Retainer ring and method for polishing a workpiece

Abstract

A chemical mechanical polishing (CMP) machine (20) includes a workpiece carrier assembly (22) having a carrier base (24) with a workpiece contacting side (26) for holding a first surface (30) of a workpiece (32). A method utilizing the CMP machine (20) to polish the workpiece (32) and achieve a minimal edge exclusion region (92) entails adapting the carrier base (24) to reduce a first diameter (53) of a workpiece contacting side (26) of the carrier base (24) to a second diameter (84). The method further calls for providing a retainer ring (68, 106) disposed concentrically on the carrier base (24) for retaining the workpiece (32), and applying pressure on the carrier base (24) to urge a second surface (34) of the workpiece (36) against a polishing pad (36) of the CMP machine (20). In a first embodiment, the retainer ring (68) includes a body portion (70) and a holding lip (78) protruding radially inward from an inner periphery (80) of the body portion (70) and overlying an outer edge of the workpiece (32) to reduce the first diameter (53) of the workpiece contacting side (26) to the second diameter (84). In an alternative embodiment, the carrier base (24) is modified to reduce the first diameter (53) of the workpiece contacting side to the second diameter (84). Correspondingly, a width of the retainer ring 106 is defined to include a value substantially equivalent to one half of the difference between the first diameter (53) and the second diameter (84).

Description

TECHNICAL FIELD OF THE INVENTION

[0001] The present invention relates to the field of chemical mechanical polishing machines. More specifically, the present invention relates to a method and apparatus for polishing a semiconductor wafer to obtain a minimal edge exclusion.

BACKGROUND OF THE INVENTION

[0002] The production of integrated circuits begins with the creation of high quality semiconductor wafers. The semiconductor wafers are typically polished prior to integrated circuit fabrication so that a flat surface is available upon which the circuit fabrication can take place. Additionally, during the integrated circuit fabrication process, layers of, for example, conductors and dielectrics, are built up on the wafer, on top of which other such layers are to be created. Thus, it is typically necessary to “re-flatten” the wafer surface during the actual fabrication of the integrated circuit and not merely before it. The act of re-flattening is referred to as planarization.

[0003] Chemical mechanical polishing (CMP) is a process for improving the surface planarity of a semiconductor wafer and involves the use of mechanical pad polishing systems usually with a silica-based slurry. CMP generally includes attaching one side of the wafer to a flat surface of a wafer carrier or chuck and pressing the wafer against a flat polishing surface. The polishing surface is moved under the wafer, and the wafer may also be rotated about its vertical axis and oscillated back and forth to improve polishing action. The polishing surface is generally a pad attached to a rigid flat table which is rotated to provide movement and onto which an abrasive and/or chemical slurry is pumped. The joint functions of the pad, the slurry, and the relative movements of the components produce a combined chemical and mechanical process at the wafer surface which produces a highly flat surface on a wafer where surface variations are kept to less than, for example, 0.5 &mgr;m.

[0004] However, prior art CMP systems for planarizing semiconductor wafers have a limitation related to polishing uniformity known as “edge exclusion.” Edge exclusion occurs when too much of the exposed surface of the semiconductor wafer surface is polished. This causes the edge or outer portion of the wafer to be unusable for integrated circuit fabrication. Thus, the larger the edge exclusion on the semiconductor wafer, the lower the number of integrated circuits that a fabrication facility can produce per wafer. For example, prior art CMP systems typically produce an edge exclusion of approximately six millimeters wide on an eight inch (i.e., 203.2 mm) diameter wafer. This six millimeter edge exclusion represents an approximate eleven and a half percent reduction of surface area of a wafer that may be used for integrated circuit fabrication.

[0005] Given semiconductor processing costs, it is quite possible that a single eight inch partially processed wafer is worth $10,000 or more in United States currency when planarization is performed. Accordingly, the high cost of complex semiconductor wafers combined with a highly competitive market has driven the need for a reduction in the size of the edge exclusion in order to maximize the number of integrated circuits that may be fabricated on a single wafer.

