Method for detecting thickness uniformity of VCSEL epitaxial wafer based on white light interference

Abstract

The present application relates to the technical field of thickness uniformity detection, in particular to a VCSEL epitaxial wafer thickness uniformity detection method based on white light interference. It comprises the following steps: collecting the interference image of the surface of the VCSEL epitaxial wafer to be detected, and pre-processing the interference image; using the polarization state rotation reflection suppression method to suppress the polarization reflection of the pre-processed interference image, using the edge detection method to extract the stripe feature of the interference image after polarization reflection suppression, identifying the pixel position of the interference stripe, and generating the stripe pixel coordinate information; based on the stripe pixel coordinate, the optical path difference is converted from the interference stripe, and the thickness digital signal sequence corresponding to each stripe pixel point is generated. The present application realizes the cooperative suppression of high reflection, mirror reflection and scattering noise on the surface of the VCSEL epitaxial wafer by introducing the polarization state rotation reflection suppression method and the adaptive multi-modal edge convergence algorithm.

Description

Technical Field

[0001] This invention relates to the field of thickness uniformity detection technology, and more specifically, to a method for detecting the thickness uniformity of VCSEL epitaxial wafers based on white light interference. Background Technology

[0002] Vertical-cavity surface-emitting lasers (VCSELs) are widely used in optical communication, 3D sensing, and lidar due to their advantages such as low threshold current, circular beam, and ease of integration into two-dimensional arrays. Their performance is highly dependent on the thickness uniformity of the multilayer heterostructure during epitaxial growth, especially the precise control of key layers such as the distributed Bragg mirror (DBR) and the active region, typically requiring thickness errors on the sub-nanometer to several-nanometer scale. White light interferometry, as a non-contact, high-resolution surface topography detection method, theoretically possesses the potential to achieve this level of precision measurement. However, its practical application in VCSEL epitaxial wafer inspection faces numerous challenges: First, the VCSEL epitaxial structure is composed of multiple layers of highly reflective semiconductor materials, resulting in strong surface and interface reflections. This easily leads to problems such as specular reflection saturation, scattered light interference, and polarization sensitivity, resulting in low signal-to-noise ratio, broken or distorted fringes in the interferometric image, severely affecting measurement reliability. Second, under strong reflection backgrounds, traditional edge detection algorithms struggle to accurately extract continuous and realistic interference fringe features, are susceptible to noise interference, and cause deviations in fringe center positioning, affecting the accuracy of subsequent phase calculations. Third, VCSEL materials exhibit significant dispersion characteristics, while traditional white light interferometry methods often employ a constant refractive index model for thickness inversion, neglecting the variation of refractive index with wavelength, introducing systematic errors, and limiting the accuracy of thickness measurement. Furthermore, existing detection methods generally lack effective calibration mechanisms for systematic errors and multi-wavelength consistency verification capabilities, making it difficult to achieve high-confidence two-dimensional thickness distribution reconstruction and comprehensive uniformity quantification. Therefore, this paper proposes a white light interferometry-based method for VCSEL epitaxial wafer thickness uniformity detection. Summary of the Invention

[0003] The purpose of this invention is to provide a method for detecting the thickness uniformity of VCSEL epitaxial wafers based on white light interference, so as to solve the problems of low thickness measurement accuracy and unreliable uniformity assessment of VCSEL epitaxial wafers caused by high surface reflectivity, difficulty in extracting interference fringes, material dispersion effects, and uncalibrated system errors, as mentioned in the background art.

[0004] To achieve the above objectives, the present invention aims to provide a method for detecting the thickness uniformity of VCSEL epitaxial wafers based on white light interferometry, comprising the following steps: S1. Acquire interference images of the surface of the VCSEL epitaxial wafer under test and preprocess the interference images; S2. The polarization reflection suppression method is used to suppress the polarization reflection of the preprocessed interference image. The edge detection method is used to extract the fringe features of the polarization reflection suppressed interference image to identify the pixel position of the interference fringes and generate fringe pixel coordinate information. S3. Based on the fringe pixel coordinates, the interference fringes are converted into optical path difference, and the thickness digital signal sequence corresponding to each fringe pixel is generated. S4. Arrange the thickness digital signal sequence according to the spatial position of the stripe pixels on the epitaxial wafer surface to generate a two-dimensional thickness matrix, and calculate the uniformity index based on the two-dimensional thickness matrix.

[0005] As a further improvement to this technical solution, step S2, identifying the pixel positions of the interference fringes and generating fringe pixel coordinate information, includes the following steps: S2.1. Polarization reflection suppression is performed on the preprocessed interferometric image using the polarization state rotation reflection suppression method. The resulting interferometric image after polarization reflection suppression... Perform pixel-by-pixel grayscale value calculations and calculate the gradient components of each pixel in the horizontal and vertical directions; S2.2 Calculate the edge intensity value and orientation angle of the pixel based on the gradient components in the horizontal and vertical directions, and generate an edge intensity map; S2.3, Use an adaptive multimodal edge convergence algorithm to generate a set of candidate edge pixels from the edge intensity map; S2.4 Apply threshold segmentation and region connectivity analysis to candidate pixels at the edges of interference fringes to remove isolated noise points; S2.5. Within the connected edge regions of the stripes, calculate the stripe width and extract the geometric center position to form the stripe centerline trajectory; S2.6 Record the coordinates of the pixels on the center line trajectory of the stripes as two-dimensional coordinate information of the stripe pixels, and output them as a set of stripe pixel coordinates.

[0006] As a further improvement to this technical solution, in step S2.1, the polarization reflection suppression method is used to suppress polarization reflection of the preprocessed interference image, including the following steps: S2.11. Integrate a programmable liquid crystal polarization controller at the output end of the white light interferometer to generate an incident light sequence with four linear polarization states; S2.12. For the same VCSEL epitaxial wafer region, use the four polarization states generated in step S2.11 to perform imaging, acquire four sets of interference images, and form a polarization diversity image set. S2.13. Construct a reflection suppression weight map using the principle of polarization reflection difference. ; S2.14, Based on reflection suppression weight graph By fusing a set of images with diverse polarization characteristics, an interferometric image with suppressed polarization reflection is generated. .

