Patent Publication Number: US-6905400-B2

Title: Method and apparatus for dressing polishing cloth

Description:
This is a Divisional Application of U.S. patent application Ser. No. 08/881,616, filed Jun. 25, 1997, and now U.S. Pat. No. 6,364,752. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a method and apparatus for dressing a polishing cloth, and more particularly to a method and apparatus for dressing a polishing cloth for restoring the polishing capability of the polishing cloth in a polishing apparatus for polishing a workpiece such as a semiconductor wafer having a device pattern thereon to a flat mirror finish by bringing the surface of the workpiece into contact with a surface of the polishing cloth. 
   2. Description of the Prior Art 
   Recent rapid progress in semiconductor device integration demands smaller and smaller wiring patterns or interconnections and also narrower spaces between interconnections which connect active areas. One of the processes available for forming such interconnections is photolithography. Though the photolithographic process can form interconnections that are at photolithographic process can form interconnections that are at most 0.5 μm wide, it requires that surfaces on which pattern images are to be focused by a stepper be as flat as possible because the depth of focus of the optical system is relatively small. 
   It is therefore necessary to make the surfaces of semiconductor wafers flat for photolithography. One customary way of flattening the surfaces of semiconductor wafers is to polish, them with a polishing apparatus, and such a process is called Chemical Mechanical Polishing (CMP). In CMP the semiconductor wafers are chemically and mechanically polished while supplying an abrasive liquid comprising abrasive grains and a chemical solution such as an alkaline solution. 
   Conventionally, a polishing apparatus has a turntable and a top ring which rotate at respective individual speeds. A polishing cloth is attached to the upper surface of the turntable. A semiconductor wafer to be polished is placed on the polishing cloth and clamped between the top ring and the turntable. An abrasive liquid containing abrasive grains is supplied onto the polishing cloth and retained on the polishing cloth. During operation, the top ring exerts a certain pressure on the turntable, and the surface of the semiconductor wafer held against the polishing cloth is therefore polished to a flat mirror finish while the top ring and the turntable are rotating. In the conventional polishing apparatus, a nonwoven fabric cloth is often used as a polishing cloth for polishing the semiconductor wafer having a device pattern thereon. 
   However, the recent higher integration of IC or LSI demands a more and more planarized finish of the semiconductor wafer. In order to satisfy such a demand, harder materials, such as polyurethane foam, have been recently used as the polishing cloth. After, for example, one or more semiconductor wafers have been polished by bringing the semiconductor wafer into sliding contact with the polishing cloth and rotating the turntable, abrasive grains in the abrasive liquid or ground-off particles of the semiconductor wafer are attached to the polishing cloth. In the case of the nonwoven fabric cloth, the polishing cloth is napped. In the case where the semiconductor wafers are repeatedly polished by the same polishing cloth, the polishing performance of the polishing cloth is degraded, thus lowering the polishing rate and causing a nonuniform polishing action. Therefore, after polishing a semiconductor wafer or during polishing of a semiconductor wafer, the polishing cloth is processed to recover its original polishing capability by a dressing process. 
   For a dressing process for recovering the polishing capability of the polishing cloth made of relatively hard material such as polyurethane foam, there has been proposed a dresser having diamond grains. This dressing process using the diamond grain dresser is effective in restoring the polishing capability of the polishing cloth and tends not to rapidly lower the polishing rate thereof. 
   To be more specific, the dressing process is classified into two processes, one of which is a process for raising the napped polishing cloth by a blush, water jet or gas jet and washing out the remaining abrasive grains or the ground-off particles from the polishing cloth, and the other of which is a process for scraping off a surface of the polishing cloth by diamond or SiC to create a new surface of the polishing cloth. In the former case, even if the dressing is not uniformly performed over the entire dressing area of the polishing cloth, the polished surface of the semiconductor wafer is not greatly affected by the thus dressed polishing cloth. However, in the latter case, the polished surface of the semiconductor wafer is greatly affected by the polishing cloth which has been nonuniformly dressed. 
