A method for detecting the warpage of VCSEL epitaxial wafers

Abstract

This invention relates to the field of industrial inspection technology, specifically to a method for detecting the warpage of VCSEL epitaxial wafers. The method includes: acquiring a three-dimensional height field on the surface of the VCSEL epitaxial wafer to be inspected; extracting a macroscopic warpage field based on the original three-dimensional height field by solving a variational optimization model; subtracting the original height field from the macroscopic warpage field to obtain a high-frequency residual field; calculating the morphological gradient of each pixel in the high-frequency residual field in multiple directions, and determining the texture index accordingly; classifying pixels with a texture index higher than a threshold as texture pixels, and those lower than or equal to the threshold as noise pixels; performing local mean filtering on the positions of the corresponding noise pixels in the macroscopic warpage field to obtain a corrected warpage field; calculating the warpage based on the corrected warpage field, and if it is within a set error range, determining that the VCSEL epitaxial wafer to be inspected is qualified. This invention solves the problem of low detection accuracy in existing algorithms.

Description

Technical Field

[0001] This invention relates to the field of industrial testing technology. More specifically, this invention relates to a method for detecting the warpage of VCSEL epitaxial wafers. Background Technology

[0002] In recent years, vertical-cavity surface-emitting lasers (VCSELs) have been applied in high-speed optical communication, 3D sensing, and consumer electronics. Their performance stability largely depends on the surface morphology quality of the epitaxial wafer. With the continuous increase in chip size and the ongoing improvement in process precision, controlling the flatness of the wafer surface has become a key indicator affecting device yield and packaging reliability. Therefore, in the manufacturing process of VCSEL epitaxial wafers, achieving high-precision, non-contact detection of the macroscopic warpage of the wafer surface has become a widely recognized technical challenge in the industry.

[0003] Currently, machine vision-based stripe projection contour measurement technology has become the mainstream method for inspecting the three-dimensional topography of wafer surfaces. This technology projects a series of grating stripes with a sinusoidal intensity distribution onto the wafer surface and simultaneously acquires images of the deformed stripes after height modulation using an industrial camera. Since surface height undulations cause local distortion of the stripes, this distortion can be encoded using phase information. By combining phase demodulation algorithms with system geometric calibration parameters, the spatial height value of each pixel can be accurately inverted, thereby reconstructing a high-density three-dimensional height field on the wafer surface, achieving non-contact, high-resolution surface topography measurement. Based on this three-dimensional data, the warp degree of the overall wafer deformation can be calculated, providing a basis for epitaxial process quality assessment and equipment calibration.

[0004] However, in the actual production process of VCSEL epitaxial wafers, after undergoing complex processes such as epitaxial growth, annealing, and chemical mechanical polishing, the wafer surface often forms microstructural features with obvious directionality or quasi-periodicity, such as micro-scratches, lattice steps, and local growth textures. These features are usually much smaller than macroscopic warpage in spatial scale, but their optical response introduces high-frequency signal components in fringe projection measurements. Therefore, the total height signal acquired by the system is actually a superposition of signals from macroscopic warpage, microstructural textures, and random noise.

[0005] Existing technologies generally employ low-pass filtering or smoothing algorithms to extract macroscopic warpage components from the total signal, but this approach has significant limitations. Since both microstructure texture signals and random noise signals are high-frequency components in the frequency domain, traditional low-pass filters, while suppressing random noise, also weaken or even lose some of the true microstructure information. More seriously, even after partial filtering, the residual energy of these texture signals may still leak into the low-frequency band, thus contaminating the macroscopic warpage signal. As a result, the warpage field obtained after filtering contains artifacts and distortions, causing the calculated warpage to deviate from the actual deformation state of the wafer, leading to low detection accuracy. Summary of the Invention

[0006] To address the problem of low detection accuracy mentioned in the background art, the present invention provides solutions in the following aspects.