[0007] As a further improvement to this technical solution, in S2.13, a reflection suppression weight map is constructed using the principle of polarization reflection difference, involving the following specific steps: for each pixel of the four sets of interference images The variance of gray intensity and the average gray value are calculated under four linear polarization states. An exponential weighting function with the variance of gray intensity and the average gray value as variables is constructed using the difference in polarization reflection, generating a pixel-level reflection suppression weight map. .

[0008] As a further improvement to this technical solution, in step S2.14, an interference image after polarization reflection suppression is generated. This involves the following specific steps: processing each pixel in the polarization diversity image set. Based on the corresponding reflection suppression weight map Assign fusion weights; at each pixel location, sum the pixel values ​​of the four polarization state images according to the fusion weights, and simultaneously compensate for regions where the fusion weight is less than the weight threshold b using median statistics; map the fused pixel values ​​to a two-dimensional coordinate space to generate an interference image after polarization reflection suppression. .

[0009] As a further improvement to this technical solution, in step S2.3, an adaptive multimodal edge convergence algorithm is applied to the edge intensity map to generate a set of candidate edge pixels, including the following steps: S2.31. Using the edge intensity map as input, construct image boundary conditions and normalize the image to eliminate overall brightness scale differences. S2.32. Construct a multi-resolution pyramid from top to bottom on the edge intensity map, statistically analyze the extreme value distribution and orientation consistency of the local neighborhood at each scale, calculate the local modality confidence of each pixel, and identify the edge modality center through multi-scale fusion. S2.33. Based on the edge modality center, map the pixels to the edge manifold space; S2.34. Based on the edge manifold space, a diffusion process is used to propagate modal information between pixels; S2.35. Based on the modal distribution characteristics of the edge manifold space, generate an adaptive threshold for each local mode; S2.36. On the multi-scale edge map of the edge intensity map, an adaptive threshold is used for discrimination; S2.37 Output the set of edge candidate pixels obtained after adaptive multimodal convergence.

[0010] As a further improvement to this technical solution, in step S3, based on the fringe pixel coordinates, the interference fringes are converted into optical path differences to generate a thickness digital signal sequence corresponding to each fringe pixel, including the following steps: S3.1 For each pixel in the stripe pixel coordinate set, extract the gray intensity value sequence from the original multi-wavelength interference signal, and perform spectral decomposition using Fast Fourier Transform in the frequency domain to separate each characteristic wavelength. The corresponding interference components, including amplitude and initial phase ; S3.2, for each wavelength initial phase A continuous phase distribution is obtained by applying the phase extraction method. ; S3.3. Based on the principle of optical interference, the continuous phase distribution is... Converted to optical path difference distribution ; S3.4, Refractive index of materials used in VCSEL epitaxial wafers The optical path difference distribution is determined based on the spectral adaptive dispersion compensation thickness inversion algorithm. Convert to thickness value ; S3.5, Match pixel position with thickness value By performing the corresponding steps, a thickness digital signal sequence is constructed.

[0011] As a further improvement to this technical solution, in step S3.4, the optical path difference distribution is determined based on the spectral adaptive dispersion compensation thickness inversion algorithm. Converted to thickness distribution This includes the following steps: S3.51. Based on the material properties of VCSEL epitaxial wafers, establish a thickness-dependent model. and wavelength A model of varying dispersive refractive index; S3.52, Based on optical path difference distribution Construct a cost function based on optical path difference matching; S3.53 Calculate the thickness results for different wavelength combinations and verify their consistency; S3.54. For pixels with insufficient consistency, an iterative update formula is used for optimization to generate an iteratively optimized thickness value. ; S3.55, Thickness value obtained based on iterative optimization The system calibration item based on the standard sample is introduced to obtain the final thickness value. .

[0012] As a further improvement to this technical solution, in step S3.51, the material properties of the VCSEL epitaxial wafer are considered to establish a thickness-dependent property. and wavelength The varying dispersive refractive index model involves the following specific steps: based on the dispersive properties of the epitaxial wafer material, using the fundamental refractive index... As a reference, the trend of material refractive index variation with wavelength is modeled by introducing the rate of linear shift of material refractive index with wavelength and the degree of nonlinear bending of material refractive index with wavelength under different thickness conditions.

[0013] As a further improvement to this technical solution, step S4, which calculates the uniformity index based on the two-dimensional thickness matrix, includes the following steps: S4.1 The thickness digital signal sequence obtained in step S3 is sorted according to the actual spatial coordinates of the sampling points on the surface of the VCSEL epitaxial wafer, and the thickness values ​​are mapped to the corresponding matrix units according to the coordinate positions to generate a two-dimensional thickness matrix. S4.2 Calculate the uniformity index based on the thickness distribution matrix, including at least the maximum thickness difference, the standard deviation of the thickness, and the root mean square error of the thickness; S4.3 Based on the calculated uniformity index, identify local thickness anomaly areas, determine the overall thickness control level, and output the uniformity analysis index results.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. The VCSEL epitaxial wafer thickness uniformity detection method based on white light interferometry of this invention achieves synergistic suppression of high reflectivity, specular reflection, and scattering noise on the VCSEL epitaxial wafer surface by introducing a polarization state rotational reflection suppression method and an adaptive multimodal edge convergence algorithm. Specifically, a polarization diversity image set is acquired using four linear polarization states (0°, 45°, 90°, 135°), and an exponential weight map is constructed based on pixel-level grayscale variance and average intensity. Low weights are assigned to reflection-sensitive areas, effectively weakening strong reflection interference during the fusion process. Simultaneously, a median compensation mechanism is employed to prevent excessive suppression of the true interference signal. Based on this, by constructing a multi-scale pyramid and edge manifold space, and combining local modal confidence and orientation consistency for diffusion optimization, the enhancement of true fringe edges and global suppression of noise are achieved. This dual suppression strategy significantly improves the signal-to-noise ratio and fringe continuity of the interferometric image, enabling edge detection to accurately extract the fringe centerline trajectory even in a high-reflectivity background. This provides a reliable input for subsequent high-precision phase calculation and thickness inversion, and is especially suitable for the detection of epitaxial wafers with complex surface reflection characteristics, such as VCSELs with multilayer heterostructures.

