A method for obtaining spatial image of patterned wafer based on strict vector diffraction integral

Abstract

The present invention discloses a method for obtaining an aerial image of a patterned wafer based on a strict vector diffraction integral, which belongs to the technical field of wafer defect detection and comprises the following steps: discretizing the wafer pattern into a plurality of discrete points, and at the same time, discretizing the shape of the illumination light source into a plurality of point light sources according to the type of illumination light source and obtaining the coordinates of a single point light source; for each point light source, obtaining an aerial image of the wafer pattern corresponding to each discrete point when illuminated by the point light source by using its coordinates by a strict vector diffraction integral model; superimposing the aerial images of the wafer pattern corresponding to all the point light sources to obtain an aerial image of the wafer pattern corresponding to partially coherent illumination, thereby achieving accurate acquisition of the aerial image of the wafer pattern, thereby effectively improving the reliability and efficiency of wafer defect detection, meeting the urgent demand of the semiconductor industry for high-precision and high-adaptability detection technology, and promoting the improvement of the manufacturing quality of integrated circuit chips.

Description

Technical Field

[0001] The present invention belongs to the technical field of wafer defect detection, and in particular relates to a method for obtaining an aerial image of a patterned wafer based on strict vector diffraction integration. Background Art

[0002] In today's digital age, integrated circuit chips, as core components of various electronic devices, have a reliability and performance that directly determines the quality and functionality of these products. Defect detection in integrated circuit chips has become a critical step in ensuring high-quality chip production, primarily encompassing two key areas: electrical performance testing and machine vision inspection.

[0003] Machine vision inspection is further categorized into macro-level chip appearance inspection (AOI) and micro-level nano-level defect detection. Macro-level AOI can quickly detect obvious surface defects such as scratches, stains, and pin deformation, providing strong support for initial chip screening. Nano-level defect detection, on the other hand, focuses on extremely small flaws within the chip. These nano-level defects can have a profound impact on chip performance, and therefore are more challenging to detect.

[0004] In mainstream nano-level defect inspection equipment, the operating principle is that light from a light source first passes through a precision shaping device to adjust the light into a specific shape, and then focuses it onto the wafer. The light diffracts on the wafer surface and is accurately transmitted to the camera plane through a high-precision microscope system, thereby acquiring an aerial image of the wafer pattern. This seemingly simple process actually involves cutting-edge technologies in multiple fields, including optics and precision mechanics. Even the slightest deviation in any step can lead to inaccurate inspection results.

[0005] Patent applications CN 102495535 A and CN 102323722 A, for example, offer new insights into aerial image acquisition. However, these methods remain limited when applied to wafer defect detection. In actual nanoscale defect detection, the accuracy of these aerial images remains insufficient for detecting minute defects, and the computational complexity and time-consuming nature of these methods make it difficult to meet the efficiency requirements of large-scale production inspections.

[0006] The golden die inspection method is a commonly used algorithm in semiconductor defect detection. Its core principle is to rely on a reference image (the golden image) as a comparison basis. By subtracting the target image from the model database built from the calculated results, defect contrast can be significantly improved, resulting in accurate defect detection results. However, in some practical semiconductor inspection applications, reference images are either difficult to obtain or of poor quality, making them unreliable as a basis for comparison. Therefore, the main technical challenge facing the golden die inspection method is how to establish a highly stable and accurate reference image.

[0007] To overcome this challenge and establish a high-precision, highly stable reference image, the industry currently often faces the challenge of calculating the field using extremely rigorous methods. One approach is to distance oneself from scattering objects to reduce scattering interference on the calculation results. Another approach is to perform the calculation on surfaces with lateral dimensions much larger than the wavelength, which can simplify the calculation process to a certain extent. In certain specific cases, through clever mathematical derivation and application of physical principles, analytical solutions can be obtained, successfully avoiding these complexities. However, numerical methods such as the finite-difference time-domain method (FDTD) or the finite element method (FEM) are difficult to achieve accurate calculations, even using supercomputers, due to memory and computational time limitations. Therefore, for the task of accurately calculating the wafer diffraction field at any position in space, there is an urgent need to explore new methods that simplify the calculation process while maintaining accuracy. This has become a key technical bottleneck that needs to be overcome in the field of integrated circuit chip defect detection. Summary of the Invention

[0008] In view of the above, the purpose of the present invention is to provide a method for obtaining a pattern wafer aerial image based on strict vector diffraction integral, which realizes the accurate acquisition of the wafer pattern aerial image, thereby effectively improving the reliability and efficiency of wafer defect detection, meeting the semiconductor industry's urgent demand for high-precision and high-adaptability detection technology, and promoting the improvement of the manufacturing quality of integrated circuit chips.