[0007] In a first aspect, the present invention provides a method for detecting the warpage of a VCSEL epitaxial wafer, comprising: acquiring an original three-dimensional height field of the surface of the VCSEL epitaxial wafer to be detected; extracting a macroscopic warpage field by solving a variational optimization model based on the original three-dimensional height field; subtracting the macroscopic warpage field from the original three-dimensional height field to obtain a high-frequency residual field; calculating morphological orientation gradients in multiple preset directions for each pixel of the high-frequency residual field; calculating a texture index for each pixel of the high-frequency residual field based on the morphological orientation gradients; and calculating a texture index for each pixel of the high-frequency residual field based on the texture index and the texture index of all morphological orientation gradients at the same pixel. The difference between the maximum and minimum values ​​of the morphological gradient is positively correlated and negatively correlated with the sum of the maximum and minimum values. Pixels with a texture index greater than a set threshold are identified as texture pixels, and pixels with a texture index less than or equal to the set threshold are identified as noise pixels. Local mean filtering is performed on the positions corresponding to the noise pixels in the macroscopic warping field to obtain a corrected macroscopic warping field. The warping degree of the VCSEL epitaxial wafer to be tested is calculated based on the corrected macroscopic warping field. If the warping degree is within a set error range, the VCSEL epitaxial wafer to be tested is determined to be qualified.

[0008] The aforementioned technical solution, by introducing a variational optimization model and morphological directional gradient analysis, effectively separates macroscopic warpage, microstructure texture, and random noise from the height signal on the surface of VCSEL epitaxial wafers. Compared with traditional low-pass filtering methods, this method can adaptively identify and retain microstructure texture information with directional characteristics while suppressing random noise interference, thereby obtaining a purer and more realistic macroscopic warpage field. After local mean filtering correction, the calculated warpage more accurately reflects the overall deformation state of the wafer, significantly improving the accuracy and stability of warpage detection, and substantially enhancing the quality assessment and production consistency control of VCSEL epitaxial wafers.

[0009] Furthermore, the variational optimization model is as follows: , The domain of the image of the VCSEL epitaxial wafer to be detected. The macroscopic warped field to be solved. For the original three-dimensional height field, To preset the first hyperparameter, To find the minimum value of the function, It is a function Spatial coordinates The second-order partial derivative, It is a function Spatial coordinates The second-order partial derivative, It is a function The mixed second-order partial derivatives.

[0010] The aforementioned technical solution can effectively smooth high-frequency noise and micro-texture interference in the original height field while preserving the macroscopic deformation characteristics of the wafer, thus achieving accurate extraction of the macroscopic warpage field. This model minimizes the difference between the height field and the macroscopic warpage field, and applies a smoothing constraint to the second-order spatial derivative of the macroscopic warpage field, making the solution results continuous and smooth in overall shape and truly reflecting the overall bending state of the wafer, thereby significantly improving the accuracy and stability of warpage calculation.

[0011] Furthermore, the variational optimization model is solved using the finite difference method to extract the macroscopic warping field.

[0012] Furthermore, pixels In direction Morphological directional gradient for: , For expansion operations, For erosion calculation, For a length of Angle is pixel lines, For high-frequency residual fields, For high-frequency residual field medium pixel The value at that location.

[0013] The above technical solution, by introducing an analysis method based on multi-directional morphological gradients, can effectively characterize the local structural features of each pixel in different directions in the high-frequency residual field, and realize the quantitative description of the microstructure texture of the wafer surface. It can not only enhance the directional texture signal, but also suppress the interference of random noise on the macroscopic warp extraction, thereby maintaining the true continuity of the macroscopic warp field while separating the microstructure texture from the noise.

[0014] Furthermore, the plurality of preset directions include at least eight directions that are evenly spaced within the range of 0° to 180°.

