Method for analyzing metrology data

Abstract

Preferred embodiments relate to a metrology method, e.g., for sag analysis in semiconductor fabrication, including generating a sample image using atomic force microscope (AFM) data of a sample having an array of 2D periodic features, and calculating a periodicity of the features. The method may identify peaks of the periodicity to determine a characteristic period and lattice angle, and construct a lattice mask registered with the image to perform alignment calculations. The mask is offset, and alignment calculations are made to optimize cost.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority under 35 USC §1.119(e) to U.S. Provisional Patent Application Serial No. 63 / 352,120, filed on June 14, 2022. The entire contents of the subject matter of this application are incorporated herein by reference. Background of the Invention Technical Field

[0004] Preferred embodiments relate to the field of atomic force microscopy data analysis. In particular, they relate to analyzing spatial and topographical data of sample features, such as detection of periodic features in a lattice. Preferred embodiments are particularly suitable for making measurements in high-throughput applications, such as performing recess analysis in semiconductor manufacturing. Background Art

[0005] Scanning probe microscopes, such as atomic force microscopes (AFM), are devices that use a probe with a tip that interacts with the surface of a sample with appropriate force to characterize the surface to atomic dimensions. Typically, the probe is guided to the surface of the sample, and surface property data on a specific area of ​​the sample can be acquired by providing a relative scanning movement between the tip and the sample, and a corresponding sample map can be generated.

[0006] Generally, the instrument is capable of generating relative motion between a probe and a sample while measuring the topography or other surface properties of the sample, as described in US Pat. Nos. RE 34,489 to Hansma et al.; 5,266,801 to Elings et al.; and 5,412,980 to Elings et al.

[0007] In a common configuration, the probe is often coupled to an oscillating actuator or driver that is used to drive the probe at or near the resonant frequency of the cantilever. Alternative arrangements can measure deflection, torsion, or other motion of the cantilever. The probe is often a microfabricated cantilever with an integrated tip.

[0008] Typically, an electrical signal is applied from an AC signal source under the control of the SPM controller to cause an actuator or scanner to drive the probe to oscillate. The probe-sample interaction is typically controlled via feedback from the controller. It is noteworthy that the actuator can be coupled to the scanner and probe, but can also be integrally formed with the cantilever of the probe as part of a self-actuated cantilever / probe.

[0009] AFMs can be designed to operate in a variety of modes, including contact and oscillating modes. Operation is accomplished by moving the sample or probe assembly up and down relative to a surface perpendicular to the sample in response to deflections of the probe assembly's cantilever as it scans across the surface. Scanning typically occurs in the "xy" plane, which is at least approximately parallel to the surface of the sample, while vertical movement occurs in the "z" direction, which is perpendicular to the xy plane. It is important to note that many samples have roughness, curvature, and tilt that deviate from a flat plane, hence the term "approximately parallel." In this way, data associated with this vertical motion can be stored and later used to construct an image of the sample surface that corresponds to the sample property being measured (e.g., surface topography). In a technique called TappingMode, the image is taken from a sample surface and is then imaged. TM AFM (Tapping Mode TM ) is a trademark of the present assignee, the tip oscillates at or near the resonant frequency of the probe's associated cantilever. A feedback loop attempts to keep the amplitude of this oscillation constant to minimize the "tracking force", i.e., the force generated by the tip / sample interaction. Alternative feedback arrangements keep the phase or oscillation frequency constant. As with the contact mode, these feedback signals are then collected, stored, and used as data to characterize the sample. It is noted that the acronyms "SPM" and specific types of SPM may be used herein to refer to the microscope apparatus or associated technology, e.g., "atomic force microscope." In the context of the popularized Tapping Mode, the tip oscillates at or near the resonant frequency of the probe's associated cantilever. TM A recent improvement in AFM (called Peak Force In the PFT mode (discussed in U.S. Pat. Nos. 8,739,309, 9,322,842, and 9,588,136, which are expressly incorporated herein by reference), feedback is based on the force measured in each oscillation cycle (also called the transient probe-sample interaction force).