[0006] In an attempt to respond to this need, original equipment manufacturers (OEMs) are manufacturing CMP systems that now yield an edge exclusion of approximately three millimeters. Thus, on an eight inch wafer, this represents nearly a six and a half percent increase in useable surface area over wafers polished using CMP systems producing a six millimeter edge extension. These newly designed CMP systems may cost in the range of two to three million dollars. For those fabrication facilities that have significant capital to invest, the purchase of a new CMP system may be acceptable. However, for those fabrication facilities in which financial resources may not be so readily available or for those that already own a CMP system, the investment of a new CMP system may be quite objectionable.

[0007] Other OEMs and second source manufacturers have attempted to retrofit existing CMP systems in order to yield the desired three millimeter edge exclusion. Such retrofits involve software and hardware configuration changes that involve the replacement of, for example, the wafer carrier assembly of a CMP system, the inclusion of a variable pressurized retaining ring and corresponding software processes, redesigned polishing pads, and so forth. Such aftermarket parts are typically not part of an OEM's core business. Hence, this creates problems for the OEMs in terms of investment of time and effort in engineering and producing these aftermarket products. Moreover, the development cost of new components and software is typically passed to the consumer, i.e., the fabrication facilities that purchase the retrofit components for their existing CMP systems. While this investment may not be as great as purchasing a new CMP system, these modifications to existing equipment can still cost in the range of fifteen to seventy thousand dollars when installed. Again, such costs may be objectionable to some fabrication facilities.

SUMMARY OF THE INVENTION

[0008] Accordingly, it is an advantage of the present invention that an improved retainer ring for a wafer carrier assembly and a method for polishing a workpiece utilizing an existing polishing machine are provided.

[0009] It is another advantage of the present invention that it limits edge exclusion compared to that which occurs on a semiconductor wafer polished by known processes.

[0010] Yet another advantage of the present invention is that it forms a simple modification to existing wafer carrier assemblies and through the modification improves the CMP process for semiconductor wafers.

[0011] The above and other advantages of the present invention are carried out in one form by a retainer ring for retaining a workpiece within a workpiece carrier assembly of a polishing machine. The workpiece carrier assembly includes a carrier base for holding a first surface of the workpiece and for abutting a second surface, opposite the first surface, of the workpiece against a polishing pad of the polishing machine. The retainer ring comprises a body portion configured to be disposed concentrically on an outer periphery of the carrier base and a holding lip for retaining the workpiece, the holding lip protruding radially inward from an inner periphery of the body portion.

[0012] The above and other advantages of the present invention are carried out in another form by a method for utilizing a polishing machine to polish a workpiece having a minimal edge exclusion region. The polishing machine includes a workpiece carrier assembly having a carrier base with a workpiece contacting side for holding a first surface of the workpiece. The workpiece contacting side of the carrier base exhibits a first diameter. The method calls for adapting the carrier base to reduce the first diameter of the workpiece contacting side to a second diameter and providing a retainer ring disposed concentrically on an outer periphery of the carrier base for retaining the workpiece when the workpiece is held by the carrier base. The method further calls for applying pressure on an upper side, opposite from the workpiece contacting side, of the carrier base to urge a second surface of the workpiece into sliding engagement with a polishing pad of the polishing machine.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] A more complete understanding of the present invention may be derived by referring to the detailed description and claims when considered in connection with the Figures, wherein like reference numbers refer to similar items throughout the Figures, and:

[0014] FIG. 1 shows a partial block diagram of a chemical mechanical polishing (CMP) machine that may use the preferred embodiment of the present invention;

[0015] FIG. 2 shows a bottom view of a semiconductor wafer surrounded by an existing retainer ring attached to a carrier base of the CMP machine of FIG. 1;

[0016] FIG. 3 shows a perspective view of a retainer ring in accordance with a preferred embodiment of the present invention;

[0017] FIG. 4 shows a cross-sectional side view of a workpiece carrier assembly of the CMP machine of FIG. 1 with the retainer ring of FIG. 3;

[0018] FIG. 5 shows a semiconductor wafer polished in accordance with a preferred embodiment of the present invention; and

[0019] FIG. 6 shows a cross-sectional side view of a workpiece carrier assembly of the CMP machine of FIG. 1 with a carrier base and a retainer ring in accordance with an alternative embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] FIG. 1 shows a partial block diagram of a chemical mechanical polishing (CMP) machine 20 that may use the preferred embodiment of the present invention. CMP machine 20 generally includes a workpiece carrier assembly 22 having a carrier base 24 with a workpiece contacting side 26 and an upper side 28, opposite from workpiece contacting side 26. Workpiece contacting side 26 is configured to hold a first surface 30 of a workpiece, or semiconductor wafer 32. Workpiece carrier assembly 22 picks up semiconductor wafer 32 by a vacuum force and places a second surface 34, opposite first surface 30, of wafer 32 in contact with a polishing pad 36 supported by a platen 38. Slurry 40 is applied to polishing pad 36.