[0015] Furthermore, pixels Texture index for: , For pixels In the preset direction Morphological gradient on This is the maximum value of the morphological gradient over all preset directions θ at pixel (x,y); This is the minimum morphological gradient along all preset directions θ at pixel (x,y). This is the preset second hyperparameter.

[0016] The above technical solution can highlight texture signals with obvious directionality and strong local changes by comparing the gradient differences and total amplitude of pixels in different directions, while suppressing the influence of disordered noise. This reduces artifact interference in the macroscopic warp extraction process and improves the accuracy of warp calculation and the reliability of wafer quality inspection.

[0017] Furthermore, local mean filtering is performed on the positions corresponding to the noise pixels in the macroscopic warped field. Specifically, the height value of the noise pixel in the macroscopic warped field is replaced with the average height of its four adjacent pixels (up, down, left, and right).

[0018] The above technical solution can effectively smooth out local height anomalies caused by random noise by performing local mean filtering on the positions of noisy pixels in the macroscopic warped field, while preserving the overall morphological characteristics of the macroscopic warping.

[0019] Furthermore, the first hyperparameter is preset. It is 0.1.

[0020] Furthermore, the set threshold is 0.5.

[0021] Furthermore, the set error range is ±10μm.

[0022] The beneficial effects of this invention are as follows:

[0023] This invention separates high-frequency residuals from the original three-dimensional height field and the macroscopic warpage field extracted by variational optimization. It effectively distinguishes microstructure texture from random noise using multi-directional morphological gradients and texture indices, and then corrects the macroscopic warpage field through local mean filtering. This achieves high-precision extraction of macroscopic warpage on the surface of VCSEL epitaxial wafers. This invention can suppress noise interference while preserving the true microstructure texture, making warpage calculation more accurate, stable, and repeatable. It significantly improves the reliability of wafer flatness assessment and the quality control level of the manufacturing process, while providing a valid basis for subsequent process adjustments and yield assessment. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a method for detecting the warpage of a VCSEL epitaxial wafer according to an embodiment of the present invention. Detailed Implementation

[0025] An embodiment of a method for detecting the warpage of VCSEL epitaxial wafers.

[0026] like Figure 1 As shown, a flowchart of a VCSEL epitaxial wafer warpage detection method according to an embodiment of the present invention includes the following steps:

[0027] S1: Obtain the original three-dimensional height field of the VCSEL epitaxial wafer surface to be tested.

[0028] In a preferred embodiment, a standard fringe projection measurement device is used to acquire the original three-dimensional height field of the VCSEL epitaxial wafer surface to be inspected. The measurement device includes a digital projector, an industrial camera, and a synchronization control unit. The digital projector projects a four-step phase-shifted sinusoidal fringe pattern onto the wafer surface, with a phase shift step size of one-quarter of a period, ensuring a fixed phase difference between adjacent fringe patterns. The industrial camera, under synchronous control, continuously acquires four frames of deformed fringe images modulated by the wafer surface. Subsequently, a four-step phase-shift algorithm is used to process the four acquired images to calculate the encapsulated phase distribution map, and a phase unwrapping algorithm is used to recover the continuous absolute phase information. Combined with the geometric and optical parameters obtained through calibration before measurement, the absolute phase information is converted into a three-dimensional height distribution in a real spatial coordinate system, thereby obtaining the original three-dimensional height field of the wafer surface.

[0029] S2: Based on the original three-dimensional height field, the macroscopic warping field is extracted by solving the variational optimization model.

[0030] In a preferred embodiment, the variational optimization model is: , The domain of the image of the VCSEL epitaxial wafer to be detected. The macroscopic warped field to be solved. For the original three-dimensional height field, The first hyperparameter is preset, where the first hyperparameter is preset. The preferred value is 0.1, but it can also be set according to the actual situation. To find the minimum value of the function, It is a function Spatial coordinates The second-order partial derivative, It is a function Spatial coordinates The second-order partial derivative, It is a function The mixed second-order partial derivatives.