[0010] Regardless of its operating mode, AFM can achieve resolution down to the atomic level on a variety of insulating or conducting surfaces in air, liquid, or vacuum by using piezoelectric scanners, optical lever deflection detectors, and very small cantilevers made using photolithography. Due to its resolution and versatility, AFM has become an important measurement device in many different fields, from semiconductor manufacturing to biological research.

[0011] In this regard, AFM can be used for automated applications, including high-precision processes such as semiconductor manufacturing. AFM has proven to be very useful in the semiconductor field because it can perform high-resolution measurements of nanometer-scale surface features (e.g., topography).

[0012] A variety of different analyses can be performed on the acquired AFM data to determine different characteristics about a particular sample. Depending on the sample being studied and its intended use, the characteristics of interest and the analyses used may vary. For example, in semiconductor manufacturing and wafer bonding processes, there may be copper pads surrounded by dielectrics. In this case, planarity between the copper pad and the surrounding dielectric is sought. There is a tolerable threshold for the degree of concavity or convexity between the boundary of the copper pad and the dielectric. In addition, planarity is required across the sample with respect to the dielectric itself. In addition, planarity is also required for the copper pad itself.

[0013] The overall flatness of the sample is the goal of the planarization process. However, it has proven to be a time-consuming and costly process to determine whether the resulting sample falls within a specific threshold range to perform its semiconductor function. Existing AFM analysis (such as Depth, CFA & FinFET) is too application-specific to work in this area. Using known techniques, users need to manually identify areas where features are expected to exist, and then each of these areas needs to be analyzed individually to discern their morphology and spatial characteristics. This time-consuming process is not practical for a high-volume-manufacturing environment.

[0014] Take depth analysis, for example, which is a histogram-based analysis that returns Z information in an AFM image. CFA is an analysis that analyzes square features in a square lattice and compares their subfeatures. FinFet analysis is designed to measure the fin height, gate height, and gate-to-fin height for each fin in an image by comparing the image to a CAD clip of the same area. Useful data can be obtained using these existing analyses, but due to the uniqueness of the problem, the user must spend so much time and effort to set up the calculations that they are not practical as a solution for high-volume manufacturing. These analyses become even more cumbersome if the number of pads or the absolute locations of those pads are unknown.

[0015] What is needed is a method for a user to quickly and with minimal user intervention obtain meaningful data regarding the spatial location and topographic comparison of features of a particular sample. Summary of the invention

[0016] The preferred embodiments overcome the shortcomings of current AFM data analysis techniques by enabling autonomous measurement of multiple key metrics for multiple regions of interest within a single AFM image without requiring user intervention to locate these regions of interest (ROIs). Previously, if customers wanted to obtain similar data, they had to manually process the data, which required many dedicated man-hours. With the present invention, users can obtain meaningful data about sample quality in a few minutes or even less. Since lithography is an evolving discipline, the data required for quality assurance is also evolving. The present invention helps meet the needs of users to check the quality of their samples quickly and with minimal human intervention.

[0017] The present invention is particularly useful for analyzing novel bond pads in hybrid bonding processes used in semiconductor manufacturing. Automatic pad detection creates an easy-to-use environment that does not require a priori knowledge of the number of pads in an AFM image or the absolute positions of those pads in the AFM image. In most cases, the number of pads in an AFM image exceeds 20. It is now feasible to accurately place measurement regions of interest ("ROIs") on all pads in one image of multiple images for high volume manufacturing environments.

[0018] Automatic shim detection ensures that the subsequent measurement ROI is well placed on each shim for accurate, repeatable and reproducible metrology. Metrology in this process step requires sub-nm precision, which is only possible if the measurement ROI is precisely placed for each measurement. A shift of the measurement ROI relative to the shim will measure slightly different areas on the shim. Due to the inherent shim topography, this shift will produce a less repeatable data set.

