Patent Publication Number: US-2006009134-A1

Title: Grinding wheel, grinding apparatus and grinding method

Description:
BACKGROUND OF THE INVENTION  
      1. Field of the Invention  
      The present invention relates to a grinding wheel, a grinding apparatus and a grinding method, and more particularly, to a grinding wheel, a grinding device and a grinding method to obtain a thin wafer by grinding one surface of a semiconductor wafer or the like.  
      2. Description of the Related Art  
      A wafer of silicone or the like which becomes a material of a semiconductor device, an electronic component and the like is sliced with a sliding device such as an inner peripheral blade and a wire saw from an ingot state, and thereafter, chamfering work is performed for an outer peripheral part as shown in  FIG. 9A  to prevent occurrence of a cracking, chipping and the like at an peripheral edge of the wafer in the forming process of a semiconductor device, an electronic component and the like. In  FIG. 9A , reference character W designates a wafer, and reference character S designates a protection sheet for the wafer surface.  
      Recently, however, in order to manufacture extremely thin semiconductor chips incorporated into a smart card and a thin IC card, a back surface side of the wafer, which has a semiconductor device or an electronic component is formed on its front surface side, is ground to be an extremely thin wafer, and this extremely thin wafer is diced to manufacture individual extremely thin chips.  
      However, since in this extremely thinning work, the wafer is thinned to a half of the thickness of the wafer before the work, there arises the problem that the outer peripheral part of the wafer, which is worked to be extremely thin, is in a sharp shape due to chamfering of the outer peripheral part previously performed, and is easy to break.  
      In order to solve the problem, there is provided a method for cutting the peripheral edge part of the wafer vertically or by inclining the peripheral edge toward the center before grinding of the back surface of the wafer is performed, and thereafter, performing the back surface grinding (for example, see Japanese patent Application Laid Open No. 2003-273053).  
      A method for performing grinding by inclining the peripheral edge part of the wafer toward the center before performing the back surface grinding of the wafer, and thereafter performing the back surface grinding, or a method for performing the back surface grinding and chamfering grinding at the same time by providing a general chamfering grindstone applied to a thin wafer on the opposite side from a back surface grindstone with the axis of the wafer therebetween is proposed (for example, see embodiment 1, and embodiment 2 in Japanese Patent Application Laid Open No. 08-037169).  
      Further, a method for performing the back surface grinding and chamfering grinding at the same time by providing an inclined cylindrical chamfering grindstone at the opposite side from the back surface grinding grindstone with the axis of the wafer therebetween (for example, see Japanese Patent Application Laid Open No. 11-033887).  
     SUMMARY OF THE INVENTION  
      However, in the method disclosed in the aforementioned Japanese Patent Application Laid Open No. 2003-273053, cutting of the peripheral edge part of the wafer and the back surface grinding have to be worked by using the separate apparatuses in the separate process steps, and there exists the problem of increasing the number of working process steps and increasing time and cost.  
      In the method disclosed in embodiment  1  in the aforementioned Japanese Patent Application Laid Open No. 08-037169, work can be performed with one apparatus, but inclination grinding of the peripheral edge part of the wafer and the back surface grinding are performed in the separate process steps, and therefore, there exists the problem of increasing the number of working process steps and increasing time and cost as in the Japanese patent Application Laid Open No. 2003-273053.  
      In the method disclosed in the embodiment  2  of the aforementioned Japanese Patent Application Laid Open No. 08-037169 and the method disclosed in the aforementioned Japanese Patent Application Laid Open No. 11-033887, the back surface grinding and chamfering grinding can be performed at the same time, but in both of them, the chamfering grindstones are provided at the opposite sides from the back surface grinding grindstones with the axes of the wafers therebetween, and therefore, there exists the problem of increasing the size of the apparatus, increasing the manufacturing cost of the apparatus and enlarging the footprint.  
      The present invention is made in view of the above circumstances, and it is an object of the present invention to provide a grinding wheel, a grinding apparatus and a grinding method which restrain increase in the size of the apparatus and are capable of preventing an peripheral edge part of an extremely thin wafer from being sharpened, and preventing cracking and chipping of the wafer peripheral part by performing the back surface grinding of the wafer and grinding of the peripheral edge part of the wafer at the same time.  
