A method for analyzing wafer structure using AFM scanning based on image and data processing

Abstract

The present invention discloses an AFM scanning wafer structure analysis method based on image and data processing, comprising the following steps: S1, performing Gaussian fitting and denoising on the height map data row by row; S2, performing least squares polynomial fitting on the height map data row by row, and obtaining leveling data using the new data; S3, normalizing the leveling data to form a grayscale image; finding all circular regions and excluding them to the edge; S4, cutting out three-dimensional data clusters in the leveling data and performing clustering processing to separate each corresponding bottom hole data cluster and upper surface data cluster; obtaining the corresponding bottom hole cloud diameter based on the bottom hole data cluster, averaging each data in the bottom hole data cluster to obtain the hole bottom height. The present invention processes the AFM data through an improved flattening method, converts it into a two-dimensional image, and then cuts out the three-dimensional data for clustering and denoising, which can effectively extract the actual contour data and analyze the circular structure size of the wafer, improve the calculation process, and enhance data stability and calculation accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of wafer scanning analysis, and in particular to an AFM scanning wafer structure analysis method based on image and data processing. Background Art

[0002] AFM, short for Atomic Force Microscope, is one of the most precise measuring instruments in the field of three-dimensional inspection, capable of achieving nanometer-level spatial resolution, making it suitable for studying nanostructures and surface features. AFM uses the interaction between a silicon or silicon nitride probe and the sample surface to measure surface topography. Later, through image processing and data analysis, it extracts data on local structures, enabling the calculation of the dimensions of circular structures on the wafer surface.

[0003] The data generated by AFM scanning of wafers usually includes height maps, phase maps and spectrum maps. Through image processing and data processing, the data structure can be organized and visualized. Using noise removal, data enhancement, feature extraction and other technologies, the surface details of the microstructure on the wafer surface can be highlighted. Subsequently, local data can be further quantitatively analyzed to facilitate further exploration and utilization of the wafer morphology.

[0004] In recent years, image processing technology has made breakthroughs in the field of computer vision, enabling computers to understand and process images at a higher level. Data analysis of atomic force microscopy scans has become a research hotspot in microscopic analysis. Combining these two technologies allows for further exploration and application of scanned microscopic data.

[0005] However, there are currently two problems when using AFM to scan wafers and perform structural analysis:

[0006] 1) When measuring wafer surface structures, the data generated by AFM scanning is often tilted. When performing topography analysis in this tilted state, the lack of a reference surface often significantly reduces measurement accuracy. Furthermore, probe jitter, thermal drift, and electronic noise during the scanning process also reduce imaging quality and hinder subsequent data leveling efforts.

[0007] 2) For AFM data with high density and small height spacing, it is difficult to quantitatively analyze the size of the structure. It is impossible to measure the microstructure size of the wafer well, and the accuracy is worrying. Summary of the Invention

[0008] In response to the above two problems, the purpose of the present invention is to propose an AFM scanning wafer structure analysis method based on image and data processing. By improving the flattening method, noise interference is effectively removed to make the data smoother and more reliable; the image is also excluded from the edge to determine the area of ​​non-edge structure and locate the upper hole cloud and the corresponding diameter; in addition, the data is multi-processed with the help of Gaussian fitting, least squares polynomial fitting, normalization and clustering processing, which not only enhances the stability of complex data while retaining the characteristic information, but also effectively completes the analysis of the size of circular-like structures in the wafer.

[0009] This is achieved through the following technical solutions:

[0010] An AFM scanning wafer structure analysis method based on image and data processing includes the following steps:

[0011] S1. Extracting height map data from the AFM scanning data of the wafer, performing row-by-row Gaussian fitting and row-by-row denoising on the height map data to obtain optimized scanning data;

[0012] S2. Perform least squares polynomial fitting on the scan data optimized in step S1 row by row, and use the fitting parameter equation corresponding to the fitting to form new data with the same length as the fitting data; use the new data to remove the scan data optimized in step S1 to obtain leveled data;

[0013] S3, normalizing the leveling data in step S2 to form a grayscale image; then finding all the circular regions in the grayscale image and excluding each circular region from the edge to obtain each upper hole cloud and the corresponding diameter of each upper hole cloud;

[0014] S4. Based on each upper hole cloud and the corresponding diameter of each upper hole cloud in step S3, each corresponding three-dimensional data cluster is cut out from the leveling data, and each three-dimensional data cluster is clustered to separate each corresponding bottom hole data cluster and upper surface data cluster; the corresponding diameter of each lower hole cloud is obtained according to each bottom hole data cluster, and each data in each bottom hole data cluster is averaged to obtain each corresponding hole bottom height.

