Patent Publication Number: US-2012038936-A1

Title: Measurement System Using Alignment Unit And Position Measuring Method

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application claims the benefit of Korean Patent Application No. 2010-0077257, 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 system and method to measure a position and posture of a workpiece, such as a substrate (or a semiconductor wafer), using an 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 desirable to acquire a position 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 desirable to acquire positions of the respective alignment units so as to accurately measure a position and posture of the workpiece. 
     SUMMARY 
     At least one embodiment provides a system and/or method to measure a position and posture of a workpiece, such as a substrate (or a semiconductor wafer), using a plurality of alignment units. 
     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. 
     In one example embodiment, a method of measuring 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 an alignment unit, moving the moving table such that the fiducial mark is located at the center of a field of view of the alignment unit to acquire a position of the alignment unit, acquiring view information of the workpiece using the alignment unit, acquiring a position of an alignment mark formed on the workpiece using a position of the moving table, the position of the alignment unit, and the view information acquired by the alignment unit, and measuring the position and posture of the workpiece using the acquired position of the alignment mark. 
     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 alignment unit may be one or more in number. 
     The acquiring the position of the alignment mark may include sequentially processing positions of a plurality of alignment units and view information acquired by the alignment units to acquire the position of the alignment mark formed on the workpiece. 
     The acquiring the view information of the workpiece may include moving the moving table such that the fiducial mark is located within the field of view of the alignment unit to calculate a mounting error of the alignment unit and measuring the position of the fiducial mark with respect to a coordinate system of a stage using the alignment unit having the mounting error to acquire the view information of the workpiece. The moving table is supported by the stage. 
     The acquiring the position of the alignment unit may include acquiring the position of the moving table using a feedback signal of a stage when the position of the fiducial mark is located at the center of the field of view of the alignment unit to acquire the position of the alignment unit. The moving table is supported by the stage. 
     The acquiring the position of the alignment mark may include acquiring position coordinates of the alignment mark formed on the workpiece using the position of the moving table, the position of the alignment unit, and the view information acquired by the alignment unit. 
     The measuring the position and posture of the workpiece may include acquiring two or more position coordinates of the alignment mark to measure the position and posture of the workpiece. 
     In accordance with another embodiment, a measurement system includes a moving table configured to move a workpiece, an alignment unit configured to measure a position of a fiducial mark formed on the moving table, and a controller. The controller is configured to move the moving table such that the fiducial mark is located at the center of a field of view of the alignment unit so as to acquire a position of the alignment unit, configured to acquire view information of the workpiece using the alignment unit, configured to acquire a position of an alignment mark formed on the workpiece using the position of the alignment unit and the view information acquired by the alignment unit, and configured to measure a position and posture of the workpiece using the acquired position of the alignment mark. 
     The alignment unit may include a scope to measure position coordinates of the fiducial mark. 
     The controller may be configured to move the moving table such that the fiducial mark is located within the field of view of the alignment unit to calculate a mounting error of the alignment unit, and may be configured to measure the position of the fiducial mark with respect to a coordinate system for a stage using the alignment unit having the mounting error to acquire the view information of the workpiece. The moving table is supported by the stage. 
     The controller may be configured to acquire the position of the moving table using a feedback signal of a stage when the position of the fiducial mark is located at the center of the field of view of the alignment unit to acquire the position of the alignment unit. The moving table is supported by the stage. 
     The controller may be configured to acquire position coordinates of the alignment mark formed on the workpiece using the position of the moving table, the position of the alignment unit, and the view information acquired by the alignment unit. 
     The controller may be configured to acquire two or more position coordinates of the alignment mark to measure the position and posture of the workpiece. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and/or other aspects of the embodiments 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 an 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 acquiring positions of alignment units using a fiducial mark in the measurement system according to an embodiment; and 
         FIG. 8  is a view illustrating a process of acquiring positions of alignment marks formed on a workpiece using a plurality of alignment units 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 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 , a plurality of 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  or an alignment mark AM formed on the workpiece W is located within a field of view F.O.V of each alignment unit  140 . 
     The alignment units  140  may be alignment scope units (ASU) provided above the stage  110  to measure the position of the fiducial mark FM formed on the moving table  100  and the position of the alignment mark AM formed on the workpiece W. 
     The mark capturing units  150  are provided above the respective the alignment units  140  to capture the fiducial mark FM formed on the moving table  100  and the alignment mark AM formed on the workpiece W and transmit the captured images to the controller  160 . The captured images may be transmitted wirelessly or by wireline to the controller  160 . At this time, the movement of the stage  110  is controlled according to an instruction from the controller  160  until the fiducial mark FM and the alignment mark AM are captured by the mark capturing units  150 . 
     The controller  160  acquires positions of the respective alignment units  140  using the fiducial mark FM formed on the moving table  100  and moves the moving table  100  such that the alignment mark AM formed on the workpiece W is located within a field of view F.O.V of each alignment unit  140  so as to measure a position of the alignment mark AM through each alignment unit  140 . Subsequently, a position and posture of the workpiece W are measured based on the position of each alignment unit  140  and the position of the alignment mark AM measured by each alignment unit  140 . 
     Hereinafter, a method of measuring a position and posture of the workpiece W in the measurement system  10  in which the alignment units  140  are mounted will be described. 
     Before measuring the position and posture of the workpiece W, the position of the fiducial mark FM and the position of each alignment unit  140  based on a mounting error of each alignment unit  140  are acquired. 
     First, a method of acquiring the position of the fiducial mark FM based on the mounting error of each alignment unit  140  will be described with reference to  FIGS. 4 to 6 . 
       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, 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 , γ S ) is a body fixed coordinate system of the stage  110  (hereinafter, referred to as a stage coordinate system). 
     Σ ASU (Σ V ) is a body fixed coordinate system of the k-th alignment unit  140  (hereinafter, referred to as a view coordinate system). 
     Where, k=0, 1, 2 . . . . 
       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 γ 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 γ 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 γ k  with respect to the stage coordinate system Σ S  as shown in  FIG. 5 . 
     Due to the mounting error γ 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, a mounting error γ k  generated upon mounting of the k-th alignment unit  140  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 of the present invention 
     It is assumed that the alignment unit of  FIG. 6  is a k-th alignment unit  140 . 
     A mounting error γ 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 mounting error γ k  may be explained as unit scale factors (S i , S j ) with respect to directions (i, j) in the field of view F.O.V acquired by the k-th alignment unit  140 . 
     When the mounting error γ k  is 0, which is ideal, a position  AUSk d of the fiducial mark FM on the stage coordinate system Σ S  measured by the k-th alignment unit  140  is defined as represented by Equation 1 (see  FIG. 4 ). 
     