   Conventionally, the polishing apparatus having a diamond grain dresser comprises a top ring for holding the semiconductor wafer and pressing the semiconductor wafer against a polishing cloth on a turntable, and a dresser for dressing the surface of the polishing cloth, the top ring and the dressing being supported by respective heads. The dresser is connected to a motor provided on the dresser head. The dresser is pressed against the surface of the polishing cloth while the dresser is rotated about its central axis and the dresser head is swung, thereby dressing a certain area of the polishing cloth which is to be used for polishing. That is, the dressing of the polishing cloth is preformed by rotating the turntable, pressing the rotating dresser against the polishing cloth, and moving the dresser radially of the polishing cloth by swinging the dresser head. In the conventional dressing process, the rotational speed of the dresser is equal to the rotational speed of the turntable. 
   However, when the polishing cloth is dressed by the diamond grain dresser, the polishing cloth is slightly scraped off. Unless the polishing cloth is uniformly scraped off in any vertical cross section, i.e., is uniformly scraped off in a radial direction of the polishing cloth, the semiconductor wafer, which is a workpiece to be polished, cannot be uniformly polished as the number of dressing processes increases. It is confirmed by the inventors of the present application that when the dressing is performed in such a manner that the rotational speed of the dresser is equal to the rotational speed of the turntable, the amount of material removed from the inner circumferential region of the polishing cloth is greater than the amount of material removed from the outer circumferential region of the polishing cloth. 
     FIG. 6  shows measurements of the removal amount of material in the polishing cloth which has been dressed by the conventional dressing method. In  FIG. 6 , the horizontal axis represents a distance from a center of rotation, i.e., a radius (cm) of the polishing cloth, and the vertical axis represents the amount of material removed from the polishing cloth, which is expressed by a removal thickness (mm) of material.  FIG. 6  shows measurements of the removal thickness were the same and about 500 semiconductor wafers were polished on the polishing cloth and the corresponding number of dressing processes were applied to the polishing cloth. Two kinds of diamond grain sizes were used in the experiment. For example, the rotational speed of the turntable was 13 rpm, the rotational speed of the dresser was 13 rpm, 500 semiconductor wafers were polished on the polishing cloth made of polyurethane foam, and a corresponding number of the dressing processes were applied to the polishing cloth. In this case, the difference in a removal thickness of material between the outer circumferential region and the inner circumferential region of the polishing cloth was about 100 μm. 
   SUMMARY OF THE INVENTION 
   It is therefore an object of the present invention to provide a method and apparatus for dressing a polishing cloth which can uniformly scrape off the polishing cloth in a radial direction thereof. 
   According to one aspect of the present invention, there is provided a method of dressing a polishing cloth mounted on a turntable by bringing a dresser into contact with the polishing cloth, comprising measuring heights of a surface of the polishing cloth at radial positions of the polishing cloth in a radial direction thereof, determining a rotational speed of the dresser with respect to a rotational speed of the turntable on the basis of the measured heights, and dressing the polishing cloth by pressing the dresser against the polishing cloth while the turntable and the dresser are rotating. 
   According to another aspect of the present invention, there is provided a method of dressing a polishing cloth mounted on a turntable by bringing a dresser in contact with the polishing cloth, comprising setting a rotational speed of the dresser with respect to a rotational speed of the turntable so that the rotational speed of the dresser is lower than the rotational speed of the turntable and dressing the polishing cloth by pressing the dresser against he polishing cloth while the turntable and the dresser are rotating. 
   According to still another aspect of the present invention, there is provided an apparatus for dressing a polishing cloth mounted on a turntable, comprising a dresser for contacting the polishing cloth, an actuator for rotating the dresser about a central axis of the dresser, and a measuring device for measuring heights of a surface of the polishing cloth at radial positions of the polishing cloth in a radial direction thereof. A rotational sped of the dresser with respect to a rotational speed of the turntable is determined on the basis of the measured heights, and the polishing cloth is dressed by pressing the dresser against the polishing cloth while the turntable and the dresser are rotating. 