[0019] The present invention overcomes this and the above-mentioned shortcomings of current AFM analysis by using several algorithms to analyze the data acquired by the AFM and return information about the quality of the sample. The present invention combines a lattice detection algorithm with a novel lattice alignment technique. After applying the detection step and the alignment step, the found lattice is used to analyze the local depth, variance, slope, etc. of each feature. The returned data can then be used to determine the quality of the sample. The present metrology method can be used to analyze any feature in a periodic lattice as well as the contact folds and other morphological and spatial features of the sample.

[0020] According to a preferred embodiment, a metrology method for analyzing an AFM image includes using Fast Fourier Transform Autocorrelation to calculate the periodicity of the AFM image. Next, the method includes searching radially outward from the center of the image to find the peak of the periodicity. Then, the method includes quantizing the circular shell of the peak of the periodicity to obtain possible lattice periods and angles. In addition, the image can be downsampled to speed up cost calculations. Next, a lattice mask is constructed using the previously acquired lattice period and angle. The lattice mask is then overlaid on the image to enable the algorithm to distinguish between feature pixels and background pixels. User input parameters are then applied to alignment calculations. From here, the method can vary depending on the data required by the user.

[0021] In one aspect, the standard deviation of the background pixels is calculated and this value is set as the cost. Then, an offset covered by the lattice mask is applied and the cost is recalculated. The cost is calculated at each offset within a 1.2 cycle range to cover all alignment options. Finally, the offset that gives the minimum cost is found and set as the final lattice alignment. This embodiment using the standard deviation may be used when the background is rough.

[0022] In another aspect, the median between the background pixel and the feature pixel is calculated and set as the cost. Then, an offset is applied to the lattice mask cover and the cost is recalculated. The cost is calculated at each offset within a 1.2 cycle range to cover all alignment options. Finally, the offset that gives the maximum cost is found and set as the final lattice alignment. In this embodiment, the median may be preferred when the background is smooth.

[0023] According to another aspect of the preferred embodiment, the method further comprises iterating 2D model types including at least two of square, rectangle, hexagon and oblique, and then selecting a periodicity of the lattice type that produces a minimum deviation between the model lattice type and the acquired data.

[0024] In yet another aspect of the preferred embodiment, the method further comprises applying an adaptive flattening algorithm to the sample image.

[0025] In another embodiment, a metrology method includes using atomic force microscopy (AFM) data to generate an image of a sample and calculating the periodicity of features of the image. Next, the method searches for at least one peak of the periodicity and obtains a characteristic period and a lattice angle. The method then constructs a lattice mask template using the characteristic period and the lattice angle and overlays the image with the lattice mask template. The method then performs an alignment calculation to determine a cost, and applies an offset of the lattice mask template to the image and recalculates the cost. The applying and recalculating steps are repeated to determine the alignment between the lattice mask template and the image.

[0026] In another embodiment, an AFM for collecting sample AFM data includes a probe that interacts with the surface of the sample and a controller that controls the probe-sample interaction and collects atomic force microscopy (AFM) data of a sample having a periodic feature array. The controller uses the AFM data to generate a sample image having feature pixels and background pixels, and calculates the periodicity of the features. In addition, the controller can also identify the peak of the periodicity to determine the feature period and lattice angle, and use the feature period and lattice angle to construct a lattice mask template. Next, the image is overlaid with the lattice mask template, and the controller performs an alignment calculation to determine the cost. An offset of the lattice mask template is applied to the image, and the cost is recalculated. The application and recalculation steps are repeated to determine the alignment between the lattice mask template and the image, which is particularly important in semiconductor manufacturing.

[0027] According to another aspect of this embodiment, the controller performs the alignment step by at least one of: a) calculating a standard deviation of the background pixels and setting the standard deviation as a cost value; and b) calculating a median of the background pixels and the feature pixels and setting the median as a cost value. If the standard deviation is calculated, the controller may further determine an offset of a lattice that can determine a minimum cost value, and if the median is calculated, the controller may further determine an offset of a lattice that can determine a maximum cost value.

