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WO2022083735A1 - 一种计算光刻投影物镜中朗奇剪切干涉图像的方法 - Google Patents

一种计算光刻投影物镜中朗奇剪切干涉图像的方法 Download PDF

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WO2022083735A1
WO2022083735A1 PCT/CN2021/125704 CN2021125704W WO2022083735A1 WO 2022083735 A1 WO2022083735 A1 WO 2022083735A1 CN 2021125704 W CN2021125704 W CN 2021125704W WO 2022083735 A1 WO2022083735 A1 WO 2022083735A1
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electric field
expression
function
image
light
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PCT/CN2021/125704
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English (en)
French (fr)
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牛志元
施伟杰
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深圳晶源信息技术有限公司东方晶源微电子科技（北京）有限公司深圳分公司
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Publication of WO2022083735A1 publication Critical patent/WO2022083735A1/zh

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    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
    • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
    • G03F7/70—Microphotolithographic exposure; Apparatus therefor
    • G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
    • G03F7/70591—Testing optical components
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
    • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
    • G01J9/0215—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods by shearing interferometric methods
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
    • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
    • G03F7/70—Microphotolithographic exposure; Apparatus therefor
    • G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
    • G03F7/70605—Workpiece metrology
    • G03F7/70616—Monitoring the printed patterns
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation

Definitions

  • the invention relates to the technical field of optical measurement, in particular to a method for calculating a Ronchi shearing interference image in a lithography projection objective lens.
  • the detection system that extracts the wave aberration of the projection objective lens with high precision and high speed is the core subsystem of the high-end lithography machine.
  • Wave aberration is the main parameter of the imaging quality of the projection objective, which directly determines the resolution and overlay accuracy of the lithography machine.
  • the wave aberration of the projection objective of the high-end lithography machine has reached below 1nm. The difference is more pronounced.
  • the object-side grating is an ideal periodic line grating (that is, a grating with infinitely many lines, and the line length is infinite), and the object-side grating is a 2D graphics, rather than complex two-dimensional graphics, has limitations; and the traditional detection method assumes that the imaging model is a scalar model rather than a strict vector model in the calculation process, and the receiving screen interference image calculation in the traditional detection method defaults to Far-field approximation technology (ie Fraunhofer diffraction region), however, these approximation conditions have certain limitations in practical applications, and it is difficult to obtain shear interference images accurately.
  • Far-field approximation technology ie Fraunhofer diffraction region
  • the present invention provides a Ronchi shearing interference in a computational lithography projection objective lens. image method.
  • the present invention provides a method for calculating the Langchi shearing interference image in a lithography projection objective lens, which is used to calculate and obtain the wave aberration of the measured projection objective lens,
  • the method includes the following steps, step S1: obtaining the scalar electric field function of the light incident on the object-side grating and the object-side grating spectrum of the object-side grating by calculating to obtain the electric field spectrum spatial distribution function of the light diffracted by the object-side grating
  • Step S2 the light passes through the measured projection objective lens, calculates the pupil function of the measured projection objective lens and calculates the electric field distribution expression at the exit pupil of the light in conjunction with the described electric field spectral spatial distribution function
  • the polarization information of the grating is obtained from the upper surface of the grating, and the electric field distribution expression at the exit pupil is converted from the sp component
  • Step S4 Calculate the RS integral kernel function, and calculate the electric field expression on the upper surface of the image square grating to obtain the electric field expression on the lower surface of the image square grating, which is based on the expression of the electric field on the lower surface of the image square grating formula and combined with the RS integral kernel function to calculate to obtain the shear interference pattern formed by multiple lights on the receiving screen;
  • Step S5 define the IMM (f x , f y ; f' x , f' y ) variable matrix and calculate it
  • the eigenvalue decomposition is performed to rewrite a plurality of shearing interference patterns and obtain the decomposition results, and the accurate shearing interference images of different shearing positions of the light on the receiving screen are obtained by repeatedly calculating the decomposition results.
  • the light irradiated on the object-side grating is multi-directional incident light output by the light source
  • the step S1 further includes the following steps; step S11: obtaining the light source frequency (s) of the light irradiated on the object-side grating by calculation x , s y ) and spatial frequency (f x , f y ), and obtain the scalar electric field function of the incident parallel light as U(x, y);
  • Step S13 further calculate the electric field spectrum spatial distribution function of the light diffracted by the object-side grating is M 1 (f x -s x ,f y -s y ), and its expression is:
  • step S11 the frequency of the light source (s x , s
  • the pupil function is P(f x , f y ), and its function expression is:
  • the radiation correction factor when the light is imaged at the exit pupil is calculated, and its expression is: Multiply the electric field spectral spatial distribution function, the pupil function and the radiation correction factor in turn to obtain the electric field distribution expression at the exit pupil:
  • the step S3 includes the following steps: Step S31 : the geometric rotation matrix R 3 ⁇ 2 is a 3 ⁇ 2 dimensional geometric rotation matrix, and the expression of the electric field distribution at the exit is expanded into a vector form by Jones vector. Obtain the electric field distribution vector expression at the exit; Step S32: convert the sp component of the local coordinate system of the electric field distribution vector expression at the exit into the xyz component of the global coordinate system to calculate the upper surface of the image square grating electric field expression; in step S31, the Jones vector for x polarization is For y polarization the Jones vector is Using the geometric rotation matrix R 3 ⁇ 2 to obtain the vector form expression of the electric field distribution expression at the exit pupil is: In step S32, the surface electric field expression on the image square grating is:
  • the electric field expression on the lower surface of the image-square grating is used to describe the electric field distribution of light after passing through the image-square grating, and the electric field expression on the lower surface of the image-square grating is:
  • the step S4 includes the following steps:
  • Step S41 Calculate the electric field distribution function expression of the receiving screen based on the lower surface electric field expression of the image square grating combined with the RS integral kernel function through diffraction integration, and the receiving screen electric field distribution function expression is:
  • Step S42 The ( ⁇ , ⁇ ) degrees of freedom in the expression of the electric field distribution function of the receiving screen are eliminated by integration and then perform fast Fourier calculation to obtain the scalar electric field function of the electric field formed by light on the receiving screen; the scalar electric field
  • the expression of the function is:
  • the RS integral kernel function is a Rayleigh-Sommerfeld integral kernel function
  • the expression of the RS integral kernel function is:
  • the function expression of r is:
  • the step S4 further includes the following steps: Step S43 : obtaining the light source function I(s x , s y ) used to describe the intensity distribution of the light source in the frequency space by calculation, and incoherently superposing the scalar electric field function
  • the superposition weight is the light source function I(s x , s y );
  • the step 5 further includes the following steps: Step S51: Store the decomposition result obtained by decomposing the eigenvalues of the IMM (f x , f y ; f′ x , f′ y ) variable matrix for multiple computations Using, the decomposition result includes eigenvalues and eigenvectors obtained by eigenvalue decomposition.
  • the method for calculating the Ronchi shearing interference image in a lithography projection objective lens has the following advantages:
  • a geometric rotation matrix R 3 ⁇ 2 is defined to represent the The sp component of the local coordinate system of the electric field distribution expression at the exit is converted into the xyz component of the global coordinate system, and the expression of the electric field distribution at the exit is further extended to a vector form through the Jones vector to obtain the vector expression of the electric field distribution at the exit.