[0021] Pressure, as represented by an arrow 42, is applied on upper side 28 of carrier base 24 so that semiconductor wafer 32 contacts polishing pad 36. Rotation of carrier assembly 22, as represented by a second arrow 43, urges second surface 34 of semiconductor wafer 32 in sliding engagement with polishing pad 36 so that semiconductor wafer 32 is conditioned in the CMP process.

[0022] CMP machine 20 represents a conventional chemical mechanical polishing system. Hence, those skilled in the art will recognize that CMP machine 20 may include features such as a user interface, input and output elements for supplying and receiving semiconductor wafers, multiple workpiece carrier assemblies, necessary cabinets and access panels for the mechanical and electrical components within machine 20, and so forth (not shown) and will not be discussed in detail herein. Software programs resident in computer memory of CMP machine 20 function to control the downward pressure on semiconductor wafer 32, the rotational speed of carrier assembly 22, the application of slurry 40 on polishing pad 36, and so forth.

[0023] In addition, CMP machine 20 is shown using rotary motion to rotate semiconductor wafer 32 relative to polishing pad 36 for clarity of illustration. However, it should be understood to those skilled in the art that CMP machine 20 may use a combination of rotational and orbital motion, or rotational and linear motion. That is, carrier assembly 22 may rotate in a circular path, while polishing pad 36 rotates in an orbital path. Alternatively, carrier assembly 22 may rotate in a circular path, while polishing pad 36 moves in a linear path.

[0024] FIG. 2 shows a bottom view of semiconductor wafer 32 surrounded by an existing retainer ring 44 attached to carrier base 24 of CMP machine 20 of FIG. 1. Retainer ring 44 was not shown in FIG. 1 so that semiconductor wafer 32 would be viewable between carrier base 24 and polishing pad 36. However, CMP machine 20 typically includes retainer ring 44 which functions to retain wafer 32 within a pocket of workpiece carrier assembly 22 (FIG. 1) formed by workpiece contacting side 26 and an inner periphery 48 of retainer ring 44.

[0025] FIG. 2 further shows semiconductor wafer 32 having an edge exclusion region 50 about a perimeter 52 of wafer 32 that forms in the conventional CMP process. Wafer 32 floats within the pocket formed by workpiece contacting side 26 and inner periphery 48 of retainer ring 44. Workpiece contacting side 26 exhibits a first diameter 53, defined by inner periphery 48, that is greater than a diameter 55 of wafer 32. Accordingly, when pressure 42 (FIG. 1) is applied on upper side 28 (FIG. 1) of carrier base 24 (FIG. 1) so that wafer 32 contacts polishing pad 36 (FIG. 1), polishing pad 36 may be forced into a gap 54 between inner periphery 48 of retainer ring 44 and perimeter 52 of wafer 32. Consequently, excessive polishing of semiconductor wafer 32 occurs about perimeter 52 to form edge exclusion region 50.

[0026] Edge exclusion region 50 is defined by a width 57. Width 57 of edge exclusion region 50 significantly affects the ability to include integrated circuits on semiconductor wafer 32. For example, an integrated circuit pattern 56 is formed on second surface 34 of semiconductor wafer 32. As can be seen, in integrated circuit pattern 56, integrated circuits 58, 60, 62 and 64 cannot be used because they fall, at least in part, within edge exclusion region 50. Thus, edge exclusion region 50 forms an area on second surface 34 of wafer 32 which excludes the acceptable fabrication of integrated circuits. Width 57 of edge exclusion region 50 typically ranges from 5 to 7 mm.

[0027] The present invention limits width 57 of edge exclusion region 50 when polishing wafer 32 utilizing CMP machine 20 compared to that which occurs on a semiconductor wafer polished by known processes. In particular, width 57 of edge exclusion region 50 is decreased from 5 to 7 mm on an eight inch (i.e. 203.2 mm) diameter wafer to approximately 3 mm. Width 57 of edge exclusion region 50 is decreased by adapting carrier base 24 to reduce first diameter 53 of workpiece contacting side 24, thus decreasing gap 54 and allowing less space in which wafer 32 may float and in which polishing pad 36 may be forced.