   The above and other objects, features, and advantages of the present invention will become apparent from the following description when taken in conjunction with the accompanying drawings, which illustrate a preferred embodiment of the present invention by way of example. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a vertical cross-sectional view of a polishing apparatus having a dressing apparatus according to an embodiment of the present invention; 
       FIG. 2A  is a bottom view of a dresser according to an embodiment of the present invention; 
       FIG. 2B  is a cross-sectional view taken along line a—a of  FIG. 2A ; 
       FIG. 2C  is an enlarged view of a section b of  FIG. 2B ; 
       FIG. 3  is a plan view showing an arrangement of the dresser and a polishing cloth mounted on a turntable according to the embodiment of the present invention; 
       FIG. 4  is a graph showing measurements of the removal thickness of material in the polishing cloth which has been dressed according to the embodiment of the present invention; 
       FIG. 5A  is a view showing the distribution of relative velocity vectors when a rotational speed ratio of the turntable to the dresser is 1:0.5; 
       FIG. 5B  is a view showing the distribution of relative velocity vectors when a rotational speed ratio of the turntable to the dresser is 1:1; 
       FIG. 5C  is a view showing the distribution of relative velocity vectors when a rotational speed ratio of the turntable to the dresser is 1:1.5; 
       FIG. 6  is a graph showing measurements of the removal thickness of material in the polishing cloth which has been dressed according to the conventional method; 
       FIG. 7  is a side view of the dressing apparatus according to an embodiment of the present invention; 
       FIG. 8  is a plan view of the dressing apparatus shown in  FIG. 7 ; 
       FIG. 9  is a flow chart showing steps of the dressing process according to the embodiment of the present invention; 
       FIG. 10  is a graph showing heights of a surface of the polishing cloth at radial positions of the polishing cloth in a radial direction thereof, measured by a measuring device of the dressing apparatus according to the embodiment of the present invention; and 
       FIG. 11  is a graph showing a removal thickness of material in a radial direction of the polishing cloth which has been dressed by the dressing apparatus of the present invention. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The dressing apparatus according to an embodiment of the present invention will be described below with reference to  FIGS. 1 through 5 . 
   A dressing apparatus is installed in a polishing apparatus in FIG.  1 . As shown in  FIG. 1 , the polishing apparatus comprises a turntable  20 , and a top ring  3  positioned above the turntable  20  for holding a semiconductor wafer  2  and pressing the semiconductor wafer  2  against the turntable  20 . The turntable  20  is coupled to a motor  7  and is rotatable about its own axis as indicated by an arrow. A polishing cloth  4  (for example, IC-1000 manufactured by Rodel Products Corporation) is mounted on the upper surface of the turntable  20 . 
   The top ring  3  is coupled to a motor and also to a lifting/lowering cylinder (not shown). The top ring  3  is vertically movable and rotatable about its own axis as indicated by arrows by the motor and the lifting/lowering cylinder. The top ring  3  can therefore press the semiconductor wafer  2  against the polishing cloth  4  under a desired pressure. The semiconductor wafer  2  is attached to a lower surface of the top ring  3  under a vacuum or the like. A guide ring  6  is mounted on the outer circumferential edge of the lower surface of the top ring  3  for preventing the semiconductor wafer  2  from being disengaged from the top ring  3 . 
   An abrasive liquid supply nozzle  5  is disposed above the turntable  20  for supplying an abrasive liquid onto the polishing cloth  4  attached to the turntable  20 . A dresser  10  for performing dressing of the polishing cloth  4  is positioned in diametrically opposite relation to the top ring  3 . The polishing cloth  4  is supplied with a dressing liquid such as water from a dressing liquid supply nozzle  9  extending over the turntable  20 . The dresser  10  is coupled to a motor  15  and also to a lifting/lowering cylinder  16 . The dresser  10  is vertically movable and rotatable about its own axis as indicated by arrows by the motor  15  and the lifting/lowering cylinder  16 . 
   The dresser  10  has an annular diamond grain layer  13  on its lower surface. The dresser  10  is supported by a dresser head (not shown) and is movable in a radial direction of the polishing cloth  4 . The abrasive liquid supply nozzle  5  and the dressing liquid supply nozzle  9  extend to a region near the central axis of the turntable  20  above the upper surface thereof for supplying the abrasive liquid and the dressing liquid such as water, respectively, to the polishing cloth  4  at a predetermined position thereon. 
   The polishing apparatus operates as follows. The semiconductor wafer  2  is held on the lower surface of the top ring  3 , and is pressed against the polishing cloth  4  on the upper surface of the turntable  20 . The turntable  20  and the top ring  3  are rotated relatively to each other to thereby bring the lower surface of the semiconductor wafer  2  in sliding contact with the polishing cloth  4 . At this time, the abrasive liquid nozzle  5  supplies the abrasive liquid to the polishing cloth  4 . The lower surface of the semiconductor wafer  2  is now polished by a combination of a mechanical polishing action of abrasive grains in the abrasive liquid and a chemical polishing action of an alkaline solution in the abrasive liquid. 
