23 and the bottom surface 14 of the optical film, the effective incident depth D' is the distance between the equivalent working interface 23 and the surface 15 of the optical film, and the light intensity is The incident light 21 of I _si irradiates on the equivalent working interface 23 for reflection and transmission. The initial light intensity of the reflected light 24 is I _sr0 , and the light intensity of the light 22 returning to the vacuum environment is I _sr =I _si ·R, and the transmission The light intensity I _st =I _si T of the light 25 is analyzed for the tiny area 26 with the illumination area S,

Let the attenuation factor $\mathrm{AF}=\exp (-\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\&Integral;}_0^{{\mathrm{D.}}^{,}}k(z,\mathrm{no}\left({\mathrm{\&theta;}}_i\right))\mathrm{dz}),$ Then according to the law of conservation of energy:

I _si ·AF·S· _cosθi ＝I _sr0 ·S· _cosθr +I _st ·S· _cosθt (1)

In the formula, θ _r is the reflection angle, which is equal to the incident angle θ _i , and θ _t is the refraction angle of light in the optical substrate, which can be obtained by the formula n ₀ sinθ _i = n _s Sinθ _t , where n _s is the substrate refraction rate, n ₀ is the refractive index of vacuum;

Wherein the initial light intensity I _sr0 of the reflected light 24 continues to propagate in the optical film and finally returns to the vacuum to reach the light intensity I _sr of the transmitted light 25. This process can be expressed as:

I _sr = I _sro AF (2)

Combine formula (1) and formula (2) to get:

$<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; AF</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; AF</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Right now: $\mathrm{AF}=\frac{T\frac{\cos {\mathrm{\&theta;}}_t}{\cos {\mathrm{\&theta;}}_i}+\sqrt{{\left(T\frac{\cos {\mathrm{\&theta;}}_t}{\cos {\mathrm{\&theta;}}_i}\right)}^2+4R}}{2}---\left(4\right)$

When T<<R, This is the same as the formula $R=\exp (-\frac{8\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\&Integral;}_0^{{\mathrm{D.}}^{,}}k(z,\mathrm{no}\left({\mathrm{\&theta;}}_i\right))\mathrm{dz})$ is the same expression.

formula All parameters except the effective depth of incidence D' in are known or can be obtained by the method of characteristic matrix of optical thin film. Through this formula, the effective depth of incidence D' of optical thin film can be obtained to complete the construction of the equivalent working interface.

In order to realize the consistency between the model and the existing optical software symbol rules, an additional thickness D of the optical film is introduced, whose absolute value is the difference between the total thickness tT of the optical film and the effective depth of incidence D', according to the general symbol rules in the field of optical design, In the reflective element, when light is incident from left to right, the refractive index of the subsequent medium that the optical film is close to is negative, and vice versa, it is positive. According to the physical meaning shown by the effective incident depth D', it can be known that the optical film is on the optical substrate Additional thickness D=(tT-D')n on 11;

In the formula, n is the ideal substrate refractive index in optical system design. For example, for mirrors, the refractive index n=1 or -1, and its positive and negative values are related to the direction of light propagation.

Based on the additional thickness D and the substrate surface 14, use the fitting algorithm to solve the parameters of the equivalent working interface used by the optical design software, such as the radius of curvature, high-order aspheric parameters, etc.; or use Zernike polynomial fitting to solve the equivalent representation The Zernike coefficient of the working interface is used to construct an equivalent working system.

In conjunction with Fig. 3, the method for analyzing and designing an optical system based on the law of energy conservation of the present invention is described, including the following steps:

(1) The optimization analysis begins with a known bare optical system, and according to the structural parameters of the bare optical system, ray tracing is performed on each point of view, and the weighted average incident angle of the light emitted by the full field of view on each mirror surface to be analyzed is obtained , and its weight factor is the normalized light intensity of each field point in the field of view. For an axisymmetric bare optical system without central occlusion, it can be considered that the incident angle of the light emitted by the central field point on each mirror is its relative The average incident angle of reflection;