[0009] To achieve the above-mentioned object of the invention, an embodiment provides a method for obtaining an aerial image of a patterned wafer based on strict vector diffraction integration, comprising the following steps:

[0010] Discretize the wafer pattern into multiple discrete points, and discretize the shape of the illumination light source into multiple point light sources according to the type of illumination light source and obtain the coordinates of a single point light source;

[0011] For each point light source, the coordinates of the light source are used to obtain the spatial image of the wafer pattern at each discrete point when the light source is illuminated by the strict vector diffraction integral model.

[0012] The aerial images of the wafer pattern corresponding to all point light sources are superimposed to obtain the aerial image of the wafer pattern corresponding to the partially coherent illumination.

[0013] Preferably, for each point light source, using its coordinates to obtain an aerial image of the wafer pattern corresponding to each discrete point when illuminated by the point light source using a strict vector diffraction integral model, including:

[0014] According to the coordinates of the point light source, calculate the electric field distribution of the near-field diffraction of the light emitted by the point light source at N*M discrete points on the surface of the wafer pattern after being reflected by the wafer pattern and magnetic field distribution ;

[0015] Calculating the electric field distribution using Fourier optical imaging theory and magnetic field distribution Fourier transform results on the spectrum plane and , where the coordinates of the spectrum surface are Obtained by transformation of the global coordinate system (x, y);

[0016] Calculate the transfer function of each polarization component of the electromagnetic field based on the rigorous vector diffraction integral model;

[0017] From the transfer function and Fourier transform results and Multiply and calculate the diffraction pattern produced by a given aperture;

[0018] Using Fourier optical imaging theory, the diffraction pattern is inversely Fourier transformed to obtain the far-field electric field distribution and magnetic field distribution , according to the electric field distribution Obtain an aerial image I(x, y) of the wafer pattern at each discrete point corresponding to the point light source.

[0019] Preferably, the electric field distribution of the near-field diffraction at N*M discrete points on the wafer pattern surface is calculated and magnetic field distribution ,include:

[0020] Wafer patterning Perform rigorous numerical calculations , and the electric field distribution is obtained and magnetic field distribution ;

[0021] in, Indicates the coordinate position is The wafer pattern of discrete point areas, Indicates rigorous numerical computation using the finite element method, finite-difference time-domain method, finite integration method, or rigorous coupled-wave method.

[0022] Preferably, the transfer function of each polarization component of the electromagnetic field is calculated based on a strict vector diffraction integral model, including:

[0023] According to the propagation of electromagnetic field strictly follows Maxwell's equations, the vector Helmholtz equation can be derived from Maxwell's equations, and according to the vector Green's theorem, after a series of vector operations, any point light source can be i Observe a point in space The electromagnetic field distribution is expressed as a superposition integral form:

[0024] ;

[0025] ;

[0026] Where z is the propagation distance, is the wavelength of illumination light, represents the wave vector, and Represents observation points in space The electric and magnetic field distributions at i Expressed as i A point light source, represents the electromagnetic field with n different polarization components, The electric fields of different polarization components representing near-field diffraction, represents the magnetic field of different polarization components corresponding to the near-field diffraction, represents the coefficient of the electric field component, represents the coefficient of the magnetic field component, represents the global coordinate system, represents the position of any observation point in space, j represents a complex factor;

[0027] The above and Rewritten in the form of convolution, we get:

[0028] ;

[0029] ;

[0030] in, represents the spread function of different electric field polarization components, The spread function representing the polarization components of the magnetic field;

[0031] The diffusion function and Perform Fourier transform to obtain the transfer functions of different electric field polarization components and different magnetic field polarization components and .

[0032] Preferably, the transfer function and the Fourier transform result and Multiply the diffraction pattern produced by a given aperture by:

[0033] The transfer functions of different electric field polarization components are and Multiply to get the electric field diffraction pattern , the transfer functions of different magnetic field polarization components are and Multiply to get the magnetic field diffraction pattern .