[0028] These and other features and advantages of the present invention will become apparent to those skilled in the art from the following detailed description and accompanying drawings. However, it should be understood that the detailed description and specific examples, although indicating preferred embodiments of the present invention, are given by way of illustration and not limitation. Many changes and modifications may be made within the scope of the present invention without departing from the spirit of the present invention, and the present invention includes all such modifications. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Preferred exemplary embodiments of the present invention are illustrated in the accompanying drawings, wherein like reference numerals represent like parts throughout, and wherein:

[0030] Figure 1 is an image of a scanning probe microscope system;

[0031] Figure 2A is an image of the raw AFM data;

[0032] Figure 2B is a schematic diagram showing the steps of detecting periodicity in raw AFM data;

[0033] Figure 2C is a schematic diagram showing the steps of analyzing periodic rings in AFM data;

[0034] Figure 2D is a schematic diagram showing the steps of generating a lattice from AFM data;

[0035] Figure 3 is a flow chart of the present metering method of a preferred embodiment;

[0036] Figure 4A is an image of the raw AFM data;

[0037] Figure 4B yes Figure 4A Image of the raw AFM data after applying adaptive flattening to eliminate image tilt;

[0038] Figure 4C Yes Figure 4B An image of a periodic image obtained by performing fast Fourier transform autocorrelation processing on the flattened AFM data;

[0039] Figure 4D It is shown Figure 4C An image of periodic peaks in ;

[0040] Figure 4E is an image of a lattice mask template; and

[0041] Figure 5 is a sketch of the hexagonal lattice showing the features of interest and the height differences between them. DETAILED DESCRIPTION

[0042] The preferred embodiment relates to a metrology method for analyzing spatial and topographic data of 2D elements / features in a lattice from raw atomic force microscopy (AFM) data. The method described herein combines a lattice detection algorithm with a novel lattice alignment technique. After applying the detection step and the alignment step, the found lattice is used to analyze the local depth, variance, slope, etc. of each feature. The present invention helps meet the needs of users to check the quality of their samples quickly and with minimal user intervention.

[0043] First turn Figure 1 , shows a scanning probe microscope instrument 150 (e.g., AFM) according to a preferred embodiment. In this embodiment, a probe 152 is held by a probe holder (not shown) supported by a piezoelectric tube scanner 156, with a tip 154 ​​of the probe 152 extending from the distal end of a cantilever 155. The scanner 156 may be a "Z" type or vertical scanner that responds to sample properties in a closed loop control system to position the tip 154 ​​relative to the sample 158 during AFM imaging. The tube scanner 156 is coupled to an XY scanner 160 (preferably also a piezoelectric tube) that is used to raster the probe tip 154 ​​relative to the surface of the sample 158 during AFM operation. It is noted that a scanned sample may be used as an alternative. A mechanical Z stage 162 is included to provide large Z-direction movement between the tip 154 ​​and the sample 158 to engage the tip 154 ​​and the sample 158, for example, during the start of AFM image acquisition.

[0044] The sample 158 is mounted on an XY stage 164, which primarily provides coarse XY motion to position the probe 152 at a region of interest of the sample 158. An XY stage controller 166 controls the stage 164 to position the probe / sample at the region of interest. However, similarly, the stage 164 can also be configured to provide relative scanning motion (e.g., raster) between the tip 154 ​​and the sample 158 at a selected scanning speed. The controller 166 is also responsive to the AFM controller 174 to position the image scan at the region of interest. The controllers 166, 174 are implemented by a computer 180.

[0045] In operation, as discussed above, after the tip 154 ​​is engaged with the sample 158, high-speed scanning of the sample is initiated in an AFM operating mode (e.g., PFT mode) using the XY scanner 160. When the tip 154 ​​interacts with the surface of the sample 158, the probe 152 deflects, and this deflection is measured by an optical beam-bounce deflection detection device 168. The device 168 includes a laser 170 that directs a light beam "L" from the back of the cantilever 155 to a photodetector 172, which transmits the deflection signal to, for example, a DSP 176 of an AFM controller 174 for high-speed processing of the deflection signal.

