Patent Publication Number: US-11389925-B2

Title: Offset head-spindle for chemical mechanical polishing

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Patent Application No. 62/770,716, filed Nov. 21, 2018, which is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Field 
     The present invention relates generally to a method and an apparatus used to polish a substrate. More specifically, this invention relates to a chemical mechanical polishing system. 
     Description of the Related Art 
     An integrated circuit is typically formed on a substrate by the sequential deposition of conductive, semiconductive, or insulative layers on a silicon wafer. One fabrication step involves depositing a filler layer over a non-planar surface and planarizing the filler layer. For certain applications, the filler layer is planarized until the top surface of a patterned layer is exposed. A conductive filler layer, for example, can be deposited on a patterned insulative layer to fill the trenches or holes in the insulative layer. After planarization, the portions of the metallic layer remaining between the raised pattern of the insulative layer form vias, plugs, and lines that provide conductive paths between thin film circuits on the substrate. For other applications, such as oxide polishing, the filler layer is planarized until a predetermined thickness is left over the nonplanar surface. In addition, planarization of the substrate surface is usually required for photolithography. 
     Chemical mechanical polishing (CMP) is one accepted method of planarization. This planarization method typically requires that the substrate be mounted on a carrier or polishing head. The exposed surface of the substrate is typically placed against a rotating polishing surface of a polishing pad. The carrier head provides a controllable load on the substrate to push it against the polishing surface. An abrasive polishing slurry is typically supplied to the surface of the polishing surface as the substrate is urged against the polishing surface. 
     Variations in the slurry distribution, the polishing surface condition of the polishing pad, the relative speed between the polishing surface and the substrate, and the load on the substrate can cause variations in the material removal rate across the substrate. One drawback of CMP systems in the current art is a small variation in the head sweep, which causes the polishing surface to go over the same area multiple times and results in the non-uniform polishing of the wafers. 
     Therefore, there is a need in the art for a way to provide a uniform polishing of a substrate. 
     SUMMARY OF INVENTION 
     Embodiments of the disclosure may provide a polishing system, including two polishing stations. The polishing stations include a platen for holding a polishing surface. The polishing system also includes a support structure that is moveable between the two polishing stations. The polishing system includes a motor, attached to the support structure, which is located an offset distance horizontally from the carrier head, and connected to the carrier head by a coupling. The polishing system may also include a controller that moves the carrier head from station to station. 
     In one embodiment, a polishing system is provided, including a first polishing station, including a platen that has a polishing surface and a platen central axis about which the platen is configured to rotate, and a carrier head assembly. The carrier head assembly includes a carriage that is configured to be positioned relative to a portion of a support structure of the polishing system by a carrier motor, a carrier head that is configured to retain a substrate, an offset coupler; and a carrier head motor having a drive shaft. The carrier head motor is coupled to the carriage. The drive shaft and the carrier head are coupled together by the offset coupler. A rotational axis of the drive shaft is located an offset distance parallel to the polishing surface from a head central axis of the carrier head. The head central axis is not, or is only intermittently, collinear with the platen central axis during the polishing process. 
     In another embodiment, a carrier head assembly is provided, including a carrier head that is configured to retain a substrate and urge the substrate against a polishing surface of a platen, an offset coupler, and a carrier head motor having a drive shaft. The carrier head motor is coupled to a supporting structure. The drive shaft and the carrier head are coupled together by the offset coupler. A rotational axis of the drive shaft is located an offset distance parallel to the polishing surface from a central axis of the carrier head. 
     In another embodiment, a method of polishing a substrate is provided, including urging the substrate against a polishing surface of a platen by a carrier head assembly, rotating the carrier head about a rotational axis of a drive shaft, and rotating the platen about a platen central axis. The carrier head assembly includes a carrier head that is configured to retain the substrate, an offset coupler and a carrier head motor having a drive shaft. The carrier head motor is coupled to a supporting structure. The drive shaft and the carrier head are coupled together by the offset couple. The rotational axis of the drive shaft is located an offset distance parallel to the polishing surface from a central axis of the carrier head. The rotating the carrier head is caused by the carrier head motor. The central axis is not, or is only intermittently, collinear with a platen central axis during the polishing process. 
