Design of a Precision Chemical Mechanical Planarization Research
System
By
Fardad All Hashemi
B.S., Mechanical Engineering
University of California at Berkeley, 1998
SUBMITTED TO THE DEPATMENT OF MECHANICAL ENGINEERING IN
PARTIAL FULFILMENT OF THE REQUIREMETS FOR THE DEGREE OF
MASTERS OF SCIENCE IN MECHANICAL ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUNE, 2000
©2000 Massachusetts Institute of Technology
All rights reserved.
Signature of Author:
.1 - '- . --1 -
Department of Mechaini'cal Engi-neering
9 May, 2000
Certified by:
esto E. Blanco
Professor of Mechanical Engineering
_mb jgsis Supervisor
Accepted by:
A.ooni
AmM
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
SE P 2 0 2000
LIBRARIES
Professor of Mechanical Engineering
Chairman, Committee for Graduate Students
ENG
Design of a Precision Chemical Mechanical Planarization Research
System
By
Fardad Ali Hashemi
Submitted to the Department of Mechanical Engineering
9 May, 2000, in Partial Fulfillment of the degree of
Master of Science in Mechanical Engineering
ABSTRACT
The main focus of this study was to design the platen spindle, supporting machine
structure, and a novel gimbal mechanism for use in a precision CMP system. Principles
of kinematic coupling and precision machine design were used to insure easy and precise
assembly of the machine. Many design types were studied to achieve compact yet
practical final designs. Stresses arising from the deformations of the machine due to
changes in temperature were evaluated and resolved via type synthesis. Three novel
designs for a gimbal mechanism with an offset center of rotation were proposed and
evaluated.
Thesis Supervisor: Ernesto E. Blanco
Title: Professor of Mechanical Engineering
In memory of Morteza Hashemi
September, 1908 to April, 2000
Reflection
It seems only appropriate, to take some time to reflect on this stage of my life
before finishing off the completing piece. I came here two years ago, with hope and
expectations regarding the important new path that I was about to embark on. In most
ways, right from the beginning MIT surpassed those expectations beyond anything that I
could have imagined. In others, it has taken a concentrated and often challenging effort to
shape my path towards what I hoped at the onset. In both ways, this has been a most
valuable learning experience.
A very important part of this experience has been the people that I have been in
contact with. Perhaps, the most important of those people is my advisor Prof. Ernesto
Blanco. I met him at the end of my first semester and ever since then I have enjoyed the
benefit of his advice in both engineering and life matters. I could not have completed this
thesis without him. He has been a mentor to me in the truest sense of the word. I shall
forever be grateful.
It would be far from a complete reflection, if I did not reflect on the influence that
my friends Amir, Jamie, and Farid have had on my experience here at MIT. Amir and
Jamie made my time in the lab so much more interesting. I have never met anyone as
well intentioned and kind hearted as Jamie. He is a person of true character. I was once
told that if you work hard you must party even harder on your spare time to keep you
sanity. I have a feeling Amir and Farid must be very, very hard working people. I would
like to furthermore thank Farid for our detailed discussions regarding dynamics and
kinematics on the steps of the student union. I admire his passion and detailed
understanding of the science of engineering.
The recent passing away of my grandfather has also made me reflect deeply on
the role that he has had in helping me get to this stage. I guess the path did not begin two
years ago or when I was born but long before then. It has been a cumulative process that
began long time ago. I firmly believe that each generation endeavors to build a
foundation for the next generations to continue to build upon. Their accomplishments and
sacrifices are the bricks that make up this foundation. The more I grow the more I realize
how much the success of each new generation depends on the foundation that has been
laid beneath them. In that sense I am most lucky. I could never possibly thank my parents
enough for the sacrifices that they made so that my brother and I could have a better
education.
In fact, as I sit here at brink of a new dawn, both figuratively and literally, seeking
to finish laying this very important brick in my layer, I can only hope to be so lucky as to
lay a layer as thick and as solid as the two that I stand upon. To my parents and my
brother I am eternally grateful for their teaching and continuing support. Their influence
on me is the inner silent voice that guides me even when they are not there. I couldn't
have done it without you.
ACHNOWLEDGEMENTS
I would like to take this opportunity to acknowledge and thank Silicon Valley
Group for their help and support, which funded the primary stage of this research. In
addition, to their financial support, their advice and comments at the review meetings
were very critical in guiding me in the right direction. In particular, I would like to thank
Mr. Jim Kenon whose insight helped me reduce the height of platen assembly by almost
half.
I would also like to take the opportunity to thank Prof. Chun and Prof. Suh for
giving me the benefit of their advice. I am very grateful for their understanding and
patience during difficult times in this project.
Most of all I would like to thank Prof. Ernesto Blanco who is my immediate
advisor for his advice in engineering and life matters. I have learned a lot from him and
feel very privileged to have had him as my advisor. I admire his dedication to teaching
and the integrity and engineering insight with which he carries out the task.
Table of Contents
1
INTRODUCTION........................................................................................................................14
2
DESIGN GOALS.........................................................................................................................15
3
CHOOSING POLISH CONFIGURATION.............................................................................16
3.1
C MP C ONFIGURATIONS ...........................................................................................................
16
3.2
ADVANTAGES AND DISADVANTAGES OF EACH CONFIGURATION ...............................................
20
3.3
REASONS FOR CHOOSING THE ROTARY CONFIGURATION .........................................................
24
4
TWO PLATEN MACHINE.........................................................................................................24
5
MACHINE CONFIGURATION..............................................................................................26
5.1
CONCEPTUAL DESIGNS FOR Two PLATEN MACHINE CONFIGURATION.......................................26
5.2
WAFER AND PLATEN CENTER TO CENTER OFFSET DISTANCE...................................................34
MACHINE LOWER STRUCTURE .......................................................................................
6
6.1
CONCEPTUAL DESIGNS FOR MACHINE LOWER STRUCTURE......................................................38
6.2
CHOOSING A CONCEPT FOR THE LOWER STRUCTURE ................................................................
38
46
DETAILED DESIGN OF THE MACHINE LOWER STRUCTURE....................................48
7
7.1
DESIGN OF THE Top TABLE.......................................................................................................48
7.2
ATTACHMENT OF THE GANTRY RAILS TO THE TABLE................................................................56
7.3
DESIGN OF THE LOWER FRAME.................................................................................................69
8
PLATEN ASSEMBLY.................................................................................................................79
9
TORQUE AND SPEED CONSIDERATIONS........................................................................80
10
CHOSEN MOTOR ......................................................................................................................
84
11
BEARING SELECTION AND DESIGN ................................................................................
93
6
12
DESIGN OF THE PLATEN......................................................................................................103
13
DESIGN OF THE CAPSULE....................................................................................................117
14
DESIGN OF THE PLATEN SPINDLE ASSEMBLY...............................................................124
14.1
ASSEMBLY PROCEDURE OF MAJOR COMPONENTS.................................................................
124
14.2
ASSEMBLY OF THE DETACHABLE SECTION ...........................................................................
131
14.3
ASSEMBLY OF THE ENDPOINT DETECTION COMPONENTS ......................................................
133
15
HEAD GIMBAL DESIGN.........................................................................................................140
16
CONCLUSION..........................................................................................................................184
7
Table of Figures
SIDE VIEW SCHEMATIC OFROTARY CONFIGURATION. .................................................................
17
FIGURE 2. TOP VIEW SCHEMATIC OF ROTARY CONFIGURATION. .....................................................................
18
FIGURE
FIGURE
1.
3. SIDE VIEWSCHEMATICOFLINEAR
CONFIGURATION. .....................................................................
19
FIGURE 4. TOP VIEW SCHEMATIC OF PAD-BELTALIGNMENT ......................................................................
23
FIGURE 5. SCHEMATIC OF A POSSIBLE TWO TYPE PAD PLATEN. ......................................................................
25
. ..................................................................................................
27
FIGURE 7. OVERVIEW OF CONCEPT#] .................................................................................................
28
FIGURE 8. LAYOUT OF CONCEPT #2 . ..........................................................................................................
29
FIGURE 9. OVERVIEW OF CONCEPT#2. .............................................................................
30
FIGURE 10. LA YOUT OF CONCEPT#3. ........................................................................................................
31
FIGURE 11. GANTRY STRUCTURE FOR CONCEPT #3 ..................................................................................
32
FIGURE 6. LAYOUT VIEW OF CONCEPT
FIGURE 12. GANTRY STRUCTURE FOR CONCEPT #3...................................................................................33
FIGURE
13.
THE VALUE OF THE MINIMUM WAFER OFFSET DISTANCE AS FUNCTION OF POLISH VELOCITYAND
PLATEN ROTATIONAL VELOCITY LIMITS. ..............................................................................................
36
FIGURE 14. MACHINE FOOTPRINTAS FUNCTION OFPOLISH VELOCITYAND PLATEN ROTATIONAL VELOCITY LIMITS.
......................................................................................................................................................
36
FIGURE 15. THE MAGNITUDE SQUARED OF THE GRADIENT OF FOOTPRINTAS FUNCTION OFPOLISH VELOCITYAND
PLATEN ROTATIONAL VELOCITY LIMITS. ..............................................................................................
37
FIGURE 16. WELDED STAINLESS STEEL LOWER STRUCTURE (CONCEPT #]A). .................................................
39
FIGURE 17. WELDED STAINLESS SIDE STRUCTURE . ......................................................................................
40
FIGURE 18. WELDED STAINLESS STEEL LOWER BASE. ..................................................................................
41
FIGURE 19. A CAST POLYMER COMPOSITE LOWER STRUCTURE (CONCEPT#1B). .........................................
42
FIGURE 20. CONCEPT #JB DESIGN WITH THE THRU HOLES FOR THE RAIL BOLTS..............................................43
FIGURE 21. CONCEPT #1 C DESIGN WITH THE THRU HOLES FOR THE RAIL BOLTS...........................................44
FIGURE 22. METHOD OF ASSEMBLY FOR A CONCEPT#JC DESIGN...............................................................45
FIGURE 23. RENDERED VIEW DIAGRAM OF THE TOP TABLE SHOWING THE LARGE PLATEN HOLES...................49
FIGURE 24. RENDERED VIEW DIAGRAM SHOWING THE LOCATION PINS FOR THE PLATEN ASSEMBLY...................50
8
FIGURE 25. RENDERED VIEW DIAGRAM SHOWING THE BOLT CLEARANCE HOLES FOR THE PLATEN ASSEMBLY. ..... 51
FIGURE 26. RENDERED VIEW DIAGRAM SHOWING MOUNTING FEATURE FOR THE GANTRY LINEAR ENCODER STRIP.
