CN103226241A - Optical system analysis design method based on energy conservation law - Google Patents

Abstract

The invention provides an optical system analysis design method based on an energy conservation law and belongs to the field of optical design. The method solves the problems that a processing mode of the existing optical design software for an optical thin film cannot predict the imaging quality of the optical system additionally provided with the optical thin film reasonably, so that the designed and processed optical system is not compatible with the optical thin film. The method establishes an equivalent working interface from energy modulation by taking a strict electromagnetic field theory as a starting point, constructs the equivalent optical system additionally provided with the optical thin film according to bare optical system parameters, and evaluates and analyzes the system. The method overcomes defects in processing the optical thin film with the existing optical design software, a complicated physical optic course in the optical thin film is equivalent to a geometrical optic course, and the time and cost are saved in comparison with the existing optical software.

Description

A kind of optical system analysis design method based on law of conservation of energy

Technical field

The present invention relates to a kind of optical system analysis design method, can be applied in the evaluation analysis and optimal design of optical system, belong to the optical design field based on law of conservation of energy.

Background technology

Extreme ultraviolet lithography (EUVL) adopts the extreme ultraviolet (EUV) of 13.5nm as operation wavelength, all opaque and refractive index approaches 1 to nearly all material to this wavelength, therefore the EUVL system must adopt the total-reflection type system, and must be coated with Mo/Si increase the reflectivity optical thin film on minute surface.The existing Mo/Si film thickness of extreme ultraviolet lithography that is used for is about about 300nm, much larger than its operation wavelength, calculate through strict Theory of Electromagnetic Field, luminous energy incides certain depth in film after, its energy is with (energy that often refers in the optical field is reduced to the 1/e of zero energy in whole reflected back vacuum environments ²), therefore, optical thin film must be introduced aberration to system as a kind of energy modulation scheme.In the optical design process, the feasible design proposal of one cover must be considered the factor that following process is made, optical thin film must take in design process as a gordian technique in the extreme ultraviolet lithography, must carry out reasonable assessment to the optical system behind the interpolation optical thin film.

In the prior art, optical design software is generally taked the mode (referring to CODEV, ZEMAX optical design software instructions) of the basad growth inside of film to the processing of optical thin film, promptly only consider the transmitance of film drawing-in system and between [π, π] phasic difference, when carrying out the picture element assessment is workplace with naked optical system substrate still, therefore can't make reasonable assessment to the image quality of adding the optical system behind the optical thin film, cause by Design and Machining gained optical system can't with the problem of optical thin film compatibility.

Summary of the invention

The objective of the invention is to solve existing optical design software can't make rationally the imaging system quality of adding optical thin film the processing mode of optical thin film and estimating, cause by Design and Machining gained optical system can't with the problem of optical thin film compatibility, a kind of optical system analysis design method based on law of conservation of energy is provided, is used to have the evaluation analysis and the optimal design of film optical system.

The invention provides a kind of optical system analysis design method based on law of conservation of energy, this method may further comprise the steps:

(1) optimal design optical thin film in naked optical system;

(2) make up equivalent working interface according to optical thin film and naked optical system structure parameter, building process is as follows:

The absorptivity R of calculating optical film, transmissivity T;

T＜＜during R, according to formula $R=\exp (-\frac{8\mathrm{\π}}{\mathrm{\λ}}{\∫}_0^{D^{,}}k(z,n\left({\mathrm{\θ}}_i\right))\mathrm{dz})$ Try to achieve effective incident depth D ', in the formula, z is for being initial point with the film surface, perpendicular to the downward coordinate of film surface, θ _iBe incident angle, n (θ _i) be the real part of optical thin film material medium refractive index, k (z, n (θ _i)) be the extinction coefficient distribution of optical thin film;

Make up the equivalent working interface that has the identical energy modulating action with optical thin film between optical thin film surface and optical thin film bottom surface, the vertical range on described equivalent working interface and optical thin film surface is D ';

(3) systematic parameter of utilizing fitting algorithm to find the solution can to characterize equivalent working interface and being used by optical design software obtains equivalent optical system;

(4) equivalent optical system is carried out image quality evaluation.