[0031] Macroscopic warping is an overall deformation caused by thermal mismatch or stress release during epitaxial growth or chemical mechanical polishing. Its spatial variation is slow, manifesting as large-scale bending or twisting. Therefore, its three-dimensional morphology should be a highly smooth surface with minimal local curvature variation. Based on this physical prior, this step introduces a curvature regularization term to suppress the interference of high-frequency fluctuations caused by microstructure texture and noise on macroscopic deformation estimation.

[0032] Among them, the integral on the left side is called the data fidelity term. At the pixel At this point, the macroscopic warping field to be solved is calculated. The height value and the original three-dimensional height field The difference between the height values ​​is squared to ensure that the contribution of all differences, regardless of whether they are positive or negative, is positive, and to amplify the effect of the difference; the physical meaning of the integral is to expand the domain of the image of the VCSEL epitaxial wafer to be detected. The summation of the squared residuals of all pixels within the entire wafer surface, and the final result of the integral on the left side, measures the macroscopic warpage field. Compared with the original three-dimensional height field A scalar measure of the overall degree of difference between them;

[0033] The integral on the right side is called the surface smoothing term. It is a macroscopic warped field Spatial coordinates The second-order partial derivative. It quantifies the macroscopic warping field. Along Local curvature along the axial direction. The larger its absolute value, the stronger the curvature of the surface at that pixel point. The more severe the curvature in direction, the better. It is a macroscopic warped field Spatial coordinates The second-order partial derivative quantifies the macroscopic warping field. Along Local curvature in the axial direction; It is a macroscopic warped field The mixed second-order partial derivative quantifies the rate of change of the slope of a surface in one direction in another perpendicular direction, and characterizes the degree of distortion of the surface. It is a macroscopic warped field At pixel An approximation of the local total curvature is obtained by summing the degree of bending and twisting in each direction in the form of squares, resulting in a scalar value that is always positive and represents the severity of the total bending of the pixel.

[0034] The first hyperparameter is preset and acts as a weighting coefficient to balance the two mutually constraining objectives of the left-side integration and the right-side integration. When When the value is large, the optimization process tends to minimize the smoothing regularization term, resulting in a very smooth but potentially biased outcome. ;when When the value is small, the optimization process tends to minimize the data fidelity term, resulting in a data that closely matches the original data but may not be smooth enough. By choosing a suitable This value can effectively filter out high-frequency, drastic fluctuations caused by microstructure textures and noise while preserving macroscopic warping information to the greatest extent.

[0035] The finite difference method is used to solve the variational optimization model to extract the macroscopic warping field. The finite difference method is an existing technology and will not be described in detail here.

[0036] S3: Subtract the original three-dimensional height field from the macroscopic warping field to obtain the high-frequency residual field; calculate the morphological orientation gradient in multiple preset directions for each pixel of the high-frequency residual field; calculate the texture index of each pixel of the high-frequency residual field based on the morphological orientation gradient.

[0037] In a preferred embodiment, the plurality of preset directions include at least eight directions that are evenly spaced within the range of 0° to 180°.

[0038] pixel In direction Morphological directional gradient for: , For expansion operations, For erosion calculation, For a length of Angle is pixel lines, For high-frequency residual fields, For high-frequency residual field medium pixel The value at that location. The result of expansion is when As the center of the object slides across each pixel, it is... The brightest pixel in the coverage area will replace the center pixel in the coverage area; The result of corrosion is when As the center of the pixel slides across each pixel, it is... The darkest pixel in the coverage area will replace the center pixel in the coverage area.

[0039] At the pixel single pixel line Morphological orientation gradient, if the direction of a texture is... Vertically, with a narrow texture width, a single pixel line simultaneously covers both textured and non-textured areas. The results of dilation and erosion are very different, and the calculated... It will be very large; if the texture direction is... Parallel lines, where a single pixel only covers the texture area, and the height values ​​within the same texture area are approximately the same, result in almost identical dilation and erosion effects. It will be very small. Due to the single pixel line There are 12 angles, and each pixel will output 12 morphological direction gradients.

