Patent Publication Number: US-2023147149-A1

Title: Pattern matching method

Description:
TECHNICAL FIELD 
     The present invention relates to a method of matching a pattern formed on a surface of a workpiece, such as a wafer or a glass substrate, used for manufacturing semiconductor devices with a CAD pattern created from pattern design data. 
     BACKGROUND ART 
     A die-to-database method is a pattern matching method for matching a pattern formed on a surface of a workpiece, such as a wafer or a glass substrate, with a CAD pattern created from pattern design data. More specifically, the die-to-database method includes obtaining coordinates of an area to be inspected from design data, moving a stage on which the workpiece is placed to the coordinates, generating an image of a pattern on the workpiece by electron-beam irradiation, superimposing the image and a CAD pattern created from the design data, producing a gray-level profile of the image within a set range starting from an edge of the CAD pattern, determining an edge of the pattern on the image based on the gray-level profile, and determining a matching position that minimize a bias value between the determined edge position and the edge of the corresponding CAD pattern (see, for example, Patent Document 1). 
     CITATION LIST 
     Patent Literature 
     
         
         Patent document 1: Japanese laid-open patent publication No. 5-324836 
         Patent document 2: Japanese laid-open patent publication No. 2012-519391 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     Double patterning, which is capable of forming a highly integrated circuit having a narrower pattern interval, has recently been attracting attention. The double patterning is a technique of forming a first pattern and a second pattern separately, which are arranged alternately, in two steps. However, in certain areas, a variation in pattern dimension (CD, or Critical Dimension) is likely to occur. Therefore, in such an area, it is necessary to acquire accurate statistical data of CD (Critical Dimension) in order to optimize the process and monitor the process fluctuation. 
     Patent Document 2 discloses a technique of measuring CD of a pattern 1 and a pattern 2 using only features of a pattern profile of a SEM image. However, with this technique, it is difficult to analyze a problem in design or process because information that can be added to design information other than the measured value of CD cannot be obtained. 
     The conventional die-to-database method can realize operations of directly specifying an area that is expected to be greatly affected by process fluctuation of the double patterning on the CAD coordinate system in the design data to obtain CD statistical data, and evaluating a CD variation in a memory cell. Furthermore, the die-to-database method can measure the CD while correcting effects of magnification change and rotation of a SEM image using the design data, and can therefore obtain a difference between the CDs and a large amount of accurate design values. In addition, since additional information, such as peripheral pattern information, can be obtained from the design data, the die-to-database method is considered to be most suitable for CD measurement data analysis for the purpose of photomasks and changing of process parameters. 
     Usually, at an end of a memory cell, a pattern is easily deformed greatly due to influence of the light proximity effect, etc. Therefore, in order to acquire the data of the CD fluctuation caused by the double patterning, it is ideal to perform the CD measurement at the central part of the memory cell. However, in the central part of the memory cell, it is difficult to judge whether the pattern matching is correct or not. For example, as shown in  FIG.  16   , although repeating patterns  505  on a SEM image  500  match CAD patterns  510  on design data, a pitch shift may occur. 
     Therefore, the present invention provides a pattern matching method capable of achieving correct matching between a pattern formed by multi-patterning and a corresponding CAD pattern. 
     Solution to Problem 
     In an embodiment, there is provided a pattern matching method comprising: generating an image of a first region in a pattern region containing patterns formed by multi-patterning; performing first matching between a plurality of reference patterns on the image of the first region and a plurality of first CAD patterns that have been classified in advance into a first group and a second group according to layer information; classifying the plurality of reference patterns into the first group and the second group according to the layer classification of the first CAD patterns; measuring widths of the plurality of reference patterns belonging to the first group and widths of the plurality of reference patterns belonging to the second group; determining a first integrated value by integrating measured values of the widths of the plurality of reference patterns belonging to the first group; determining a second integrated value by integrating measured values of the widths of the plurality of reference patterns belonging to the second group; determining a magnitude relationship between the first integrated value and the second integrated value; generating an image of a second region in the pattern region; performing second matching between a plurality of patterns on the image of the second region and a plurality of second CAD patterns that have been classified in advance into a first group and a second group according to layer information; classifying the plurality of patterns on the image of the second region into the first group and the second group according to the layer classification of the second CAD patterns; measuring widths of the plurality of patterns belonging to the first group and widths of the plurality of patterns belonging to the second group: determining a third integrated value by integrating measured values of the widths of the plurality of patterns belonging to the first group; determining a fourth integrated value by integrating measured values of the widths of the plurality of patterns belonging to the second group; determining a magnitude relationship between the third integrated value and the fourth integrated value; determining that the second matching has been performed correctly when the magnitude relationship between the third integrated value and the fourth integrated value coincides with the magnitude relationship between the first integrated value and the second integrated value. 
     In an embodiment, the first region is an edge region including an edge of the pattern region, and the second region is within the pattern region and is located more inwardly than the first region. 
     In an embodiment, the patterns formed by the multi-patterning are repeating patterns. 
     In an embodiment, the pattern matching method further comprises: shifting the plurality of patterns on the image of the second region relative to the plurality of second CAD patterns by one pitch when the magnitude relationship between the third integrated value and the fourth integrated value does not coincide with the magnitude relationship between the first integrated value and the second integrated value; and then performing the second matching again. 
     In an embodiment, an absolute value of a difference between the first integrated value and the second integrated value and an absolute value of a difference between the third integrated value and the fourth integrated value are larger than a predetermined value. 
