Abstract:
The alignment marks formed in a scribe line of a semiconductor substrate include at least one main mark, a first sub-mark and second sub-marks. The first sub-mark is formed at a central portion of the main mark. The second sub-marks are disposed symmetrically with respect to the first sub-mark and are used for detecting asymmetry of the main mark by measuring distances between respective side edges of the main mark and the first sub-mark, and by measuring respective side edges between the main mark and each of the second sub-marks. Alternatively, the alignment marks include main outer and inner marks and a sub-mark disposed in between the main outer and inner marks. In this case, the sub-mark is used for detecting asymmetry of the main mark by measuring distances between respective side edges of the main outer mark and the sub-mark, and by measuring respective side edges between the main inner mark and the sub-mark. Thus, accurate alignment information can be obtained regardless of whether the main mark was inadvertently formed as asymmetrical.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to the forming of superimposed patterns on a substrate in the manufacturing of semiconductor devices and the like. More particularly, the present invention relates to a substrate inscribed with alignment marks for ensuring that an upper pattern is formed in alignment with a lower pattern on the substrate. The present invention also relates to a method of forming such alignment marks and to a method of obtaining alignment information for use in superimposing patterns on a substrate, in the manufacturing of a semiconductor device. 
     2. Description of the Related Art 
     In general, a semiconductor device is manufactured by forming patterns on a semiconductor substrate. Each pattern is formed through a series of processes. The processes are performed selectively and repeatedly to form the patterns one above the other on the substrate. In this respect, it is very important for a lower pattern (formed by a first series of processes) and an upper pattern (formed by a subsequent series of processes) to be aligned with each other. To this end, alignment marks are used. The alignment marks are formed on a scribe line of the semiconductor substrate which demarcates regions (dies) in which circuit structures are formed 
     Referring to  FIGS. 1 and 2 , conventional alignment marks  10  include a main alignment mark  11  in the form of a rectangular band, and a sub-alignment mark  12  disposed at a central region of the main alignment mark  11 . The main alignment mark  11  is part of a conductive pattern. The sub-alignment mark  12  is part of a photoresist pattern. 
     That is, the main alignment mark  11  is formed by a sputtering process in a first series of processes aimed at forming a lower conductive pattern on the semiconductor substrate. The sub-alignment mark  12  is formed by a photolithographic process in a subsequent series of processes aimed at forming an upper pattern on the semiconductor substrate. Distances between the main alignment mark  11  and the sub-alignment mark  12  are measured in lengthwise and widthwise directions of the scribe line. The degree to which the upper pattern and the lower pattern are aligned is determined based on these overlay measurements. Moreover, the overlay measurements are fed back to the processing equipment for use in adjusting the equipment, if necessary, to ensure that subsequently formed patterns are accurately aligned with the previously formed patterns. 
     However, as shown in  FIGS. 1 and 2 , the sputtering process may form a protrusion  13  at an inner side of the main alignment mark  11 . In this case, a first distance d 1  between one inner side of the main alignment mark  11  and an adjacent outer side of the sub-alignment mark  12  is different from a second distance d 2  between the other inner side of the main alignment mark  11  and the adjacent outer side of the sub-alignment mark  12 . That is, results of the overlay measurements (alignment information) will indicate a difference between the first distance d 1  and the second distance d 2  even though the sub-alignment mark  12  was centered relative to the main alignment mark  11 . Therefore, the results of the overlay measurements will incorrectly indicate that the sub-alignment mark  12  was formed as offset relative to the main alignment mark  11 , i.e., that the upper pattern and the lower pattern are misaligned. As a result, the data fed back to the processing equipment as a result of the overlay measurement process will cause the equipment to form a subsequent pattern out of alignment. 
     SUMMARY OF THE INVENTION 
     A feature of the present invention is to provide alignment marks by which accurate alignment information may be obtained in the manufacturing of semiconductor devices and the like. 
     Another feature of the present invention is to provide a method of obtaining alignment information which accurately represents the degree to which superimposed patterns are aligned in the manufacturing of semiconductor devices and the like. 