  • the technical personnel can finally calculate the electric field expression on the upper surface of the image square grating through the vector expression; it can be understood that the method for calculating the Ronchi shear interference image in the lithography projection objective involved in the present invention is in the calculation of the image square
  • a strict vector model is used in the expression of the surface electric field on the grating, because when the light passes through the projection objective, it is more convenient to use the sp component to calculate, and when the light passes through the projection objective and irradiates the image square grating, it needs to be
  • the electric field is converted into the xyz components of the global coordinate system to facilitate the calculation, and finally the electric field expression on the upper surface of the image square grating is obtained by calculation.
  • This calculation method simplifies the calculation process and makes the calculation more convenient and effective for technicians. The work efficiency of technicians is improved, and the problem of time-consuming and labor-intensive caused by low calculation efficiency is avoided.
  • the method for calculating the Ronchi shear interference image in the lithography projection objective lens involved in the present invention combines the expression of the electric field on the lower surface of the image square grating with the RS integral kernel function and calculates the diffraction integral to finally obtain the expression used to express the light in The expression of the electric field distribution function of the receiving screen of the electric field distribution on the receiving screen; it can be understood that the method for calculating the Ronchi shear interference image in the lithography projection objective lens involved in the present invention calculates the process of the light from the image-side grating to the receiving screen When the electric field distribution in the light source is 1, the strict Rayleigh-Sommerfeld diffraction integral is used to calculate the electric field distribution function expression of the receiving screen, which makes the final result of the electric field distribution of the light more accurate, which is beneficial to finally obtain an accurate shearing interference image. It solves the problem that the traditional detection method is difficult to obtain the clipped interference image accurately.
  • an IMM(f x , f y is defined in the process of calculating the shearing interference image formed by the light on the receiving screen ; f′ x , f′ y ) variable matrix for decomposing sheared interference images at different clipping positions, and the IMM(f x , f y ; f′ x , f′ y ) variable matrix is the light source function I(s x , s y ) and the spectrum of the object-side grating, technicians can study different wave aberrations (that is , different effective pupil functions P ( f x , f y )), different image square gratings and shearing interference images at different shearing positions; it can be understood that the precise shearing interference images are mainly used to reflect the image on the receiving screen
  • the technician can calculate the wave aberration of the projection objective lens to be measured by inverse calculation by precisely shearing the interference image.
  • the calculation of diffraction integral improves the accuracy, so that the finally obtained wave aberration data is accurate and reliable, and avoids the problem of unreliable detection results caused by insufficient detection accuracy of traditional detection methods; further, the calculation method involved in the present invention
  • the method of Ronchi shearing interference images in the lithography projection objective can obtain multiple precise shearing interference images by decomposing the IMM (f x , f y ; f′ x , f′ y ) variable matrix at one time.
  • the decomposition result is stored in the disk, so that the technician can directly use the decomposition result in the subsequent calculation, which effectively improves the work efficiency of the technician and realizes the function of decomposing one time and using it multiple times.
  • FIG. 1 is a schematic block diagram of a process flow of a method for calculating a Ronchi shear interference image in a lithography projection objective lens provided by the first embodiment of the present invention
  • FIG. 2 is a schematic diagram of the Ronchi shearing interference principle of a method for calculating a Ronchi shearing interference image in a lithography projection objective lens provided by the first embodiment of the present invention
  • Fig. 3 is the object square grating pattern of a specific detection process provided by the second embodiment of the present invention.
  • FIG. 4 is an object-side grating space imaging of a specific detection process provided by the second embodiment of the present invention.
  • FIG. 5 is a shearing interference image of a specific detection process provided by the second embodiment of the present invention.
  • the object-side grating 2. The projection objective lens to be tested; 3. The image-side grating; 4. The receiving screen; z, the distance between the receiving screen and the image-side grating.
  • the first embodiment of the present invention provides a method for calculating the Ronchi shear interference image in a lithography projection objective lens, which is used to calculate and obtain the wave aberration of the projection objective lens 2 under test,
  • the method includes the following steps, step S1: obtaining the scalar electric field function of the light incident on the object-side grating 1 and the object-side grating spectrum of the object-side grating 1 by calculating to obtain the electric field spectrum of the light diffracted by the object-side grating 1 Spatial distribution function;
  • Step S2 light passes through the measured projection objective lens 2, calculates the pupil function of the measured projection objective lens 2, and calculates the electric field distribution expression at the exit pupil of the light in combination with the electric field spectrum spatial distribution function;
  • Step S3 light irradiation When the upper surface of the image-side grating (the upper surface of the image-side grating, that is, the side where the light first contacts the image-side grating 3), its polarization information is
  • the surface electric field expression is calculated in combination with the RS integral kernel function to obtain the shear interference pattern formed by a plurality of lights on the receiving screen 4;
  • Step S5 define IMM (f x , f y ; f′ x , f′ y ) variables matrix and perform eigenvalue decomposition on it to rewrite multiple shearing interference patterns and obtain the decomposition results, and obtain accurate shearing interference images of different shearing positions of light on the receiving screen 4 by repeatedly calculating the decomposition results.
  • Step S1 further includes the following steps; Step S11 : The light source frequency (s x , s y ) and spatial frequency (f x , f y ) of the light irradiated on the object-side grating 1 are obtained by calculation, and the scalar electric field function of the incident parallel light is U(x, y); Step S12: measure the perspective function of the object-side grating as m 1 (x′, y′) and perform Fourier transform on it to obtain the object-side grating spectrum as M 1 (f x , f y ); Step S13: further calculate the electric field spectrum spatial distribution function of the light diffracted by the object-side grating 1 as M 1 (f x -s x , f y -s
  • the receiving screen 4 will Obtain different clipped interference images.
  • the shearing interference image on the receiving screen 4 contains the aberration information of the projection objective lens 2 under test, and the technician can extract the projection objective lens under test by synthesizing the shearing interference images with different phase shifts 2 wave aberration.
  • step S2 the pupil function is P(f x , f y ), and its function expression is:
  • the radiation correction factor when the light is imaged at the exit pupil is calculated, and its expression is: Multiply the electric field spectral spatial distribution function, pupil function and radiation correction factor in turn to obtain the electric field distribution expression at the exit pupil:
  • step S3 includes the following steps: Step S31 : the geometric rotation matrix R 3 ⁇ 2 is a 3 ⁇ 2 dimensional geometric rotation matrix, and the expression of the electric field distribution at the outlet is extended to a vector form through the Jones vector to obtain the electric field distribution at the outlet.
  • Step S32 convert the sp component of the local coordinate system of the electric field distribution vector expression at the exit into the xyz component of the global coordinate system to calculate the electric field expression on the upper surface of the image square grating;
  • step S31 for The x-polarized Jones vector is The Jones vector for y polarization is Using the geometric rotation matrix R 3 ⁇ 2 , the vector form expression of the electric field distribution expression at the exit pupil is obtained as:
  • step S32 the surface electric field expression on the image square grating is:
  • the geometric rotation matrix R 3 ⁇ 2 represents the transformation of the sp component of the local coordinate system into the xyz component of the global coordinate system. It is more convenient to use the sp component to calculate the light when it passes through the projection objective After projecting the objective lens, in order to facilitate the calculation, it is necessary to convert the electric field of the light into the xyz components of the global coordinate system, and finally obtain the expression of the electric field on the upper surface of the image square grating.
  • a geometric rotation matrix R 3 ⁇ 2 is defined to represent the sp component of the local coordinate system of the electric field distribution expression at the exit pole is converted into the global coordinate.
