A method for measuring angularly resolved scattering micro-nano structures by multi-exposure fusion

Abstract

The application discloses a kind of multi-exposure fusion's angle resolution scattering micro-nano structure measurement method, it is related to integrated circuit measurement technical field.The method includes: obtaining multi-exposure sequence image set, camera response function CRF is modeled;Overexposed pixel value is estimated using linear extrapolation method based on tangent line at response curve end point, and the confidence of extrapolated pixel is calculated;When the confidence of extrapolated pixel is lower than basic confidence, segmented conservative estimation strategy is used to enhance to extrapolated pixel;Corrected image set and corresponding confidence image set are obtained by iterative processing;Weight distribution is carried out to the image in corrected image set, and corresponding normalized weight set is obtained;According to normalized weight set and corrected image set, multi-scale fusion is carried out, and fusion image is obtained.Pixel level correction is carried out to image, and the pixel irradiance of overexposure area is effectively reconstructed, and multi-scale fusion is carried out to image, and high-fidelity fusion of Fourier space intensity is realized.

Description

Technical Field

[0001] This invention relates to the field of integrated circuit measurement technology, and in particular to a multi-exposure fusion angle-resolved scattering micro / nano structure measurement method. Background Technology

[0002] Photolithography is one of the most complex processes in semiconductor manufacturing, and angle-resolved scattering (ARS) is an important method for measuring semiconductor micro and nanostructures. It utilizes a detector to capture the diffraction pattern of a large numerical aperture (NA) objective lens (BFP) and solves for the measured dimension using empirical or model-matching methods. However, a practical challenge in angle-resolved scattering measurements is determining the optimal exposure parameters for each object under test. Due to the non-uniform intensity distribution in the diffraction image, a single exposure image often contains both underexposed regions with low signal-to-noise ratios and saturated regions with excessive intensity, and the optimal exposure time varies significantly for different marker structures. This situation alters the amplitude fidelity of the diffraction image and directly affects the accuracy of OVL measurements. Therefore, exposure non-uniformity greatly limits the accuracy of scattering measurements.

[0003] Existing micro / nano measurement methods based on scattering include: 1. Methods and systems that generate semiconductor material property images based on scattering measurement data and update the geometry by comparing with a model to improve measurement accuracy. 2. Methods for measuring overlay errors using multiple wavelengths, which simultaneously illuminate the overlay measurement marks with two or more discrete wavelengths to increase the effective signal and thus improve measurement repeatability. 3. Methods that employ a wide-band light source and a normal incident optical path to achieve high-precision measurement of overlay errors by analyzing the asymmetry of higher-order diffraction spectra. This method has a large depth of focus, strong adaptability, and effectively reduces the difficulty of focal plane control.

[0004] Methods related to MEF include: 1. A multi-exposure fusion method based on the feature distribution weights of multi-exposure images, which combines image brightness distribution weights, image exposure distribution weights, and image local gradient weights, solving the technical problem that existing multi-exposure fusion methods do not consider the overall feature distribution of multi-exposure images. 2. By extracting the structural, naturalness, and color features of multi-exposure fused images and aggregating them using a quality regression model, accurate assessment of image visual quality is achieved. This method fully integrates the three types of features, significantly improving the accuracy of multi-exposure fused image quality assessment. 3. By combining preset and historical data weighted average fusion, weights are quickly and adaptively set, effectively improving the naturalness and detail of the fused image, overcoming the problems of poor flexibility and low accuracy of traditional methods.

[0005] According to existing technologies, current techniques for measuring the angle-resolved scattering (MEF) of integrated circuit micro / nano structures include instrument improvements and innovative extraction algorithms. However, no existing technology has yet addressed the issue of exposure time affecting the accuracy of results in MEF micro / nano measurements. Furthermore, multi-exposure fusion methods are primarily designed for imaging natural scenes and optimized for human visual perception, aiming to enhance features such as detail and contrast. Even when used for measurement, these methods are designed for imaging measurements, not scattering measurements. For the former, the measured quantity is directly obtained through image processing and geometric feature extraction, while the latter relies on the absolute fidelity of the angle-intensity scattering distribution. Traditional MEF methods irreversibly distort the intensity distribution characteristics in Fourier space during the fusion process. This distortion introduces pixel-level systematic errors, ultimately affecting the scattering measurement results. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-exposure fusion angle-resolved scattering micro / nano structure measurement method, which aims to solve or improve at least one of the above-mentioned technical problems.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] A multi-exposure fusion method for measuring angle-resolved scattering micro / nano structures includes:

[0009] Acquire a set of multi-exposure sequence images and model the camera response function (CRF).

