Determination method and apparatus, program, information recording medium, exposure apparatus, layout information providing method, layout method, mark detection method, exposure method, and device manufacturing method

Abstract

A determination apparatus has a calculation section, where first and second direction pitches intersecting within a predetermined plane of a plurality of detection areas are D 1 and D 2 , respectively, sizes in the first and second directions of each of a plurality of divided areas arranged two-dimensionally along the first and second directions on a substrate are W 1 and W 2 , respectively, and first and second direction pitches of a plurality of marks arranged on the substrate are p 1 and p 2 , respectively, calculates pitch p1 and pitch p2 of the plurality of marks that satisfy formulas (a) and (b) below, based on pitch D 1 , pitch D 2 , size W 1 , and size W 2 . p 1 =D 1 /i ( i denotes a natural number)= W 1 /m ( m denotes a natural number)  (a) p 2 =D 2 /j ( j denotes a natural number)= W 2 /n ( n denotes a natural number)  (b)

1 . A layout information providing method in which layout information is provided to arrange a plurality of marks that is detected using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, wherein
 information related to an arrangement of the plurality of marks obtained based on arrangement information on the plurality of detection areas is provided as the layout information.   
     
     
         2 . The layout information providing method according to  claim 1 , wherein
 information related to the arrangement of the plurality of marks includes pitch information on the plurality of marks.   
     
     
         3 . The layout information providing method according to  claim 1 , wherein
 information related to the arrangement of the plurality of marks includes information related to at least one candidate for an arrangement of the plurality of marks.   
     
     
         4 . The layout information providing method according to  claim 3 , wherein
 the at least one candidate for the arrangement of the plurality of marks includes an arrangement which makes concurrent detection of the plurality of marks on the substrate in the plurality of detection areas possible.   
     
     
         5 .- 106 . (canceled) 
     
     
         107 . The layout information providing method according to  claim 3 , wherein
 where pitches in the first direction and the second direction of the plurality of detection areas are D 1  and D 2 , respectively, and pitch in the first direction and the pitch in the second direction of the plurality of marks are p 1  and p 2 , respectively, information related to the arrangement of the plurality of marks includes information on pitch p 1  in the first direction and pitch p 2  in the second direction of the plurality of marks that satisfy formulas (c) and (d) below.
     p   1   =D   1   /i ( i  denotes a natural number)  (c)
 
     p   2   =D   2   /j  ( j  denotes a natural number)  (d)
 
   
     
     
         108 . The layout information providing method according to  claim 1 , wherein
 the plurality of detection areas includes a first detection area, a second detection area arranged apart in a first direction with respect to the first area, and a third detection area arranged apart in a second direction which intersects the first direction within a predetermined plane with respect to the first detection area.   
     
     
         109 . The layout information providing method according to  claim 108 , wherein
 the first detection area and the second detection area are arranged along the first direction.   
     
     
         110 . The layout information providing method according to  claim 109 , wherein
 the arrangement information on the detection areas includes information related to space between the first area and the second area in the first direction.   
     
     
         111 . The layout information providing method according to  claim 108 , wherein
 the second detection area is arranged apart in the first direction and the second direction with respect to the first detection area.   
     
     
         112 . The layout information providing method according to  claim 111 , wherein
 the arrangement information on the detection areas includes information related to space between the first area and the second area in the first direction.   
     
     
         113 . The layout information providing method according to  claim 108 , wherein
 the first detection area and the third detection area are arranged along the second direction.   
     
     
         114 . The layout information providing method according to  claim 113 , wherein
 the arrangement information on the detection areas includes information related to space between the first area and the third area in the second direction.   
     
     
         115 . The layout information providing method according to  claim 108 , wherein
 the third detection area is arranged apart in the first direction and the second direction with respect to the first detection area.   
     
     
         116 . The layout information providing method according to  claim 115 , wherein
 the arrangement information on the detection areas includes information related to space between the first area and the third area in the second direction.   
     
     
         117 . The layout information providing method according to  claim 108 , wherein
 the space between the first area and the third area in the second direction is larger than the space between the first area and the second area in the first direction.   
     
     
         118 . The layout information providing method according to  claim 108 , wherein
 the plurality of detection areas is arranged in a matrix shape in the first direction and the second direction.   
     