       
         
           
             
               
                 
                   
                     
                       
                           
                         
                           ASU 
                           k 
                         
                       
                        
                       d 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               x 
                               ASU 
                             
                           
                         
                         
                           
                             
                               y 
                               ASU 
                             
                           
                         
                       
                       ] 
                     
                   
                   , 
                   
                     { 
                     
                       
                         
                           
                             
                               x 
                               ASU 
                             
                             ≡ 
                             
                               
                                 s 
                                 i 
                               
                               · 
                               
                                 ( 
                                 
                                   i 
                                   - 
                                   
                                     I 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               ASU 
                             
                             ≡ 
                             
                               
                                 - 
                                 
                                   s 
                                   j 
                                 
                               
                               · 
                               
                                 ( 
                                 
                                   j 
                                   - 
                                   
                                     J 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 1, i indicates a pixel index of 0 to I, j indicates a pixel index of 0 to J, S i  indicates a scale vector (nm/pixel) in the i direction, and S j  indicates a scale vector (nm/pixel) in the j direction. 
     When the mounting error γ k  is not 0, which is general, a position of the fiducial mark FM on the stage coordinate system Σ S  measured by the k-th alignment unit  140 , i.e., view information  S d acquired by the k-th alignment unit  140 , may be defined as represented by Equation 2 (see  FIG. 5 ). 
         S   d=R (γ k )· ASUk   d   [Equation 2]
 