     The offset distance allows a shifted carrier head to cover more surface area of the polishing surface. The offset distance effectively provides an additional rotation of the carrier head about the axis, which allows for a greater area traversed on the polishing surface, resulting in greater substrate surface uniformity. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the above recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only exemplary embodiments and are therefore not to be considered limiting of its scope, and may admit to other equally effective embodiments. 
         FIG. 1A  is a top view of a CMP system with multiple polishing stations and a curved track for the movement of a carrier head, according to one embodiment. 
         FIG. 1B  is a top view of a CMP system with multiple polishing stations and a cross carousel for the movement of carrier heads, according to one embodiment. 
         FIG. 2A  is a side cross sectional view of a polishing station, according to one embodiment. 
         FIG. 2B  is a side cross sectional view of a polishing station with an independent motor, according to one embodiment. 
         FIG. 3A  is a diagram of the path of the outline of the substrate during a polishing cycle without a head-sweep offset. 
         FIG. 3B  is a diagram of the path of the outline of the substrate during a polishing cycle with a head-sweep offset, according to one embodiment. 
         FIG. 3C  is a diagram of the outline of the substrate at an instant of time during a polishing cycle in which a head-sweep offset is used, according to one embodiment. 
         FIG. 3D  is a diagram of the outline of the substrate at an instant of time during a polishing cycle in which a head-sweep offset is used, showing the outline of the substrate with different head-sweep offsets, according to one embodiment. 
         FIG. 4A  is a plot of the normalized friction force respect to the spindle angle at a zero degree sweep angle. 
         FIG. 4B  is a plot of the normalized friction force respect to the spindle angle at a two degree sweep angle. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the disclosure provided herein include a polishing method and apparatus used to provide a uniform polishing of a surface of a substrate. In some embodiments, a carrier head is shifted relative to the attachment point of the support structure. The rotation of the carrier head around the offset attachment point results in more of the polishing surface being accessed due to a larger surface area of the pad being accessed, and reduces the amount of frictional force provided to a carrier head motor attached to a carriage that supports carrier head during operation. Embodiments of the disclosure provided herein may be especially useful for, but are not limited to, improving the polishing performance of a chemical mechanical polishing system. 
       FIG. 1A  is a plan view of a polishing system  100 , which contains an overhead track  128 , and several carrier head assemblies  119 , which carry the substrates  10  around the system during processing. The geometry of the polishing system  100  is often limited due to various physical constraints, such as the size constraint of the polishing system and the interaction of the polishing stations  124  with various other processing chambers and components within the polishing system. Therefore, it is often not possible to substantially change the locations of the polishing stations  124  or the radius of overhead track  128  which is used to guide and transfer the carrier heads  126  within the carrier head assemblies  119  to the various polishing stations. A modification to a polishing system is shown in  FIG. 2A . Here, the carrier head  126  is offset from axis  127  about which the carrier head motor  156  rotates. As shown in  FIG. 3B , this allows the carrier head  126  to reach more of the surface area of the polishing surface  130  of the polishing pad, without changing the geometry of the components within the polishing system  100 , such as the platen  120  and overhead track  128 . As shown in  FIG. 2A , the polishing surface  130  is positioned on a top surface of the platen  120 . 
       FIG. 4A  shows a plot of the normalized friction force at different rotational angles of the carrier head  126  with respect to the axis  127 , where 100% on the Y-axis signifies the frictional force experienced by a traditional carrier head with no offset during a polishing process. The frictional force on the carrier head  126  will cause a corresponding opposite but equal force to be applied to the carrier motor  157 . The vector component of the frictional forces that is in the direction of travel of the carrier head assemblies  119  along the overhead track  128  requires the carrier motor  157  to apply an equal and opposite force to maintain its position along the overhead track  128 , and thus otherwise prevent the carrier head assemblies  119  from sliding along the track  128 . The forces applied to the carrier motor  157  during processing puts extra wear and tear on the carrier motor  157 , and thus shortens its useable life and often cause the carrier motor  157  to be oversized to compensate for the applied loads. However,  FIG. 4A  shows that the normalized frictional force for one or more of the embodiments of the carrier head  126  described herein, such as the use of an offset carrier head  126 , is reduced with respect to the normalized frictional force for a conventional carrier head which has no offset. Thus, the normalized frictional force is always, at the worst case, the same as a carrier head  126  with no offset, while for the majority of the angles, the normalized frictional force is less. Thus, the embodiments of the offset carrier head  126  described herein always results in an equal or reduced normalized force provided to the carrier motor  157 . Therefore, the offset carrier head  126  improves the polishing of the substrate  10  without modifications being made to the rest of the polishing system  100  and size of the carrier motor  157 . 