     
         119 . The layout information providing method according to  claim 108 , wherein
 information related to the arrangement of the plurality of marks includes information on pitch of the plurality of marks formed along the first direction and pitch of the plurality of marks formed along the second direction.   
     
     
         120 . The layout information providing method according to  claim 108 , wherein
 the layout information includes information related to a size of the divided areas obtained based on the arrangement information on the plurality of detection areas, and   the information related to the size of the divided areas includes size in the first direction and size in the second direction.   
     
     
         121 . The layout information providing method according to  claim 120 , wherein
 the information related to the size of the divided areas includes information related to at least one candidate for the size of the divided areas.   
     
     
         122 . The layout information providing method according to  claim 121 , wherein
 the layout information includes information related to a plurality of candidates for the size of the divided areas, and information related to a plurality of candidates for an arrangement of the plurality of marks corresponding to the plurality of candidates for the size of the divided areas.   
     
     
         123 . The layout information providing method according to  claim 121 , wherein
 at least one of size in the first direction and size in the second direction differs from each other in the plurality of candidates for the size of the divided areas.   
     
     
         124 . The layout information providing method according to  claim 120 , wherein
 where pitches in the first direction and the second direction of the plurality of detection areas are D 1  and D 2 , respectively, sizes in the first direction and the second direction of the divided areas are W 1  and W 2 , respectively, and pitch in the first direction and the pitch in the second direction of the plurality of marks are p 1  and p 2 , respectively, information related to the arrangement of the plurality of marks includes information on pitch p 1  in the first direction and pitch p 2  in the second direction of the plurality of marks that satisfy formulas (a) and (b) below.
     p   1   =D   1   /i  ( i  denotes a natural number)= W   1   /m  ( m  denotes a natural number)   (a)
 
     p   2   =D   2   /j  ( j  denotes a natural number)= W   2   /n  ( n  denotes a natural number)  (b)
 
   
     
     
         125 . The layout information providing method according to  claim 124 , wherein
 the layout information includes information on the size W 1  and the size W 2  that satisfy the formulas (a) and (b).   
     
     
         126 . The layout information providing method according to  claim 108 , wherein
 where pitches in the first direction and the second direction of the plurality of detection areas are D 1  and D 2 , respectively, and pitch in the first direction and the pitch in the second direction of the plurality of marks are p 1  and p 2 , respectively, information related to the arrangement of the plurality of marks includes information on pitch p 1  in the first direction and pitch p 2  in the second direction of the plurality of marks that satisfy formulas (c) and (d) below.
     p   1   =D   1   /i  ( i  denotes a natural number)  (c)
 
     p   2   =D   2   /j  ( j  denotes a natural number)  (d)
 
   
     
     
         127 . The layout information providing method according to  claim 1 , wherein
 the layout information includes information related to size of the divided areas which is obtained based on the arrangement information on the plurality of detection areas.   
     
     
         128 . The layout information providing method according to  claim 127 , wherein
 the information related to the size of the divided areas includes information related to at least one candidate for the size of the divided areas.   
     
     
         129 . The layout information providing method according to  claim 128 , wherein
 information related to the arrangement of the plurality of marks includes information related to at least one candidate for an arrangement of the plurality of marks corresponding to at least one candidate for the size.   
     
     
         130 . The layout information providing method according to  claim 1 , wherein
 the arrangement information on the detection areas includes information on space between the plurality of detection areas.   
     
     
         131 . The layout information providing method according to  claim 1 , wherein
 the plurality of detection areas is arranged at a predetermined pitch, and   the arrangement information on the plurality of detection areas includes information on the predetermined pitch.   
     
     
         132 . The layout information providing method according to  claim 1 , wherein
 each of the divided areas includes a pattern area on which a device pattern is formed, and   candidates for the arrangement of the plurality of marks includes an arrangement in which a part of the plurality of marks is formed within the pattern area on the substrate.   
     
     
         133 . The layout information providing method according to  claim 1 , further comprising:
 displaying the layout information on a display screen.   
     
     
         134 . A program, to make a computer execute the layout information providing method according to  claim 1 . 
     
     
         135 . An information recording medium that can be read by a computer in which the program according to  claim 134  is stored. 
     