     In Equation 2, γ k  is a mounting error of the k-th alignment unit  140 , and 
     
       
         
           
             
               R 
                
               
                 ( 
                 
                   γ 
                   k 
                 
                 ) 
               
             
             = 
             
               [ 
               
                 
                   
                     
                       cos 
                        
                       
                           
                       
                        
                       
                         γ 
                         k 
                       
                     
                   
                   
                     
                       
                         - 
                         sin 
                       
                        
                       
                           
                       
                        
                       
                         γ 
                         k 
                       
                     
                   
                 
                 
                   
                     
                       sin 
                        
                       
                           
                       
                        
                       
                         γ 
                         k 
                       
                     
                   
                   
                     
                       cos 
                        
                       
                           
                       
                        
                       
                         γ 
                         k 
                       
                     
                   
                 
               
               ] 
             
           
         
       
     
     Generally, the respective alignment units  140  are mounted in a state in which each of the alignment units  140  has a mounting error γ. 
     In this embodiment, it is assumed that the view information acquired by the k-th alignment unit  140  has the same direction as an intuitional view from above for convenience. In a case in which the direction of an image is mirrored through an optical device, such as a beam splitter or a mirror, symbols + and − are added in consideration of the directionality. 
     Subsequently, a method of acquiring positions of the alignment units  140  mounted having mounting errors γ will be described with reference to  FIG. 7 . 
       FIG. 7  is a view illustrating a process of acquiring positions of alignment units using a fiducial mark in the measurement system according to an embodiment of the present invention. 
     Referring to  FIG. 7 , a 0-th alignment unit  140  and a k-th alignment unit  140  are used, and it is assumed that the 0-th alignment unit  140  and the k-th alignment unit  140  have mounting errors γ 0  and γ k , respectively. 
     First, the moving table  100  is moved such that the 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 . When the fiducial mark FM is located at the center of the field of view F.O.V of the k-th alignment unit  140 , the position of the moving table  100  is acquired through a feedback signal of the stage  110 , thereby acquiring a center position  S P k  of the k-th alignment unit  140  on the stage coordinate system Σ S . 
     A center position  S P 0  of the 0-th alignment unit  140  is acquired in the same manner as the above. 
     When the position Sd of the fiducial mark FM based on the mounting error γ k  of the k-th alignment unit  140  and the center position  S P k  of the k-th alignment unit  140  are acquired, the position of the alignment mark AM formed on the workpiece is acquired using the k-th alignment unit  140 , which will be described with reference to  FIG. 8 . 
       FIG. 8  is a view illustrating a process of acquiring positions of alignment marks formed on a workpiece using a plurality of alignment units in the measurement system according to an embodiment. 
     A position  S r k  of the alignment mark AM measured by the k-th alignment unit  140  on the stage coordinate system Σ S  is defined as represented by Equation 3. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           k 
                             
                             
                             
                           S 
                         
                         = 
                           
                          
                         
                           
                             p 
                             k 
                               
                               
                               
                             S 
                           
                           + 
                           
                             
                               R 
                                
                               
                                 ( 
                                 
                                   γ 
                                   k 
                                 
                                 ) 
                               
                             
                             · 
                             
                               
                                   
                                 ASUk 
                               
                                
                               d 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 p 
                                 0 
                                   
                                   
                                   
                                 S 
                               
                               + 
                               
                                 p 
                                 k 
                                   
                                   
                                   
                                 0 
                               
                             
                             ) 
                           