  • the method for calculating the Ronchi shear interference image in the lithography projection objective involved in the present invention adopts a strict vector model in the process of calculating the surface electric field expression on the image square grating, because the light When passing through the projection objective lens, it is convenient to use the sp component for calculation, and in the process of light passing through the projection objective lens and irradiating the image square grating 3, it is necessary to convert the electric field into the xyz component of the global coordinate system to facilitate the calculation, and finally through the calculation The electric field expression on the upper surface of the square grating is obtained.
  • This calculation method simplifies the calculation process, makes it more convenient for technicians to perform calculations, effectively improves the work efficiency of technicians, and avoids the time-consuming and laborious work caused by low calculation efficiency. question.
  • the electric field expression on the lower surface of the image-square grating is used to describe the electric field distribution of light after passing through the image-square grating 3, and the electric field expression on the lower surface of the image-square grating is:
  • step S4 includes the following steps:
  • Step S41 Calculate the electric field distribution function expression of the receiving screen based on the lower surface electric field expression of the image square grating combined with the RS integral kernel function through diffraction integration, and the electric field distribution function expression of the receiving screen is:
  • Step S42 the ( ⁇ , ⁇ ) degrees of freedom in the expression of the electric field distribution function of the receiving screen are eliminated by integration and then perform a fast Fourier calculation to obtain a scalar electric field function that multiple lights form an electric field on the receiving screen 4;
  • the RS integral kernel function is the Rayleigh-Sommerfeld integral kernel function, and the expression of the RS integral kernel function is:
  • the method for calculating the Langqi shear interference image in the lithography projection objective adopts a strict lithography vector model and the Rayleigh-Sommerfeld diffraction integral to perform the electric field distribution (ie, the light intensity distribution). Therefore, there is no need to consider the near-field or far-field of the object-side grating 1 and the image-side grating 3, and the receiving screen 4 also does not need to consider factors such as paraxial approximation, which avoids the limitation of traditional testing methods, which makes it difficult to accurately obtain sheared interference images. The problem.
  • the present invention relates to The method of calculating the Ronchi shearing interference image in the lithography projection objective uses the strict Rayleigh-Sommerfeld diffraction integral to calculate the electric field distribution of the receiving screen when calculating the electric field distribution in the process of light from the image square grating 3 to the receiving screen 4.
  • the calculation of the function expression makes the final result of the electric field distribution of the light more accurate, which is beneficial to finally obtain an accurate shearing interference image, and solves the problem that the traditional detection method is difficult to obtain the shearing interference image accurately.
  • step S4 further includes the following steps: Step S43 : obtaining the light source function I(s x , s y ) for describing the intensity distribution of the light source in the frequency space by calculation, and performing incoherent superposition of the scalar electric field functions to obtain multiple
  • the shear interference pattern formed by the light in the incident direction on the receiving screen 4, its superposition weight is the light source function I(s x , s y );
  • the expression of the shearing interference pattern is:
  • step 5 further includes the following steps: Step S51: Store the decomposition result obtained by decomposing the eigenvalues of the IMM (f x , f y ; f′ x , f′ y ) variable matrix for multiple use, and the decomposition result includes The eigenvalues and eigenvectors obtained by eigenvalue decomposition; it can be understood that the method for calculating the Ronchi shear interference image in the lithography projection objective provided in the present invention decomposes the IMM(f x , f y ; f′ x , f′ y ) variable matrix to obtain multiple precise shearing interference images, and technicians can store the decomposition results obtained by eigenvalue decomposition into the disk, so as to facilitate technicians in subsequent calculations directly By using the decomposition result, the work efficiency of the technician is effectively improved, and the function of decomposing one time and using it multiple times is realized.
  • Step S51 Store the decomposition result obtained by decomposing the eigenvalue
  • the eigenvalue decomposition of the IMM(f x , f y ; f′ x , f′ y ) variable matrix can obtain its eigenvalues and eigenvalue vectors, IMM(f x , f y ; f′ x , f′ y )
  • the expression formula for eigenvalue decomposition of variable matrix is: The skilled person can rewrite the expression of the sheared interference pattern according to the above formula to obtain the expression of the exact sheared interference image as:
  • the IMM(f x , f y ; f′ x , f′ y ) variable matrix is a function of the light source function I (s x , s y ) and the spectrum of the object-side grating, and is used to study different wave aberrations (ie different The effective pupil function P(f x , f y )), different image square gratings 3 (that is, m 2 ( ⁇ , ⁇ ) parameters are different) and shear interference images at different shear positions;
  • the precise shearing interference image is mainly used to reflect the light intensity distribution of the light on the receiving screen 4, and the technician can perform inverse calculation through the precise shearing interference image to obtain the wave aberration of the projection objective lens to be tested;
  • the precise shearing interference image is obtained by using a strict vector model and strict diffraction integral calculation, which improves the accuracy, makes the final wave aberration data accurate and reliable, and avoids the lack of detection accuracy caused by traditional detection methods. Unreliable test results.
  • the second embodiment of the present invention provides a specific detection process.
  • the detection process is based on the method for calculating the Ronchi shearing interference image in the lithography projection objective provided in the first embodiment of the present invention. It is a calculation method, which is substituted into a concretely constructed application scenario to further illustrate the content of the present invention, but is not intended to limit the present invention, and its specific implementation steps are as follows:
  • Step 1 Input the illumination mode to the light source, so that the illumination mode is traditional illumination, the coherence factor of the light emitted by the light source in this illumination mode is 1, the wavelength is 632 nm, and the polarization direction is X;
  • Step 3 Input the parameters of the object-side grating 1.
  • the GDS pattern of the object-side grating 1 is a 4-line grating (as shown in Figure 3), and the specific parameters of the object-side grating 1 are: the period of the object-side grating 1 is 25um , the line width of the object-side grating 1 is 12.5um, and the length of the object-side grating 1 is 100um; the object-side mask type of the input object-side grating 1 is a binary mask and has a dark field;
  • Step 4 Enter the information of the image-side grating 3, which is set to be exactly the same as the object-side mask.
  • Step 5 Input the phase shift of the image square grating 3, and its phase shift is 0um and 6.25um in turn (ie 1/4 period);
  • Step 6 The distance z between the input receiving screen and the image square grating 3 is 5000um, the size of the calculated image is 5000um*5000um, and the sampling pixels of the receiving screen 4 are 256*256 pixels;
  • Step 7 Perform the calculation task with the method for calculating the Ronchi shearing interference image in the lithography projection objective provided in the first embodiment of the present invention. After the calculation task is completed, the aerial image of the object-side grating 1 can be obtained (as shown in FIG. 4 ). shown) and the result of clipping the interference image (shown in Figure 5).
  • the method for calculating the Ronchi shearing interference image in a lithography projection objective lens has the following advantages:
  • a geometric rotation matrix R 3 ⁇ 2 is defined to represent the The sp component of the local coordinate system of the electric field distribution expression at the exit is converted into the xyz component of the global coordinate system, and the expression of the electric field distribution at the exit is further extended to a vector form through the Jones vector to obtain the vector expression of the electric field distribution at the exit.
  • the technical personnel can finally calculate the electric field expression on the upper surface of the image square grating through the vector expression; it can be understood that the method for calculating the Ronchi shear interference image in the lithography projection objective involved in the present invention is in the calculation of the image square
  • a strict vector model is used in the expression of the surface electric field on the grating, because when the light passes through the projection objective, it is more convenient to use the sp component to calculate, and when the light passes through the projection objective and irradiates the image square grating, it needs to be
  • the electric field is converted into the xyz components of the global coordinate system to facilitate the calculation, and finally the electric field expression on the upper surface of the image square grating is obtained through calculation.
  • the work efficiency of technicians is improved, and the problem of time-consuming and labor-intensive caused by low calculation efficiency is avoided.