52
......................................................................................................................................................
FIGURE 27. RENDERED VIEW DIAGRAM SHOWING THE MOUNTING FEATURES FOR THE GANTRY RAILS AND MOTOR,
53
AND BALLSCREW BRACKETS. ...........................................................................................................
FIGURE 28. RENDERED VIEW DIAGRAM SHOWING CONDUITS IN THE TOP TABLE. .............................................
54
FIGURE 29. RENDERED VIEW DIAGRAM SHOWING CLEARANCE HOLES FOR METAL INSETS. .............................
55
FIGURE 30. RENDERED VIEW OF THE LAPPING CONFIGURATION FOR THE TOP TABLE .................................
56
FIGURE 31. SCHEMATIC DIAGRAM OFA BOLT BEING SUBJECTED TO SHEAR BETWEEN TWO MATERIALS WITH
DIFFERENTAMOUNTS OFEXPANSION. ...........................................................................................
57
FIGURE 32. SCHEMATIC OF A MATERIAL SPECIMEN UNDERGOING THE UNIAXIAL TENSION TEST. ........................
60
FIGURE 33. RENDERED SCHEMATIC OF THRU HOLE BOLT DESIGN. ..............................................................
61
FIGURE 34. 2-D SCHEMATICS THE BOLT BEING MODELED AS A FIXED/FIXED BEAM IN BOTH THE NEUTRAL AND
.
STRAINED STATES. ...................................................................................
..............
.....
62
63
FIGURE 35. SCHEMATIC OFAX LONG SECTION OF THE BOLTAT LOCATION X. ..............................................
LONG SECTION OF THE BOLT UNDER ANGULAR DEFLECTION. ............................
65
FIGURE 37. SCHEMATIC OF AX LONG SECTION OF THE BOLT UNDER TRANSLATION DEFLECTION. ...................
67
FIGURE
36. SCHEMATIC OFAX
FIGURE 38. RENDERED VIEW DIAGRAM OFTHE LOWER FRAME CAST IRON PLATES.......................................71
FIGURE
39. RENDERED VIEW DIAGRAM
SHOWING ACCESS PORTS IN THE LOWER FRAME ..................................
72
FIGURE 40. RENDERED VIEW DIAGRAM SHOWING THE BOLT PATTERNS REQUIRED FOR THE ASSEMBLY OF THE
LO WER FRAM E. .....................................................................................
...
-------
.
.--------.--
73
FIGURE 41. RENDERED VIEW DIAGRAM SHOWING NECESSARY FINISHED SURFACES FOR THE LOWER FRAME. ..... 74
FIGURE 42. RENDERED VIEW DIAGRAM SHOWING THE LOWER FRAME ASSEMBLY READY FOR LAPPING. ............. 75
FIGURE 43. RENDERED VIEW DIAGRAM OF COMPLETED LOWER FRAME. .....................................................
76
FIGURE 44. RENDERED VIEW DIAGRAM OF THE ASSEMBLY OF THE TOP TABLE ONTO THE LOWER FRAME...........77
FIGURE 45. COEFFICIENT OF KINETIC FRICTIONAS A FUNCTION OF THE RATIO OF POLISH PRESSURE OVER POLISH
VELOCITY FOR 7PSI PRESSURE. ............................................................................................
...... 81
FIGURE 46. COEFFICIENTOF KINETIC FRICTION AS A FUNCTION OF POLISH PRESSURE AND VELOCITY..............82
9
FIGURE 47. REQUIRED MOTOR TORQUE AS A FUNCTION OF POLISH PRESSURE AND VELOCITY..........................83
FIGURE 48. REQUIRED MOTOR POWER AS A FUNCTION OFPOLISH PRESSURE AND VELOCITY............................84
FIGURE 49. SCHEMATIC OF ROTOR AND STATOR CLAMPED FITS. .................................................................
87
FIGURE 50. SCHEMATIC OFROTOR AND STATOR FITS ................................................................................
88
FIGURE 51. SCHEMATIC OFA SHAFT SUPPORTED BYA RADIAL BALL BEARING................................................93
FIGURE 52. SCHEMATIC OFA SHAFT SUPPORTED BY ONE RADIAL AND ONE AXIAL BALL BEARING CONFIGURATION.
94
......................................................................................................................................................
FIGURE 53. SCHEMATIC OFA SHAFT SUPPORTED BY TWO RADIAL AND ONE AXIAL BALL BEARING CONFIGURATION.
95
......................................................................................................................................................
FIGURE 54. SCHEMATIC OF A SINGLE DIRECTION AXIAL HYDROSTATIC BEARING. .......................................
96
FIGURE 55. SCHEMATIC OF SINGLE DIRECTIONAXIAL, RADIAL, AND MOMENT SUPPORTING HYDROSTATIC BEARING
CONFIG URATION. .................................................................................................
........
----........- 97
FIGURE 56. SCHEMATIC OF AN AXIAL SELF-COMPENSATING HYDROSTATIC BEARING. .................................
98
FIGURE 57. MAGNIFIED SECTION OF AN AXIAL SELF-COMPENSATING HYDROSTATIC BEARING. ....................
99
FIGURE 58. RENDERED CUT-AWAY VIEW OF A CROSS ROLLER BEARING. ........................................................
100
FIGURE 59. SCHEMATIC OF THE ROLLER ELEMENT ALIGNMENT IN A CROSS ROLLER BEARING..........................101
FIGURE 60. SCHEMATIC SHOWING THE RESULTING PLATEN DIAMETER .........................................................
105
FIGURE 61. RENDERED VIEW OF THE TOP PLATEN SECTION.................
106
FIGURE 62. RENDERED VIEW OF THE PLATEN ROTOR SHAFT .................
107
FIGURE 63. RENDERED VIEW OF THE POSITIONING STEP ON THE ROTOR SHAFT ...........
108
FIGURE 64. RENDERED VIEW OFBEARING DISPLACEMENT FEATURE ............................................................
109
FIGURE 65. RENDERED VIEW OF BEARING LOCATION FEATURE................110
FIGURE 66. RENDERED VIEW SHOWING THE ASSEMBLY OF THE BEARING AND LOWER RETAINING RING.............111
FIGURE 67. RENDERED SECTION VIEW OF PLATEN CAVITY FEATURES. ..........................................................
112
FIGURE 68. RENDERED VIEW OF STIFFENING RIB STRUCTURES. ................
113
FIGURE 69. DiSPLACEMENT FEA RESULTS FOR PLATEN STRUCTURE WITH THICK TOP PLATE UNDER POLISH LOAD.
FIGURE 70. DISPLACEMENT FEA RESULTS OF PLATEN STRUCTURE WITH RIB SECTION UNDER POLISH LOAD. ... 115
10
FIGURE 7 1. RENDERED VIEW OFSPLASHGUARD AND PLATEN INTER FACE. ....................................................
117
FIGURE 72. RENDERED VIEW OF THE BEARING SEAT ON THE CAPSULE.........................................................
118
FIGURE 73. RENDERED VIEW OF THE BEARING ASSEMBLY INSIDE THE CAPSULE ............................................
119
FIGURE 74. RENDERED VIEW OF BEARING LUBRICATION HOLES..................................................................120
FIGURE 75. RENDERED VIEW OF HALF RING RETAINING RINGS.....................................................................121
FIGURE 76. RENDERED VIEW SHO WING RETAINING RING INTERFACE FEATURE ..............................................
121
FIGURE 77. RENDERED VIEW SHO WING HOW THE HALF RING RETAINING RINGS CLAMP DOWN ON THE OUTER RACE
OF THE BEARING. .........................................................................................
-
................
122
FIGURE 78. SCHEMATIC BEARING RETAINING RINGS. ..............................................................................
123
FIGURE 79. RENDERED SECTION ViEW OF THE PLATEN ASSEMBLY. ...............................................................
124
FIGURE 80. RENDERED VIEW
OFSPLASHGUARD
IN THE PLATEN ASSEMBLY...................................................125
FIGURE 81. RENDERED VIEW PLATEN AND CAPSULE SUBASSEMBLIES AS THEY ARE ASSEMBLED TOGETHER. ......
126
FIGURE 82. RENDERED SECTION VIEW OFTHE PLATEN ASSEMBLY WITH THE ALL RETAINING RINGS ATTACHED..
127
FIGURE 83. RENDERED VIEW OF THE ROTARY ELECTRICAL COUPLING IN THE ASSEMBLY. ...............................
128
FIGURE 84. RENDERED VIEW OF THE ROTARY FLUID UNION IN THE ASSEMBLY..............................................
128
FIGURE 85. RENDERED VIEW SHOWING THE BRACKET IN THE PLATEN ASSEMBLY. ..........................................
130
FIGURE 86. SCHEMATIC SHOWING THE RELATION BETWEEN THE PINS AND THE UNDERSIDE GROOVES OF THE
DETACHABLE SECTION (BOTTOM VIEW)...................................................................
132
FIGURE 87. RENDERED SECTIONED VIEW OF THE ENDPOINT DETECTION SENSOR IN THE ASSEMBLY ...............
134
FIGURE 88. RENDERED VIEW OF THE AMPLIFIER AND ADAPTER PLATE. ........................................................
135
FIGURE 89. RENDERED VIEW OFAMPLIFIER AND ADAPTER PLATE IN ASSEMBLY............................................136
FIGURE 90. RENDERED VIEW OF THE OVERALL PLATEN ASSEMBLY ..............................................................
137
FIGURE 91. RENDERED SECTION VIEW OF THE OVERALL PLATEN ASSEMBLY. .................................................
138
FIGURE 92. RENDERED VIEW OF THE
OVERALL
PLATEN ASSEMBLY SHOWING THE COMPONENTS INSIDE THE
PLATEN ROTOR SHAFT ..............................................................................
139
FIGURE 93. SCHEMATIC OFAN EXAGGERATED WAFER VS. PAD SPINDLE AXES MISALIGNMENT. ........................
140
FIGURE 94. SCHEMATIC OF THE KINEMATIC CONFIGURATION OF A UNIVERSAL JOINT....................................