[0015] Preferably, when performing row-by-row Gaussian fitting in step S1, the Gaussian function equation used is: , where x corresponds to each row of data, A is the amplitude, μ is the mean, and σ is the standard deviation.

[0016] Preferably, when performing row-by-row denoising in step S1, the denoising process for any row is as follows: determine whether there are multiple peaks in the data after Gaussian fitting; if not, normalize the data after Gaussian fitting to between 2% and 95% of the original; if so, take the minimum data in the data after Gaussian fitting as the minimum value, and take the last peak value in this row as the maximum value, and then replace each data greater than the maximum value in the data after Gaussian fitting with the maximum value; wherein, the minimum spacing is met between any adjacent peaks.

[0017] Preferably, when performing the least squares polynomial fitting in step S2, a first-order polynomial equation is used to perform the first-order polynomial fitting.

[0018] Preferably, when a first-order polynomial equation is used for first-order polynomial fitting, the first-order polynomial equation is set to y=kx+b, and the corresponding specific values ​​of k and b are calculated to determine the fitting parameter equation.

[0019] Preferably, the normalization formula in step S3 is:

[0020] ;

[0021] Among them, height min is the minimum value of the original data height, and height max is the maximum value of the original data height.

[0022] Preferably, after the grayscale image is formed in step S3, the grayscale image is binarized using the Otsu method, and the maximum inter-class variance of the background and structure in the grayscale image is used as the binarization threshold.

[0023] Preferably, after forming the grayscale image in step S3, the grayscale image is first segmented, and the low area value areas corresponding to the leveling data are discarded, and the areas with roundness values ​​lower than a specific roundness value are discarded; wherein the specific roundness value is calculated as follows: circularity = area of ​​the area / (π × radius of the circumscribed circle) 2 ); each area after segmentation and discarding is then regarded as a quasi-circle area, and the minimum distance from each quasi-circle area to the four boundaries in the image corresponding to the height map data is calculated. When the minimum distance from any processed area to the boundary is 0, the corresponding quasi-circle area is regarded as close to the image boundary and excluded from the edge; each area after the edge exclusion in each quasi-circle area is regarded as an upper hole cloud, the center position of each upper hole cloud is obtained, and the diameter of each corresponding minimum circumscribed circle is calculated as the diameter of each upper hole cloud.

[0024] Preferably, when clustering any three-dimensional data cluster in step S4, a feature point cloud of density difference is extracted from the three-dimensional data cluster, and the center of the three-dimensional data cluster is used as the seed point, and each other data point in the three-dimensional data cluster is traversed for clustering to form two data clusters, namely the bottom hole data cluster and the upper surface data cluster.

[0025] Preferably, after separating the bottom hole data cluster from any three-dimensional data cluster in step S4, RANSAC is used to fit the circle to calculate the bottom hole diameter as the lower hole cloud diameter, and the data of the bottom hole cluster are averaged to calculate the hole bottom height; then, each data in the upper surface data cluster is averaged to calculate the upper surface height; and the hole height difference is obtained based on the upper surface height and the hole bottom height.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] The technical solution of the present invention effectively removes noise interference by improving the flattening method, making the data smoother and more reliable; it also excludes the edge of the image to determine the area of ​​non-edge structure and locate the upper hole cloud and the corresponding diameter; in addition, it also uses Gaussian fitting, least squares polynomial fitting, normalization and clustering processing to perform multiple processing on the data, which not only enhances the stability of complex data while retaining the characteristic information, but also effectively completes the analysis of the size of circular-like structures in the wafer. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a flow chart of an AFM scanning wafer structure analysis method based on image and data processing;

[0029] Figure 2 A flowchart detailing an image and data processing-based AFM scanning wafer structure analysis method. DETAILED DESCRIPTION

[0030] The following is a combination of the embodiments of the present invention Figure 1 and Figure 2 , the technical solutions in the embodiments of the present invention are described in detail.

