Abstract:
Apparatus and associated method that contemplates performing a first atomic force microscope (AFM) scan of a first region of a sample centered at a first position at a first angle to produce a first scan image, the first AFM scan including a first component scan at a first speed and a second component scan at a second speed; performing a second AFM scan of the first region of the sample at a second angle to produce a second scan image, the second AFM scan including performing a third component scan at the first speed and a fourth component scan at the second speed; and correcting a first error in the first scan image based on the second scan image to produce a corrected image output.

Description:
RELATED APPLICATIONS 
       [0001]    This application is a continuation of U.S. patent application Ser. No. 12/179,688 filed Jul. 25, 2008 and entitled “ATOMIC FORCE MICROSCOPY OF SCANNING AND IMAGE PROCESSING” which is a divisional of U.S. Pat. No. 7,406,860, issued Aug. 15, 2008 and entitled “ATOMIC FORCE MICROSCOPY OF SCANNING AND IMAGE PROCESSING.” 
     
    
     BACKGROUND 
       [0002]    The present invention relates to scanning probe microscopy, and more particularly to using atomic force microscopy to produce an image profile representative of a structure. 
         [0003]    Atomic force microscopy (AFM) is a metrology technique that is useful for measuring and imaging surface features of structures having dimensions in the nanometer and micrometer range. AFM may be used to scan structures made of any material in a short period of time to produce high resolution two-dimensional and three-dimensional images of the structure. AFM is an important tool for measuring dimensions of devices in the semiconductor industry, including magnetic recording devices and microelectromechanical system (MEMS) devices. 
         [0004]    The lateral resolution of an image produced from an AFM scan of a structure is defined by the scan area size and the number of pixels in the image. Thus, in order to increase the lateral resolution of an image, the size of the scan area may be reduced or the amount of data in the image (i.e., the number of pixels) may be increased. However, a reduction in the size of the scan area removes contextual details around the scanned area of interest, which makes determining the relative sizes and positions of features within the structure difficult. On the other hand, to increase in the amount of data in the scan, the scan speed may be reduced, which decreases measurement throughput and may result in drift errors in the image. The increased amount of data in the scan also wastes the limited available data on areas outside of the areas of interest in the scan. 
         [0005]    In addition, the small dimensions of the scanned structure result in missed details or the introduction of artifacts into the resulting image. For example, when scanning a structure including features having significant topographical transitions, feedback overshoot may occur at the transition locations, resulting in lost details in the representative image at the transition locations. In addition, a scan of a flat or planar feature in the structure may result in a curving or bowing artifact in the resulting image at the location of the flat or planar feature. This may be caused by the relative sizes and shapes of the scanning probe tip and the scanned feature. Image curvature may also occur when the scanning probe tip moves faster in one direction than the other along the structure surface because environmental vibrations, thermal drifting, and air flow along the probe tip may affect the image in the slower scan direction. 
       SUMMARY 
       [0006]    Some embodiments of the claimed technology contemplate a method including: performing a first atomic force microscope (AFM) scan of a first region of a sample centered at a first position at a first angle to produce a first scan image, the first AFM scan including a first component scan at a first speed and a second component scan at a second speed; performing a second AFM scan of the first region of the sample at a second angle to produce a second scan image, the second AFM scan including performing a third component scan at the first speed and a fourth component scan at the second speed; and correcting a first error in the first scan image based on the second scan image to produce a corrected image output. 
         [0007]    Some embodiments of the claimed technology contemplate an atomic force microscopy (“AFM”) tool that is adapted to: perform a first scan of a sample at a first position at a first angle; perform a second scan of the sample at the first position at a second angle substantially perpendicular to the first angle; and correct a first error in the first scan based on the second scan. 
         [0008]    Some embodiments of the claimed technology contemplate a method including: performing a first atomic force microscope (AFM) raster scan of a sample at a first position at a first angle to produce a first scan image; performing a second AFM raster scan of the sample at a second position offset from the first position to produce a second scan image, wherein the second position is located within a portion of the sample that has a substantially level surface; and correcting a first error in the first scan image based on the second scan image. 
         [0009]    Some embodiments of the claimed technology contemplate an atomic force microscopy (“AFM”) tool adapted to: perform a first scan of a first region of a sample centered at a first position at a first angle to produce a first image having multiple scan lines in a first direction, the multiple scan lines each having a unique positioning in a second direction different than the first direction; perform a second scan of a second region of the sample centered at a second position offset from the first position to produce a second image, wherein the second position includes a flat reference point of the sample; and correct a first error in the first image based on the second image. 
         [0010]    Some embodiments of the claimed technology contemplate a method including: performing a global atomic force microscope (AFM) scan of a first selected area of a sample at a first position, the global AFM scan including a larger area of the sample than a local AFM scan; performing the local AFM scan of a second selected area of the sample at a second position, the second selected area including a smaller area within the first selected area; and correcting a slope error in the local AFM scan based on the global AFM scan. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]      FIG. 1  is a perspective view of an atomic force microscope probe positioned over a surface of a structure. 
           [0012]      FIG. 2  is a perspective view of a cavity transition feature for measuring with atomic force microscopy (AFM) techniques. 
           [0013]      FIG. 3A  is a schematic view of a scanning method for increasing the amount of data at an area of interest on a structure. 
           [0014]      FIG. 3B  is a schematic view of another scanning method for increasing the amount of data at an area of interest on a structure. 
           [0015]      FIG. 4A  is a two-dimensional plot of a raw scanned image profile of a cavity transition feature. 
           [0016]      FIG. 4B  is a two-dimensional plot of a tilted image profile of the cavity transition feature. 
           [0017]      FIG. 4C  is a three-dimensional plot of the tilted image profile shown in  FIG. 4B . 
           [0018]      FIG. 4D  is a three-dimensional plot of a true image profile of the cavity transition feature. 
           [0019]      FIG. 5A  is a schematic view of a first scan for use in correcting image curvature artifacts in an AFM scan. 
           [0020]      FIG. 5B  is a schematic view of a second scan for use in correcting image curvature artifacts in an AFM scan. 
           [0021]      FIG. 6  is a flow diagram showing a process for correcting image curvature artifacts in an AFM scan. 
           [0022]      FIG. 7  is a flow diagram showing steps for correcting image curvature artifacts using a master reference scan. 
       
