Nanostructure morphology parameter inversion method and system based on EUV scattering spectrum

Abstract

The invention belongs to the technical field of semiconductor manufacturing and nanometer metering, and particularly discloses a nanometer structure morphology parameter inversion method and system based on an EUV scattering spectrum. In a parameter reverse extraction link, residual errors of images under multiple azimuth angles are calculated pixel by pixel and are spliced to form a high-dimensional global residual error vector, and the norm of the vector is taken as an optimization target. By adopting a multi-azimuth joint measurement strategy and constructing the global residual vector, information dimensions of diversified illumination data are fused, so that global error optimization and multi-parameter decoupling extraction are realized in a full-parameter space, accidental errors and random noise interference in single-angle measurement are effectively inhibited, and the measurement accuracy is improved. Precise decoupling and extraction of key morphology parameters are realized; in the physical model construction link, a rigorous coordinate rotation transformation and projection correction algorithm is introduced, geometric projection errors caused by large-angle oblique incidence are eliminated from the mathematical physical level, and the physical authenticity of forward simulation is ensured.

Description

Technical Field

[0001] This application belongs to the field of semiconductor manufacturing and nanometerization technology, and more specifically, relates to a method and system for inverting the morphological parameters of nanostructures based on EUV (Extreme Ultraviolet) scattering spectra. Background Technology

[0002] Faced with the physical limitations of traditional optical detection methods in terms of sensitivity and resolution, measurement schemes based on the EUV light band, with their extremely short operating wavelength (approximately 13.5 nm), have become a key cutting-edge technology for breaking through the bottleneck of advanced node measurement. This scheme utilizes the strong absorption characteristics of high-energy photons in matter and the advantage of short wavelengths to deeply probe feature sizes shrunk to the atomic scale.

[0003] In order to obtain high signal-to-noise ratio structural information and optimize the interaction between light and materials, EUV measurement systems often require fine design of incident geometry (usually using large-angle grazing incidence). However, existing technical solutions still face a series of severe challenges in practical applications: (1) Insufficient accuracy of forward modeling: In the EUV band, the real part of the refractive index of the material is close to 1 and the imaginary part is large. Combined with large grazing incidence illumination, the near-field coupling and evanescent wave effect inside the structure are extremely strong. Existing models based on scalar diffraction theory or simplified electromagnetic approximation models (such as effective medium approximation) cannot accurately describe the vector propagation behavior of the light field, resulting in serious deviation of simulation accuracy from the real physical situation. (2) Difficulty in solving the inverse problem: Simultaneously inverting multiple geometric parameters (such as period, linewidth, lineheight, sidewall angle and overlay error) from a finite scattered signal is a highly nonlinear ill-conditioned inverse problem. There are strong physical couplings between the parameters (for example, changes in linewidth and sidewall angle may cause similar changes in light intensity), which makes the inversion process very easy to fall into local optima, and the uniqueness and stability of the solution are poor. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the purpose of this application is to provide a method and system for inverting the morphological parameters of nanostructures based on EUV scattering spectrum, which aims to solve the problems of insufficient accuracy in forward modeling and difficulty in solving inverse problems in the existing methods.

[0005] To achieve the above objectives, in a first aspect, this application provides a method for inverting the morphological parameters of nanostructures based on EUV scattering spectra, comprising: acquiring EUV scattering measurement images collected from multiple azimuth angles for a nanostructure sample; constructing a simulated far-field scattering image with the parameters to be inverted for each azimuth angle; calculating the pixel-level residual between the simulated far-field scattering image and the EUV scattering measurement image for each azimuth angle; fusing the pixel-level residuals from multiple azimuth angles as a global residual vector to determine the boundary constraints of the parameters to be inverted for the sample; and minimizing the L2 norm of the global residual vector under the premise of satisfying the boundary constraints as the inversion objective to obtain the optimal parameters to be inverted for the sample.

[0006] Preferably, the construction of the simulated far-field scattering image with the sample inversion parameters is specifically as follows: A rigorous coupled-wave analysis algorithm is used to construct the near-field scattering distribution of the outgoing wavefront of the nanostructured sample based on the sample inversion parameters; using the Fraunhofer diffraction propagation model, the near-field scattering distribution is mapped to the far-field observation plane to obtain the spatial coordinates and light intensity distribution of the far-field observation plane; the light intensity distribution of the far-field observation plane is preprocessed to correct the radiation intensity attenuation and distribution deviation caused by the non-perpendicularity between the far-field observation plane and the scattering optical axis; the spatial coordinates of the far-field observation plane are preprocessed to transform the electromagnetic field components of the near-field scattering distribution under inclined incidence to the coordinate system of the far-field observation plane and compensate for the geometric distortion caused by the projection of the spherical wave under the near-field distribution onto the far-field observation plane; through bilinear interpolation, the light intensity distribution of the preprocessed far-field observation plane is resampled to the spatial coordinates of the preprocessed far-field observation plane to obtain the simulated far-field scattering image.