[0015] 2. The VCSEL epitaxial wafer thickness uniformity detection method based on white light interferometry involved in this invention employs multi-wavelength spectral analysis combined with a spectral adaptive dispersion compensation thickness inversion algorithm during the phase-to-thickness conversion process, overcoming the bottleneck of thickness error caused by neglecting material dispersion in traditional white light interferometry. Interference components at various characteristic wavelengths are extracted using fast Fourier transform, and a continuous phase distribution is obtained through phase expansion. Furthermore, a dispersion refractive index model related to thickness and wavelength is established to accurately reflect the optical response of the material at different wavelengths. Based on this model, an optical path difference matching cost function is constructed, and the optimal thickness value is solved through iterative optimization (such as gradient descent), with a standard sample calibration term introduced for system error compensation. In addition, an abnormal region is identified through a multi-wavelength combination consistency verification mechanism to ensure the physical rationality of the inversion results. Finally, a high-resolution two-dimensional thickness matrix is ​​generated, supporting the calculation of multi-dimensional uniformity indicators such as maximum thickness difference, standard deviation, and root mean square error. This not only achieves sub-nanometer thickness resolution but also significantly improves the ability to identify local thickness anomalies, providing a highly reliable quantitative basis for online monitoring and quality feedback of VCSEL epitaxial growth processes. Attached Figure Description

[0016] Figure 1 This is a flowchart of the overall method of the present invention. Detailed Implementation

[0017] 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 of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0018] Example: Please refer to Figure 1 As shown, this embodiment provides a method for detecting the thickness uniformity of VCSEL epitaxial wafers based on white light interferometry, including the following steps: S1. Acquire interference images of the surface of the VCSEL epitaxial wafer under test and preprocess the interference images; In this embodiment, the VCSEL epitaxial wafer to be tested is cleaned and fixed on the testing platform to ensure that the surface is flat and free of dust or particles. The white light interferometry system is started, and the light source, interferometer, and detector are calibrated to ensure that the interference fringes are clear and the interference light path is aligned. The white light interferometer scans the surface of the VCSEL epitaxial wafer to obtain the interference light intensity information at different positions and form an interference image. The experimental light source itself is broadband (such as white light interference). The information includes fringe spatial distribution information (the position and shape of the interference fringes on the surface of the epitaxial wafer, reflecting the spatial variation of the thickness), fringe intensity information (the gray value or brightness of each pixel, representing the interference light intensity), fringe phase information (the order of brightness of the interference fringes corresponds to the phase change, and a continuous phase distribution can be obtained after phase calculation), noise and reflection information (including specular reflection, scattered light, diffraction distortion, or shooting noise), and multi-wavelength or polarization characteristics (the interference intensity information of each pixel at different wavelengths or polarization states).