[0040] Morphological gradients are typically defined as the difference between an image after dilation and erosion. They effectively extract the edges and textures of objects. This invention builds upon this by defining a directional morphological gradient. After obtaining the morphological gradients of each pixel in all directions, a scalar is needed to describe its directionality.

[0041] pixel Texture index for: , For pixels In the preset direction Morphological gradient on This is the maximum value of the morphological gradient over all preset directions θ at pixel (x,y); This is the minimum morphological gradient along all preset directions θ at pixel (x,y). This is the preset second hyperparameter.

[0042] For texture pixels: Because textures have a clear directionality, their morphological gradients in the direction perpendicular to the texture are very large, while those in the direction parallel to the texture are very small. Therefore, the denominator is large, and the numerator is also large and close to the denominator, leading to... The value is very close to 1;

[0043] For noisy pixels: An isolated noisy pixel is isotropic; regardless of the direction from which the single-pixel line traverses it, the calculated morphological gradient values ​​are similar in magnitude. Therefore, the maximum and minimum values ​​will be very close, causing the denominator to approach zero. The value is very close to 0.

[0044] In summary, texture index Essentially, it is a measure of the degree of anisotropy in local geometry. The microstructure texture on the surface of VCSEL epitaxial wafers typically has a clear dominant direction, manifesting as continuous ridges or trenches, thus exhibiting significant morphological response differences in a certain direction, leading to... The value tends to 1. Random imaging noise is spatially isotropic; regardless of the detection direction, its morphological response is similar. The value approaches 0. By setting a threshold, effective separation of the two types of high-frequency components can be achieved.

[0045] S4: Pixels with a texture index greater than a set threshold are identified as texture pixels, and pixels with a texture index less than or equal to the set threshold are identified as noise pixels; local mean filtering is performed on the positions corresponding to the noise pixels in the macroscopic warping field to obtain the corrected macroscopic warping field.

[0046] In a preferred embodiment, the threshold value is set to 0.5; however, it can also be set according to actual circumstances.

[0047] The position corresponding to the noise pixel in the macroscopic warped field is subjected to local mean filtering. Specifically, the height value of the noise pixel in the macroscopic warped field is replaced with the average height of its four adjacent pixels (up, down, left, and right) to obtain the corrected macroscopic warped field.

[0048] S5: Calculate the warpage of the VCSEL epitaxial wafer to be tested based on the corrected macroscopic warpage field. If the warpage is within the set error range, the VCSEL epitaxial wafer to be tested is deemed qualified.

[0049] In a preferred embodiment, the calculated warpage is compared with a pre-set error range. The calculation of warpage is a well-known technique and will not be elaborated upon here. If the warpage is within the allowable range, the surface flatness of the VCSEL epitaxial wafer under test is determined to meet the process requirements, and the test result is qualified. Conversely, if the warpage is outside the allowable range, the VCSEL epitaxial wafer under test is determined to have excessive warpage or abnormal morphology, requiring process adjustment. In this embodiment, the set error range is ±10 micrometers. This range can balance the measurement accuracy with the process tolerance of the epitaxial wafer production line, thereby ensuring the stability and repeatability of the warpage determination result.

[0050] This invention combines the original three-dimensional height field with the macroscopic warp field extracted by variational optimization, and utilizes multi-directional morphological gradients and texture indices to effectively distinguish between microstructure textures and random noise. Local mean filtering is applied to noise pixels within the macroscopic warp field to correct them, resulting in a more continuous and realistic macroscopic warp field. This approach can suppress high-frequency interference while preserving the macroscopic deformation characteristics of the wafer surface, significantly improving the accuracy and stability of warp calculation. Furthermore, by setting reasonable texture thresholds and error ranges, reliable determination of the flatness of VCSEL epitaxial wafer surfaces is achieved, ensuring accurate and highly repeatable detection results, and effectively improving the reliability of wafer quality assessment and manufacturing process control.