                           + 
                           
                             
                               R 
                                
                               
                                 ( 
                                 
                                   γ 
                                   k 
                                 
                                 ) 
                               
                             
                             · 
                             
                               
                                   
                                 ASUk 
                               
                                
                               d 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 3,  S P k  of is the center position of the k-th alignment unit  140  on the stage coordinate system Σ S , which is already known through the discussion of  FIG. 7  above. 
     A position  S r ik  of an i-th alignment mark AM measured by the k-th alignment unit  140  on the stage coordinate system Σ S  using Equation 3 may also be acquired as represented by Equation 4. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           ik 
                             
                             
                             
                           S 
                         
                         = 
                           
                          
                         
                           
                             p 
                             k 
                               
                               
                               
                             S 
                           
                           + 
                           
                             
                               R 
                                
                               
                                 ( 
                                 
                                   γ 
                                   k 
                                 
                                 ) 
                               
                             
                             · 
                             
                               d 
                               i 
                                 
                                 
                                 
                               ASUk 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 
                                     
                                   S 
                                 
                                  
                                 
                                   p 
                                   0 
                                 
                               
                               + 
                               
                                 p 
                                 k 
                                   
                                   
                                   
                                 0 
                               
                             
                             ) 
                           
                           + 
                           
                             
                               R 
                                
                               
                                 ( 
                                 
                                   γ 
                                   k 
                                 
                                 ) 
                               
                             
                             · 
                             
                               d 
                               i 
                                 
                                 
                                 
                               ASUk 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 4, k is 0, 1, 2 . . . (alignment unit  140 ), and i is 1, 2, 3 . . . (alignment mark AM). 
     The position and posture of the workpiece are measured using the position  S r ik  of the i-th alignment mark AM measured by the k-th alignment unit  140  on the stage coordinate system Σ S  acquired by Equation 4. 
     To this end, physical quantities of Σ O  and Σ M  are defined first. 
     Σ O (X O , γ 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 , γ O ) is provided on the moving table  100 . 
     Σ M (X M , γ M ) is a body fixed coordinate system of the moving table  100  (hereinafter, referred to as a moving coordinate system). The center of Σ M  is an arbitrary point on the moving table  100 . The center of Σ M  may be a significant design position or a fiducial mark FM. 
     Therefore, the position  S r ik  of the i-th alignment mark AM measured by the k-th alignment unit  140  on the stage coordinate system Σ S  is a position  S r ik  of the i-th alignment mark AM on the moving coordinate system Σ M  as represented by Equation 5. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           ik 
                             
                             
                             
                           S 
                         
                         = 
                           
                          
                         
                           
                             p 
                             k 
                               
                               
                               
                             S 
                           
                           + 
                           
                             
                               R 
                                
                               
                                 ( 
                                 
                                   γ 
                                   k 
                                 
                                 ) 
                               
                             
                             · 
                             
                               d 
                               i 
                                 
                                 
                                 
                               ASUk 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 p 
                                 0 
                                   
                                   
                                   
                                 S 
                               
                               + 
                               
                                 p 
                                 k 
                                   
                                   
                                   
                                 0 
                               
                             
                             ) 
                           
                           + 
                           
                             
                               R 
                                
                               
                                 ( 
                                 
                                   γ 
                                   k 
                                 
                                 ) 
                               
                             
                             · 
                             
                               d 
                               i 
                                 
                                 
                                 
                               ASUk 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             r 
                             M 
                               
                               
                               
                             S 
                           
                           + 
                           
                             r 
                             i 
                               
                               
                               
                             M 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 5,  S r M  is an arbitrary point on the moving table with respect to the stage coordinate system Σ S .  S r M  is measured through a feedback signal of the stage  110 .  M r i  is the position of an i-th alignment mark AM measured on the moving coordinate system Σ M . 
     Therefore, the position  M r i  of the i-th alignment mark AM measured on the moving coordinate system Σ M  is defined as represented by Equation 6. 
         M   r   i =− S   r   M +( S   P   O + O   P   k )+ R (γ k )· ASUk   d   [Equation 6]
 