[0019] S2. The polarization reflection suppression method is used to suppress the polarization reflection of the preprocessed interference image. The edge detection method is used to extract the fringe features of the polarization reflection suppressed interference image to identify the pixel position of the interference fringes and generate fringe pixel coordinate information. In this embodiment, the stripe features include at least stripe position, stripe width, grayscale value / light intensity, and stripe direction angle. Stripe feature extraction is integrated throughout the entire process: First, edge intensity and direction are obtained by calculating the pixel-by-pixel grayscale gradient, which initially reflects the position and direction of the stripes; then, through multimodal edge convergence, threshold segmentation, and region connectivity analysis, isolated noise is removed and stripe continuity is enhanced to obtain a set of edge candidate pixels; finally, the stripe width is calculated and the geometric center is extracted within the connected stripe region to form the stripe centerline trajectory, and the stripe pixel coordinate set is output, thereby obtaining the complete spatial position, width, direction, and continuity features of the stripes, providing input for subsequent phase or thickness calculations; The process of identifying the pixel positions of interference fringes and generating fringe pixel coordinate information includes the following steps: S2.1. Polarization reflection suppression is performed on the preprocessed interferometric image using the polarization state rotation reflection suppression method. The resulting interferometric image after polarization reflection suppression... Perform pixel-by-pixel grayscale value calculations, and calculate the gradient components of each pixel in the horizontal and vertical directions to reflect the rate of change of pixel grayscale: ; ; In the formula, For horizontal gradient components, The vertical gradient component; Furthermore, the polarization-state rotational reflection suppression method, in the detection of VCSEL epitaxial wafer thickness uniformity based on white light interferometry, mainly addresses the problem of decreased interference image quality caused by specular reflection or local strong reflection on the epitaxial wafer surface. VCSEL epitaxial wafer surfaces typically exhibit high reflectivity, which can mask or distort the true interference fringe signal, causing fringe distortion, intensity saturation, or noise enhancement. This interferes with fringe feature extraction and phase calculation, ultimately leading to thickness measurement errors and inaccurate uniformity assessments. This method generates multiple linearly polarized incident light sequences by integrating a programmable liquid crystal polarization controller and constructs an exponential weighted map using the principle of polarization reflection difference for adaptive fusion. This effectively distinguishes between reflection-sensitive areas and true interference fringe signals, assigns low weights to specular reflection and local strong reflection to suppress their influence, and maintains fringe continuity and contrast through median compensation. This approach significantly improves the signal-to-noise ratio and fringe clarity of the interference image, enhances the accuracy and robustness of thickness inversion, overcomes the limitations of traditional methods in high-reflectivity surface processing, and provides more reliable thickness uniformity data for VCSEL epitaxial wafer process quality assessment. The polarization reflection suppression method is used to suppress polarization reflection in the preprocessed interferometric image, including the following steps: S2.11. Integrate a programmable liquid crystal polarization controller at the output end of the white light interferometer to generate incident light sequences with four linear polarization states (0°, 45°, 90°, 135°); S2.12. For the same VCSEL epitaxial wafer region, use the four polarization states generated in step S2.11 to perform imaging, acquire four sets of interference images (each set corresponds to one incident polarization state), and form a polarization diversity image set. This set is used to distinguish between real interference fringes and surface specular reflection or local strong reflection signals by utilizing the intensity differences of interference images under different polarization states, thereby achieving polarization reflection suppression. S2.13. Utilizing the principle of polarization reflection difference (the intensity of the reflected component changes significantly under different polarization states, while the intensity of the real interference fringes changes relatively little), construct a reflection suppression weight map. ( The range is [0,1]), and a reflection suppression weight is assigned to each pixel so that the weight of specular reflection or local strong reflection areas is reduced during the fusion process, thereby significantly suppressing their interference with the interference fringes; Furthermore, utilizing the principle of polarization reflection difference, a reflection suppression weight map is constructed, involving the following specific steps: for each pixel of the four sets of interferometric images The gray intensity variance (reflecting the intensity stability under different polarization states) and average gray value (reflecting the overall brightness level of the pixel under different polarization states) are calculated under four linear polarization states. Utilizing the difference in polarization reflection (the intensity change of the interference fringe signal is small under different polarization states, with variance close to zero, while specular reflection or saturation effects are highly sensitive to polarization, resulting in significantly increased variance), an exponential weighting function is constructed with the gray intensity variance and average gray value as variables. This exponential weighting function assigns lower weights to interference signals generated by specular reflection or localized strong reflection, thus significantly suppressing their influence during the fusion process. This generates a pixel-level reflection suppression weighting map. ; in, Indicates coordinates as The scalar variance of the grayscale intensity of the pixels under four linear polarization states. This represents the average gray value of the pixel across the four sets of polarization state interferometric images; This variance is used only to identify the spatial location of the pixel corresponding to the variance value in the interference image. The random variable used in the variance calculation is the gray intensity value of the pixel in the four polarization states. ; The reflection suppression weight map is as follows: ; ; In the formula, The reflection sensitivity coefficient has a value range of [0.5, 3.0] and is calibrated experimentally. This indicates that the variance calculation is performed along the polarization state dimension. The polarization state index represents the first of the four linear polarization states. Types (k=1, 2, 3, 4 correspond to 0°, 45°, 90°, 135°), For the first Under certain polarization states, this pixel point The corresponding grayscale intensity values ​​of the interference image, For pixels The average gray value in the four sets of polarization state interferometric images; S2.14, Based on reflection suppression weight graph By fusing a set of images with diverse polarization characteristics, an interferometric image with suppressed polarization reflection is generated. This is used to obtain interference images with minimal interference and high fringe contrast, providing reliable input for subsequent fringe pixel extraction and thickness calculation; Among them, the interference image after polarization reflection suppression is generated. The specific steps involved are as follows: For each pixel in the polarization diversity image set Based on the corresponding reflection suppression weight map Assign fusion weights; at each pixel location, calculate the average gray value of the four polarization state images. and median gray value (i.e., the median of the gray values ​​of the four polarization states); then, weights are used. Linear fusion of the average gray value and median is performed to generate an interferometric image with suppressed polarization reflection. : ; In the formula, The median gray value is the median gray value of the pixel in the four sets of interference images, and is used to compensate for low-weight regions. S2.2 Calculate the edge intensity value and orientation angle of the pixel based on the gradient components in the horizontal and vertical directions, and generate an edge intensity map; Among them, the edge intensity of the pixel is calculated: ; Calculate the edge direction angle: ; In the formula, This represents the edge strength value. For local edge direction; S2.3. The edge intensity map is subjected to an adaptive multimodal edge convergence algorithm to generate a set of candidate pixels for the edge, which is used to remove non-extreme points and retain the candidate pixel positions of the interference fringe edges. Among them, the adaptive multimodal edge convergence algorithm, in the thickness detection of VCSEL epitaxial wafers based on white light interferometry, mainly addresses specific problems encountered in the extraction of interference fringe edges, such as noise sensitivity, fringe breakage, and false edge interference. Due to minute defects, particulate contamination, and inherent noise of the interferometric system on the surface of VCSEL epitaxial wafers, traditional edge detection methods often generate a large number of broken edge fragments and false edge responses, severely affecting the continuity and accuracy of the fringe centerline trajectory, leading to errors in subsequent phase calculation and thickness inversion. Compared to traditional fixed-threshold edge detection methods, this algorithm constructs a multi-resolution pyramid for multi-scale analysis and combines the diffusion propagation mechanism of the edge manifold space to adaptively identify and enhance true fringe modes while effectively suppressing noise and false edge responses. Its advantage lies in its ability to fully utilize the local geometric features and directional consistency information of the fringes. Through modal confidence calculation and adaptive threshold adjustment, it significantly improves the signal-to-noise ratio while maintaining edge continuity, thus providing more complete and accurate fringe centerline coordinate information for thickness calculation, greatly improving the reliability and repeatability of thickness measurement results. An adaptive multimodal edge convergence algorithm is applied to the edge intensity map to generate a set of candidate edge pixels, including the following steps: S2.31. Using the edge intensity map as input, construct the image boundary conditions and normalize the image to eliminate the overall brightness scale difference (that is, map the gray value of each pixel to the [0,1] interval), in preparation for multi-scale analysis and manifold mapping. S2.32. Construct a multi-resolution pyramid (e.g., Gaussian / Laplacian pyramid) from top to bottom on the edge intensity map. At each scale, statistically analyze the extreme value distribution and orientation consistency of the local neighborhood (here, scale refers to the image hierarchy at different spatial resolutions in the multi-resolution image pyramid; when constructing the pyramid, the original edge intensity map is downsampled or filtered layer by layer (e.g., Gaussian smoothing + downsampling), with each layer representing a different scale). Calculate the local modality confidence of each pixel and identify potential edge modality centers through multi-scale fusion, using them as initial seed points for the convergence process. Specifically: First, construct the multi-resolution pyramid, using the original edge intensity map as the highest resolution layer, and generate low-resolution images layer by layer through Gaussian filtering and downsampling; in each scale of the image, calculate the local modality confidence of each pixel using a fixed neighborhood window (e.g., 3×3 or 5×5). The maximum and minimum values ​​of pixel grayscale intensity within the neighborhood and their distribution are determined (the maximum and minimum values ​​are identified, and the intensity range is calculated accordingly; simultaneously, the pixel intensity within the window is statistically analyzed using a histogram or probability distribution to reflect the distribution characteristics of local extrema, such as whether the extrema are concentrated in a single direction or uniformly distributed; through these maximum, minimum, and distribution information, the local contrast and edge saliency of pixels within the neighborhood can be characterized), and the gradient direction distribution of pixels in the neighborhood is extracted and the direction concentration is calculated to measure edge direction consistency; subsequently, the extrema features and direction consistency are combined to calculate the local modal confidence of each pixel, and the modal confidence is fused across different scale levels, so that pixels that maintain a stable response at different scales are identified as potential edge modal centers, providing initial seed points for the subsequent edge convergence process; Among them, local modal confidence for: ; In the formula, The maximum gray value in the neighborhood. The minimum gray value in the neighborhood. To prevent tiny constants with a denominator of zero, It is a measure of the consistency of the gradient direction of pixels in the neighborhood (achieved by statistically analyzing the gradient direction distribution within a fixed window around each pixel, calculating the degree of deviation between the gradient direction in the neighborhood and the direction of the center pixel; the smaller the deviation, the more consistent the direction, thus providing a basis for judging whether local edges are continuous or belong to the same stripe mode). Represents pixels The center's neighborhood window, This is a weighting parameter for local contrast, with a value range of [0.4, 0.8]. It is an empirical parameter. The weight parameter for directional consistency has a value range of [0.2, 0.6], and is an empirical parameter. ; S2.33. Based on edge modality centers, pixels are mapped to the edge manifold space (a low-dimensional embedding space formed by constraining local geometric features and orientation consistency in an image through edge modality centers). This space is represented by high-dimensional feature vectors, including edge intensity, gradient direction, local spectral features, and modality confidence, thereby transforming geometric proximity relationships on the image into topological proximity relationships on the manifold. Specifically: First, using the multi-scale edge modality centers obtained in step S2.32 as anchor points, a local edge manifold coordinate system is constructed, and the grayscale intensity, gradient magnitude, and gradient direction of each pixel are mapped to the edge manifold coordinate system. The first step involves representing the features as local geometric vectors. Then, similarity weights are calculated using the spatial distance and directional consistency between a pixel and its neighboring modal centers. Pixels are progressively projected into a low-dimensional edge manifold space constructed with the modal centers as anchor points (this low-dimensional edge manifold space is defined by the local geometric features and directional consistency of each modal center, used to maintain the topological continuity of the edge structure). Next, a weighted mapping is performed using normalized weights to ensure the continuity of the spatial structure and edge orientation. Finally, the embedding representation of each pixel in the edge manifold space is obtained, thereby achieving global modeling and saliency enhancement of the edge structure. S2.34. Based on the edge manifold space, a diffusion process is used to propagate modal information between pixels, so that pixels belonging to the same true fringe mode gradually aggregate in the feature space, while isolated noise points and spurious extrema are smoothly attenuated during the diffusion process. The diffusion process uses modal confidence as the initial value and iterates across multiple scales to enhance robustness. Specifically, firstly, a weighted graph structure is constructed based on the adjacency relationship of pixels, where the edge weights are determined by local geometric similarity and directional consistency. Then, a diffusion operator (such as a normalized Laplacian matrix) is defined on this graph, and the high-confidence modal center information is gradually propagated to neighboring pixels through an iterative diffusion process, realizing the smooth expansion of information from dense edge regions to sparse or uncertain regions. During the diffusion process, edge direction constraints are maintained to ensure that the propagation path unfolds along the true edge direction, thereby obtaining a globally consistent and locally continuous edge modal distribution. S2.35. Based on the modal distribution characteristics of the edge manifold space, generate an adaptive threshold for each local mode. In the formula, This represents the mean intensity of edge modes within a local neighborhood, reflecting the overall background level. The standard deviation of edge mode intensity within a local neighborhood characterizes the volatility and significance of edge intensity. The standard deviation adjustment factor is used to control the contribution of edge intensity fluctuations to the threshold. Its value ranges from [1.0, 3.0] and was determined experimentally. Indicates at pixel point The orientation consistency or local responsivity index reflects whether a point is consistent with the dominant edge direction. For each pixel, gradient magnitude, orientation consistency, and local modality confidence are comprehensively considered in its neighborhood. These features are weighted or fused to obtain a numerical index. This is a direction constraint factor used to suppress the influence of non-uniform directions or noise responses on the threshold. Its value range is [0.1, 1.0], and it was determined experimentally. This involves mapping the enhanced modal information back to the image space to guide subsequent thresholding. This mapping process relies on the inherent pixel location correspondence between the manifold space and the original image space, i.e., the pixel locations in each image space. Each pixel has a unique embedding representation in the manifold space. By directly or weightedly assigning the feature values ​​obtained after diffusion optimization in the manifold space for each pixel (e.g., principal components representing its edge saliency or modal confidence after information aggregation) back to their corresponding positions in the original image space (or the corresponding multi-scale pyramid), an enhanced edge intensity map that has undergone global optimization and noise suppression in the manifold space is generated. This map preserves the original spatial structure and incorporates the topological continuity obtained from manifold learning, providing higher-quality input data for subsequent adaptive thresholding processing. S2.36. On the multi-scale edge map of the edge intensity map, an adaptive threshold is used for discrimination, retaining the intensity higher than the adaptive threshold. Pixels that satisfy the conditions of orientation consistency and connectivity are selected as final edge candidate pixels; at the same time, isolated regions smaller than the minimum connected area are eliminated to suppress residual noise. S2.37 Output the set of edge candidate pixels obtained after adaptive multimodal convergence; S2.4. Threshold segmentation and region connectivity analysis are applied to candidate pixels at the edges of interference fringes to remove isolated noise points and enhance the continuity of the fringes edges. Specifically, for candidate pixels at the edges of interference fringes, the edge intensity of each pixel is first compared with an adaptive threshold. The comparison is performed, and pixels with intensity above the threshold are retained as edge points, while pixels below the threshold are set as background, thus achieving threshold segmentation. Subsequently, region connectivity analysis is performed on the obtained binarized edge map. By marking all connected regions and calculating the number of pixels in each region, isolated regions smaller than the preset minimum area A are removed, and only connected stripe edge regions are retained, thereby removing noise points and enhancing the continuity of stripe edges. S2.5 Within the connected stripe edge region, calculate the stripe width and extract the geometric center position to form the stripe centerline trajectory. Specifically, first, along the normal direction of the stripe edge or the local direction perpendicular to the stripe, measure the boundary distance on both sides of each pixel to calculate the local width of the stripe; then, take the geometric center position (centroid) on each width measurement line, and connect all the local geometric centers in sequence to form a continuous stripe centerline trajectory; this centerline trajectory reflects the spatial position of the stripes and also provides accurate sampling point coordinates for subsequent phase extraction or thickness calculation; S2.6 Record the pixel coordinates on the stripe centerline trajectory as two-dimensional coordinate information of the stripe pixels, and output the stripe pixel coordinate set as input for subsequent phase value or optical path difference calculation.