      In order to attain the above-described object, a grinding wheel of the present invention is characterized by comprising a cup-shaped grindstone, and a small-diameter grindstone provided at a center part of an inside of the cup-shaped grindstone. The small-diameter grindstone is a grindstone in a cylindrical shape or a truncated cone shape.  
      According to the grinding wheel of the present invention, one surface of the wafer is ground with the cup-shaped grindstone, and the peripheral edge part of the wafer can be ground with the small-diameter grindstone at the same time. Therefore, increase in the size of the grinding apparatus can be restrained, and the back surface grinding of the wafer and grinding of the peripheral edge part of the wafer are performed at the same time, whereby the peripheral edge part of the extremely thin wafer can be prevented from being sharpened, and cracking and chipping of the wafer peripheral edge part can be prevented.  
      The grinding wheel of the present invention is characterized in that the small-diameter grindstone has an entire shape formed into a truncated cone shape, and a clearance groove is formed at a mid-portion of an inclined side surface of the truncated cone. According to this, grinding of the peripheral edge part of the wafer is finished before the final grinding of the back surface grinding of the wafer, the small-diameter grindstone is moved away from the peripheral edge part of the wafer at the time of the final grinding of the wafer back surface grinding, and chipping of the wafer peripheral edge part can be restrained.  
      The grinding wheel of the present invention is characterized in that the small-diameter grindstone is integrally formed at a base of the cup-shaped grindstone, or detachably provided at a base of the cup-shaped grindstone. When the small-diameter grindstone is integrally formed at the base of the cup-shaped grindstone, the positional relationship of the cup-shaped grindstone and the small-diameter grindstone is determined by the manufacturing accuracy of the grindstone, and adjustment is not required. When the small-diameter grindstone is detachably provided at the base of the cup-shaped grindstone, only the small-diameter grindstone can be easily replaced when the small-diameter grindstone is worn.  
      The grinding wheel of the present invention is characterized in that the small-diameter grindstone is a composite grindstone with a rough grinding grindstone and a fine grinding grindstone being stacked. Thus, the peripheral edge part of the wafer is roughly ground with the rough grinding grindstone of the small-diameter grindstone, and subsequently, the peripheral edge part of the wafer can be finely ground with the fine grinding grindstone. Therefore, the peripheral edge part of the wafer can be smoothly finished by one work.  
      A grinding apparatus of the present invention is, in a grinding apparatus which grinds one surface of the wafer, characterized by comprising a chuck table which rotates with a wafer placed thereon, a hollow spindle which is provided eccentrically with respect to an axis of rotation of the chuck table and mounted with a cup-shaped grindstone on a tip end of the hollow spindle, a small spindle which is provided by being inserted through the hollow spindle and mounted with a smaller-diameter grindstone than the cup-shaped grindstone on a tip end of the small spindle, a cup-shaped grindstone driving motor which rotationally drives the hollow spindle, a small-diameter grindstone driving motor which rotationally drives the small spindle, and a cut-in driving device which brings the hollow spindle and the small spindle, and the chuck table relatively closer to and away from each other in the rotational axis direction of the chuck table.  
      In addition to the above described construction, the grinding apparatus of the present invention is characterized by further comprising a transverse driving device which brings an axis of the hollow spindle and an axis of the small spindle, and a rotational axis of the chuck table relatively closer to and away from each other.  
      According to the grinding apparatus of the present invention, the hollow spindle and the small spindle provided by being inserted through the hollow spindle are included, and therefore, by mounting the cup-shaped grindstone to the hollow spindle and by mounting the smaller-diameter grindstone than the cup-shaped grindstone at the small spindle, the one surface of the wafer is ground with the cup-shaped grindstone and the peripheral edge part of the wafer can be ground with the small-diameter grindstone at the same time.  
      Therefore, increase in the size of the grinding apparatus is suppressed, the back surface grinding of the wafer and grinding of the peripheral edge part of the wafer are performed at the same time, whereby the peripheral edge part of the extremely thin wafer is prevented from being sharpened, and cracking and chipping of the wafer peripheral edge part can be prevented.  
      A grinding method of the present invention is characterized by comprising the step of grinding one surface of the wafer with the cup-shaped grindstone and grinding a circumferential side surface of the wafer with the small-diameter grindstone with using a grinding wheel comprising a cup-shaped grindstone, and a small-diameter grindstone provided at a center portion of the inside of the cup-shaped grindstone.  