[0007] Preferably, the preprocessing of the light intensity distribution on the far-field observation plane is as follows:

[0008] in, The light intensity distribution on the transformed far-field observation plane. The light intensity distribution on the far-field observation plane. , The angle between the line connecting the CCD pixel and the center of the sample and the optical axis. For far-field propagation distance, This represents the distance from the CCD pixel to the sample.

[0009] Preferably, the preprocessing of the spatial coordinates of the far-field observation plane is as follows: The spatial coordinates of the far-field observation plane are transformed into the far-field observation plane coordinate system through coordinate rotation transformation; By applying a geometric projection correction factor, a tilted incidence transformation is performed on the spatial coordinates in the rotated far-field observation plane coordinate system, as follows:

[0010]

[0011] in, The x-coordinate is after tilt correction. This is the y-coordinate after tilt correction. These are the spatial coordinates in the far-field observation plane coordinate system after rotation. For the incident angle, the geometric projection correction factor is... Distance from CCD pixel to sample , The spatial coordinates of the far-field observation plane, For far-field propagation distance; The spatial coordinates in the far-field observation plane coordinate system after the tilted incident transformation are reversed to obtain the spatial coordinates restored to the original coordinate system.

[0012] Preferably, for each azimuth angle, calculating the pixel-level residual between the simulated far-field scattering image and the EUV scattering measurement image specifically involves: for each azimuth angle, the EUV scattering measurement image is cropped based on its geometric center, retaining only the central region containing the 0th order and major higher-order diffraction signals as the ROI of the measurement image; for each azimuth angle, the simulated far-field scattering image is cropped in the same way to obtain the ROI of the simulated far-field scattering image; and the pixel-level residual of the ROI under each azimuth angle is calculated.

[0013] To achieve the above objectives, in a second aspect, this application provides a nanostructure morphology parameter inversion system based on EUV scattering spectroscopy, comprising a memory and one or more processors; the memory is coupled to the one or more processors, the memory is used to store computer program code, the computer program code including computer instructions; the one or more processors invoke the computer instructions to cause the system to execute the inversion method as described in the first aspect.

[0014] To achieve the above objectives, in a third aspect, this application provides a computer-readable storage medium including instructions that, when executed on an electronic device, cause the electronic device to perform the inversion method as described in the first aspect.

[0015] It is understood that the beneficial effects of the second and third aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0016] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: (1) This application proposes a method for inverting nanostructure morphology parameters based on EUV scattering spectrum. In the parameter inverse extraction stage, the residuals of images under multiple azimuth angles are calculated pixel by pixel and stitched together to form a high-dimensional global residual vector. The norm of this vector is used as the optimization target. This application adopts a multi-azimuth angle joint measurement strategy. By constructing the above-mentioned global residual vector, the information dimensions of diverse lighting data are fused, thereby realizing global error optimization and decoupling extraction of multiple parameters in the full parameter space. This effectively suppresses random errors and random noise interference in single-angle measurement and achieves accurate decoupling and extraction of five key morphology parameters, including overlay error.

[0017] (2) In view of the insufficient accuracy of the existing forward modeling method, this application proposes a nanostructure morphology parameter inversion method based on EUV scattering spectrum. In the physical model construction stage, a rigorous coupled wave analysis algorithm is adopted. By optimizing the spatial harmonic truncation order, the propagating wave and the key high-order evanescent wave components are accurately captured. More importantly, for grazing incidence geometry, this application introduces a rigorous coordinate rotation transformation and projection correction algorithm to eliminate the geometric projection error caused by large-angle tilted incidence from a mathematical and physical perspective, so as to ensure the physical authenticity of forward simulation.

[0018] (3) This application proposes a method for inverting the morphological parameters of nanostructures based on EUV scattering spectrum. In the parameter inverse extraction process, a region of interest (ROI) screening mechanism is introduced. That is, the low signal-to-noise ratio edge is removed by the center clipping algorithm, and only the core region containing the 0th order and the main high-order diffraction signals is retained as the fitting object. This allows this application to focus on the core diffraction region containing rich feature fingerprints, and the accuracy of the nanostructure measurement results is greatly improved. Attached Figure Description

[0019] Figure 1 This is a flowchart of a method for inverting the morphological parameters of nanostructures based on EUV scattering spectra, provided in an embodiment of this application.

[0020] Figure 2 It is a pseudo-far-field scattering image calculated according to the embodiments of this application.

[0021] Figure 3 This is a far-field diffraction image with a real CCD noise model added, provided in an embodiment of this application.

[0022] Figure 4 This is a schematic diagram of the far-field simulation results for a single-layer grating provided in an embodiment of this application.

[0023] Figure 5 This is a schematic diagram of the far-field simulation results for the upper and lower gratings provided in the embodiments of this application. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0025] In this application, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A existing alone, A and B existing simultaneously, and B existing alone. In this application, the symbol " / " indicates that the related objects are in an "or" relationship, for example, A / B means A or B.