[0010] Based on the camera response function (CRF), the values ​​of overexposed pixels are estimated using a linear extrapolation method based on the tangent at the endpoint of the response curve, and the confidence level of the extrapolated pixels is calculated.

[0011] When the confidence level of the extrapolated pixel is lower than the base confidence level, a piecewise conservative estimation strategy is used to enhance the extrapolated pixel.

[0012] The corrected image set and the corresponding confidence image set are obtained through iterative processing;

[0013] Weights are assigned to the images in the calibration image set to obtain the corresponding normalized weight set;

[0014] Multi-scale fusion is performed based on the normalized weight set and the corrected image set to obtain a fused image, and the measurement value is obtained based on the fused image.

[0015] Furthermore, a multi-exposure image sequence set is obtained, and the camera response function (CRF) is modeled, including: the multi-exposure image sequence set, with the expression:

[0016]

[0017] In the formula, Let j be the j-th image, consisting of m×n pixels; p is the number of images;

[0018] By measuring {Z} ij ,t j Solving for unknowns in an overdetermined system composed of} and ; where: Z ij Let i be the pixel value at pixel i in image j; t represents the irradiance at pixel i; j Let be the exposure time of image j;

[0019] The camera response function is estimated using regularized least squares optimization. The expression is:

[0020] ;

[0021] In the formula, N = m × n is the total number of pixels in the image; For regularization parameters; and These represent the maximum and minimum values ​​within the pixel's value range, respectively; r represents the possible values ​​for each pixel. for The second derivative; The weighting function for pixel values;

[0022] The expression is:

[0023] ;

[0024] ;

[0025] ;

[0026] In the formula, Standard deviation; The position with the highest weight; and These represent the minimum and maximum values ​​within the range of pixel values.

[0027] Furthermore, based on the camera response function (CRF), the values ​​of overexposed pixels are estimated using a linear extrapolation method based on the tangent at the endpoint of the response curve, and the confidence level of the extrapolated pixels is calculated, including:

[0028] When the pixel value is below the upper limit of the calibration range, Hermite interpolation is used to calculate the pixel value, with a confidence level of [missing information]. =1; When the upper limit is exceeded, linear extrapolation is performed using the slope at the endpoint of the curve.

[0029] The pixel value expression for extrapolated pixels is:

[0030] ;

[0031] In the formula, The pixel value at the extrapolated location; The slope at the endpoint of the curve; This represents the upper limit of pixel values.

[0032] Based on the current pixel value and the calibration range, determine the confidence level of each pixel using the following expression:

[0033] ;

[0034] In the formula, Confidence level for pixels; This is the base confidence level; This is the decay rate coefficient; This is the average sampling interval of the calibration curve in the logarithmic domain.

[0035] Furthermore, when the confidence level of the extrapolated pixel is lower than the base confidence level, a piecewise conservative estimation strategy is used to enhance the extrapolated pixel, including:

[0036] ;

[0037] In the formula, To enhance pixels; extrapolated pixels; The confidence level of the extrapolated pixels; is the average intensity of ±1st order diffracted light in the (j-1)th image;

[0038] The confidence level of the pixel value obtained by conservative estimation is set as the base confidence level. .