     According to one aspect of the present invention, alignment marks of a substrate, formed in a scribe line of the substrate, include at least one main mark, a first sub-mark and second sub-marks. The first sub-mark is centrally located with respect to inner side edges of the main mark. The second sub-marks are disposed symmetrically with respect to the first sub-mark. The alignment marks are formed as part of the processes that form upper and lower patterns on a region (die) of the substrate. 
     According to another aspect of the present invention, there is provided a method of obtaining alignment information using the alignment marks. In addition to steps of forming the alignment marks, the method includes determining a degree of alignment between the at least one main mark and the first sub-mark, determining a degree of alignment between the at least one main mark and one of the second sub-marks, and determining a degree of alignment between the at least one main mark and the other of the second sub-marks. Values corresponding to the degree of alignment between the at least one main mark and the first sub-mark, the degree of alignment between the at least one main mark and the one second sub-mark, and the degree of alignment between the at least one main mark and the other second sub-mark are assigned to thereby provide first, second and third values, respectively. The average of the second and third values is subtracted from the first value to yield a final alignment value representative of the degree of alignment between upper and lower patterns formed on the substrate. 
     The main mark may have a first inner side edge, a second inner side edge, a first outer side edge, and a second outer side edge facing in opposite directions at opposite sides of the first and the second inner side edges, respectively. In this case, each of the second sub-marks has inner side edges located on opposite sides of a respective pair of the inner and outer side edges of the main mark, respectively. 
     In this case, the degree of alignment between the main mark and the first sub-mark is determined by measuring the distance between the first inner side edge of the main mark and the first outer side edge of the first sub-mark, measuring the distance between the second inner side edge of the main mark and the second outer side edge of the first sub-mark, and dividing the difference between the distances by two. Likewise, the degree of alignment between the main mark and each of the second sub-marks is determined by measuring the distance between a respective one of the inner side edges of the main mark and a first one of the inner side edges of the second sub-mark, measuring the distance between the second inner side edge of the main mark and a second one of the inner side edges of the second sub-mark, and dividing the difference between the distances by two. 
     Alternatively, and according to another aspect of the invention, the at least one main mark includes a central main mark and peripheral main marks. The central main mark has inner side edges facing each other and in between which the first sub-mark is situated. The peripheral main marks are disposed to both sides of the central mark, respectively. Each of the peripheral main marks has inner side edges facing each other in the same direction as the inner side edges of the central mark, and each of the second sub-marks is situated in between the inner side edges of a respective one of the peripheral marks. For example, the peripheral main marks have corners that are disposed diagonally across from each other. In this case, the sub-marks are disposed adjacent the corners of the peripheral main marks, respectively. 
     In this case, the degree of alignment between the at least one main mark and the first sub-mark is determined by measuring the distance between the first inner side edge of the central main mark and the first outer side edge of the first sub-mark, measuring the distance between the second inner side edge of the central main mark and the second outer side edge of the first sub-mark, and dividing the difference between the distances by two. The degree of alignment between the at least one main mark and each of the second sub-marks is determined by measuring the distance between one inner side edge of a respective one of the peripheral main marks and one outer side edge of the second sub-mark associated with the peripheral main mark, measuring the distance between the other inner side edge of the respective one of the peripheral main marks and the other outer side edge of the second sub-mark, and dividing the difference between the distances by two. 
     According to still another aspect of the present invention, alignment marks, formed in a scribe line of a substrate, include a main outer mark, a main inner mark and a sub-mark. The main outer mark has a first inner side edge and a second inner side edge faced towards each other. The main inner mark is disposed at the same level as the main mark and is situated in between the inner side edges of the main outer mark. Thus, the main inner mark has a first outer side edge and a second outer side edge faced towards the first and the second inner side edges of the main outer mark, respectively. The sub-mark is disposed on the substrate at a level different from those at which the main inner and outer marks are disposed, and is situated intermediate the main outer and inner marks. The sub-mark has outer side edges faced in directions towards the inner side edges of the main outer mark, respectively, and inner side edges faced in directions towards the outer side edges of the main inner mark, respectively. 
