Abstract:
An edge detection method includes preparing a transparent substrate which includes a first main face having a first main region and a first peripheral region and a second main face having a second main region and a second peripheral region, the first peripheral region having an inclination angle of θa 1  and the second peripheral region having an inclination angle of θa 2 , causing measuring light to enter the first peripheral region from a direction perpendicular to the first main region, detecting a non-emitting region where the measuring light is not emitted from the second peripheral region, and detecting an edge of the transparent substrate on the basis of the non-emitting region, wherein if a refractive index of the transparent substrate is n, the inclination angles θa 1  and θa 2 satisfy the following expression:
 
 n× sin(θ a 1+θ a 2−arcsin(sin θ a 1/ n ))≧1.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from prior Japanese Patent Application No. 2008-195017, filed Jul. 29, 2008, the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to an edge detection method. 
     2. Description of the Related Art 
     When the edge of a substrate is detected, if the substrate is opaque, the edge can be detected easily by an optical method. Specifically, when a region including the edge of the substrate is irradiated with measuring light, the measuring light is blocked by the substrate in the region where the substrate exists, with the result that the light does not reach a light detecting part (or a light-receiving part). The edge can be detected by detecting a region where the measuring light does not reach the light detecting part (or a dark region). However, in the case of a transparent substrate, since measuring light passes through the transparent substrate, the dark region cannot be detected. Accordingly, it is not easy to detect the edge of a transparent substrate by an optical method. 
     To overcome the above problem, a method of beveling the peripheral part of the transparent substrate to form an inclined surface and refracting measuring light at the inclined surface has been proposed (refer to Jpn. Pat. Appln. KOKAI Publication No. 2005-109376). Specifically, since the measuring light is refracted at the inclined surface, producing a dark region, the edge of the transparent substrate can be detected. However, it is difficult to make the width of the dark region sufficiently wide by just refracting the measuring light. This causes the problem of being incapable of detecting the dark region reliably. 
     In addition, a method of causing measuring light to obliquely enter a transparent substrate to produce a dark region by total internal reflection has been proposed (refer to Jpn. Pat. Appln. KOKAI Publication No. 2007-165655). However, with this method, if the thickness or refractive index of the transparent substrate changes, the measurement system has to be adjusted. For example, when the refractive index of the transparent substrate has changed, the total internal reflection angle has also changed. Therefore, the incident angle of the measuring light has to be changed. It is not easy for the user to make such an adjustment. 
     As described above, it has been difficult to detect the edge of a transparent substrate easily and reliably by an optical method. 
     BRIEF SUMMARY OF THE INVENTION 
     A first aspect of the present invention, there is provided an edge detection method comprising: preparing a transparent substrate which includes a first main face that has a first main region and a first peripheral region outside the first main region and a second main face that has a second main region in parallel with the first main region and a second peripheral region outside the second main region, the first peripheral region having an inclination angle of θa 1  and the second peripheral region having an inclination angle of θa 2 ; causing measuring light to enter the first peripheral region of the first main face from a direction perpendicular to the first main region of the first main face; detecting a non-emitting region where the measuring light is not emitted from the second peripheral region of the second main face; and detecting an edge of the transparent substrate on the basis of the non-emitting region, wherein if a refractive index of the transparent substrate is n, the inclination angles θa 1  and θa 2  satisfy the following expression:
 
