A Broadband Interferometric Weak Signal Enhancement Method for Measuring High Aspect Ratio Micro / Nano Structures

Abstract

This invention discloses a method for enhancing weak signals in broadband interferometric measurements of high aspect ratio micro / nano structures, relating to the field of semiconductor measurement technology. The method includes: acquiring a broadband interferogram; performing a two-layer two-dimensional discrete wavelet transform to obtain a first-stage wavelet coefficient set; performing nonlinear enhancement on the wavelet coefficients to output a nonlinearly enhanced broadband interferogram; performing a three-layer two-dimensional discrete wavelet transform on the nonlinearly enhanced broadband interferogram to obtain a second-stage wavelet coefficient set, and calculating a Bayesian threshold; setting a neighborhood sliding window function combined with the Bayesian threshold to perform local denoising enhancement on the second-stage wavelet coefficients; reconstructing the locally denoised and enhanced second-stage wavelet coefficients to obtain a locally denoised and enhanced broadband interferogram; determining the optical path position using an improved centroid method based on the locally denoised and enhanced broadband interferogram, and calculating the depth value of the sample to be measured. This invention enhances fringe contrast and suppresses noise, while simultaneously improving depth measurement capabilities.

Description

Technical Field

[0001] This invention relates to the field of semiconductor measurement technology, and in particular to a broadband interferometric weak signal enhancement method for measuring high aspect ratio micro / nano structures. Background Technology

[0002] The rapid development of Micro-Electro-Mechanical Systems (MEMS) has driven the widespread demand and application expansion of High Aspect Ratio (HAR) structures. These structures typically have a width of only 1–10 micrometers and an aspect ratio generally greater than 10:1. Deep trench structures, as a typical HAR structure, play a crucial role in advanced devices such as inertial sensors, microfluidic chips, and optical microcavities. The three-dimensional morphological parameters of deep trenches, especially sidewall perpendicularity, bottom surface flatness, and trench depth uniformity, directly determine key indicators of MEMS devices such as mechanical stability, fluid transport efficiency, and optical performance.

[0003] Therefore, achieving high-precision, non-destructive, and online measurement of the three-dimensional topography of HAR structures has become a key technological bottleneck in ensuring the performance and reliability of MEMS devices. Optical interferometry, with its advantages of non-contact, full-field measurement, and high precision, is considered the most promising solution. Among them, broadband interferometry, by utilizing the low coherence characteristics of broadband light sources, overcomes the phase ambiguity problem in monochromatic interferometers and has become the mainstream technology for measuring the three-dimensional topography of micro and nanostructures. Compared with laser interferometry, broadband interferometry has a larger measurement range, reaching several millimeters. Its advantages, such as being unaffected by 2π phase jumps and insensitivity to environmental vibrations, make it particularly suitable for characterizing MEMS devices with step-type structures. However, when applied to HAR structures, the effective interference fringes in images obtained by traditional broadband interferometry only occupy 5% to 10% of the field of view, and the fringe contrast is extremely low, making it difficult to meet the signal-to-noise ratio requirements for topography reconstruction.

[0004] Therefore, how to improve the measurement accuracy of HAR structures using broadband interferometry is a problem that needs to be solved by those in this field. Summary of the Invention

[0005] The purpose of this invention is to provide a method for enhancing weak signals by broadband interferometry in the measurement of high aspect ratio micro / nano structures, aiming to solve or improve at least one of the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A broadband interferometric weak signal enhancement method for high aspect ratio micro / nano structure measurements includes:

[0008] Step 1: Obtain the broadband interferogram of the sample to be tested, perform two-level two-dimensional discrete wavelet transform, and obtain the first-stage wavelet coefficient group;

[0009] Step 2: Determine the adaptive threshold based on the wavelet coefficients and image information entropy in the first stage, perform nonlinear enhancement on the wavelet coefficients, and output a nonlinearly enhanced broadband interferogram.

[0010] Step 3: Perform a three-level two-dimensional discrete wavelet transform on the nonlinearly enhanced broadband interferogram to obtain the second-stage wavelet coefficient set, and calculate the Bayes threshold.