     According to another aspect of the present invention, there is provided a method of obtaining alignment information using these alignment marks. In addition to steps of forming the alignment marks, the method includes determining a degree of alignment between the main outer mark and the sub-mark, and determining a degree of alignment between the main inner mark and the sub-mark. Values corresponding to the degree of alignment between the main outer mark and the sub-mark, and the degree of alignment between the main inner mark and the sub-mark are assigned to thereby provide first and second values, respectively. The first and second values are averaged to yield a final alignment value representative of the degree of alignment between upper and lower patterns formed on the substrate. 
     For example, the degree of alignment between the main outer mark and the sub-mark is determined by measuring the distance between the first inner side edge of the main outer mark and the first outer side edge of the sub-mark, measuring the distance between the second inner side edge of the main outer mark and the second outer side edge of the sub-mark, and dividing the difference between the distances by two. Likewise, the degree of alignment between the main inner mark and the sub-mark is determined by measuring the distance between the first outer side edge of the main inner mark and the first inner side edge of the sub-mark, measuring the distance between the second outer side edge of the main inner mark and the second inner side edge of the sub-mark, and dividing the difference between the distances by two. According to the present invention, accurate alignment information, which reflects a protrusion inadvertently produced by the series of processes used to form the lower pattern and the main alignment mark, may be obtained. That is, the present invention compensates for any asymmetry in the main alignment mark(s). Thus, the degree of alignment between an upper pattern and a lower pattern formed on the substrate may be precisely determined using the alignment information. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other objects, features and advantages of the invention will become readily apparent by referring to the following detailed description of the preferred embodiments thereof made in conjunction with the accompanying drawings wherein: 
         FIG. 1  is a plan view of a conventional alignment inscription; 
         FIG. 2  is a cross-sectional view taken along a line II-II′ in  FIG. 1 ; 
         FIG. 3  is a plan view of a section of a substrate having an example embodiment of an alignment inscription in accordance with the present invention; 
         FIG. 4  is a cross-sectional view taken along a line IV-IV′ in  FIG. 3 ; 
         FIG. 5  is a flow chart of a method of obtaining alignment information using the alignment inscription of  FIG. 3 ; 
         FIG. 6  is a plan view of an example embodiment of an alignment inscription in accordance with the present invention; 
         FIG. 7  is a flow chart of a method of obtaining alignment information using the alignment inscription of  FIG. 6 ; and 
         FIG. 8  is a plan view of an example embodiment of an alignment inscription in accordance with the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     The present invention will described more fully hereinafter with reference to the accompanying drawings. In the drawings, the size and relative sizes of layers and regions may be exaggerated for the sake of clarity. Also, like reference numerals designate like elements throughout the drawings. Also, certain element(s)/layer(s) may be omitted for the sake of clarity. That is, the specification may refer to an element/layer as being disposed “on” another element/layer. In this case, the description means that the referenced element/layer may be disposed directly on the other element/layer or that an intervening element(s) or layer(s) may be present between the referenced element/layer and the other element/layer. Still further, the specification uses the relative terms “right”, “left”, “up” and “down” in connection with certain features of the present invention. However, it will be understood that these terms are not limiting in any respect but are merely used in connection with identifying the relative locations at which such features of the present invention are shown the drawings. Likewise, the terms “first”, “second”, etc. are used in the specification only as a means to differentiate similar features or steps from one another and do not necessarily identify any particular order associated with the forming of such features or any particular order in which such steps are carried out. 
     Referring to  FIGS. 3 and 4 , a semiconductor substrate W has alignment marks  100  confined to a scribe line  101 . The scribe line  101  demarcates regions A, B (dies) of the substrate W in which circuit structures are formed. The alignment marks  100  include a main mark  110 , a first sub-mark  120  and second sub-marks  130 . 
     For example, the main mark  110  is a band in the form of a rectangle. Thus, the main mark  110  has a first inner side edge  111 , a second inner side edge  112  opposite and extending parallel to the first inner side edge  111 , a third inner side edge  113  substantially perpendicular to the first and second inner side edges  111  and  112 , and a fourth inner side edge  114  opposite and extending parallel to the third inner side edge  113 . The main mark  110  may be formed simultaneously with a lower pattern formed on a die A, B of the semiconductor substrate W. More specifically, the main mark  110  may be part of a conductive (metal) pattern that is formed by subjecting the substrate W to a first series of processes including a sputtering process. Such a sputtering process, though, may form a protrusion  118  as an integral part of the main mark  110  and at only one inner side of the main mark  110 . In this case, for example, the distance between the center of the main mark  110  and the first inner side edge  111  is different from the distance between the center of the main mark  110  and the second inner side edge  112 . 