[0020] S3. Based on the fringe pixel coordinates, the interference fringes are converted into optical path differences, and the thickness digital signal sequence corresponding to each fringe pixel (i.e., sampling point) is generated. In this embodiment, based on the fringe pixel coordinates, the interference fringes are converted into optical path differences, and a thickness digital signal sequence corresponding to each fringe pixel is generated, including the following steps: S3.1 For each pixel in the fringe pixel coordinate set, extract the gray intensity value sequence (as a wavelength function) from the original multi-wavelength interference signal (because the experimental light source itself is broadband (white light interference), so the original fringes received by the detector are the multi-wavelength interference signal), and perform spectral decomposition in the frequency domain using Fast Fourier Transform (FFT) to separate each characteristic wavelength. The corresponding interference components map the grayscale signal in the time / wavelength domain to the frequency domain; in the spectrum, the frequency positions of different wavelength components corresponding to the periodicity of the interference fringes are used to separate each characteristic wavelength. The corresponding spectral peaks are then reconstructed using inverse transform or bandpass filtering to obtain the interference component sequence of each pixel at various characteristic wavelengths, including amplitude. and initial phase ; S3.2, for each wavelength initial phase Phase extraction method is applied to eliminate factors. The periodic phase jumps result in a continuous phase distribution. To ensure the spatial continuity of the phase of adjacent pixels, specifically: for each wavelength initial phase First at the pixel Calculate the phase difference within the local neighborhood, for values ​​exceeding [a certain threshold]. or less Addition and subtraction of jumps The process involves continuous phase processing to eliminate discontinuities caused by phase periodicity; then, the phase is gradually unfolded along the scanning direction or a two-dimensional pixel grid to ensure smooth and continuous phase changes between adjacent pixels; finally, noise interference is further suppressed by filtering or least-squares fitting to obtain the continuous phase distribution corresponding to each pixel. ; S3.3. Based on the principle of optical interference (referring to the phenomenon where, when two or more coherent light waves are superimposed, the phase difference between the light waves strengthens or weakens them, thus forming alternating bright and dark interference fringes in space), the continuous phase distribution... Converted to optical path difference distribution This is used to quantify phase information into actual optical path difference, providing a physical basis for further calculation of epitaxial wafer thickness; S3.4, Refractive index of materials used in VCSEL epitaxial wafers The optical path difference distribution is determined based on the spectral adaptive dispersion compensation thickness inversion algorithm. Convert to thickness value This allows us to obtain the actual thickness information of each pixel. Among them, the spectrally adaptive dispersion compensation thickness inversion algorithm mainly addresses the problem of decreased measurement accuracy caused by material dispersion effects in VCSEL epitaxial wafer thickness measurement. The refractive index of VCSEL epitaxial wafer materials (usually compound semiconductors such as gallium arsenide) varies significantly with wavelength. This dispersion characteristic causes inconsistencies in the optical path difference-thickness conversion relationship for different wavelength components, leading to systematic errors in traditional methods based on a single wavelength or simple averaging. This is particularly problematic in thickness uniformity detection requiring sub-micron precision, where such dispersion-induced errors directly impact the accuracy of process evaluation. Compared to traditional thickness inversion methods that ignore dispersion or use a fixed refractive index, this algorithm establishes a dispersion refractive index model that dynamically varies with thickness and wavelength, and combines it with a collaborative verification mechanism of multi-wavelength interference components to achieve accurate compensation for material dispersion effects. Its core advantage lies in its spectrally adaptive cost function optimization and iterative update strategy, which can automatically identify and correct wavelength inconsistencies caused by dispersion, significantly improving the accuracy and reliability of thickness inversion results. It is particularly suitable for accurate thickness measurement of VCSEL multilayer epitaxial structures, providing a more reliable quantitative basis for process monitoring. The optical path difference distribution is determined based on the spectral adaptive dispersion compensation thickness inversion algorithm. Converted to thickness distribution This includes the following steps: S3.51. Based on the material properties of VCSEL epitaxial wafers, establish a thickness-dependent model. and wavelength A variable dispersive refractive index model is used to accurately describe the change of material refractive index with wavelength and thickness, providing a physical basis for the inversion of optical path difference to thickness; Furthermore, considering the material properties of VCSEL epitaxial wafers, a method was established that allows for variation with thickness. and wavelength The varying dispersive refractive index model involves the following specific steps: based on the dispersive properties of the epitaxial wafer material, using the fundamental refractive index... As a reference (at the reference wavelength) The underlying refractive index This value reflects the thickness at a given level. (under the condition of the material's reference refractive index level), by introducing the rate of change of the material's refractive index with the linear shift of wavelength (i.e., the first term) ) and the degree of nonlinear bending of the material's refractive index with wavelength (i.e., the quadratic term) The variation trend of material refractive index with wavelength under different thickness conditions is modeled: ; In the formula, For thickness is Epitaxial wafers at wavelength Effective refractive index at reference wavelength The bottom, thickness is The material's base refractive index represents the reference refractive index level of the material under that thickness condition. The rate of linear change of a material's refractive index with wavelength reflects the degree of linear shift in the refractive index with wavelength. The coefficient representing the quadratic variation of the material's refractive index with wavelength indicates the degree of nonlinear bending of the refractive index with respect to wavelength. The current wavelength of light; S3.52, Based on optical path difference distribution A cost function based on optical path difference matching is constructed. This cost function is the fitting error function of the optical path difference of each pixel at different wavelengths, which is used to guide the thickness inversion. The cost function is : ; In the formula, Wavelength index; S3.53. Calculate the thickness results for different wavelength combinations and verify their consistency. When performing thickness inversion for different wavelength combinations, each wavelength group will independently solve for a candidate thickness value. Due to noise, dispersion modeling errors, or local reflection effects, different wavelength combinations may produce differences. Therefore, it is necessary to verify the consistency of each combination result, that is, to statistically analyze their dispersion (such as standard deviation or variance). If the thickness result remains highly consistent under different wavelengths (fluctuation is less than the preset threshold a), then the thickness inversion result of that pixel is considered reliable. If the difference is large, it indicates that the point is disturbed or the modeling is insufficient, and it needs to enter the subsequent depth dispersion compensation iteration for further correction. S3.54. For pixels with insufficient consistency, an iterative update formula is used for optimization to generate an iteratively optimized thickness value. (For inconsistent or abnormal pixels, the gradient descent iterative update formula is used to correct them. The thickness value obtained after iterative convergence is the optimized thickness value.) The iterative update formula is: ; In the formula, For the number of iterations, For the first The thickness value of the next iteration. The learning rate or step size coefficient controls the magnitude of each update. The gradient of the cost function is used to indicate the direction of descent. S3.55, Thickness value obtained based on iterative optimization And introduce system calibration items based on standard samples. (That is, by performing interferometry on a standard sample, the deviation distribution between the measurement result and the actual thickness is obtained, and then this deviation information is used to form a calibration compensation term to correct the thickness of each pixel in the actual measurement, so as to obtain the final thickness value.) ; S3.5, Match pixel position with thickness value By performing the corresponding steps, a thickness digital signal sequence is constructed.