[0011] Step 4: Set up a neighborhood sliding window function combined with a Bayesian threshold to perform local denoising enhancement on the wavelet coefficients in the second stage;

[0012] Step 5: Reconstruct the wavelet coefficients of the second stage after local denoising and enhancement to obtain the broadband interferogram after local denoising and enhancement;

[0013] Step 6: Determine the optical path position using the improved centroid method based on the broadband interferogram after local denoising and enhancement, and calculate the depth value of the sample to be tested.

[0014] Furthermore, the two-dimensional discrete wavelet transform in step 1 includes:

[0015] ;

[0016] In the formula, h represents the low-pass filter coefficients; g represents the high-pass filter coefficients; m and n represent the coordinate indices of the j-th layer coefficients; and k and l represent the coordinate indices of the (j-1)-th layer coefficients. These are the approximate coefficients for layer j; , and These are the detail coefficients for horizontal, vertical, and diagonal measurements, respectively.

[0017] Further, step 2 includes:

[0018] The wavelet feature vector is constructed based on the wavelet coefficients of the first stage, and the expression is as follows:

[0019] ;

[0020] In the formula, It is a one-dimensional wavelet eigenvector; This represents the first level of detail subbands of the wavelet coefficients in the first stage. This represents the second level of detail subbands of the wavelet coefficients in the first stage.

[0021] The adaptive threshold factor is calculated using the following expression:

[0022] ;

[0023] In the formula, p is the adaptive threshold factor; Image information entropy of broadband interferogram:

[0024] ;

[0025] In the formula, Image pixel grayscale; grayscale value Frequency of appearance in the image.

[0026] The adaptive threshold is calculated based on the wavelet eigenvector and the adaptive threshold scaling factor, and the expression is:

[0027] ;

[0028] In the formula, An adaptive threshold; is a one-dimensional wavelet eigenvector; p is an adaptive threshold factor; This is a quantile function that returns the quantiles of p.

[0029] The wavelet coefficients c in the first stage are nonlinearly enhanced, and the expression is as follows:

[0030] ;

[0031] In the formula, c represents the enhanced first-stage wavelet coefficients; c represents the first-stage wavelet coefficients. An adaptive threshold;

[0032] Based on the enhanced first-stage wavelet coefficients c, the nonlinearly enhanced broadband interferogram is calculated.

[0033] Further, step 3 includes:

[0034] The expression for the second-stage wavelet coefficients is set as follows:

[0035] ;

[0036] In the formula, The wavelet coefficients are for the second stage; x is the true signal component; n is the Gaussian noise component.

[0037] The expression for noise variance estimation is:

[0038] ;

[0039] In the formula, This is an estimate of the noise variance; This is the first layer of diagonal detail sub-bands; It is a median function;

[0040] To minimize the Bayesian risk, the expression is:

[0041] ;

[0042] In the formula, This is an estimate of the true signal; For Bayesian estimators; These are the wavelet coefficients for the second stage; The variance of the true signal; This is an estimate of the noise variance;

[0043] The expression for the variance estimation of the true signal is:

[0044] ;

[0045] In the formula, An estimate of the variance of the true signal; M×N is the normalization factor; M×N is the size of the wavelet subband. The wavelet coefficients of the wavelet subband; This is an estimate of the noise variance;

[0046] The Bayesian threshold is calculated using the following expression:

[0047] ;

[0048] In the formula, Use the Bayesian threshold; This is an estimate of the noise variance; This represents the standard deviation of the true signal.

[0049] Further, step 4 includes:

[0050] The neighborhood energy is calculated using the following expression:

[0051] ;

[0052] In the formula, For The energy in the vicinity of the center; The coordinates of the center of the current wavelet coefficients are i; i and j are the neighborhood offset indices. These are the wavelet coefficients within the neighborhood; The squared energy of the wavelet coefficients in the neighborhood;

[0053] Set the adaptive shrinkage factor, expressed as follows:

[0054] ;

[0055] In the formula, It is an adaptive shrinkage factor; For The energy in the vicinity of the center; This represents the maximum local energy of the wavelet subband.

[0056] The second-stage wavelet coefficients are locally denoised and enhanced based on the Bayesian threshold and adaptive shrinkage factor, as expressed in the following expression:

[0057] ;

[0058] In the formula, These are the second wavelet coefficients after local denoising and enhancement; It is an adaptive shrinkage factor; These are the wavelet coefficients from the second stage before denoising and enhancement. These are estimates of the actual signal components; This is the Bayesian threshold.