[0046] The AFM controller 174 continuously determines control signals depending on the AFM operating mode and transmits the signals to the piezoelectric tube scanner 156 to maintain the Z position of the probe 152 relative to the sample 158, and more specifically, to maintain the deflection of the probe at a feedback set point.

[0047] Steering Figures 2A-2D , shows a series of schematic diagrams depicting the progression of the analysis of AFM data according to the present metrology method. Figure 2A In FIG. 2 , raw AFM data is shown as image 200. This raw AFM data is generated by the scanning probe microscope instrument and method described above. The data consists of features 202 and background 204. Next, Figure 2B is a schematic representation of detecting periodicity in the raw AFM data 206. This is preferably accomplished by fast Fourier transform (FFT) autocorrelation to find peaks and periodicity in the raw AFM data. The image is correlated with itself, and the peaks represent points where the image is symmetrical to itself 208. In addition, Figure 2C , a schematic diagram of a periodic ring 210 found in the data is shown. Figure 2C Each point 208 in represents a periodic peak. The positions of these peaks relative to the center and the distances and 2D angles relative to each other are quantified and used to construct different lattices (described in more detail below). Figure 2D is a schematic 212 representation of a lattice that may be generated in a region of feature 202 adjacent to a region of background 204 for use as a mask to extract sample information.

[0048] Now turn to Figure 3 , shows a simplified diagram of the metrology method 300. In step 302, raw AFM surface data is collected from a sample. Next, in step 304, a Fast Fourier Transform (FFT) is used to calculate the periodicity of the image. In step 306, periodic rings are found by searching radially outward from the center of the image (see Figure 2C). In the case of a hexagonal lattice, a set of four can be used when looking for rings. Other sets can be sought when using different lattices (rectangular, triangular, octagonal, etc.). These periodic rings provide information about the location of the peaks relative to the center in terms of distance, and also provide information about the distances and angles of the peaks relative to each other. Similarly, moving radially outward from the center will also find multiple periodic rings. Then, in step 308, the circular shells of the periodic peaks are quantized, and possible lattice periods and angles are obtained. In step 310, the image can be downsampled to speed up cost calculations. Then, in step 312, the lattice mask is constructed using the lattice periods and angles previously obtained. As Figure 2D As shown, several such lattices are generated.

[0049] At step 314, a lattice mask is overlaid on the image to enable the algorithm to distinguish feature pixels from background pixels. Here, the mask matrix is ​​added / multiplied with the image matrix to extract the feature pixels. Figure 2D ) decomposes the image into black area and white area pixels. The white area pixels represent sample features, while the black area pixels represent background. Then, in step 316, the alignment calculation user input parameters are applied. The user can choose to use standard deviation calculation or median calculation. When the background is rough, the standard deviation may be applied, and when the background is smooth, the median may be applied.

[0050] Depending on the parameters selected by the user, the next step may be different. If the user selects standard deviation, the standard deviation of the background pixels (black areas) is calculated in step 318 and the standard deviation value is set as the cost. Then, in step 322, the offset covered by the lattice mask is applied and the cost is recalculated. Preferably, the cost is calculated at each offset within a range of 1.2 cycles to cover all alignment options. This is an exhaustive search of the area of ​​one unit cell in order to test all possible offsets. Finally, in step 324, the offset that gives the minimum cost is found and set as the final lattice alignment.

[0051] If the user selects the median as the input parameter, the method will be different. In this case, the next step after step 316 is step 320, in which the median is calculated. Figure 2DThe median difference between the background pixels (black areas) and the feature pixels (white areas) in . The difference between the medians of background pixel 204 and feature pixel 202 is calculated and set as the cost. Next, in step 322, the offset covered by the lattice mask is applied and the cost is recalculated, as in the case of the standard deviation. The cost is calculated at each offset within a 1.2 cycle range to cover all alignment options. This is an exhaustive search of the area of ​​a unit cell in order to test all possible offsets. Finally, in step 326, the offset that gives the maximum cost value is found and set as the final lattice alignment.