141
11
FIGURE 95. SCHEMATIC SHOWING THE MOMENT EXERTED ABOUT THE CENTER OF ROTATION OF THE WAFER BY
143
THE FRICTION FORCE. ...............................................................................................................
FIGURE 96. SIMPLE FOUR-BAR LINKAGE...................................................................................................145
FIGURE 97. SCHEMATIC OF A FOUR-BAR LINKAGE SHOWING THE LOCATION OF THE INSTANT CENTER OF THE
...................
CO UPLER LINK. ........................................................................................................
146
FIGURE 98. RENDERED VIEW OF A FOUR-BAR GIMBALED MECHANISM DESIGN. .............................................
147
FIGURE 99. ALTERNATIVE FOUR-BAR GIMBA LED MECHANISM DESIGN. .........................................................
148
FIGURE 100. SCHEMATIC OF A FOUR BAR LINKAGE SYSTEM WITH A DESIRED INSTANT CENTER FOR THE COUPLER
LIN K. ....................................................................................................
. --- ....
... .-14 9
.. -.. --------
FIGURE 101. SCHEMATIC OFA FOUR BAR LINKAGE SYSTEM SHOWING THE LOCATION OF THE INSTANT CENTER OF
THE COUPLER LINK. ..............................................................................
153
.......................
FIGURE 102. SCHEMATIC OF A FOUR BAR LINKAGE SYSTEM SHOWING THE LOCATION OF THE ACTUAL INSTANT
...... 156
CENTER OF THE COUPLER LINK.......................................................................................
FIGURE 103. SCHEMATIC OF THE SECONDARY LINKAGE SYSTEM SHOWING THE LOCATION OF THE ACTUAL
INSTANT
CENTER OF THE COUPLER LINK................................................................................
FIGURE 104. SCHEMATIC OF THE PRIMARY LINKAGE SYSTEM SHOWING THE LOCATION OF THE ACTUAL
INSTANT
CENTER OF THE SECONDARY COUPLER LINK................................................................................
FIGURE 105. MAGNITUDE OF MOMENT ARM FOR MOMENTS ABOUT THE PRIMARY
...........................................................................................................
INSTANT CENTER
160
162
OFROTATION.
.......................................
16 5
FIGURE 106. MAGNITUDE OF MOMENT ARM FOR MOMENTS ABOUT THE SECONDARY INSTANT CENTER OF
ROTATION.................................................................................
166
FIGURE 107. RENDERED VIEW SCHEMATIC OFA SIMPLE SPHERICAL JOINT. ...................................................
168
FIGURE 108. SCHEMATIC OF THE TARGET BODIES TO BE COUPLED FOR THE TRANSMISSION OF TORQUE. .........
169
FIGURE 109. SCHEMATIC SHOWING THE TWO TARGET BODIES CONNECTED BY A TELESCOPING JOINT. ............. 170
FIGURE 110. SCHEMATIC SHOWING THE UNIVERSAL JOINT CONFIGURATION ON THE MOVING BODY................171
FIGURE
111.
SCHEMATIC SHOWING THE COMPLETED COUPLING OF THE TARGET BODIES TO EACH OTHER USING A
TELESCOPING CONSTANT VELOCITY JOINT......................................................................
172
12
FIGURE
112.
SCHEMATIC SHOWING THE TWO TARGET BODIES AND COUPLING INAN ARBITRARY CONFIGURATION.
....................................................................................................................................................
17 3
174
FIGURE 113. RENDERED VIEW DIAGRAM OF THE HEAD SPINDLE ASSEMBLY............
FIGURE 114. RENDERED VIEW DIAGRAM OF THE MAIN BRACKET................175
FIGURE 115. RENDERED VIEW DIAGRAM SHO WING THE HEAD CAPSULE AND THE SPHERICAL SECTIONS. ......... 176
177
FIGURE 116. RENDERED VIEW DIAGRAM SHO WING SPHERICAL JOINTASSEMBLY. ..........
FIGURE 117. RENDERED VIEW DIAGRAM SHOWING THE INITIAL COMPONENTS OF THE TELESCOPING CONSTANT
VELOCITY JOINTASSEMBLY. .....................................................................................
---....-.-..----..
178
FIGURE 118. RENDERED VIEW DIAGRAM SHOWING THE SECONDARY RING OF THE MOVING UNIVERSAL JOINT. .. 179
FIGURE 119. RENDERED VIEW DIAGRAM SHO WING THE PRIMARY RING OF MOVING UNIVERSAL JOINT. ............. 180
FIGURE 120. RENDERED VIEW DIAGRAM OF THE COMPLETED TELESCOPING JOINT IMPLEMENTATION. ............ 181
FIGURE 121. RENDERED VIEW DIAGRAM OF THE COMPLETED TELESCOPING CONSTANT VELOCITY JOINT
ASSEM BLY.......................................................................................
FIGURE 122. RENDERED SECTION VIEW OF A BELLOW. ...................
.. ........ .....
. . . . . . 182
------------...
183
FIGURE 123. RENDERED SECTION VIEW OF HEAD ASSEMBLY USING A BELLOW TO TRANSMIT TORQUE. ............ 184
13
1
Introduction
The trend in the semiconductor industry has always been to continuously reduce
the size of solid-state chips. To this end, the industry has employed multiple layered
circuit designs with increasingly smaller line widths. To achieve small line widths within
the range of 5pm a small depth of focus is required during the lithography steps. This in
turn requires the topography of the surface that the pattern is projected on to, to be very
flat. In recent years, semiconductor manufacturers have used different techniques to
planarize the wafer surface before each lithography step. One of these techniques is
Chemical Mechanical Planarization (CMP). CMP is a method of producing extremely
flat surfaces on materials such as tungsten, aluminum or silicon using slurries such as
aluminum oxide, silica, or cerium oxide abrasives. CMP is a lapping process by which
two-body and three-body abrasion is used with the assistance of a chemical agent to
globally planarize the surface of silicon wafers. Compared to other semiconductor
technologies, CMP is still at an early stage of development. As such, there is still much to
study and learn about the process, such as the wafer/pad contact characteristic and the
role of chemistry in the polishing process. There is a collaborating research group at MIT
that is trying to study the underlying science behind the CMP process. They require a
flexible and easily modifiable machine to use in their research. It is the goal of this
project to design a machine that can be used as a research tool to learn more about the
CMP process and that can serve as stepping stone for the design of competitive
production CMP tools in the future. These two goals complement each other since any
14
information obtained from the use of the tool in process research will facilitate the
understanding that is necessary to design a capable production tool.
2
Design Goals
As a research tool, this machine must first and foremost be as flexible as possible
in its design. It should be easily and endlessly modifiable after its production to allow for
the changes and additions that may be deemed necessary after initial research results. It
should also allow multiple CMP process recipes (pad texture and slurry combinations) to
be run on the machine with the minimum required changeover effort and expense. To be
a good research tool, it must produce as little vibration as possible and have high
damping as not to introduce extra variables into the process parameters. Finally, at the
request of the collaborating research group, the machine must also allow two separate
recipes to be run, consecutively and without machine downtime, on the same wafer.
As a predecessor of a production CMP tool, this machine must take into account
potential end-customer needs. It must have the minimum amount of footprint possible
while still maintaining its design flexibility. It must be easily transportable with a
minimum amount of preparation. It must also have easy and repeatable assembly.
Furthermore, it must withstand the temperature ranges present in it operating
environment and during its transport, without sustaining any damage or misalignment.
Finally, it must not generate any particles during its operation since this would
compromise the clean environment that most commercial CMP tools operate in.
15
3
3.1
Choosing Polish Configuration
CMP Configurations
As mentioned before CMP is a lapping process in which the wafer surface is
pressed against a pad surface that polishes it. In most configurations the wafer is held
upside down and lowered down onto the pad. The pad is usually loaded with slurry that
contains abrasive particles and a fresh supply of slurry is delivered to the contact surface
over time. It is the relative motion of the pad with respect to the wafer that polishes the
wafer surface via two-body and three-body abrasion. In two-body abrasion, abrasive
particles, embedded and stuck to the top surface of the pad, are dragged over the wafer
surface under pressure and hence remove material. In three-body abrasion, abrasive
particles that are within the pad-wafer contact area hit the wafer surface with an
impingement angle and velocity and remove material as a result. In both cases, the
amount of contact pressure and the relative velocity of the pad on the wafer influence the
amount of material that is removed. As such, in order to achieve uniform, global material
removal rate, the contact pressure on every point of the wafer must be the same. In
addition, the relative velocity of the pad with respect to any point on the wafer must also
be the same (uniform across the wafer surface).
There are three main configurations used in commercial CMP tools that try to
achieve these conditions. The first and most widely used configuration is a rotary
configuration. In this configuration the wafer is lowered down onto a pad of larger area as
shown below.
16
Application of
Polishing Force
Op
Wafer Carrier
Wafer
Platen
Figure 1. Side view schematic of rotary configuration.
A force exerting mechanism then presses the wafer surface against the pad surface
has
in order to generate the necessary polishing pressure. In most cases, the wafer spindle
The
a gimbaled mechanism to insure uniform pressure distribution at the contact surface.
in section
design of the gimbaled mechanism is critical and several options are discussed
generate the
15. Both the wafer and pad are attached to spindles that rotate them to
wafer carrier
relative motions necessary for polishing to occur. The wafer is held inside a
a platen that is
that is then attached to a spindle via a gimbal and the pad is bonded onto
pad center
attached to another spindle. The wafer center of rotation is separated from the
of rotation by the distance s denoted in the following figure.
17
PLATEN
WAFER
Figure 2. Top view schematic of rotary configuration.
In this configuration, the velocity of the pad relative to any point on the wafer, at
a location (r,0) in the reference frame of the wafer, is given by Eq. 1 in the coordinates of
the ground reference frame. A detailed derivation of this equation is included in the
Appendix section.
(Eq. 1)
-=VH
(aH
P )rsin0
As can be seen from Eq. 1, if op = oH= og then
relative velocity i
(
=
H rc
oPS]
-wes j regardless of rand 0. The
in the coordinates of the rotating wafer reference frame is given by
Eq. 2 below (assuming that the two reference frames are initially coincident at t=O).