     
         136 . A layout information providing method in which layout information is provided to arrange a plurality of marks for detection using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, the method comprising:
 where pitches of a first direction and a second direction intersecting within a predetermined plane of the plurality of detection areas are D 1  and D 2 , respectively, sizes in the first direction and the second direction of each of the plurality of divided areas arranged two-dimensionally along the first direction and the second direction on the substrate are W 1  and W 2 , respectively, and pitch in the first direction and pitch in the second direction of the plurality of marks arranged on the substrate are p 1  and p 2 , providing as the layout information candidates for the size W 1  and the size W 2  and candidates for pitch p 1  in the first direction and pitch p 2  in the second direction of the plurality of marks corresponding thereto that satisfy formulas (a) and (b) below.
     p   1   =D   1   /i  ( i  denotes a natural number)= W   1   /m  ( m  denotes a natural number)   (a)
 
     p   2   =D   2   /j  ( j  denotes a natural number)= W   2   /n  ( n  denotes a natural number)  (b)
 
   
     
     
         137 . A program, to make a computer execute the layout information providing method according to  claim 136 . 
     
     
         138 . An information recording medium that can be read by a computer in which the program according to  claim 137  is stored. 
     
     
         139 . A layout information providing method in which layout information is provided to arrange a plurality of marks for detection using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, the method comprising:
 where pitches of a first direction and a second direction intersecting within a predetermined plane of the plurality of detection areas are D 1  and D 2 , respectively, and pitch in the first direction and pitch in the second direction of the plurality of marks arranged on the substrate are p 1  and p 2 , respectively, providing candidates for pitch p 1  in the first direction and pitch p 2  in the second direction of the plurality of marks that satisfy formulas (c) and (d) described below as the layout information described above.
     p   1   =D   1   /i  ( i  denotes a natural number)  (c)
 
     p   2   =D   2   /j  ( j  denotes a natural number)  (d)
 
   
     
     
         140 . A program, to make a computer execute the layout information providing method according to  claim 139 . 
     
     
         141 . An information recording medium that can be read by a computer in which the program according to  claim 140  is stored. 
     
     
         142 . A layout information providing method in which layout information is provided to arrange a plurality of marks for detection using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, the method comprising:
 calculating (D 1 /i) and (D 2 /j), which are pitch D 1  in a first direction within a predetermined plane divided by natural number i (i=1 to I) and pitch D 2  in a second direction intersecting the first direction within the predetermined plane divided by natural number j (j=1 to J) of the plurality of detection areas as a plurality of candidates p 1i  for pitch p 1  in the first direction of a plurality of marks arranged on a substrate and a plurality of candidates p 2j  for pitch p 2  in the second direction of a plurality of marks arranged on a substrate, along with calculating m·p 1i , which is a plurality of candidates p 1i  sequentially multiplied by a natural number m (m=1 to M), and n·p 2j , which is a plurality of candidates p 2j  sequentially multiplied by a natural number n (n=1 to N), as candidates for size W 1  in the first direction and size W 2  in the second direction of a plurality of divided areas arranged two-dimensionally along the first direction and the second direction on the substrate, and   providing candidates W 1m  for the size W 1  and candidates W 2n  for size W 2  which are calculated, and candidates p 1i  for pitch p 1  in the first direction and candidates p 2j  for pitch p 2  in the second direction of the plurality of marks corresponding thereto as the layout information.   
     
     
         143 . A program, to make a computer execute the layout information providing method according to  claim 142 . 
     
     
         144 . An information recording medium that can be read by a computer in which the program according to  claim 143  is stored. 
     
     
         145 . A layout information providing method in which layout information is provided to arrange a plurality of marks for detection using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, the method comprising:
 calculating (D 1 /i) and ( D 2/j), which are pitch D 1  in a first direction divided by natural number i (i=1 to I) and pitch D 2  in a second direction divided by natural number j (j=1 to J) of a plurality of virtual points arranged in the first direction and the second direction intersecting each other in a predetermined plane including points in each of the plurality of detection areas, as a plurality of candidates p 1i  for pitch p 1  in the first direction of the plurality of marks arranged on the substrate and a plurality of candidates p 2j  for pitch p 2  in the second direction of the plurality of marks arranged on the substrate, along with calculating m·p 1i , which is a plurality of candidates p 1i  sequentially multiplied by a natural number m (m=1 to M), and n·p 2j , which is a plurality of candidates p 2j  sequentially multiplied by a natural number n (n=1 to N), as candidates for size W 1  in the first direction and size W 2  in the second direction of a plurality of divided areas arranged two-dimensionally along the first direction and the second direction on the substrate, and   providing candidates for the size W 1  and candidates for size W 2  which are calculated, and candidates p 1i  for pitch p 1  in the first direction and candidates p 2j  for pitch p 2  in the second direction of the plurality of marks corresponding thereto as the layout information.   
     