[0028] Referring to FIGS. 3 and 4, FIG. 3 shows a perspective view of a retainer ring 68 in accordance with a preferred embodiment of the present invention. FIG. 4 shows a cross-sectional side view of workpiece carrier assembly 22 of CMP machine 20 (FIG. 1) with retainer ring 68. Retainer ring 68 is provided to replace existing retainer ring 44 (FIG. 2) of workpiece carrier assembly 22 and functions to retain wafer 32 within workpiece carrier assembly 22 of CMP machine 20 (FIG. 1).

[0029] Retainer ring 68 includes a body portion 70 configured to be disposed concentrically on an outer periphery 72 of carrier base 24 of workpiece carrier assembly 22. Body portion 70 includes threaded holes 74, and bolts 76 couple retainer ring 68 to carrier base 24.

[0030] Retainer ring 68 further includes a holding lip 78 protruding radially inward from an inner periphery 80 of body portion 70. A width 79 of holding lip 78 is shown greatly exaggerated in FIG. 4 for clarity of illustration. However, retainer ring 68 is manufactured such that width 79 of holding lip 78 is in a range of 0.005 to 0.012 inches (0.127 to 0.3048 mm). For example, for a CMP machine, such as CMP machine 20, configured to polish semiconductor wafer 32 having diameter 55 (FIG. 2) of eight inches (203.2 mm), holding lip 78 may protrude radially inward substantially 0.010 inches (0.254 mm) from inner periphery 80.

[0031] When retainer ring 68 is coupled to carrier base 24, retainer ring 68 is positioned such that holding lip 78 overlies an outer edge 82 of workpiece contacting side 26 of carrier base 24 to reduce first diameter 53 of workpiece contacting side 26 to a second diameter 84. By way of example when width 79 of holding lip 78 is substantially 0.010 inches, second diameter 84 is reduced substantially 0.020 inches from first diameter 53. Thus, when wafer 32 is held in workpiece carrier assembly 22, holding lip 78 approaches perimeter 52 of wafer 32 and a gap 86 formed between wafer 32 and inner periphery 80 of body portion 70 is minimized.

[0032] Holding lip 78 exhibits a height 88 configured to accommodate the thickness of wafer 32. Thus, like retainer ring 44, retainer ring 68 functions to retain wafer 32 within a pocket 90 of workpiece carrier assembly 22 formed by workpiece contacting side 26 and holding lip 78 of retainer ring 68 when wafer 32 is held by carrier base 24.

[0033] In a preferred embodiment, retainer ring 68 is readily machined from polyphenyl sulfide (PPS). PPS may be unmodified or modified with modifiers such as Teflon® PTFE (Polytetrafluoroethylene), MoS (Molybdenum disulfide), graphite, and so forth. PPS is rigid, hard, and resistant to corrosion. Alternatively, retainer ring 68 may be fabricated from Delrin® also characterized by strength, stiffness, hardness, and solvent and fuel resistance. Retainer ring 68 is precision machined to achieve tolerances of +/− one micron for holding lip 78.

[0034] FIG. 5 shows semiconductor wafer 32 polished in accordance with a preferred embodiment of the present invention and having an edge exclusion region 92. It has been discovered that the replacement of existing retainer ring 44 (FIG. 2) with retainer ring 68 in workpiece carrier assembly 22 results in edge exclusion region 92 having a width 93 of approximately 3 mm being formed on wafer 32 during the chemical mechanical polishing process utilizing CMP machine 20. Edge exclusion region 92 with width 93 of 3 mm represents a minimal edge exclusion currently achievable on newly designed CMP machines and CMP machines with redesigned workpiece carrier assemblies.

[0035] Width 93 of edge exclusion region 92 represents nearly a fifty percent reduction of edge exclusion region 92 over edge exclusion region 50 (FIG. 2) formed during a conventional CMP process using retainer ring 44 (FIG. 2). This reduction of the edge exclusion nets an approximate 6.4% increase in usable surface area of semiconductor wafer 32 over edge exclusion region 50. As such, an integrated circuit pattern 94, having the same surface area as integrated circuit pattern 56 of FIG. 2, includes integrated circuits 96, 98, 100, and 102. By minimizing edge exclusion region 92 on semiconductor wafer 32, the yield of integrated circuits from wafer 32 increases.