(Eq. 2)
=cosJO, sin(w0 t)I -wOjos -COS(wot)
18
Another type of configuration that is used widely in commercial CMP tools is the
linear configuration. In this configuration the wafer is lowered upside down upon a pad
that is attached to moving linear belt. The linear belt is usually made of stainless steel and
raps around two large drums. The motion of the belt is supplied by the rotation of these
drums. In most commercial CMP tools, only one of the drums is driven by a motor and
the other is allowed to rotate freely. As with the rotary configuration, there is a force
exerting system that provides the necessary polishing pressure and a gimbaled
mechanism to distribute the pressure evenly over the contact surface. A schematic of this
configuration is shown in the following figure.
Application of
Polishing Force
Wafer Carrier
Wafer
Pad
Steel
Belt
VB
B
H
(0B
+9
Rotating Drums
Figure 3. Side view schematic of linearconfiguration.
In addition to the motion of the belt, the wafer rotates with a speed ft . The velocity of
the linear pad relative to any point on the wafer, at location (r,0) in the reference frame of
the wafer, is given by Eq. 3 in the coordinates of the ground reference frame. The relative
19
velocity in the coordinates of the rotating wafer reference frame is given by the Eq. 4
(assuming that the two reference frames are initially coincident at t=O).
V =VB +rWHsin0
(Eq. 3)
(Eq. 4)
H=
-
[y + rOJFsin(Ht + )Ios(y )- rH
rWH
rWHCosOj
cos(Ht+O)sin
t)i
cos(wHt +O)0os(Hot)- [yB + rojH sin (wHt +0)]sin (CHt) J
3.2 Advantages and Disadvantages of each Configuration
One advantage of the rotary configuration is that it provides a uniform velocity
profile at the contact surface when op = wH= oN. In addition, as can be seen from Eq. 2,
the direction of the relative velocity profile over the wafer surface changes continuously
with time. This way any scratch patterns left on wafer surface from the polishing action
are not always in one direction. Instead, any such patterns will superimpose on each other
from all directions and average out during each rotation. In effect, the net distance
traveled by the pad over any point on the wafer is zero for each rotation. This can be seen
by taking the time integral of Eq. 2 over one rotation as shown below.
21r
coos sin(wt)
(Eq. 5) Dnet =
-oos
-cos(wot)i dt = coos
- cos(wot)-o - [sin(wot)to
=0
0
20
However, under the necessary condition that o>H=W)p the wafer and pad will
always rotate with the same phase that they started out with at the beginning of the
process. In this manner, any given point on the pad will always follow the same path of
travel on the wafer surface at each rotation. This can be a disadvantage if the polishing
properties of the pad are not uniform over its entire area. For example, if a small region
on the pad contains a higher concentration of abrasive particles than another, then this
region will polish the areas of the wafer that it is contact with faster. Since the pad and
the wafer are in phase, such a region will contact the same area on the wafer at each
rotation and selectively polish that area of the wafer faster than others. The effect is not
distributed over the entire surface of the wafer.
As was already mentioned above, the rotational velocities of both the platen and
the wafer have to be the same in order to achieve a uniform velocity profile across the
wafer surface. It is clear that if the wafer rotates faster than the platen the edges of the
wafer will be polished faster. If the platen rotational speed is faster than that of the wafer,
then again the edges of the wafer will polish faster. Therefore it is very critical to
maintain the two speeds the same, as the effects of any random variations will
superimpose instead of cancel (even if the average or mean of the variation is zero). With
the linear system, however, small errors in the wafer rotation velocity or the belt linear
velocity will not significantly affect the uniformity of the velocity profile across the
wafer. This is an advantage of the linear system that allows for more design flexibility
and reduced cost concerning the selection and implementation of the wafer and belt
spindle drive systems.
21
One disadvantage of the linear configuration is that the relative velocity profile is
not uniform across the wafer surface. As can be seen from Eq. 3 the velocity of the pad
relative to a point on the wafer is a function of the location of that point. If (%were equal
to zero, then the velocity profile would be uniform. However, in that case, the direction
of the relative velocity profile would always remain the same. In this manner any scratch
patterns left on the wafer surface from the polishing action does not average out. With the
linear configuration there is a compromise between maintaining a uniform velocity
profile and averaging out the effects of the direction of that profile. Most commercial
CMP tools optimize between the two limitations by using low values of (%compared to
vo. In this way, they achieve some direction averaging with a minimum effect on the
uniformity of the profile. However, the rate at which the direction is averaged is not as
fast as that of the rotary configuration.
In practice, the linear configuration has some additional disadvantages to the
rotary configuration that are not obvious from the kinematic analysis. The collaborating
research team here at MIT polished many wafers using a test bed that contains both
configurations. Experience shows that it is much easier to replace the pad on rotary
configuration tool than the linear one. In the rotary configuration the self-adhesive
circular pad is simply placed over the platen and then gradually pressed into it from one
side to another, thus releasing the trapped air bubbles. Since the pad area is larger than
the platen it does not have to be accurately centered with the platen and the excess pad
material can be trimmed off at the end. This job takes one person roughly five minutes to
complete.
22
The linear pad, on the other hand, is a long rectangular self-adhesive pad that
needs to be rapped around the metal belt from one end to another. As with the rotary pad,
the linear pad is gradually pressed onto the metal belt in a single direction to expel any air
bubbles trapped between the pad/belt contact surfaces. In this case, however, the
pad/metal belt alignment is very critical. As the pad is gradually attached to the belt, great
care must be taken to insure that the edge of the pad is aligned with that of the belt.
Otherwise, the pad will travel off of the belt or wrinkle to maintain its path along it as
shown below.
Belt
Pad
rums
Figure 4. Top view schematic of Pad-Belt alignment.
Any small deviations at the start will amplify during the rest of the installation process in
the same manner that the separation between two intersecting lines increases with
distance from the intersection point. As a result, it takes two to three people ten minutes
to rotate the belt, release all the air bubble, and maintain pad-belt alignment in order to
install the linear pad.
The linear configuration is also harder to maintain than the rotary one. As the pad
and belt stretch, the tension on the metal stainless steel belt needs to be adjusted.
23
However, if at any time the stainless steel belt is stretched too much and then relaxed, the
pad, which sustains permanent deformation when stretched, will not relax as much as the
flexible metal belt that it is glued on to. As a result, after relaxation the pad has been
observed to crawl up on the belt during the next polishing run. The latter in turn generates
bumps on the pad that affect the pressure distribution within the pad-wafer contact
surface.
Reasons for Choosing the Rotary Configuration
3.3
As was mentioned earlier, the kinematics of the rotary system are such that it
produces the desired uniform relative velocity profile with a time variant direction when
wp =
oH
=
ot. The variation of direction with time is constant and continuous and
averages out to be zero over each rotation as can be seen from Eq. 5. In addition the
rotary configuration is easier to maintain in practice than the linear one. Furthermore, the
rotary configuration requires two spindles instead of three which makes it easier to design
and manufacture. Finally, since there are more rotary configured commercial CMP tools
than linear ones, there are a wider variety of pads available for that design. As a result,
the decision was made to use the rotary configuration in the design of this machine.
4
Two Platen Machine
As was mentioned earlier, one of the design goals of this machine is to allow two
separate recipes to be run consecutively and without machine down time on the same
wafer. Such flexibility will allow one process recipe to be used to quickly remove
material and another to be used to more accurately planarize the surface of the wafer.
24
Two separate recipes may involve two different pads and two different slurries in
addition to different polish pressure and relative velocity parameters. A single and very
large platen can be provided with two different pad materials in concentric rings, as
shown in the figure below.
Type 1 Pad
Type 1 Pad
Figure 5. Schematic of a possible two type pad platen.
In addition, each of the two slurries can be separately supplied to the platen during its
respective run. However, some chemical slurries are acidic while others are basic. If two
slurries of varying pH are used on the same platen, then the pad needs to be flushed with
plenty of water to neutralize the pH back to seven before the application of the second
slurry. Experience with the test bed machine shows that once a pad is loaded with an
acidic or basic slurry, it acts like a sponge and soaks up the slurry. Although conditioning
can help the situation, it is still very difficult and time consuming to flush out the old
slurry and neutralize the pH on the pad. Furthermore, a platen large enough to contain
two separate pads, as shown in Figure 5, would have four times the area of the two
smaller platens large enough to contain one pad. As a result the decision was made to
25
design the machine with two single pad platens in order to satisfy the requirement for a
two-recipe step process.
5
5.1
Machine Configuration
Conceptual Designs for Two Platen Machine Configuration
Four conceptual designs were generated for the two platen machine layout. The
key goal in all of the concepts was to increase the throughput/footprint ratio while still
meeting process requirements and not compromising the accessibility that is required for
maintenance. All four concepts also include a washing station to clean off the wafer in
between the two recipe steps and after the completion of the second step.
The first and simplest of these concepts is to lay the platens and washing station
side by side along the length of the machine. This concept is shown in the figure below
where the two large blue disks represent the platens and the small silver disk represents
the washing station.
26
Platen 1
Figure 6. Layout view of Concept #1.
Concept #1 can be implemented with a different motor for each platen or using one motor
and center shaft to drive both platens as shown in Figure 6. With this design a gantry
structure holding the wafer carrier and force application mechanisms can be mounted as
shown in the following figure. Such a structure would ride on rails and transfer the wafer
between the two platens and washing station.
27
Wafer Motor
- Wafer Carrier
Figure 7. Overview of Concept #1
In its most compact form, a Concept #1 machine will be 6ft long, 2.5ft wide, and roughly
4.5-5ft high for an 8in-diameter wafer and 27in-diameter platens. It requires 2 linear axis
of motion: one for lowering and raising the wafer onto the platens and the cleaning
station; and another along the length of the machine for wafer sweep and transportation.
As expected, this concept also requires three axis of rotation, one for each platen and one
for the wafer.
A second concept reduces the footprint of the machine even more but adds extra
complexity to the design. The layout of this design can be seen in the following figure.
28
-jjtton Pe
Washing
Center
.SaftLC
Figure 8. Layout of Concept #2.
Since the wafer diameter (8in) is much smaller than that of the platen (27in), it does not
cover the entire area of the platen during the lapping process. In Concept #2, the area of
platen 1 that is not covered by the wafer carrier is tucked under the cleaning station.