[0052] Once the cost is calculated correctly, the final lattice alignment can be determined and the design of the feature can be determined. For example, if the feature is determined to be a series of concentric rectangles, the pixels corresponding to each area of ​​the rectangles can be extracted from the AFM image and the specific pixels corresponding to specific parts of the feature can be analyzed.

[0053] Note that when the 2D lattice type is unknown, it is possible to iterate over all possible lattice types rendered in 2D: square, rectangular, hexagonal, or italic (see https: / / en.wikipedia.org / wiki / Bravais_lattice ), and the periodicity of the lattice type that produces the smallest deviation between the model lattice and the acquired data is selected. Here, the smallest deviation corresponds to the best alignment cost.

[0054] Now turn to Figures 4A-4E , shows a series of images illustrating the progress of the analysis of AFM data according to the present metrology method. Figure 4A The raw AFM data are shown in . Figure 4A The image 400 shown in FIG. 4 is generated in step 302 of the metrology method described above. The data consists of features 402 and background 404. Defects 406 may also exist in the sample and the resulting data. Next, Figure 4B is an image of the AFM data after applying “adaptive flattening” to remove image tilt. Figure 4C : is an image showing a periodic image obtained by fast Fourier transform autocorrelation. Point 408 in the image represents a peak of the periodicity. Figure 4C This corresponds to step 304 of the above measurement method. Figure 4D is an image showing the periodic ring 410 . Figure 4D This corresponds to step 306 of the above-mentioned measurement method. In addition, Figure 4E 4 is an image showing a lattice mask template 412 generated using the distribution of peaks. This mask is generated in step 312 above. This lattice mask template 412 is then overlaid on the AFM image. In this process, the mask matrix is ​​multiplied with the image matrix, so that only certain pixels are analyzed. This corresponds to step 314 above.

[0055] Steering Figure 5 , shows a sketch of a hexagonal lattice 500 showing features of interest and the height differences between them. Instead of a square lattice, a hexagonal lattice is shown here. The dark squares 502 represent design features of interest 502 found by the present method (e.g., Figure 4A Once the features of interest 502 are identified, they can be analyzed to quantify the height distribution between the features 502. The shadows 504 on the features 502 represent the height differences between the features 502. Figure 5 is a sketch of the result that will be obtained in step 324 or 326 above. Figure 5 The center of the image (where the square is not shaded) indicates that features in this part of the sample may be missing, or barely printed on the wafer. When a wafer is printed, it is always periodic, so in theory, feature 502 should be present at every square in the image. Information about the local depth, variance, slope height, etc. of each feature 502 is very important to the quality of the sample and its functionality.

[0056] Preferred embodiments are particularly useful in semiconductor manufacturing. Diffusion analysis, for example, enables critical metrology for IC processes in which two semiconductor wafers having patterned surfaces are bonded together. Such wafer-to-wafer bonding requires highly accurate topographical knowledge of the post-polishing (CMP) wafer surfaces, which consist of metal pads surrounded by dielectric material. Effectiveness of the bonding requires that the surfaces be very flat. Diffusion analysis calculates the height difference of the metal pad relative to the surrounding dielectric (called dishing), the local slope of the dielectric material near the metal pad, and the global flatness of the entire field of view.

[0057] The output of the dishing analysis allows IC manufacturers to make critical process decisions based on the percentage of roughness and slope areas that are out of specification.

[0058] Although the best mode of implementing the present invention contemplated by the inventor has been disclosed above, the practice of the above invention is not limited thereto. Obviously, various additions, modifications and rearrangements can be made to the features of the present invention without departing from the spirit and scope of the basic inventive concept.