     In an embodiment, there is provided a pattern matching method comprising: generating an image of a first region in a pattern region containing patterns formed by multi-patterning; performing first matching between a plurality of reference patterns on the image of the first region and a plurality of first CAD patterns that have been classified in advance into a first group and a second group according to layer information; classifying the plurality of reference patterns into the first group and the second group according to the layer classification of the first CAD patterns; calculating slopes of brightness profiles of edges of the plurality of reference patterns belonging to the first group and slopes of brightness profiles of edges of the plurality of reference patterns belonging to the second group; determining a first integrated value by integrating calculated values of the slopes of the brightness profiles of the edges of the plurality of reference patterns belonging to the first group; determining a second integrated value by integrating calculated values of the slopes of the brightness profiles of the edges of the plurality of reference patterns belonging to the second group; determining a magnitude relationship between the first integrated value and the second integrated value; generating an image of a second region in the pattern region; performing second matching between a plurality of patterns on the image of the second region and a plurality of second CAD patterns that have been classified in advance into a first group and a second group according to layer information; classifying the plurality of patterns on the image of the second region into the first group and the second group according to the layer classification of the second CAD patterns; calculating slopes of brightness profiles of edges of the plurality of patterns belonging to the first group and slopes of brightness profiles of edges of the plurality of patterns belonging to the second group; determining a third integrated value by integrating calculated values of the slopes of the brightness profiles of the edges of the plurality of patterns belonging to the first group; determining a fourth integrated value by integrating calculated values of the slopes of the brightness profiles of the edges of the plurality of patterns belonging to the second group; determining a magnitude relationship between the third integrated value and the fourth integrated value: determining that the second matching has been performed correctly when the magnitude relationship between the third integrated value and the fourth integrated value coincides with the magnitude relationship between the first integrated value and the second integrated value. 
     In an embodiment, the first region is an edge region including an edge of the pattern region, and the second region is within the pattern region and is located more inwardly than the first region. 
     In an embodiment, the patterns formed by the multi-patterning are repeating patterns. 
     In an embodiment, the pattern matching method further comprises: shifting the plurality of patterns on the image of the second region relative to the plurality of second CAD patterns by one pitch when the magnitude relationship between the third integrated value and the fourth integrated value does not coincide with the magnitude relationship between the first integrated value and the second integrated value; and then performing the second matching again. 
     In an embodiment, an absolute value of a difference between the first integrated value and the second integrated value and an absolute value of a difference between the third integrated value and the fourth integrated value are larger than a predetermined value. 
     Advantageous Effects of Invention 
     According to the present invention, accurate pattern matching in the second region can be guaranteed by referring to the magnitude relationship of the pattern width in the first region. In particular, according to the present invention, the measured value of the pattern width can be used for optimizing the process parameters. In addition, it is possible to monitor the pattern width in an area where the process margin is small. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       [ FIG.  1   ]  FIG.  1    is a schematic diagram showing an embodiment of an image generating apparatus. 
       [ FIG.  2   ]  FIG.  2    is a schematic diagram showing a pattern region formed on a wafer 
       [ FIG.  3   ]  FIG.  3    is a schematic diagram showing an example of an image of a first region. 
       [ FIG.  4   ]  FIG.  4    is a diagram explaining first matching of a plurality of reference patterns on the image of the first region and a plurality of corresponding CAD patterns. 
       [ FIG.  5   ]  FIG.  5    is a diagram illustrating a process of classifying a plurality of reference patterns on an SEM image into a first group and a second group. 
       [ FIG.  6   ]  FIG.  6    is a graph showing a relationship between the number of integrated widths of reference patterns and first and second integrated values. 
       [ FIG.  7   ]  FIG.  7    is a schematic diagram showing another example of patterns in the first region. 
       [ FIG.  8   ]  FIG.  8    is a schematic diagram showing an example of an image of a second region. 
       [ FIG.  9   ]  FIG.  9    is a diagram illustrating second matching between a plurality of patterns on the image of the second region and a plurality of corresponding CAD patterns. 
       [ FIG.  10   ]  FIG.  10    is a diagram illustrating a process of classifying a plurality of patterns on an SEM image into a first group and a second group. 
       [ FIG.  11   ]  FIG.  11    is a flowchart explaining an embodiment of a pattern matching method. 
       [ FIG.  12   ]  FIG.  12    is a schematic diagram showing another example of an image of a first region. 
       [ FIG.  13   ]  FIG.  13    is a schematic diagram showing another example of an image in a second region. 
       [ FIG.  14   ]  FIG.  14    is a diagram showing an example of a brightness profile of a pattern on an image. 
       [ FIG.  15   ]  FIG.  15    is a flowchart explaining an embodiment of a pattern matching method. 
       [ FIG.  16   ]  FIG.  16    is a diagram explaining a problem that may occur in conventional pattern matching. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, embodiments of the present invention will be described with reference to the drawings. 
       FIG.  1    is a schematic diagram showing an embodiment of an image generation apparatus. As shown in  FIG.  1   , the image generating apparatus includes a scanning electron microscope  50  and an arithmetic system  150 . The scanning electron microscope  50  is coupled to the arithmetic system  150 , and operations of the scanning electron microscope  50  are controlled by the arithmetic system  150 . 
     The arithmetic system  150  includes a memory  162  storing a database  161  and programs therein, a processor  163  configured to perform arithmetic operations according to instructions included in the programs, and a display screen  165  configured to display an image and a GUI (graphical user interface). The processor  163  includes a CPU (central processing unit) or a GPU (graphic processing unit) that performs arithmetic operations according to instructions included in the programs stored in the memory  162 . The memory  162  includes a main memory (e.g., random access memory) to which the processor  163  is accessible and an auxiliary memory (e.g., hard disk drive or solid state drive) for storing data and the programs. 