Similarly, the uncovered area of platen 2 is tucked under platen 1. As with Concept #1,
this concept also allows for the use of one motor and a center shaft (as shown), or the use
of two motors to drive each platen. In order to prevent slurry from splashing from one
platen onto another the design of the splashguards around the platens will be critical with
this concept. The overview of this concept is shown in the figure below.
29
Figure 9. Overview of Concept #2.
In its most compact form, a Concept #2 machine will be 4ft long, 2.5ft wide, and roughly
6ft high. This machine is slightly taller than a Concept #1 machine in order to have the
same amount of space available for the placement of the different components such as
slurry pumps under the two platens. Concept #2 has the same axis of motion as Concept
#1.
An even more complex concept is to stack the two platens and the cleaning station
one on top of another in order to save space. After all, the footprint of this machine is
more critical in a fab environment than its height. Thus it would make sense to reduce the
footprint of the machine at the expense of increased height. To this futile end, Concept
#3, which is shown in the figure below, was generated.
30
Platen
Wafer Motor
1
Wafer Carrier
Platen 2
Figure 10. Layout of Concept #3.
In this concept the wafer carrier fits in between the two platens during the polishing
process. To achieve this, the structure that is holding the wafer carrier has to be
cantilevered and a belt has to be used to transfer the torque from the head motor to the
wafer carrier as shown below.
31
Wafer Motor
Cantilevered
Structure
Pulley System
Wafer Carrier
Figure 11. Gantry structurefor Concept #3.
At first look it might seem that such a design saves a lot of footprint at the expense of
increased height, complexity, and an undesirable cantilevered force application structure.
However, a closer look at Figure 10 will reveal that the gantry structure needs to travel
back in order to clear the cantilevered wafer carrier structure from the platens, before it
can raise and lower the wafer carrier to the other platen or the cleaning station. In fact, in
its most compact form, a Concept #3 machine is still 4ft long, 2.5ft wide. Although it is
9ft high and very complex it offers no reduction in footprint over Concept #2.
In fact, the only way to reduce footprint by stacking the machine components
vertically is to stack the platens, the cleaning station, and the gantry structure one on top
of another as shown below.
32
Wasing:
Wafer Motor
Platen 1
Wafer Carrier
Platen 2
Center Shaft
Motor
Figure 12. Gantry structurefor Concept #3.
In the figure above the gantry is shown in its resting position. This is also the position
that the gantry will be at in order to feed the wafer to the cleaning station. In order to
polish the wafer on platen 1, both the gantry and platen 1 move forward and the wafer is
lowered onto platen 1. Similarly in order to polish the wafer on platen 2, platen 1 moves
back in and platen 2 moves forward. In its most compact form, Concept #4 is only 3.5ft
long, 2.5ft wide, and 9ft high. Concept #4 provides the smallest footprint of all four
concepts. However, two additional linear axis of motion have been introduced in order to
achieve this. Concept #4 is the most complex of all four concepts as well and saves only
12.5% of foot print over Concept #2.
33
It is clear that there is no advantage in choosing Concept #3. Among the
remaining choices, Concetp#4 offers the smallest footprint. However, the complexity that
is gained is not worth the small 12.5% reduction that it offers over Concept #2. Thus the
choices are limited to either of the first two concepts. Concept #2 also offers a small
11.1% reduction in footprint over the first concept. However, the extra complexity gained
with Concept #2 over Concept #1 is no as much that of Concept #4 over Concept #2. If
this machine were to be developed purely a commercial tool, Concept #2 would be the
best of all. However, considering that this machine's is a first attempt at a prototype
design and will also be primarily used in a research environment where it needs to be
endlessly modifiable, it is best to choose Concept #1 for the sake of the simplicity and
future flexibility that it offers.
5.2
Wafer and Platen Center to Center Offset Distance
Once the machine configuration is chosen the wafer and platen center to center
offset can be chosen. This offset is the minimum distance between the center of the wafer
and the center of the platen. When the wafer is at its inner most position during the wafer
sweep, this offset distance corresponds to the s dimension in Figure 2. It is important to
note that the center of the platen can be inside the wafer surface. As can be seen form
equations 1 and 2 there is nothing that requires the dimension s to be larger than the
wafer radius. In fact, as long s is not zero, any other value will achieve the required
constant velocity profile. However, as can be seen from equation 2 for smaller values of s
the value of at must be larger in order to achieve the same magnitude for relative polish
velocity. Thus, larger values of s will increase the machine footprint while smaller values
34
of s will increases the required rotational velocities of the motors. The latter extreme will
either require larger motors or the need for gear increase mechanisms and can present
many other problems associated with wear and tear and harmonic vibrations in the
machine. Either extreme will most likely increase the machine's volume and thus present
a disadvantage as far as a commercial tools is concerned. The footprint of the machine
given a value for s can be approximately calculated, although it will not be accurate since
a detailed design for the machine is not yet complete at this stage. In addition, the size of
the motors and gear increase mechanisms required to provide the necessary torques and
rotational velocities depends, among other things, on the market availability of parts and
is thus not a closed form function of s. As a result, choosing the appropriate value for the
minimum offset distance is an iterative process. First, after reviewing the types of motors
that are available in the market and taking into account wear and tear and vibration
considerations, a range is chosen for the upper limit of the rotational velocities that can be
required of the motor. This range was chosen to be between 400RPM to 500RPM. Ideally
it is best to remain on the lower side of this range, as there are many more practical
options available that way. Next, a range is chosen for the upper limit of the desired
relative polish velocity. This range was chosen to be between 3.75 m/s and 4 m/s. Ideally,
it is best to remain on the upper limit of this range, as this will allow higher polish
velocity experiments to be carried out and adds to the flexibility of this machine as a
research tool. Next, the values of s are calculated for each of the polish velocity and
motor rotational velocity combinations possible within the two ranges. This plot is
included in the following figure.
35
3.83.6
3.4*
o~3.2
34
3 --
3.95
2.8
3.9
50 480
-.
460
8
403.8
RPM
420
400
3.75
velocity (m/s)
Figure 13. The value of the minimum wafer offset distance asfunction of polish velocity
andplaten rotationalvelocity limits.
As is expected the value of s is larger for higher polish velocities and lower platen
rotational velocities. At this point it is helpful to evaluate the estimated footprint of the
entire machine for each of the combinations within the chosen ranges.
46004500
6 4400
C- 4300
0
LL
4
4200
4100
500
-
3.95
-3.9
-3.85
480
460
403.8
RPM
420
400
3.75
velocity (m/s)
Figure 14. Machinefootprint as function of polish velocity and platen rotationalvelocity
limits.
36
As is expected, the magnitude of the machine footprint is higher for higher values of
polish velocity and lower values of RPM. If this were not the case there would be no
compromise. The previous figure also shows that foot print changes less with respect to
changes in the required maximum polish velocity, than it does with respect to changes in
the maximum allowed motor speed. The following figure shows the magnitude of the
gradient of the footprint, squared, as a function of polish velocity and motor speed.
1400
a 1200
1000
'
800-
0
600
(
500
-3.95
400
CM
-8
-3.9
-3.85
480
460
3.8
RPM
400
3.75
velocity (m/s)
Figure 15. The magnitude squaredof the gradientoffootprint asfunction of polish
velocity andplaten rotationalvelocity limits.
As can be seen from the previous figure, the evaluated footprint function has a higher
gradient at lower motor speed allowances. To reduce the footprint of the machine as
much as possible, it is best to choose values for s corresponding to polish velocity
requirement of 3.75 m/s and motor speed allowance of 500RPM(See Figure 14). At the
same time it is desired to operate at lower motor speed allowances while achieving higher
polish velocities. According the previous figures, the change between 3.75 m/s and 4 m/s
37
for polish velocity requirements will change the footprint by a relatively small amount.
As a result the desired 4 m/s requirement is chosen. However, the change between
400RPM and 500 RPM for motor speed allowances makes relatively larger changes to
the machine footprint. In fact, according to the gradient function, larger changes of
footprint per change in motor speed allowance can be expected near the 400RPM limit.
As a result, 500RPM is chosen as the motor speed allowance. With this combination a
value of 3.00in. is obtained for the minimum wafer offset distance from Figure 13.
6
6.1
Machine Lower Structure
Conceptual Designs for Machine Lower Structure
As was mentioned before, the machine Lower Structure is the structure that
houses the two platens, the cleaning station, the motors for each of the two platens, all
slurry and DI water pumps, and all electronic equipment such as power amplifiers. The
gantry structure is mounted on the Lower Structure using rails to allow its motion along
the length of the machine. Two motors that drive two ball screws, with ball nuts attached
to the gantry, provide the gantry's back and forth motion. These motors and the bearings
that support the ball screws on either side are also mounted on the Lower Structure. The
Lower Structure also contains conduits for the power and fluid lines that supply the
platens, cleaning station, and the gantry structure to pass through. Furthermore, the
Lower Structure, like every other component of the machine, must also be able to
withstand
the expected temperature changes
in
its operational
and transport
environments. Finally, the Lower Structure must also be stiff and have high damping.
38
With these requirements in mind three conceptual designs were generated for the Lower
Structure.
The first concept is to make the entire Lower Structure out of welded Stainless
Steel extruded tubes. Stainless Steel is chosen because of its stiffness and ability to resist
the corrosive properties of the slurries present. The overall structure for this concept is
shown below.
Side Structure
End Structure
Lower Base
Figure 16. Welded Stainless Steel Lower Structure (Concept #1a).
This Stainless Steel structure is made of five sub assemblies that are welded first, and
then welded together to form the overall structure. The Side Structure, which is shown
39
below, consists of a large 8in by 4in and
in thick tubing. The rails for the gantry
structure are attached to the top surface of this tube. This large rectangular tube is then
supported off of the Lower Base via four lin by lin cross tubes and three 2in by 2in pillar
tubes.
Surface for mounting
gantry rails
8X4 tubing
Cross Tubes
Pillar Tubes
Figure 17. Welded Stainless Side Structure.
The two End Structures shown in Figure 16 are there to add torsional rigidity to
the overall structure. The latter structure is made of 3in by 2in and 3in by lin tubes. The
end structures will be welded onto the large 8in by 4in tubes on the Side Structure and
onto the Lower Base at the bottom.
40
The Lower Base, which is shown in the following figure, is made of 3in by 3in
and 3in by 6in rectangular tubes on the sides with 3in by 2in rectangular tubes used as
crossbeams.