[0026] In this application, the terms "first" and "second," etc., are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0027] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0028] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0029] The embodiments of this application are described below with reference to the accompanying drawings.

[0030] like Figure 1 As shown, this application provides a method for inverting the morphological parameters of nanostructures based on EUV scattering spectra, including: For nanostructured samples, EUV scattering measurement images acquired from multiple azimuth angles were obtained; For each azimuth angle, construct a simulated far-field scattering image with the parameters to be inverted from the sample; For each azimuth angle, calculate the pixel-level residual between the simulated far-field scattering image and the EUV scattering measurement image; By fusing pixel-level residuals from multiple azimuth angles as a global residual vector, the boundary constraints of the parameters to be inverted in the sample are determined. The inversion objective is to minimize the L2 norm of the global residual vector while satisfying the boundary constraints, and the optimal parameters for the sample to be inverted are obtained by solving the problem.

[0031] The following section will elaborate on each step of the entire inversion method.

[0032] Specifically, acquiring EUV scattering measurement images from multiple azimuth angles for nanostructured samples includes: This application relies on multi-azimuth scattering image acquisition, which first requires defining the rotation azimuth sequence of the sample stage during the measurement process. ,in, m is the total number of azimuth angles. For each azimuth angle... Acquire the corresponding far-field scattering images .

[0033] Preferably, the construction of the simulated far-field scattering image with the sample inversion parameters is specifically as follows: A rigorous coupled-wave analysis algorithm was used to construct the near-field distribution of the outgoing wavefront of the nanostructured sample based on the parameters to be inverted in the sample. Using the Fraunhofer diffraction propagation model, the near-field scattering distribution is mapped to the far-field observation plane to obtain the spatial coordinates and light intensity distribution of the far-field observation plane; The light intensity distribution on the far-field observation plane is preprocessed to correct the radiation intensity attenuation and distribution deviation caused by the non-perpendicularity between the far-field observation plane and the scattered light axis; The spatial coordinates of the far-field observation plane are preprocessed to transform the electromagnetic field components of the near-field scattered distribution under oblique incidence to the coordinate system of the far-field observation plane and to compensate for the geometric distortion caused by the projection of the spherical wave under the near-field distribution onto the far-field observation plane. By using bilinear interpolation, the light intensity distribution of the preprocessed far-field observation plane is resampled to the spatial coordinates of the preprocessed far-field observation plane to obtain a simulated far-field scattering image.

[0034] Specifically, the method employs a rigorous coupled-wave analysis algorithm to construct the near-field scattering distribution of the emitted wavefront of the nanostructured sample based on the parameters to be inverted from the sample. (1) Initialize the extreme ultraviolet illumination source and nanostructure parameters, construct a physical model based on the material refractive index and geometric morphology, and perform layered discretization to obtain the complex permittivity distribution matrix and incident wave vector components of the structure under test.

[0035] For non-rectangular gratings, layer slicing is required when initializing the geometric parameters of the nanostructure, i.e., a multi-layer stepped approximation strategy is adopted. The core idea of ​​layer slicing is to automatically divide the nanostructure of arbitrary shape into a series of thin layers in the vertical direction, and approximate each thin layer as a rectangle with a specific width, thereby transforming the complex non-rectangular structure problem into a problem of superimposing a series of standard rectangular layers. The specific operation is as follows: The nanostructure type is identified based on the input geometric parameters. If it is identified as a rectangular structure, it is directly treated as an independent single-layer grating model because of its translational invariance in the vertical direction. For non-rectangular structures with inclined sidewalls, a multi-layer segmentation strategy is applied, dividing it into multiple thin layers in the vertical direction according to a preset number of slices. By calculating the critical dimensions at the top and bottom and the sidewall offset, a linear interpolation algorithm is used to determine the width and lateral displacement of each thin layer layer by layer. The total height is evenly distributed to each thin layer, forming a series of rectangular thin layer stacks with gradually varying widths. Finally, material optical constants are assigned to each thin layer, and the dielectric constant distribution coefficient of each thin layer is calculated using analytical Fourier transform, thereby transforming the complex non-rectangular structure into a multi-layer rectangular structure model that can be processed by RCWA.

[0036] To measure the overlay error between the upper and lower grating layers, the initialization of the nanostructure geometric parameters requires stacking two grating layers and setting a relative lateral offset. Next, the complex refractive index (n,k) of each layer of the nanostructure and the substrate in the extreme ultraviolet (EUV) band needs to be specified. Simultaneously, the illumination source parameters need to be set to accurately define the physical properties of the EUV plane wave. This application uses a plane wave, and based on the actual configuration of the EUV lithography machine or measurement equipment, the physical properties of the incident plane wave are accurately defined. The parameters to be set include the incident wavelength, incident angle, azimuth angle, and polarization angle. The specific steps are: based on the preset angle parameters, establish a three-dimensional wave vector coordinate system and determine the direction cosine of the incident wave vector K; and then, by interpolating the incident wave vector K with the sample surface normal vector... The vector cross product operation is used to construct mutually orthogonal polarization basis vectors TE (electric field perpendicular to the incident plane) and TM (magnetic field perpendicular to the incident plane). Based on the preset polarization angle, the total incident electric field is projected and decomposed onto these two basis vector directions, and the complex amplitude components of the incident electric field in the x, y, and z directions are calculated. This fully defines the extreme ultraviolet plane wave illumination conditions with arbitrary incident directions and polarization states. These components will serve as the initial boundary conditions for Maxwell's equations in the subsequent RCWA electromagnetic field solution. Finally, the effective geometric area of ​​the illumination spot needs to be set. This parameter will serve as an energy scaling factor, converting the relative diffraction efficiency calculated by RCWA into an absolute photon count on the detector.