[0031] like Figure 1 As shown in FIG, it is an AFM scanning wafer structure analysis method based on image and data processing; Figure 2 The figure shows a detailed operation flow chart of an AFM scanning wafer structure analysis method based on image and data processing; combined with Figure 1 and Figure 2As shown in the figure, the method first flattens the height map data of the AFM data through an improved flattening method and converts it into a two-dimensional image in the form of leveled data. Secondly, the center of the target area is located from the two-dimensional image, and then the corresponding AFM data is cut out according to the position of the center point to form each three-dimensional data cluster. Then, each three-dimensional data cluster is clustered and denoised to separate the background and bottom hole data clusters. Finally, the upper diameter, lower diameter and height dimensions of the circular structure can be calculated to complete the wafer structure analysis.

[0032] The method mainly includes the following steps:

[0033] S1. Extract height map data from the AFM scanning data of the wafer, analyze the height map data line by line, first perform Gaussian fitting on each line of data to smooth the data and retain the main peak features, then perform denoising on a line by line to further optimize the data and obtain optimized scanning data.

[0034] In this embodiment, when performing row-by-row Gaussian fitting, the Gaussian function equation used is: , where x corresponds to each row of data, A is the amplitude, which corresponds to the peak height, μ is the mean, σ is the standard deviation, and e is the base of the natural logarithm.

[0035] In this embodiment, when performing row-by-row denoising, the denoising process for any row is as follows: determine whether there are multiple peaks in the data after Gaussian fitting. If not, normalize the data after Gaussian fitting to between 2% and 95% of the original value, thereby retaining the valid signal while suppressing extreme values. If so, take the smallest data in the data after Gaussian fitting as the minimum value, the last peak value in this row as the maximum value, and then replace each data in the data after Gaussian fitting that is greater than the maximum value with the maximum value to avoid interference from abnormally high values. It should be emphasized that when determining whether there are multiple peaks, it is actually necessary to check whether the minimum spacing between adjacent peaks is met. The minimum spacing must be greater than 1 / 10 of the total length of the corresponding row to ensure that the data has a clear outline when the corresponding hole cloud is subsequently processed.

[0036] S2. Perform least squares polynomial fitting on the scan data optimized in step S1 row by row, and use the fitting parameter equation corresponding to the fitting to form new data with the same length as the fitting data; use the new data to remove the scan data optimized in step S1 to obtain leveled data.

[0037] In this embodiment, a first-order polynomial equation is used for the least squares polynomial fit in step S2. Specifically, when using a first-order polynomial equation for the first-order polynomial fit, the first-order polynomial equation can be set to y = kx + b, and the corresponding specific values ​​of k and b are calculated to determine the fitting parameter equation. During AFM scanning, the sample may have installation tilt or instrument drift, which may cause overall tilt. The first-order fit can remove linear tilt trends, such as k representing the slope and b representing the offset.

[0038] It should be noted that leveling is a data preprocessing process that removes any overall tilt or curvature in the AFM image, thereby leveling the image's reference surface. When scanning a wafer with an AFM, factors such as uneven sample mounting, offset during scanning, and overall sample surface tilt can cause the scanned image to appear as an inclined or curved surface, rather than an ideal horizontal plane. Without leveling, height measurements can be inaccurate, impacting subsequent data analysis.

[0039] S3. Normalize the leveled data from step S2 to eliminate dimensional differences in the data for easier processing, and then form a grayscale image. Next, find all target areas in the grayscale image, i.e., circular regions. Each circular region is edge-excluded, i.e., the influence of areas close to the image boundary is eliminated, thereby obtaining each upper hole cloud and the corresponding diameter of each upper hole cloud.

[0040] In this embodiment, the normalization formula in step S3 is:

[0041] ;

[0042] Among them, height min is the minimum value of the original data height, and height max is the maximum value of the original data height.