Crossbeam
3X3 tubing
6X3 tubing
Figure 18. Welded Stainless Steel Lower Base.
The two platens sit in capsules that rest on top of these crossbeams and are bolted onto
them. The capsules hold the platen motors and contain the bearings necessary to support
each platen. For more detail on the capsule and platen designs refer to section 14.
Another concept for the machine Lower Structure is to make it entirely out of a
non-metallic polymer composite casting. The damping properties of this material are very
high and complex shapes can be readily cast instead of machined. A compact design
using this material follows. Features such as threaded metal inserts for screws can also be
cast into the material for attachment purposes.
41
Holes for Platen
Capsules to sit
in.
Holes for metal
inserts for the
gantry rails to
bolt onto.
Figure 19. A cast polymer composite Lower Structure (Concept #1b).
In the design shown above, two large holes are cast in for the placement of the
two platen capsules. The polymer composite can be cast in many complex shapes and
offers flexibility on the design form. For example, a Concept #1b Lower Structure can be
cast such that the rails bolt onto metal inserts in the structure or it can just easily be cast
such that the bolts pass all the way through and fasten into nuts on the other side, as
shown below.
42
Upside down
grooves to hide
away rail nuts.
Figure 20. Concept #1b design with the thru holes for the rail bolts.
With the polymer composite material, special feature forms such as the upside down
grooves shown in Figure 20 can also be easily cast in, in order to hide away the nuts for
the rail bolts. The form flexibility of the cast polymer composite gives the freedom to
make a machine that is both aesthetically pleasing, a key advantage for a commercial
tool, and also free of sharp protruding features. While such features can be machined into
the steel and granite structures as well, they will cost more per unit than that cast polymer
structure for high volume production runs. These issues are of concern from a
commercial point of view and need to be examined in the design of this machine if it is to
be used as a stepping stone for the design of commercial tools in the future.
43
Another design option that is available is to make the entire Lower Structure out
of slabs of granite. As with the cast polymer composite structure, metal inserts would
have to be used for the necessary assembly features. The damping of granite, is roughly
three times that of stainless steel and one third that of the cast polymer composite
material and is thus a compromise between the two. The top of surface of the granite can
also be machine to a flatness of 0.0005in over the entire top surface of the Lower
Structure. This allows the top surface to be used as a datum plane from which the
alignment of the rest of the machine components can be adjusted during assembly. A
typical first order design using this concept is shown below.
Hole for Platen
Capsules.
Top Table
Pillars--
Bottom Base
Figure 21. Concept #Ic design with the thru holes for the rail bolts.
44
As the separation lines in the above figure indicate, the Lower Structure is broken into six
different pieces: the Top Table, the four pillars, and the bottom base. Each piece is made
entirely of one piece of granite and then assembled together using dowels and epoxy as
shown below.
Mating Piece A
Contact
Surface
Mating Piece BStePg
Figure 22. Method of assembly for a Concept #Ic design.
In order to attach to mating pieces, a large hole is drilled into each piece at the contact
surfaces. Then epoxy is brushed on the two contacting surfaces and inside each hole.
Next, an appropriately sized steel peg, slightly shorter than twice the depth of each hole,
is inserted inside one of the holes. Then the two pieces are connected such that the
protruding section of the steel peg is inserted into the hole on the other mating piece. In
this manner the length of the steel peg is shared between the two holes and offers extra
strength to the contact surface bond by increasing the overall surface area that the epoxy
can bond to.
45
6.2
Choosing a Concept for the Lower Structure
In all of the above concept designs, the machine Lower Structure is made entirely
of one material. This was primarily done to insure that the entire Lower Structure would
expand and contract uniformly with changes in temperature. Each of the concepts above
has its own advantages and disadvantages, some of which are listed below.
1. The Stainless Steel structure is much stiffer than the cast polymer
composite and granite ones.
2. For small volume production (in this case a single unit production) the
stainless steel and granite designs are less costly to make since they do
not incur patterning costs.
3.
If extra components need to be attached to the Lower Structure after
production, the stainless steel structure can be easily drilled and tapped
for the addition of fastener holes. The cast polymer and granite
structures, however, both require additional metal inserts to be fixed
using epoxy.
4. While the stainless steel structure has the advantage of having the
same coefficient of thermal expansion as the Stainless Steel rails that
mount on it, the cast and granite structures have a lower coefficient of
thermal expansion and will hold the their shape better over time with
cyclic changes in temperature.
5. The granite and cast polymer structures also have considerably better
damping properties than the steel. In fact, the cast polymer composite,
46
which has the best damping properties of all three materials, has ten
times the damping of Stainless Steel.
6. The cast polymer material provides a greater flexibility concerning
design form and is also less costly for high volume productions.
7. The top surface of the granite structure can be machined to flatness of
0.0005in and serve as a datum plane for the precise assembly of the
other components that are attached to it.
After analyzing the three concept designs above, it was difficult to clearly rate
them and choose one over the others. In fact, at the end of this particular concept
generation phase none of the options presented itself as a viable option to proceed upon.
Furthermore, new methods, which will be discussed in detail in later sections, were
explored to overcome problems associated with the difference in the thermal expansion
coefficient of two mating parts. As a result, it was decided to use the information
obtained in the concept generation phase to make the machine Lower Structure out of two
different materials, taking advantage of the properties of each.
After careful
consideration, the Lower Structure was split into two parts: a Top Table were the platens,
the cleaning station, and gantry structure are attached; and a supporting lower frame that
holds up the Top Table and contains other components such as the slurry pumps and
power amps. It was decided to attach all components that require precision assembly or
alignment to the Top Table and to place any components whose position is not critical
underneath the Top Table. The latter components are to be fixed both directly and via
mounting brackets to the Lower Frame. This latter design path decouples structural
47
requirements, such as damping and stiffness, from the assembly feature requirements that
are necessary for the precision attachment of the platens, the cleaning station, and the
gantry components.
7
7.1
Detailed Design of the Machine Lower Structure
Design of the Top Table
Since granite can be lapped to a flatness of 0.0005in over areas as large as 5940in2
and since it can also resist the corrosive properties of the slurries present, it was chosen to
be the material for the Top Table. The basic design of the Top Table is a platform large
enough to hold all the necessary components and thick enough to withstand the weight of
the gantry that rides on top of it. The table is also the central piece, upon which nearly all
components of the machine are mounted. The design starts out with a large, thick slab of
granite with two large holes to hold the two platen assemblies. The assemblies are
designed and built as separate modules that are then assembled onto the table (See section
14). The following figure shows this initial stage of the table design. Although the actual
table will be made of granite, it is shown in green metallic color so that the described
features can be seen more clearly.
48
Figure 23. Rendered view diagram of the Top Table showing the largeplaten holes.
The two large holes are actually slightly larger in diameter than the component of the
platen assembly that will be placed inside them. This is done for two reasons. The first is
to allow for the flow of air around the platen assembly for cooling purposes. This is of
concern since the large motors used for the platen spindles can generate a substantial
amount of heat. The second reason is to allow the fine positioning of the platen
assemblies inside the table to be independent of the location of the two large holes. This
relaxes the location tolerances for the holes and thus reduces cost. It is still necessary to
define the location of the platen by a method that is both repeatable and accurate. To
achieve this, a set of two smaller holes is provided on one side of each of the two large
49
holes. Steel dowel pins will be inserted into these holes in order to provide a position
reference for the placing of the platen assemblies. Once the dowel pins are in place the
entire platen assembly is placed inside the large holes and pushed until the outer rim of
the capsule (See section 13) sits against the two steel dowel pins. In this manner the
location of the assembly is kinemtacially defined in the plane of the table. This method is
used in order to satisfy the requirement on the machine to have repeatable assembly with
minimum assembly effort. The following figure shows how the capsule sits against the
outer edge of the dowel pins in the complete machine assembly.
Figure 24. Rendered view diagram showing the location pinsfor the platen assembly.
Once the position of the platen is define it is necessary to fix it to the table at that
50
position. For this purpose, 12 long 3/8 in. diameter bolts are used. The bolts will be
placed through the holes from underneath and bolted onto the capsule. Note that the bolt
holes are clearance holes and as such do not constrain the position of the capsule with
respect to table.
Figure 25. Rendered view diagram showing the bolt clearanceholes for the platen
assembly.
Next, holes necessary for the mounting of the gantry rails are provided. Next to
each row of holes, is a groove that will run the length of the rails. This groove is provided
to position a linear encoder strip to be used to sense the exact location of the gantry with
respect to table. In addition, in order to prevent chipping of the granite table, all outer
51
sharp edges are rounded with a Iin. radius.
Figure 26. Rendered view diagram showing mounting featurefor the gantry linear
encoder strip.
In similar fashion as the platen assemblies, three steel dowel pins are used to
define the location of the rail with respect to the table. Unlike the platen assemblies, the
rails are not circular. Therefore it is necessary to define their orientation as well as
position and thus three dowel pins are required. The following figure shows the location
of these holes and the threaded insert holes that are provided for the mounting of the xaxis motor and ballscrew brackets.
52
Figure 27. Rendered view diagram showing the mountingfeaturesfor the gantry rails
and motor, and ballscrew brackets.
In addition, four other, relatively, large conduit holes are cut out of the gantry as shown.
The circular conduit in the middle of the table is to allow for the passage of fluid lines
required for the washing station that will be mounted in the center of the machine. The
two rectangular conduits are used to deliver de-ionized water to the splashguards and
slurry over the top of the platens. Finally, the smaller circular conduit which is off to one
side will be used to deliver power and sensor electrical lines to the gantry. These lines
will be used for power and sensors for the head spindle, wafer carrier, and z-axis stage.
53
Figure 28. Rendered view diagram showing conduits in the Top Table.
At this point, it is necessary to provide a means of attaching the Lower Frame to
the table from underneath. For this purpose, 8 holes are drilled along the long edges of
the table and two along the short edges, as shown. In addition, in order to provide a
means of attaching all machine components that are placed underneath the table, a total
of 18 other lin. diameter,
in. deep clearance holes are drilled underneath the table.
Metal inserts with threaded holes will then be placed inside all of these holes and epoxied
to the granite. These threaded inserts will be used to fasten the Lower Frame sections and
mounting brackets, used for the attachment of different components, to the table.