[0059] Further, step 5 includes:

[0060] The second wavelet coefficients are recombined based on the wavelet packet structure, and the expression is:

[0061] ;

[0062] In the formula, This is the wavelet packet coefficient vector; This is the third approximate sub-band; For the third layer of detail sub-band; For the second layer of detail sub-bands; This is the first layer of detail sub-bands;

[0063] The final refactored expression is:

[0064]

[0065] In the formula, The enhanced broadband interferogram; The wavelet coefficients of the third-layer approximate subband at position (k,l); Let be the wavelet coefficients of the detail subband in direction i of layer j at position (k,l); This is the db8 scaling function; It is a db8 ​​wavelet function.

[0066] Furthermore, step 6 includes:

[0067] The squared intensity difference between adjacent frames of a broadband interferogram is calculated using the following expression:

[0068] ;

[0069] In the formula, The square of the light intensity difference between adjacent frames; The intensity value of the broadband interferogram after enhancement in the nth frame; represents the light intensity value of the enhanced broadband interferogram of the (n-1)th frame; N is the total number of frames in the broadband interferogram.

[0070] The optical path position is calculated using the following expression:

[0071] ;

[0072] In the formula, P is the optical path position; The square of the light intensity difference between adjacent frames;

[0073] The depth value of the sample under test is obtained by reconstructing the three-dimensional morphology after locating the coherent peak using the improved centroid method.

[0074] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0075] This invention discloses a broadband interferometric weak signal enhancement method for measuring high aspect ratio micro / nano structures. It consists of two modules: wavelet transform adaptive hard thresholding enhancement and adaptive soft thresholding denoising. First, low-frequency and high-frequency components are separated using a low-order wavelet transform, enhancing structural details and interference fringes, but also amplifying the high-frequency noise. Soft thresholding denoising based on a neighborhood sliding window function removes the amplified noise and introduced artifacts. This enhances fringe contrast, suppresses noise, and improves depth measurement capabilities. Attached Figure Description

[0076] 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.

[0077] Figure 1 This is a schematic flowchart of the method of the present invention;

[0078] Figure 2 This is a schematic diagram of the processing effects of simulated images and ideal experimental images in an embodiment of the present invention; images a, b, and c are grayscale images, noise-added images, and noise-reduced and enhanced images of broadband interference simulation images based on MATLAB; images d, e, and f are grayscale images, noise-added images, and noise-reduced and enhanced images of interference images when interference occurs on a smooth silicon-based wafer in the experiment of the embodiment;

[0079] Figure 3This is a comparison of the enhancement effects of interference images of the top and bottom of the slots in a set of experimental datasets in this invention before and after enhancement; where DWT is a two-dimensional discrete wavelet transform based on hard threshold enhancement; BAYES is a soft threshold denoising enhancement based on Bayesian threshold estimation; CLAHE is a contrast-limited adaptive histogram equalization; and TWDE is the two-stage wavelet decomposition enhancement algorithm proposed in this invention.

[0080] Figure 4 This is a line graph showing the depth calculation of the experimental dataset after five consecutive measurements of the same sample in this embodiment of the invention, and the comparison between the depth values ​​obtained after enhancement and calculation by three other mainstream image enhancement methods and the calibration values. Here, SEM represents the depth value obtained from scanning electron microscopy, i.e., the true depth value; DWT is a two-dimensional discrete wavelet transform based on hard thresholding enhancement; BAYES is a soft thresholding denoising enhancement based on Bayesian threshold estimation; CLAHE is contrast-limited adaptive histogram equalization; and TWDE is the two-stage wavelet decomposition enhancement algorithm proposed in this invention.

[0081] Figure 5 This is a schematic diagram of a broadband interference optical path system in an embodiment of the present invention.

[0082] In the figure, 1. White LED light source; 2. First lens; 3. Second lens; 4. Interference objective; 5. HAR structure sample; 6. Piezoelectric ceramic displacement stage; 7. Beam splitter; 8. Third lens; 9. Fourth lens; 10. Fifth lens; 11. Color CCD camera. Detailed Implementation

[0083] 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.

[0084] The purpose of this invention is to provide a method for enhancing weak signals by broadband interferometry in the measurement of high aspect ratio micro / nano structures, aiming to solve or improve at least one of the above-mentioned technical problems.

[0085] 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.