  • the method for calculating the Ronchi shear interference image in the lithography projection objective lens involved in the present invention combines the expression of the electric field on the lower surface of the image square grating with the RS integral kernel function and calculates the diffraction integral to finally obtain the expression used to express the light in The expression of the electric field distribution function of the receiving screen of the electric field distribution on the receiving screen; it can be understood that the method for calculating the Ronchi shear interference image in the lithography projection objective lens involved in the present invention calculates the process of the light from the image-side grating to the receiving screen When the electric field distribution in the light source is 1, the strict Rayleigh-Sommerfeld diffraction integral is used to calculate the electric field distribution function expression of the receiving screen, which makes the final result of the electric field distribution of the light more accurate, which is beneficial to finally obtain an accurate shearing interference image. It solves the problem that the traditional detection method is difficult to obtain the clipped interference image accurately.
  • an IMM(f x , f y is defined in the process of calculating the shearing interference image formed by the light on the receiving screen ; f′ x , f′ y ) variable matrix for decomposing sheared interference images at different clipping positions, and the IMM(f x , f y ; f′ x , f′ y ) variable matrix is the light source function I(s x , s y ) and the spectrum of the object-side grating, technicians can study different wave aberrations (that is , different effective pupil functions P ( f x , f y )), different image square gratings and shearing interference images at different shearing positions; it can be understood that the precise shearing interference image is mainly used to reflect the light intensity distribution of the light on the receiving screen, and the technician can use the The precise shearing interference image is
  • the precise shearing interference image is calculated by using a strict vector model and strict diffraction integration, its accuracy has been improved.
  • the final obtained wave aberration data is accurate and reliable, and the problem of unreliable detection results caused by insufficient detection accuracy of the traditional detection method is avoided.
  • decomposing the IMM (f x , f y ; f′ x , f′ y ) variable matrix at one time multiple precise shearing interference images can be obtained.
  • the technician stores the decomposition results in the disk to facilitate the technicians in the follow-up.
  • the decomposition result is directly used in the calculation of , which effectively improves the work efficiency of technicians, and realizes the function of decomposing one time and using it many times.

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  • Spectroscopy & Molecular Physics (AREA)
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Abstract

一种计算光刻投影物镜(2)中朗奇剪切干涉图像的方法，在方法中，光源发出的光从物方光栅(1)到像方光栅(3)的过程中采用严格的光刻矢量模型进行计算，同时可以适用于任意形状的物方、像方光栅；并且光从像方光栅(3)到接收屏(4)的过程中采用严格的Rayleigh-Sommerfeld衍射积分进行计算。计算光刻投影物镜(2)中朗奇剪切干涉图像的方法由于采用严格的光刻矢量模型以及Rayleigh-Sommerfeld衍射积分进行计算，所以无需考虑物方、像方光栅(1、3)的近场或远场，接收屏(4)也无需考虑傍轴近似等因素，避免了传统测试方法局限性大导致难以精确的得到剪切干涉图像的问题。

Description

一种计算光刻投影物镜中朗奇剪切干涉图像的方法 【技术领域】
本发明涉及光学测量技术领域，特别涉及一种计算光刻投影物镜中朗奇剪切干涉图像的方法。
【背景技术】
高精度、高速度提取投影物镜波像差的检测系统是高端光刻机的核心分系统。波像差是投影物镜成像质量的主要参数，直接决定光刻机的分辨率和套刻精度，高端光刻机投影物镜波像差已达到1nm以下，而随着产率提高，透镜的热像差更加显著。