    
    
     DETAILED DESCRIPTION 
       [0023]      FIG. 1  is a perspective view an atomic force microscope  10  positioned over a surface of structure  12 . Atomic force microscope  10  includes probe  11  having cantilever portion  14  and tip portion  16 . Atomic force microscope  10  also includes light source  18 , position sensitive detector  20 , and processor  22 . Light source  18  emits a beam  24  that is reflected by cantilever  14  and received by position sensitive detector  20 . Processor  22  receives signals from position sensitive detector  20  and provides signals to control movement of probe  11  relative to structure  12 . 
         [0024]    Structure  12  is the pole tip region of a magnetic recording system, including slider  26  carrying reader structure  28  and writer structure  30 . The atomic force microscopy (AFM) techniques described herein are useful for measuring and imaging feature characteristics of structure  12 , such as pole tip recession (PTR) features of reader structure  28  and writer structure  30 . It should be noted that structure  12  is shown merely for purposes of illustration, and the AFM techniques described herein are also useful for measuring and imaging nanometer and micrometer scale surface features of other structures. For example, the AFM techniques may also be used to measure feature characteristics in other magnetic recording device structures, such as a cavity transition feature as shown in  FIG. 2 . 
         [0025]    Atomic force microscope  10  measures physical characteristics or properties of structure  12 , such as feature dimensions and surface finish. Probe tip  16  is positioned in very close proximity (i.e., within picometers) to the surface of structure  12  to allow measurements of structure  12  over a small area. Probe tip  16  is moved relative to structure  12  using extremely precise positioning. For example, processor  22  may control motion of probe  11  such that probe tip moves along the surface of stationary structure  12 . Alternatively, processor  22  may control a device such as a tube scanner to move structure  12  while probe  11  remains stationary. As probe tip  16  moves over the surface of structure  12 , features on the surface of structure  12  cause cantilever  14  to bend in response to the force between probe tip  16  and structure  12 . 
         [0026]    A position detector measures the amount of deflection in cantilever  14 , which may be used to generate an image representation of structure  12 . In particular, light source  18  (e.g., a laser) reflects light beam  24  off of cantilever  14  to position sensitive detector  20 . Position sensitive detector  20  may include two side-by-side photodiodes such that the difference between the signals generated by the photodiodes indicates the position of light beam  24  on position sensitive detector  20 , and thus the angular deflection of cantilever  14 . Because the distance between cantilever  14  and position sensitive detector  20  is generally thousands of times the length of cantilever  14 , the motions of probe tip  16  are greatly magnified. 
         [0027]      FIG. 2  is a perspective view of slider  26  including air bearing surface (ABS)  42 , transition edge  43 , cavity transition  44 , and cavity  46 . Cavity transition  44 , which may be defined using ion milling techniques, has very small features varying from nanometer to micrometer scale sizes. Measurement of the features of cavity transition  44  is important in various aspects in the development of the device, including design improvement, device model validation, and device performance enhancement. For example, in a magnetic recording device, the measurement of cavity transition  44  is important for understanding flying performance of slider  26 . The AFM techniques described herein may be used to measure the properties of cavity transition feature  44 . 
       Variable Scan Data Density 
       [0028]    The lateral resolution of an image produced from a scan of a structure is defined by the scan area size and the number of pixels in the image. Conventionally, atomic force microscope  10  moves relative to the structure at a constant speed, and the position of probe  11  is periodically sampled by processor  22 . The resulting image has a uniform resolution across the entire scanned region. 
         [0029]    Some structures may include a region or area of interest having a target feature or characteristic of which a more detailed scan may be desired. For example, a detailed scan of cavity transition  44  of slider  40  shown in  FIG. 2  may be desirable for precise measurement of the dimensions and other characteristics of the transition profile. In order to increase the resolution in the area of interest, the number of pixels or data points in the area of interest may be increased. Because the number of pixels available for a given scan is often fixed, the resolution in the area of interest is thus increased at the expense of limited views of the areas surrounding the area of interest. However, it is also important to maintain the contextual details around the area of interest such that the relative sizes and positions of features within the area of interest are more easily determinable. 
         [0030]      FIG. 3A  is a schematic view of an approach for increasing the amount of data at an area of interest on a scanned structure while maintaining the contextual details of the surrounding areas. In  FIG. 3A , the scan area  50  of a structure is shown including area of interest  52 . Probe  11  moves around scan area  50  in scan pattern  54  during image acquisition in response to control signals from processor  22 . In particular, scan pattern  54  is programmed in processor  22 , and processor  22  controls movement of probe  11  relative to the structure in the programmed scan pattern  54 . As probe  11  is moved relative along scan pattern  54  within scan area  50 , data points or pixels  56  are sampled by processor  22 . That is, processor  22  periodically communicates with position sensitive detector  20  to receive information about the position of probe tip  16  relative to position sensitive detector  20 . This information is used by processor  22  to set locations of data points  56 , which correspond to the pixels in the image generated from data points  56  by processor  22 . The resulting image is representative of the structure includes graphical representations of the surface features and characteristics of the structure. 