     The first sub-mark  120  is formed on a region of the substrate W corresponding to a central portion of the main mark  110 . That is, the center of the first sub-mark  120  is substantially coincident with a line passing directly above the intended center of the main mark  110 . The first sub-mark  120  may be formed simultaneously with an upper pattern that is formed over the lower pattern. More specifically, the first sub-mark  120  may be part of a photoresist pattern that is formed by subjecting the substrate W to a second series of processes including a photolithographic process. For example, the first sub-mark  120  is rectangular, i.e., is a solid rectangle of photoresist. Thus, the first sub-mark  120  has a first outer side edge  121  facing the first inner side edge  111  of the main mark  110 , a second outer side edge  122  facing the second inner side edge  112  of the main mark  110 , a third outer side edge  123  facing the third inner side edge  113  of the main mark  110 , and a fourth outer side edge  124  facing the fourth inner side edge  114  of the main mark  110 . 
     The second sub-marks  130  include a left mark  131  formed on a first side of the main mark  110 , and a right mark  135  formed on a second side of the main mark  110  opposite the first side. For example, the left mark  131  and the right mark  135  have substantially the same shape and more preferably, both have the form of a square band. Moreover, the left mark  131  and the right mark  135  are symmetrical with respect to the first sub-mark  120 . Thus, in an example embodiment, the centers of the left mark  131  and the right mark  135  both lie along a line that passes through the center of the main mark  110 . 
     Also, the left mark  131  has a first inner side edge  132  facing the first inner side edge  111  of the main mark  110 , and a second inner side edge  133  facing a first outer side edge  115  of the main mark  110  opposite to the first inner side edge  111  of the main mark  110 . Furthermore, the right mark  135  has a first inner side edge  136  facing the second inner side edge  112  of the main mark  110 , and a second inner side edge  137  facing a second outer side edge  116  of the main mark  110  opposite to the second inner side edge  112  of the main mark  110 . 
     As will be described below, the degree of alignment between the upper pattern and the lower pattern is determined based on measurements of the alignment marks  100  taken in two orthogonal directions, namely in both the widthwise direction of the scribe line  101  and in the lengthwise direction of the scribe line  101 . In the embodiment shown in  FIG. 3 , the protrusion  118 , if formed, influences these measurements in the widthwise direction of the scribe line  101 . Therefore, the alignment marks  100  may also include third sub-marks  140  corresponding to the second sub-marks  130 . Specifically, the third sub-marks  140  include a lower mark  141  formed on a third side of the main mark  110  and an upper mark  145  formed on a fourth side of the main mark opposite the third side. The dispositions of the third sub-marks  140  relative to the outer side edges  123  and  124  of the second sub-mark  120  are substantially the same as the dispositions of the second sub-marks  130  with respect to the outer side edges  121  and  122  of the second sub-mark  120 . Therefore, the third sub-marks  140  will not be described any further for the sake of brevity. 
       FIG. 5  is a flow chart of a method for determining a degree of alignment between an upper pattern and a lower pattern, using the alignment marks  100 , according to the present invention. 
     Referring to  FIGS. 3 to 5 , the main mark  110  is formed on the semiconductor substrate W in the scribe line  101  by a series of first processes including a sputtering process (S 150 ). The first series of processes also forms a lower pattern (not shown) on the substrate W within a die A, B of the substrate. The main mark  110  is intended to have a uniform width. In an example embodiment, however, the sputtering process forms an unintended protrusion  118  extending inwardly at one side of the main mark  110 . The protrusion  118  has a width of about 10 nm. 