[0037] In the actual algorithm software interface or configuration file, four types of core parameters need to be input in step (1): geometric morphology parameters (period, line width, height, left wall corner, right wall corner, interlayer offset and number of cut layers), material optical parameters (wavelength and complex refractive index of each layer of material), illumination configuration parameters (incident angle, azimuth angle, polarization angle and illumination area L) and simulation control parameters (truncation order M).

[0038] (2) Based on the RCWA method, the scattering near-field solution is obtained to obtain the complex reflection coefficient and electromagnetic field complex amplitude distribution of each diffraction order.

[0039] Specifically, using the dielectric constant matrix initialized in step (1) and the incident wave vector as input, electromagnetic eigenvalue equations are constructed using rigorous coupled-wave analysis. By solving the eigenvalue problem and applying the electromagnetic field boundary continuity condition, the vector diffraction response of the nanostructure to extreme ultraviolet light is accurately simulated, and finally the Jones matrix characterizing the polarization transmission characteristics of each diffraction order is obtained.

[0040] First, based on the Floquet-Bloch theorem, and combining illumination configuration parameters and geometric topography parameters, the transverse wave vector components of each diffraction order are calculated:

[0041]

[0042]

[0043] in, The transverse x-component of the m-th order diffracted wave vector (this physical quantity is equivalent to the one in the subsequent steps) ), The transverse y-component of the m-th order diffracted wave vector (this physical quantity is equivalent to the one in the subsequent steps) ), The longitudinal z-component of the diffraction wave vector. The wave number in a vacuum. The refractive index of the incident / reflected region. Angle of incidence It is the azimuth angle. The diffraction order is... The incident wavelength, For the grating period, It is the imaginary unit.

[0044] Next, obtain the tangential electric field components and magnetic field matrix of the global output interface.

[0045] Set the initial matrix of the underlying medium (usually a substrate):

[0046] in, and These are the diagonal forms of the substrate's admittance matrix and impedance matrix, respectively. It is an identity matrix.

[0047] For a homogeneous dielectric layer, the following characteristic matrix is ​​constructed, including the calculation of propagation parameters and the assembly of the characteristic matrix:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] in, This is the distribution vector of the normalized longitudinal wave vector (z-direction). For the reason The diagonal matrix formed This is the coupling diagonal matrix related to the magnetic field components. It is a single-layer phase propagation diagonal matrix. Let be the electric field eigenvector matrix of the uniform layer. The magnetic field eigenvector matrix of the uniform layer, This is the eigenvalue propagation matrix for the entire layer. The equivalent refractive index of the uniform layer, To convert to a diagonal matrix, To achieve uniform layer thickness, It is the identity matrix. It is a zero matrix.

[0055] For the grating layer, the following characteristic matrices are constructed, including the dielectric constant matrix construction, eigenvalue problem solving, and polarization-dependent system matrix.

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] in, The dielectric constant matrix of the grating layer is... The refractive index of the grating ridge material, The refractive index of the grating valley material, The Fourier coefficient matrix of the dielectric constant distribution (from layer cutting). The coupling coefficient matrix is ​​related to the electric field components. This is the diagonal matrix of the transverse x-component wave vectors corresponding to each diffraction order. This is the diagonal matrix of the transverse y-component wave vectors corresponding to each diffraction order. The eigenvector matrix after decoupling. It is an eigenvalue diagonal matrix. This is the coupling coefficient matrix related to the magnetic field components. , , These are the block submatrices of the magnetic field characteristic matrix. This is the azimuth cosine diagonal matrix. This is a diagonal matrix of azimuth sine. This is the ss polarization component coupling submatrix used to construct the total matrix W (electric field characteristic matrix) after coordinate rotation. To construct the sp polarization component coupling submatrix of the total matrix W after coordinate rotation, To construct the ps polarization component coupling submatrix of the total matrix W after coordinate rotation, To construct the pp polarization component coupling submatrix of the total matrix W after coordinate rotation, To construct the ss polarization component coupling submatrix of the total matrix V after coordinate rotation, To construct the sp polarization component coupling submatrix of the total matrix V after coordinate rotation, To construct the ps polarization component coupling submatrix of the total matrix V after coordinate rotation, To construct the pp polarization component coupling submatrix of the total matrix V after coordinate rotation, The phase propagation diagonal matrix of the eigenvalues ​​of the first type of characteristic mode. The phase propagation diagonal matrix is ​​the eigenvalue phase propagation matrix of the second type of characteristic mode.