[0021] S4. Arrange the thickness digital signal sequence according to the spatial position of the stripe pixels on the surface of the epitaxial wafer to generate a two-dimensional thickness matrix, and calculate the uniformity index based on the two-dimensional thickness matrix. In this embodiment, the uniformity index is calculated based on a two-dimensional thickness matrix, including the following steps: S4.1. The thickness digital signal sequence obtained in step S3 is sorted according to the actual spatial coordinates of the sampling points on the VCSEL epitaxial wafer surface, and the thickness values ​​are mapped to the corresponding matrix units according to the coordinate positions to generate a two-dimensional thickness matrix, ensuring that each element in the matrix corresponds one-to-one with a physical location on the epitaxial wafer surface. Specifically: First, the actual spatial coordinates of the sampling points on the epitaxial wafer surface are sorted... Determine its row and column indices in the matrix. The corresponding unit position is obtained by normalizing and rounding the spatial coordinates according to the matrix resolution; then the thickness value of each sampling point is... Assigning values ​​to matrix elements Repeat this process until all sampling points are mapped, thereby generating a two-dimensional thickness matrix for each matrix unit corresponding to the position on the surface of the epitaxial wafer, ensuring that the thickness distribution information accurately reflects the spatial position in the matrix; S4.2 Calculate the uniformity index based on the thickness distribution matrix, including at least the maximum thickness difference, the standard deviation of the thickness, and the root mean square error of the thickness; S4.3 Based on the calculated uniformity index, identify local thickness anomaly areas, determine the overall thickness control level, and output the uniformity analysis index results as the basis for epitaxial wafer process quality assessment and feedback control.