[0086] like Figure 1 As shown, this invention provides a method for enhancing weak, wide-spectrum interferometric signals in high aspect ratio micro / nano structure measurements, comprising:

[0087] Broadband interferometric imaging technology utilizes a light source with a wide spectral range, typically covering the visible light band, to perform interferometric measurements. When a broadband beam of light is split into a reference beam and a measurement beam by a beam splitter, they rejoin and interfere after passing through different paths, generating a broadband interferogram.

[0088] Let the spectral power density distribution of the light source be... The reference light and the measurement light have equal intensity and ideal contrast at a spatial point. At this location, the corresponding optical path difference Interference signal intensity The expression is:

[0089] ;

[0090] In the formula, The intensity of the interference signal; The spectral power density distribution; Wavelength; For optical path difference; This is the AC component that oscillates with the optical path difference.

[0091] In the above expression, the interference signal strength For the light source is The integral result in the wavelength domain after modulation. Significant oscillation amplitude, i.e., high-contrast fringes, is only observed when the optical path difference δ≈0, and the oscillations contain rich multi-scale frequency information. With increasing optical path difference... As the phase difference increases, light waves of different wavelengths change due to their phase difference. Unlike other methods, the superposition of interference fringes causes a rapid decrease in overall contrast. The energy of the interference signal is mainly concentrated in a finite range near the optical path difference δ≈0, and the final interference pattern is a linear superposition of the interference contributions of all wavelength components λ of the light source.

[0092] Step 1: Obtain the broadband interferogram of the sample to be tested, perform a two-level two-dimensional discrete wavelet transform, and obtain the first-stage wavelet coefficient set, expressed as:

[0093] ;

[0094] In the formula, h represents the low-pass filter coefficients; g represents the high-pass filter coefficients; m and n represent the coordinate indices of the j-th layer coefficients; and k and l represent the coordinate indices of the (j-1)-th layer coefficients. These are the approximate coefficients for layer j; , and These are the detail coefficients for horizontal, vertical, and diagonal measurements, respectively.

[0095] Step 2: Determine the adaptive threshold based on the wavelet coefficients of the first stage and the image information entropy, perform nonlinear enhancement on the wavelet coefficients of the first stage, and output a nonlinearly enhanced broadband interferogram, including the following steps:

[0096] The wavelet feature vector is constructed based on the wavelet coefficients of the first stage, and the expression is as follows:

[0097] ;

[0098] In the formula, It is a one-dimensional wavelet eigenvector; This represents the first level of detail subbands of the wavelet coefficients in the first stage. This represents the second level of detail subbands of the wavelet coefficients in the first stage.

[0099] The adaptive threshold factor is calculated using the following expression:

[0100] ;

[0101] In the formula, p is the adaptive threshold factor; Image information entropy of broadband interferogram:

[0102] ;

[0103] In the formula, Image pixel grayscale; grayscale value Frequency of appearance in the image.

[0104] The adaptive threshold is calculated based on the wavelet eigenvector and the adaptive threshold scaling factor, and the expression is:

[0105] ;

[0106] In the formula, An adaptive threshold; is a one-dimensional wavelet eigenvector; p is an adaptive threshold factor; This is a quantile function that returns the quantiles of p.

[0107] The wavelet coefficients c in the first stage are nonlinearly enhanced, and the expression is as follows:

[0108] ;

[0109] In the formula, c represents the enhanced first-stage wavelet coefficients; c represents the first-stage wavelet coefficients. An adaptive threshold;

[0110] Based on the enhanced first-stage wavelet coefficients c, the nonlinearly enhanced broadband interferogram is calculated.

[0111] The above steps efficiently and quickly distinguish high-frequency (interference fringes, structural details) and low-frequency (flat regions, invalid regions) components through global adaptive thresholding, thus initially improving the contrast of broadband images.

[0112] After the above processing steps, some high-frequency noise in the original image is amplified, and artifacts or distortions caused by nonlinear transformations are introduced. At this point, a stronger and more refined secondary denoising operation is required, along with localized thresholding capabilities.