[0034] Preferably, the method further comprises: when the partially coherent light source composed of point light sources obliquely illuminates the wafer pattern, the spectrum plane moves backward along the light propagation direction, and a frequency shift is added to each point light source on the spectrum. The frequency shift provided by the oblique illumination of a single point light source is:

[0035] ;

[0036] or

[0037] ;

[0038] in, is the refractive index of air, is the incident angle of the point light source onto the wafer, is the diffraction angle of the light diffracted by the wafer, is the wavelength of illumination light, Represents the frequency shift, the positive and negative in the formula depends on the single point light source i Coordinates, adding the electromagnetic field transfer function of the lighting angle frequency shift , becomes , .

[0039] Preferably, the method further comprises: when the partially coherent light source composed of point light sources illuminates the wafer pattern vertically, the spectrum plane remains unchanged, and the frequency shift range for all point light sources is calculated based on the internal and external coherence coefficients:

[0040] ;

[0041] in, is the refractive index of air, NA is the numerical aperture of the objective lens, is the internal coherence factor, is the external coherence factor, is the wavelength of illumination light, The electromagnetic field transfer function represents the frequency shift range of all point light sources i, adding the illumination angle frequency shift , becomes , .

[0042] Preferably, the method further comprises: transforming the spatial image of the wafer pattern corresponding to the partially coherent illumination to the image plane through a conversion matrix between global coordinates and image plane coordinates, to obtain an image surface result of the wafer pattern on the image plane.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] The present invention discretizes the illumination light source into multiple point light sources and calculates the imaging in the corresponding space for different point light sources respectively, which has the advantage of high precision. This method can be applied to light sources of different shapes and sizes and meets the wafer pattern simulation requirements of 28nm and below technology nodes.

[0045] The present invention establishes a matrix-form analytical expression of the spatial image under the vector diffraction imaging model, which eliminates the need for multiple grid divisions and is conducive to the rapid calculation of the strict vector diffraction integral model, thereby realizing rapid and accurate spatial imaging of wafer patterns at discrete points. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0047] Figure 1 is a flow chart of a method for obtaining an aerial image of a patterned wafer based on strict vector diffraction integral provided by an embodiment;

[0048] Figure 2 This is a schematic diagram of the point light source provided in the embodiment obliquely illuminating the wafer pattern and, after being reflected, being collected by the microscope objective lens and forming an image at the position corresponding to the wafer pattern;

[0049] Figure 3 This is a schematic diagram of the point light source provided in the embodiment illuminating the wafer pattern vertically and then being reflected and collected by the microscope objective lens to form an image at the position corresponding to the wafer pattern;

[0050] Figure 4 Schematic diagram of calculation of added frequency shift amount of a point light source provided by an embodiment;

[0051] Figure 5is a schematic diagram comparing transfer functions of various polarization components provided in the embodiment;

[0052] Figure 6 is a schematic diagram of an initial binary wafer pattern provided in an embodiment;

[0053] Figure 7 Schematic diagram of the total light intensity of the diffraction near field of a wafer pattern based on strict vector diffraction integration under point light source illumination provided by an embodiment;

[0054] Figure 8 It is a schematic diagram of obtaining a spatial image of a pattern wafer by diffraction integral under illumination by a point light source provided in an embodiment. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0056] The inventive concept of the present invention is: in the current mainstream nano-level defect detection, the traditional scalar approximate imaging model fails to fully consider the three-dimensional diffraction electric field generated by the wafer pattern and its transfer function in the system, resulting in deviations in the calculation of the far-field spatial image, making it difficult to accurately reflect the actual situation of the wafer, affecting the accuracy of defect detection. At the same time, faced with diverse wafer patterns and complex detection systems, traditional methods are difficult to adapt flexibly, and their application scope is relatively narrow. Based on this, in order to solve the problems of insufficient calculation accuracy and limited applicability in existing wafer defect detection technologies. An embodiment of the present invention provides a method for obtaining pattern wafer spatial images based on strict vector diffraction integrals, which realizes the accurate acquisition of pattern wafer spatial images, and has wide adaptability and is not restricted.