[0039] Furthermore, weights are assigned to the images in the calibration image set to obtain the corresponding normalized weight set, including:

[0040] The composite weights of pixels in an image are defined by the following expression:

[0041] ;

[0042] ;

[0043] In the formula, Let be the composite weight of pixel i in image j; These are the weighting coefficients for the intensity normalization of image j±1; The sensitivity of the detector to changes in diffraction intensity at pixel i;

[0044] Sensitivity to changes in diffraction intensity The expression is:

[0045] ;

[0046] In the formula, This indicates the value of the i-th pixel in image j to be corrected. This is the attenuation coefficient, used to calculate the weight of overexposed pixels; This is the mapping function from pixel values ​​to sensitivity. This represents the maximum value in the sensitivity function. For the derivative sign;

[0047] The composite weights of pixels in the image are normalized to obtain a normalized weight set, expressed as:

[0048] ;

[0049] In the formula, For normalized weights; Let be the composite weight of pixel i in image j; It is the sum of the composite weights of pixel i across all images.

[0050] Furthermore, based on the normalized weight set and the corrected image set, multi-scale fusion is performed to obtain the fused image, including:

[0051] The pyramid depth expression is:

[0052] ;

[0053] In the formula, m×n represents the number of layers; m×n represents the dimensions of the image.

[0054] The corrected image set is sorted from darkest to brightest based on brightness. A Laplacian pyramid is generated based on the residuals between consecutive Gaussian layers in the Gaussian pyramid, expressed as:

[0055] ;

[0056] In the formula, This is the k-th corrected image; image Gauss Pyramid; It is an upsampling function;

[0057] The Gaussian pyramid is constructed using the normalized weight set, expressed as:

[0058]

[0059] In the formula, For normalized weight set; To construct the l-th layer of the Gaussian pyramid; This represents the result of weight processing at layer l.

[0060] Based on the Laplace pyramid and the Gaussian pyramid, the fused Laplace layer is calculated using the following expression:

[0061] ;

[0062] In the formula, P represents the number of images to be fused; The normalized weights of the k-th image in the l-th layer; Let the k-th image be represented by the Laplacian pyramid at layer l.

[0063] By collapsing the Laplacian pyramid, upsampling is performed step by step, and residuals are summed from the coarsest to the finest scale to obtain the fused image.

[0064] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0065] This invention discloses a multi-exposure fusion method for measuring angle-resolved scattering micro / nano structures. The method effectively reconstructs the pixel irradiance of overexposed areas by performing pixel-level correction on the image and achieves high-fidelity fusion of Fourier spatial intensity through multi-scale image fusion. This effectively alleviates the problem of uneven exposure affecting the overlay measurement accuracy of single-exposure diffraction images. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 This is a schematic diagram of the measurement method in this invention;

[0068] Figure 2 This is a schematic diagram illustrating the specific process of the measurement method in this embodiment;

[0069] Figure 3 This is a schematic diagram of the DBO marking structure of the diffraction-type sleeve marking in this embodiment; wherein, Figure 3 (a) shows the design layout of the diffraction-type overlay mark; Figure 3 (b) is a schematic diagram of an ideal overlay mark;

[0070] Figure 4 This is a SEM image of a typical diffraction-type overlaid DBO-labeled sample in this embodiment; wherein, Figure 4(a) is a top view with 4 units labeled. Figure 4 neutralize Figure 4 In the middle, ③ represents the +D and -D markings in the x-direction. Figure 4 neutralize Figure 4 In the middle, ④ represents the +D and -D markings in the y direction; Figure 4 (b) is a partial view, where 532nm is the grating linewidth and 998nm is the period;

[0071] Figure 5 This is a schematic diagram of the optical path of the angle-resolved scattering device in this embodiment;

[0072] Figure 6 These are BFP images acquired by the +D and -D units at different exposure times in this embodiment;

[0073] Figure 7 This is a schematic diagram of the measurement results of two sets of overlay marks under different exposure times in this embodiment;

[0074] Figure 8 This is a schematic diagram illustrating the impact of image correction on the measurement results of the two sets of markers in this embodiment; wherein, Figure 8 (a) shows the single-exposure measurement method; Figure 8 (b) shows the multi-exposure measurement method;

[0075] Figure 9 This is a schematic diagram illustrating the impact of multi-scale fusion on the two sets of labeled measurement results in this embodiment; Figure 9 (a) shows the result without correction. Figure 9 (b) shows a schematic diagram with the correction results;

[0076] Figure 10 This diagram illustrates the comparison results with different methods in this embodiment and the percentage reduction in total error. Figure 10 (a) is a schematic diagram showing the comparison results with the fusion method; Figure 10 (b) is a schematic diagram showing the comparison results with the single exposure method. Detailed Implementation

[0077] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0078] The purpose of this invention is to provide a multi-exposure fusion angle-resolved scattering micro / nano structure measurement method, which aims to solve or improve at least one of the above-mentioned technical problems.