In the technical scheme of the present invention, step (1) detailed process of optimal design optical thin film in naked optical system is: according to the distribution of naked optical system structure parametric solution angle of incidence of light with minute surface effective lighting area, obtain the optical thin-film structure parameter by average incident angle distribution and the optimization of optical thin film performance requirement again.

In the technical scheme of the present invention, the detailed process of the described image quality evaluation of step (4) is: the systematic parameter that step (3) obtains is imported optical design software, if directly meet the demands, finish design, claim that naked optical system and optical thin film compatibility are excellent, if can not meet the demands, be optimization variable then, equivalent optical system is optimized first, if meet the demands with the image distance, then finish design, claiming naked optical system and optical thin film compatible good, if still do not meet the demands, is that variable is to equivalent optical system suboptimization again with the structural parameters in the equivalent optical system then, if meet the demands, then finish design, claim that naked optical system and optical thin film compatibility are qualified, if do not meet the demands, claim that naked optical system and optical thin film compatibility are defective, redesign.

The invention has the beneficial effects as follows:

(1) for the extreme ultraviolet system, calculate through strict Theory of Electromagnetic Field, luminous energy incides certain depth in film after, its energy is with in whole reflected back vacuum environments, the present invention finds the solution the effective incident degree of depth of luminous energy in film according to law of conservation of energy, and making up one virtual in conjunction with factors such as optical thin film, minute surface substrates, equivalence is called equivalent working interface for adding the real work face of the optical system behind the optical thin film;

(2) made up equivalent working interface in the optical system analysis design method of the present invention, film is converted to more intuitive geometrical optics process to this physical optics process of the modulation of luminous energy, thereby realized and the combining of existing optical design software, the coated optics performance has been made more comprehensively assessment reliably, overcome existing analytical approach and only can introduce [π optical thin film, π] relative phase shift and the weakness analyzed of transmitance, more directly perceived, clearer and more definite explanation optical thin film has been finished the evaluation analysis and the optimal design of coated optics apace to the effect of optical system;

(3) optical system analysis design method of the present invention is applicable to the extreme ultraviolet photolithographic reflecting system of optical film thickness much larger than the system works wavelength, also is applicable to other coated optics, as refraction type system, reflect system or refraction-reflection system.

Description of drawings

Fig. 1 is for adding the coated optical element synoptic diagram that forms behind the optical thin film on the optical substrate;

Fig. 2 incides the design sketch that obtains according to equivalent working interface behind the coated optical element for light;

Fig. 3 analyzes design flow diagram for utilizing equivalent working interface to carry out optical system.

Among the figure: 11, optical substrate, 12, the first film layer, 13, second thin layer, 14, the optical thin film bottom surface, 15, the optical thin film surface, 21, incident light, 22, return the light of vacuum environment, 23, equivalent working interface, 24, reflected light, 25, transmitted light, 26, lighting area is the tiny area of S.

Embodiment

Fig. 1 and Fig. 2 are central principle figure of the present invention, set forth the structure principle of the equivalent working interface of the present invention in optical system analysis design in conjunction with Fig. 1 and Fig. 2.

Fig. 1 is for adding the coated optical element synoptic diagram that forms behind the optical thin film on the optical substrate 11, described optical thin film is generally assembly of thin films, replacing arrangement by the first film layer 12 and second thin layer 13 constitutes, the material that the first film layer 12 and second thin layer 13 are adopted is the material of two kinds of different refractivities, 14 is the optical thin film bottom surface, with optical substrate 11 surface co-planar, 15 is the optical thin film surface.