[0057] Based on the above invention concept, the embodiment provides a method for obtaining a pattern wafer spatial image based on strict vector diffraction integral, which is used to perform spatial imaging of wafer patterns. The entire spatial imaging principle is as follows: Figure 2 and Figure 3 As shown, 201 represents the oblique illumination source; 202 represents the spectrum plane, which can be the objective lens's back focal plane or moved to another position via a relay lens; 203 is a beam splitter, which splits the beam intensity into different proportions; 204 represents the partially coherent light source, which can be a ring illumination, a dipole illumination, a quadrupole illumination, or other variations; and 205 is a condenser. The patterned wafer surface is illuminated using both oblique and annular illumination. Scattered light within a specific angular range on the wafer surface is received by the entrance pupil, propagates to the spectrum plane for Fourier transform, then exits through the exit pupil and is ultimately projected onto the image plane.

[0058] Assume that the optical axis direction is the z axis, and establish a global coordinate system (x, y, z) with the z axis as the thumb direction according to the left-hand coordinate system principle. Assume that the global coordinates of any point on the illumination light source surface are (x0, y0, z0). The light emitted by this point light source is incident on the wafer surface (x s ,y s ,0), the direction cosine of the plane wave emitted from the wafer surface and incident on the entrance pupil of the microscope objective is ( α s , β s , γ s ), then the spectrum coordinate system ( f x ，f y ) and the direction cosines are:

[0059] ;

[0060] Assume that the global coordinates of any point on the image plane are (x1, y1, z1), and the direction cosine of the plane wave incident from the spectrum plane to the image plane is ( α i ，β i , γ i ),in,( α i ，β i , γ i ) is the coordinate system after Fourier transform of the global coordinate system (x1, y1, z1) on the image plane.

[0061] Based on the above-mentioned wafer pattern wafer aerial image imaging principle, a method for obtaining a pattern wafer aerial image based on strict vector diffraction integral is implemented, which includes the following steps:

[0062] S1, discretize the wafer pattern into multiple discrete points, and at the same time, discretize the shape of the illumination light source into multiple point light sources according to the type of illumination light source and obtain the coordinates of a single point light source.

[0063] In this embodiment, wafer pattern A is discretized into N*M discrete points, each corresponding to a sub-region where the wafer pattern diffracts the received light. Furthermore, because illumination sources corresponding to different light source types may have various shapes, it is necessary to discretize them based on their shapes. The shape of the partially coherent illumination source is discretized into multiple point light sources, and the light source coordinates (x0, y0, z0) of each point light source in the light source global coordinate system are obtained.

[0064] S2, for each point light source, using its coordinates by a strict vector diffraction integral model to obtain the aerial image of the wafer pattern corresponding to each discrete point when the point light source is illuminated.

[0065] In an embodiment, obtaining an aerial image of a wafer pattern corresponding to each discrete point when illuminated by a point light source using a strict vector diffraction integral model includes:

[0066] S2-1, based on the coordinates of the point light source (x0, y0, z0), calculate the electric field distribution of the near-field diffraction of the light emitted by the point light source at N*M discrete points on the wafer pattern surface after being reflected by the wafer pattern and magnetic field distribution , specifically including:

[0067] Wafer patterning Perform rigorous numerical calculations , and the electric field distribution is obtained and magnetic field distribution ;

[0068] in, Indicates the coordinate position is The wafer pattern of discrete point areas, Indicates rigorous numerical calculations using the finite element method (FEM), finite difference time domain method (FDTD), finite integration technique (FIT), or rigorous coupled wave analysis (RCWA), where the electric field distribution and magnetic field distribution They are all vector matrices of N*M*3, where 3 represents the three polarization components in the x, y, and z directions in the diffraction field.

[0069] S2-2, Calculate the electric field distribution using Fourier optical imaging theory and magnetic field distribution Fourier transform results on the spectrum plane and , where the coordinates of the spectrum surface are Obtained by transforming the global coordinate system (x, y).

[0070] In the embodiment, the electric field distribution and magnetic field distribution Perform Fourier transform and get the Fourier transform result and , the Fourier transform result and Used to calculate the diffraction pattern by subsequent multiplication with the transfer function, where the coordinates of the spectrum plane are Obtained by transforming the global coordinate system (x, y).

[0071] S2-3, calculate the transfer function of each polarization component of the electromagnetic field based on the strict vector diffraction integral model.