 n ×sin(θ a 1+θ a 2−arcsin(sin θ a 1 /n ))≧1
 
     A second aspect of the present invention, there is provided an edge detection method comprising: preparing a transparent substrate which includes a first main face that has a first main region and a first peripheral region outside the first main region and a second main face that has a second main region in parallel with the first main region and a second peripheral region outside the second main region, each of the first peripheral region and the second peripheral region having an inclination angle becoming smaller toward the inner part; causing measuring light to enter the first peripheral region of the first main face from a direction perpendicular to the first main region of the first main face; detecting a non-emitting region where the measuring light is not emitted from the second peripheral region of the second main face; and detecting an edge of the transparent substrate on the basis of the non-emitting region. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
         FIG. 1  is a schematic view to explain an edge detection method according to a first and a second embodiment of the invention; 
         FIG. 2  is a schematic plan view showing the configuration of a substrate to be processed according to the first and second embodiments; 
         FIG. 3  is a detail view of a part of  FIG. 1  according to the first embodiment; 
         FIG. 4  is a view showing the inclination angle of a peripheral region of a transparent substrate according to the first embodiment; 
         FIG. 5  is a diagram showing the result of calculating a region where total internal reflection takes place in the first embodiment; 
         FIG. 6  is a diagram showing the result of calculating a region where total internal reflection takes place in the first embodiment; 
         FIG. 7  is a diagram for calculating the upper limit of the inclination angle in the first embodiment; and 
         FIG. 8  is a detail view of a part of  FIG. 1  in the second embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Hereinafter, referring to the accompanying drawings, embodiments of the invention will be explained. 
     (First Embodiment) 
       FIG. 1  is a schematic view to explain an edge detection method according to a first embodiment of the invention.  FIG. 2  is a schematic plan view showing the configuration of a substrate to be processed shown in  FIG. 1 .  FIG. 3  is a detail view of a part of  FIG. 1 . 
     A substrate to be processed  100  is composed of a transparent substrate  110 , such as a glass substrate, and a semiconductor substrate (or a semiconductor wafer)  120  provided on the transparent substrate  110 . On the semiconductor substrate  120 , an element region including active elements and interconnections is provided. In the first embodiment, an image sensor (e.g., a CMOS image sensor) including light-receiving elements and transistors is formed in the element region. The transparent substrate  110  is for securing the mechanical strength of the semiconductor substrate  120  and protecting the element region of the semiconductor substrate  120 . The substrate  100  is placed on a stage  200  and can be rotated by the rotation of the stage  200 . While the substrate  100  is being rotated, the edge position of the substrate  100  is detected, thereby enabling the center position of the substrate  100  to be determined. 
     On the side of a first main face  111  of the transparent substrate  110 , there is provided a light supplying part  300  composed of a light-emitting part and others. The light-supplying part  300  supplies measuring light for detecting the edge of the transparent substrate  110  to the first main face  111  of the transparent substrate  110 . On the side of a second main face  112  of the transparent substrate  110 , there is provided a light detecting part  400  composed of a light-receiving part and others. The edge of the transparent substrate  110  can be detected by detecting a dark region where measuring light is not emitted from the second main face  112  of the transparent substrate  110  (or non-emitting region). Hereinafter, the principle of edge detection in the first embodiment will be explained with reference to  FIG. 3 . 
     As shown in  FIG. 3 , the transparent substrate  110  has the first main face  111 , the second main face  112 , and an end face  113 . The first main face  111  has a first main region  111   a  and a first peripheral region  111   b  outside the first main region  111   a . The second main face  112  has a second main region  112   a  in parallel with the first main region  111   a  and a second peripheral region  112   b  outside the second main region  112   a . Each of the first peripheral region  111   b  and second peripheral region  112   b  has an oblique plane (inclined surface) produced by a beveling process. 
     When the edge of the transparent substrate  110  is detected, the measuring light  310  is caused to enter the first peripheral region  111   b  of the first main face  111  from a direction perpendicular to the transparent substrate  110 . That is, the measuring light  310  is caused to enter the first peripheral region  111   b  from a direction perpendicular to the first main region  111   a  of the first main face  111  and the second main region  112   a  of the second main face  112 . The measuring light  310  is refracted at the first peripheral region  111   b  and reaches the second peripheral region  112   b  of the second main face  112 . Here, the inclination angle of each of the first peripheral region  111   b  and second peripheral region  112   b  has been set so that the measuring light may reflect totally at the second peripheral region  112   b . As a result of the total internal reflection, there appears a non-emitting region where the measuring light is not emitted from the second peripheral region  112   b  of the second main face  112 , that is, a dark region. On the basis of the dark region, the edge (or end face  113 ) of the transparent substrate  110  can be detected. That is, the edge of the transparent substrate  110  can be detected by detecting a dark region with the light detecting part  400 . When a CCD line sensor where pixels are arranged in one direction is used as the light detecting part  400 , if a dark region is detected across not less than a specific number of consecutive pixels, the edge is assumed to have been detected. The place corresponding to the boundary between the pixels detecting a bright region (bright signal) and the pixels detecting a dark region (dark signal) is detected as an edge. 
     Hereinafter, the inclination angle of each of the first peripheral region  111   b  and second peripheral region  112   b  will be explained with reference to  FIG. 4 .  FIG. 4  shows the vicinity of the edge of the transparent substrate  110 . 
     As shown in  FIG. 4 , let the inclination angle of the first peripheral region  111   b  (or the angle defined by the first main region  111   a  and first peripheral region  111   b  of the first main face) be θa 1  and the inclination angle of the second peripheral region  112   b  (or the angle defined by the second main region  112   a  and second peripheral region  112   b  of the second main face) be θa 2 . In addition, let the incident angle and output angle of the measuring light to the first peripheral region  111   b  be θ 1  and θ 2 , respectively, and the incident angle and output angle of the measuring light to the second peripheral region  112   b  be θ 3  and θ 4 , respectively. Moreover, let the refractive index of the transparent substrate  110  be n. 
     The refractive index n of the transparent substrate  110  is expressed as:
 
 n =sin θ4/sin θ3
 
     When total internal reflection takes place, θ 4 =90 degrees. Accordingly, if the critical angle at the time when total internal reflection takes place is θc, it follows that
 
 n =1/sin θ c  
 
Accordingly, θc=arcsin(1 /n )  (1)
 