Fig. 2 is for after light incides coated optical element, the design sketch that obtains according to equivalent working interface; Angle from the energy modulation, the equivalent working interface of supposing this coated optical element is 23, so, no matter be for transmission-type element or reflecting element, its additional thickness D is equivalent working interface 23 to the distance between the optical thin film bottom surface 14, effective incident depth D ' be equivalent working interface 23 to the distance between the optical thin film surface 15, light intensity is I _Si Incident light 21 shine on the equivalent working interface 23 reflection and transmission take place, the initial light intensity of reflected light 24 is I _Sr0, the light intensity of returning the light 22 in the vacuum environment is I _Sr=I _SiR, the light intensity I of transmitted light 25 _St=I _SiT is that the tiny area 26 of S is analyzed to lighting area,

Make decay factor $\mathrm{AF}=\exp (-\frac{4\mathrm{\π}}{\mathrm{\λ}}{\∫}_0^{D^{,}}k(z,n\left({\mathrm{\θ}}_i\right))\mathrm{dz}),$ Then have according to law of conservation of energy:

I _si·AF·S·cosθ _i＝I _sr0·S·cosθ _r+I _st·S·cosθ _t (1)

In the formula, θ _rBe reflection angle, equal incident angle θ _i, θ _tBe the refraction angle of light in optical substrate, can pass through formula n ₀Sin θ _i=n _sSin θ _tTry to achieve, in the formula, n _sBe substrate refractive index, n ₀Refractive index for vacuum;

The initial light intensity I of reflected light 24 wherein _Sr0Continuation is propagated in optical thin film and is returned the light intensity I that reaches transmitted light 25 in the vacuum at last _Sr, this process can be expressed as:

I _sr＝I _sroAF (2)

Obtain in conjunction with (1) formula and (2) formula:

$(\mathrm{AF}-\frac{R}{\mathrm{AF}})\cos {\mathrm{\θ}}_i=T\cos {\mathrm{\θ}}_t---\left(3\right)$

That is: $\mathrm{AF}=\frac{T\frac{\cos {\mathrm{\θ}}_t}{\cos {\mathrm{\θ}}_i}+\sqrt{{\left(T\frac{\cos {\mathrm{\θ}}_t}{\cos {\mathrm{\θ}}_i}\right)}^2+4R}}{2}---\left(4\right)$

Work as T During＜＜R,

This and formula $R=\exp (-\frac{8\mathrm{\π}}{\mathrm{\λ}}{\∫}_0^{D^{,}}k(z,n\left({\mathrm{\θ}}_i\right))\mathrm{dz})$ It is identical expression.

Formula

In except that effective incident depth D ' all parameters all knownly maybe can try to achieve by optical thin film eigenmatrix method, can try to achieve effective incident depth D of optical thin film by this formula ', finish the structure of equivalent working interface.

For realizing the consistance of described model and existing optics software symbolic rule, introduce optical thin film additional thickness D, its absolute value is optical thin film total thickness t T and effective incident depth D ' poor, according to general symbol(s) rule in the optical design field, in reflecting element, when light incident from left to right, the subsequent medium refractive index that optical thin film is close to is for negative, otherwise then for just, again according to effective incident depth D ' shown in the physics meaning, as can be known, the additional thickness D=of optical thin film on optical substrate 11 (tT-D ') n;

In the formula, n is a refractive index at the bottom of the ideal basis in the design of Optical System, as for catoptron, and its refractive index n=1 or-1, its positive and negative value is relevant with the light ray propagation direction.

Based on additional thickness D and substrate surface 14, adopt fitting algorithm to find the solution the parameter of the equivalent working interface that is used by optical design software, as radius-of-curvature, high order aspheric surface parameter etc.; Or adopt the Zernike fitting of a polynomial to find the solution the Zernike coefficient that characterizes equivalent working interface, construct equivalent work system.