     
         146 . The layout information providing method according to  claim 145 , wherein
 the plurality of virtual points includes a detection center of the plurality of detection areas.   
     
     
         147 . A program, to make a computer execute the layout information providing method according to  claim 145 . 
     
     
         148 . An information recording medium that can be read by a computer in which the program according to  claim 147  is stored. 
     
     
         149 . Layout information to arrange a plurality of marks detected using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, comprising:
 information related to an arrangement of the plurality of marks obtained based on arrangement information on the plurality of detection areas.   
     
     
         150 . Layout information to arrange a plurality of marks for detection using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, the information comprising:
 where pitches of a first direction and a second direction intersecting within a predetermined plane of the plurality of detection areas are D 1  and D 2 , respectively, sizes in the first direction and the second direction of each of the plurality of divided areas arranged two-dimensionally along the first direction and the second direction on the substrate are W 1  and W 2 , respectively, and pitch in the first direction and pitch in the second direction of the plurality of marks arranged on the substrate are p 1  and p 2 , respectively, candidates for the size W 1  and the size W 2  and candidates for pitch p 1  in the first direction and pitch p 2  in the second direction corresponding thereto that satisfy formulas (a) and (b) below, obtained from the pitches D 1  and D 2 .
     p   1   =D   1   /i  ( i  denotes a natural number)= W   1   /m  ( m  denotes a natural number)   (a)
 
     p   2   =D   2   /j  ( j  denotes a natural number)= W   2   /n  ( n  denotes a natural number)  (b)
 
   
     
     
         151 . A determination method to determine an arrangement of a plurality of marks for detection using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, the method comprising:
 determining an arrangement of the plurality of marks based on arrangement information on the plurality of detection areas.   
     
     
         152 . The determination method according to  claim 151 , wherein
 the arrangement of the plurality of marks is an arrangement which allows concurrent detection of a plurality of marks on the substrate in the plurality of detection areas.   
     
     
         153 . The determination method according to  claim 151 , wherein
 determining the arrangement of the plurality of marks includes determining at least one candidate for the arrangement of the plurality of marks, based on the arrangement information on the plurality of detection areas.   
     
     
         154 . The determination method according to  claim 151 , wherein
 determining the arrangement of the plurality of marks includes selecting at least one from a plurality of candidates for the arrangement of the plurality of marks obtained based on the arrangement information on the plurality of detection areas.   
     
     
         155 . The determination method according to  claim 151 , wherein
 the plurality of detection areas includes a first detection area, a second detection area arranged apart in a first direction with respect to the first detection area, and a third detection area arranged apart in a second direction intersecting with the first direction within a predetermined plane.   
     
     
         156 . The determination method according to  claim 155 , wherein
 the plurality of detection areas is arranged in a matrix shape in the first direction and the second direction.   
     
     
         157 . The determination method according to  claim 155 , wherein
 the plurality of detection areas includes three or more detection areas arranged at a first pitch in the first direction and three or more detection areas arranged at a second pitch in the second direction, and   arrangement information on the plurality of detection areas includes information on the first pitch and the second pitch.   
     
     
         158 . The determination method according to  claim 155 , wherein
 determining the arrangement of the plurality of marks includes determining pitch of a plurality of marks formed along the first direction and pitch of a plurality of marks formed along the second direction.   
     
     
         159 . The determination method according to  claim 155 , wherein
 where pitches in the first direction and the second direction of the plurality of detection areas are D 1  and D 2 , respectively, as the arrangement information on the plurality of detection areas, and sizes in the first direction and the second direction of the divided areas are W 1  and W 2 , respectively, as the information related to size of the divided areas, pitch p 1  in the first direction and pitch p 2  in the second direction of the plurality of marks that satisfy formulas (a) and (b) below are determined.
     p   1   =D   1   /i  ( i  denotes a natural number)= W   1   /m  ( m  denotes a natural number)   (a)
 
     p   2   =D   2   /j  ( j  denotes a natural number)= W   2   /n  ( n  denotes a natural number)  (b)
 
   
     
     
         160 . The determination method according to  claim 159 , further comprising:
 determining size W 1  in the first direction and size W 2  in the second direction of the divided areas that satisfy the formulas (a) and (b).   
     