[0079] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0080] like Figure 1 As shown, this invention provides a multi-exposure fusion angle-resolved scattering micro / nano structure measurement method, comprising:

[0081] Step 1: Obtain a set of multi-exposure image sequences and model the camera response function (CRF), including the following steps:

[0082] A multi-exposure sequence image set, expressed as:

[0083]

[0084] In the formula, Let j be the j-th image, consisting of m×n pixels; p is the number of images;

[0085] By measuring {Z} ij ,t j Solving for unknowns in an overdetermined system composed of} and ; where: Z ij Let i be the pixel value at pixel i in image j; t represents the irradiance at pixel i; j Let be the exposure time of image j;

[0086] Due to Z ij Z is a discrete integer, where the value range of the discrete integer is [0, 255]. For an 8-bit system, Z... min =0, Z max =255;

[0087] The camera response function is estimated using regularized least squares optimization. The expression is:

[0088] ;

[0089] In the formula, N = m × n is the total number of pixels in the image; The regularization parameter controls the balance between smoothness and accuracy (λ>0). A smaller λ increases the sensitivity of the response curve to noise, while an excessively large λ can make the curve overly smooth, potentially approaching linearity and reducing fitting accuracy. and These represent the maximum and minimum values ​​of the pixel value range, respectively; r represents the possible values ​​of each pixel (0-255), which do not correspond to the pixel value of any pixel in the image, and defines the range of potential light intensity values. for The second derivative of is numerically approximated as ; The weighting function for pixel values;

[0090] The expression is:

[0091] ;

[0092] ;

[0093] ;

[0094] In the formula, Standard deviation; The position with the highest weight; and These represent the minimum and maximum values ​​within the range of pixel values.

[0095] By using the methods described above, the standard deviation can be set. The impact of extreme pixel values ​​was reduced; the influence of overexposed and underexposed pixels was weakened by using a Gaussian weighting function, while emphasizing pixels within the effective exposure range.

[0096] Step 2: Based on the camera response function (CRF), estimate the overexposed pixel values ​​using a linear extrapolation method based on the tangent at the endpoint of the response curve, and calculate the confidence level of the extrapolated pixels, including the following steps:

[0097] Step 21: When the pixel value is below the upper limit of the calibration range, Hermite interpolation is used to calculate the pixel value with confidence level. =1; When the upper limit is exceeded, linear extrapolation is performed using the slope at the endpoint of the curve.

[0098] The pixel value expression for extrapolated pixels is:

[0099] ;

[0100] In the formula, The pixel value at the extrapolated location; The slope at the endpoint of the curve; This represents the upper limit of pixel values.

[0101] Step 22: Based on the fact that the current pixel value exceeds the calibration range, determine the confidence level of each pixel, expressed as:

[0102] ;

[0103] In the formula, Confidence level for pixels; This is the base confidence level; This is the decay rate coefficient; This is the average sampling interval of the calibration curve in the logarithmic domain.

[0104] In the above steps, the expression for extrapolating pixel values ​​is derived from a first-order Taylor expansion, ensuring the continuity of the response curve as the boundary expands. The confidence expression uses an exponential decay model, representing a natural fit of the estimation error of the observed values ​​as the extrapolation distance increases. Linear extrapolation ensures continuity with the calibration curve at the boundary.

[0105] Step 3: When the confidence level of the extrapolated pixel is lower than the base confidence level, a piecewise conservative estimation strategy is used to enhance the extrapolated pixel, as expressed in the following expression:

[0106] ;

[0107] In the formula, To enhance pixels; extrapolated pixels; Confidence level for pixels; is the average intensity of ±1st order diffracted light in the (j-1)th image;

[0108] The confidence level of the pixel value obtained by conservative estimation is set as the base confidence level. .