Set forth the optical system analysis design method that the present invention is based on law of conservation of energy in conjunction with Fig. 3, may further comprise the steps:

(1) optimizes analysis and start from a known naked optical system, according to naked optical system structure parameter, each visual field point is carried out ray tracing, find the solution the weighted mean incident angle of light on each minute surface to be analyzed of sending full visual field, its weight factor is the normalization light intensity of each visual field point in the visual field, for rotational symmetry and there is not the naked optical system of central obscuration, can think that light that center visual field point sent is in the incident angle of each minute surface average incident angle for its mapping;

(2) according to average incident angle and optical thin film performance requirement, utilize the optical thin film optimizing Design Software or write the optical thin film that the corresponding program design meets the demands, with the transmitance threshold value, the realized grade that uniformity requirement and film thickness distribute judges for standard whether the optical thin film initial designs is qualified, consider the situation of optical thin film for needs to systematic influence, the general method of exhaustion design optical thin film that adopts, promptly with the film periodic thickness, thicknesses of layers when incident angle is a variable, find the solution its transmitance distribution plan and aftermentioned additional thickness distribution plan etc., final from distribution plan, be met requirement, the optical thin-film structure parameter that distributes with mirror position;

(3) utilize the structural parameters of optical thin film eigenmatrix calculating optical film, make up equivalent working interface, detailed process is:

A. according to law of conservation of energy, do not considering under the scattared energy loss prerequisite that the optical thin film roughness causes, the luminous energy that incides in the film system can be divided into three parts, be respectively absorption portion, reflecting part and transmission part, wherein reflecting part and transmission part generally can obtain by calculating or measuring, according to the law of conservation of energy part that can be absorbed, do as giving a definition:

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

I wherein ₀Be incident optical energy, I _AbsorbBe absorption portion luminous energy, I _ReflectBe reflecting part luminous energy, I _TransmiFor transmissive portions divides luminous energy, A, R, T are respectively absorptivity, reflectivity and the transmitance of film system, all can calculate by the optical thin film eigenmatrix and try to achieve;

B. T＜＜have during R, according to formula $R=\exp (-\frac{8\mathrm{\π}}{\mathrm{\λ}}{\∫}_0^{D^{,}}k(z,n\left({\mathrm{\θ}}_i\right))\mathrm{dz})$ Try to achieve the effective incident depth D of luminous energy in film ';

In the formula, z is for being initial point with the film surface, perpendicular to the downward coordinate of film surface, and θ _iBe incident angle, n (θ _i) be the real part of optical thin film dielectric material refractive index, k (z, n (θ _i)) be that the optical thin film extinction coefficient distributes, for optical thin film, it is film thickness z and incident angle θ _iFunction;

C. make up the equivalent working interface 23 that has the identical energy modulating action with optical thin film between optical thin film surface 15 and optical thin film bottom surface 14, equivalent working interface 23 is D ' with the vertical range on optical thin film surface 15;

(3) adopt fitting algorithm to find the solution the systematic parameter of can characterized with good accuracy equivalence working interface and can be used by optical design software, as radius-of-curvature, high order aspheric surface parameter etc.; Or adopt the Zernike fitting of a polynomial to find the solution the Zernike coefficient that characterizes equivalent working interface, construct equivalent work system;

(4) utilize existing optical design software, as CODEV, ZEMAX carries out assay to equivalent work system, if meet the demands, finish design, claim that naked optical system and optical thin film compatibility are excellent, designed optical system is excellent, if can not meet the demands, it then is optimization variable with the image distance, equivalent optical system is optimized first, and estimate equivalent optical system after this suboptimization, if meet the demands, finish design, because for the system of having worked, adjusting its image distance more easily realizes, claim naked optical system and optical thin film compatible good, designed optical system is good, if still do not meet the demands, then with structural parameters the least possible in the equivalent optical system, as only comprising distance and object distance between each element, image distance be variable to system's suboptimization again, and do assay, if meet the demands, finish to optimize, and since very big to the adjustment difficulty of whole optical system, claim that naked optical system and optical thin film compatibility are qualified, and designed optical system is qualified, if do not meet the demands, claim that then naked optical system and optical thin film compatibility are defective, designed optical system is defective, needs redesign.

In the specific embodiment of the invention, for desirable film be extinction coefficient k (z, n (θ _i)) along with the rectangular toothed that is varied to of film thickness distributes, because the absorption that light was taken place when propagating in absorbing medium is relevant with concrete transmission path, relevant with the incident degree of depth when in film, propagating with incident angle, and effective incident depth D of being calculated ' only be height perpendicular to film surface, so extinction coefficient should be modulated by angle of incidence of light with the distribution function of incident depth z; If consider the phase counterdiffusion of each rete interface in the film system, then its extinction coefficient can be with non-regular sinusoid function representation.