54
Figure 29. Rendered view diagramshowing clearanceholes for metal insets.
Once all the features of Top Table are completed it is necessary to make sure the
top and bottom surfaces of the table are both flat and parallel to each other. To achieve
this the granite table is first placed, top face down, over a bed of molding sand. Next, the
table is pounded upon over the top. This will help settle the table evenly in the molding
sand. In this manner, the molding sand provides complete and well distributed support
underneath the table. At this point, the bottom surface of the table, which is now facing
up is lapped flat. Since the table is supported everywhere underneath it will not deflect at
all under the loads exerted by the lapping tool during the lapping process.
55
Figure 30. Rendered view of the lapping configurationfor the Top Table.
Once this is done, the table is turned around and again placed on a bed of molding
sand with the bottom surface facing down as shown in the following figure. Again, the
table is pounded upon from the top. Three conical metal stops in the sand will serve as
point supports that define a plane parallel to the base axis of the lapping tool. This is done
to make sure that the bottom surface of the table is parallel to the axis of the lapping tool.
At this point, the top surface of the table is lapped flat and parallel to the bottom surface.
7.2 Attachment of the gantry rails to the table
One of the main concerns with choosing black granite as a material for the Top
Table, is the difference between its coefficient of thermal expansion and that of the
stainless steel rails for the gantry. The coefficient of thermal expansion for stainless steel
0
is 17.2x1061/ 0C compared to 3.89x1061/ C for granite. During its transport, storage, and
0
0
operation this machine is expected to experience a temperature range of 5 C-45 C. The
0
the
target ambient temperature for the operation of the machine is 25 C. The latter is also
56
temperature at which the machine will be assembled. In a worst case, the machine will be
20 0C hotter or colder than its original assembly state. During the 20 0C temperature
transition, the stainless steel rails will contract or expand more than the granite table will.
If the rails are simply bolted into the granite, then the bolt shanks will experience axial
stretch and shear, as shown below.
BOlt
Stainless
Granite
Figure 31. Schematic diagramof a bolt being subjected to shearbetween two materials
with different amounts of expansion.
In a worst case scenario, the rail will be fixed to the granite table only at the two ends,
with the bolts in the middle being too loose to take any of the load. In the latter case the
strained length, which is the maximum length that could be strained under these
conditions, is 80in (the full length of the rail). Assuming that the rail is simply bolted into
the granite, and the two end bolts do not fail in shear, then the rail and granite table are
forced to have zero elongation relative to each other. Since the rails sit flat against the
granite, the strained length is the same for both materials. This requires that the strains
also be the same. The strains for the rails and the granite table are given by Eq. 6 and Eq.
7 respectively, where AT is 20 0 C and a is the coefficient of thermal expansion for each
material.
57
(Eq. 6)
Eral =
(Eq. 7)
rad
+ a,,teAT
Etable =Otable +agraniteAT
E granite
As was mentioned before, the strains in the two materials must be equal, hence Eraii =
Egranite = E0. Furthermore, the stresses araii and
Ttable
are exerted on one material by the
other. Thus, by Newton's third law, the forces that the rail and table exert on each other
must be equal and opposite. The latter relation is expressed by the equation below, where
Araji is the cross section area of each rail and Atable is the cross sectional area of the granite
table.
2
(Eq. 8)
AraiOyraii =
Aabletable
Note that the cross sectional area of the granite is not constant along its entire length. In
some regions, the cross section area is much smaller due to holes for the conduits,
cleaning station, and platens. The following can be seen in Figure 29.
However, a solid granite table is less conforming and exerts more stresses on the
bolts than one with the holes. Therefore, as a factor of safety, the calculations are done
for a solid granite table of the same size where Atable is the maximum cross sectional area
of the Top Table rather than its average cross sectional area.
The shear stress in the bolt cross-section between the granite table and the steel rail is
given by Eq. 9 below.
(Eq. 9)
1,bo,
_
rail Arail _ jrgranitelAgranite
Abol,
2A
Solving the above equations using Estee= 215GPa and Egranie= 78.4 GPa yields the
following values:
58
Urail =
Uable =
E0
=
-5.67 x l0 7Pa = 56.7 MPa (in compression)
1.601 x l0 5Pa = 106.1 KPa (in tension)
Erail = Egranite= 7.984
rbolt =
x 10-5
7.173 x 10 8Pa = 717.3 MPa
Note the latter calculation is a worst case scenario where: the two end bolts are the only
bolts resisting the difference in thermal expansion; they are loose enough such that the
contact friction between the rail and table does not take a substantial amount of the load;
and both bolts are sitting against the inward facing surfaces of their clearance holes.
While the latter situation is unlikely to occur, it is possible for it occur within the
manufacturing tolerances and thus should be considered.
The 0.2% offset yield stress ayield for stainless steel is around 450 MPa depending
on the stainless steel type. The latter value is obtained from the widely used uniaxial
tension test. In such a test the maximum shear stress that material experiences occurs
along a plane at 450 from the cross section area, as shown in the figure below.
59
Planes of
Max. or Principal
4
q45'
ESpecimen
X~
Figure 32. Schematic of a material specimen undergoing the uniaxialtension test.
The equation for principal shear stress given below shows that the value of the principal
shear stress during a uniaxial tension test is half of the measured principal normal stress,
where ax is the measured stress and ay and xy are equal to zero.
(Eq. 10)
I
=
Ix
y )2
+
2
+r
X
Since yielding occurs along the shear planes for most metals, it is appropriate to assume
that the stainless steel specimens that yields when the principal normal stress is 450MPa
can at most withstand 225MPa in shear before failure. Therefore, the stainless steel bolts
60
used for the rails will fail if they experience 717.3 MPa in pure shear. As a result it is
unsafe to fix the rails to the granite table by simply bolting them down.
Another alternative is to design the fastening method such that the bolts can
deflect and compensate between the difference in the strains of the rails and the granite
table. One way to do this is to have the bolts penetrate all the way through the granite
table and fasten into nuts on the other side as shown in the following figure.
II
Figure 33. Rendered schematic of thru hole bolt design.
In this manner if the holes that bolts penetrate through are made larger than the bolt body
diameter, then the bolt body has to room to deflect laterally within the granite table. The
bolt counter-sink hole in the rail holds the head section of the bolt tightly. The use of a
61
plug (shown in red in the figure above) then holds the other end of the bolt tightly as
well. In this manner the entire bolt body acts as a beam that is fixed at both ends. In the
neutral (Assembly Temperature) state, the boundary conditions at both ends are zero
translation and zero angular deflection. As the rail and table system experience a
temperature change, the difference in the strains causes the counter-sink in hole the rail to
move with respect to the corresponding bolt hole in the granite table. In this latter case,
while the fixed end that is held by the plug still has zero translation and angular
deflection, the end that is held by the rail hole has a finite displacement corresponding to
the relative motion caused by the difference in the expansions. Note that the bolt is now
acting like a fixed/railed beam with no distributed load over it. Note also that both ends
of the bolt still have zero angular deflections. A 2-D schematic of the two states is shown
below with appropriate coordinate systems.
olt Head
Neutral State
Rail
Strained State
Bolt Head
Rail
Bolt
Bolt
Plug
Plug
Figure 34. 2-D schematics the bolt being modeled as a fixed/fixed beam in both the
neutral and strainedstates.
62
In the coordinates of the figure above, x is the measure of distance along the length of the
bolt body and v is the measure of deflection at each point on x along the body.
The following section quickly reviews the derivation of the beam equations to
show that they can be applied to the beam model of the bolt in this design.
The following figure shows the convention used for representing the internal
forces V(x) of the bolt. Note that by this convention a positive distributed load has the
units of force per unit length (N/in) points up on the beam, where x points to the right.
q(x)
M(x)
/(X
M(x+Ax)
V(x+Ax)
/
\-IPoint
A
Ax
Figure 35. Schematic of Ax long section of the bolt at location x.
63
In the convention shown above, the internal force V(x) is pointing down on the right and
up on the left. This is logical, since any section Ax that is being pulled down on the right
hand side in turn pulls up on the left hand side of the next section Ax that is to its right. In
addition, even though q(x) varies with x it can be assumed to be constant over a section
Ax for very small values of Ax. Using this assumption and taking the sum of forces in the
vertical direction and setting them equal to zero yields the equations below. Note that
even though q(x) is zero for case of the bolt, no assumptions have been made in the
derivation that make the following equation invalid for the bolt case.
SFY, =-q(x)Ax+V(x+Ax)-V(x)=0
q(x)Ax=V(x+Ax)-V(x)
hm
.
.
.Oq(x)= hm
V(x+Ax)-V(x)
0O
Ax
q(x) = dV
dx
q(x)=O
V(x) =fq(x)dx + A = A
(Eq. 11)
Using the section shown in Figure 35 again, and taking the moments about point A and
setting them equal to zero yields the following equations.
E
MA =M(x+
Ax)- M(x)-V(x)Ax -q(x)Ax
2
=0
For very small values of Ax, the value of Ax2 is a second order term and small enough to
be considered negligible. As a result the term q(x)Ax2 is ignored.
V(x)Ax = M(x+ Ax) - M(x)
64
lim
.V
-O V (x) =hlm A-O'
V(x)=
(Eq. 12)
M(x+Ax)-M(x)
AAx
dM
M(x)=JV(x)dx+B=Ax+B
It is also expected that any beam under loading, including the bolt beam model,
will experience both angular and translation deflections. The figure below shows a Ax
long section of the beam experiencing an angular deflection of AO, where AO is in
radians.
A
/
/
/
\
\
\
t/
t/ 2
S
Ax
Figure 36. Schematic of Ax long section of the bolt under angulardeflection.
65
Using the constitutive relationships and the figure above, the angular deflection at any
point on the beam section can be related to its internal Moment at that point. The main
constitutive relationship that is being used is e
Mt
-_2
EI
==AV2
Ax
Ax
AO
Ax
MV2
EI
M
EI
For very small values of Ax and AO, the above equation can be expressed as:
dO
dx
(Eq. 13)
1
O(x)=-
EI
M
EI
x
r1]l
M(x)dx+C =-IA[
EI 12
2
+Bx+C
Finally, in order to relate the angular deflection of a point on the beam to its translation
deflection, the small angle assumption that O=sinO is used (again ignoring second order
and higher terms). This assumption imposes the condition that the angular deflection O(x)
along the entire bolt length be checked after the calculations are done to make sure they
are small enough. The figure below shows a Ax section of the beam experiencing both
angular and translation deflections.