      According to the grinding method of the present invention, the back surface grinding of the wafer and grinding of the peripheral edge part of the wafer are performed at the same time, whereby the peripheral edge part of the extremely thin wafer is prevented from being sharpened, and cracking and chipping of the wafer peripheral edge part can be prevented.  
      A grinding method of the present invention is characterized by comprising the steps of mounting a cup-shaped grindstone at the hollow spindle and a smaller-diameter grindstone than the cup-shaped grindstone is mounted to the small spindle, independently setting a number of rotations of the cup-shaped grindstone and a number of rotations of the small-diameter grindstone respectively, and grinding one surface of the wafer with the cup-shaped grindstone and grinding a circumferential side surface of the wafer with the small-diameter grindstone with using the grinding apparatus of the above described present invention.  
      According to the grinding method described above, the number of rotations of the cup-shaped grindstone and the number of rotations of the small-diameter grindstone are respectively set independently, and therefore, grinding of one surface of the wafer and grinding of the peripheral edge part of the wafer can be performed at the optimal numbers of rotations of the grindstone for the respective grindings.  
      The grinding method of the present invention is characterized by further comprising the steps of bringing the cup-shaped grindstone and the small-diameter grindstone, and the chuck table relatively close to each other in a rotational axis direction of the chuck table, and grinding the one surface and the circumferential side surface of the wafer while bringing a rotational axis of the rotating cup-shaped grindstone and small-diameter grindstone, and the rotational axis of the chuck table relatively close to each other, or while bringing the rotational axis of the cup-shaped grindstone and the small-diameter grindstone, and the rotational axis of the chuck table relatively close to and away from the rotational axis of the chuck table.  
      According to this grinding method of the present invention, the small-diameter grindstone can be moved along the initial chamfered shape of the peripheral edge part of the wafer, and edge grinding of the wafer can be performed with a small cut-in. Therefore, edge grinding can be favorably performed for the peripheral edge part of the extremely thin wafer.  
      As explained above, according to the grinding wheel, the grinding apparatus and the grinding method of the present invention, increase in the size of the grinding apparatus can be suppressed, and the back surface grinding of the wafer and the grinding of the peripheral edge part of the wafer are performed at the same time, whereby the peripheral edge part of the extremely thin wafer is prevented from being sharpened, and cracking and chipping of the wafer peripheral edge part can be prevented. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIG. 1  is a perspective view showing a grinding wheel according to an embodiment of the present invention;  
       FIG. 2  is a sectional view showing the grinding wheel according to the embodiment of the present invention;  
       FIG. 3  is a sectional view showing a grinding wheel according to another embodiment of the present invention;  
       FIG. 4  is a sectional view showing a modified example of a grinding wheel according to another embodiment of the present invention;  
       FIG. 5  is a side view showing a grinding apparatus according to the embodiment of the present invention;  
       FIG. 6  is a sectional side view showing a grinding method according to the embodiment of the present invention;  
       FIG. 7  is a schematic view showing the grinding method according to the embodiment of the present invention;  
       FIG. 8  is a schematic view showing a grinding method according to another embodiment of the present invention; and  
       FIGS. 9A and 9B  are sectional views showing a wafer for which conventional back surface grinding is performed. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
      A preferred embodiment of a grinding wheel, a grinding apparatus and a grinding method according to the present invention will be explained in detail with reference to the attached drawings hereinafter. In each of the drawings, the same members are given the same reference numerals or characters.  
       FIG. 1  is a perspective view showing a grinding wheel according to an embodiment of the present invention. The grinding wheel  10  is constructed by a segment type cut-shaped grinding wheel  11  in which a plurality of grindstone chips  11 B are formed on an end surface of a base  11 A, and a small-diameter grindstone  12  formed at a center part of the cup-shaped grindstone  11 .  
       FIG. 2  is a sectional view when the grindstone chips  11 B of the grinding wheel  10  are faced downward. As shown in  FIG. 2 , the small-diameter grindstone  12  is a cylindrical grindstone, and its undersurface is provided to project from the undersurfaces of the grindstone chips  11 B.  