In the specific embodiment of the invention, described naked optical system is the techniques well known noun, refer to uncoated optical system, as uncoated extreme ultraviolet photolithographic reflecting system, uncoated refraction type system, uncoated reflect system or uncoated refraction-reflection system.

In the specific embodiment of the invention, the optimal design optical thin film is a state of the art in naked optical system, as the optical thin film that is coated with on the minute surface of extreme ultraviolet photolithographic reflecting system, refraction type system, reflect system or refraction-reflection system.

In the specific embodiment of the invention, has consistance about optical element shape, refractive index, the isoparametric definition of element spacing in related each parameter and the existing optical design software.

In the specific embodiment of the invention, the deliberated index whether optical system meets the demands is a technology as well known to those skilled in the art, be optical design evaluation index commonly used, comprise that system aberration control, thin-film technique realizability, element are processed and machinery is debug feasibility etc.

In the specific embodiment of the invention, the optical system compatibility is analyzed with optimizing process in, be not to implement according to this route simply.In optimizing process, must comprehensively weigh debug, the difficulty of the difficulty of processing, film preparation and pure optical design, select the scheme of the easiest realization.Such as, if optical system finish debug after not easily-disassembled debugging, or may cause irremediable loss in the debug process, then, just need the redesign scheme image distance being optimized the back if system does not satisfy performance, should not carry out two and take turns optimization.

Claims (3)

1. the optical system analysis design method based on law of conservation of energy is characterized in that, may further comprise the steps:

(1) optimal design optical thin film in naked optical system;

(2) make up equivalent working interface according to optical thin film and naked optical system structure parameter, building process is as follows:

The absorptivity R of calculating optical film, transmissivity T;

T＜＜during R, according to formula $R=\exp (-\frac{8\mathrm{\π}}{\mathrm{\λ}}{\∫}_0^{D^{,}}k(z,n\left({\mathrm{\θ}}_i\right))\mathrm{dz}),$ Try to achieve effective incident depth D ', in the formula, z is for being initial point with the film surface, perpendicular to the downward coordinate of film surface, θ _iBe incident angle, n (θ _i) be the real part of optical thin film material medium refractive index, k (z, n (θ _i)) be the extinction coefficient distribution of optical thin film;

Make up the equivalent working interface that has the identical energy modulating action with optical thin film between optical thin film surface and optical thin film bottom surface, the vertical range on described equivalent working interface and optical thin film surface is D ';

(3) systematic parameter of utilizing fitting algorithm to find the solution can to characterize equivalent working interface and being used by optical design software obtains equivalent optical system;

(4) equivalent optical system is carried out image quality evaluation.

2. a kind of optical system analysis design method according to claim 1 based on law of conservation of energy, it is characterized in that, step (1) detailed process of optimal design optical thin film in naked optical system is: according to the distribution of naked optical system structure parametric solution angle of incidence of light with minute surface effective lighting area, obtain the optical thin-film structure parameter by average incident angle distribution and the optimization of optical thin film performance requirement again.

3. a kind of optical system analysis design method according to claim 1 based on law of conservation of energy, it is characterized in that, the detailed process of the described image quality evaluation of step (4) is: the systematic parameter that step (3) obtains is imported optical design software, if directly meet the demands, finish design, claim that naked optical system and optical thin film compatibility are excellent, if can not meet the demands, it then is optimization variable with the image distance, equivalent optical system is optimized first, if meet the demands, then finish design, claim naked optical system and optical thin film compatible good, if still do not meet the demands, then with the structural parameters in the equivalent optical system be variable to equivalent optical system suboptimization again, if meet the demands, then finish design, claim that naked optical system and optical thin film compatibility are qualified, if do not meet the demands, claim that naked optical system and optical thin film compatibility are defective, redesign.

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