[0072] Specifically, the propagation of electromagnetic fields strictly follows Maxwell's equations, from which the vector Helmholtz equations can be derived. According to the vector Green's theorem, after a series of vector operations, any point light source can be i Observe a point in space The electromagnetic field distribution is expressed as a superposition integral form:

[0073] ;

[0074] ;

[0075] Where z is the propagation distance, is the wavelength of illumination light, represents the wave vector, and Represents observation points in space The electric and magnetic field distributions at i Expressed as i A point light source, Represents the electromagnetic field of n different polarization components. Note that the electromagnetic field is a vector and can be decomposed into the electromagnetic field of n different polarization components as needed. The electric fields of different polarization components representing near-field diffraction, represents the magnetic field of different polarization components corresponding to the near-field diffraction, represents the coefficient of the electric field component, Represents the coefficient of the magnetic field component. This coefficient can be a constant or a variable related to global coordinates, spectrum coordinates, etc. represents the global coordinate system, represents the position of any observation point in space, j represents a complex factor;

[0076] Since the numerical aperture NA of the objective lens in the optical imaging system is small, generally less than 0.6, the distance approximation between the observation point and the object plane is introduced. These approximations are established on the binomial expansion. Considering the relevant distance in the electromagnetic field component coefficient, the direction cosine terms are binomially expanded and approximated. Specifically, these approximations are based on the mathematical formula Taylor expansion, as follows:

[0077] ;

[0078] in , is a vector;

[0079] In this way, the above and Rewritten in the form of convolution, we get:

[0080] ;

[0081] ;

[0082] in, represents the spread function of different electric field polarization components, The spread function representing the polarization components of the magnetic field;

[0083] The diffusion function and Perform Fourier transform to obtain the transfer functions of different electric field polarization components and different magnetic field polarization components and .

[0084] Equations for calculating transfer functions can be derived from vector Rayleigh-Sommerfeld diffraction integrals, Stratton-Chuintegrals, Hertz vector diffraction integrals, and Franz diffraction integrals. These equations can be used to derive different transfer function forms, all of which are applicable to the calculation framework proposed in this invention. The specific transfer function selected depends on the actual application.

[0085] S2-4, from the transfer function and Fourier transform results and Multiply and calculate the diffraction pattern produced by a given aperture.

[0086] In the embodiment, the transfer function and the Fourier transform result and Multiply the diffraction pattern produced by a given aperture, including: the transfer function of the different electric field polarization components and Multiply to get the electric field diffraction pattern , the transfer functions of different magnetic field polarization components are and Multiply to get the magnetic field diffraction pattern .

[0087] S2-5, using Fourier optical imaging theory, the diffraction pattern is inverse Fourier transformed to obtain the far-field electric field distribution and magnetic field distribution , according to the electric field distribution Obtain an aerial image I(x, y) of the wafer pattern at each discrete point corresponding to the point light source.

[0088] In the embodiment, the diffraction pattern and Perform inverse Fourier transform to obtain the electric field distribution on the image plane and magnetic field distribution , according to the electric field distribution Obtain the spatial image I(x, y) of the wafer pattern at each discrete point corresponding to the point light source. and Each is a vector matrix of size N*M*3, where 3 represents the three polarization components in the diffraction field in the x, y, and z directions. The far-field distribution can be the electromagnetic field distribution at the focal plane of the optical system, at the defocused plane, or at the entrance pupil plane of the objective lens.

[0089] S3, superimposing the aerial images of the wafer pattern corresponding to all the point light sources to obtain the aerial image corresponding to the wafer pattern under partially coherent illumination.

[0090] In the embodiment, it is determined whether the aerial images of the wafer pattern corresponding to all point light sources have been calculated. If so, step S3 is executed, otherwise step S2 is returned. In S3, the aerial images I(x, y) corresponding to each point light source are superimposed according to the Abbe method to obtain the aerial image I corresponding to the pattern wafer position when the partially coherent light source is illuminated. total .