[0064] Next, the numerical instability problem in deep subwavelength structure simulation is solved by using an enhanced, bottom-up algorithm for the enhanced T matrix. By constructing a unified boundary matching matrix equation and utilizing its sparsity properties for efficient solution, the responses of all diffraction orders can be obtained in one go.

[0065]

[0066] Where dim is the computational dimension. It is the identity matrix. For boundary condition matching matrix, The solution to the system of linear equations. This is the coefficient vector of the backpropagation mode. This represents the tangential electric field component at the output interface. This represents the tangential magnetic field component at the output interface.

[0067] The above describes the calculation of the tangential electric and magnetic field components at the output interface of one layer. Then, starting from the bottom layer (layer N), it is necessary to recursively calculate upwards to the top layer (layer 1), performing the construction of the characteristic matrix and partial T-matrix calculation for each layer (whether it's a uniform layer or a grating layer). When the recursive calculation reaches the top layer (layer 1, i.e., the incident medium interface), the global matrix is ​​obtained.

[0068]

[0069] in, This represents the tangential electric field component at the output interface. This represents the tangential magnetic field component at the output interface.

[0070] Finally, through two orthogonal basis incident calculations, the Jones matrix that fully describes the polarization conversion characteristics is directly extracted from the global matrix above.

[0071] Specifically, at the interface between the incident medium and the nanostructure, the continuity condition of the tangential component of the electromagnetic field constructs the boundary matching equation. By solving the above large-scale sparse linear equation system, the reflection coefficient vectors of all diffraction orders can be obtained at once. and :

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] Where ind is the length of the convergence order, YI is the admittance factor of the incident medium, ZI is the impedance factor of the incident medium, and dd0 is a single incident plane wave. The electric field characteristic matrix of the incident medium is divided into blocks. Divide the magnetic field characteristic matrix of the incident medium into blocks. Let be the polarization vector of the incident electric field. Let be the polarization vector of the incident magnetic field. The system matrix of the reflected wave in the incident region is... The total excitation source vector, The global field response matrix of the nanostructure. This is the total boundary condition matching matrix. To solve the system of linear equations, Let TE be the reflection coefficient vector. is the reflection coefficient vector of TM polarization.

[0087] The coefficients are obtained by solving the TM polarization incident solution independently for the two orthogonal reference incident polarization states. and The coefficients are obtained by solving the TE polarized incident solution. and .

[0088]

[0089]

[0090]

[0091]

[0092] in, These represent the s-polarized reflection coefficients for TE incident, s-polarized reflection coefficients for TM incident, p-polarized reflection coefficients for TE incident, and p-polarized reflection coefficients for TM incident, respectively. Finally, the algorithm outputs a complex array of dimensions 2×2×N. ,in, The number of diffraction orders to be output, as specified by the user. That is, the corresponding number The complete reflection Jones matrix of a specified diffraction order is obtained, and the electric field vectors of the scattered waves at each order are obtained from the input initial incident plane wave:

[0093] in, The s-polarization component of the electric field vector. The p-polarization component of the electric field vector. For the u-th order scattering field, For the incident field.

[0094] Furthermore, the first Amplitude of the reflected wave By performing Rayleigh expansion with the corresponding phase, the near-field electric field distribution of the emitted wavefront on the surface of the nanostructure is obtained. :

[0095]

[0096] in, Let m be the amplitude of the m-th order reflected wave. For the lighting area, The height is the synthesized height of the scattered electric field. Based on the above formula and method, the near-field of the scattered field is calculated. The calculation.

[0097] Specifically, the method of using the Fraunhofer diffraction propagation model to map the near-field scattering distribution to the far-field observation plane to obtain the spatial coordinates and light intensity distribution of the far-field observation plane includes: The calculated near-field electric field distribution of the emitted wavefront from the nanostructure surface contains three orthogonal vector components:

[0098] First, a zero-fill technique is employed to extend the near-field distribution of each component to a sufficiently large computational region, thereby increasing the resolution of the far-field image and avoiding edge artifacts. For each electric field component, the following Fraunhofer diffraction calculations are performed:

[0099] in, Indicates Fast Fourier Transform; This refers to the near-field sampling interval; Spatial frequency coordinates are defined as follows:

[0100] in, The number of sampling points in the x-direction. The number of sampling points in the y-direction. This represents the size of the near-field simulation region.

[0101] The spatial coordinates of the far-field observation plane are determined by the following formula:

[0102] in, For transmission distance, For the far-field x-coordinate, Let y be the far-field y-coordinate.