在现有的基于朗奇剪切干涉图像的检测方法中，通常假定物方光栅是理想的周期线条光栅(即具有无穷多线条的光栅，并且线条长度为无穷长)，该物方光栅为一维图形，而不是复杂的二维图形，具有局限性；并且传统检测方法的计算过程中假定成像模型是标量模型，而非严格的矢量模型，并且传统检测方法中的接收屏干涉图像计算默认采用远场近似技术(即夫琅禾费衍射区域)，然而这些近似条件在实际应用当中都具有一定局限性，难以精确的得到剪切干涉图像。
【发明内容】
为了克服目前现有的基于朗奇剪切干涉图像的检测方法中计算方法局限性大导致难以精确的得到剪切干涉图像的问题，本发明提供一种计算光刻投影物镜中朗奇剪切干涉图像的方法。
本发明为解决上述技术问题，提供的技术方案如下：本发明提供了一种计算光刻投影物镜中朗奇剪切干涉图 像的方法，用于计算并得出被测投影物镜的波像差，该方法包括以下步骤，步骤S1：通过计算得出射入物方光栅的光的标量电场函数及物方光栅的物方光栅频谱以得出被物方光栅衍射后的光的电场频谱空间分布函数；步骤S2：光通过被测投影物镜，计算得出被测投影物镜的光瞳函数并结合所述电场频谱空间分布函数算得光的出瞳处电场分布表达式；步骤S3：光照射在像方光栅上表面时得出其偏振信息，并通过几何旋转矩阵R 3×2将出瞳处电场分布表达式从局部坐标系的sp分量转化为全局坐标系的xyz分量以计算得出入射光的像方光栅上表面电场表达式；步骤S4：计算得出RS积分核函数，并将像方光栅上表面电场表达式进行计算得出光的像方光栅下表面电场表达式，基于像方光栅下表面电场表达式并结合RS积分核函数进行计算以得到多个光在接收屏上形成的剪切干涉图形；步骤S5：定义IMM(f x,f y；f′ x,f′ y)变量矩阵并对其进行本征值分解以重写多个剪切干涉图形并得到分解结果，通过重复计算所述分解结果以得出光在接收屏上不同剪切位置的精确剪切干涉图像。
优选地，照射到物方光栅上的光为光源输出的多方向的入射光，所述步骤S1进一步包括以下步骤；步骤S11：通过计算得出照射在物方光栅上的光的光源频率(s x,s y)及空间频率(f x,f y)并得出射入平行光的标量电场函数为U(x,y)；步骤S12：测得物方光栅透视率函数为m 1(x′,y′)并对其进行傅里叶变换以得出物方光栅频谱为M 1(f x,f y)；步骤S13：进一步算出经过物方光栅衍射后的光的电场频谱空间分布函数为M 1(f x-s x,f y-s y)，其表达式为：
Figure PCTCN2021125704-appb-000001
在步骤S11中光源频率(s x,s y)用于描述光的入射方向，标量电场函数U(x,y)的表达式为：
Figure PCTCN2021125704-appb-000002
优选地，在所述步骤S2中，所述光瞳函数为P(f x,f y)，其函数表达式为：
Figure PCTCN2021125704-appb-000003
计算得出光在出瞳处成像时的辐射修正因子，其表达式为：
Figure PCTCN2021125704-appb-000004
将所述电场频谱空间分布函数、所述光瞳函数及所述辐射修正因子依次相乘以得到所述出瞳处电场分布表达式：
Figure PCTCN2021125704-appb-000005
优选地，所述步骤S3包括以下步骤：步骤S31：所述几何旋转矩阵R 3×2为3x2维的几何旋转矩阵，并通过琼斯矢量将所述出曈处电场分布表达式扩展为矢量形式以得到出曈处电场分布矢量表达式；步骤S32：将所述出曈处电场分布矢量表达式的局部坐标系的sp分量转化为全局坐标系的xyz分量以计算得出所述像方光栅上表面电场表达式；在步骤S31中，对于x偏振所述琼斯矢量为
Figure PCTCN2021125704-appb-000006
对于y偏振所述琼斯矢量为
Figure PCTCN2021125704-appb-000007
利用所述几何旋转矩阵R 3×2得出所述出瞳处电场分布表达式的矢量形式表达式为：
Figure PCTCN2021125704-appb-000008
在步骤S32中，所述像方光栅上表面电场表达式为：
Figure PCTCN2021125704-appb-000009
Figure PCTCN2021125704-appb-000010
优选地，所述像方光栅下表面电场表达式用于描述光在经过像方光栅后的电场分布，所述像方光栅下表面电场表达式为：
Figure PCTCN2021125704-appb-000011
优选地，所述步骤S4包括以下步骤：
步骤S41：基于所述像方光栅下表面电场表达式并结合RS积分核函数经过衍射积分计算得出接收屏电场分布函数表达式，所述接收屏电场分布函数表达式为：
Figure PCTCN2021125704-appb-000012
Figure PCTCN2021125704-appb-000013
步骤S42：将所述接收屏电场分布函数表达式中 的(ε,η)自由度通过积分消除后进行快速傅里叶计算以得到光在接收屏上形成电场的标量电场函数；所述标量电场函数的表达式为:
Figure PCTCN2021125704-appb-000014
Figure PCTCN2021125704-appb-000015
优选地，所述RS积分核函数为Rayleigh-Sommerfeld积分核函数，所述RS积分核函数的表达式为：
Figure PCTCN2021125704-appb-000016
在所述RS积分核函数的表达式中，r的函数表达式为：
Figure PCTCN2021125704-appb-000017
优选地，所述步骤S4进一步包括以下步骤：步骤S43：通过计算得到用于描述光源在频率空间中强度分布的光源函数I(s x,s y)，将所述标量电场函数进行非相干叠加以得到多个入射方向的光在接收屏上形成的剪切干涉图形，其叠加权重为光源函数I(s x,s y)；
所述剪切干涉图形的表达式为：
Figure PCTCN2021125704-appb-000018
优选地，所述步骤5进一步包括以下步骤：步骤S51：将IMM(f x,f y；f′ x,f′ y)变量矩阵本征值分解得到的所述分解结果储存以供多次计算使用，所述分解结果包括通过本征值分解得到的本征值及本征向量。
优选地，在所述步骤S5中，所述IMM(f x,f y；f′ x,f′ y)变量矩阵为厄密的矩阵且本征值为实数，其函数表达式为：IMM(f x,f y；f′ x,f′ y)＝∫ds xds yI(s x,s y)M(f x-s x,f y-s y)M *(f′ x-s x,f′ y-s y)；对所述IMM(f x,f y；f′ x,f′ y)变量矩阵进行本征值分解可得：
Figure PCTCN2021125704-appb-000019
Figure PCTCN2021125704-appb-000020
以此将所述剪切干涉图形的表达式重写以得到所述精确剪切干涉图像的表达式：
Figure PCTCN2021125704-appb-000021
与现有技术相比，本发明提供的一种计算光刻投影物镜中朗奇剪切干涉图像的方法，具有以下优点：
(1)在本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法中，由于采用严格的光刻矢量模型以及Rayleigh-Sommerfeld衍射积分对电场分布(即光强分布)进行计算，所以无需考虑物方光栅及像方光栅的近场或远场，接收屏也无需考虑傍轴近似等因素，避免了传统测试方法局限性大导致难以精确的得到剪切干涉图像的问题。
(2)在本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法中，在计算光在像方光栅上的电场分布时，通过定义一几何旋转矩阵R 3×2以表示把出曈处电场分布表达式的局部坐标系的sp分量转化为全局坐标系的xyz分量，并进一步通过琼斯矢量把出曈处电场分布表达式扩展为矢量形式以得到出曈处电场分布的矢量表达式，技术人员最终可通过该矢量表达式计算得出像方光栅上表面电场表达式；可以理解的是，本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法在计算像方光栅上表面电场表达式的过程中采用了严格的矢量模型，因为光在通过投影物镜时，用sp分量对计算比较方便，而在光通过投影物镜后并照射到像方光栅的过程中就需要把电场转化为全局坐标系的xyz分量以方便计算，最终通过计算得出像方光栅上表面电场表达式，这种计算方法使得计算流程得到了简化，技术人员在进行计算时更加方便，有效地提高了技术人员的工作效率，避免了计算效率低导致费时费力的问题。