[0043] In this embodiment, after the grayscale image is formed in step S3, in order to more clearly distinguish the circular-like structure in the wafer, the grayscale image can also be binarized using the Otsu method, and the maximum inter-class variance between the background and the circular-like structure in the grayscale image is used as the binarization threshold, thereby making it easier to distinguish between the circular-like structure and the background.

[0044] In this embodiment, after forming the grayscale image in step S3, the grayscale image may be segmented first, and the low area value regions corresponding to the leveling data are discarded, and the regions with roundness values ​​lower than a specific roundness value are discarded; wherein the specific roundness value is calculated as follows: circularity = region area / (π × circumscribed circle radius) 2 ). We discard them here because we only focus on the analysis of circular structures. If the circularity is below a certain level, it is likely to be impurity interference and therefore needs to be discarded.

[0045] Furthermore, each area discarded after segmentation is regarded as a quasi-circular area, and the minimum distance from each quasi-circular area to the four boundaries in the image corresponding to the height map data is calculated. When the minimum distance from any processed area to the boundary is 0, the corresponding quasi-circular area is regarded as close to the image boundary and excluded from the edge; each area after the edge exclusion in each quasi-circular area is regarded as an upper hole cloud, and the center position of each upper hole cloud is obtained. At the same time, the diameter of each corresponding minimum circumscribed circle is calculated as the diameter of each upper hole cloud, thereby completing the upper hole positioning.

[0046] S4. Based on each upper hole cloud and the corresponding upper hole cloud diameter in step S3, each corresponding 3D data cluster is re-cut from the leveling data. Each 3D data cluster is clustered to sequentially separate each corresponding bottom hole data cluster and upper surface data cluster. The bottom hole data cluster corresponds to the lower hole point cloud, and the upper surface data cluster corresponds to the background point cloud. The corresponding lower hole cloud diameter can be obtained based on the bottom hole data cluster. Each data in each bottom hole data cluster is averaged to obtain each corresponding hole bottom height.

[0047] In this embodiment, when clustering is performed in step S4, a feature point cloud of density difference can be extracted from each three-dimensional data cluster; then, the center of each three-dimensional data cluster is used as a seed point, and each other data point in the three-dimensional data cluster is traversed for clustering. After clustering, any three-dimensional data cluster can form two corresponding data clusters, namely the bottom hole data cluster and the upper surface data cluster.

[0048] In this embodiment, after separating each bottom hole data cluster in step S4, RANSAC fitting circle can also be used to calculate the corresponding bottom hole diameter as the bottom hole cloud diameter, and at the same time, the data in each bottom hole cluster are averaged to calculate the corresponding bottom height of each hole. Similarly, each data in each upper surface data cluster is averaged to calculate the corresponding upper surface height; the upper surface height minus the hole bottom height can obtain the height difference of the corresponding hole. It should be noted that RANSAC is called Random Sample Consensus, which is a random sampling consensus algorithm. It is an iterative method that can be used to estimate the parameters of a mathematical model from a set of data containing outliers. In this method, the height is obtained as a parameter.

[0049] In summary, the present invention effectively removes noise interference by improving the flattening method, making the data smoother and more reliable; it also excludes the edge of the image to determine the area of ​​non-edge structure and locate the upper hole cloud and the corresponding diameter; in addition, it also uses Gaussian fitting, least squares polynomial fitting, normalization and clustering processing to perform multiple processing on the data, which not only enhances the stability of complex data while retaining feature information, but also effectively completes the analysis of the size of circular-like structures in the wafer, can meet the needs of different scientific research and industrial applications, and has significant progress.