   The polishing process comes to an end when the semiconductor wafer  2  is polished to a predetermined thickness of a surface layer thereof. When the polishing process is finished, the polishing properties of the polishing cloth  4  have been changed and the polishing performance of the polishing cloth  4  deteriorates. Therefore, the polishing cloth  4  is dressed to restore its polishing properties. 
   In an embodiment of the present invention, an apparatus for dressing a polishing cloth has a dresser  10  shown in  FIGS. 2A through 2C .  FIG. 2A  is a bottom view of the dresser  10 ,  FIG. 2B  is a cross-sectional view taken along the line a—a of  FIG. 2A , and  FIG. 2C  is an enlarged view showing a portion b of FIG.  2 B. 
   The dresser  10  comprises a dresser body  11  of a circular plate, an annular projecting portion  12  which projects from an outer circumferential portion of the dresser body  11 , and an annular diamond grain layer  13  on the annular projecting portion  12 . The annular diamond grain layer  13  is made of diamond grains which are electrodeposited on the annular projecting portion  12 . The diamond grains are deposited on the annular projecting portion  12  by nickel plating. The sizes of the diamond grains are in the range of 10 to 40 μm. 
   One example of the dresser  10  is as follows. The dresser body  11  has a diameter 250 mm. The annular diamond grain layer  13 , having a width of 6 mm, is formed on the circumferential area of the lower surface of the dresser body  11 . The annular diamond grain layer  13  comprises a plurality of sectors (eight in this embodiment). The diameter of the dresser body  11  is larger than the diameter of the semiconductor wafer  2 , which is a workpiece to be polished. Thus, the dressed surface of the polishing cloth has margins at inner and outer circumferential regions with respect to the surface of the semiconductor wafer being polished. 
   The polishing cloth is dressed by the dresser in a manner shown in FIG.  3 . The polishing cloth  4  made of polyurethane foam to be dressed is attached to the upper surface of the turntable  20 , which rotates in a direction indicated by the arrow A. The dresser  10 , which rotates in a direction indicated the by the arrow B, is pressed against the polishing cloth so that the annular diamond grain layer  13  is brought in contact with rotated relative to each other to thereby bring the lower surface of the diamond grain layer  13  in sliding contact with the polishing cloth  4 . In this case, the dresser is not swung. 
   In the polishing apparatus, the turntable  20  is rotated by the motor  7  and the rotational speed of the turntable  20  is variable. The dresser  10  is rotatable by the motor  15  and the rotational speed of the dresser  10  is also variable. Specifically, the rotational speed of the dresser  10  can be set to a desired value which is independent from the rotational speed of the turntable  20 . 
   In the embodiments of dressing processes described below, the rotational speed ratios of the turntable to the dresser are 20 rpm:12 rpm, 50 rpm:30 rpm, and 150 rpm:90 rpm, which are each set to a ratio of 1:0.6. 
     FIG. 4  is a graph showing measurements of the removal thickness of material in the polishing cloth which has been dressed according to the embodiment of the present invention. In  FIG. 4 , the horizontal axis represents a radial position on the polishing cloth (cm), and the vertical axis represents a removal thickness (mm) of material from the polishing cloth. L T  represents the area where the dresser contacts the polishing cloth. The dresser  10  is pressed against the polishing cloth  4  at a pressure of 450 gf/cm 2 . As described above, the dressing area (L T ) is larger than the area (L D ) where the semiconductor wafer to be polished contacts the polishing cloth to provide margins at inner and outer circumferential regions of the polishing cloth in a radial direction thereof. 