     The refractive index n of the transparent substrate  110  is also expressed as:
 
 n =sin θ1/sin θ2
 
     Since the incident direction of the measuring light is perpendicular to the first main region  111   a , this gives
 
θ1=θ a 1
 
     Accordingly, it follows that
 
θ2=arcsin(sin θ a 1 /n )  (2)
 
     If the angle between the normal line of the first peripheral region  111   b  and the normal line of the second peripheral region  112   b  is θb, θb is expressed as:
 
θ b= 360−90−90−θ a 1−θ a 2  (3)
 
     Here,
 
θ3=180−θ2−θ b   (4)
 
     Accordingly, from equation (3) and equation (4),
 
θ3=θ a 1+θ a 2−θ2  (5)
 
     Substituting equation (2) into equation (5) gives:
 
θ3=θ a 1+θ a 2−arcsin(sin θ a 1 /n ) (6)
 
     If θc≦θ 3 , total internal reflection will take place. Accordingly, from equation (1) and equation (6), it follow that
 
arcsin(1/ n )≦θ a 1+θ a 2−arcsin(sin θ a 1 /n )  (7)
 
     Accordingly, the condition for the occurrence of total internal reflection is:
 
 n ×sin(θ a 1+θ a 2−arcsin(sin θ a 1 /n ))≧1  (8)
 
     Here, let the left side of expression (8) be an index value A. 
       FIG. 5  shows the result of calculating a range where total internal reflection takes place using expression (8). In  FIG. 5 , the refractive index n of the transparent substrate  110  is 1.5. The abscissa axis indicates a lower inclination angle (or inclination angle θa 1  of the first peripheral region  111   b ). The ordinate axis indicates an upper inclination angle (inclination angle θa 2  of the second peripheral region  112   b ). The shaded regions (a), (b), and (c) represent a range where total internal reflection will take place. 
       FIG. 6  also shows the result of calculating a range where total internal reflection takes place using expression (8). However,  FIG. 6  is based on the assumption that inclination angle θa 1  of the first peripheral region  111   b  is equal to inclination angle θa 2  of the second peripheral region  112   b . The abscissa axis indicates inclination angles θa 1  and θa 2 . The ordinate axis indicates the refractive index n of the transparent substrate  110 . The shaded regions (a), (b), and (c) represent a range where total internal reflection will take place. 
     As described above, in the first embodiment, each of the first peripheral region  111   b  and second peripheral region  112   b  of the transparent substrate  110  is configured to have an oblique plane and both inclination angle θa 1  of the first peripheral region  111   b  and inclination angle θa 2  of the second peripheral region  112   b  are set so as to fulfill expression (8). This enables the measuring light entering the first peripheral region  111   b  to totally reflect at the second peripheral region  112   b . As a result, the width of the non-emitting region (or dark region) where the measuring light is not emitted from the second peripheral region  112   b  can be increased sufficiently. Accordingly, the dark region can be detected reliably and therefore the edge of the transparent substrate can be detected reliably. Moreover, in the first embodiment, setting inclination angles θa 1  and θa 2  so as to fulfill expression (8) makes it unnecessary to change the incident angle of the measuring light even if the thickness or refractive index of the transparent substrate  110  has changed and therefore make a complicated adjustment work. Therefore, according to the first embodiment, the edge of the transparent substrate can be detected easily and reliably by the optical method. 
     From the viewpoint of ease of beveling, it is desirable that inclination angle θa 1  of the first peripheral region  111   b  should be made equal to inclination angle θa 2  of the second peripheral region  112   b  and that the first peripheral region  111   b  and second peripheral region  112   b  should be symmetrical vertically with respect to the center plane of the transparent substrate  110 . However, inclination angle θa 1  may be different from the inclination angle θa 2 , provided that expression (8) is fulfilled. In addition, either inclination angle θa 1  or inclination angle θa 2  may be 0 degree. In this case, one of the first peripheral region  111   b  and second peripheral region  112   b  has no oblique plane, but can produce the same effect as described above, provided that expression (8) is fulfilled. 
     Next, in the first embodiment, the upper limit of the inclination angle θ (θ=θa 1 =θa 2 ) will be explained in a case where inclination angle θa 1  of the first peripheral region  111   b  is equal to inclination angle θa 2  of the second peripheral region  112   b.    
       FIG. 7  shows typical dimensions of various parts to calculate the upper limit of the inclination angle θ. The transparent substrate has a standard thickness of 350 μm. To secure the mechanical strength at the peripheral part of the transparent substrate, the thickness of the end face  113  is not less than ½ of the thickness (350 μm) of the transparent substrate. The size of one pixel of the line sensor constituting the light detecting part is 20 μm. The condition for detecting an edge is that a dark region is detected across not less than five consecutive pixels, that is, the width of a dark region is not less than 100 μm. 
     Calculating the upper limit of the inclination angle θ under the above condition gives
 