       FIG. 1A  illustrates a plan view of a polishing system  100  for processing one or more substrates, according to one embodiment. The polishing system  100  includes a polishing platform  106  that at least partially supports and houses a plurality of polishing stations  124   a - 124   d  and load cups  123   a - 123   b . However, in some embodiments, the number of polishing stations can be equal to or greater than one. For example, the polishing apparatus can include four polishing stations  124   a ,  124   b ,  124   c  and  124   d . Each polishing station  124  is adapted to polish a substrate that is retained in a carrier head  126  within a carrier head assembly  119  that translates along an overhead track  128 . The carrier head assembly  119  is moved along the track  128  by a carrier motor  157  attached to the carriage  108 . The carriage  108  generally includes structural elements that that are able to guide and facilitate the control of the position of the carrier head assembly  119  along the overhead track  128 . In some embodiments, carrier motor  157  and carriage  108  include a linear motor and linear guide assembly that are configured to position the carrier head assembly  119  along all points of the circular overhead track  128 . 
     The polishing system  100  also includes a multiplicity of carrier heads  126 , each of which is configured to carry a substrate  10 . The number of carrier heads can be an even number equal to or greater than the number of polishing stations, e.g., four carrier heads or six carrier heads. For example, the number of carrier heads  126  can be two greater than the number of polishing stations. This permits loading and unloading of substrates to be performed from two of the carrier heads while polishing occurs with the other carrier heads at the remainder of the polishing stations, thereby providing improved throughput. 
     The polishing system  100  also includes a loading station  122  for loading and unloading substrates from the carrier heads. The loading station  122  can include a plurality of load cups  123 , e.g., two load cups  123   a ,  123   b , adapted to facilitate transfer of a substrate between the carrier heads  126  and a factory interface (not shown) or other device (not shown) by a transfer robot  110 . The load cups  123  generally facilitate transfer between the robot  110  and each of the carrier heads  126 . 
     A controller  190 , such as a programmable computer, is connected to each motor  152 ,  156  to independently control the rotation rate of the platen  120  and the carrier heads  126 . For example, each motor can include an encoder that measures the angular position or rotation rate of the associated drive shaft. Similarly, the controller  190  is connected to a carrier motor  157  ( FIGS. 1A and 2A ) in each carriage  108  to independently control the lateral motion and position of each carrier head  126  along the track  128 . For example, each carrier motor  157  can include a linear encoder that monitors and controls the position of the carriage  108  along the track  128 . 
     The controller  190  can include a central processing unit (CPU)  192 , a memory  194 , and support circuits  196 , e.g., input/output circuitry, power supplies, clock circuits, cache, and the like. The memory  194  is connected to the CPU  192 . The memory is a non-transitory computable readable medium, and can be one or more readily available memory such as random access memory (RAM), read only memory (ROM), floppy disk, hard disk, or other form of digital storage. In addition, although illustrated as a single computer, the controller  190  could be a distributed system, e.g., including multiple independently operating processors and memories. This architecture is adaptable to various polishing situations based on programming of the controller  190  to control the order and timing that the carrier heads are positioned at the polishing stations. 
     For example, some polishing recipes are complex and require three of four polishing steps. Thus, a mode of operation is for the controller  190  to cause a substrate to be loaded into a carrier head  126  at one of the load cups  123 , and for the carrier head  126  to be positioned in turn at each polishing station  124   a ,  124   b ,  124   c .  124   d  so that the substrate is polished at each polishing station in sequence. After polishing at the last station, the carrier head  126  is returned to one of the load cups  123  and the substrate is unloaded from the carrier head  126 . 