   In  FIG. 4 , an open symbol ∘ represents a verification example of the conventional dressing method. That is, the rotational speed of the turntable is 13 rpm and the rotational speed of the dresser is 13 rpm. In this case, as described above, the removal thickness of material from the polishing cloth is greater at the inner circumferential region than at the outer circumferential region of the polishing cloth. In contrast, an open symbol □ represents a verification example in which the rotational speed of the turntable is 20 rpm and the rotational speed of the dresser is 12 rpm. In this case, the removal thickness of material from the polishing cloth is substantially uniform at all radial positions of the polishing cloth in a radial direction thereof. An open symbol Δ represents a verification example in which the rotational speed of the turntable is 50 rpm and the rotational speed of the dresser is 30 rpm. In this case also, the removal thickness of material from the polishing cloth is substantially uniform at all radial positions of the polishing cloth in a radial direction thereof. A solid symbol ▪ is a verification example in which the rotational speed of the turntable is 150 rpm and the rotational speed of the dresser is 90 rpm. In this case also, the removal thickness of material from the polishing cloth is substantially uniform at all radial positions of the polishing cloth in a radial direction of the dressing area (L T ). 
   In the above examples, the rotational speed ratio of the turntable to the dresser is 1:0.6, however, the removal thickness of material from the polishing cloth is greater as the absolute value of the rotational speed is larger. Further, it is confirmed from the experiments by the inventors of the present application that in the case where the rotational speed ratio of the turntable to the dresser is in the range of 1:0.4 to 1:0.85, the removal thickness of material from the polishing cloth is substantially uniform at all radial positions of the polishing cloth in a radial direction thereof. 
   As described above, according to the present invention, the rotational speed ratio of the turntable to the dresser is set to be in the range of 1:0.4 to 1:0.85, and the removal thickness of material from the polishing cloth is substantially uniform at all radial positions of the polishing cloth in a radial direction thereof. As a result, when polishing a semiconductor wafer by the thus dressed polishing cloth, the polished surface of the semiconductor wafer becomes flat. 
   Next, the theory in which the removal thickness of material from the polishing cloth is substantially uniform from the inner circumferential region to the outer circumferential region of the polishing cloth by setting the rotational speed ratio of the turntable to the dresser to a range of 1:0.4 to 1:0.85 will be described. This theory is based on the assumption that the relative velocity between the dresser and the polishing cloth affects the amount of material removed from the polishing cloth, and the amount of material removed from the polishing cloth is greater as the relative velocity is larger. 
     FIGS. 5A ,  5 B and  5 C show the distribution of relative velocity vectors between the polishing cloth and the dresser. The center (O) of the turntable is located at the left side of the dresser.  FIG. 5A  shows a verification example in which the rotational speed of the turntable is 100 rpm and the rotational speed of the dresser is 50 rpm.  FIG. 5B  shows a verification example in which the rotational speeds of the turntable and the dresser are 100 rpm, respectively.  FIG. 5C  shows a verification example in which the rotational speed of the turntable is 100 rpm and the rotational speed of the dresser is 150 rpm, i.e., the rotational speed of the dresser is higher than that of the turntable. In  FIGS. 5A ,  5 B and  5 C, “O” represents a center of the turntable  20  and a number of arrows in the annular diamond grain layer  13  of the dresser  10  represents relative velocity vectors, which are vectors of relative velocities between the diamond grain layer  13  and the polishing cloth  4  at respective positions. As the absolute value of the relative velocity vector is larger, the removal thickness of material from the polishing cloth is greater at the position concerned. As in the conventional method, when the rotational speed of the dresser is equal to the rotational speed of the turntable, the relative velocity vectors are uniform in all areas which are dressed by the dresser  10  as shown in FIG.  5 B. In this condition, the removal thickness of material from the polishing cloth is greater at the inner circumferential region of the polishing cloth, which is nearer to the center (O) of the turntable, and the removal thickness of material from the polishing cloth is smaller at the outer circumferential region, which is farther away from the center (O) of the turntable. Therefore, in order to correct nonuniform tendency of the removal thickness of material from the polishing cloth, it is desirable that the relative velocity be higher at the outer circumferential region, which is farther away from the center (O) of the turntable, and the relative velocity be lower at the inner circumferential region, which is nearer to the center (O) of the turntable. 
   As shown in  FIG. 5A , when the rotational speed of the dresser is lower than the rotational speed of the turntable, the relative velocity is lower at the inner circumferential region, which is nearer to the center (O) of the turntable, and is higher at the outer circumferential region, which is farther away from the center (O) of the turntable. Therefore, the removal thickness of material from the polishing cloth is smaller at the inner circumferential region of the polishing cloth and is greater at the outer circumferential region of the polishing cloth, because as the absolute value of the relative velocity vector is larger, the removal thickness of material from the polishing cloth is greater at the position concerned. 