(2) According to the average incident angle and the performance requirements of the optical film, use the optical film optimization design software or write the corresponding program to design the optical film that meets the requirements, and use the transmittance threshold, uniformity requirements and the realization of the film thickness distribution as the standard to judge Whether the initial design of the optical thin film is qualified, for the situation where the influence of the optical thin film on the system needs to be considered, the optical thin film is generally designed by the exhaustive method, that is, the periodic thickness of the thin film, the thickness ratio of the film layer and the incident angle are used as variables to solve the transmittance distribution diagram And the additional thickness distribution diagram described later, etc., and finally obtain the optical film structural parameters that meet the requirements and are distributed with the position of the mirror surface from the distribution diagram;

(3) Calculate the structural parameters of the optical film by using the characteristic matrix of the optical film, and construct an equivalent working interface. The specific process is:

a. According to the law of energy conservation, without considering the scattering energy loss caused by the roughness of the optical film, the light energy incident into the film system can be divided into three parts, namely the absorption part, the reflection part and the transmission part, among which the reflection part and the transmission part can generally be obtained by calculation or measurement, and the absorption part can be obtained according to the energy conservation law, which is defined as follows:

A=I _Absorb /I ₀ ，R=I _Reflect /I ₀ ，T=I _Transmit /I ₀

Where I ₀ is the incident light energy, I _Absorb is the absorbed part of the light energy, I _Reflect is the reflected part of the light energy, I _Transmi is the transmitted part of the light energy, A, R, T are the absorptivity, reflectivity and transmittance of the film system, respectively. The rate can be obtained by calculating the characteristic matrix of the optical film;

b. Yes when T<<R, according to the formula $R=\exp (-\frac{8\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\&Integral;}_0^{{\mathrm{D.}}^{,}}k(z,\mathrm{no}\left({\mathrm{\&theta;}}_i\right))\mathrm{dz})$ Obtain the effective incident depth D' of light energy in the film;

In the formula, z is the coordinate perpendicular to the film surface downwards with the film surface as the origin, θ _i is the incident angle, n(θ _i ) is the real part of the refractive index of the optical film medium material, k(z,n(θ _i )) is the optical film extinction coefficient distribution, for the existing optical film, it is a function of film thickness z and incident angle θ _i ;

c. construct the equivalent working interface 23 that has the same energy modulation effect as the optical film between the optical film surface 15 and the optical film bottom surface 14, and the vertical distance between the equivalent working interface 23 and the optical film surface 15 is D';

(3) Use the fitting algorithm to solve the system parameters that can characterize the equivalent working interface with high precision and can be used by optical design software, such as radius of curvature, high-order aspheric parameters, etc.; or use Zernike polynomial fitting to solve the equivalent working interface The Zernike coefficient of , to construct an equivalent working system;

(4) Use the existing optical design software, such as CODEV and ZEMAX, to analyze and evaluate the equivalent working system. If the requirements are met, the design is terminated, and the compatibility between the bare optical system and the optical film is said to be excellent, and the designed optical system is excellent. If the requirements cannot be met Requirements, then use the image distance as the optimization variable to optimize the equivalent optical system for the first time, and evaluate the equivalent optical system after this optimization. If the requirements are met, the design ends. It is easy to realize. It is said that the bare optical system has good compatibility with the optical film, and the designed optical system is good. If it still does not meet the requirements, use as few structural parameters as possible in the equivalent optical system, such as only including the distance between the components and the object The distance and the image distance are variables to optimize the system again, and analyze and evaluate it. If the requirements are met, the optimization will end. Since the adjustment of the entire optical system is very difficult, it is said that the compatibility between the bare optical system and the optical film is qualified, and the designed If the optical system is qualified, if it does not meet the requirements, it is said that the compatibility between the bare optical system and the optical film is unqualified, and the designed optical system is unqualified and needs to be redesigned.