     The stations of the polishing system  100 , which include the loading station  122  and the polishing stations  124 , can be positioned at substantially equal angular intervals around the center of the polishing platform  106 . This is not required, but can provide the polishing system  100  with a good lateral footprint. Each polishing station  124  of the polishing system  100  can include a port, e.g., at the end of a carousel arm  138 , to dispense polishing liquid  136  (see  FIG. 2A ), such as abrasive slurry, onto the polishing surface  130 . Each polishing station  124  of the polishing system  100  can also include pad conditioning apparatus  132  to abrade the polishing surface  130  to maintain the polishing surface  130  in a consistent abrasive state. The platen  120  at each polishing station  124  is operable to rotate about a platen central axis  121 . For example, a motor  152  can turn a drive shaft  150  to rotate the platen  120 . Each carrier head  126  is operable to hold a substrate  10  against the polishing surface  130 . In operation, the platen  120  is rotated about the platen central axis  121 , which provides polishing to the substrate  10 . Each carrier head  126  can have independent control of some of the polishing parameters, for example pressure, associated with each respective substrate. In particular, each carrier head  126  can include a retaining ring  142  to retain the substrate  10  below a flexible membrane  144 . 
     Each carrier head assembly  119  is suspended from the track  128 . A connection axis  160  extends through the carrier motor  157  to the polishing surface  130 . The connection axis  160  is separated from the axis  127  of the drive shaft  153  by an extended distance  133 . Each carrier head assembly includes a carrier head  126  that is connected by a carrier head drive shaft  154 , through an offset coupler  155 , to a carrier head motor  156 . The carrier head  126  is coupled to the carriage  108  via a supporting structure  158 , which may include brackets and other mounting components. The axis  127 , which extends through the drive shaft  153  of the carrier head motor  156  and the carrier head axis  129  are separated by an offset distance  131  (alternately referred to as an offset). As shown in  FIG. 3B , the offset distance  131  allows the carrier head  126  to reach more of the surface area of the polishing surface  130 , without changing the geometry of the polishing station or of the platen  120  and polishing surface  130 . In one embodiment, the offset coupler  155  length is fixed, and thus the offset distance  131  is fixed. In one example, the offset distance  131  is set to a fixed distance of between about 1 mm and about 150 mm, such as between about 2 mm and about 50 mm. In one example, the offset distance  131  is between about 0.01% and about 25% of the diameter of a track  128  that is curved. In another example, the offset distance  131  is between about 0.1% and about 10% of the diameter of a track  128  that is curved. In one embodiment, the extended distance  133  and the offset distance  131  are the same, which allows the carrier head  126  to rotate directly under and be positioned directly under the circular track  128 . Defining the extended distance  133  so that it is substantial equal to the offset distance  131  will allow the carrier head to be statically positioned so that no apparent offset exists, which facilitates the loading and unloading from inboard load cups  123   a ,  123   b , and thus help to reduce the overall size of the polishing system  100 . 
     In one embodiment, each carrier head  126  can oscillate laterally (X-Y plane in  FIG. 1A ) during polishing, e.g., by driving the carriage  108  on the track  128 . The carrier head  126  is generally translated laterally across the top surface of the polishing surface  130  during polishing. The lateral sweep is in a direction parallel to the polishing surface  212  ( FIG. 2A ). The lateral sweep can be a linear or arcuate motion. Each of the above embodiments that allow for additional modes of oscillation or motion allows for even more relative motion between the polishing surface  130  and the substrate  10 , increasing the polishing rate on the substrate. 
       FIG. 2B  illustrates a side view of a polishing station  124  for processing one or more substrates, according to one embodiment. Although the polishing station  124  is similar to that as shown in  FIG. 2A , in this embodiment, a secondary motor  156   a  is included, which is attached between the offset coupler  155  and the carrier head  126 . The secondary motor  156   a  allows for an additional rotational motion about the carrier head axis  129  of the carrier head  126 . The additional rotation of the carrier head  126  about the carrier head axis  129  allows for even more relative motion between the polishing surface  130  and the substrate  10 , increasing the polishing rate on the substrate. In another embodiment, the platen  120  rotation and the carrier head  126  rotation is mismatched, which prevents repeatedly polishing a point in the substrate with the same portion of the pad at subsequent rotations of the platen. With a small mismatch, the point in the substrate will be polished at subsequent rotations by neighboring portions of the polishing surface  130 . 