         [0031]    Processor  22  samples data points  56  in the portions of scan area  50  outside of area of interest  52  as probe  11  moves along the y-direction relative to the structure. The data points  56  are separated by a distance d y1  in the y-direction and a distance d x1  in the x-direction in areas outside of area of interest  52 . In one embodiment, distance d x1  and distance d y1  are equal to provide a continuous lateral resolution in the portions of scan area  50  outside area of interest  52 . 
         [0032]    In order to increase the resolution at area of interest  52 , scan pattern  54  is programmed such that more data points  56  are sampled in area of interest  52  during the scan than in the portions surrounding area of interest  52 . The programmed location of area of interest  52  in scan pattern  54  may be determined during the scan based on known position information on the scanned structure, or based on surrounding feature characteristics sensed by probe tip  16 . When probe tip  16  is close to area of interest  52 , processor  22  reduces the distance between adjacent scan lines in the x-direction to distance d x2  to increase the density of data points  56  in the x-direction (i.e., probe tip  16  moves a smaller distance relative to the structure between adjacent scan lines). When probe tip  16  is in area of interest  52 , processor  22  increases the number of data points  56  sampled along each scan line (i.e., decreases the spacing between each data point  56  to d y2 ), which increases the data density in area of interest  52  in the y-direction. The resolution in the y-direction may be increased by, for example, increasing the rate at which processor  22  samples the position information of cantilever  14  from position sensitive decoder  20 , by adjusting the rate at which probe  11  is moved relative to the structure, or a combination of increasing the sample rate and decreasing the relative motion between probe  11  and the structure. In the embodiment shown, the resolution of the scan in area of interest  52  is three times that in the portions of scan area  50  surrounding area of interest  52 . 
         [0033]    Atomic force microscope  10  allows the density of data points  56  to be adjusted during the scanning process. From a single scan, the resulting image of the structure has a higher resolution in area of interest  52  than in the remainder of scan area  50 . This scan process not only preserves the contextual details in the areas around area of interest  52 , but also allows for greater throughput of scans and measurements of the structure since multiple scans are not required. 
         [0034]    It should be noted that scan pattern  54  is merely illustrative, and other scan patterns may be used for imaging a structure having different characteristics. For example, if a structure includes multiple areas of interest, the scan pattern may be programmed to increase the sampling rate or reduce the scan speed at the multiple areas of interest to increase the resolution in those areas. In addition, scan pattern  54  may include multiple levels of resolution within the same scan area  50 . 
         [0035]      FIG. 3B  is a schematic view of an alternative approach for increasing the amount of data at area of interest  52  while maintaining the contextual details of the surrounding areas in scan area  50 . In this embodiment, multiple scans having different resolutions are combined to produce an image profile having a higher resolution at the area of interest than in the surrounding areas of the scan area. 
         [0036]    A first scan is performed in a scan pattern  60  across the scan area  50  at a first data density. In particular, processor  22  samples data points  62  in scan area  50  as probe  11  moves in the x-direction and y-direction relative to the structure. The data points  62  are separated by a distance d x1  in the x-direction and a distance d y1  in the y-direction. In some embodiments, data points  62  are evenly distributed throughout scan area  50 . The resulting scan pattern  60  thus provides a relatively low resolution sampling of scan area  50 . 
         [0037]    A second scan is performed in a scan pattern  64  at a second data density higher than the first data density in area of interest  52 . In particular, processor  22  samples data points  66  in area of interest  52  as probe  11  moves in the x-direction and y-direction relative to the structure. The data points  66  of the second scan are separated by a distance d x2  in the x -direction and a distance d y2  in the y-direction. In order to increase the data density within area of interest  52 , distances d x2  and d y2  are smaller than the corresponding distances d x1  and d y1  of the first scan. In the embodiment shown, the data density of the second scan is three times greater than the data density of the first scan. 
         [0038]    The two scans are then integrated by aligning common data points  68  that are shared between scan pattern  60  and scan pattern  62 . For example, during the scanning process, processor  22  may record the location of each data point sampled. The scans would then be integrated together by matching locations of data points  62  in scan pattern  60  with data points  66  in scan pattern  64 . Processor  22  may also record topographical characteristics of each data point sampled, which would allow the scan patterns to be integrated by matching the topographical pattern of scan pattern  60  with that of scan pattern  62 . In any case, when the scans have been integrated, the resulting image of scan area  50  has a higher resolution in area of interest  52  than in the remainder of scan area  50 . 