tan θ=87.5/100
 
     Accordingly, it follows that
 
θ=arctan(87.5/100)=41.2 degrees
 
     That is, the upper limit of the inclination angle θ is preferably about 41 degrees. 
     (Second Embodiment) 
     Next, an edge detection method according to a second embodiment of the invention will be explained. Since the basic configuration and method are the same as those of the first embodiment, what has been explained in the first embodiment will be omitted. 
       FIG. 8  is a detail view of a part of  FIG. 1 . Hereinafter, referring to  FIG. 8 , the principle of edge detection in the second embodiment will be explained. 
     As shown in  FIG. 8 , a transparent substrate  110  has a first main face  111  and a second main face  112 . The first main face  111  has a first main region  111   a  and a first peripheral region  111   b  outside the first main region  111   a . The second main face  112  has a second main region  112   a  in parallel with the first main region  111   a  and a second peripheral region  112   b  outside the second main region  112   a . The inclination of the first peripheral region  111   b  and that of the second peripheral region  112   b  become gentler toward the center of the transparent substrate  110 . That is, the inclination angle of the first peripheral region  111   b  and that of the second peripheral region  112   b  become smaller toward the inner part of the substrate. In the example of  FIG. 8 , each of the first peripheral region  111   b  and second peripheral region  112   b  has a curved surface as a result of beveling. The first peripheral region  111   b  and second peripheral region  112   b  are symmetrical vertically with respect to the center plane of the transparent substrate  110 . 
     When the edge of the transparent substrate  110  is detected, measuring light  310  is caused to enter the first peripheral region  111   b  of the first main face  111  from a direction perpendicular to the transparent substrate  110  as in the first embodiment. That is, the measuring light  310  is caused to enter the first peripheral region  111   b  from a direction perpendicular to the first main region  111   a  of the first main face  111  and to the second main region  112   a  of the second main face  112 . The measuring light  310  is refracted at the first peripheral region  111   b  and reaches the second peripheral region  112   b  of the second main face  112 . Since the inclination of the second peripheral region  112   b  becomes gentler toward the center of the substrate, total internal reflection can be caused to take place in a wide range of the second peripheral region  112   b . As a result of the total internal reflection, a non-emitting region where the measuring light is not emitted from the second peripheral region  112   b  of the second main face  112 , or a dark region, is produced as in the first embodiment. On the basis of the dark region, the edge (or end part) of the transparent substrate  110  can be detected. That is, by detecting the dark region with the light detecting part  400 , the edge of the transparent substrate  110  can be detected. When a CCD line sensor composed of pixels arranged in one direction is used as the light detecting part  400 , if a dark region is detected across not less than a specific number of pixels, the edge is assumed to have been detected. The place corresponding to the boundary between the pixels that have detected a bright region (bright signal) and the pixels that have detected a dark region (dark signal) is detected as an edge. 
     As described above, in the second embodiment, since the inclination angle of each of the first peripheral region  111   b  and second peripheral region  112   b  of the transparent substrate  110  becomes smaller toward the inner part of the substrate, the thickness of the transparent substrate  110  at the peripheral part can be secured sufficiently (or the mechanical strength can be secure sufficiently) and total internal reflection can be caused to take place in a wide range of the second peripheral region  112   b . As a result, the width of the non-emitting region (dark region) where the measuring light is not emitted from the second peripheral region  112   b  can be increased sufficiently, which enables the dark region to be detected reliably. Even when the thickness or refractive index of the transparent substrate  110  has changed, the incident angle of the measuring light need not be changed and therefore a complicated adjustment work need not be done. Therefore, according to the second embodiment, the edge of the transparent substrate can be detected easily and reliably by the optical method. 
     While in the example of  FIG. 8 , each of the first peripheral region  111   b  and second peripheral region  112   b  has a curved surface, the shape of the curved surface is not limited. For example, the curved surface may take various forms, including a circular form, an elliptical form, and a hyperbolic form. 
     Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and representative embodiments shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.