Claims

1. A measurement method comprising the following steps: using atomic force microscopy (AFM) data of a sample having a periodic array of features to generate a sample image having feature pixels and background pixels; calculating the periodicity of the feature; identifying peaks of the periodicity to determine characteristic periods and lattice angles; constructing a lattice mask template using the characteristic period and the lattice angle; covering the image with the lattice mask template; Perform alignment calculations to determine costs; applying an offset of the lattice mask template to the image and recalculating the cost; as well as The applying and recalculating steps are repeated to determine the alignment between the lattice mask template and the image.

2. The method according to claim 1, wherein: The execution step includes at least one of: a) calculating a standard deviation of the background pixels and setting the standard deviation as a cost value; and b) calculating a median of the background pixels and the feature pixels and setting the median as a cost value.

3. The method of claim 2, further comprising determining a shift of a lattice that determines a minimum cost value if the standard deviation is calculated, and determining a shift of a lattice that determines a maximum cost value if the median is calculated.

4. The method of claim 1, further comprising extracting data associated with the feature after applying the alignment.

5. The method according to claim 4, wherein: The data corresponds to at least one of characteristic properties including height, depth, shape, uniformity, variance, and slope.

6. The method of claim 5, further comprising comparing the at least one feature characteristic to a known model to determine feature quality.

7. The method according to claim 6, wherein: The comparison step is used for semiconductor manufacturing dishing analysis.

8. The method according to claim 1, wherein: The feature is a 2D periodic feature, and the step of identifying a peak of the periodicity starts from the center of the sample image and continues radially outward.

9. The method according to claim 8, further comprising the steps of: Iterating 2D model types including at least two of square, rectangle, hexagon, and italic; and The periodicity of the lattice type is chosen that produces the smallest deviation between the model lattice type and the acquired data.

10. The method according to claim 1, wherein: The step of calculating the periodicity is performed using a Fast Fourier Transform (FFT) algorithm.

11. The method according to claim 1, wherein: The lattice mask template is hexagonal.

12. The method of claim 1, further comprising applying an adaptive flattening algorithm to the sample image.

13. A measurement method comprising the following steps: Use atomic force microscopy (AFM) data to generate images of samples; calculating the periodicity of features of the image; searching for at least one peak of the periodicity; Obtain characteristic periods and lattice angles; constructing a lattice mask template using the characteristic period and the lattice angle; covering the image with the lattice mask template; Perform alignment calculations to determine costs; applying an offset of the lattice mask template to the image and recalculating the cost; as well as The applying and recalculating steps are repeated to determine the alignment between the lattice mask template and the image.

14. The measuring method according to claim 13, wherein: The cost is calculated based on the entire area of ​​one unit cell.

15. The metrology method according to claim 13, further comprising the step of downsampling the image in order to speed up the calculation of the cost.

16. The measuring method according to claim 13, wherein: The step of searching for at least one peak of periodicity starts from the center of the image and continues radially outwards.

17. The measuring method according to claim 13, wherein: The step of calculating the periodicity is accomplished by using a Fast Fourier Transform (FFT) algorithm.

18. An AFM for collecting sample AFM data, comprising: a probe, interacting with a surface of the sample; a controller that controls probe-sample interactions and collects atomic force microscopy (AFM) data of a sample having a periodic array of features; and Wherein, the controller: Using the AFM data to generate a sample image having feature pixels and background pixels; calculating the periodicity of the feature; identifying peaks of the periodicity to determine characteristic periods and lattice angles; constructing a lattice mask template using the characteristic period and the lattice angle; covering the image with the lattice mask template; Perform alignment calculations to determine costs; applying an offset of the lattice mask template to the image and recalculating the cost; and The applying and recalculating steps are repeated to determine the alignment between the lattice mask template and the image.

19. The AFM of claim 18, wherein: The controller performs the alignment step by at least one of: a) calculating a standard deviation of the background pixels and setting the standard deviation as a cost value; and b) calculating a median of the background pixels and the feature pixels and setting the median as a cost value.

20. The AFM of claim 19, wherein: If the standard deviation is calculated, the controller further determines an offset of the lattice that may determine a minimum cost value, and if the median is calculated, the controller further determines an offset of the lattice that may determine a maximum cost value.

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