   On the other hand, in the case where the rotational speed of the turntable is equal to the rotational speed of the dresser, the relative velocity vectors are uniform at all positions as shown in FIG.  5 B. In this case, as shown in  FIGS. 6 , the removal thickness of material from the polishing cloth is greater at the inner circumferential region of the polishing cloth and is smaller at the outer circumferential region thereof. Therefore, by combination of the tendency shown in FIG.  6  and the tendency shown in  FIG. 5A , in which the relative velocity is higher at the outer circumferential region of the polishing cloth, i.e., by making the rotational speed of the dresser lower than the rotational speed of the turntable, the removal thickness of material from the polishing cloth is substantially uniform at all radial positions of the polishing cloth in a radial direction thereof. 
   In the embodiment shown in  FIG. 2 , the dresser is provided with the annular diamond grain layer made of diamond grains which are electrodeposited on the annular projecting portion. However, silicon carbide (SiC) may be used instead of diamond grains. Further, the material and structure of the dresser may be freely selected, and the same dressing effect may be obtained by utilizing the above principles. 
   Next, the dressing apparatus for obtaining a desired surface of the polishing cloth by utilizing the above principles will be described below with reference to  FIGS. 7 and 8 . As shown in  FIG. 7 , the dresser  10  having the annular diamond grain layer  13  is supported by a dresser head  21  which is supported by a rotating shaft  22 . A measuring device  23  for measuring a surface contour of the polishing cloth  4  is fixed to the dresser head  21 . The measuring device  23  comprises a measuring unit  24  comprising a micrometer, a support unit  25  for supporting the measuring unit  24 , and a contact  26  comprising a roller which is fixed to the forward end of the measuring unit  24 . 
   As shown in  FIG. 7 , the rotation of the turntable  20  is stopped, the contact  26  contacts the surface of the polishing cloth  4 , and the dresser head  21  is swung about the rotating shaft  22  by rotating the rotating shaft  22  about its won axis. Thus, as shown in  FIG. 8 , the contact  26  is moved radially while it contacts the surface of the polishing cloth  4 , and the heights at radial positions of the polishing cloth in a radial direction thereof are measured during movement of the contact  26 . That is, the surface contour, i.e., the undulation of the surface of the polishing cloth  4  in a radial direction thereof, is measured. Since the dressing liquid such as water remains on the surface of the polishing cloth  4  in a radial direction thereof, is measured. Since the dressing liquid such as water remains on the surface of the polishing cloth  4 , the contact type of sensor is desirable to measure the surface contour, rather than a noncontact type of sensor, when measuring the undulation of the surface of the polishing cloth. Next, the process for using the dressing apparatus shown in  FIGS. 7 and 8  will be described below with reference to FIG.  9 . 
   In step  1 , the heights at radial positions of the polishing cloth in a radial direction thereof are measured, and the obtained values which are set to initial values are memorized.  FIG. 10  shows the heights of the surface of the polishing cloth at radial positions of the polishing cloth in a radial direction thereof. In  FIG. 10 , the horizontal axis represents a radius (mm) of the polishing cloth, and the vertical axis represents the heights which are actually measured. In  FIG. 10 , the curve A shows initial values which are the heights at radial positions of the polishing cloth in a radial direction thereof. In step  2 , the rotational speed of the turntable  20  and the rotational speed of the dresser  10  are set. In step  3 , the semiconductor wafer  2  is polished by the use of the polishing cloth  4  while supplying the abrasive liquid from the abrasive liquid supply nozzle  5  (see FIG.  1 ). In step  4 , the dressing of the polishing cloth  4  is performed by the dresser  10 . 
   Next, in step  5 , the heights at radial positions of the polishing cloth in a radial direction thereof are measured by the measuring device  23 . In  FIG. 10 , the curve B shows the heights at radial positions of the polishing cloth in a radial direction thereof when the rotational speed ratio of the turntable to the dresser is 1:0.5. The curve C shows the heights at radial positions of the polishing cloth in a radial direction thereof when the rotational speed ratio of the turntable to the dresser is 1:0.7. 