     The arithmetic system  150  includes at least one computer. For example, the arithmetic system  150  may be an edge server coupled to the scanning electron microscope  50  by a communication line, or may be a cloud server coupled to the scanning electron microscope  50  by a communication network, such as the Internet or a local network. The arithmetic system  150  may be a fog computing device (gateway, fog server, router, etc.) installed in a network coupled to the scanning electron microscope  50 . The arithmetic system  150  may be a combination of a plurality of servers. For example, the arithmetic system  150  may be a combination of an edge server and a cloud server coupled to each other by a communication network, such as the Internet or a local network. In another example, the arithmetic system  150  may include a plurality of servers (computers) that are not coupled by a network. 
     The scanning electron microscope  50  includes an electron gun  111  configured to emit an electron beam composed of primary electrons (charged particles), a converging lens  112  configured to converge the electron beam emitted by the electron gun  111 , and an X deflector  113  configured to deflect the electron beam in an X direction, a Y deflector  114  configured to deflect the electron beam in a Y direction, and an objective lens  115  configured to focus the electron beam on a wafer  124 , which is an example of a workpiece. Configuration of the electron gun  111  is not particularly limited. For example, a field-emitter type electron gun, a semiconductor-photocathode type electron gun, etc. can be used as the electron gun  111 . 
     The converging lens  112  and the objective lens  115  are coupled to a lens controller  116 , and operations of the converging lens  112  and the objective lens  115  are controlled by the lens controller  116 . The lens controller  116  is coupled to the arithmetic system  150 . The X deflector  113  and the Y deflector  114  are coupled to a deflection controller  117 , and deflecting operations of the X deflector  113  and the Y deflector  114  are controlled by the deflection controller  117 . The deflection controller  117  is also coupled to the arithmetic system  150  as well. A secondary electron detector  130  and a backscattered electron detector  131  are coupled to an image acquisition device  118 . The image acquisition device  118  is configured to convert output signals of the secondary electron detector  130  and the backscattered electron detector  131  into image(s). The image acquisition device  118  is also coupled to the arithmetic system  150  as well. 
     A specimen stage  121  arranged in a specimen chamber  120  is coupled to a stage controller  122 , and a position of the specimen stage  121  is controlled by the stage controller  122 . The stage controller  122  is coupled to the arithmetic system  150 . A transfer device  140  for transporting the wafer  124  onto the specimen stage  121  in the specimen chamber  120  is also coupled to the arithmetic system  150 . 
     The electron beam emitted by the electron gun  111  is converged by the converging lens  112  and then focused by the objective lens  115  on a surface of the wafer  124  while the electron beam is deflected by the X deflector  113  and the Y deflector  114 . When the wafer  124  is irradiated with the primary electrons of the electron beam, the secondary electrons and backscattered electrons are emitted from the wafer  124 . The secondary electrons are detected by the secondary electron detector  130 , and the backscattered electrons are detected by the backscattered electron detector  131 . Signals of the detected secondary electrons and signals of the detected backscattered electrons are input to the image acquisition device  118  and converted into image(s). The image is transmitted to the arithmetic system  150 . 
     Design data of patterns formed on the wafer  124  is stored in advance in the memory  162 . The design data includes pattern design information, such as coordinates of vertices of each pattern formed on the wafer  124 , a position, a shape and a size of each pattern, and the number of a layer to which each pattern belongs. The database  161  is constructed in the memory  162 . The design data of patterns is stored in advance in the database  161 . The arithmetic system  150  can read out the design data of each pattern from the database  161  stored in the memory  162 . 
     Next, an embodiment of a method of matching between a pattern on an image generated by the scanning electron microscope  50  and a corresponding CAD pattern on the design data will be described. In the following descriptions, an image generated by the scanning electron microscope  50  may be referred to as a SEM image. The pattern of the wafer  124  has been manufactured based on the design data (also referred to as CAD data). CAD is an abbreviation for computer-aided design. 
     The design data includes design information of the pattern formed on the wafer  124 , and specifically, includes design information, such as coordinates of vertices of the pattern, a position, a shape and a size of the pattern, and the number of a layer to which the pattern belongs. The CAD pattern in the design data is a virtual pattern defined by design information of a pattern included in the design data. In the following description, a pattern already formed on the wafer  124  may be referred to as a real pattern. 
       FIG.  2    is a schematic view showing a pattern region  200  formed on the wafer  124 . Patterns formed in the pattern region  200  are real patterns formed by multi-patterning, such as double patterning or quadruple patterning. In the present embodiment, the real patterns formed in the pattern region  200  are line-and-space patterns which are an example of repeating patterns. An example of the pattern region  200  is a memory cell. 
     First, an image of a first region  201  in the pattern region  200  including patterns formed by the multi-patterning is generated by the scanning electron microscope  50 . After the image of the first region  201  is generated, an image of a second region  202 , which is different from the first region  201 , is generated by the scanning electron microscope  50 . The second region  202  is a region within the pattern region  200 , as well as the first region  201 . Sizes of the first region  201  and the second region  202  are not particularly limited, but are, for example, a size of a field of view (FOV) of the scanning electron microscope  50  or a size of a combination of a plurality of fields of view of the scanning electron microscope  50 . 
     The first region  201  is a region including a distinctive pattern whose position can be specified in order to ensure that subsequent first matching and second matching can be performed correctly. In the present embodiment, the first region  201  is an edge region including an edge of the pattern region  200 . The second region  202  is located within the pattern region  200  and located more inwardly than the first region  201 . 
       FIG.  3    is a schematic diagram showing an example of an image  205  of the first region  201 . As shown in  FIG.  3   , patterns in the first region  201  include two sets of patterns  210 A and  210 B individually formed by the double patterning. These patterns  210 A and  210 B are arranged alternately. The patterns  210 A and  210 B in the first region  201  are repeating patterns including the edge of the pattern region  200 . Specifically, an outermost pattern  210 A is a distinctive pattern whose position can be specified. Therefore, although these patterns  210 A and  210 B are repeating patterns, accurate pattern matching is ensured. In the following description, the patterns  210 A and  210 B on the image  205  of the first region  201  are referred to as reference patterns. The number of reference patterns  210 A and  210 B included in the first region  201  is not limited to the example shown in  FIG.  3   . 
     As shown in  FIG.  3   ,the reference patterns  210 A and  210 B do not include a pattern end. Specifically, each of the reference patterns  210 A and  210 B extends across the entire first region  201 . The reason why the reference patterns  210 A and  210 B do not include the pattern end is that pattern shrinkage is likely to occur at the pattern end and a correct pattern width may not be measured. The size and position of the first region  201  can be set manually or automatically. A plurality of first regions  201  may be provided. 
     Next, as shown in  FIG.  4   , the arithmetic system  150  performs the first matching between the plurality of reference patterns  210 A and  210 B on the image  205  of the first region  201  and a plurality of corresponding CAD patterns  215 A and  215 B. The CAD patterns  215 A and  215 B are classified in advance into a first group and a second group according to layer information of these CAD patterns. In the example shown in  FIG.  4   , the CAD patterns  215 A are classified into the first group, and the CAD patterns  215 B are classified into the second group. The CAD patterns  215 A and  215 B are created by the arithmetic system  150  based on the design data of the reference patterns  210 A and  210 B. 
     The first matching is performed as follows. The arithmetic system  150   superimposes one of the SEM image  205  and the CAD patterns  215 A and  215 B on another, and produces gray-level profiles of the SEM image  205  within a range set starting from the edges of the CAD patterns  215 A and  215 B created from the design data. Then, the arithmetic system  150  determines edges of the reference patterns  210 A and  210 B on the SEM image  205  from the gray-level profiles, and determines a matching position that can minimize bias values between positions of the determined edges and positions of the edges of the corresponding CAD patterns  215 A and  215 B. Each of the bias values is an index value indicating an amount of deviation (or a distance) between an edge determined from each gray-level profile and each edge of the corresponding CAD patterns  215 A and  215 B. The bias values are calculated for all edges in the SEM image  205 . 
     As shown in  FIG.  5   , the arithmetic system  150  classifies the plurality of reference patterns  210 A and  210 B on the SEM image  205  into the first group and the second group according to the layer classification of the CAD patterns  215 A and  215 B. The layer classification of CAD patterns  215 A and  215 B is predetermined based on a pattern-formation order of the multi-patterning (double patterning in this embodiment). In the example shown in  FIG.  5   , the arithmetic system  150  classifies the odd-numbered reference patterns  210 A into the first group and the even-numbered reference patterns  210 B into the second group. Depending on the layer classification of the CAD patterns  215 A and  215 B, the arithmetic system  150  may classify the even-numbered reference patterns  210 B into the first group and the odd-numbered reference patterns  210 A into the second group. 
     Next, the arithmetic system  150  measures widths of the plurality of reference patterns  210 A belonging to the first group and widths of the plurality of reference patterns  210 B belonging to the second group. The measured values of the widths of the reference patterns  210 A and  210 B are CD (Critical Dimension) values of the reference patterns  210 A and  210 B. A process of measuring the widths of the reference patterns  210 A and  210 B is not particularly limited. In one example, the arithmetic system  150  may calculate the sum of an average of the bias values of each reference pattern and a width of the corresponding CAD pattern, and may use the calculated sum as a measured value of the width (i.e., a CD value). In another example, the arithmetic system  150  may measure a distance between peaks of a brightness profile of each reference pattern. In general, a brightness of an edge of a pattern on an image may be higher than those of other parts of the pattern. Therefore, the distance between the peaks of the brightness profile can be used as a measured value of the width of the reference pattern. 
     The arithmetic system  150  determines a first integrated value by integrating the measured values of the widths of the plurality of reference patterns  210 A belonging to the first group, and determines a second integrated value by integrating the measured values of the widths of the plurality of reference patterns  210 B belonging to the second group. Further, the arithmetic system  150  compares the first integrated value and the second integrated value, and determines a magnitude relationship between the first integrated value and the second integrated value. Specifically, the arithmetic system  150  determines which of the first integrated value and the second integrated value is larger than the other. The arithmetic system  150  stores the determined magnitude relationship between the first integrated value and the second integrated value in the memory  162 . 
     The reference patterns  210 A belonging to the first group and the reference patterns  210 B belonging to the second group are real patterns formed by individual steps in the multi-patterning. Usually, in the multi-patterning, widths of real patterns formed by individual steps are slightly different. Therefore, the widths of the reference patterns  210 A belonging to the first group and the widths of the reference patterns  210 B belonging to the second group are also slightly different. The first integrated value calculated for the first group and the second integrated value calculated for the second group reflect the widths of the reference patterns  210 A and  210 B belonging to these two groups. 
       FIG.  6    is a graph showing a relationship between the number of integrated widths of the reference patterns and the first and second integrated values. As can be seen from  FIG.  6   , as the number of integrated widths of the reference patterns  210 A and  210 B increases, the difference between the first integrated value and the second integrated value increases. The difference between the width of each reference pattern  210 A belonging to the first group and the width of each reference pattern  210 B belonging to the second group is extremely small, but there is a significant difference between the first integrated value and the second integrated value. Therefore, the arithmetic system  150  can determine either the width of the reference pattern  210 A belonging to the first group or the width of the reference pattern  210 B belonging to the second group is larger than the other based on the difference between the first integrated value and the second integrated value. In the example shown in  FIG.  6   , the magnitude relationship between the first integrated value and the second integrated value is such that the first integrated value is larger than the second integrated value. 
     In order to determine the magnitude relationship between the first integrated value and the second integrated value, it is desirable that there is a significant difference between the first integrated value and the second integrated value. From this point of view, the number of integrated reference patterns may be a preset number or more. Alternatively, the arithmetic system  150  may integrate the measured values of the widths of the plurality of reference patterns  210 A belonging to the first group and integrate the measured values of the widths of the plurality of reference patterns  210 B belonging to the second group until an absolute value of the difference between the first integrated value and the second integrated value exceeds a predetermined value. In order to increase the number of reference patterns existing in the first region  201 , the field of view (FOV) may be increased or a plurality of fields of view may be combined. 
     In general, an outermost pattern in the pattern region  200  may have a width significantly different from other patterns due to the influence of a light proximity effect etc., as shown in  FIG.  7   . Therefore, the arithmetic system  150  may calculate the first integrated value and the second integrated value without using at least one reference pattern at the outermost side in the first region  201 . In one embodiment, the arithmetic system  150  may exclude reference pattern(s) having a width exceeding a threshold value from the plurality of reference patterns  210 A and  210 B in the first region  201 , and then calculate the first integrated value and the second integrated value. 
     The arithmetic system  150  calculates integrated values for patterns in the second region  202  shown in  FIG.  2    in the same manner as the reference patterns  210 A and  210 B in the first region  201 .  FIG.  8    is a schematic diagram showing an example of an image  225  of the second region  202 . As shown in  FIG.  8   , patterns in the second region  202  include two sets of patterns  220 A and  220 B individually formed by the double patterning, as well as the reference patterns  210 A and  210 B in the first region  201 . These patterns  220 A and  220 B are arranged alternately. 
     The patterns  220 A and  220 B in the second region  202  are repeating patterns that do not include an edge of the pattern region  200  (see  FIG.  2   ). In one example, the second region  202  is located at the center of the pattern region  200  shown in  FIG.  2   . As can be seen from  FIG.  8   , the patterns  220 A and  220 B in the second region  202  extend across the entire second region  202  and do not have a distinctive shape that enables a position to be specified. The size and position of the second region  202  can be set manually or automatically. The number of patterns  220 A and  220 B included in the second region  202  is not limited to the example shown in  FIG.  8   . 
     As shown in  FIG.  9   , the arithmetic system  150  performs a second matching between the plurality of patterns  220 A and  220 B on the image  225  of the second region  202  and a plurality of corresponding CAD patterns  230 A and  230 B. The CAD patterns  230 A and  230 B are classified in advance into a first group and a second group according to layer information of these CAD patterns. In the example shown in  FIG.  9   , the CAD patterns  230 A are classified into the first group, and the CAD patterns  230 B are classified into the second group. Since the second matching is performed in the same manner as the first matching described above, the repetitive descriptions thereof will be omitted. 
     As shown in  FIG.  10   , the arithmetic system  150  classifies the plurality of patterns  220 A and  220 B on the SEM image  225  into the first group and the second group according to the layer classification of the CAD patterns  230 A and  230 B. In the present embodiment, the arithmetic system  150  classifies the odd-numbered patterns  220 A into the first group and the even-numbered patterns  220 B into the second group. Then, the arithmetic system  150  measures widths of the plurality of patterns  220 A belonging to the first group and widths of the plurality of patterns  220 B belonging to the second group. 
     The arithmetic system  150  determines a third integrated value by integrating the measured values of the widths of the plurality of patterns  220 A belonging to the first group, and determines a fourth integrated value by integrating the measured values of the widths of the plurality of patterns  220 B belonging to the second group. Furthermore, the arithmetic system  150  compares the third integrated value and the fourth integrated value, and determines a magnitude relationship between the third integrated value and the fourth integrated value. Specifically, the arithmetic system  150  determines which of the third integrated value and the fourth integrated value is larger than the other. The arithmetic system  150  stores the determined magnitude relationship between the third integrated value and the fourth integrated value in the memory  162 . 
     Similar to the first integrated value and the second integrated value, the number of integrated patterns may be a preset number or more. Alternatively, the arithmetic system  150  may integrate the measured values of the widths of the plurality of patterns  220 A belonging to the first group and integrate the measured values of the widths of the plurality of patterns  220 B belonging to the second group until an absolute value of the difference between the third integrated value and the fourth integrated value exceeds a predetermined value. In order to increase the number of patterns existing in the second region  202 , the field of view (FOV) may be increased or a plurality of fields of view may be combined. 
     Next, the arithmetic system  150  determines that the second matching is performed correctly when the magnitude relationship between the third integrated value and the fourth integrated value matches the magnitude relationship between the first integrated value and the second integrated value. In the example shown in  FIG.  6   , since the first integrated value is larger than the second integrated value, the arithmetic system  150  determines that the magnitude relationship between the third integrated value and the fourth integrated value coincides with the magnitude relationship between the first integrated value and the second integrated value when the third integrated value is larger than the fourth integrated value. 
     The arithmetic system  150  displays on the display screen  165  the first integrated value, the second integrated value, the third integrated value, the fourth integrated value, the difference between the first integrated value and the second integrated value, the difference between the third integrated value and the fourth integrated value, etc. An operator can visually confirm the results displayed on the display screen  165 . 
     When the magnitude relationship between the third integrated value and the fourth integrated value does not coincide with the magnitude relationship between the first integrated value and the second integrated value (e.g., when the third integrated value is smaller than the fourth integrated value), it is presumed that the third integrated value is an integrated value of the widths of the plurality of patterns belonging to the second group, and the fourth integrated value is an integrated value of the widths of the plurality of patterns belonging to the first group. Therefore, in this case, the arithmetic system  150  shifts the plurality of patterns  220 A and  220 B on the image  225  of the second region  202  by one pitch relative to the plurality of corresponding CAD patterns  230 A and  230 B, and then performs the second matching again. 
     According to the present embodiment, accurate pattern matching in the second region  202  can be ensured with reference to the magnitude relationship of the pattern widths in the first region  201 . In particular, according to the present embodiment, the measured values of the pattern widths can be used for optimizing process parameters. In addition, it is possible to monitor pattern widths in a region where a process margin is small. 
       FIG.  11    is a flowchart illustrating an embodiment of the pattern matching method. 
     In step  1 , the scanning electron microscope  50  generates the image  205  of the first region  201  in the pattern region  200  including the repeating patterns (see  FIG.  3   ). The image  205  of the first region  201  is sent to the arithmetic system  150 . 
     In step  2 , the arithmetic system  150  performs the first matching between the reference patterns  210 A,  210 B on the image  205  of the first region  201  and the CAD patterns  215 A,  215 B that have been classified in advance into a first group and a second group based on the layer information (see  FIG.  4   ). 
     In step  3 , the arithmetic system  150  classifies the plurality of reference patterns  210 A and  210 B into the first group and the second group according to the layer classification of the CAD patterns  215 A and  215 B (see  FIG.  5   ). 
     In step  4 , the arithmetic system  150  measures the widths of the plurality of reference patterns  210 A belonging to the first group and the widths of the plurality of reference patterns  210 B belonging to the second group. 
     In step  5 , the arithmetic system  150  integrates the measured values of the widths of the plurality of reference patterns  210 A belonging to the first group to determine the first integrated value, and integrates the measured values of the widths of the plurality of reference patterns  210 B belonging to the second group to determine the second integrated value. 
     In step  6 , the arithmetic system  150  determines the magnitude relationship between the first integrated value and the second integrated value. Specifically, the arithmetic system  150  determines which of the first integrated value and the second integrated value is larger than the other. 
     In step  7 , the scanning electron microscope  50  generates the image  225  of the second region  202  in the pattern region  200  (see  FIG.  8   ). The image  225  of the second region  202  is sent to the arithmetic system  150 . 
     In step  8 , the arithmetic system  150  performs the second matching between the patterns  220 A,  220 B on the image  225  of the second region  202  and the CAD patterns  230 A,  230 B that have been classified in advance into a first group and a second group based on the layer information (see  FIG.  9   ). 
     In step  9 , the arithmetic system  150  classifies the plurality of patterns  220 A and  220 B on the image  225  of the second region  202  into the first group and the second group according to the layer classification of the CAD patterns  230 A and  230 B (see  FIG.  10   ). 
     In step  10 , the arithmetic system  150  measures the widths of the plurality of patterns  220 A belonging to the first group and the widths of the plurality of patterns  220 B  belonging to the second group. 
     In step  11 , the arithmetic system  150  integrates the measured values of the widths of the plurality of patterns  220 A belonging to the first group to determine the third integrated value, and integrates the measured values of the widths of the plurality of patterns  220 B belonging to the second group to determine the fourth integrated value. 
     In step  12 , the arithmetic system  150  determines the magnitude relationship between the third integrated value and the fourth integrated value. 
     In step  13 , the arithmetic system  150  compares the magnitude relationship between the third integrated value and the fourth integrated value with the magnitude relationship between the first integrated value and the second integrated value, and determines whether the second matching has been correctly performed based on the comparison result. Specifically, the arithmetic system  150  determines that the second matching has been performed correctly when the magnitude relationship between the third integrated value and the fourth integrated value coincides with the magnitude relationship between the first integrated value and the second integrated value. When the magnitude relationship between the third integrated value and the fourth integrated value does not coincide with the magnitude relationship between the first integrated value and the second integrated value, the arithmetic system  150  shifts the plurality of patterns  220 A and  220 B on the image  225  of the second region  202  by one pitch relative to the plurality of corresponding CAD patterns  230 A and  230 B, and then performs the second matching again. 
     In the above-described embodiments, the repeating patterns are formed by the double patterning, but the present invention is not limited to the above-described embodiments. The present invention is also applicable to repeating patterns formed by other multi-patterning, such as quadruple patterning. For example, patterns formed by the quadruple patterning are classified into four groups according to layer classification of corresponding CAD patterns, four integrated values are calculated for these four groups, and a magnitude relation of these four integrated values is determined. 
     Furthermore, the present invention can be applied to repeating patterns other than the line and space patterns.  FIG.  12    is a schematic diagram showing hole patterns on an image  305  of a first region  201 . The hole patterns are an example of repeating patterns formed by the double patterning. In the example shown in  FIG.  12   , the hole patterns on the image  305  includes two sets of hole patterns  310 A.  310 B individually formed by the double patterning. These patterns  310 A and  310 B are arranged alternately in the X direction and the Y direction. In the following descriptions, these hole patterns  310 A and  310 B will be referred to as reference patterns. In order to specify the positions of the reference patterns  310 A and  310 B in the X direction and the Y direction, the first region  201  is an edge region and a corner region of the pattern region  200  shown in  FIG.  2   . 
     The arithmetic system  150  classifies the reference patterns  310 A and  310 B into a first group and a second group according to layer classification of corresponding CAD patterns. In one embodiment, the arithmetic system  150  classifies the first reference pattern  310 A into the first group and the second reference pattern  310 B into the second group. 
       FIG.  13    is a schematic diagram showing hole patterns on an image  325  of a second region  205 . As shown in  FIG.  13   , the patterns constituted of the hole patterns in the second region  202  include two sets of patterns  320 A and  320 B individually formed by the double patterning. These patterns  320 A and  320 B are arranged alternately in the X direction and the Y direction. The arithmetic system  150  classifies the hall patterns  320 A and  320 B into a first group and a second group according to layer classification of corresponding CAD patterns. In one embodiment, the arithmetic system  150  classifies the hall pattern  320 A into the first group and the hall pattern  320 B into the second group 
     The pattern matching of this embodiment is performed in the same manner as the embodiment described with reference to  FIG.  11   . 
     In step  1 , the scanning electron microscope  50  generates the image  305  of the first region  201  in the pattern region  200  including the repeating patterns (see  FIG.  12   ). The image  305  of the first region  201  is sent to the arithmetic system  150 . 
     In step  2 , the arithmetic system  150  performs the first matching between the reference patterns  310 A,  310 B on the image  305  of the first region  201  and the CAD patterns that have been classified in advance into a first group and a second group based on the layer information. 
     In step  3 , the arithmetic system  150  classifies the plurality of reference patterns  310 A and  310 B into the first group and the second group according to the layer classification of the corresponding CAD patterns. 
     In step  4 , the arithmetic system  150  measures widths of the plurality of reference patterns  310 A belonging to the first group and widths of the plurality of reference patterns  310 B belonging to the second group. 
     In step  5 , the arithmetic system  150  integrates the measured values of the widths of the plurality of reference patterns  310 A belonging to the first group to determine a first integrated value, and integrates the measured values of the widths of the plurality of reference patterns  310 B belonging to the second group to determine a second integrated value. 
     In step  6 , the arithmetic system  150  determines a magnitude relationship between the first integrated value and the second integrated value. Specifically, the arithmetic system  150  determines which of the first integrated value and the second integrated value is larger than the other. 
     In step  7 , the scanning electron microscope  50  generates the image  325  of the second region  202  in the pattern region  200  (see  FIG.  13   ). The image  325  of the second region  202  is sent to the arithmetic system  150 . 
     In step  8 . the arithmetic system  150  performs the second matching between the patterns  320 A,  320 B on the image  325  of the second region  202  and the CAD patterns that have been classified in advance into a first group and a second group based on the layer information. 
     In step  9 , the arithmetic system  150  classifies the plurality of patterns  320 A and  320 B on the image  325  of the second region  202  into the first group and the second group according to the layer classification of the corresponding CAD patterns. 
     In step  10 , the arithmetic system  150  measures widths of the plurality of patterns  320 A belonging to the first group and widths of the plurality of patterns  320 B belonging to the second group. 
     In step  11 , the arithmetic system  150  integrates the measured values of the widths of the plurality of patterns  320 A belonging to the first group to determine a third integrated value, and integrates the measured values of the widths of the plurality of patterns  320 B belonging to the second group to determine a fourth integrated value. 
     In step  12 . the arithmetic system  150  determines a magnitude relationship between the third integrated value and the fourth integrated value. 
     In step  13 , the arithmetic system  150  compares the magnitude relationship between the third integrated value and the fourth integrated value with the magnitude relationship between the first integrated value and the second integrated value, and determines whether the second matching has been correctly performed based on the comparison result. Specifically, the arithmetic system  150  determines that the second matching has been performed correctly when the magnitude relationship between the third integrated value and the fourth integrated value coincides with the magnitude relationship between the first integrated value and the second integrated value. When the magnitude relationship between the third integrated value and the fourth integrated value does not coincide with the magnitude relationship between the first integrated value and the second integrated value, the arithmetic system  150  shifts the plurality of patterns on the image  325  of the second region  202  by one pitch relative to the plurality of corresponding CAD patterns, and then performs the second matching again. 
     In the embodiments described previously, the integrated value of the widths of the patterns belonging to each group is calculated. Instead of the widths of the patterns, an integrated value of slopes of brightness profiles of edges of patterns on an image may be calculated. Usually, in the multi-patterning, slopes of edges of real patterns formed by individual steps may be slightly different due to an etching process. Therefore, the slopes of the brightness profiles of the edges of the patterns appearing on the image are also slightly different between groups. 
       FIG.  14    is a diagram showing an example of a brightness profile of a pattern on an image. The brightness profile of the pattern is a distribution of brightness along a direction across the pattern. The brightness is represented by, for example, a numerical value ranging from 0 to 255 according to a gray scale. As can be seen from  FIG.  14   , a slope S of the brightness profile of the edge of the pattern can be calculated from brightness values and a distance (number of pixels). 
     Hereinafter, in the examples shown in  FIGS.  2  to  5   , an embodiment in which the slope of the brightness profile of the edge of the pattern is used instead of the width of the pattern will be described. Since the details of the following embodiments, which will not be particularly described, are the same as the details of the embodiments described with reference to  FIGS.  2  to  13   , the duplicated descriptions thereof will be omitted. 
       FIG.  15    is a flowchart illustrating an embodiment of a pattern matching method using the slope of the brightness profile of the pattern edge. 
     In step  2 - 1 , the scanning electron microscope  50  generates the image  205  of the first region  201  in the pattern region  200  including the repeating patterns (see  FIG.  3   ). The image  205  of the first region  201  is sent to the arithmetic system  150 . 
     In step  2 - 2 , the arithmetic system  150  performs the first matching between the reference patterns  210 A,  210 B on the image  205  of the first region  201  and the CAD patterns  215 A.  215 B that have been classified in advance into a first group and a second group based on the layer information (see  FIG.  4   ). 
     In step  2 - 3 . the arithmetic system  150  classifies the plurality of reference patterns  210 A and  210 B into the first group and the second group according to the layer classification of the CAD patterns  215 A and  215 B (see  FIG.  5   ). 
     In step  2 - 4 , the arithmetic system  150  calculates slopes of brightness profiles of the edges of the plurality of reference patterns  210 A belonging to the first group and slopes of brightness profiles of the edges of the plurality of reference patterns  210 B belonging to the second group. 
     In step  2 - 5 , the arithmetic system  150  integrates the calculated values of the slopes of the brightness profiles of the edges of the plurality of reference patterns  210 A belonging to the first group to determine a first integrated value, and integrates the calculated values of the slopes of the brightness profiles of the edges of the plurality of reference patterns  210 B belong to the second group to determine a second integrated value. 
     The difference between the slope of the brightness profile of the edge of each reference pattern  210 A belonging to the first group and the slope of the brightness profile of the edge of each reference pattern  210 B belonging to the second group is extremely small, but there is a significant difference between the first integrated value and the second integrated value. In step  2 - 6 , the arithmetic system  150  determines a magnitude relationship between the first integrated value and the second integrated value. Specifically, the arithmetic system  150  determines which of the first integrated value and the second integrated value is larger than the other. 
     In step  2 - 7 , the scanning electron microscope  50  generates the image  225  of the second region  202  in the pattern region  200  (see  FIG.  8   ). The image  225  of the second region  202  is sent to the arithmetic system  150 . 
     In step  2 - 8 , the arithmetic system  150  performs the second matching between the patterns  220 A,  220 B on the image  225  of the second region  202  and the CAD patterns  230 A,  230 B that have been classified in advance into a first group and a second group based on the layer information (see  FIG.  9   ). 
     In step  2 - 9 , the arithmetic system  150  classifies the plurality of patterns  220 A and  220 B on the image  225  of the second region  202  into the first group and the second group according to the layer classification of the CAD patterns  230 A and  230 B (see  FIG.  10   ). 
     In step  2 - 10 , the arithmetic system  150  calculates slopes of brightness profiles of edges of the plurality of patterns  220 A belonging to the first group and slopes of brightness profiles of edges of the plurality of patterns  220 B belonging to the second group. 
     In step  2 - 11 , the arithmetic system  150  integrates the calculated values of the slopes of the brightness profiles of the edges of the plurality of patterns  220 A belonging to the first group to determine a third integrated value, and integrates the calculated values of the slopes of the brightness profiles of the edges of the plurality of patterns  220 B belonging to the second group to determine a fourth integrated value. 
     In step  2 - 12 , the arithmetic system  150  determines a magnitude relationship between the third integrated value and the fourth integrated value. 
     In step  2 - 13 , the arithmetic system  150  compares the magnitude relationship between the third integrated value and the fourth integrated value with the magnitude relationship between the first integrated value and the second integrated value, and determines whether the second matching has been correctly performed based on the comparison result. Specifically, the arithmetic system  150  determines that the second matching has been performed correctly when the magnitude relationship between the third integrated value and the fourth integrated value coincides with the magnitude relationship between the first integrated value and the second integrated value. When the magnitude relationship between the third integrated value and the fourth integrated value does not coincide with the magnitude relationship between the first integrated value and the second integrated value, the arithmetic system  150  shifts the plurality of patterns  220 A and  220 B on the image  225  of the second region  202  by one pitch relative to the plurality of corresponding CAD patterns  230 A and  230 B, and then performs the second matching again. 
     Although detailed descriptions are omitted, the embodiment described with reference to  FIG.  15    can be applied to the hole patterns shown in  FIGS.  12  and  13    as well. 
     The previous description of embodiments is provided to enable a person skilled in the art to make and use the present invention. Moreover, various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles and specific examples defined herein may be applied to other embodiments. Therefore, the present invention is not intended to be limited to the embodiments described herein but is to be accorded the widest scope as defined by limitation of the claims. 
     Industrial Applicability 
     The present invention is applicable to a method of performing matching between a pattern formed on a surface of a workpiece, such as a wafer or a glass substrate, used for manufacturing semiconductor devices and a CAD pattern created from pattern design data. 
     REFERENCE SIGNS LIST 
     
         
           50  scanning electron microscope 
           111  electron gun 
           112  converging lens 
           113  X deflector 
           114  Y deflector 
           115  objective lens 
           116  lens controller 
           117  deflection controller 
           118  image acquisition device 
           120  specimen chamber 
           121  specimen stage 
           122  stage controller 
           124  wafer 
           130  secondary electron detector 
           131  backscattered electron detector 
           140  transfer device 
           150  arithmetic system 
           161  database 
           162  memory 
           163  processor 
           165  display screen 
           200  pattern region 
           201  first region 
           202  second region 
           205  image 
           210 A,  210 B reference pattern 
           220 A,  220 B pattern 
           225  image