     Next, the first sub-mark  120  is formed on a central portion of the main mark  110  by a second series of processes including processes that form a photoresist pattern (S 152 ). In this respect, the first sub-mark  120  is part of the photoresist pattern. The second series of processes is also for forming an upper pattern on the substrate W within a die A, B of the substrate. Also, the second sub-marks  130  are formed on the main mark  110  (S 154 ). More specifically, the left mark  131  is formed on the first side of the main mark  110 , and the right mark  135  is formed on the second side of the main mark  110 . A degree of alignment between the main mark  110  and the first sub-mark  120  is determined (S 156 ) once the second sub-marks  130  have been formed. This degree of alignment will be designated as the first degree of alignment. Specifically, a first distance X 1  between the first inner side edge  111  of the main mark  110  and the first outer side edge  121  of the first sub-mark  120  is measured. Also, a second distance X 2  between the second inner side edge  112  of the main mark  110  and the second outer side edge  122  of the first sub-mark  120  is measured. In the example shown in  FIG. 3 , the second distance X 2  is less than the first distance X 1  by the width of the protrusion  118 , i.e., about 10 nm. The difference between the first distance X 1  and the second distance X 2  is divided by two, and the first degree alignment is assigned this value. Accordingly, for example, the first degree of alignment is about 5 nm. 
     A degree of alignment between the main mark  110  and the left mark  130  is also determined (S 158 ).This degree of alignment will be designated as the second degree of alignment. Specifically, a first distance Y 1  between the first inner side edge  111  of the main mark  110  and the first inner side edge  132  of the left mark  131  is measured. Also, a second distance Y 2  between the first outer side edge  115  of the main mark  110  and the second inner side edge  133  of the left mark  131  is measured. The difference between the first distance Y 1  and the second distance Y 2  is divided by two to obtain the degree of alignment between the main mark  110  and the left mark  131 . For example, the difference between the first distance Y 1  and the second distance Y 2  is about 0 because the sputtering process did not produce any protrusion at the first side of the main mark  110 . Therefore, the second degree of alignment is assigned a value about 0. 
     A degree of alignment between the main mark  110  and the right mark  135  is also determined (S 160 ). This degree of alignment will be designated as the third degree of alignment. Specifically, a first distance Z 1  between the second inner side edge  112  of the main mark  110  and the first inner side edge  136  of the right mark  135  is measured. Furthermore, a second distance Z 2  between the second outer side edge  116  of the main mark  110  and the second inner side edge  137  of the right mark  135  is measured. The difference between the first distance Z 1  and the second distance Z 2  is divided by two, and the degree of alignment between the main mark  110  and the right mark  135  is assigned the resulting value. For example, the difference between the first distance Z 1  and the second distance Z 2  is about 10 nm. Therefore, the third degree of alignment is assigned a value of about 5 nm. 
     A final degree of alignment is then calculated (S 162 ). This final degree of alignment represents an actual degree of alignment between the main mark  110  and the first sub-mark  120 . First, the difference between the second degree of alignment and the third degree of alignment is divided by two. The result is subtracted from the first degree of alignment to obtain the final degree of alignment. For example, the first degree of alignment is about 5 nm and the average of the second and third degrees of alignment is about 2.5 nm. Therefore, the final degree of alignment is about 2.5 nm. 
     Note, the final degree of alignment calculated according to the present invention factors in the protrusion  118 , but not any misalignment of the first sub-mark  120  relative to the main mark  110 . Also, degrees of alignment between the fourth sub-marks  140  and the main mark  110  can be determined, respectively, in a manner similar to that used to determine the third degree of alignment. The results may be used to verify the final degree of alignment. Finally, the final degree of alignment is converted to a compensation value corresponding to the width of the protrusion  118 . The compensation value is fed back to an alignment measuring device for determining the degree of alignment between the upper and lower patterns formed on the die A, B of the substrate W. The results produced by the measuring device are adjusted by the compensation value. Therefore, the results produced by the alignment measuring device will indicate that the upper and lower patterns are aligned (normal) even when the alignment marks  100 , scrutinized by the alignment measuring device, include a main mark  110  that has not been formed properly, i.e., is asymmetrical. 
       FIG. 6  shows another example embodiment of a substrate having alignment marks  200  according to the present invention. Those aspects of this example embodiment which are the same as those described above in connection with first embodiment, e.g., the forming of the alignment marks  200 , will not be described for the sake of brevity. 