     In some embodiments, each carrier head  126  also includes a plurality of independently controllable pressurizable chambers  146  defined by the membrane, e.g., three chambers  146   a - 146   c , which can apply independently controllable pressurizes to associated zones on the flexible membrane  144  and thus on the substrate  10 . Although only three chambers are illustrated in  FIG. 2A  for ease of illustration, there could be one or two chambers, or four or more chambers, e.g., five chambers. 
     Each polishing station  124  includes a polishing surface  130  supported on a platen  120 , according to one embodiment. The polishing surface  130  can be a two-layer polishing pad with an outer polishing layer  130   a  and a softer backing layer  130   b , according to one embodiment. In some embodiments, the polishing surface  130  comprises a sheet of polishing material. In one embodiment, the sheet is delivered by rollers attached to the sides of the polishing station  124 , and drawn taut. 
     In one embodiment, for a polishing operation, one carrier head  126  is positioned at each polishing station. Two additional carrier heads can be positioned in the loading station  122  to exchange polished substrates for unpolished substrates while the other substrates are being polished at the polishing stations  124 . 
     The carrier heads  126  are held by a support structure that can cause each carrier head to move along a path that passes, in order, the first polishing station  124   a , the second polishing station  124   b , the third polishing station  124   c , and the fourth polishing station  126   d . This permits each carrier head to be selectively positioned over the polishing stations  124  and the load cups  123 . In some embodiments, the support structure comprises a carriage  108  that is mounted to an overhead track  128 . By moving a carriage  108  along the overhead track  128 , the carrier head  126  can be positioned over a selected polishing station  124  or load cup  123 . A carrier head  126  that moves along the track  128  will traverse the path past each of the polishing stations. 
     In the embodiment depicted in  FIG. 1A , the overhead track  128  has a circular configuration which allows the carriages  108  retaining the carrier heads  126  to be selectively orbited over and/or clear of the loading stations  122  and the polishing stations  124 . The overhead track  128  may have other configurations including elliptical, oval, linear or other suitable orientation. 
     Alternatively, in some implementations the support structure comprises a carousel  135  with a plurality of carousel arms  138  and the supporting structure  158  attaches directly to a carousel arm  138 , so that rotation of the carousel moves all of the carrier heads simultaneously along a circular path ( FIG. 1B ). The carousel  135  allows uniform transfer of all the carrier heads  126  and associated substrates  10  simultaneously. In one embodiment, the carousel  135  can rotationally oscillate during polishing. The carrier head  126  is generally translated laterally across the top surface of the polishing surface  130  during polishing. The lateral sweep is in a direction parallel to the polishing surface  212  ( FIG. 2A ). The lateral sweep can be a linear or arcuate motion. Each of the above embodiments that allow for additional modes of oscillation or motion allows for even more relative motion between the polishing surface  130  and the substrate  10 , increasing the polishing rate on the substrate. 
       FIG. 3A  illustrates an overhead view of the polishing surface  130 , which comprises carrier head outline  126   o . The carrier head outline  126   o  shows the spatial extent of the carrier head  126  while being rotated by the carrier head motor  156  about axis  127 . The polishing surface outline  130   o  shows the spatial extent of the entire polishing surface  130 , with an ‘x’ indicating the center of the polishing surface  130   x  and rotational axis  121  ( FIG. 2A ) of the platen  120 . The overheard track outline  128   o  shows the path the carrier head  126  moves across the polishing surface  130 , with arrows indicating the motion of the carrier head along the overhead track  128 . In this embodiment, the offset distance  131  is zero, and the axis  127  and carrier head axis  129  lie on top of one another, and thus illustrates a conventional configuration that has no offset distance  131 . 