   Next, in step  6 , the measured values obtained in step  5  are subtracted from the initial values obtained in step  1  to obtain the removal thickness of material from the polishing cloth at radial positions of the polishing cloth in a radial direction thereof.  FIG. 11  shows the removal thickness of material from the polishing cloth at radial positions of the polishing cloth in a radial direction thereof. In  FIG. 11 , the horizontal axis represents the radius (mm) of the polishing cloth, and the vertical axis represents the removal thickness of material from the polishing cloth. In  FIG. 11 , the curve D shows the removal thickness of material at radial positions of the polishing cloth in a radial direction thereof when the rotational speed ratio of the turntable to the dresser is 1:0.5. The curve E shows the removal thickness of material at radial position of the polishing cloth in a radial direction thereof when the rotational speed ratio of the turntable to the dresser is 1:0.7. 
   Next, in step  7 , the obtained curve, such as the curve D or E, is compared with the preset desired surface of the polishing cloth. If the removal thickness of material from the polishing cloth is greater at the inner circumferential region than at the outer circumferential region, the rotational speed of the dresser  10  is lowered in step  8 . If the removal thickness of material from the polishing cloth is in an allowable range at the inner and outer circumferential regions, the rotational speed of the dresser  10  is not changed in step  9 . If the removal thickness of material from the polishing cloth is greater at the outer circumferential region than at the inner circumferential region, the rotational speed of the dresser  10  is increased in step  10 . In steps  8  through  10 , the rotational speed of the turntable is not changed. After setting the rotational speed of the dresser  10  to an optimum value in steps  8  through  10 , a next dressing process is performed by the set value of the rotational speed of the dresser  10 . 
   In the above embodiments, the heights of a surface of the polishing cloth at radial positions of the polishing cloth are measured. The heights of the surface of the polishing cloth are directly related to the thickness of the polishing cloth. That is, irregularities of the removal thickness of material from the polishing cloth cause irregularities of the thickness of the polishing cloth, resulting in irregularities of the heights of the surface of the polishing cloth. To correct the heights of the surface of the polishing cloth corresponds to correction of the thicknesses of the surface of the polishing cloth. In the embodiments, the contact type of the sensor is used to measure the heights of the polishing cloth, and the surface contour of the polishing cloth is controlled on the basis of the measured values. It is also possible to control the surface contour of the polishing cloth by measuring the thicknesses of the polishing cloth with a thickness detector and utilizing the measured values. 
   Further, in the embodiments, the surface contour of the polishing cloth is controlled so as to be flat by the dressing process. However, in some cases, the surface of the turntable may be slightly convex, and thus the surface of the polishing cloth mounted on the turntable may be slightly convex in accordance with the purpose or condition of the polishing process. In this case, the surface contour of the polishing cloth may be controlled so as to be slightly convex by adjusting a rotational speed ratio of the turntable to the dresser according to the present invention. 
   In the embodiments, although the annular diamond grain layer and the annular SiC layer have a circular outer shape and a circular inner shape, respectively, they may have an elliptical outer shape and an elliptical inner shape, respectively, or a circular outer shape and a heart-shaped inner shape, or any other shapes. Further, the dresser may have a solid circular diamond layer or a solid circular SiC layer without having a hollow portion. The dresser may also comprise a dresser body, and a plurality of small circular contacting portions made of diamond grains and arranged in a circular array on the dresser body. 
   As is apparent from the above description, the present invention offers the following advantages. 
   Since the heights of the surface of the polishing cloth at radial positions of the polishing cloth in a radial direction thereof are measured, the rotational speed of the dresser relative to the rotational speed of the turntable is determined on the basis of the measured values, and a dressing process is performed in the determined rotational speed ratio of the turntable to the dresser. The polishing cloth is thus uniformly dressed in a radial direction to have a desired surface contour from the inner circumferential region to the outer circumferential region thereof. 
   Further, the polishing cloth is dressed in such a manner that the rotational speed of the dresser is lower than the rotational speed of the turntable. Specifically, the rotational speed ratio of the turntable to the dresser is in the range of 1:0.4 to 1:0.85. The removal thickness of material from the polishing cloth is substantially uniform from the inner region to the outer region of the polishing cloth. Therefore, a workpiece such as a semiconductor wafer having a device pattern thereon can be polished to a flat mirror finish by the use of the thus dressed polishing cloth. 
   Although certain preferred embodiments of the present invention have been shown and described in detail, it should be understood that various changes and modifications may be made therein without departing from the scope of the appended claims.