(3)本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法通过将像方光栅下表面电场表达式结合RS积分核函数并经过衍射积分计算以最终得出用于表达光在 接收屏上电场分布的接收屏电场分布函数表达式；可以理解的是，本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法在计算光从像方光栅到接收屏这一过程中的电场分布时，采用了严格的Rayleigh-Sommerfeld衍射积分对接收屏电场分布函数表达式进行计算，使得最终得到的光的电场分布结果更为准确，有利于最终得到精确的剪切干涉图像，解决了传统检测方法难以精确地得到剪切干涉图像的问题。
(4)在本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法中，通过在计算光在接收屏上形成的剪切干涉图像的过程中定义一IMM(f x,f y；f′ x,f′ y)变量矩阵以用于分解不同剪切位置的剪切干涉图像，且IMM(f x,f y；f′ x,f′ y)变量矩阵为光源函数I(s x,s y)和物方光栅频谱的函数，技术人员可通过IMM(f x,f y；f′ x,f′ y)变量矩阵研究不同波像差(即不同的有效光瞳函数P(f x,f y))、不同像方光栅及不同剪切位置的剪切干涉图像；可以理解的是，精确剪切干涉图像主要用于反映接收屏上
(5)光的光强分布，技术人员可通过精确剪切干涉图像进行反推计算以得出待测投影物镜的波像差，由于精确剪切干涉图像是通过采用严格的矢量模型及严格的衍射积分计算所得，使其精确度得到了提高，使得最终得出的波像差数据精确可靠，避免了传统检测方法检测精确度不足导致检测结果不可靠的问题；进一步地，本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法通过一次性分解IMM(f x,f y；f′ x,f′ y)变量矩阵即可得到多个精确剪切干涉图像，技术人员通过将分解结果存入磁盘中，以方便技术人员在后续的计算中直接使用该分解结果，有效提高了技术人员的工作效率，实现了一次分解多次使用的功能。
【附图说明】
图1是本发明第一实施例提供的一种计算光刻投影物镜中朗奇剪切干涉图像的方法的流程示意框图；
图2是本发明第一实施例提供的一种计算光刻投影物镜中朗奇剪切干涉图像的方法之朗奇剪切干涉原理示意图；
图3是本发明第二实施例提供的一种具体的检测流程之物方光栅图形；
图4是本发明第二实施例提供的一种具体的检测流程之物方光栅空间成像；
图5是本发明第二实施例提供的一种具体的检测流程之剪切干涉图像。
附图标记说明：
1、物方光栅；2、被测投影物镜；3、像方光栅；4、接收屏；z、接收屏距离像方光栅的距离。
【具体实施方式】
为了使本发明的目的，技术方案及优点更加清楚明白，以下结合附图及实施实例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。
需要说明的是，当元件被称为“固定于”另一个元件，它可以直接在另一个元件上或者也可以存在居中的元件。当一个元件被认为是“连接”另一个元件，它可以是直接连接到另一个元件或者可能同时存在居中元件。本文所使用的术语“垂直的”、“水平的”、“左”、“右”以及类似的表述只是为了说明的目的。
请结合参阅图1-图2，本发明第一实施例提供了一种 计算光刻投影物镜中朗奇剪切干涉图像的方法，用于计算并得出被测投影物镜2的波像差，该方法包括以下步骤，步骤S1：通过计算得出射入物方光栅1的光的标量电场函数及物方光栅1的物方光栅频谱以得出被物方光栅1衍射后的光的电场频谱空间分布函数；步骤S2：光通过被测投影物镜2，计算得出被测投影物镜2的光瞳函数并结合电场频谱空间分布函数算得光的出瞳处电场分布表达式；步骤S3：光照射在像方光栅上表面时(像方光栅上表面即光首先接触像方光栅3的一面)得出其偏振信息，并通过几何旋转矩阵R 3×2将出瞳处电场分布表达式从局部坐标系的sp分量转化为全局坐标系的xyz分量以计算得出入射光的像方光栅上表面电场表达式(即出瞳处电场分布表达式扩展为矢量形式)；步骤S4：计算得出RS积分核函数，并将像方光栅上表面电场表达式进行计算得出光的像方光栅下表面电场表达式(像方光栅下表面即光离开像方光栅3时最后接触的一面)，基于像方光栅下表面电场表达式并结合RS积分核函数进行计算以得到多个光在接收屏4上形成的剪切干涉图形；步骤S5：定义IMM(f x,f y；f′ x,f′ y)变量矩阵并对其进行本征值分解以重写多个剪切干涉图形并得到分解结果，通过重复计算分解结果以得出光在接收屏4上不同剪切位置的精确剪切干涉图像。
具体地，照射到物方光栅1上的光为光源输出的多个方向的入射光，其中相同方向的光为相干光，而不同方向的光是非相干光；步骤S1进一步包括以下步骤；步骤S11：通过计算得出照射在物方光栅1上的光的光源频率(s x,s y)及空间频率(f x,f y)并得出射入平行光的标量电场函数为U(x,y)；步骤S12：测得物方光栅透视率函数为m 1(x′,y′)并对其进行傅里叶变换以得出物方光栅频谱为M 1(f x,f y)；步骤S13：进一步算出经过物方光栅1衍射后的光的电场频谱空间分布函数为M 1(f x-s x,f y-s y)，其表达式为：
Figure PCTCN2021125704-appb-000022
在步骤S11中光源频率(s x,s y)用于描述光的入射方向，标量 电场函数U(x,y)的表达式为：
Figure PCTCN2021125704-appb-000023
光源频率(s x,s y)用于描述光的方向。
请继续参阅图2，不同方向的平行光(不同方向的光是非相干的，即非相干光，如图2中箭头所示方向射入)照射到物方光栅1上，光被物方光栅1衍射后，进入被测投影物镜2；光在通过被测投影物镜2过程中，携带了投影物镜的波像差信息，在其通过被测投影物镜2后，被位于像平面的像方光栅3再次衍射，最终成像在远处的接收屏4上；当像方光栅3移动不同的距离，即接收屏4距离像方光栅3的距离z发生变化(即移相)时，接收屏4上将得到不同的剪切干涉图像。在该过程中，可以看出，接收屏4上的剪切干涉图像包含了被测投影物镜2的像差信息，技术人员通过综合不同移相的剪切干涉图像就可以提取出被测投影物镜2的波像差。
具体地，在步骤S2中，光瞳函数为P(f x,f y)，其函数表达式为：
Figure PCTCN2021125704-appb-000024
计算得出光在出瞳处成像时的辐射修正因子，其表达式为：
Figure PCTCN2021125704-appb-000025
将电场频谱空间分布函数、光瞳函数及辐射修正因子依次相乘以得到出瞳处电场分布表达式：
Figure PCTCN2021125704-appb-000026
具体地，步骤S3包括以下步骤：步骤S31：几何旋转矩阵R 3×2为3x2维的几何旋转矩阵，并通过琼斯矢量将出曈处电场分布表达式扩展为矢量形式以得到出曈处电场分布矢量表达式；步骤S32：将出曈处电场分布矢量表达式的局部坐标系的sp分量转化为全局坐标系的xyz分量以计算得出像方光栅上表面电场表达式；在步骤S31中，对于x偏振琼斯矢量为
Figure PCTCN2021125704-appb-000027
对于y偏振琼斯矢量为
Figure PCTCN2021125704-appb-000028
利用几何旋 转矩阵R 3×2得出出瞳处电场分布表达式的矢量形式表达式为：
Figure PCTCN2021125704-appb-000029
在步骤S32中，像方光栅上表面电场表达式为：
Figure PCTCN2021125704-appb-000030
Figure PCTCN2021125704-appb-000031
进一步地，几何旋转矩阵R 3×2表示把局部坐标系的sp分量转化为全局坐标系的xyz分量，光在通过被测投影物镜2时用sp分量对其进行计算比较方便，而在其通过投影物镜后，为了计算方便则需要把光的电场转化为全局坐标系的xyz分量，最终得到像方光栅上表面电场表达式。
可以理解的是，在计算光在像方光栅3上的电场分布时，通过定义一几何旋转矩阵R 3×2以表示把出曈处电场分布表达式的局部坐标系的sp分量转化为全局坐标系的xyz分量，并进一步通过琼斯矢量把出曈处电场分布表达式扩展为矢量形式以得到出曈处电场分布的矢量表达式，技术人员最终可通过该矢量表达式计算得出像方光栅上表面电场表达式；可以理解的是，本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法在计算像方光栅上表面电场表达式的过程中采用了严格的矢量模型，因为光在通过投影物镜时，用sp分量对计算比较方便，而在光通过投影物镜后并照射到像方光栅3的过程中就需要把电场转化为全局坐标系的xyz分量以方便计算，最终通过计算得出像方光栅上表面电场表达式，这种计算方法使得计算流程得到了简化，技术人员在进行计算时更加方便，有效地提高了技术人员的工作效率，避免了计算效率低导致费时费力的问题。