[0091] Based on the above analysis, a matrix-based analytical expression of the spatial image under the vector diffraction imaging model is established, and the overall imaging process can be described as:

[0092] ;

[0093] ;

[0094] That is, the near-field electric field distribution and magnetic field distribution Perform Fourier transform , and multiply it by the corresponding transfer function, and then perform inverse Fourier transform on the product of the two , and finally sum the different components and multiply them by a fixed value , and the electric field distribution at the image plane is obtained and magnetic field distribution , the amount of movement frequency caused by oblique lighting and the shape of the lighting source is reflected in the transfer function )and Specifically, each discrete point light source will affect the transfer function , , the range (f x , f y ) produces a frequency shift , The specific calculation methods include:

[0095] like Figure 4 As shown, when the partially coherent light source is obliquely illuminated, the light source is discretized into multiple point light sources according to the shape of the partially coherent light source. The spectrum surface moves backward along the light propagation direction, that is, from the initial position 301 to the position 302, and a frequency shift is added to each point light source on the spectrum. The frequency shift provided by the oblique illumination of a single point light source is:

[0096] ;

[0097] or

[0098] ;

[0099] in, is the refractive index of air, is the incident angle of the point light source onto the wafer, is the diffraction angle of the light diffracted by the wafer, is the wavelength of illumination light, Represents the frequency shift, the positive and negative in the formula depends on the single point light source i Coordinates, adding the electromagnetic field transfer function of the lighting angle frequency shift , becomes , .

[0100] When the partially coherent light source is vertically illuminated, the light source is discretized into multiple point light sources according to the shape of the partially coherent light source, and the frequency shift of all point light sources in the partially coherent light source is calculated based on the internal and external coherence coefficients 303 and 304. :

[0101] ;

[0102] in, is the refractive index of air, NA is the numerical aperture of the objective lens, is the internal coherence factor, is the external coherence factor, is the wavelength of illumination light, The electromagnetic field transfer function represents the frequency shift and adds the frequency shift of the lighting angle. , becomes , .

[0103] like Figure 5 As shown, 401 is Quantity correspondence Quantity, Quantity correspondence The transfer function of the component, 402 is Quantity correspondence The transfer function of the component, 403 is Quantity correspondence The transfer function of the component, where 1 represents complete transmission and 0 represents complete absorption, can be seen that the transfer functions corresponding to different polarization components are significantly different.

[0104] Figure 6 Schematic diagram of the initial binary wafer pattern with a critical dimension of 200 nm. 1 represents a protrusion and 0 represents a groove. The wafer groove plane is located in the XY plane, and the lines are parallel to the Y axis. Figure 7 Schematic diagram of the total light intensity of the diffraction near field of the wafer pattern based on strict vector diffraction integral under point light source illumination. Figure 8 Schematic diagram of obtaining the spatial image of the pattern wafer by diffraction integral under point light source illumination. Figure 7 and Figure 8 , Figure 7 The represented spatial image is more detailed, which illustrates the superiority of the calculation method of this patent.

[0105] The aerial image obtained above is located in the global coordinates. Therefore, the aerial image of the wafer pattern under partially coherent illumination can also be transformed to the image plane through the conversion matrix between the global coordinates and the image plane coordinates to obtain the image surface result of the wafer pattern on the image plane.

[0106] The method of the present invention achieves accurate acquisition of the wafer pattern aerial image, thereby effectively improving the reliability and efficiency of wafer defect detection, meeting the semiconductor industry's urgent demand for high-precision and high-adaptability detection technology, and promoting the improvement of integrated circuit chip manufacturing quality.

[0107] The specific implementation methods described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for obtaining an aerial image of a patterned wafer based on strict vector diffraction integral, characterized in that: The following steps are involved: Discretize the wafer pattern into multiple discrete points, and discretize the shape of the illumination light source into multiple point light sources according to the type of illumination light source and obtain the coordinates of a single point light source; For each point light source, the coordinates of the light source are used to obtain the spatial image of the wafer pattern at each discrete point when illuminated by the point light source using a strict vector diffraction integral model, including: According to the coordinates of the point light source, calculate the electric field distribution of the near-field diffraction of the light emitted by the point light source at N*M discrete points on the surface of the wafer pattern after being reflected by the wafer pattern and magnetic field distribution ; Calculating the electric field distribution using Fourier optical imaging theory and magnetic field distribution Fourier transform results on the spectrum plane and , where the coordinates of the spectrum surface are Obtained by transformation of the global coordinate system (x, y); Calculate the transfer function of each polarization component of the electromagnetic field based on the rigorous vector diffraction integral model; From the transfer function and Fourier transform results and Multiply and calculate the diffraction pattern produced by a given aperture; Using Fourier optical imaging theory, the diffraction pattern is inversely Fourier transformed to obtain the far-field electric field distribution and magnetic field distribution , according to the electric field distribution Obtain the spatial image I(x, y) of the wafer pattern at each discrete point corresponding to the point light source; The aerial images of the wafer pattern corresponding to all point light sources are superimposed to obtain the aerial image of the wafer pattern corresponding to the partially coherent illumination.