     In comparison,  FIG. 3B  shows a diagram of the carrier head outline  126   o  while being rotated by the carrier head motor  156  about axis  127  and the carrier head axis  129  is separated from the axis by an offset distance  131 . The polishing surface outline  130   o  shows the extent of the entire polishing surface  130 , with an ‘x’ indicating the center of the polishing surface  130   x  and rotational axis  121  ( FIG. 2A ) of the platen  120 . The overheard track outline  128   o  shows the path the carrier head  126  moves across the polishing surface  130 , with arrows indicating the motion of the carrier head along the overhead track  128 . In this embodiment, the offset distance  131  is nonzero; in other words, the axis  127  and the carrier head axis  129  no longer lie on top of one another. As the offset coupler  155   o  rotates around the axis  127 , the carrier head outline  126   o  also moves around the surface of the polishing surface  130 . Thus, with a nonzero offset distance  131 , the substrate  10  experiences a wider area of polishing (e.g., item  301 ), allowing it to be polished by more varied portions of the polishing surface  130 . Since polishing on the same portion of the polishing surface  130  degrades the surface of the polishing surface, repeated polishing on the same worn down portion leads to uneven polishing. Thus, allowing the substrate to be polished by larger and more varied portions of the polishing surface  130  leads to less surface degradation of the polishing surface, and thus a more uniform polish. In addition, a larger portion of the polishing surface  130  is activated, and this lower costs to the consumer, who gets more use out of each polishing surface  130 . 
       FIG. 3C  illustrates a diagram of the carrier head, when the carriage  108  is stationary on the track outline  1280 . A carrier head (CH) sweep angle A 1  is formed between a line from the center  101  ( FIG. 1A ) of the circular track  128  to the center of the polishing surface  130   x , and a line from the center of the circular track to the axis  127 . An offset angle A 2  is formed between a line that is normal to the tangent of the circular track  128   o  at the location of the axis  127 , and a line that extends from the axis  127  and the carrier head axis  129 . The offset angle A 2  will vary between 0° and 360° as the carrier head motor  156  makes one revolution about the axis  127 . One will note that a 0° angle of the offset angle A 2  is defined as a point where the axis  129  is coincident with a line NL ( FIG. 3C ), which is normal to the tangent line of the arc of the track  128  at the carriage  108 &#39;s current position. The extent of the carrier head sweep angle A 1 , which typically varies in a system due to substrate size, the size of the track  128 , and size of platen  120 , is set so that the substrate  10  disposed in the carrier head  126  does not extend past the polishing surface outline  130   o  during a polishing process, and thus can vary, for example, between +/−5°. The carrier head axis  129  will only intermittently be collinear with the platen central axis  121  during the polishing process, depending on the location of the carrier head  126  along the circular track  128 , the offset distance  131 , and the CH sweep angle A 1 . If the offset distance  131  is shorter than the shortest distance between the circular track  128  and the center of the polishing surface  130   x , then the carrier head axis  129  will never be collinear with the platen central axis  121  during the polishing process. 
       FIG. 3D  illustrates a diagram of the carrier head, when the carriage  108  is stationary on the track outline  128   o , showing the outline of the substrate with different head-sweep offsets  131 ,  131 ′,  131 ″. The axis  127  is fixed on the circular track  128   o , but the different length of the offsets  131 ,  131 ′,  131 ″ results in a shifted carrier head axis  129 . The position of the carrier head  126   o  on the surface of the polishing surface  130  also varies with the length of the offset  131 ,  131 ′,  131 ″. 
     The carrier head sweep angle A 1  may be restricted, such that no portion of the substrate  10  is displaced over the edge of the polishing surface  130 , since this processing position can cause process variability and a reduced radial polishing uniformity. The maximum carrier head sweep angle is 2θ L , wherein θ L  may be calculated by 
               θ   L     =       cos     -   1       ⁡     (         d   center   2     +       (     r     o   -   sw       )     2     -       (       r   platen     -     r   ring     -   d     )     2         2   ⁢           ⁢       d   center     ⁡     (     r     o   -   sw       )           )             
where d center  is the distance from the center  101  of the circular track  128  to the center  130   x  of the polishing surface  130 , r o-sw  is the distance from the center  101  of the circular track to the axis  127 , d is equal to the offset distance  131 , r platen  is the radius of the polishing surface  130 , and r ring  is the radius of the retaining ring  142 .