具体地，像方光栅下表面电场表达式用于描述光在经过像方光栅3后的电场分布，像方光栅下表面电场表达式为：
Figure PCTCN2021125704-appb-000032
具体地，步骤S4包括以下步骤：
步骤S41：基于像方光栅下表面电场表达式并结合RS 积分核函数经过衍射积分计算得出接收屏电场分布函数表达式，接收屏电场分布函数表达式为：
Figure PCTCN2021125704-appb-000033
Figure PCTCN2021125704-appb-000034
步骤S42：将接收屏电场分布函数表达式中的(ε,η)自由度通过积分消除后进行快速傅里叶计算以得到多个光在接收屏4上形成电场的标量电场函数；
标量电场函数的表达式为:
Figure PCTCN2021125704-appb-000035
具体地，RS积分核函数为Rayleigh-Sommerfeld积分核函数，RS积分核函数的表达式为：
Figure PCTCN2021125704-appb-000036
在RS积分核函数的表达式中，r的函数表达式为：
Figure PCTCN2021125704-appb-000037
可以理解的是，由于本发明中提供的计算光刻投影物镜中郎奇剪切干涉图像的方法采用的是严格的光刻矢量模型以及Rayleigh-Sommerfeld衍射积分对电场分布(即光强分布)进行计算，所以无需考虑物方光栅1及像方光栅3的近场或远场，接收屏4也无需考虑傍轴近似等因素，避免了传统测试方法局限性大导致难以精确的得到剪切干涉图像的问题。
进一步地，通过将像方光栅下表面电场表达式结合RS积分核函数并经过衍射积分计算，以得出用于表达光在接收屏4上电场分布的接收屏电场分布函数表达式，本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法在计算光从像方光栅3到接收屏4这一过程中的电场分布时，采用了严格的Rayleigh-Sommerfeld衍射积分对接收屏电场分布函数表达式进行计算，使得最终得到的光的电场分布结果更为准确，有利于最终得到精确的剪切干涉图像，解决了传统检测方法难以精确地得到剪切干涉图像的问题。
具体地，步骤S4进一步包括以下步骤：步骤S43：通 过计算得到用于描述光源在频率空间中强度分布的光源函数I(s x,s y)，将标量电场函数进行非相干叠加以得到多个入射方向的光在接收屏4上形成的剪切干涉图形，其叠加权重为光源函数I(s x,s y)；
剪切干涉图形的表达式为：
Figure PCTCN2021125704-appb-000038
具体地，步骤5进一步包括以下步骤：步骤S51：将IMM(f x,f y；f′ x,f′ y)变量矩阵本征值分解得到的分解结果储存以供多次使用，分解结果包括通过本征值分解得到的本征值及本征向量；可以理解的是，本发明中提供的计算光刻投影物镜中朗奇剪切干涉图像的方法通过一次性分解IMM(f x,f y；f′ x,f′ y)变量矩阵即可得到多个精确剪切干涉图像，技术人员可将本征值分解得出的分解结果存入磁盘中，以方便技术人员在后续的计算中直接使用该分解结果，有效提高了技术人员的工作效率，实现了一次分解多次使用的功能。
具体地，在步骤S5中，IMM(f x,f y；f′ x,f′ y)变量矩阵为厄密的矩阵且本征值为实数，其函数表达式为：IMM(f x,f y；f′ x,f′ y)＝∫ds xds yI(s x,s y)M(f x-s x,f y-s y)M *(f′ x-s x,f′ y-s y)；容易证明IMM(f x,f y；f′ x,f′ y)＝IMM *(f′ x,f′ y；f x,f y)，所以可得IMM(f x,f y；f′ x,f′ y)变量矩阵为厄密的，且其本征值为实数；
对IMM(f x,f y；f′ x,f′ y)变量矩阵进行本征值分解可得到其本征值以及本征值向量，IMM(f x,f y；f′ x,f′ y)变量矩阵进行本征值分解的表达公式为：
Figure PCTCN2021125704-appb-000039
技术人员可根据上述公式将剪切干涉图形的表达式重写以得到精确剪切干涉图像的表达式为：
Figure PCTCN2021125704-appb-000040
进一步地，IMM(f x,f y；f′ x,f′ y)变量矩阵为光源函数I(s x,s y)和物方光栅频谱的函数，并用于研究不同波像差(即不同的有效光瞳函数P(f x,f y))、不同像方光栅3(即m 2(ε,η)参数不同)及不同剪切位置的剪切干涉图像；
可以理解的是，精确剪切干涉图像主要用于反映接收屏4上光的光强分布，技术人员可通过精确剪切干涉图像进行反推计算以得出待测投影物镜的波像差；由于精确剪切干涉图像是通过采用严格的矢量模型及严格的衍射积分计算所得，使其精确度得到了提高，使得最终得出的波像差数据精确可靠，避免了传统检测方法检测精确度不足导致检测结果不可靠的问题。
请结合参阅图3-图5，本发明第二实施例提供一种具体的检测流程，该检测流程以本发明第一实施例中提供的计算光刻投影物镜中朗奇剪切干涉图像的方法为计算方法，以将其代入到具体构建的应用场景中以进一步说明本发明内容，但并不用于限定本发明，其具体实施步骤如下所示：
步骤1：对光源输入照明模式，使其照明模式为传统照明，光源在该照明模式下发出的光的相干因子为1，且其波长为632nm、偏振方向为X；
步骤S2：输入被测投影物镜2的数值孔径NA＝0.4，并输入被测投影物镜2的波像差Z9＝632nm；
步骤3：将物方光栅1参数输入，该物方光栅1的GDS图形为4线条光栅(如图3所示)，且该物方光栅1的具体参数为：物方光栅1的周期为25um，物方光栅1的线条宽度为12.5um，物方光栅1的长度为100um；输入的物方光栅1的物方掩模类型为二元掩模，并具有暗场；
步骤4：输入像方光栅3信息，这里设置为同物方掩模完全相同。
步骤5：输入像方光栅3的移相，其移相依次为0um和6.25um(即1/4周期)；
步骤6：输入接收屏距离像方光栅3的距离z为5000um，计算图像的大小为5000um*5000um，且该接收屏4的采样像素为256*256像素；
步骤7：以本发明第一实施例中提供的计算光刻投影物镜中朗奇剪切干涉图像的方法进行计算任务，当计算任务完成后，可以得到物方光栅1的空间像(如图4所示)以及剪切干涉图像的结果(如图5所示)。
与现有技术相比，本发明提供的一种计算光刻投影物镜中朗奇剪切干涉图像的方法，具有以下优点：
(1)在本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法中，由于采用严格的光刻矢量模型以及Rayleigh-Sommerfeld衍射积分对电场分布(即光强分布)进行计算，所以无需考虑物方光栅及像方光栅的近场或远场，接收屏也无需考虑傍轴近似等因素，避免了传统测试方法局限性大导致难以精确的得到剪切干涉图像的问题。
(2)在本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法中，在计算光在像方光栅上的电场分布时，通过定义一几何旋转矩阵R 3×2以表示把出曈处电场分布表达式的局部坐标系的sp分量转化为全局坐标系的xyz分量，并进一步通过琼斯矢量把出曈处电场分布表达式扩展为矢量形式以得到出曈处电场分布的矢量表达式，技术人员最终可通过该矢量表达式计算得出像方光栅上表面电场表达式；可以理解的是，本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法在计算像方光栅上表面电场表达式的过程中采用了严格的矢量模型，因为光在通过投影物镜时，用sp分量对计算比较方便，而在光通过投影物镜后并照射到像方光栅的过程中就需要把电场转化为全局坐 标系的xyz分量以方便计算，最终通过计算得出像方光栅上表面电场表达式，这种计算方法使得计算流程得到了简化，技术人员在进行计算时更加方便，有效地提高了技术人员的工作效率，避免了计算效率低导致费时费力的问题。
(3)本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法通过将像方光栅下表面电场表达式结合RS积分核函数并经过衍射积分计算以最终得出用于表达光在接收屏上电场分布的接收屏电场分布函数表达式；可以理解的是，本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法在计算光从像方光栅到接收屏这一过程中的电场分布时，采用了严格的Rayleigh-Sommerfeld衍射积分对接收屏电场分布函数表达式进行计算，使得最终得到的光的电场分布结果更为准确，有利于最终得到精确的剪切干涉图像，解决了传统检测方法难以精确地得到剪切干涉图像的问题。