[0113] Step 3: Perform a three-level two-dimensional discrete wavelet transform on the nonlinearly enhanced broadband interferogram to obtain the second-stage wavelet coefficient set, and calculate the Bayes threshold, including the following steps:

[0114] The expression for the second-stage wavelet coefficients is set as follows:

[0115] ;

[0116] In the formula, The second-stage wavelet coefficients are: x, the true signal component, which follows a generalized Gaussian distribution; and n, the Gaussian noise component, which follows a Gaussian distribution. ; The standard deviation of noise;

[0117] The expression for noise variance estimation is:

[0118] ;

[0119] In the formula, This is an estimate of the noise variance; This is the first layer of diagonal detail sub-bands; This is a median function.

[0120] In the steps described above, the first layer of detail coefficients typically contains higher-frequency information in the broadband interferogram, such as edges and textures. The diagonal detail coefficients, in particular, contain high-frequency information in the diagonal direction of the broadband interferogram. Using the first layer of detail coefficients directly reflects the high-frequency noise and details in the broadband interferogram, and compared to higher-level detail coefficients, the first layer contains more image information, while noise is more easily distinguishable compared to the original image.

[0121] To minimize the Bayesian risk, the expression is:

[0122] ;

[0123] In the formula, This is an estimate of the true signal; For Bayesian estimators; These are the wavelet coefficients for the second stage; The variance of the true signal; This is an estimate of the noise variance;

[0124] The expression for the variance estimation of the true signal is:

[0125] ;

[0126] In the formula, An estimate of the variance of the true signal; M×N is the normalization factor; M×N is the size of the wavelet subband. The wavelet coefficients of the wavelet subband; This is an estimate of the noise variance;

[0127] The Bayesian threshold is calculated using the following expression:

[0128] ;

[0129] In the formula, Use the Bayesian threshold; This is an estimate of the noise variance; This represents the standard deviation of the true signal.

[0130] Step 4: Set up a neighborhood sliding window function combined with a Bayesian threshold to perform local denoising enhancement on the wavelet coefficients in the second stage, including the following steps:

[0131] The neighborhood energy is calculated using the following expression:

[0132] ;

[0133] In the formula, For The energy in the vicinity of the center; The coordinates of the center of the current wavelet coefficients are i; i and j are the neighborhood offset indices. These are the wavelet coefficients within the neighborhood; The squared energy of the wavelet coefficients in the neighborhood;

[0134] Set the adaptive shrinkage factor, expressed as follows:

[0135] ;

[0136] In the formula, It is an adaptive shrinkage factor; For The energy in the vicinity of the center; This represents the maximum local energy of the wavelet subband.

[0137] The second-stage wavelet coefficients are locally denoised and enhanced based on the Bayesian threshold and adaptive shrinkage factor, as expressed in the following expression:

[0138] ;

[0139] In the formula, These are the wavelet coefficients from the second stage after local denoising and enhancement. It is an adaptive shrinkage factor; These are the wavelet coefficients from the second stage before denoising and enhancement. These are estimates of the actual signal components; Use the Bayesian threshold;

[0140] In the above steps, based on the Bayesian estimation framework, a statistically optimal shrinkage basis is provided. By calculating the neighborhood energy, the processing result is adapted to the local features of the broadband interferogram. The original coefficients are retained in the strong signal region (high α), and the Bayesian shrinkage value is used in the weak signal region (low α) to better smooth image features and optimize structural edges. Coefficients below the threshold are directly set to zero to effectively suppress noise.

[0141] Step 5: Reconstruct the wavelet coefficients of the second stage after local denoising and enhancement to obtain the broadband interferogram after local denoising and enhancement, including the following steps:

[0142] The wavelet coefficients in the second stage are reorganized according to the wavelet packet structure, and the expression is:

[0143] ;

[0144] In the formula, This is the wavelet packet coefficient vector; This is the third approximate sub-band; For the third layer of detail sub-band; For the second layer of detail sub-bands; This is the first layer of detail sub-bands;

[0145] The final refactored expression is:

[0146]

[0147] In the formula, The enhanced broadband interferogram; The second wavelet coefficient of the third approximate subband at position (k,l); Let be the second wavelet coefficient of the detail subband in direction i of layer j at position (k,l); This is the db8 scaling function; It is a db8 ​​wavelet function.

[0148] Step 6: Determine the optical path position using the improved centroid method based on the locally denoised and enhanced broadband interferogram, and calculate the depth value of the sample to be measured, including the following steps:

[0149] The squared intensity difference between adjacent frames of a broadband interferogram is calculated using the following expression:

[0150] ;

[0151] In the formula, The square of the light intensity difference between adjacent frames; The intensity value of the broadband interferogram after enhancement in the nth frame; represents the light intensity value of the enhanced broadband interferogram of the (n-1)th frame; N is the total number of frames in the broadband interferogram.

[0152] The optical path position is calculated using the following expression:

[0153] ;

[0154] In the formula, P is the optical path position; It is the square of the light intensity difference between adjacent frames.

[0155] In the above steps, the square of the light intensity difference between adjacent frames is calculated. The influence of background light intensity is eliminated by incorporating a center of gravity algorithm.

[0156] The depth value of the sample under test is obtained by reconstructing the three-dimensional morphology after locating the coherent peak using the improved centroid method. Specific Implementation Example 1

[0158] To verify the effectiveness of the method of this invention in improving fringe contrast and noise reduction, MATLAB was used to calculate the monochromatic light interference intensity using the Michaelson interference model, and then the planar broadband interferogram was obtained by spectral integration, as shown below. Figure 2 As shown in image a; a planar broadband interferogram was acquired by using an experimental optical path to generate interference on the surface of a smooth silicon-based wafer, as shown in image a. Figure 2 The image in the middle (d) is shown. The broadband interference fringe pattern is first converted to grayscale, and then Gaussian white noise is added to simulate external noise in the experiment and the blurred, dark fringes of high aspect ratio structures, as shown below. Figure 2 The images b and e are shown in the figure; the denoised and enhanced image obtained by the method of this invention is as follows. Figure 2 The c and f images are shown in the figure.

[0159] For image evaluation, three reference quality evaluation functions were selected: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Root Mean Square Error (RMSE). PSNR represents the ratio of effective information to noise in an image; the higher the PSNR value, the better the image quality. SSIM represents the similarity to the original image in terms of brightness, contrast, and structure; the closer the value is to 1, the closer the image is to the original image. RMSE represents the root mean square of the pixel value difference in the image; the smaller the value, the smaller the difference from the original image. Three no-reference quality assessment functions were selected: Standard Deviation (SD), Information Entropy (IE), and Natural Image Quality Evaluator (NIQE). SD represents the contrast of the image; dark images have lower contrast than images with normal illumination. IE represents the information content of the image; a higher information entropy indicates that the image carries more information (which could be useful information or noise). NIQE extracts features from the natural landscape and fits them into a multivariate Gaussian model to evaluate the image. Essentially, it measures the difference of a test image across a multivariate distribution, which is more in line with human visual habits; a smaller NIQE value indicates a better visual effect. The data obtained after evaluating the three sets of images are shown in Table 1.

[0160] Table 1

[0161]

[0162] Through subjective evaluation by the human eye and a comprehensive evaluation of six image quality evaluation indicators, it can be concluded that the TWDE image enhancement method proposed in this invention has excellent contrast enhancement, structure restoration, and noise removal capabilities for interference fringes. It ensures high fringe contrast, structural reliability, and high signal-to-noise ratio in the enhanced image, which is beneficial for subsequent topography restoration algorithms to more accurately locate the zero optical path difference position. Specific Implementation Example 2

[0164] like Figure 5As shown, to verify the improvement in depth measurement accuracy of HAR structures by the method of the present invention in a real-world scenario, a broadband interferometry system was constructed. Incident light emitted from a white LED light source 1 passes through a first lens 2, a second lens 3, and an interferometer lens 4 before illuminating the HAR structure sample 5. The light is then reflected back to the color CCD camera 11 through a third lens 8, a fourth lens 9, and a fifth lens 10. Image acquisition begins when interference occurs at the top and proceeds vertically downwards until interference occurs at the bottom, ending the acquisition process. The scanning step size is 100 nm / step. The color CCD camera 11 simultaneously acquires one image per shift of the piezoelectric ceramic displacement stage, ultimately obtaining an interferometric image set that completely reconstructs the morphology of the HAR structure.

[0165] In this embodiment, an experimental measurement was performed on a silicon-based array deep trench sample with a linewidth of 20 micrometers and a depth of 120 micrometers. The experiment was repeated 5 times. The resulting image sets were processed by the method of this invention and three other mainstream image enhancement methods. The enhanced image sets were then subjected to morphological restoration and depth calculation using the improved centroid method. The obtained depth values ​​were compared with the depth values ​​marked on the structure SEM chart taken by atomic force scanning electron microscopy (considered as the actual depth values ​​of the sample). This comparative example only uses the accuracy of depth value measurement as the evaluation standard.

[0166] Interference fringe patterns from a randomly selected experimental interference image set, showing interference between the top and bottom of the slots, were cropped to obtain the fringe regions. Grayscale images were then processed using four methods: two-dimensional discrete wavelet transform (DWT) based on hard thresholding enhancement, soft thresholding enhancement (BAYES) based on Bayesian threshold estimation, contrast-limited adaptive histogram equalization (CLAHE), and the TWDE proposed in this invention. The results are shown below. Figure 3As shown in the figure. The DWT method improves the brightness of the stripes, but the overall brightness is also increased at the same time, which cannot better locate the zero optical path difference position. Moreover, the stripes and structural details are relatively blurred, the edges are jagged and artifacts are produced, and the noise is also significantly amplified. The BAYES method has the best effect in preserving image details, with no artifacts and good noise reduction effect, but the contrast is almost not improved, and it cannot improve the accuracy of zero optical path difference position. The CLAHE method has a more balanced grayscale distribution, but the contrast is not significantly improved and the overall image quality is smoother, which still does not meet the needs of this study for higher-precision positioning of the zero optical path difference position. Compared with the above methods, the TWDE method in this paper has a significant improvement in contrast, good detail preservation, good noise reduction effect, and better stripe enhancement effect, showing a stronger enhancement effect than other methods. The ability to locate the zero optical path difference position with higher precision can be verified by subsequent topography restoration and depth calculation. The image sets enhanced by the four different image enhancement methods are subjected to the same topography restoration algorithm (improved centroid method) for topography restoration and depth calculation. The results of the comparison between the five depth values ​​and SEM values ​​are shown in the figure. Figure 4 As shown in the line graph, the method of this invention outperforms the other three methods in any single measurement, more closely approximating the SEM calibration values ​​and demonstrating higher accuracy in depth measurement.

[0167] This invention discloses a broadband interferometric weak signal enhancement method for measuring high aspect ratio micro / nano structures. It consists of two modules: wavelet transform adaptive hard thresholding enhancement and adaptive soft thresholding denoising. First, low-frequency and high-frequency components are separated using a low-order wavelet transform, enhancing structural details and interference fringes, but also amplifying the high-frequency noise. Furthermore, soft thresholding denoising based on a neighborhood sliding window function effectively removes the amplified noise and introduced artifacts from the previous step. Simulation analysis and experimental verification demonstrate that this method enhances fringe contrast, suppresses noise, and improves depth measurement capabilities.

[0168] 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.

[0169] 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 method for enhancing weak signals in wide-spectrum interferometry for high-aspect-ratio micro-nano structure measurement, characterized in that, The method comprises the following steps: Step 1, obtaining a wide-spectrum interferogram of a sample to be measured, performing two-dimensional discrete wavelet transform on two layers to obtain a first-stage wavelet coefficient array; Step 2, determining an adaptive threshold according to the first-stage wavelet coefficient array and image information entropy, performing nonlinear enhancement on the wavelet coefficient, and outputting the nonlinearly enhanced wide-spectrum interferogram; Step 3, performing three-dimensional discrete wavelet transform on the nonlinearly enhanced wide-spectrum interferogram to obtain a second-stage wavelet coefficient array, and calculating a Bayesian threshold; Step 4, setting a neighborhood sliding window function to combine the Bayesian threshold to perform local denoising enhancement on the second-stage wavelet coefficient array; Step 5, reconstructing the second-stage wavelet coefficient array after local denoising enhancement to obtain the wide-spectrum interferogram after local denoising enhancement; Step 6, determining an optical path position according to the wide-spectrum interferogram after local denoising enhancement by using an improved gravity center method, and calculating a depth value of the sample to be measured. In the step 2, the method comprises the following steps: constructing a wavelet feature vector according to the first-stage wavelet coefficient, and the expression is as follows: ； wherein is a one-dimensional wavelet feature vector; is a first layer of detail subbands of the first stage wavelet coefficients; is a second layer of detail subbands of the first stage wavelet coefficients; calculating an adaptive threshold factor, and the expression is as follows: ； In the formula, p is an adaptive threshold factor; Image information entropy of the wide-spectrum interferogram: ； wherein is the image pixel gray level; is the gray value frequency of occurrence in the image; calculating an adaptive threshold according to the wavelet feature vector and the adaptive threshold proportion factor, and the expression is as follows: ； wherein is an adaptive threshold value; is a one-dimensional wavelet feature vector; p is an adaptive threshold factor; is a quantile function that returns the quantile of p; performing nonlinear enhancement on the first-stage wavelet coefficient c, and the expression is as follows: ； wherein are the enhanced first stage wavelet coefficients; c is the first stage wavelet coefficient; is an adaptive threshold value; calculating the nonlinearly enhanced wide-spectrum interferogram according to the first-stage wavelet coefficient c after enhancement. 2.The method of claim 1, wherein, In the step 1, the two-dimensional discrete wavelet transform comprises the following steps: ； where h is a low-pass filter coefficient; g is a high-pass filter coefficient; m and n are coordinate indices of the j-th layer coefficients; k and l are coordinate indices of the j-1-th layer coefficients; are approximation coefficients for the j-th layer; , and are horizontal, vertical and diagonal detail coefficients, respectively. 3.The method of claim 1, wherein, In the step 3, the method comprises the following steps: setting the expression of the second-stage wavelet coefficient is as follows: ； wherein are second stage wavelet coefficients; x is a real signal component; n is a Gaussian noise component; the expression of noise variance estimation is as follows: ； wherein is an estimate of the noise variance; is the first layer diagonal detail subband; is the median function; performing minimum Bayesian risk, and the expression is as follows: ； wherein is an estimate of the true signal; is a Bayesian estimator; is a second stage wavelet coefficient; is an estimate of the true signal variance; is an estimate of the noise variance; the expression of real signal variance estimation is as follows: ； wherein an estimate of the variance of the real signal; is a normalization factor; M x N is the size of the wavelet subband; is a wavelet coefficient of the wavelet subband; is an estimate of the variance of the noise. calculating the Bayesian threshold, and the expression is as follows: ； wherein is a Bayesian threshold; is an estimate of the noise variance; is the standard deviation of the true signal.

4. The method of claim 1, wherein, In the step 4, the method comprises the following steps: calculating neighborhood energy, and the expression is as follows: ； wherein is the center of the neighborhood; is the center of the neighborhood; is the center coordinate of the current wavelet coefficient; i and j are the neighborhood offset indices; is the wavelet coefficient within the neighborhood; is the squared energy of the wavelet coefficient within the neighborhood; setting an adaptive shrinkage factor, and the expression is as follows: ； wherein is an adaptive shrinkage factor; is the energy of the neighborhood centered at is the energy of the neighborhood centered at is the maximum local energy of the wavelet subband; performing local denoising enhancement on the second-stage wavelet coefficient according to the Bayesian threshold and the adaptive shrinkage factor, and the expression is as follows: ； wherein are the second stage wavelet coefficients after local denoising enhancement; is an adaptive shrinkage factor; are the second stage wavelet coefficients before denoising enhancement; is an estimate of the true signal component; is a Bayesian threshold.

5. The method of claim 1, wherein, In the step 5, the method comprises the following steps: the second-stage wavelet coefficient is recombined according to a wavelet packet structure, and the expression is as follows: ； wherein is a wavelet packet coefficient vector; is a third layer approximation subband; is a third layer detail subband; is a second layer detail subband; is a first layer detail subband; the expression of final reconstruction is as follows: ； wherein is the enhanced wideband interferogram; is the wavelet coefficient of the third approximation subband at position (k, l); is the wavelet coefficient of the jth level detail subband in direction i at position (k, l); is the db8 scaling function; is the db8 wavelet function.

6. The method of claim 1, wherein, In the step 6, the method comprises the following steps: calculating a square of an optical intensity difference value between adjacent frames of the wide-spectrum interferogram, and the expression is as follows: ； wherein is the square of the light intensity difference between adjacent frames; is the light intensity value of the enhanced wide-spectrum interferogram of the nth frame; is the light intensity value of the enhanced wide-spectrum interferogram of the n-1th frame; and N is the total number of frames of the wide-spectrum interferogram. calculating the optical path position, and the expression is as follows: ； P is an optical path position; is the square of the light intensity difference between adjacent frames; reconstructing a three-dimensional topography after locating a coherent peak by using the improved gravity center method to obtain the depth value of the sample to be measured.

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