[0103] The phase correction factor for Fraunhofer diffraction is:

[0104] The far-field complex amplitude distribution is as follows:

[0105] The corresponding light intensity distribution is as follows:

[0106] Considering that the observation direction is not parallel to the surface normal, preferably, the light intensity distribution of the far-field observation plane is preprocessed, specifically as follows:

[0107] in, The light intensity distribution on the transformed far-field observation plane. The light intensity distribution on the far-field observation plane. , The angle between the line connecting the CCD pixel and the center of the sample and the optical axis. For far-field propagation distance, This represents the distance from the CCD pixel to the sample. It combines the projected area effect and the radiation intensity distribution.

[0108] Preferably, the preprocessing of the spatial coordinates of the far-field observation plane is as follows: The spatial coordinates of the far-field observation plane are transformed to the far-field observation plane coordinate system through coordinate rotation transformation, as follows:

[0109] in, The coordinates before rotation, These are the coordinates after rotation.

[0110] By applying a geometric projection correction factor, a tilted incidence transformation is performed on the spatial coordinates in the rotated far-field observation plane coordinate system, as follows:

[0111]

[0112] in, The x-coordinate is after tilt correction. This is the y-coordinate after tilt correction. These are the spatial coordinates in the far-field observation plane coordinate system after rotation. For the incident angle, the geometric projection correction factor is... Distance from CCD pixel to sample , The spatial coordinates of the far-field observation plane, For far-field propagation distance; The spatial coordinates in the far-field observation plane coordinate system after the tilted incident transformation are inversely rotated to obtain the spatial coordinates restored to the original coordinate system, as follows:

[0113]

[0114] in, To restore the coordinates to the original coordinate system.

[0115] In one illustrated embodiment, by Implement bilinear interpolation, where, It is a bilinear interpolation function. Indicates linear interpolation. Values ​​outside the interpolation region are set to 0. The calculated simulated far-field scattering image is as follows: Figure 2 As shown.

[0116] Preferably, for each azimuth angle, calculating the pixel-level residual between the simulated far-field scattering image and the EUV scattering measurement image specifically involves: For each azimuth angle, the EUV scattering measurement image is cropped based on its geometric center, retaining only the central region containing the 0th order and major higher order diffraction signals as the ROI of the measurement image; For each azimuth angle, the simulated far-field scattering image is cropped in the same way to obtain the ROI of the simulated far-field scattering image; Calculate the pixel-level residuals of the ROI at each azimuth angle.

[0117] The fusion of pixel-level residuals from multiple azimuth angles as a global residual vector determines the boundary constraints of the parameters to be inverted in the sample, specifically including:

[0118] in, To represent the pixel-level residual between the simulated image and the measured image, the measured image vector... Simulated image vector , To measure the image, The simulated image after preprocessing. This is the scattering image matrix after center cropping preprocessing. and These represent the width and height of the cropped image, respectively.

[0119] Concatenate the residual vectors of all azimuth angles into a global residual vector:

[0120] This application defines the set of morphological parameters of the nanostructure to be inverted. Typical nanostructure geometric parameters include, but are not limited to: pitch (period), line width (line width), height (line height), LSWA (left side wall corner), RSWA (right side wall corner), and overlay (overlay error). The number of geometric parameter components to be measured.

[0121] Based on physical realizability and prior knowledge, a reasonable search space is set for each parameter to be inverted:

[0122] in, For the first The lower bound of each parameter, For the first The upper bound of each parameter.

[0123] The inversion objective is to minimize the L2 norm of the global residual vector while satisfying the boundary constraints, and the optimal parameters for the sample to be inverted are obtained by solving the problem.

[0124] The goal of the inversion problem is to minimize the L2 norm of the residual vector:

[0125] In one illustrated embodiment, the Levenberg-Marquardt nonlinear least squares algorithm is used to solve the above optimization problem. This algorithm combines the advantages of gradient descent and Gauss-Newton methods, exhibiting robust convergence performance. Specifically, it includes: (1) Set the initial parameter vector Boundary constraints [LB, UB] and optimization options (including maximum number of iterations, maximum number of function evaluations, and convergence tolerance threshold, etc.).

[0126] (2) For the first In the next iteration, calculate the residual vector under the current parameters. And Jacobi matrix Solve the linearized equation ,in, For damping parameters, This refers to the update volume.

[0127] (3) Update parameters .

[0128] (4) Apply boundary constraints .

[0129] (5) Stop iteration when any of the following conditions are met: residual The change is less than the preset threshold ,parameter The change is less than the preset threshold Reaching the maximum number of iterations .

[0130] (6) After optimization convergence, the optimal parameter estimate is obtained. .

[0131] (7) Calculate the residual norm for each azimuth angle. .

[0132] (8) Evaluate the inversion quality and identify azimuth angles that may have systematic errors.

[0133] This application utilizes scattering information from multiple azimuth angles to automatically determine the cropping region based on the image content, using the physically achievable parameter range as an optimization constraint, thereby maintaining stable inversion performance even in the presence of measurement noise.