     
         161 . The determination method according to  claim 155 , further comprising:
 determining size in the first direction and size in the second direction of the divided areas, based on the arrangement information on the plurality of detection areas.   
     
     
         162 . The determination method according to  claim 151 , further comprising:
 determining the size of the divided areas, based on the arrangement of the plurality of detection areas.   
     
     
         163 . The determination method according to  claim 162 , wherein
 determining the size of the divided areas includes determining at least one candidate for the size of the divided areas.   
     
     
         164 . The determination method according to  claim 163 , wherein
 determining arrangement of the plurality of marks includes determining a plurality of candidates for the arrangement of the plurality of marks corresponding to at least one candidate for the size of divided areas.   
     
     
         165 . The determination method according to  claim 151 , wherein
 the arrangement of the plurality of marks is determined based on arrangement information on the plurality of detection areas and information related to the size of the divided areas.   
     
     
         166 . The determination method according to  claim 165 , wherein
 the information on the size of the divided areas includes information related the size in the first direction and the size in the second direction.   
     
     
         167 . The determination method according to  claim 166 , wherein
 determining arrangement of the plurality of marks includes determining at least one candidate for the size of the divided areas and at least one candidate for the arrangement of the plurality of marks corresponding to the at least one candidate for the size of the divided areas, based on the arrangement information on the plurality of detection areas and the information related to the size of the divided areas.   
     
     
         168 . The determination method according to  claim 165 , wherein
 the information on the size of the divided areas includes information related to a range of the size of the divided areas.   
     
     
         169 . The determination method according to  claim 168 , wherein
 determining arrangement of the plurality of marks includes determining at least one candidate for the size of the divided areas and at least one candidate for the arrangement of the plurality of marks corresponding to the at least one candidate for the size of the divided areas, based on the arrangement information on the plurality of detection areas and the information related to the size of the divided areas.   
     
     
         170 . The determination method according to any  claim 165 , wherein
 determining arrangement of the plurality of marks includes selecting one set of the size of the divided areas and the arrangement of the plurality of marks, from at least one candidate for the size of the divided areas and at least one candidate for the arrangement of the plurality of marks corresponding thereto, obtained based on the arrangement information on the plurality of detection areas and the information related to the size of the divided areas.   
     
     
         171 . The determination method according to  claim 151 , wherein
 arrangement information on the detection areas includes information on space between the plurality of detection areas.   
     
     
         172 . The determination method according to  claim 151 , wherein
 the plurality of detection areas is arranged at a predetermined pitch, and   the arrangement information on the plurality of detection areas includes information on the predetermined pitch.   
     
     
         173 . A program, to make a computer execute the determination method according to  claim 151 . 
     
     
         174 . An information recording medium that can be read by a computer in which the program according to  claim 173  is stored. 
     
     
         175 . A determination method to determine an arrangement of a plurality of marks for detection using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, the method comprising:
 where pitches of a first direction and a second direction intersecting within a predetermined plane of the plurality of detection areas are D 1  and D 2 , respectively, sizes in the first direction and the second direction of each of the plurality of divided areas arranged two-dimensionally along the first direction and the second direction on the substrate are W 1  and W 2 , respectively, and pitch in the first direction and pitch in the second direction of the plurality of marks arranged on the substrate are p 1  and p 2 , respectively, determining pitch p 1  in the first direction and pitch p 2  in the second direction of the plurality of marks that satisfy formulas (a) and (b) below, based on the pitch D 1 , the pitch D 2 , the size W 1  and the size W 2 .
     p   1   =D   1   /i  ( i  denotes a natural number)= W   1   /m  ( m  denotes a natural number)   (a)
 
     p   2   =D   2   /j  ( j  denotes a natural number)= W   2   /n  ( n  denotes a natural number)  (b)
 
   
     
     
         176 . A program, to make a computer execute the determination method according to  claim 175 . 
     
     
         177 . An information recording medium that can be read by a computer in which the program according to  claim 176  is stored. 
     