[0109] Step 4: Obtain the corrected image set through iterative processing. and the corresponding confidence image set This includes: improving the accuracy of the solution by iterative sampling method that gradually increases the sample size until the change in the solution between two iterations is small enough; in each iteration, using the current sample size, randomly selecting pixels from the image, constructing a matrix, and then calling a camera response function solution function based on weighted least squares to solve for the camera response function g and the irradiance IE.

[0110] The pixel-level correction of the image is completed through steps 1-4 above.

[0111] Step 5 involves assigning weights to the images in the calibration image set to obtain the corresponding normalized weight set, including the following steps:

[0112] Step 51, define the composite weights of pixels in the image, with the following expression:

[0113] ;

[0114] ;

[0115] In the formula, Let be the composite weight of pixel i in image j; These are the weighting coefficients for the intensity normalization of image j±1; Let be the sensitivity of the detector in image j to the change in diffraction intensity at pixel i;

[0116] Sensitivity to changes in diffraction intensity The expression is:

[0117] ;

[0118] In the formula, This indicates the value of the i-th pixel in image j to be corrected. This is the attenuation coefficient, used to calculate the weight of overexposed pixels; This is the mapping function from pixel values ​​to sensitivity. This represents the maximum value in the sensitivity function. For the derivative sign;

[0119] Step 52: Normalize the composite weights of the pixels in the image to obtain a normalized weight set, expressed as:

[0120] ;

[0121] In the formula, For normalized weights; Let be the composite weight of pixel i in image j; It is the sum of the composite weights of pixel i across all images.

[0122] The above steps involve weight allocation to suppress saturation artifacts and highlight the optimal exposure area.

[0123] Step 6: Perform multi-scale fusion based on the normalized weight set and the corrected image set to obtain the fused image, including the following steps:

[0124] The pyramid depth expression is:

[0125] ;

[0126] In the formula, m×n represents the number of layers; m×n represents the dimensions of the image.

[0127] The corrected image set is sorted from darkest to brightest based on brightness. A Laplacian pyramid is generated based on the residuals between consecutive Gaussian layers in the Gaussian pyramid, expressed as:

[0128] ;

[0129] In the formula, This is the k-th corrected image; image Gauss Pyramid; It is an upsampling function;

[0130] The Gaussian pyramid is constructed using the normalized weight set, expressed as:

[0131]

[0132] In the formula, For normalized weight set; To construct the l-th layer of the Gaussian pyramid; This represents the result of weight processing at layer l.

[0133] Based on the Laplace pyramid and the Gaussian pyramid, the fused Laplace layer is calculated using the following expression:

[0134] ;

[0135] In the formula, P represents the number of images to be fused; The normalized weights of the k-th image in the l-th layer; Let the k-th image be represented by the Laplacian pyramid at layer l.

[0136] By collapsing the Laplacian pyramid, upsampling is performed step by step, and residuals are summed from the coarsest to the finest scale to obtain the fused image.

[0137] In the above steps, multi-scale image decomposition is used to suppress halo artifacts while addressing the trade-off between preserving local details and maintaining global consistency.

[0138] In this embodiment, the overlay mark is selected as the measurement object, and the overlay extraction method based on the empirical relationship (within the effective measurement range, using the approximate linear response relationship between the differential intensity of ±1st order diffraction order and the overlay error (OVL)) is used to calculate the OVL value. The expression is as follows:

[0139] ;

[0140] ;

[0141] ;

[0142] In the formula, These are the intensities of ±1st order diffraction measured from a cell with a preset deviation value; and These represent the intensity differences of ±1st order diffraction between units with -D and +D deviation values, respectively. For diffraction intensity difference Sensitivity coefficient to ε; D is the preset bias; ε is the overlay error;

[0143] Typical Diffraction Based Overlay (DBO) markings are used. Figure 3 Figure (a) describes the design layout of the markings (402 μm × 402 μm), which includes four measurement units. Units 1 and 4 are used to measure the overlay error in the x-direction. Units 2 and 3 are used to measure the superposition overlay error in the y-direction. .