         [0039]    It should be noted that scan patterns  60  and  64  are merely illustrative, and other scan patterns may be used for imaging a structure having different characteristics. For example, if a structure includes multiple areas of interest, additional scans may be performed to produce a scan pattern for each area of interest for ultimate integration into the contextual scan pattern. In addition, scan pattern  54  may include multiple levels of resolution within the same area of interest  52 . That is, multiple scans may be taken of area of interest  52  with varying data densities such that the most relevant or interesting portions of area of interest  52  have the highest data density, and the data density decreases with increasing distance from area of interest  52 . 
       Transition Profile Skew Correction 
       [0040]    When a structure (such as slider  26 ) is scanned by atomic force microscope  10 , it is held in position on a linear stage or other positioning device, such as in a tray, by a fixture, or with adhesive. However, due to positioning errors, the structure may not be precisely aligned with atomic force microscope  10  with respect to the contours of the programmed scan pattern. For example, the structure may be skewed in one direction relative to the scan pattern, or the structure may be tilted relative to the plane of the scan pattern. The image resulting from the misaligned scan thus may not represent the true profile of the structure, making an accurate measurement of the dimensions of the scanned structure and features of the structure difficult. In addition, even if the positioning of the structure relative to atomic force microscope  10  is perfect, variations in the components of atomic force microscope  10  (e.g., due to environmental conditions) may result in a misaligned image. 
         [0041]    For example, in a scan of slider  26  ( FIG. 2 ), the dimensions and characteristics of cavity transition  44  may be measured. Measurement of cavity transition  44  is important for understanding flying performance of slider  26 , as well as for device design improvement, model validation, and performance enhancement. Cavity transition  44  may be measured relative to another feature on slider  26 , such as ABS  42 , to allow for analysis of the shape of cavity edge  43  and cavity transition  44 . However, if the image of ABS  42  is skewed or tilted due to mispositioning of slider  26  or due to performance of atomic microscope  10 , characteristics of cavity transition  44  may be difficult to measure. 
         [0042]      FIGS. 4A-4D  show an approach to correcting the skew and tilt in an image based on a scan of slider  26  including cavity transition feature  44 . To minimize alignment artifacts caused by variations in the components of atomic force microscope  10  and environmental conditions, the scan was performed at a 0.2 Hz sampling rate with probe tip  16  having a radius of less than about 30 nm proximate to slider  26 . Each step described herein with regard to correcting the skew and tilt in the image may be performed by processor  22  or by a microprocessor based system external to atomic force microscope  10 . 
         [0043]      FIG. 4A  is a two-dimensional plot of a raw scanned image profile based on a scan of slider  26  including cavity transition  44  under the above conditions. The contour lines shown in the plot in  FIG. 4A  represent height changes in slider  26  relative to the z-axis. For context, transition edge  43  and cavity transition  44  are labeled in the image. As is shown, the image representative of slider  26  is skewed relative to the y-axis. In addition, the height change relative to the z-axis should be more pronounced at cavity transition  44 , and ABS  42  should include no contour lines because it should be co-planar with the x-axis and the y-axis. However, because few contour lines are shown at cavity transition  44  and several contour lines are shown around ABS  42 , the image is also tilted relative to the desired orientation (i.e., with ABS  42  parallel with the xy-plane). The correction of the tilt in the image will be described with regard to  FIGS. 4C and 4D . 
         [0044]    The skew in the two-dimensional view of slider  26  may be corrected by choosing a feature in the scan and re-orienting the image based on that feature. For example, a derivative map of the image (i.e., a plot of the derivative at every location in the image) shown in  FIG. 4A  may be generated to determine the locations of transition features (e.g., transition edge  43 ) in slider  26 . The transition feature may then be used as an alignment index for aligning the image within the two-dimensional view.  FIG. 4B  shows the two-dimensional image of slider  26  including cavity transition  44  after aligning the image relative to the x-axis and y-axis based on transition edge  43 . 
         [0045]      FIG. 4C  is a three-dimensional plot of the tilted image profile of slider  26 . As can be seen, while transition edge  43  is aligned with the y-axis, ABS  42  is tilted relative to the xy-plane. To facilitate measurement of cavity transition  44 , the image of slider  26  may be rotated relative to the xy-plane. While this rotation may be performed in Cartesian coordinates, the rotation is simplified by first converting each data point in the image of slider  26  to spherical coordinates. Thus, for each data point having coordinates (x, y, z), the corresponding spherical coordinates (R, θ, φ) are given by 
         [0000]    
       