     
         178 . A determination method to determine an arrangement of a plurality of marks for detection using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, the method comprising:
 where pitches of a first direction and a second direction intersecting within a predetermined plane of the plurality of detection areas are D 1  and D 2 , respectively, sizes in the first direction and the second direction of each of the plurality of divided areas arranged two-dimensionally along the first direction and the second direction on the substrate are W 1  and W 2 , respectively, and pitch in the first direction and pitch in the second direction of the plurality of marks arranged on the substrate are p 1  and p 2 , respectively, determining at least one candidate for each of pitch p 1  in the first direction and pitch p 2  in the second direction of the plurality of marks that satisfy formulas (a) and (b) below, based on the pitch D 1 , the pitch D 2 , the size W 1  and the size W 2 .
     p   1   =D   1   /i  ( i  denotes a natural number)= W   1   /m  ( m  denotes a natural number)   (a)
 
     p   2   =D   2   /j  ( j  denotes a natural number)= W   2   /n  ( n  denotes a natural number)  (b)
 
   
     
     
         179 . A program, to make a computer execute the determination method according to  claim 178 . 
     
     
         180 . An information recording medium that can be read by a computer in which the program according to  claim 179  is stored. 
     
     
         181 . A determination method to determine an arrangement of a plurality of marks for detection using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, and size of the divided areas, the method comprising:
 where pitches of a first direction and a second direction intersecting within a predetermined plane of the plurality of detection areas are D 1  and D 2 , respectively, sizes in the first direction and the second direction of each of the plurality of divided areas arranged two-dimensionally along the first direction and the second direction on the substrate are W 1  and W 2 , respectively, and pitch in the first direction and pitch in the second direction of the plurality of marks arranged on the substrate are p 1  and p 2 , respectively, determining size W 1  and size W 2  of the divided areas and pitch p 1  in the first direction and pitch p 2  in the second direction of the plurality of marks that satisfy formulas (a) and (b) below, based on the pitch D 1  and the pitch D 2 .
     p   1   =D   1   /i  ( i  denotes a natural number)= W   1   /m  ( m  denotes a natural number)   (a)
 
     p   2   =D   2   /j  ( j  denotes a natural number)= W   2   /n  ( n  denotes a natural number)  (b)
 
   
     
     
         182 . A program, to make a computer execute the determination method according to  claim 181 . 
     
     
         183 . An information recording medium that can be read by a computer in which the program according to  claim 182  is stored. 
     
     
         184 . A determination method to determine an arrangement of a plurality of marks for detection using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, and size of the divided areas, the method comprising:
 where pitches of a first direction and a second direction intersecting within a predetermined plane of the plurality of detection areas are D 1  and D 2 , respectively, sizes in the first direction and the second direction of each of the plurality of divided areas arranged two-dimensionally along the first direction and the second direction on the substrate are W 1  and W 2 , respectively, and pitch in the first direction and pitch in the second direction of the plurality of marks arranged on the substrate are p 1  and p 2 , respectively, determining at least one candidate for each of size W 1  and size W 2 , and at least one candidate for each of pitch p 1  in the first direction and pitch p 2  in the second direction of the plurality of marks corresponding thereto that satisfy formulas (a) and (b) below.
     p   1   =D   1   /i  ( i  denotes a natural number)= W   1   /m  ( m  denotes a natural number)   (a)
 
     p   2   =D   2   /j  ( j  denotes a natural number)= W   2   /n  ( n  denotes a natural number)  (b)
 
   
     
     
         185 . A program, to make a computer execute the determination method according to  claim 184 . 
     
     
         186 . An information recording medium that can be read by a computer in which the program according to  claim 185  is stored. 
     