      The small-diameter grindstone  12  may be formed integrally at the base  11 A of -the cup-shaped grind stone  11 , or the small-diameter grindstone  12  may be formed at a small-diameter grindstone base  13 A which will be described later and may be detachably mounted to the base  11 A of the cup-shaped grindstone  11  with a screw or the like. The cup-shaped grindstone  11  is a segment type, but it is not limited to the segment type, and it may be in the ring shape in which the grindstone parts are connected.  
      When the small-diameter grindstone  12  is made detachable, it is preferable because only the small-diameter grindstone  12  can be replaced when the small-diameter grindstone  12  is worn. When the cup-shaped grind stone  11  is of a segment type, supply of the grind water to the grinding point and discharge of the grinding powder are favorably performed.  
      When the grinding wheel  10  is used for back surface grinding of the silicon (Si) wafer of a semiconductor, the diamond abrasive grain of the grain size of #800 to #1500 is used for the abrasive grain of the grindstone chip  11 B, and a metal bond or a resin bond is used as a bonding agent. The diamond abrasive grain of the grain size of #2000 to #3000 is used for the abrasive grain of the small-diameter grindstone  12 , and a metal bond or a resin bond is used for the binder. Considering the required worked surface roughness and working speed, a fine grindstone of a resin bond is more suitable than a rough grindstone of the metal bond.  
      When the diameter of the wafer W for which the back surface grinding work is performed is 200 mm, the outer diameter of the cup-shaped grindstone  11  is preferably about 250 mm, and when the diameter of the wafer W is 300 mm, the outer diameter of the cup-shaped grindstone  11  is preferably about 350 mm. In both cases, the outer diameter of the small-diameter grindstone  12  is about 30 mm to 50 mm.  
       FIG. 3  is a sectional side view showing another embodiment of the grinding wheel according to the present invention. In this other embodiment, a small-diameter grindstone  13  is provided at a center part of the cup-shaped grindstone  11 . The small-diameter grindstone  13  is formed into a truncated cone at a small-diameter grindstone base  13 A, and is screwed onto the center part of the base  11 A of the cup-shaped grindstone  11  and is detachably provided.  
      The small-diameter grindstone  13  in the truncated cone shape is not limited to a detachable type, and it may be formed integrally at the base  11 A. When the small-diameter grindstone  13  is made a detachable type, it is preferable because only the small-diameter grindstone  13  can be replaced when the small-diameter grindstone  13  is worn.  
      The small-diameter grindstone  13  formed into the truncated cone shape is constructed by a stacked structure of a rough grinding grindstone  13 B on a tip end side of the truncated cone and a fine grinding grindstone  13 C on a base side of the truncated cone. In the grinding wheel of the present invention, the small-diameter grindstone  13  in the truncated cone shape is not limited to the stacked structure of the rough grinding grindstone  13 B and the fine grinding grindstone  13 C. It may be constructed by only the rough grinding grindstone  13 B, or only the fine grinding grindstone  13 C in accordance with the use purpose.  
       FIG. 4  shows a modified example of the aforementioned embodiment shown in  FIG. 3 . In this modified example, a clearance groove  13 D is formed on the inclined side surface of the small-diameter grindstone  13  formed into the truncated cone shape. The position of the clearance groove  13 D is at such a position as the extension surface of the undersurface of the grindstone chip  11 B of the cup-shaped grindstone  11  slightly lies on the lower side of the clearance groove  13 D.  
      When a wafer is ground by using the grinding wheel of this modified example, setting can be made so that the peripheral edge of the wafer is ground with the small-diameter grindstone  13  prior to the grinding of the wafer back surface by the grindstone chip  11 B of the cup-shaped grindstone  11 , and the peripheral edge of the wafer goes into the clearance groove  13 D just before the wafer has the final thickness. Therefore, at the time of the final grinding of the wafer back surface, grinding of the peripheral edge part of the wafer is completed, and the back surface grinding can be performed in the state without contact with the small-diameter grindstone  13 . Therefore, chipping of the peripheral edge part of a thin wafer can be suppressed.  