     Referring now to  FIG. 6 , the alignment marks  200  are formed on a scribe line of a semiconductor substrate which scribe line demarcates the dies of the substrate (refer to  FIGS. 3 and 4 ). The alignment marks  200  include main mark  210 , a first sub-mark  220  and second sub-marks  230 . The main marks  210 , in turn, include a central main mark  211 , a left (peripheral) main mark  212  disposed to and adjacent one side of the central main mark  211 , and a right (peripheral) main mark  213  disposed to and adjacent the other side of the central mark  211 . The central main mark  211 , the left main mark  212  and the right main mark  213  have substantially the same shape, e.g., are all in the form of a rectangular band. The sputtering process used to form the main marks (and a lower pattern on a die of the substrate) also inadvertently forms protrusions  218  at inner sides of the central main mark  210  facing one another. Characteristically, the sputtering process will also form protrusions  216  and  214  at a left inner side of the left main mark  212  and at a right inner side of the right main mark  214 , respectively. The first sub-mark  220  is formed on a central portion of the central mark  211 . For example, the first sub-mark  220  is part of a photoresist pattern and has a solid square shape. 
     The second sub-marks  230  include a left sub-mark  231  and a right sub-mark  235 . The left sub-mark  231  and the right sub-mark  235  have substantially the same size and shape. The left sub-mark  231  is disposed on the interior region of the left main mark  212 , i.e., on the region bounded by the left main mark  212 . Specifically, the left sub-mark  231  is located over the interior region of the left main mark  212  at an upper left corner of the left main mark  212 . The right sub-mark  235  is disposed on the interior region of the right main mark  213 . Specifically, the right sub-mark  235  is located on the interior region of the right main mark  213  at a lower right corner of the right main mark  213 . Thus, the left sub-mark  231  and the right sub-mark  235  are located on a diagonal line that extends from the upper left corner of the left main mark  212  to the lower right corner of the right main mark  213  through the center of the central main mark  211 . In particular, the left sub-mark  231  and the right sub-mark  235  are arranged symmetrically with respect to the first sub-mark  220 . 
       FIG. 7  is a flow chart of a method for determining a degree of alignment between an upper pattern and a lower pattern, using the alignment marks  200 , according to the present invention. 
     Referring to  FIGS. 6 and 7 , the central main mark  211  is formed on a scribe line of a semiconductor substrate by a sputtering process (S 250 ). At this time, the protrusions  218  may be formed at the inner opposite sides of the central main mark  211  as integral parts of the mark. The protrusions may not, however, have the same widths. 
     The left main mark  212  and the right main mark  213  are formed adjacent to opposite sides of the central main mark  211  (S 252 ). The left main mark  212  and the right main mark  213  may be formed by the same sputtering process that forms the central main mark  211 , i.e., simultaneously with the central main mark  211 . At this time, the protrusions  214 ,  216  may be formed at the inner opposite-most sides of the left main mark  212  and the right main mark  213 , respectively, as integral parts of the marks. 
     Next, the first sub-mark  220  is formed on the central portion of the central main mark  211  (S 254 ). 
     Also, the left sub-mark  231  is formed on the region bounded by the left main mark  212 , and the right sub-mark  235  is formed on the region bounded by the right main mark  213  (S 256 ). As described previously, the left sub-mark  231  is located adjacent the upper left corner of the left main mark  212 , and the right sub-mark  235  is located adjacent the lower right corner of the right main mark  213 . 
     Subsequently, a degree of alignment between the central main mark  211  and the first sub-mark  220  is determined (S 258 ) in substantially the same manner as that described in connection with the degree of alignment between the main mark  110  and the first sub-mark  120  in the first embodiment. This degree of alignment will also be designated as the first degree of alignment. 
     A degree of alignment between the left main mark  212  and the left sub-mark  231  is also determined (S 260 ). Specifically, a first distance between a first inner (left) side edge of the left main mark  212  and a first outer (left) side edge of the left sub-mark  231  faced towards the first inner side edge of the left main mark  212  is measured. Furthermore, a second distance between a second inner (right) side edge of the left main mark  212  and a second outer (right) side edge of the left sub-mark  231 , opposite the first outer side edge of the left sub-mark  231  and faced towards the second inner side edge of the left main mark  212 , is measured. The difference between the first and second distances is divided by two, and the resulting value is assigned as the degree of alignment between the left main mark  212  and the left sub-mark  231  (hereinafter designated as the second degree of alignment). 