[0144] like Figure 3 As shown in (b), taking unit 1 as an example, the layered structure from top to bottom includes: PR-1 photoresist grating, and the middle... The structure consists of a PR-2 photoresist film, a bottom Si grating layer, and a Si substrate. The corresponding dimensional parameters are shown in Table 1. A series of DBO markers were fabricated using electron beam lithography (EBL).

[0145] Table 1. Parameter settings for DBO markers

[0146]

[0147] like Figure 4 The image shown is a typical labeled SEM image.

[0148] like Figure 5 As shown, an angle-resolved scattering apparatus was used for the experiment. Based on the sample structure, the device parameters (such as objective magnification, light source wavelength, and focal length ratio of the Fourier lens group) were determined. Simultaneously, to eliminate the mutual interference between the ±1st order diffraction signals and the zeroth order light, an annular aperture was placed in the incident light path. This created a specific annular incident beam at the rear focal plane of the objective lens. By precisely adjusting the inner and outer diameters of the aperture, the incident light angle distribution could be optimized, and spatial separation of the ±1st order diffraction orders could be achieved, avoiding diffraction pattern overlap. It should be noted that the wavelength and polarization state of the probe light have a significant impact on the sensitivity of the overlay measurement; therefore, a 520nm laser source and TM polarized light illumination were used to enhance the contrast of the diffraction signal and suppress defect interference.

[0149] Based on the aforementioned OVL extraction method and angle-resolved scattering (ARS) apparatus, measurements were performed on two typical overlay marks, Target1 and Target2. A uniform sampling strategy (exposure time range [1000 μs, 5000 μs], step size 1000 μs) was employed to obtain diffraction patterns within the underexposed to overexposed range, such as... Figure 6As shown. The reference dimensions are obtained after image processing and calculation, based on FIB microscopy calibration. Due to unavoidable manufacturing errors, the displacement between the double-layer gratings within a single unit is not ideally uniform. The average value is taken as the reference value to represent the overall OVL level of each unit. The preset bias values ​​D for Target1 and Target2 are 22.05 nm and 20.87 nm, respectively, corresponding to actual OVLs of -5.512 nm and -9.844 nm, respectively. Finally, the measurement results of the two sets of markers at different exposure times are shown below. Figure 7 As shown, it can be observed that the OVL measurement results are significantly affected by the exposure time.

[0150] In pixel-level correction, the method of this invention is expressed as:

[0151] ;

[0152] The regularization parameter λ typically ranges from 0 to 100; in this embodiment, it is set to 20 to achieve a balance between smoothing constraints and data fidelity. To ensure the stability of the fitted response function, the number of iterations is defined. =50, each iteration uses the sampling point increment. =500. When there are three consecutive iterations... and When the maximum difference between the values ​​is less than the threshold of 0.005, the fitted response function is considered convergent. During confidence estimation, the base confidence β0 is set to 0.7; the minimum confidence threshold βmin is set to 0.15; and the decay rate coefficient ρ is set to 0.6 to control the rate of decrease in confidence as the extrapolation distance increases. In the multi-scale fusion process, the expression is:

[0153] ;

[0154] In the formula, the attenuation coefficient α was experimentally determined to be 0.005, which is used to adjust the weight distribution of overexposure correction pixels to ensure that the weight gradually decreases rather than drops sharply.

[0155] As shown in Table 2, this embodiment verifies the effectiveness of the proposed method and the contribution of each module through ablation and comparison experiments. Five classic MEF methods are compared: 1) pixel-based fusion; 2) image-based fusion; 3) block-based fusion; 4) gradient domain fusion; and 5) multi-scale decomposition-based fusion.