       FIG. 5  is a side view showing a grinding apparatus according to the embodiment of the present invention. A grinding apparatus  20  has a Y table  22  supported movably in the Y-direction in the drawing by a guide not shown on a machine base  21 , a θ-table  23  which is mounted to the Y-table  22  and rotates around an axis (WC) in a Z-direction orthogonal to the Y-direction, and a chuck table  24  which is mounted to the θ table  23  and fixes the wafer W by suction. The Y table  22  is fed horizontally in the Y-direction in the drawing at the time of grinding by a transverse driving device  25  constructed by a motor  25 A and a ball screw  25 B.  
      A column  26  fixed on the machine base  21  is provided with a grindstone table  27  which is guided by a guide not shown and for which cut-in feed in the Z-direction in the drawing is performed by a cut-in driving device  28  constructed by a motor  28 A and a ball screw not shown.  
      The grindstone table  27  is in a horseshoe shape, a hollow spindle  31  and a cup-shaped grindstone driving motor  32  are mounted to a lower side of the horseshoe shape, and the hollow spindle  31  and the cup-shaped grindstone driving motor  32  are connected by a belt  33  via pulleys respectively provided at them. A hollow cup-shaped grindstone  15  is mounted to a tip end of the hollow spindle  31 , and is rotationally driven around an axis (SC) by the cup-shaped grindstone driving motor  32 .  
      A small spindle  34  which penetrates through the hollow spindle  31  and the hollow cup-shaped grindstone  15 , and a small-diameter grindstone driving motor  35  are mounted on an upper side of the horseshoe shape of the grindstone table  27 , and the small spindle  34  and the small-diameter grindstone driving motor  35  are connected by a belt  36  via pulleys respectively provided at them. A small-diameter grindstone  16  is mounted to a tip end of the small spindle  34 , and is rotationally driven around the axis (SC) by the small-diameter grindstone driving motor  35 .  
      The grinding apparatus  20  of the present invention is provided with the hollow spindle  31  and the small spindle  34  penetrating through the hollow spindle  31 , and they are respectively rotated by the independent driving devices. Therefore, optimal rotation can be given to the hollow cup-shaped grindstone  15  mounted to the hollow spindle  31  and the small-diameter grindstone  16  mounted to the small spindle  34 .  
      It is the basic form that the axis of the hollow spindle  31  and the axis of the small spindle  34  are concentric, but it is possible to take the structure in which the axis of the hollow spindle  31  and the axis of the small spindle  34  are eccentric by a predetermined amount.  
      In the case where the numbers of rotations of the cup-shaped grindstone  15  and the small-diameter grindstone  16  may be the same, rotation control of the cup-shaped grindstone driving motor  32  and the small-diameter grindstone driving motor  35  may be performed so that the number of rotations of the hollow spindle  31  and the number of rotations of the small spindle  34  become the same, or grinding work may be performed with only the hollow spindle  31  by mounting the grinding wheel  10  shown in the aforementioned  FIGS. 1 and 2  to the hollow spindle  31  without using the small spindle  34 .  
      The structure in which cut-in feed in the Z-direction of the hollow spindle  31  and the small spindle  34  is performed together is adopted, but the structure capable of performing the cut-in feed in the Z-direction independently for each of the hollow spindle  31  and the small spindle  34  may be adopted.  
      Further, the structure in which the cut-in feed in the Z-direction is performed for the grindstone and the transverse feed in the Y-direction is performed for the wafer W is adopted, but the present invention is not limited to this structure, and the structure in which the cut-in feed in the Z-direction is performed for the wafer W and the transverse feed in the Y-direction is performed for the grindstone may be adopted, or the structure in which the cut-in feed in the Z-direction and the transverse feed in the Y-direction are performed for the grindstone, or the structure in which the cut-in feed in the Z-direction and the transverse feed in the Y-direction are performed for the wafer W may be adopted.  
       FIGS. 6 and 7  schematically shows a back surface grinding method of the wafer W using the grinding wheel  10  shown in the aforementioned  FIGS. 1 and 2 . As shown in  FIG. 6 , the wafer W has a protection sheet S attached on the main surface side on which the circuit pattern is formed, fixed by suction onto a chuck table  24  with the back surface up, and is rotated around the axis WC. The grinding wheel  10  is disposed to oppose to the back surface of the wafer W, and is rotated around the axis SC.  