     A degree of alignment between the right main mark  213  and the right sub-mark  235  is also determined (S 262 ). Specifically, a first distance between a first inner (right) side edge of the left main mark  213  and a first outer (right) side edge of the left sub-mark  235  faced towards the first inner side edge of the right main mark  213  is measured. Furthermore, a second distance between a second inner (left) side edge of the left main mark  213  and a second outer (left) side edge of the left sub-mark  235 , opposite the first outer side edge of the left sub-mark  235  and faced towards the second inner side edge of the left main mark  213 , is measured. The difference between the first and second distances is divided by two, and the resulting value is assigned as the degree of alignment between the right main mark  213  and the right sub-mark  235  (hereinafter designated as the third degree of alignment). 
     Next, the difference between the second degree of alignment and the third degree alignment is divided by two. The resulting value is subtracted from the first degree of alignment to obtain a value representing the actual degree of alignment between the central mark  211  and the first sub-mark  220  (S 264 ). 
       FIG. 8  shows another example embodiment of a substrate having alignment marks  300  according to the present invention. Those aspects of this embodiment which are the same as those described above in connection with first embodiment will not be described for the sake of brevity. 
     Referring to  FIG. 8 , the alignment marks  300  are formed on a scribe line of a semiconductor substrate and which scribe line demarcates dies of the substrate (refer to  FIGS. 3 and 4 ). The alignment marks  300  include a main outer mark  310 , a main inner mark  320  and a sub-mark  330 . 
     The main outer mark  310  is formed on the semiconductor substrate simultaneously with the forming of a lower pattern using a series of processes including a sputtering process. For example, the main outer mark  310  is part of a conductive pattern and has the shape of a rectangular band. Furthermore, the main outer mark  310  may have a protrusion  318  at an inner side thereof, formed as a result of an error in the sputtering process used to form the lower pattern and the main outer mark  310 . 
     The main inner mark  320  is formed inside of the main outer mark  310 . In this respect, the main inner mark  320  may be formed simultaneously with the main outer mark  310 . Furthermore, the main inner mark  320  has the shape of a rectangular band smaller than that of the main outer mark  310 . 
     The sub-mark  330  is formed on a region between the main outer mark  310  and the main inner mark  320  by a second series of processes for forming an upper pattern on the lower pattern. Therefore, the sub-mark  330  is smaller than the main outer mark  310  and larger than the main inner mark  320 . 
     The sub-mark  330  may be part of the photoresist pattern formed by the second series of processes and preferably, has the shape of a rectangular band. Distances between outer side edges of the sub-mark  330  and inner side edges of the main outer mark  310  facing the outer side edges of the sub-mark  330  are measured and averaged to obtain a first value representing the degree of alignment between the main outer mark  310  and the sub-mark  330 . Furthermore, distances between inner side edges of the sub-mark  330  and outer side edges of the main inner mark  320  are measured and averaged to obtain a second value representing the degree of alignment between the main inner mark  320  and the sub-mark  330 . 
     The second degree of alignment is subtracted from the first degree of alignment and the result is used as a value representing the degree of alignment between the main outer mark  310  and the sub-mark  330 . 
     According to the present invention as described above, a value representing an actual degree of alignment between a main mark and a sub-mark is produced even if the main mark is asymmetrical. Thus, the degree of alignment between an upper pattern and a lower pattern formed on a substrate can be accurately determined. As a result, patterns sequentially formed on a semiconductor substrate or the like can be accurately superimposed, i.e., can be aligned with a high degree of precision. 
     Finally, although the present invention has been described in connection with the preferred embodiments thereof, it is to be understood that the scope of the present invention is not so limited. On the contrary, various modifications of and changes to the preferred embodiments will be apparent to those of ordinary skill in the art. Thus, changes to and modifications of the preferred embodiments may fall within the true spirit and scope of the invention as defined by the appended claims.