[0036] Moreover, the replacement of retainer ring 44 with retainer ring 68 on workpiece carrier assembly 22 is far less costly than replacement of the entire workpiece carrier assembly on an existing CMP machine, or purchase of an entirely new CMP machine. For example, through its simple manufacture and retrofit onto the existing carrier base 24 (FIG. 3), retainer ring 68 results in significant savings for the consumer in terms of time and effort in testing and qualifying replacement carrier assemblies or purchasing a replacement CMP machine. Thus, retainer ring 68 may be one to three hundredths of the cost of a replacement carrier assembly or one thousandth of the cost of a replacement CMP machine.

[0037] FIG. 6 shows a cross-sectional side view of workpiece carrier assembly 22 of the CMP machine of FIG. 1 with a carrier base 104 and a retainer ring 106 in accordance with an alternative embodiment of the present invention. Carrier base 104 may be a replacement unit for carrier base 24 (FIG. 4). As such, carrier base 104 and retainer ring 106 may form a retrofit kit that may be used to upgrade an existing CMP machine to polish wafers to achieve edge exclusion region 92 with width 93 (FIG. 5) of 3 mm rather than edge exclusion region 50 (FIG. 2) with width 57 (FIG. 2) of 6 mm. Alternatively, carrier base 104 may be adapted from carrier base 24 by precision machining the existing carrier base 24. In either case, carrier base 104 has a workpiece contacting side 108 exhibiting second diameter 84 that is reduced from first diameter 53 (FIG. 2) by a value in a range of 0.010 to 0.024 inches (0.254 to 0.6096 mm).

[0038] Retainer ring 106 is provided to replace retainer ring 44 (FIG. 2). That is, retainer ring 106 is disposed concentrically on an outer periphery 112 of carrier base 104 and serves to retain semiconductor wafer 32 when wafer 32 is held by carrier base 104. A width 114 of retainer ring 106 is defined to include a value substantially equivalent to a one half of a difference between first diameter 53 and second diameter 84. By way of example, when second diameter 84 is reduced from diameter 53 by a total of 0.020 inches, width 114 is a sum of a width (not shown) of retainer ring 44 and 0.010 inches.

[0039] The reduction of second diameter 84 from first diameter 53, and the corresponding increase of width 114 of retainer ring 106 relative to retainer ring 44, achieves a decrease in a gap 116 between retainer ring 106 and perimeter 52 of wafer 32 relative to gap 54 (FIG. 2). As such, edge exclusion region 92 (FIG. 5) with width 93 of 3 mm is produced.

[0040] The replacement of carrier base 24 with carrier base 104, or alternatively, adaptation of carrier base 24 to produce carrier base 104, and the replacement of retainer ring 44 with retainer ring 106, achieves significant cost savings over the replacement of workpiece carrier assembly 22 or the replacement of CMP machine 20.

[0041] In summary, the present invention teaches of an improved retainer ring for a wafer carrier assembly and a method for polishing a workpiece using an existing chemical mechanical polishing machine. By decreasing the amount of gap between the perimeter of a semiconductor wafer and a retainer ring, when the wafer is positioned in a carrier base of a workpiece carrier, the edge exclusion region is reduced by nearly fifty percent over that which occurs on a semiconductor wafer polished by previously known chemical mechanical polishing processes. In addition, the retainer ring and the adaptation of the carrier base to reduce the diameter of the workpiece contacting side of the carrier base form a simple and cost effective modification to existing wafer carrier assemblies and through the modification improves the CMP process for semiconductor wafers.

[0042] Although the preferred embodiments of the invention have been illustrated and described in detail, it will be readily apparent to those skilled in the art that various modifications may be made therein without departing from the spirit of the invention or from the scope of the appended claims. For example, the teachings of the present invention may be adapted to successfully achieve minimal edge exclusion regions on workpieces of different diameters and manufactured from a variety of materials. In addition, the teachings of the present invention art not limited to existing CMP machines but may be adapted for use with new CMP machines to achieve minimal edge exclusion regions on workpieces.