     
         187 . A determination method to determine size of a plurality of divided areas and mark pitch so that a plurality of marks for detection that uses a mark detection system having a plurality of detection areas is arranged along with a plurality of divided areas on a substrate, the method comprising:
 sequentially calculating (D 1 /i) and (D 2 /j), which are pitch D 1  in a first direction divided by natural number i (i=1 to I) and pitch D 2  in a second direction divided by natural number j (j=1 to J) of a plurality of virtual points arranged in the first direction and the second direction intersecting each other in a predetermined plane including points in each of the plurality of detection areas, as a plurality of candidates p 1i  for pitch p 1  in the first direction and a plurality of candidates p 2j  for pitch p 2  in the second direction of the plurality of marks arranged on the substrate,   calculating m·p 1i , which is a plurality of candidates p 1i  (i=1 to I) sequentially multiplied by a natural number m (m=1 to M), and n·p 2j , which is a plurality of candidates p 2j  (j=1 to J) sequentially multiplied by a natural number n (n=1 to N), as candidates for size W 1  in the first direction and candidates for size W 2  in the second direction of the plurality of divided areas arranged two-dimensionally along the first direction and the second direction on the substrate, and   of the candidates for size W 1  and the candidates for size W 2  which are calculated, determining candidates whose values satisfy conditions decided in advance as final candidates for each of the size W 1  and the size W 2 , and determining candidates p 1i  for pitch p 1  in the first direction and candidates p 2j  for pitch p 2  in the second direction of the plurality of marks corresponding to the final candidates that are determined as final candidates for the pitch p 1  and final candidates for the pitch p 2 .   
     
     
         188 . The determination method according to  claim 187 , further comprising:
 creating mark layout information in which a plurality of marks are arranged two-dimensionally in the first direction and the second direction at the pitch p 1  and the pitch p 2  on the divided areas, based on the final candidates for each of the size W 1  and the size W 2  that have been determined and the final candidates for each of the pitch p 1  and the pitch p 2  that have been determined.   
     
     
         189 . The determination method according to  claim 188 , further comprising:
 displaying the mark layout information created on a display screen.   
     
     
         190 . The determination method according to  claim 187 , wherein
 the plurality of virtual points includes a detection center of each of the plurality of detection areas.   
     
     
         191 . A program, to make a computer execute the determination method according to  claim 187 . 
     
     
         192 . An information recording medium that can be read by a computer in which the program according to  claim 191  is stored. 
     
     
         193 . A determination method to determine an arrangement of a plurality of detection areas of a mark detection system used to detect a plurality of marks arranged on a substrate with a plurality of divided areas, along with an arrangement of the plurality of marks, the method comprising:
 sequentially calculating (W 1 /m) and (W 2 /n), which are size W 1  in a first direction and size W 2  in the second direction divided by a natural number m (m=1 to M) and a natural number n (n=1 to N), respectively, of the plurality of divided areas arranged two-dimensionally along the first direction and the second direction intersecting each other on the substrate, as a plurality of candidates p 1m  (m=1 to M) for pitch p 1  in the first direction and a plurality of candidates p 2n  (n=1 to N) for pitch p 2  in the second direction of the plurality of marks arranged on the substrate,   calculating i·p 1m  and j·p 2n , which are the plurality of candidates p 1m  (m=1 to M) and the plurality of candidates p 2n  (n=1 to N), sequentially multiplied by a natural number i (i=1 to I) and a natural number j (j=1 to J), respectively, as candidates D 1im  for pitch D 1  in the first direction and candidates D 2jn  for pitch D 2  in the second direction of a plurality of virtual points arranged in the first direction and the second direction within a predetermined plane parallel to the substrate, and   of the candidates D 1im  for pitch D 1  and candidates D 2jn  for pitch D 2  that have been calculated, determining candidates whose values satisfy conditions decided in advance as final candidates for each of the pitch D 1  and the pitch D 2 , along with determining the arrangement of the plurality of detection areas of the mark detection system so that at least a part of the plurality of virtual points decided according to the final candidates which are determined is positioned within each detection area, and determining a plurality of candidates p 1m  for pitch p 1  in the first direction and a plurality of candidates p 2n  for pitch p 2  in the second direction of the plurality of marks corresponding to the final candidates that are determined as final candidates for the pitch D 1  and final candidates for the pitch D 2 .   
     
     
         194 . The determination method according to  claim 193 , wherein
 the arrangement of the plurality of detection areas of the mark detection system is determined so that each of the at least a part of the plurality of virtual points coincides with a detection center of the plurality of detection areas.   
     
     
         195 . A program, to make a computer execute the determination method according to  claim 193 . 
     
     
         196 . An information recording medium that can be read by a computer in which the program according to  claim 195  is stored. 
     
     
         197 . A determination method to determine an arrangement of a plurality of detection areas of a mark detection system used to detect a plurality of marks on a substrate on which a plurality of divided areas is set, the method comprising:
 determining the arrangement of the plurality of detection areas, based on size of the plurality of divided areas arranged two-dimensionally along in a first direction and a second direction intersecting each other on the substrate.   
     