[0050] The above embodiments are only for illustrating the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for analyzing wafer structure by scanning with AFM based on image and data processing, characterized in that: The steps include: S1. Extracting height map data from the AFM scanning data of the wafer, performing row-by-row Gaussian fitting and row-by-row denoising on the height map data to obtain optimized scanning data; When performing row-by-row denoising, the denoising process for any row is as follows: determine whether there are multiple peaks in the data after Gaussian fitting. If not, normalize the data after Gaussian fitting to between 2% and 95% of the original value; if so, take the smallest data in the data after Gaussian fitting as the minimum value, and the last peak value in this row as the maximum value, and then replace each data in the data after Gaussian fitting that is greater than the maximum value with the maximum value; wherein, any adjacent peaks meet the minimum spacing, and the minimum spacing is greater than 1 / 10 of the total length of the corresponding row; S2. Perform least squares polynomial fitting on the scan data optimized in step S1 row by row, and use the fitting parameter equation corresponding to the fitting to form new data with the same length as the fitting data; use the new data to remove the scan data optimized in step S1 to obtain leveled data; S3, normalizing the leveling data in step S2 to form a grayscale image; then finding all the circular regions in the grayscale image and excluding each circular region from the edge to obtain each upper hole cloud and the corresponding diameter of each upper hole cloud; S4. Based on each upper hole cloud and the corresponding diameter of each upper hole cloud in step S3, each corresponding three-dimensional data cluster is cut out from the leveling data, and each three-dimensional data cluster is clustered to separate each corresponding bottom hole data cluster and upper surface data cluster; the corresponding diameter of each lower hole cloud is obtained according to each bottom hole data cluster, and each data in each bottom hole data cluster is averaged to obtain each corresponding hole bottom height.

2. The AFM scanning wafer structure analysis method based on image and data processing according to claim 1, characterized in that: When performing row-by-row Gaussian fitting in step S1, the Gaussian function equation used is: , where x corresponds to each row of data, A is the amplitude, μ is the mean, and σ is the standard deviation.

3. The AFM scanning wafer structure analysis method based on image and data processing according to claim 1, characterized in that: During the least squares polynomial fitting in step S2, a first-order polynomial equation is used to perform the first-order polynomial fitting.

4. The AFM scanning wafer structure analysis method based on image and data processing according to claim 3 is characterized in that: When using a first-order polynomial equation for first-order polynomial fitting, the first-order polynomial equation is set to y=kx+b, and the corresponding specific values ​​of k and b are calculated to determine the fitting parameter equation.

5. The AFM scanning wafer structure analysis method based on image and data processing according to claim 1, characterized in that: The normalization formula in step S3 is: ； Among them, height min is the minimum value of the original data height, and height max is the maximum value of the original data height.

6. The AFM scanning wafer structure analysis method based on image and data processing according to claim 1, characterized in that: After the grayscale image is formed in step S3, the grayscale image is binarized using the Otsu method, and the maximum inter-class variance of the background and structure in the grayscale image is used as the binarization threshold.

7. The AFM scanning wafer structure analysis method based on image and data processing according to claim 1, characterized in that: After the grayscale image is formed in step S3, the grayscale image is first segmented, and the low area value areas corresponding to the leveling data are discarded, and the areas with roundness values ​​lower than a specific roundness value are discarded; The calculation formula of the specific circularity value is: circularity = area / (π × circumscribed circle radius 2 ); Each discarded area after segmentation is then treated as a circle-like area, and the minimum distance from each circle-like area to the four boundaries in the image corresponding to the height map data is calculated. When the minimum distance from any processed area to the boundary is 0, the corresponding circle-like area is considered to be close to the image boundary and is excluded; Each area after the edge exclusion in each circular area is taken as the upper hole cloud, the center position of each upper hole cloud is obtained, and the diameter of each corresponding minimum circumscribed circle is calculated as the diameter of each upper hole cloud.

8. The AFM scanning wafer structure analysis method based on image and data processing according to claim 1, characterized in that: When clustering any three-dimensional data cluster in step S4, a feature point cloud of density difference is extracted from the three-dimensional data cluster. The center of the three-dimensional data cluster is used as the seed point, and each other data point in the three-dimensional data cluster is traversed for clustering to form two data clusters, namely the bottom hole data cluster and the upper surface data cluster.

9. The AFM scanning wafer structure analysis method based on image and data processing according to claim 1, characterized in that: After separating the bottom hole data cluster from any three-dimensional data cluster in step S4, RANSAC is used to fit the circle and calculate the bottom hole diameter as the lower hole cloud diameter. At the same time, the data of the bottom hole cluster are averaged to calculate the hole bottom height; then, each data in the upper surface data cluster is averaged to calculate the upper surface height; and the hole height difference is obtained based on the upper surface height and the hole bottom height.

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