      When the back surface of the wafer W is ground, the aforementioned Y-table  22  mounted with the chuck table  24  performs transverse feed for the wafer W in the Y-direction to position the wafer W at the position just before the peripheral edge part of the wafer W contacts the small-diameter grindstone  12 . In this case, the portion slightly inward from the outermost peripheral portion of the grindstone chip  11 B of the cup-shaped grindstone  11  is at the position passing through the center of the wafer W placed concentrically with the axis WC.  
      Next, the grinding wheel  10  lowers to grind the back surface of the wafer W with the grindstone chips  11 B of the cup-shaped grindstone  11 . When the grinding wheel  10  further lowers to grind to reduce the half thickness of the wafer W, the back surface and the peripheral edge part of the wafer W are ground at the same time while transverse feed of the wafer W is performed in the Y-direction so that the side surface of the small-diameter grindstone  12  cuts in the peripheral edge part of the wafer W.  
      The grinding work is thus continued, and just before the thickness of the wafer W reaches a predetermined value, the wafer W is fed in the reverse direction so that the peripheral edge part of the wafer W is slightly separated from the small-diameter grindstone  12 , and the back surface of the wafer W is finally ground with the grindstone chips  11 B of the cup-shaped grindstone  11  in the state in which the small-diameter grindstone  12  does not touch the peripheral edge part of the wafer W.  
      Moving away the small-diameter grindstone  12  at the time of final grinding of the back surface of the wafer W is for the purpose of suppressing chipping of the peripheral edge part of the thinned wafer W. When the thickness of the wafer W reaches the predetermined value in this manner, the grinding wheel  10  releases upward and the work is finished.  
      Since the wafer W thinned in this manner by the back surface grinding has the peripheral edge part ground by the small-diameter grindstone  12 , the peripheral edge part is not in the sharpened shape as shown in  FIGS. 6 and 7 , and thus, the wafer W is worked into the shape which is strong against cracking and chipping.  
       FIG. 7  schematically shows the state in which the back surface of the wafer W is ground by the cut-in feed in the Z-direction of the aforementioned small-diameter grindstone  12  and the transverse feed in the Y-direction of the wafer W, and shows the final position of the back surface grinding. In  FIG. 7 , the relative movement locus of the small-diameter grindstone  12  with respect to the wafer W is shown to be easily understood. Namely, the relative movement locus of the small-diameter grindstone  12  with respect to the wafer W becomes the locus shown by the arrow written outside the small-diameter grindstone  12  in  FIG. 7 .  
      Since transverse feed in the Y-direction is performed for the small-diameter grindstone  12  as described above, the transverse feed in the Y-direction of the grindstone chips  11 B of the cup-shaped grindstone  11  is performed at the same time, and it is necessary to have a sufficient transverse feed rate for the grindstone chip  11 B not to deviate from the center of the wafer W.  
      In the aforementioned embodiment, the peripheral edge part of the wafer W is ground with the side surface of the small-diameter grindstone  12 , but the present invention is not limited to this. The peripheral edge part of the wafer W can be ground by using both of the end surface of the small-diameter grindstone  12  or both of the end surface and the side surface.  
       FIG. 8  schematically shows the state in which the back surface of the wafer W is ground by using a grinding wheel  10 A having the small-diameter grindstone  13  in a truncated cone shape shown in the aforementioned  FIG. 3 . In this case, the wafer W is thinned by only the cut-in feed in the Z-direction of the grinding wheel  10 A without performing the transverse feed in the Y-direction of the wafer W. In this embodiment, the peripheral edge part of the wafer W is worked into the strong shape against cracking and chipping without being formed into the sharpened shape.  
      In the aforementioned embodiment, the explanation is made with the back surface grinding of the wafer W and the peripheral edge grinding performed at the same time, but the small-diameter grindstone  12  is sufficiently projected with respect to the grindstone chip  11 B of the cup-shaped grindstone  11 , the peripheral edge grinding of the wafer W is completed first, and then the back surface grinding of the wafer W can be performed. In this case, working time becomes longer as compared with the case where the back surface grinding of the wafer W and the peripheral edge grinding are performed at the same time.  
      As explained thus far, according to the present invention, the back surface grinding and the peripheral edge grinding of the wafer W can be performed at the same time while avoiding increase in the size of the grinding apparatus, the peripheral edge part of the extremely thin wafer is prevented from being into the sharpened shape, and the thin wafer W in which cracking and chipping of the peripheral edge part hardly occur can be obtained.