[0156] Table 2. Modular ablation design and comparative experiments

[0157]

[0158] This embodiment examines the performance of the single exposure method M10 with / without a pixel correction module and the multi-exposure fusion method Ours-M9. Figure 8 (a) compares the test results under single-exposure conditions: after introducing the correction module, the average measurement error of Target 1 decreased by 14.59%, Target 2 by 9.21%, and the overall error decreased by 11.31%. In multi-exposure fusion scenarios, the impact of the pixel correction module on spatial domain fusion and transform domain fusion strategies was evaluated. Among them, M1, M3, M5, M7, and M9 do not have a pixel correction module, while Our, M2, M4, M6, and M8 integrate the correction module. Figure 8 Figure (b) presents the results of all fusion experiments and quantifies the module's improvement in average measurement performance in a visual manner. Experimental results show that the correction module reduces the overall average error by 26.52%. All experimental results consistently demonstrate that the pixel correction module makes a significant contribution to improving the overall accuracy of DBO measurements.

[0159] Through comparative analysis of single exposure and multiple exposure methods, the results are as follows: Figure 9 (a) and Figure 9 As shown in (b), the multi-exposure fusion module significantly reduces the measurement error between the two sets of markers. Specifically, Figure 9 Data shows that the measurement error was reduced by 22.65% without the calibration module, while it was reduced by 35.91% with the calibration module, fully demonstrating the key role of the fusion module in improving measurement accuracy.

[0160] Based on the above experimental results, the multi-exposure fusion method based on angle-resolved scattering proposed in this invention can effectively reconstruct the pixel irradiance of overexposed areas and achieve high-fidelity fusion of Fourier spatial intensities. Comparative analysis shows that the method of this invention is superior to other fusion schemes, such as... Figure 10 As shown in (a), the maximum error, minimum error, and average error were reduced by 69.35%, 14.00%, and 41.87%, respectively. Compared to traditional single-exposure measurements, the error reduction under different exposure conditions ranged from 39.60% to 73.38%, as... Figure 10 As shown in (b). It should be noted that the method of the present invention can significantly reduce measurement errors without relying on the optimization of specific exposure parameters, thus providing an effective technical means for high-precision DBO measurement in semiconductor manufacturing.

[0161] Furthermore, this invention is not limited to the specific embodiments described above. The above embodiments are merely preferred examples of this invention, intended to provide a detailed description of the technical solution of this invention, and not to limit its scope of protection. Any modifications, equivalent substitutions, or variations made within the conceptual scope defined in the claims of this invention should still be considered to fall within the scope of protection of this invention. It should be noted that the overlay marking structure and material parameters involved in this invention are not limited to the specific structures and values ​​listed in the embodiments; the iterative processing in this method includes, but is not limited to, Monte Carlo iterative optimization, Bayesian optimization, deterministic optimization, etc., and these optimization methods are all within the scope of protection of this method; the specific parameters used in the correction module and fusion module can also be adjusted according to actual applications; at the same time, the measurement object of this invention is not limited to overlay markings, but can also be extended to gratings, thin films, high aspect ratio structures and other micro / nano structures; this invention can extend to different extraction methods according to different measurement objects.

[0162] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0163] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A multi-exposure fusion method for measuring angle-resolved scattering micro / nano structures, characterized in that, include: Acquire a set of multi-exposure sequence images and model the camera response function (CRF). Based on the camera response function (CRF), the values ​​of overexposed pixels are estimated using a linear extrapolation method based on the tangent at the endpoint of the response curve, and the confidence level of the extrapolated pixels is calculated. When the confidence level of the extrapolated pixel is lower than the base confidence level, a piecewise conservative estimation strategy is used to enhance the extrapolated pixel. The corrected image set and the corresponding confidence image set are obtained through iterative processing; Weights are assigned to the images in the calibration image set to obtain the corresponding normalized weight set; Multi-scale fusion is performed based on the normalized weight set and the corrected image set to obtain a fused image, and the measurement value is obtained based on the fused image; The step of performing multi-scale fusion based on the normalized weight set and the corrected image set to obtain the fused image includes: The pyramid depth expression is: ； In the formula, Number of floors; × The dimension of the image; The corrected image set is sorted from darkest to brightest based on brightness. A Laplacian pyramid is generated based on the residuals between consecutive Gaussian layers in the Gaussian pyramid, expressed as: ； In the formula, This is the k-th corrected image; image Gauss Pyramid; It is an upsampling function; The Gaussian pyramid is constructed using the normalized weight set, expressed as: In the formula, For normalized weight set; To construct the l-th layer of the Gaussian pyramid; This represents the result of weight processing at layer l. Based on the Laplace pyramid and the Gaussian pyramid, the fused Laplace layer is calculated using the following expression: ； In the formula, P represents the number of images to be fused; The normalized weights of the k-th image at layer l; Let the k-th image be represented by the Laplacian pyramid at layer l. By collapsing the Laplacian pyramid, upsampling is performed step by step, and residuals are summed from the coarsest to the finest scale to obtain the fused image.