(4)在本发明涉及的计算光刻投影物镜中朗奇剪切干涉图像的方法中，通过在计算光在接收屏上形成的剪切干涉图像的过程中定义一IMM(f x,f y；f′ x,f′ y)变量矩阵以用于分解不同剪切位置的剪切干涉图像，且IMM(f x,f y；f′ x,f′ y)变量矩阵为光源函数I(s x,s y)和物方光栅频谱的函数，技术人员可通过IMM(f x,f y；f′ x,f′ y)变量矩阵研究不同波像差(即不同的有效光瞳函数P(f x,f y))、不同像方光栅及不同剪切位置的剪切干涉图像；可以理解的是，精确剪切干涉图像主要用于反映接收屏上光的光强分布，技术人员可通过精确剪切干涉图像进行反推计算以得出待测投影物镜的波像差，由于精确剪切干涉图像是通过采用严格的矢量模型及严格的衍射积分计算所得，使其精确度得到了提高，使得最终得出的波像差数据精确可靠，避免了传统检测方法检测精确度不足导致检测结果不可靠的问题；进一步地，本发明涉及的计算 光刻投影物镜中朗奇剪切干涉图像的方法通过一次性分解IMM(f x,f y；f′ x,f′ y)变量矩阵即可得到多个精确剪切干涉图像，技术人员通过将分解结果存入磁盘中，以方便技术人员在后续的计算中直接使用该分解结果，有效提高了技术人员的工作效率，实现了一次分解多次使用的功能。

Claims (10)

  1. 一种计算光刻投影物镜中朗奇剪切干涉图像的方法，用于计算并得出被测投影物镜的波像差，其特征在于：该方法包括以下步骤，
    步骤S1：通过计算得出射入物方光栅的光的标量电场函数及物方光栅的物方光栅频谱以得出被物方光栅衍射后的光的电场频谱空间分布函数；
    步骤S2：光通过被测投影物镜，计算得出被测投影物镜的光瞳函数并结合所述电场频谱空间分布函数算得光的出瞳处电场分布表达式；
    步骤S3：光照射在像方光栅上表面时得出其偏振信息，并通过几何旋转矩阵R 3×2将出瞳处电场分布表达式从局部坐标系的sp分量转化为全局坐标系的xyz分量以计算得出入射光的像方光栅上表面电场表达式；
    步骤S4：计算得出RS积分核函数，并将像方光栅上表面电场表达式进行计算得出光的像方光栅下表面电场表达式，基于像方光栅下表面电场表达式并结合RS积分核函数进行计算以得到光在接收屏上形成的剪切干涉图形；
    步骤S5：定义IMM(f x,f y；f′ x,f′ y)变量矩阵并对其进行本征值分解以重写多个剪切干涉图形并得到分解结果，通过重复计算所述分解结果以得出光在接收屏上不同剪切位置的精确剪切干涉图像。
  2. 如权利要求1所述的一种计算光刻投影物镜中朗奇剪切干涉图像的方法，其特征在于：照射到物方光栅上的光为光源输出的多方向的入射光，所述步骤S1进一步包括以下步骤；
    步骤S11：通过计算得出照射在物方光栅上的光的光源频率(s x,s y)及空间频率(f x,f y)并得出射入平行光的标量电场函数为U(x,y)；
    步骤S12：测得物方光栅透视率函数为m 1(x′,y′)并对其进 行傅里叶变换以得出物方光栅频谱为M 1(f x,f y)；
    步骤S13：进一步算出经过物方光栅衍射后的光的电场频谱空间分布函数为M 1(f x-s x,f y-s y)，其表达式为：
    Figure PCTCN2021125704-appb-100001
    在步骤S11中光源频率(s x,s y)用于描述光的入射方向，标量电场函数U(x,y)的表达式为：
    Figure PCTCN2021125704-appb-100002
  3. 如权利要求2所述的一种计算光刻投影物镜中朗奇剪切干涉图像的方法，其特征在于：在所述步骤S2中，所述光瞳函数为P(f x,f y)，其函数表达式为：
    Figure PCTCN2021125704-appb-100003
    计算得出光在出瞳处成像时的辐射修正因子，其表达式为：
    Figure PCTCN2021125704-appb-100004
    将所述电场频谱空间分布函数、所述光瞳函数及所述辐射修正因子依次相乘以得到所述出瞳处电场分布表达式：
    Figure PCTCN2021125704-appb-100005
  4. 如权利要求1所述的一种计算光刻投影物镜中朗奇剪切干涉图像的方法，其特征在于：所述步骤S3包括以下步骤：
    步骤S31：所述几何旋转矩阵R 3×2为3x2维的几何旋转矩阵，并通过琼斯矢量将所述出曈处电场分布表达式扩展为矢量形式以得到出曈处电场分布矢量表达式；
    步骤S32：将所述出曈处电场分布矢量表达式的局部坐标系的sp分量转化为全局坐标系的xyz分量以计算得出所述像方光栅上表面电场表达式；
    在步骤S31中，对于x偏振所述琼斯矢量为
    Figure PCTCN2021125704-appb-100006
    对于y偏振所述琼斯矢量为
    Figure PCTCN2021125704-appb-100007
    利用所述几何旋转矩阵R 3×2得出所述出瞳处电场分布表达式的矢量形式表达式为：
    Figure PCTCN2021125704-appb-100008
    在步骤S32中，所述像方光栅上表面电场表达式为：
    Figure PCTCN2021125704-appb-100009
  5. 如权利要求1所述的一种计算光刻投影物镜中朗奇剪切干涉图像的方法，其特征在于：所述像方光栅下表面电场表达式用于描述光在经过像方光栅后的电场分布，所述像方光栅下表面电场表达式为：
    Figure PCTCN2021125704-appb-100010
  6. 如权利要求5所述的一种计算光刻投影物镜中朗奇剪切干涉图像的方法，其特征在于：所述步骤S4包括以下步骤：
    步骤S41：基于所述像方光栅下表面电场表达式并结合RS积分核函数经过衍射积分计算得出接收屏电场分布函数表达式，所述接收屏电场分布函数表达式为：
    Figure PCTCN2021125704-appb-100011
    步骤S42：将所述接收屏电场分布函数表达式中的(ε,η)自由度通过积分消除后进行快速傅里叶计算以得到光在接收屏上形成电场的标量电场函数；
    所述标量电场函数的表达式为:
    Figure PCTCN2021125704-appb-100012
  7. 如权利要求6所述的一种计算光刻投影物镜中朗奇剪切干涉图像的方法，其特征在于：所述RS积分核函数为Rayleigh-Sommerfeld积分核函数，所述RS积分核函数的表达式为：
    Figure PCTCN2021125704-appb-100013
    在所述RS积分核函数的表达式中，r的函数表达式为：
    Figure PCTCN2021125704-appb-100014
  8. 如权利要求7所述的一种计算光刻投影物镜中朗奇 剪切干涉图像的方法，其特征在于：所述步骤S 4进一步包括以下步骤：
    步骤S43：通过计算得到用于描述光源在频率空间中强度分布的光源函数I(s x,s y)，将所述标量电场函数进行非相干叠加以得到多个入射方向的光在接收屏上形成的剪切干涉图形，其叠加权重为光源函数I(s x,s y)；
    所述剪切干涉图形的表达式为：
    Figure PCTCN2021125704-appb-100015
  9. 如权利要求8所述的一种计算光刻投影物镜中朗奇剪切干涉图像的方法，其特征在于：所述步骤5进一步包括以下步骤：
    步骤S51：将IMM(f x,f y；f′ x,f′ y)变量矩阵本征值分解得到的所述分解结果储存以供多次计算使用，所述分解结果包括通过本征值分解得到的本征值及本征向量。
  10. 如权利要求9所述的一种计算光刻投影物镜中朗奇剪切干涉图像的方法，其特征在于：在所述步骤S 5中，所述IMM(f x,f y；f′ x,f′ y)变量矩阵为厄密的矩阵且本征值为实数，其函数表达式为：IMM(f x,f y；f′ x,f′ y)＝∫ds xds yI(s x,s y)M(f x-s x,f y-s y)M *(f′ x-s x,f′ y-s y)；
    对所述IMM(f x,f y；f′ x,f′ y)变量矩阵进行本征值分解可得：
    Figure PCTCN2021125704-appb-100016
    以此将所述剪切干涉图形的表达式重写以得到所述精确剪切干涉图像的表达式：
    Figure PCTCN2021125704-appb-100017
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