 
       FIG. 4A  illustrates a plot  400  of the tangential normalized friction force T versus the offset angle A 2  in degrees, where the carrier head (CH) sweep angle A 1  is zero degrees, and thus axis  127  is on a line formed between the center of the polishing surface  130   x  and the center  101  of the circular track  128 . The normalized friction force F is given by F=μN, where μ is a kinetic friction coefficient that varies between 0 and 1, and N is the normal force caused by the independently controllable pressurizable chambers  146  in the carrier head  126  that urge the substrate  10  against a polishing surface  130  disposed on the polishing surface  130 . The tangential friction force T is given by T=|F cos(A 2 )|, and thus is a measure of the friction induced load that has to be compensated for by the carrier motor  157  ( FIGS. 2A-2B ) to keep the carrier head  126  in the same position on the track  128  at any instant in time at the offset angle A 2 . When the offset angle A 2  is 0 or 180°, the tangential normalized friction force T is the same as with no offset distance  131 , and the entirety of the normalized friction force is in the direction parallel to a tangent of the arc of the track  128  at that position. However, at any other angle A 2 , the tangential normalized friction force T is reduced. 
     In  FIG. 4A , the tangential normalized friction force T curve  410  for a 25 mm offset is plotted, the normalized friction force curve  420  for a 30 mm offset is plotted, the normalized friction force curve  430  for a 35 mm offset is plotted, and the normalized friction force curve  440  for a 40 mm offset is plotted. The average normalized friction force for a 25 mm offset is on average 96% of the zero offset case, the average normalized friction force for a 30 mm offset is on average 93% of the zero offset case, the average normalized friction force for a 35 mm offset is on average 89% of the zero offset case, and the average normalized friction force for a 40 mm offset is on average 81% of the zero offset case. As discussed above, the frictional force on the carrier head  126  requires a corresponding opposite but equal force on the carrier motor  157  to prevent it from sliding along the track  128 , which puts extra wear and tear on the carrier motor. Reducing the force needed from the carrier motor  157  allows for less wear and tear on the carrier motor during operation. Alternatively, a less powerful carrier motor  157  can be used, as the carrier motor needs to produce less force to overcome the frictional force. 
       FIG. 4B  illustrates a plot  450  of the tangential normalized friction force T versus the offset angle A 2  in degrees, where the carrier head (CH) sweep angle A 1  is two degrees. As shown in  FIG. 4B , the normalized friction force curve  460  for the tangential normalized friction force T at a 25 mm offset is plotted, the normalized friction force curve  470  for a 30 mm offset is plotted, the normalized friction force curve  480  for a 35 mm offset is plotted, and the normalized friction force curve  490  for a 40 mm offset is plotted. The average normalized friction force for a 25 mm offset is on average 88% of the zero offset case, the average normalized friction force for a 30 mm offset is on average 84% of the zero offset case, the average normalized friction force for a 35 mm offset is on average 80% of the zero offset case, and the average normalized friction force for a 40 mm offset is on average 74% of the zero offset case. In all the above cases, at worst the tangential normalized friction force T is the same as the tangential normalized friction force without the offset distance  131 , and in almost all cases, the tangential normalized friction force is reduced compared to the case without the offset distance  131 . Thus, the increase in the offset distance  131  decreases the average tangential normalized friction force, which causes less wear and tear on the carrier head motor  156  and reduces the average system power usage. Additionally, a less powerful carrier head motor  156  can also be used to obtain the same normalized force, which allows use of a smaller motor that allows more room for other elements within the polishing system  100  and also reduces the piece part cost and cost to run the system. 
     The offset distance  131  also allows a shifted carrier head  126  to cover more surface area of the polishing surface  130 . The offset distance  131  effectively provides an additional rotation of the carrier head  126  about the axis  140 , which allows for a greater area traversed on the polishing surface  130 . 
     The shifted carrier head  126  improves polishing uniformity, increases used proportion of the polishing surface  130 , decreases the normalized friction force seen by the carrier motor  157 , and causes less wear and tear on the carrier motor  157 . The shifted carrier head  126  also allows for a less powerful, and thus smaller and less expensive, carrier motor  157  to achieve the same friction force as a traditional motor with no offset. As the polishing system  100  size is often fixed due to other constraints in the CMP process, the shifted carrier head  126  allows for improvements to the polishing uniformity and reduced normalized friction force, without a complete redesign of the system. 
     While the foregoing is directed to embodiments of the present disclosure, other and further embodiments of the disclosure may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.