Claims

1. A retainer ring for retaining a workpiece within a workpiece carrier assembly of a polishing machine, said workpiece carrier assembly including a carrier base for holding a first surface of said workpiece and for abutting a second surface, opposite said first surface, of said workpiece against a polishing pad of said polishing machine, said retainer ring comprising:

a body portion configured to be disposed concentrically on an outer periphery of said carrier base; and

a holding lip for retaining said workpiece, said holding lip protruding radially inward from an inner periphery of said body portion.

2. A retainer ring as claimed in claim 1 wherein said body portion is configured to be coupled to said carrier base.

3. A retainer ring as claimed in claim 1 wherein when said workpiece is held in said carrier base, said holding lip is configured to approach a perimeter of said workpiece to minimize a gap between said holding lip and said perimeter.

4. A retainer ring as claimed in claim 1 wherein said holding lip exhibits a width, said width protruding radially inward, and said width being in a range of 0.005 and 0.012 inches.

5. A retainer ring as claimed in claim 4 wherein said width of said holding lip is substantially 0.010 inches.

6. A retainer ring as claimed in claim 1 wherein said carrier base includes a workpiece contacting side having a first diameter, and said holding lip is configured to overlie an outer edge of said workpiece contacting side of said carrier base to reduce said first diameter of said workpiece contacting side to a second diameter.

7. A retainer ring as claimed in claim 1 wherein said holding lip exhibits a height configured to accommodate a thickness of said workpiece.

8. A retainer ring as claimed in claim 1 wherein said retainer ring is adapted to replace an existing retainer ring of said workpiece carrier assembly.

9. A method for utilizing a polishing machine to polish a workpiece to achieve a minimal edge exclusion region, said polishing machine including a workpiece carrier assembly having a carrier base with a workpiece contacting side for holding a first surface of said workpiece, said workpiece contacting side exhibiting a first diameter, and said method comprising:

adapting said carrier base to reduce said first diameter of said workpiece contacting side to a second diameter;

providing a retainer ring disposed concentrically on an outer periphery of said carrier base for retaining said workpiece when said workpiece is held by said carrier base; and

applying pressure on an upper side, opposite from said workpiece contacting side, of said carrier base to urge a second surface of said workpiece into sliding engagement with a polishing pad of said polishing machine.

10. A method as claimed in claim 9 wherein said carrier base is an existing carrier base exhibiting said first diameter, and said adapting operation includes modifying said existing carrier base to reduce said first diameter of said workpiece contacting side to obtain said second diameter.

11. A method as claimed in claim 10 wherein said providing operation comprises defining a width of said retainer ring to include a value substantially equivalent to one half of a difference between said first diameter and said second diameter.

12. A method as claimed in claim 11 wherein said value is in a range of 0.005 to 0.012 inches.

13. A method as claimed in claim 9 wherein said carrier base is an existing carrier base exhibiting said first diameter, and said providing operation includes:

producing said retainer ring having a body portion and a holding lip protruding radially inward from an inner periphery of said body portion, said body portion being configured to be disposed concentrically on said outer periphery of said carrier base; and

positioning said retaining ring such that said holding lip overlies an outer edge of said workpiece contacting side of said carrier base to reduce said first diameter of said workpiece contacting side to obtain said second diameter.

14. A method as claimed in claim 13 wherein said producing operation includes establishing a width of said holding lip to be substantially equivalent to one half of a difference between said first diameter and said second diameter.

15. A method as claimed in claim 14 wherein said width of said holding lip is in a range of 0.005 to 0.012 inches.

16. A workpiece carrier assembly retrofit kit for adapting a workpiece carrier assembly of a polishing machine to polish a workpiece having a minimal edge exclusion region, said workpiece carrier assembly including an existing carrier base and an existing retainer ring coupled to said existing carrier base, said existing carrier base having a workpiece contacting side exhibiting a first diameter, said existing retainer ring exhibiting a first width, and said kit comprising:

a carrier base configured to replace said existing carrier base, said carrier base having a workpiece contacting side exhibiting a second diameter, said second diameter being less than said first diameter of said existing carrier base; and

a retaining ring configured to couple to said carrier base, said retaining ring exhibiting a second width, said second width being substantially equivalent to a sum of said first width and a value substantially equivalent to one half of a difference between said first diameter and said second diameter.