         
           
             
               
                 
                   
                     R 
                     = 
                     
                       
                         
                           x 
                           2 
                         
                         + 
                         
                           y 
                           2 
                         
                         + 
                         
                           z 
                           2 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     θ 
                     = 
                     
                       arctan 
                        
                       
                         ( 
                         
                           y 
                           x 
                         
                         ) 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   and 
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     φ 
                     = 
                     
                       arctan 
                        
                       
                         ( 
                         
                           z 
                           
                             
                               
                                 x 
                                 2 
                               
                               + 
                               
                                 y 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    where R is distance from the origin to the data point, θ is the angle from the xz-plane to the point, and φ is the angle from the xy-plane to the point. 
         [0046]    The image of slider  26  may be rotated relative to the xy-plane to level ABS  42  by offsetting the angle φ by a correction angle α based on the slope of the tilted ABS  42 , 
         [0000]    
       
         
           
             
               
                 
                   
                     α 
                     = 
                     
                       arctan 
                        
                       
                         ( 
                         
                           
                              
                             y 
                           
                           
                              
                             x 
                           
                         
                         ) 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    where dy/dx is the slope of tilted ABS  42  relative to the xy-plane. To rotate the image of slider  26 , each data point may be offset by correction angle α and converted from spherical coordinate back to Cartesian coordinates. Thus, for each data point having coordinates (R, θ, φ−α), the corresponding Cartesian coordinates (x, y, z) are given by 
         [0000]        x=R  cos(φ−α)cos(θ)   (Equation 5),
 
         [0000]        y=R  cos(φ−α)sin(θ)   (Equation 6), and
 
         [0000]        z=R  sin(φ−α)   (Equation 7).
 