2. The multi-exposure fusion angle-resolved scattering micro / nano structure measurement method according to claim 1, characterized in that, The acquisition of the multi-exposure sequence image set and the modeling of the camera response function (CRF) include: the multi-exposure sequence image set, expressed as: In the formula, Let j be the j-th image, consisting of m×n pixels; p is the number of images; By measuring {Z} ij ,t j Solving for unknowns in an overdetermined system composed of} and ; where: Z ij Let i be the pixel value at pixel i in image j; t represents the irradiance at pixel i; j Let be the exposure time of image j; The camera response function is estimated using regularized least squares optimization. The expression is: ； In the formula, N = m × n is the total number of pixels in the image; For regularization parameters; and These represent the maximum and minimum values ​​within the pixel's value range, respectively; r represents the possible values ​​for each pixel. for The second derivative; The weighting function for pixel values; The expression is: ； ； ； In the formula, Standard deviation; The position with the highest weight; and These represent the minimum and maximum values ​​within the range of pixel values.

3. The multi-exposure fusion angle-resolved scattering micro / nano structure measurement method according to claim 1, characterized in that, The process of estimating overexposed pixel values ​​using a linear extrapolation method based on the tangent at the endpoint of the response curve, according to the camera response function (CRF), and calculating the confidence level of the extrapolated pixels includes: When the pixel value is below the upper limit of the calibration range, Hermite interpolation is used to calculate the pixel value, with a confidence level of [missing information]. =1; When the upper limit is exceeded, linear extrapolation is performed using the slope at the endpoint of the curve. The pixel value expression for extrapolated pixels is: ； In the formula, The pixel value at the extrapolated location; The slope at the endpoint of the curve; This represents the upper limit of pixel values. Based on the current pixel value and the calibration range, determine the confidence level of each pixel using the following expression: ； In the formula, Confidence level for a pixel; This is the base confidence level; This is the decay rate coefficient; This is the average sampling interval of the calibration curve in the logarithmic domain.

4. The multi-exposure fusion angle-resolved scattering micro / nano structure measurement method according to claim 1, characterized in that, When the confidence level of the extrapolated pixel is lower than the base confidence level, a piecewise conservative estimation strategy is used to enhance the extrapolated pixel, including: ； In the formula, To enhance pixels; extrapolated pixels; The confidence level of the extrapolated pixels; is the average intensity of ±1st order diffracted light in the (j-1)th image; The confidence level of the pixel value obtained by conservative estimation is set as the base confidence level. .

5. The multi-exposure fusion angle-resolved scattering micro / nano structure measurement method according to claim 1, characterized in that, The step of assigning weights to the images in the correction image set to obtain the corresponding normalized weight set includes: The composite weights of pixels in an image are defined by the following expression: ； ； In the formula, Let be the composite weight of pixel i in image j; These are the weighting coefficients for the intensity normalization of image j±1; The sensitivity of the detector to changes in diffraction intensity at pixel i; Sensitivity to changes in diffraction intensity The expression is: ； In the formula, Indicates the corrected image j The Middle i pixel value, This is the attenuation coefficient, used to calculate the weight of overexposed pixels; This is the mapping function from pixel values ​​to sensitivity. This represents the maximum value in the sensitivity function. For the derivative sign; The composite weights of pixels in the image are normalized to obtain a normalized weight set, expressed as: ； In the formula, For normalized weights; Let be the composite weight of pixel i in image j; It is the sum of the composite weights of pixel i across all images.

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