In the specific embodiment of the present invention, for an ideal film system, the extinction coefficient k(z,n(θ _i )) forms a rectangular tooth-shaped distribution with the change of film thickness, due to the absorption and specific The transmission path is related to the transmission path, and it is related to the incident angle and incident depth when propagating in the film, and the calculated effective incident depth D' is only the height perpendicular to the film surface, so the distribution function of the extinction coefficient with the incident depth z should pass through the light The incident angle is modulated; if the interdiffusion of each film interface in the film system is considered, the extinction coefficient can be expressed by an irregular sinusoidal function.

In the specific embodiment of the present invention, the bare optical system is a well-known technical term in the art, referring to an uncoated optical system, such as an uncoated extreme ultraviolet lithography reflection system, an uncoated refraction system, and an uncoated reflective system. system or uncoated catadioptric system.

In the specific embodiment of the present invention, it is the prior art in the art to optimize the design of the optical thin film in the bare optical system, such as coating on the mirror surface of the extreme ultraviolet lithography reflection system, refraction system, reflection system or catadioptric system Optical film.

In the specific embodiment of the present invention, the involved parameters are consistent with the definitions of parameters such as optical element shape, refractive index, and element spacing in existing optical design software.

In the specific implementation of the present invention, the evaluation index of whether the optical system meets the requirements is a well-known technology for those skilled in the art, and it is a commonly used evaluation index for optical design, including system aberration control, thin film process feasibility, component processing and mechanical assembly feasibility wait.

In the specific embodiment of the present invention, in the process of analyzing and optimizing the compatibility of the optical system, it is not simply implemented according to this route. In the optimization process, it is necessary to comprehensively weigh the difficulty of assembly, processing, and thin film preparation and the difficulty of pure optical design, and choose the most feasible solution. For example, if the optical system is not easy to disassemble and debug after the installation and adjustment, or irreparable losses may be caused during the adjustment process, then after optimizing the image distance, if the system does not meet the performance, it is necessary to redesign the scheme, and it is not suitable to carry out the second round of optimization .

Claims (3)

1. an optical system analysis and design method based on the law of conservation of energy, is characterized in that, comprises the following steps: (1) Optimize the design of optical films in bare optical systems; (2) Construct an equivalent working interface according to the structural parameters of the optical film and the bare optical system. The construction process is as follows: Calculate the reflectance R and transmittance T of the optical film; Set T<<R, according to the formula Obtain the effective incident depth D', in the formula, z is the origin with the film surface, the coordinates perpendicular to the film surface downward, _θi is the angle of incidence, n( _θi ) is the real part of the refractive index of the optical film material medium, k(z,n(θ _i )) is the extinction coefficient distribution of the optical film; An equivalent working interface having the same energy modulation effect as the optical film is constructed between the surface of the optical film and the bottom surface of the optical film, and the vertical distance between the equivalent working interface and the surface of the optical film is D'; (3) Use the fitting algorithm to solve the system parameters that can represent the equivalent working interface and can be used by the optical design software to obtain the equivalent optical system; (4) Evaluate the image quality of the equivalent optical system. 2. a kind of optical system analysis and design method based on the law of energy conservation according to claim 1, is characterized in that, step (1) the specific process of optimal design optical thin film in bare optical system is: according to bare optical system structure parameter Solve the distribution of the incident angle of light with the effective lighting area of the mirror, and then optimize the structural parameters of the optical film through the average incident angle distribution and the performance requirements of the optical film. 3. a kind of optical system analysis and design method based on the law of energy conservation according to claim 1, is characterized in that, the specific process of the described image quality evaluation of step (4) is: the system parameter that step (3) obtains Input the optical design software. If the requirements are directly met, the design is ended, and the compatibility between the bare optical system and the optical film is said to be excellent. If the requirements cannot be met, the image distance is used as the optimization variable to optimize the equivalent optical system for the first time. If the requirements are met, Then the design ends, and the bare optical system is said to have good compatibility with the optical film. If it still does not meet the requirements, then the equivalent optical system is optimized again with the structural parameters in the equivalent optical system as variables. If the requirements are met, the design ends, and it is called The compatibility between the bare optical system and the optical film is qualified. If the requirements are not met, it is said that the compatibility between the bare optical system and the optical film is unqualified and the design must be redesigned.