2. The method for obtaining an aerial image of a patterned wafer based on strict vector diffraction integral according to claim 1, characterized in that: Calculate the electric field distribution of near-field diffraction at N*M discrete points on the wafer pattern surface and magnetic field distribution ,include: Wafer patterning Perform rigorous numerical calculations , and the electric field distribution is obtained and magnetic field distribution ; in, Indicates the coordinate position is The wafer pattern of discrete point areas, Indicates rigorous numerical computation using the finite element method, finite-difference time-domain method, finite integration method, or rigorous coupled-wave method.

3. The method for obtaining an aerial image of a patterned wafer based on strict vector diffraction integral according to claim 1, wherein: The transfer functions of each polarization component of the electromagnetic field are calculated based on a rigorous vector diffraction integral model, including: According to the propagation of electromagnetic field strictly follows Maxwell's equations, the vector Helmholtz equation can be derived from Maxwell's equations, and according to the vector Green's theorem, after a series of vector operations, any point light source can be i Observe a point in space The electromagnetic field distribution is expressed as a superposition integral form: ； ； Where z is the propagation distance, is the wavelength of illumination light, represents the wave vector, and Represents observation points in space The electric and magnetic field distributions at i Expressed as i A point light source, represents the electromagnetic field with n different polarization components, The electric fields of different polarization components representing near-field diffraction, represents the magnetic field of different polarization components corresponding to the near-field diffraction, represents the coefficient of the electric field component, represents the coefficient of the magnetic field component, represents the global coordinate system, represents the position of any observation point in space, j represents a complex factor; The above and Rewritten in the form of convolution, we get: ； ； in, represents the spread function of different electric field polarization components, The spread function representing the polarization components of the magnetic field; The diffusion function and Perform Fourier transform to obtain the transfer functions of different electric field polarization components and different magnetic field polarization components and .

4. The method for obtaining an aerial image of a patterned wafer based on strict vector diffraction integral according to claim 1, wherein: From the transfer function and Fourier transform results and Multiply the diffraction pattern produced by a given aperture by: The transfer functions of different electric field polarization components are and Multiply to get the electric field diffraction pattern , the transfer functions of different magnetic field polarization components are and Multiply to get the magnetic field diffraction pattern .

5. The method for obtaining an aerial image of a patterned wafer based on strict vector diffraction integral according to claim 1, wherein: Also includes: When a partially coherent light source composed of point light sources is tilted toward the wafer pattern, the spectrum plane shifts backward along the direction of light propagation, and a frequency shift is added to the spectrum for each point light source. The frequency shift provided by the tilted illumination of a single point light source is: ； or ； in, is the refractive index of air, is the incident angle of the point light source onto the wafer, is the diffraction angle of the light diffracted by the wafer, is the wavelength of illumination light, Represents the frequency shift, the positive and negative in the formula depends on the single point light source i Coordinates, adding the electromagnetic field transfer function of the lighting angle frequency shift , becomes , .

6. The method for obtaining an aerial image of a patterned wafer based on strict vector diffraction integral according to claim 1, wherein: Also includes: When the partially coherent light source composed of point light sources illuminates the wafer pattern vertically, the spectrum surface remains unchanged. The frequency shift range calculated for all point light sources based on the internal and external coherence coefficients is: ； in, is the refractive index of air, NA is the numerical aperture of the objective lens, is the internal coherence factor, is the external coherence factor, is the wavelength of illumination light, The electromagnetic field transfer function represents the frequency shift range of all point light sources i, adding the illumination angle frequency shift , becomes , .

7. The method for obtaining an aerial image of a patterned wafer based on strict vector diffraction integral according to claim 1, wherein: Also includes: The spatial image of the wafer pattern corresponding to the partially coherent illumination is transformed to the image plane through the conversion matrix between the global coordinates and the image plane coordinates to obtain the image surface result of the pattern wafer pattern on the image plane.

Images