     In conclusion, a position  O r i  of the i-th alignment mark AM on the moving coordinate system Σ M  defined using the fiducial coordinate system Σ O  through Equation 6 is acquired as represented by Equation 7. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           i 
                             
                             
                             
                           O 
                         
                         ≡ 
                           
                          
                         
                           r 
                           i 
                             
                             
                             
                           M 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                               
                                 r 
                                 M 
                                   
                                   
                                   
                                 S 
                               
                               . 
                             
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   p 
                                   0 
                                     
                                     
                                     
                                   S 
                                 
                                 + 
                                 
                                   p 
                                   k 
                                     
                                     
                                     
                                   0 
                                 
                               
                               ) 
                             
                             . 
                           
                           + 
                           
                             
                               
                                 R 
                                  
                                 
                                   ( 
                                   
                                     γ 
                                     k 
                                   
                                   ) 
                                 
                               
                               · 
                               
                                 d 
                                 i 
                                   
                                   
                                   
                                 ASUk 
                               
                             
                             . 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 7,  S r M  is a position of the moving table  100  acquired through a feedback signal of the stage  110 , ( S P 0 + O P k )) is a position  S P k  of each alignment unit  140  (for example, the k-th alignment unit), and R(γ k ).  ASUk d i  is view information  S d acquired by each alignment unit  140  (for example, the k-th alignment unit). 
     A position  O r i  of the i-th alignment mark AM formed on the workpiece W is finally acquired based on the position  S r M  of the moving table  100 , the position  S P k  of each alignment unit  140  (for example, the k-th alignment unit), and the view information  S d acquired by each alignment unit  140  (for example, the k-th alignment unit) as represented by Equation 7. 
     In  O r i , i=1, 2 . . . (alignment mark AM). 
     Two positions  O r i=1,2  of the alignment mark AM formed on the workpiece W are acquired to measure a position and posture of the workpiece W. Meanwhile, more than two positions  O r i=1,2  . . . of the alignment mark AM formed on the workpiece W may be acquired to measure a position and posture of the workpiece W using a least square method. 
     In this embodiment, the position  O r i  of the alignment mark AM formed on the workpiece W is acquired using the k-th alignment unit  140 . However, embodiments are not limited thereto. For example, the position  O r i  of the alignment mark AM formed on the workpiece W may be acquired using a plurality of alignment units  140 . In this case, positions  S P k=0, 1,2 . . .  of the alignment units  140  may be previously determined as described above with respect to  FIG. 7 . Also, view information  S d acquired by the respective alignment units  140  may be processed in parallel (the view information may be rapidly processed by the respective alignment units in sequence, which may be considered a form of semi-parallel processing). When multiple alignment units  140  are used, the position  O r of the alignment mark AM formed on the workpiece W is more rapidly acquired, thereby more rapidly measuring the position and posture of the workpiece W. 
     Also, in this embodiment, the alignment units  140  are fixed and the moving table  100  is moved to measure the alignment mark AM formed on the workpiece W, thereby measuring the position and posture of the workpiece W. However, embodiments are not limited thereto. For example, the moving table  100  may be fixed and the alignment units  140  may be moved to measure the alignment mark AM formed on the workpiece W, thereby measuring the position and posture of the workpiece W. Alternatively, the moving table  100  and the alignment units  140  may be moved to measure the alignment mark AM formed on the workpiece W, thereby measuring the position and posture of the workpiece W. 
     As is apparent from the above description, the position and posture of a workpiece, such as a substrate (or a semiconductor wafer), are accurately measured using a plurality of alignment units within a short time. Consequently, the measurement system using the alignment units and the position measuring method are variously utilized in processing, manufacture or inspection of the workpiece. 
     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.