         [0000]    A plot of the three-dimensional image after rotation, which reflects the true profile of the slider  26  and cavity transition  44 , is shown in  FIG. 4D . 
       Artifact Curvature Correction 
       [0047]    During an AFM scan, probe tip  16  moves along the scanned surface faster in one direction than in the other direction. For example, as shown in  FIG. 3A , probe tip  16  samples the surface along scan lines that run along the y-direction. Thus, for each scan line, a group of data points  56  is sampled in the y-direction, while only a single data point is sampled in the x-direction. In the fast scan direction, probe tip  16  may take a few seconds or less to move from one end of the scan area to the other, while it may take as long as several minutes to move from one end of the scan area to the other in the slow scan direction. Without correction, environmental vibrations, machine drifting, and airflow along probe  11  can cause curvature artifacts in the image in the slow scan direction. 
         [0048]      FIGS. 5A and 5B  are schematic views of scans that may be used for correcting image curvature artifacts in an AFM scan.  FIG. 6  is a flow diagram showing a process for correcting image curvature artifacts in an AFM scan. The scan shown in  FIG. 5A  is performed within a scan area (step  100 ), and the scan shown in  FIG. 5B  is performed in the same scan area at 90° with respect to the first scan (step  102 ). For example, the scans shown may be performed within scan area  50  in  FIGS. 3A and 3B . The scan patterns shown in  FIG. 5A and 5B  are representative of any type of scan pattern having a fast scan direction and a slow scan direction, and are not necessarily representative of an actual scan pattern. 
         [0049]    In  FIG. 5A , the scan area can be represented by a matrix of data points a xy  (x, y=1˜n, where n is the periphery dimension of the scan area). For simplicity, the scan area shown is square, but the curvature artifact correction method described is also applicable to scan areas having other dimensions and characteristics. The fast scan direction is the x-direction and the slow scan direction is the y-direction. The fast scan direction has an average profile a avgx  and the slow scan direction has an average profile a avgy  (step  104 ), where 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       a 
                       avgx 
                     
                     = 
                     
                       
                         1 
                         n 
                       
                        
                       
                         
                           ∑ 
                           
                             y 
                             = 
                             1 
                           
                           n 
                         
                          
                         
                           a 
                           xy 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   and 
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     8 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       a 
                       avgy 
                     
                     = 
                     
                       
                         1 
                         n 
                       
                        
                       
                         
                           ∑ 
                           
                             x 
                             = 
                             1 
                           
                           n 
                         
                          
                         
                           a 
                           xy 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     9 
                   
                   ) 
                 
               
             
           
         
       
     
         [0050]    Similarly, in  FIG. 5B , the scan area can be represented by a matrix of data points b xy  (x, y=1˜n, where n is the periphery dimension of the scan area). In this scan, the fast scan direction is the y-direction and the slow scan direction is the x-direction. The fast scan direction has an average profile b avgy  and the slow scan direction has an average profile b avgx  (step  104 ), where 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       b 
                       avgx 
                     
                     = 
                     
                       
                         1 
                         n 
                       
                        
                       
                         
                           ∑ 
                           
                             y 
                             = 
                             1 
                           
                           n 
                         
                          
                         
                           b 
                           xy 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   and 
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     10 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     b 
                     avgy 
                   
                   = 
                   
                     
                       1 
                       n 
                     
                      
                     
                       
                         ∑ 
                         
                           x 
                           = 
                           1 
                         
                         n 
                       
                        
                       
                         
                           b 
                           xy 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     11 
                   
                   ) 
                 
               
             
           
         
       
     
         [0051]    The average profiles along the fast scan direction in the two scans, a avgx  and b avgy , represent the true profile of the structure, while the average profiles along the slow scan direction, a avgy  and b avgx  are a combination of the true profile of the structure and curvature artifacts due to drifting of atomic force microscope  10  and other environmental effects. It is difficult to separate the true shape and drifting artifacts in the slow scan direction. Thus, all information in the slow scan direction may be removed using zero order image flattening by setting the mean height of each scan line in the fast scan direction to zero (i.e., setting the average profile in the slow scan direction to zero) (step  106 ). The flattened images may thus be represented by a′ xy  and b′ xy , where a′ avgy =0 and b′ avgx =0, and 
         [0000]        a′   xy   =a   xy   −a   avgy    (Equation 12), and
 
         [0000]        b′   xy   =b   xy   −b   avgx    (Equation 13).
 