[0022] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for detecting the thickness uniformity of VCSEL epitaxial wafers based on white light interferometry, characterized in that, Includes the following steps: S1. Acquire interference images of the surface of the VCSEL epitaxial wafer under test and preprocess the interference images; S2. The polarization reflection suppression method is used to suppress the polarization reflection of the preprocessed interference image. The edge detection method is used to extract the fringe features of the polarization reflection suppressed interference image to identify the pixel position of the interference fringes and generate fringe pixel coordinate information. In step S2, identifying the pixel positions of the interference fringes and generating fringe pixel coordinate information includes the following steps: S2.

1. Polarization reflection suppression is performed on the preprocessed interferometric image using the polarization state rotation reflection suppression method. The resulting interferometric image after polarization reflection suppression... Perform pixel-by-pixel grayscale value calculations to calculate the gradient components of each pixel in the horizontal and vertical directions; in step S2.1, the polarization reflection suppression method is used to suppress polarization reflection in the preprocessed interference image, including the following steps: S2.

11. Integrate a programmable liquid crystal polarization controller at the output end of the white light interferometer to generate an incident light sequence with four linear polarization states; S2.

12. For the same VCSEL epitaxial wafer region, use the four polarization states generated in step S2.11 to perform imaging, acquire four sets of interference images, and form a polarization diversity image set. S2.