[0134] Correspondingly, this application provides a nanostructure morphology parameter inversion system based on EUV scattering spectrum, including a memory and one or more processors; the memory is coupled to the one or more processors, the memory is used to store computer program code, the computer program code includes computer instructions; the one or more processors call the computer instructions to cause the system to execute the inversion method as described above.

[0135] Example To verify the experimental results, in Figure 2Based on this, this embodiment constructs a complete detector physical noise model to simulate the imaging process of a real CCD / CMOS camera.

[0136] Conversion of photons to photoelectrons ,in, For quantum efficiency, For maximum photon flux, Normalized light intensity.

[0137] Noise source modeling mainly includes shot noise, dark current noise, and readout noise. Among these, shot noise (Poisson noise)... Dark current noise ,in, Dark current rate; Exposure time. Readout noise. ,in, To read the standard deviation of the noise, This represents a normal distribution with a mean of 0 and a standard deviation of 1. Therefore, the total number of electrons... .

[0138] Analog-to-digital conversion to obtain the best output light intensity:

[0139]

[0140]

[0141] in, For ADC depth, For ADC conversion gain, The output value of the ADC. For signal power, For noise power, To calculate the signal-to-noise ratio of an image, For linear signal-to-noise ratio.

[0142] After the above processing, a far-field diffraction image with a real CCD noise model is obtained. ,like Figure 3 As shown, this application integrates a detector physical noise model into the backend of the Fraunhofer diffraction model, explicitly simulating photon shot noise and readout noise. This makes the simulated far-field spectrum highly approximate the real experimental data in statistical characteristics, solving the problem of "simulation-experiment" mode mismatch. Furthermore, using multiple sets of set geometric structure parameters as labels and the corresponding generated far-field simulation images with physical noise as observation data, a "parameter-image" forward model is constructed. Based on this, an algorithm for measuring and analyzing the morphological parameters of nanostructures is established.

[0143] On the one hand, the high-precision inversion capability of basic morphological parameters was verified. Specifically, the light source was first initialized with an incident angle of 70 degrees, a wavelength of 13.5 nm, and a polarization angle of 0 degrees. The nanostructure was set as an Au grating stacked on a SiO2 substrate, with a period of 80 nm, a duty cycle of 0.5, a depth of 40 nm, a LSWA of 90 degrees, and an RSWA of 90 degrees. The illumination area was set as follows: The far-field propagation distance is 60 mm. This application uses variable azimuth angle measurement, so the azimuth angles are selected as 0 degrees, 20 degrees, 40 degrees, 60 degrees, 80 degrees, and 90 degrees. Since it is currently a single-layer grating, overlay error was not considered in this simulation. The simulated nanostructure parameters are period, linewidth, line height, left wall corner, and right wall corner. The simulated far-field results are as follows: Figure 4 As shown.

[0144] The nanostructure morphology parameters obtained from solving the inverse problem are: period = 80.0454 (err = 0.06%); linewidth = 39.9552 (err = 0.11%); line height = 40.0775 (err = 0.19%); left side corner = 89.8215 (err = 0.2%); right side corner = 89.9023 (err = 0.11%). This indicates good inversion accuracy, with inversion errors for all five morphology parameters below 0.2%. This result fully demonstrates that the forward model provided in this application has extremely high fidelity for typical single-layer nanograting structures, and that the inversion algorithm can still achieve high-precision and stable solutions close to the theoretical limit even with multi-parameter coupling.

[0145] On the other hand, under conditions of increased structural complexity and parameter coupling, the stable extraction performance of key process parameters (overlay error) is verified. This embodiment examines a double-layer gold (Au) grating stacked on a quartz (SiO2) substrate. While keeping all parameters constant, an additional key process parameter—overlay error—is introduced, i.e., the horizontal relative offset between the upper and lower grating layers, with a preset value of 2.4 nm. The target parameters for this inversion are expanded to six: period, linewidth, lineheight, left side corner, right side corner, and overlay error. The far-field diffraction is as follows... Figure 5 As shown.

[0146] The nanostructure morphology parameters obtained by solving the inverse problem are: period = 83.0949 (err = 3.87%); linewidth = 42.2035 (err = 5.51%); line height = 44.824 (err = 12.06%); left side corner = 84.5218 (err = 6.09%); right side corner = 100 (err = 11.11%); overlay error = 2.24405 (err = 6.5%).

[0147] Comparison revealed that the inversion errors for some topographic parameters (such as line height and sidewall angle) increased in the second simulation. This is mainly due to the significant enhancement of parameter coupling effects: in the double-layer structure, the introduction of overlay errors and the complex cross-coupling of all geometric topographic parameters in the electromagnetic scattering response increase the nonlinearity of the inversion problem and the ambiguity of the solution.

[0148] However, even under such complex coupling conditions, this application successfully separated the core process parameter, overlay error, from multiple interfering parameters, achieving a relative measurement accuracy of 6.5%. This demonstrates that the multi-parameter joint inversion framework proposed in this application possesses excellent parameter resolution and robustness. The moderate increase in topography parameter error precisely reflects the challenges of multi-parameter coupling in real industrial measurements. This application, while ensuring the accuracy of the most critical parameter, overlay error, still provides valuable topography estimates, fully meeting the core requirements of non-destructive, online, multi-parameter metrology in advanced node semiconductor manufacturing.