     
         198 . The determination method according to  claim 197 , wherein
 the plurality of detection areas has a plurality of detection areas arranged apart in the first direction and a plurality of detection areas arranged apart in the second direction,   size of the divided areas include size in the first direction and size in the second direction,   arrangement of a plurality of detection areas arranged apart in the first direction is determined, based on the size in the first direction, and   arrangement of a plurality of detection areas arranged apart in the second direction is determined, based on the size in the second direction.   
     
     
         199 . The determination method according to  claim 198 , wherein
 pitch in a plurality of detection areas arranged apart in the first direction is determined, based on the size in the first direction, and   pitch in a plurality of detection areas arranged apart in the second direction is determined, based on the size in the second direction.   
     
     
         200 . The determination method according to  claim 197 , wherein
 the plurality of detection areas includes a first detection area, a second detection area apart in the first direction with respect to the first detection area, and a third detection area apart in the second direction with respect to the second detection area.   
     
     
         201 . The determination method according to  claim 197 , wherein
 where size in the first direction and size in the second direction of the divided areas are W 1  and W 2 , respectively, pitch in the first direction and pitch in the second direction of the plurality of detection areas are D 1  and D 2 , respectively, determination of the arrangement of the plurality of detection areas includes determining pitch D 1  and pitch D 2  of the plurality of detection areas that satisfy formulas (c) and (d) below, based on size W 1  and size W 2  of the divided areas.
     D   1   /i  ( i  denotes a natural number)= W   1   /m  ( m  denotes a natural number)  (c)
 
     D   2   /j  ( j  denotes a natural number)= W   2   /n  ( n  denotes a natural number)  (d)
 
   
     
     
         202 . A program, to make a computer execute the determination method according to  claim 197 . 
     
     
         203 . An information recording medium that can be read by a computer in which the program according to  claim 202  is stored. 
     
     
         204 . A determination method to determine an arrangement of a plurality of detection areas of a mark detection system used to detect a plurality of marks on a substrate on which a plurality of divided areas is set, wherein
 the plurality of detection areas includes a plurality of detection areas apart in a first direction within a predetermined plane and a plurality of detection areas apart in a second direction intersecting the first direction within the predetermined plane, and   where pitch in the first direction of the plurality of detection areas is D 1  and pitch in the second direction of the plurality of detection areas is D 2 , size in the first direction of the plurality of divided areas arranged on the substrate is W 1  and size in the second direction of the plurality of detection areas is W 2 ,   determining the arrangement of the plurality of detection areas includes determining pitch D 1  and pitch D 2  of the plurality of detection areas that satisfy formulas (c) and (d) below, based on size W 1  and size W 2  of the divided areas.
     D   1   /i  ( i  denotes a natural number)= W   1   /m  ( m  denotes a natural number)  (c)
 
     D   2   /j  ( j  denotes a natural number)= W   2   /n  ( n  denotes a natural number)  (d)
 
   
     
     
         205 . A program, to make a computer execute the determination method according to  claim 204 . 
     
     
         206 . An information recording medium that can be read by a computer in which the program according to  claim 205  is stored. 
     
     
         207 . A determination apparatus that determines an arrangement of a plurality of marks for detection using a mark detection system having a plurality of detection areas on a substrate on which a plurality of divided areas is set, the apparatus comprising:
 a calculating means that calculates pitch p 1  and pitch p 2  of the plurality of marks that satisfy formulas (a) and (b) below, based on pitch D 1 , pitch D 2 , size W 1  and size W 2 , when pitches of a first direction and a second direction intersecting within a predetermined plane of the plurality of detection areas are D 1  and D 2 , respectively, sizes in the first direction and the second direction of each of the plurality of divided areas arranged two-dimensionally along the first direction and the second direction on the substrate are W 1  and W 2 , respectively, and pitch in the first direction and pitch in the second direction of the plurality of marks arranged on the substrate are p 1  and p 2 , respectively.
     p   1   =D   1   /i  ( i  denotes a natural number)= W   1   /m  ( m  denotes a natural number)   (a)
 
     p   2   =D   2   /j  ( j  denotes a natural number)= W   2   /n  ( n  denotes a natural number)  (b)