13. Construct a reflection suppression weight map using the principle of polarization reflection difference. The specific steps involved are as follows: for each pixel of the four sets of interferometric images The variance of gray intensity and the average gray value are calculated under four linear polarization states. An exponential weighting function with the variance of gray intensity and the average gray value as variables is constructed using the difference in polarization reflection, generating a pixel-level reflection suppression weight map. ; S2.14, Based on reflection suppression weight graph By fusing a set of images with diverse polarization characteristics, an interferometric image with suppressed polarization reflection is generated. The specific steps involved are as follows: for each pixel in the polarization diversity image set... Based on the corresponding reflection suppression weight map Assign fusion weights; at each pixel location, sum the pixel values ​​of the four polarization state images according to the fusion weights, and simultaneously compensate for regions where the fusion weight is less than the weight threshold b using median statistics; map the fused pixel values ​​to a two-dimensional coordinate space to generate an interference image after polarization reflection suppression. ; S3. Based on the fringe pixel coordinates, the interference fringes are converted into optical path difference, and the thickness digital signal sequence corresponding to each fringe pixel is generated. S4. Arrange the thickness digital signal sequence according to the spatial position of the stripe pixels on the epitaxial wafer surface to generate a two-dimensional thickness matrix, and calculate the uniformity index based on the two-dimensional thickness matrix.

2. The method for detecting the thickness uniformity of VCSEL epitaxial wafers based on white light interference according to claim 1, characterized in that: In step S2, identifying the pixel positions of the interference fringes and generating fringe pixel coordinate information further includes the following steps: S2.2 Calculate the edge intensity value and orientation angle of the pixel based on the gradient components in the horizontal and vertical directions, and generate an edge intensity map; S2.3, Use an adaptive multimodal edge convergence algorithm to generate a set of candidate edge pixels from the edge intensity map; S2.4 Apply threshold segmentation and region connectivity analysis to candidate pixels at the edges of interference fringes to remove isolated noise points; S2.

5. Within the connected edge regions of the stripes, calculate the stripe width and extract the geometric center position to form the stripe centerline trajectory; S2.6 Record the coordinates of the pixels on the center line trajectory of the stripes as two-dimensional coordinate information of the stripe pixels, and output them as a set of stripe pixel coordinates.

3. The method for detecting the thickness uniformity of VCSEL epitaxial wafers based on white light interference according to claim 2, characterized in that: In step S2.3, an adaptive multimodal edge convergence algorithm is used to generate a set of candidate edge pixels from the edge intensity map, including the following steps: S2.

31. Using the edge intensity map as input, construct image boundary conditions and normalize the image to eliminate overall brightness scale differences. S2.

32. Construct a multi-resolution pyramid from top to bottom on the edge intensity map, statistically analyze the extreme value distribution and orientation consistency of the local neighborhood at each scale, calculate the local modality confidence of each pixel, and identify the edge modality center through multi-scale fusion. S2.

33. Based on the edge modality center, map the pixels to the edge manifold space; S2.

34. Based on the edge manifold space, a diffusion process is used to propagate modal information between pixels; S2.

35. Based on the modal distribution characteristics of the edge manifold space, generate an adaptive threshold for each local mode; S2.

36. On the multi-scale edge map of the edge intensity map, an adaptive threshold is used for discrimination; S2.37 Output the set of edge candidate pixels obtained after adaptive multimodal convergence.

4. The method for detecting the thickness uniformity of VCSEL epitaxial wafers based on white light interference according to claim 1, characterized in that: In step S3, based on the fringe pixel coordinates, the interference fringes are converted into optical path differences, and a thickness digital signal sequence corresponding to each fringe pixel is generated, including the following steps: S3.1 For each pixel in the stripe pixel coordinate set, extract the gray intensity value sequence from the original multi-wavelength interference signal, and perform spectral decomposition using Fast Fourier Transform in the frequency domain to separate each characteristic wavelength. The corresponding interference components, including amplitude and initial phase ; S3.2, for each wavelength initial phase A continuous phase distribution is obtained by applying the phase extraction method. ; S3.

3. Based on the principle of optical interference, the continuous phase distribution is... Converted to optical path difference distribution ; S3.4, Refractive index of materials used in VCSEL epitaxial wafers The optical path difference distribution is determined based on the spectral adaptive dispersion compensation thickness inversion algorithm. Convert to thickness value ; S3.5, Match pixel position with thickness value By performing the corresponding steps, a thickness digital signal sequence is constructed.

5. The method for detecting the thickness uniformity of VCSEL epitaxial wafers based on white light interference according to claim 4, characterized in that: In step S3.4, the optical path difference distribution is determined based on the spectral adaptive dispersion compensation thickness inversion algorithm. Converted to thickness distribution This includes the following steps: S3.

51. Based on the material properties of VCSEL epitaxial wafers, establish a thickness-dependent model. and wavelength A model of varying dispersive refractive index; S3.52, Based on optical path difference distribution Construct a cost function based on optical path difference matching; S3.53 Calculate the thickness results for different wavelength combinations and verify their consistency; S3.

54. For pixels with insufficient consistency, an iterative update formula is used for optimization to generate an iteratively optimized thickness value. ; S3.55, Thickness value obtained based on iterative optimization The system calibration item based on the standard sample is introduced to obtain the final thickness value. .

6. The method for detecting the thickness uniformity of VCSEL epitaxial wafers based on white light interference according to claim 5, characterized in that: In S3.51, based on the material properties of the VCSEL epitaxial wafer, a method is established that varies with thickness. and wavelength The varying dispersive refractive index model involves the following specific steps: based on the dispersive properties of the epitaxial wafer material, using the fundamental refractive index... As a reference, the variation trend of material refractive index with wavelength under different thickness conditions is modeled by introducing the rate of change of linear shift of material refractive index with wavelength and the degree of nonlinear bending of material refractive index with wavelength.

7. The method for detecting the thickness uniformity of VCSEL epitaxial wafers based on white light interference according to claim 1, characterized in that: In step S4, the uniformity index is calculated based on the two-dimensional thickness matrix, including the following steps: S4.1 The thickness digital signal sequence obtained in step S3 is sorted according to the actual spatial coordinates of the sampling points on the surface of the VCSEL epitaxial wafer, and the thickness values ​​are mapped to the corresponding matrix units according to the coordinate positions to generate a two-dimensional thickness matrix. S4.2 Calculate the uniformity index based on the thickness distribution matrix, including at least the maximum thickness difference, the standard deviation of the thickness, and the root mean square error of the thickness; S4.3 Based on the calculated uniformity index, identify local thickness anomaly areas, determine the overall thickness control level, and output the uniformity analysis index results.

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