[0149] In summary, through two progressive simulations, it is fully demonstrated that the method described in this application can not only achieve ultra-high precision measurement of multiple morphological parameters of single-layer nanostructures, but also be effectively applied to the metrology of complex multilayer structures, including overlay errors. This method combines high precision, strong robustness, and specific resolution of key process parameters, providing a reliable nanometerization solution for semiconductor manufacturing in the era of extreme ultraviolet lithography.

[0150] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0151] Based on the methods in the above embodiments, this application provides an electronic device that may include a processor, a communications interface, a memory, and a communication bus, wherein the processor, communications interface, and memory communicate with each other via the communication bus. The processor may invoke logical instructions stored in the memory to execute the methods in the above embodiments.

[0152] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0153] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0154] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0155] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0156] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0157] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0158] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0159] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for inverting the morphological parameters of nanostructures based on EUV scattering spectra, characterized in that, include: For nanostructured samples, EUV scattering measurement images acquired from multiple azimuth angles were obtained; For each azimuth angle, construct a simulated far-field scattering image with the parameters to be inverted from the sample; For each azimuth angle, calculate the pixel-level residual between the simulated far-field scattering image and the EUV scattering measurement image; By fusing pixel-level residuals from multiple azimuth angles as a global residual vector, the boundary constraints of the parameters to be inverted in the sample are determined. The inversion objective is to minimize the L2 norm of the global residual vector while satisfying the boundary constraints, and the optimal parameters for the sample to be inverted are obtained by solving the problem.

2. The inversion method as described in claim 1, characterized in that, The construction of the simulated far-field scattering image with the parameters to be inverted from the sample is as follows: A rigorous coupled-wave analysis algorithm was used to construct the near-field distribution of the outgoing wavefront of the nanostructured sample based on the parameters to be inverted in the sample. Using the Fraunhofer diffraction propagation model, the near-field scattering distribution is mapped to the far-field observation plane to obtain the spatial coordinates and light intensity distribution of the far-field observation plane; The light intensity distribution on the far-field observation plane is preprocessed to correct the radiation intensity attenuation and distribution deviation caused by the non-perpendicularity between the far-field observation plane and the scattered light axis; The spatial coordinates of the far-field observation plane are preprocessed to transform the electromagnetic field components of the near-field scattered distribution under oblique incidence to the coordinate system of the far-field observation plane and to compensate for the geometric distortion caused by the projection of the spherical wave under the near-field distribution onto the far-field observation plane. By using bilinear interpolation, the light intensity distribution of the preprocessed far-field observation plane is resampled to the spatial coordinates of the preprocessed far-field observation plane to obtain a simulated far-field scattering image.

3. The inversion method as described in claim 2, characterized in that, The preprocessing of the light intensity distribution on the far-field observation plane is as follows: in, The light intensity distribution on the transformed far-field observation plane. The light intensity distribution on the far-field observation plane. , The angle between the line connecting the CCD pixel and the center of the sample and the optical axis. For far-field propagation distance, This represents the distance from the CCD pixel to the sample.

4. The inversion method as described in claim 2, characterized in that, The preprocessing of the spatial coordinates of the far-field observation plane is as follows: The spatial coordinates of the far-field observation plane are transformed into the far-field observation plane coordinate system through coordinate rotation transformation; By applying a geometric projection correction factor, a tilted incidence transformation is performed on the spatial coordinates in the rotated far-field observation plane coordinate system, as follows: in, The x-coordinate is after tilt correction. This is the y-coordinate after tilt correction. These are the spatial coordinates in the far-field observation plane coordinate system after rotation. For the incident angle, the geometric projection correction factor is... Distance from CCD pixel to sample , The spatial coordinates of the far-field observation plane, For far-field propagation distance; The spatial coordinates in the far-field observation plane coordinate system after the tilted incident transformation are reversed to obtain the spatial coordinates restored to the original coordinate system.

5. The inversion method as described in claim 1, characterized in that, For each azimuth angle, the pixel-level residual between the simulated far-field scattering image and the EUV scattering measurement image is calculated as follows: For each azimuth angle, the EUV scattering measurement image is cropped based on its geometric center, retaining only the central region containing the 0th order and major higher order diffraction signals as the ROI of the measurement image; For each azimuth angle, the simulated far-field scattering image is cropped in the same way to obtain the ROI of the simulated far-field scattering image; Calculate the pixel-level residuals of the ROI at each azimuth angle.

6. A system for inverting the morphological parameters of nanostructures based on EUV scattering spectra, characterized in that, Includes memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the system to perform the inversion method as described in any one of claims 1-5.

7. A computer-readable storage medium, characterized in that, Includes instructions that, when executed on an electronic device, cause the electronic device to perform the inversion method as described in any one of claims 1-5.

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