[0051] In the description of this specification, "multiple" or "several" means at least two, such as two, three or more, unless otherwise explicitly specified.

[0052] While this specification has shown and described numerous embodiments of the invention, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Many modifications, alterations, and alternatives will occur to those skilled in the art without departing from the spirit and essence of the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in the practice of this invention.

Claims

1. A method for detecting the warpage of a VCSEL epitaxial wafer, characterized in that, include: Obtain the original three-dimensional height field of the VCSEL epitaxial wafer surface to be tested; Based on the original three-dimensional height field, the macroscopic warping field is extracted by solving a variational optimization model; The variational optimization model is: , The domain of the image of the VCSEL epitaxial wafer to be detected. The macroscopic warped field to be solved. For the original three-dimensional height field, To preset the first hyperparameter, To find the minimum value of the function, It is a function Spatial coordinates The second-order partial derivative, It is a function Spatial coordinates The second-order partial derivative, It is a function The mixed second-order partial derivatives; The original three-dimensional height field is subtracted from the macroscopic warping field to obtain the high-frequency residual field; morphological orientation gradients in multiple preset directions are calculated for each pixel of the high-frequency residual field; the texture index of each pixel of the high-frequency residual field is calculated based on the morphological orientation gradients; the texture index is positively correlated with the difference between the maximum and minimum values ​​of all morphological orientation gradients at the same pixel, and negatively correlated with the sum of the maximum and minimum values; Pixels with a texture index greater than a set threshold are identified as texture pixels, and pixels with a texture index less than or equal to the set threshold are identified as noise pixels; local mean filtering is performed on the positions corresponding to the noise pixels in the macroscopic warp field to obtain the corrected macroscopic warp field. The warpage of the VCSEL epitaxial wafer to be tested is calculated based on the corrected macroscopic warpage field. If the warpage is within the set error range, the VCSEL epitaxial wafer to be tested is deemed qualified.

2. The method for detecting the warpage of a VCSEL epitaxial wafer according to claim 1, characterized in that, The finite difference method is used to solve the variational optimization model to extract the macroscopic warping field.

3. The method for detecting the warpage of a VCSEL epitaxial wafer according to claim 1, characterized in that, pixel In direction Morphological directional gradient for: , For expansion operations, For erosion calculation, For a length of Angle is pixel lines, For high-frequency residual fields, For high-frequency residual field medium pixel The value at that location.

4. The method for detecting the warpage of a VCSEL epitaxial wafer according to claim 1, characterized in that, The plurality of preset directions include at least eight directions that are evenly spaced within the range of 0° to 180°.

5. The method for detecting the warpage of a VCSEL epitaxial wafer according to claim 1, characterized in that, pixel Texture index for: , For pixels In the preset direction Morphological gradient on This is the maximum value of the morphological gradient over all preset directions θ at pixel (x,y); This is the minimum morphological gradient along all preset directions θ at pixel (x,y). This is the preset second hyperparameter.

6. The method for detecting the warpage of a VCSEL epitaxial wafer according to claim 1, characterized in that, Local mean filtering is performed on the positions corresponding to noise pixels in the macroscopic warped field, specifically as follows: Replace the height value of the noise pixel in the macroscopic warp field with the average height value of its four adjacent pixels (up, down, left, and right).

7. The method for detecting the warpage of a VCSEL epitaxial wafer according to claim 1, characterized in that, Preset first hyperparameter It is 0.

1.

8. The method for detecting the warpage of a VCSEL epitaxial wafer according to claim 1, characterized in that, The set threshold is 0.

5.

9. The method for detecting the warpage of a VCSEL epitaxial wafer according to claim 1, characterized in that, The set error range is ±10μm.

Images