         [0052]    The correct profile along the slow scan direction for each scan can be obtained by setting the mean height of each fast scan line according to the average profile along the fast scan direction of the other scan (step  108 ). The corrected images may thus be represented by and, where 
         [0000]        a″   xy   =a′   xy   +b′   avgy    (Equation 14), and
 
         [0000]        b″   xy   =b′   xy   +a′   avgx    (Equation 15).
 
         [0053]    While the two images represented by a″ xy  and b″ xy  may be substantially identical, small differences may exist due to variations in the performance of atomic force microscope  10 . Thus, to obtain the most accurate representation of the true profile of the structure, 
         [0000]    
       
         
           
             
               
                 
                   
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                         ( 
                         
                           
                             a 
                             xy 
                             ″ 
                           
                           + 
                           
                             b 
                             xy 
                             ″ 
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   
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                     16 
                   
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       Master Reference Subtraction 
       [0054]    At micrometer-level scan lengths, bowing can occur in traditional tube scanner atomic force microscopes, which may also produce curvature in the resulting image. The amplitude and shape of the bowing vary between atomic force microscopes, and may change with aging, temperature, and humidity. Positional offsets between scans of the same surface in the same scan area may also vary the curvature in the corresponding image. 
         [0055]    To avoid the contribution of bowing to measurement error, a reference scan may be taken on a flat surface with the same scan settings (e.g., scan size and offsets) of a regular scan. The reference scan is subsequently subtracted from the regular scan to obtain an image without curvature due to the bowing effect. However, any real curvature in the surface of the reference scan will be added to the measurement results. In addition, scan defects, irregular scan lines, and particle contamination in the reference scan may add error to the measurement results. 
         [0056]      FIG. 7  is a flow diagram showing steps for correcting image curvature artifacts due to the bowing effect using a master reference scan. A master reference scan is generated with atomic force microscope  10  by scanning a flat surface (step  120 ). For example, the flat air bearing surface of slider  26  in  FIG. 1  may be used to generate the master reference scan. The master reference scan is performed under conditions so as to minimize defects in the reference scan. In particular, atomic force microscope  10  is used in environmental conditions that minimize bowing effect and prevent irregular scan lines, and the flat surface is chosen so as to have a minimal amount of particle contamination. By performing a single master reference scan under favorable conditions, the possibility of variations between multiple reference scans due to differing scan conditions is eliminated. 
         [0057]    The structure is then placed on a linear stage and moved relative to atomic force microscope  10  with closed loop positioning (step  122 ). In particular, sensors may be positioned relative to or integrated with the structure to provide signals to processor  22  related to the position of the structure relative to atomic force microscope  10 . These signals may then be used by processor  22  to assure that the structure is accurately positioned relative to atomic force microscope  10  in accordance with the programmed scan pattern. 
         [0058]    After the structure has been scanned in accordance with the programmed pattern, the master reference scan is subtracted from the structure scan to correct curvature artifacts caused by the bowing effect in probe tip  16  (step  124 ). In other words, because the bowing effect will cause the same artifacts in the master reference scan and the structure scan, the curvature in the structure scan can be substantially eliminated by subtracting the master reference scan from the structure scan. Because the reference scan does not need to be performed after each structure scan, throughput of the scan process is improved. In addition, the closed loop position feedback on the linear stage assures that the scan pattern is performed in the correct location in the scan area, thus limiting curvature artifacts caused by positional offsets in the scan pattern. 
         [0059]    In summary, a topographic profile of a structure is generated using atomic force microscopy. The structure is scanned such that an area of interest of the structure is scanned at a higher resolution than portions of the structure outside of the area of interest. An image of the structure is then generated based on the scan. To correct skew and tilt of the image, a first feature of the image is aligned with a first axis of a coordinate system. The image is then rotated to align a second feature of the image with a second axis of the coordinate system. The structure scan may be performed in a single scan or by integrating multiple scans of the structure at different levels of resolution. The resulting image of the structure has a higher resolution in the area of interest than in the remainder of scan area. This scan process preserves the contextual details in the areas around the area of interest. 
         [0060]    Although the present invention has been described with reference to preferred embodiments, workers skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention.