Patent Publication Number: US-2012038307-A1

Title: Measurement System Using Alignment Unit And Method Of Determining System Parameters Of Alignment Unit

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application claims the benefit of Korean Patent Application No. 2010-0077255, filed on Aug. 11, 2010 in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference in its entirety. 
     BACKGROUND 
     1. Field 
     Embodiments relate to a method of determining a system parameter of an alignment unit in a system that measures the position and posture of a workpiece, such as a substrate (or a semiconductor wafer), using the alignment unit. 
     2. Description of the Related Art 
     Generally, the position and posture of a workpiece, such as a substrate (or a semiconductor wafer) constituting a liquid crystal display (LCD), a plasma display panel (PDP) or a flat panel display (FPD), are measured so as to process, manufacture or inspect the workpiece. To this end, the position and posture of the workpiece are measured using an alignment unit, such as a microscope system. 
     When the position and posture of the workpiece are measured using the alignment unit, the alignment unit is mounted to coincide with a moving table on which the workpiece is placed in the horizontal and vertical directions so as to accurately measure position and posture information of the workpiece. 
     In actuality, however, the alignment unit is not always mounted correctly. That is, the alignment unit does not coincide with the moving table in the horizontal and vertical directions. For this reason, it may be necessary to calculate a mounting error of the mounted alignment unit. In particular, when a plurality of alignment units are mounted so as to enable position and posture information of the workpiece to be rapidly measured, it may be necessary to calculate mounting errors of the respective alignment units. 
     SUMMARY 
     At least one embodiment provides a method of determining a real system parameter value of an alignment unit used to measure a position and posture of a workpiece, such as a substrate (or a semiconductor wafer) based on a mounting error of the alignment unit during assembly and mounting thereof. 
     Additional aspects of the embodiments will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention. 
     According to one embodiment, a method of determining at least one system parameter of an alignment unit that measures a position and posture of a workpiece placed on a moving table includes measuring a position of a fiducial mark formed on the moving table using the alignment unit, determining a mounting error of the alignment unit by moving the moving table such that the fiducial mark is located within a field of view of the alignment unit, determining the system parameter of the alignment unit by moving the moving table in a direction changed in correspondence to the calculated mounting error, and acquiring a first set of coordinate positions of the fiducial mark before and after movement of the moving table. 
     The moving table may have two degrees of freedom in which the moving table moves in X- and Y-directions. 
     The moving table may have three degrees of freedom in which the moving table moves in X-, Y- and Z-directions. 
     The determining a mounting error of the alignment unit may include moving the moving table in an X- or Y-direction of a coordinate system of stage such that the fiducial mark is located within the field of view of the alignment unit to acquire a second set of coordinate positions of the fiducial mark at a start position and an end position, and determining horizontal and vertical mounting errors of the alignment unit based on the second set of coordinate positions. The moving table is supported by the stage. 
     The determining a mounting error of the alignment unit may include repeatedly moving the moving table in the X- or Y-direction of the stage coordinate system a number of times at intervals to acquire first means of coordinate positions of the fiducial mark, and determining horizontal and vertical mounting errors of the alignment unit based on the first means. 
     The determining a mounting error of the alignment unit may include calculating a final mounting error of the alignment unit using the horizontal and vertical mounting errors of the alignment unit. 
     The determining the system parameter of the alignment unit may include moving the moving table in parallel to a horizontal direction of an view coordinate system using the mounting error to acquire at least a portion of the first set of coordinate positions of the fiducial mark at the start position and the end position, and determining a horizontal system parameter of the alignment unit based on the first set of coordinate positions. 
     The determining the system parameter of the alignment unit may include moving the moving table in parallel to a vertical direction of an view coordinate system using the mounting error to acquire at least a portion of the first set of coordinate positions of the fiducial mark at the start position and the end position, and determining a vertical system parameter of the alignment unit based on the first set of coordinate positions. 
     The determining the system parameter of the alignment unit may include repeatedly moving the moving table in parallel to at least one of the horizontal and vertical direction of the view coordinate system a number of times at intervals to acquire second means of coordinate positions of the fiducial mark, and determining horizontal and vertical system parameters of the alignment unit based on the second means. 
     The horizontal and vertical system parameters of the alignment unit may include a scale factor having a unit of length/pixel with respect to each direction in the field of view of the alignment unit. 
     In another example embodiment, a measurement system includes a table configured to move a workpiece, an alignment unit configured to measure a position of a fiducial mark formed on the table, and a controller. The controller is configured to move the table such that the fiducial mark is located within a field of view of the alignment unit, configured to calculate a mounting error of the alignment unit, and configured to determine a system parameter of the alignment unit by moving the table in a direction changed in correspondence to the mounting error and by acquiring a first set of coordinate positions of the fiducial mark before and after movement of the moving table. 
     The alignment unit may be plural in number. 
     The alignment unit may include a scope to measure coordinate positions of the fiducial mark. 
     The controller may be configured to move the table in an X- or Y-direction of a coordinate system of a stage such that the fiducial mark is located within the field of view of the alignment unit to acquire a second set of coordinate positions of the fiducial mark at a start position and an end position, and may be configured to calculate horizontal and vertical mounting errors of the alignment unit based on the second set of coordinate positions. The table is supported by the stage, 
     The controller may be configured to repeatedly move the table in the X- or Y-direction of the stage coordinate system a number of times at intervals to acquire first means of coordinate positions of the fiducial mark, and to determine horizontal and vertical mounting errors of the alignment unit based on the first means. 
     The controller may be configured to calculate a final mounting error of the alignment unit using the horizontal and vertical mounting errors of the alignment unit. 
     The controller may be configured to move the table in parallel to a horizontal direction of a view coordinate system using the mounting error to acquire at least a portion of the first set of coordinate positions of the fiducial mark at the start position and the end position, and to determine a horizontal system parameter of the alignment unit based on the first set of coordinate positions. 
     The controller may be configured to move the table in parallel to a vertical direction of a view coordinate system using the mounting error to acquire at least a portion of the first set of coordinate positions of the fiducial mark at the start position and the end position, and to determine a vertical system parameter of the alignment unit based on the first set of coordinate positions. 
     The controller may be configured to repeatedly move the table in parallel to at least one of the horizontal and vertical direction of the view coordinate system a number of times at intervals to acquire second means of coordinate positions of the fiducial mark, and to determine horizontal and vertical system parameters of the alignment unit based on the second means. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and/or other aspects of the invention will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which: 
         FIG. 1  is an overall construction view of a measurement system according to an embodiment; 
         FIG. 2  is an operation conceptual view of the measurement system according to the embodiment; 
         FIG. 3  is a control construction view of the measurement system according to an embodiment; 
         FIG. 4  is a first view illustrating a mark position measured by a k-th alignment unit mounted in the measurement system according to an embodiment; 
         FIG. 5  is a second view illustrating a mark position measured by the k-th alignment unit mounted in the measurement system according to an embodiment; 
         FIG. 6  is a view illustrating a process of calculating an alignment unit mounting error using a fiducial mark in the measurement system according to an embodiment; 
         FIG. 7  is a view illustrating a process of calculating an alignment unit mounting error in the horizontal direction using a fiducial mark in the measurement system according to an embodiment; 
         FIG. 8  is a view illustrating a process of calculating the mean of alignment unit mounting errors in the horizontal direction using fiducial marks in the measurement system according to an embodiment; 
         FIG. 9  is a view illustrating a process of calculating an alignment unit mounting error in the vertical direction using a fiducial mark in the measurement system according to an embodiment; 
         FIG. 10  is a view illustrating a process of calculating the mean of alignment unit mounting errors in the vertical direction using fiducial marks in the measurement system according to an embodiment; 
         FIG. 11  is a view illustrating a process of calculating a real system parameter of an alignment unit in the horizontal direction using an alignment unit mounting error in the measurement system according to an embodiment; 
         FIG. 12  is a view illustrating a process of calculating the mean of real system parameters of an alignment unit in the horizontal direction using an alignment unit mounting error in the measurement system according to an embodiment; 
         FIG. 13  is a view illustrating a process of calculating a real system parameter of an alignment unit in the vertical direction using an alignment unit mounting error in the measurement system according to an embodiment; and 
         FIG. 14  is a view illustrating a process of calculating the mean of real system parameters of an alignment unit in the vertical direction using an alignment unit mounting error in the measurement system according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Detailed example embodiments are disclosed herein. However, specific structural and functional details disclosed herein are merely representative for purposes of describing example embodiments. Example embodiments may, however, be embodied in many alternate forms and should not be construed as limited to only the embodiments set forth herein. 
     Accordingly, while example embodiments are capable of various modifications and alternative forms, embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that there is no intent to limit example embodiments to the particular forms disclosed, but to the contrary, example embodiments are to cover all modifications, equivalents, and alternatives falling within the scope of example embodiments. Like numbers refer to like elements throughout the description of the figures. 
     It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of example embodiments. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. 
     It will be understood that when an element is referred to as being “connected” or “coupled” to another element, it may be directly connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being “directly connected” or “directly coupled” to another element, there are no intervening elements present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., “between” versus “directly between”, “adjacent” versus “directly adjacent”, etc.). 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises”, “comprising,”, “includes” and/or “including”, when used herein, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     It should also be noted that in some alternative implementations, the functions/acts noted may occur out of the order noted in the figures. For example, two figures shown in succession may in fact be executed substantially concurrently or may sometimes be executed in the reverse order, depending upon the functionality/acts involved. 
       FIG. 1  is an overall construction view of a measurement system  10  according to an embodiment, and  FIG. 2  is an operation conceptual view of the measurement system  10  according to the embodiment. 
     Referring to  FIGS. 1 and 2 , the measurement system  10  includes a moving table  100  on which a workpiece (a sample, such as a wafer or glass, on which a desired or predetermined pattern is to be formed) W is placed and a plurality of alignment units  140  mounted above the moving table  100  to measure a position and posture of the workpiece W placed on the moving table  100 . The alignment units  140  are mounted to a gantry  170  such that the alignment units  140  move in X-, Y- and Z-directions. The alignment units  140  have three degrees of freedom (X, Y, Z), which is the most common configuration. The degrees of freedom may be restricted. For example, the alignment units  140  may have a degree of freedom in the X-, Y- or Z-direction. 
     Guide bar type moving members  171 ,  172  and  173  are mounted to the gantry  170  such that the moving members  171 ,  172  and  173  move in the X-, Y- or Z-direction. The alignment units  140  are coupled to the moving members  171 ,  172  and  173  such that the alignment units  140  are moved in the X-, Y- or Z-direction. 
     Each alignment unit  140  has three degrees of freedom (X, Y, Z) in which each alignment unit  140  moves in the X-, Y- and Z-directions according to the movements of the moving members  171 ,  172  and  173 . The moving table  100 , on which the workpiece W is placed, has two degrees of freedom (X, Y) in which the moving table  100  moves in the X- and Y-directions according to the movement of a stage  110 . 
       FIG. 3  is a control construction view of the measurement system  10  according to an embodiment. 
     Referring to  FIG. 3 , the measurement system  10  includes a stage  110 , alignment units  140 , mark capturing units  150 , and a controller  160 . 
     The stage  110  is a device to move the moving table  100 , on which the workpiece W is placed, in the X- and Y-directions. The stage  110  moves the moving table  100  according to an instruction from the controller  160  such that a fiducial mark FM formed on the moving table  100  is located within a field of view F.O.V of each alignment unit  140 . 
     The alignment units  140  may be scopes provided above the stage  110  to measure the position of the fiducial mark FM formed on the moving table  100 . 
     Each mark capturing unit  150  is provided above a corresponding one of the alignment units  140  to capture the fiducial mark FM formed on the moving table  100  and transmit the captured image to the controller  160 . A capturing unit  150  may transmit the image wirelessly or over a wired connection (not shown). At this time, the movement of the stage  110  is controlled according to an instruction from the controller  160  until the fiducial mark FM is captured by the mark capturing unit  150 . 
     The controller  160  calculates real system parameter values based on assembly and mounting of the respective alignment units  140  using fiducial marks FM measured by the alignment units  140 . In the measurement system  10 , in which the moving table  100  and the respective alignment units move in their degrees of freedom, the position and posture of the workpiece W is measured as follows. A mounting error y of each alignment unit  140  with respect to the moving table  100  is calculated, the moving table  100  is moved in a direction changed in correspondence to the calculated mounting error y, and coordinate positions of the fiducial mark FM on an view coordinate system Σ V  before and after movement of the moving table are acquired, thereby calculating real system parameters of each alignment unit  140  in the horizontal and vertical directions. 
     That is, the controller  160  acquires coordinate positions of the fiducial mark FM at start and end positions while moving the moving table  100  in parallel to the horizontal and vertical directions of the view coordinate system Σ V  using the calculated mounting error y, thereby calculating system parameters, i.e., unit scale factors, of each alignment unit  140  in the horizontal and vertical directions. 
     Hereinafter, a method of calculating a real system parameter value of each alignment unit  140  in the measurement system  10  will be described. 
       FIG. 4  is a first view illustrating a mark position measured by a k-th alignment unit mounted in the measurement system according to the an embodiment, and  FIG. 5  is a second view illustrating a mark position measured by the k-th alignment unit mounted in the measurement system according to an embodiment. 
     Referring to  FIGS. 4 and 5 , a fiducial mark FM formed on the moving table  100  within a field of view F.O.V of a k-th alignment unit  140  is measured. Physical quantities defined to measure the fiducial mark FM are as follows. 
     Σ S (X S , Y S ) is a body fixed coordinate system of the stage  110  (hereinafter, referred to as a stage coordinate system). 
     Σ V (X V , Y V ) is a body fixed coordinate system of the k-th alignment unit  140  (hereinafter, referred to as an view coordinate system). 
       FIG. 4  shows that the k-th alignment unit  140  is ideally mounted. The k-th alignment unit  140  coincides in posture with the stage coordinate system Σ S . That is, the mounting error y k  of the alignment unit  140  is 0. 
       FIG. 5  shows that the k-th alignment unit  140  is generally mounted. The k-th alignment unit  140  is assembled or mounted at an angle having a mounting error y k  with respect to the stage coordinate system Σ S . 
     Generally, each alignment unit  140  is not mounted so as to coincide in posture with the stage coordinate system Σ S  as shown in  FIG. 4  but at an angle having a mounting error y k  with respect to the stage coordinate system Σ S  as shown in  FIG. 5 . 
     Due to the mounting error y k , the position and posture of the workpiece W placed on the moving table  100  may not be accurately measured by each alignment unit  140 . For this reason, it may be necessary to calculate a real system parameter value of each alignment unit  140  with respect to the mounting error y k . 
     To this end, a mounting error y k  generated when an alignment unit  140  is mounted with respect to the stage coordinate system Σ S  is calculated first, which will be described with reference to  FIG. 6 . 
       FIG. 6  is a view illustrating a process of calculating an alignment unit mounting error using a fiducial mark in the measurement system according to an embodiment. 
     It is assumed that the alignment unit of  FIG. 6  is a k-th alignment unit  140 . 
     A mounting error y k  of the k-th alignment unit  140  is calculated while the moving table  100  is moved such that a fiducial mark FM formed on the moving table  100  is located within a field of view F.O.V of the k-th alignment unit  140 . 
     The details thereof will be described in more detail with reference to  FIGS. 7 to 10 . 
       FIG. 7  is a view illustrating a process of calculating an alignment unit mounting error in the horizontal direction using a fiducial mark in the measurement system according to an embodiment. 
     Referring to  FIG. 7 , physical quantities defined to calculate a horizontal mounting error (hereinafter, referred to as a horizontal error)  hori y k  of the k-th alignment unit  140  are as follows. 
     Σ O (X O , Y O ) is a fiducial coordinate system in which the position and posture of the workpiece W placed on the moving table  100  are acquired. Σ O (X O , Y O ) is provided on the moving table  100  (see  FIG. 3 ). 
     First, the moving table  100  is moved from position A to position B in the X-direction (horizontal direction) on the stage coordinate system Σ S , and coordinate positions of the fiducial mark FM on the view coordinate system Σ V  before and after movement of the moving table  100  are measured using the alignment unit  140 . 
     The horizontal error  hori y k  of the k-th alignment unit  140  based on coordinate variations of the fiducial mark FM on the view coordinate system Σ V  before and after movement of the moving table  100  is calculated as represented by Equation 1 below. 
     
       
         
           
             
               
                 
                   
                     γ 
                     k 
                       
                       
                       
                     hori 
                   
                   = 
                   
                     
                       
                         - 
                         
                           tan 
                           
                             - 
                             1 
                           
                         
                       
                        
                       
                         BC 
                         
                           A 
                            
                           
                               
                           
                            
                           C 
                         
                       
                     
                     = 
                     
                       - 
                       
                         
                           tan 
                           
                             - 
                             1 
                           
                         
                          
                         
                           ( 
                           
                             
                               
                                 Δ 
                                 v 
                               
                                
                               y 
                             
                             
                               
                                 Δ 
                                 v 
                               
                                
                               x 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 1, Δ V X is a horizontal variation of the fiducial mark FM measured on the view coordinate system Σ V  before and after movement of the moving table  100 , and Δ V y is a vertical variation of the fiducial mark FM measured on the view coordinate system Σ V  before and after movement of the moving table  100 . 
       FIG. 8  is a view illustrating a process of calculating the mean of alignment unit mounting errors in the horizontal direction using fiducial marks in the measurement system according to an embodiment. 
     Referring to  FIG. 8 , the moving table  100  is moved from position A to position B in the X-direction (horizontal direction) on the stage coordinate system Σ S , and the moving table  100  is moved in the X-direction (horizontal direction) in parallel to AB at regular or known intervals in the Y-direction (for example, intervals of DY). 
     The moving table  100  is repeatedly moved in the X-direction (horizontal direction) in parallel to AB at regular or known intervals (intervals of DY) in the Y-direction within a field of view F.O.V of the k-th alignment unit  140  a desired (or, alternatively, a predetermined) number of times n to calculate the mean M of horizontal errors  hori y k  of the k-th alignment unit  140  as represented by Equation 2 (see  FIG. 9 ). 
     
       
         
           
             
               
                 
                   
                     
                       M 
                       hori 
                     
                      
                     
                       y 
                       k 
                     
                   
                   = 
                   
                     
                       1 
                       n 
                     
                      
                     
                       
                         ∑ 
                         hori 
                       
                        
                       
                         y 
                         k 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     In the same manner as the method shown in  FIGS. 7 and 8 , a vertical mounting error (hereinafter, referred to as a vertical error)  vert y k  of the k-th alignment unit  140  may be calculated, which will be described in more detail with reference to  FIGS. 9 and 10 . 
       FIG. 9  is a view illustrating a process of calculating an alignment unit mounting error in the vertical direction using a fiducial mark in the measurement system according to an embodiment. 
     Referring to  FIG. 9 , the moving table  100  is moved from position A to position B in the Y-direction (vertical direction) on the stage coordinate system Σ S , and coordinate positions of the fiducial mark FM on the view coordinate system Σ V  before and after movement of the moving table  100  are measured using the alignment unit  140 . 
     The vertical error  vert y k  of the k-th alignment unit  140  based on coordinate variations of the fiducial mark FM on the view coordinate system Σ V  before and after movement of the moving table  100  is calculated as represented by Equation 3 (see  FIG. 9 ). 
     
       
         
           
             
               
                 
                   
                     γ 
                     k 
                       
                       
                       
                     vort 
                   
                   = 
                   
                     
                       
                         - 
                         
                           tan 
                           
                             - 
                             1 
                           
                         
                       
                        
                       
                         BC 
                         
                           A 
                            
                           
                               
                           
                            
                           C 
                         
                       
                     
                     = 
                     
                       - 
                       
                         
                           tan 
                           
                             - 
                             1 
                           
                         
                          
                         
                           ( 
                           
                             
                               
                                 Δ 
                                 v 
                               
                                
                               y 
                             
                             
                               
                                 Δ 
                                 v 
                               
                                
                               x 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 3, Δ V X is a horizontal variation of the fiducial mark FM measured on the view coordinate system Σ V  before and after movement of the moving table  100 , and Δ V y is a vertical variation of the fiducial mark FM measured on the view coordinate system Σ V  before and after movement of the moving table  100 . 
       FIG. 10  is a view illustrating a process of calculating the mean of alignment unit mounting errors in the vertical direction using fiducial marks in the measurement system according to an embodiment. 
     Referring to  FIG. 10 , the moving table  100  is moved from A to B in the Y-direction (vertical direction) on the stage coordinate system Σ S , and the moving table  100  is moved in the Y-direction (vertical direction) in parallel to AB at regular or known intervals (for example, intervals of DX) in the X-direction. 
     The moving table  100  is repeatedly moved in the Y-direction (vertical direction) in parallel to AB at regular intervals (for example, intervals of DX) in the X-direction within a field of view. F.O.V of the k-th alignment unit  140  a desired (or, alternatively, a predetermined) number of times n to calculate the mean M of vertical errors  vert y k  of the k-th alignment unit  140  as represented by Equation 4. 
     
       
         
           
             
               
                 
                   
                     
                       M 
                       vert 
                     
                      
                     
                       y 
                       k 
                     
                   
                   = 
                   
                     
                       1 
                       n 
                     
                      
                     
                       
                         ∑ 
                         vert 
                       
                        
                       
                         y 
                         k 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     The horizontal error  hori y k  calculated by Equation 2 and the vertical error  vert y k  calculated by Equation 4 are compared using Equation 5 to check perpendicularity of the stage. 
     
       
         
           
             
               
                 
                   
                     
                       
                         M 
                         vert 
                       
                        
                       
                         y 
                         k 
                       
                     
                     
                       
                         M 
                         hori 
                       
                        
                       
                         y 
                         k 
                       
                     
                   
                   ≈ 
                   1 
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     After perpendicularity of the stage is checked using Equation 5, a final mounting error y k  of the k-th alignment unit  140  is calculated using Equation 6. 
     
       
         
           
             
               
                 
                   
                     y 
                     k 
                   
                   = 
                   
                     
                       1 
                       2 
                     
                      
                     
                       ( 
                       
                         
                           
                             M 
                             hori 
                           
                            
                           
                             y 
                             k 
                           
                         
                         + 
                         
                           
                             M 
                             vert 
                           
                            
                           
                             y 
                             k 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
     When the final mounting error y k  of the k-th alignment unit  140  is calculated, the moving table  100  is moved in a direction changed in correspondence to the calculated mounting error y k , and coordinate positions of the fiducial mark FM on the view coordinate system Σ V  of a field of view F.O.V measured by the k-th alignment unit  140  before and after movement of the moving table  100  are acquired, thereby calculating real system parameters of the k-th alignment unit  140  in the horizontal and vertical directions, which will be described with reference to  FIGS. 11 to 14 . 
       FIG. 11  is a view illustrating a process of calculating a real system parameter of an alignment unit in the horizontal direction using an alignment unit mounting error in the measurement system according to an embodiment. 
     Referring to  FIG. 11 , the moving table  100  is moved from position A to position C in a direction changed in correspondence to the calculated mounting error y k  from the X-direction (horizontal direction) on the stage coordinate system Σ S , and coordinate positions of the fiducial mark FM on the view coordinate system Σ V  before and after movement of the moving table  100  are measured using the alignment unit  140 . 
     In other words, the moving table  100  is moved from position A to position C in parallel to the X-direction (horizontal direction) of the view coordinate system Σ V  using the calculated mounting error y k , and coordinate positions of the fiducial mark FM at the start position A and the end position C are measured using the alignment unit  140 . 
     The start position A and the end position C of the fiducial mark FM on the stage coordinate system Σ S  are acquired as represented by Equation 7. 
     
       
         
           
             
               
                 
                   
                     
                       start 
                        
                       
                           
                       
                        
                       pos 
                     
                     = 
                     
                       
                           
                         S 
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 S 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 S 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       end 
                        
                       
                           
                       
                        
                       pos 
                     
                     = 
                     
                       
                           
                         S 
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 
                                   X 
                                   S 
                                 
                                 + 
                                 
                                   
                                     l 
                                     AB 
                                   
                                    
                                   
                                     cos 
                                     2 
                                   
                                    
                                   
                                     γ 
                                     k 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   Y 
                                   S 
                                 
                                 + 
                                 
                                   
                                     l 
                                     AB 
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     γ 
                                     k 
                                   
                                    
                                   cos 
                                    
                                   
                                       
                                   
                                    
                                   
                                     γ 
                                     k 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
     A real horizontal parameter S x (S h , S i ) of the k-th alignment unit  140  is calculated as represented by Equation 8 using the coordinate positions, i.e., the start position A and the end position C, of the fiducial mark FM measured on the view coordinate system Σ V  before and after movement of the moving table  100  as represented by Equation 7 (see  FIG. 11 ). 
     
       
         
           
             
               
                 
                   
                     ∴ 
                     
                       
                         S 
                         x 
                       
                       ≡ 
                       
                         
                           l 
                           
                             A 
                              
                             
                                 
                             
                              
                             C 
                           
                             
                             
                             
                           S 
                         
                         
                           l 
                           
                             A 
                              
                             
                                 
                             
                              
                             C 
                           
                             
                             
                             
                           V 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         l 
                         AB 
                           
                           
                           
                         S 
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       
                         γ 
                         k 
                       
                     
                     
                       l 
                       
                         A 
                          
                         
                             
                         
                          
                         C 
                       
                         
                         
                         
                       V 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     8 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equations 7 and 8, the left superscript of each parameter indicates a fiducial coordinate system. 
     For example,  S I AC  indicates the length (mm) of a straight line AC on the stage coordinate system Σ S , and  V I AC  indicates the length (pixel) of a straight line AC on the view coordinate system Σ V . 
     The real horizontal parameter S x (S h , S i ) of the k-th alignment unit  140  calculated by Equation 8 is a scale factor having a unit of length/pixel, such as um/pixel or nm/pixel. 
     Also, the mean of horizontal parameters S x (S h , S i ) of the k-th alignment unit  140  may be calculated in the same manner as in calculating the mounting error y k  of the k-th alignment unit  140 , which will be described with reference to  FIG. 12 . 
       FIG. 12  is a view illustrating a process of calculating the mean of real system parameters of an alignment unit in the horizontal direction using an alignment unit mounting error in the measurement system according to an embodiment. 
     Referring to  FIG. 12 , the moving table  100  is moved from position A to position C in the X-direction (horizontal direction) on the view coordinate system Σ V , and the moving table  100  is moved in the X-direction (horizontal direction) in parallel to AC at regular or known intervals in the Y-direction. 
     The moving table  100  is repeatedly moved in the X-direction (horizontal direction) in parallel to AC at regular intervals in the Y-direction within a field of view F.O.V of the k-th alignment unit  140  several times to repeatedly measure real horizontal parameters S x (S h , S i ) of the k-th alignment unit  140 , thereby calculating the mean M thereof as represented by Equation 9 (see  FIG. 12 ). 
     
       
         
           
             
               
                 
                   
                     MS 
                     x 
                   
                    
                   
                     1 
                     n 
                   
                    
                   
                     
                       ∑ 
                       i 
                     
                      
                     
                         
                     
                      
                     
                       
                         ( 
                         
                           S 
                           x 
                         
                         ) 
                       
                       i 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
       FIG. 13  is a view illustrating a process of calculating a real system parameter of an alignment unit in the vertical direction using an alignment unit mounting error in the measurement system according to an embodiment. 
     Referring to  FIG. 13 , the moving table  100  is moved from A to C in a direction changed in correspondence to the calculated mounting error y k  from the Y-direction (vertical direction) on the stage coordinate system Σ S , and coordinate positions of the fiducial mark FM on the view coordinate system Σ V  before and after movement of the moving table  100  are measured using the alignment unit  140 . 
     In other words, the moving table  100  is moved from position A to position C in parallel to the Y-direction (vertical direction) of the view coordinate system Σ V  using the calculated mounting error y k , and coordinate positions of the fiducial mark FM at the start position A and the end position C are measured using the alignment unit  140 . 
     The start position A and the end position C of the fiducial mark FM on the stage coordinate system Σ S  are acquired as represented by Equation 10. 
     
       
         
           
             
               
                 
                   
                     
                       start 
                        
                       
                           
                       
                        
                       pos 
                     
                     = 
                     
                       
                           
                         S 
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 S 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 S 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       end 
                        
                       
                           
                       
                        
                       pos 
                     
                     = 
                     
                       
                           
                         S 
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 
                                   X 
                                   S 
                                 
                                 + 
                                 
                                   
                                     l 
                                     AB 
                                   
                                    
                                   cos 
                                    
                                   
                                       
                                   
                                    
                                   
                                     γ 
                                     k 
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     γ 
                                     k 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   Y 
                                   S 
                                 
                                 + 
                                 
                                   
                                     cos 
                                     2 
                                   
                                    
                                   
                                     γ 
                                     k 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     10 
                   
                   ] 
                 
               
             
           
         
       
     
     A real vertical parameter S y (S h , S j ) of the k-th alignment unit  140  is calculated as represented by Equation 11 using the coordinate positions, i.e., the start position A and the end position C, of the fiducial mark FM measured on the view coordinate system Σ V  before and after movement of the moving table  100  as represented by Equation 10 (see  FIG. 13 ). 
     
       
         
           
             
               
                 
                   
                     ∴ 
                     
                       
                         S 
                         y 
                       
                       ≡ 
                       
                         
                           l 
                           
                             A 
                              
                             
                                 
                             
                              
                             C 
                           
                             
                             
                             
                           S 
                         
                         
                           l 
                           
                             A 
                              
                             
                                 
                             
                              
                             C 
                           
                             
                             
                             
                           V 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         l 
                         AB 
                           
                           
                           
                         S 
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       
                         γ 
                         k 
                       
                     
                     
                       l 
                       
                         A 
                          
                         
                             
                         
                          
                         C 
                       
                         
                         
                         
                       V 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equations 10 and 11, the left superscript of each parameter indicates a fiducial coordinate system. 
     For example,  S I AC  indicates the length (mm) of a straight line AC on the stage coordinate system Σ S , and  V I AC  indicates the length (pixel) of a straight line AC on the view coordinate system Σ V . 
     The real vertical parameter S y (S h , S i ) of the k-th alignment unit  140  calculated by Equation 11 is a scale factor having a unit of length/pixel, such as um/pixel or nm/pixel. 
     Also, the mean of vertical parameters S y (S h , S i ) of the k-th alignment unit  140  may be calculated in the same manner as in calculating the mounting error y k  of the k-th alignment unit  140 , which will be described with reference to  FIG. 14 . 
       FIG. 14  is a view illustrating a process of calculating the mean of real system parameters of an alignment unit in the vertical direction using an alignment unit mounting error in the measurement system according to an embodiment. 
     Referring to  FIG. 14 , the moving table  100  is moved from position A to position C in the Y-direction (vertical direction) on the view coordinate system Σ V , and the moving table  100  is moved in the Y-direction (vertical direction) in parallel to AC at regular intervals in the X-direction. 
     The moving table  100  is repeatedly moved in the Y-direction (vertical direction) in parallel to AC at regular intervals in the X-direction within a field of view F.O.V of the k-th alignment unit  140  several times to repeatedly measure real vertical parameters S y (S h , S i ) of the k-th alignment unit  140 , thereby calculating the mean M thereof as represented by Equation 12 (see  FIG. 14 ). 
     
       
         
           
             
               
                 
                   
                     MS 
                     x 
                   
                    
                   
                     1 
                     n 
                   
                    
                   
                     
                       ∑ 
                       i 
                     
                      
                     
                         
                     
                      
                     
                       
                         ( 
                         
                           S 
                           y 
                         
                         ) 
                       
                       i 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     12 
                   
                   ] 
                 
               
             
           
         
       
     
     In this embodiment, the alignment unit  140  is fixed and the moving table  100  is moved to measure the fiducial mark FM formed on the moving table  100 . However, the embodiments are not limited thereto. For example, the moving table  100  may be fixed and the alignment unit  140  may be moved to measure the fiducial mark FM formed on the moving table  100 . Alternatively, both the moving table  100  and the alignment unit  140  may be moved to measure the fiducial mark FM formed on the moving table  100 . 
     As is apparent from the above description, a mounting error of the alignment unit used to measure a position and posture of a workpiece, such as a substrate (or a semiconductor wafer), during assembly and mounting thereof is calculated, and a real system parameter value of the alignment unit is calculated based on the calculated mounting error, thereby accurately measuring position and posture information of the workpiece. 
     Also, in a case in which a plurality of alignment units are provided to measure a position and posture of the workpiece, real system parameter values of the respective alignment units based on mounting errors thereof are calculated, thereby accurately measuring position and posture information of the workpiece within a short time. 
     Although a few embodiments have been shown and described, it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the claims and their equivalents.