66
Av
Figure 37. Schematic of Ax long section of the bolt under translationdeflection.
Using the small angle assumption:
AO =sinAO=-
0(x)
(Eq. 14)
=
Ax
dv
dx
v(x)=f(x)dx+D=--A'
EI
6
BX 2
2
+Cx+Dj
Note that the derivation above along with all of the assumptions made still apply to the
case of the bolt as well where E is the modulus of elasticity of stainless steel and I is the
area moment of Inertia of the bolt cross section.
The deflection at any given point on the rail is the product of the strain, which is
equal everywhere on the rail, and the length of rail that is being strained. Therefore given
a 20 0C change in temperature, the deflection of the rail will be highest at a point that is
furthest away from the next fixed point. The worst case scenario would be one where the
rail remains fixed to the granite table at one end and moves with respect to the table at the
other end. In such a case, the bolt at the moving end would have to deflect in order to
67
compensate for the difference in the thermal expansions of the two materials that it is
attached to. Note that the rails and granite table are still not free to expand and contact
independently of each other. The rails and the granite table are still able to exert forces on
each other through the bolt. In fact, the deflection of the bolt is the result of the load
interactions that are taking place at its two ends. These interactions will still force the
granite table to expand and contract more and the steel rails to do so less than they would
independently of the system. The following analysis is done for a +20 0C change with the
rails being compressed and the table being stretched as a result. The same results apply to
a -20 0C change with the signs of the stresses reversed for each component. The analysis
is also done in the reference frame of the granite table for a bolt of length L=8in.
The following are the boundary conditions imposed on the beam.
At x=O
At x=L
v(O)=O
V(L)= UraijArajj
0(0)=O
6(L)=O
v(L)=(Erail-Etable)(lengthof rail)
Table 1. Table of boundary conditions.
In this case equations 6, 7, 8, & 9 still apply. The nine equations 6-14 can be solved to
yield the nine unknowns: Erail, Etable, Grail, Gtable, Tbolt, A, B, C, and D. The detailed solution
is included in the Appendix Section. The results of the analysis are included in the table
below. In addition, once the values of Eraji and
Etable
are calculated, they are used to
calculate the difference in the position of the bolt head relative to the plugged end of the
bolt along the v-direction (along the length of the machine). Using the triangle formula
this difference is used to calculate the resulting axial stretch that occurs in the bolt.
68
Thereof, the axial strain and stress in the bolt is calculated and used along with the shear
stress on the v plane (Tbolt), to calculate the maximum shear stress that will occur at the
bolt head.
Value
Variable
Value
4 ftax
3.5390 x 10-
A
-13.268 N
7.7801 X 10--
ol
760.88 KPa
B
+1.3480E Nm
ara
-33.169 KPa
Tbolt
418.94 KPa
C
0
Oiable
93.499 Pa
Tmax(bolt)
565.90 KPa
D
0
Variable
Value
Erail
3.4385 x 10-
Atable
Variable
Table 2. Results of the Beam Calculations.
As can be seen from the results above, the maximum shear stress under the bolt head has
been reduced considerably by a factor of 1000 and is now well below the yield stress of
the material in shear. As a result, it was decided to use this method to bolt the gantry rails
onto the granite table.
7.3
Design of the Lower Frame
As was mentioned earlier it is desired for the Lower structure to have good
damping characteristics. Since the Lower Frame does not have to satisfy the precision
assembly requirements of the Top Table, it can be made from a wider range of materials
that satisfy the damping requirement. In fact, other than good damping characteristics, the
requirements of the Lower Frame are minimal. It must be stiff enough to hold the weight
of entire machine and it must provide room for the mounting of other machine
components under the granite Top Table. In addition, since the Lower Frame is not in
69
direct contact with any of the polishing equipment, and since it is not a critical moving
part itself, it can be protected from exposure to the corrosive slurries used. As a result, it
is not a requirement for the Lower Frame to be made of a material that is resistant to high
or low pH.
There are several materials that can be used for the Lower Frame. Some of these
were discussed in section 6.1 on page 38. While most of the analysis detailed in section
6.1 was carried out on the preemies that both the Top Table and Lower Frame had to be
made of the same material, many of the advantages and disadvantages detailed in that
section still apply. Stainless Steel for example still does not have adequate damping and
is prone to resonance vibration. In most smaller scale structures, the resonance frequency
of stiff material such as steel is rather high. In this application, however, the Lower
Frame has to be both large and hollow in order to support the entire length and width of
the Top Table and to provide space for all of the support components. As a result, a lower
resonance frequency can be expected and damping the structure is more critical.
Considering this critical need for a material with high damping, the best material
choices for Lower Frame are cast polymer resin or cast iron. Cast polymer resin is more
expensive than cast iron, and it is not yet as widely used in machining tools. In addition,
the material was not used in the test bed machine that is the predecessor to this one. At
the same time, cast iron has been very widely used by both this institution and many
commercial manufacturers in frames for machining tools for many years and has proven
itself to be a material of choice for this purpose. As a result, without previous experience
with cast polymer resin, it is difficult to safely justify its use over cast iron for the
70
purposes of this machine. Thus, cast iron was chosen as the material for the Lower
Frame.
Although the overall size of the machine and specifically its footprint are
important factors, its weight is not. As result, in order to increase the damping and
stiffness of the entire machine, it is best to use as much cast iron as possible without
compromising the amount of free space provided under the Top Table. For this reason, it
was decided to make the entire Lower Frame as a continuous four walled box structure
instead of several isolated legs. The design of Top Table starts out simply as a box made
from two long side pieces and two shorter end pieces, all of which are 4 in thick. The
following figure shows an exploded view of the basic design at this stage.
Figure 38. Rendered view diagram of the Lower Frame cast iron plates.
71
The two end pieces enclose the two side pieces on either side as shown in the previous
figure. The arrows indicate the assembly of the cast iron pieces. In order to provide
convenient access to all components located under the Top Table, access ports must be
provided through each of the four sides. The two end pieces are cast with two circular
ports and the two side pieces are cast with two rectangular ports with large radius corners.
The following figure shows the basic features of the Lower Frame in assembled form.
Figure 39. Rendered view diagramshowing access ports in the Lower Frame.
Next it is necessary to provide the fastening features that will hold the four cast iron
pieces together. For this purpose eight bolts, each lin. in diameter, and four positioning
72
steel pins will be used to attach each of the end pieces to each of the long side pieces.
Each side of the end pieces is drilled with two sets of three holes. Each of the three hole
sets has a center hole for a steel pin and two outer holes for the bolts. The following
figure shows the hole pattern for each side of the end pieces and how they mate with the
holes on the edges of the side pieces. Notice, since the edges of the side pieces mate with
the end pieces, they are critical surfaces and are machined after the pieces are cast.
Figure 40. Rendered view diagramshowing the bolt patternsrequiredfor the assembly
of the Lower Frame.
Similarly, the locations on the inner face of the end pieces where the side pieces touch are
also critical surfaces and are machined as shown, after the pieces are cast. For the long
73
side pieces it is critical that the two finished edges be parallel to each other. In addition,
for the two end pieces it is also critical that the finished surfaces be coplanar. It is not
however critical for the latter finished surfaces to be parallel to the cast outer side of the
end piece.
Finished surfaces
Figure 41. Rendered view diagram showing necessaryfinished surfacesfor the Lower
Frame.
Although the granite Top Table will sit on the top edge of the end pieces, it is also not
critical for the finished edges on the end pieces to be perpendicular to the two long edges.
Once the entire cast iron box that makes up the Lower Frame is assembled, all of the top
edges of all of the four sides will be finished as shown below by lapping them all at once
74
in one pass. Then the entire box is turned upside down such that the previously finished
edges sit flat on a base that is parallel to the axes of the lapping tool and the bottom edges
of all four sides are lapped flat and parallel to the top edges.
Figure 42. Rendered view diagramshowing the Lower FrameAssembly ready for
lapping.
Once that is completed, it is necessary to provide a means of fixing the Top Table to the
cast iron box. Although there are no appreciable loads that would lift Top Table off of the
Lower Frame, and although the Top Table is a very heavy object, it is still safe practice to
fasten the Top Table to the Lower Frame. At the very least this will allow for the
transport of the machine without the need for disassembly of the Top Table from the
75
Lower Frame. For this purpose, eight 1 in. diameter bolts are used in each of the long side
pieces and two in each of the end pieces as shown below.
Figure 43. Rendered view diagramof completed Lower Frame.
76
Figure 44. Rendered view diagram of the assembly of the Top Table onto the Lower
Frame.
Next, the Top Table is placed on top of the Lower Frame in the correct position. The
position of the Top Table is not every critical and thus steel dowel pins are not used in the
part of the assembly. In addition, the holes that are drilled in the Lower Frame have
clearance from the bolt body diameter to allow for relative misalignments and as such do
not impose any requirements of their own for accurate positioning of the Top Table
during assembly.
Previously, it was mentioned that the making of the Top Table is finished by
placing it flat on a bed of molding sand, lapping one of the sides, turning it upside down
77
and lapping the other side in order to insure that both sides are flat and parallel. This
method is a general method for achieving two flat and parallel surface. Another
alternative is to first place the Top Table, top face down, on a bed of molding sand.
Pound on the Top Table until it is level and the molding sand provides even and well
distributed support. Then the bottom surface of the Top Table is lapped flat. This setup is
identical to the one shown in Figure 30. At this point, however, the Top Table is
assembled onto the Lower Frame, with the finished bottom surface of the Top Table
sitting flat on the top finished surfaces of the Lower Frame.
Next, the entire assembly is placed on a flat bed on the lapping machine and the top
surface of the Top Table is lapped. This latter method provides certain advantages over
the previous method. Since the top surface of the table is lapped flat with entire machine
assembled, it insures that this surface is flat and parallel to the bottom surface of the
Lower Frame. This is the case regardless of any error in the parallelism or flatness of the
bottom surface of the table or the top surface of the Lower Frame. This latter method also
has some disadvantages. When mounted upon the Lower Frame, the Top Table is only
supported under its outer edge perimeter. As a result it prone to deflect under the loads
from the lapping process. However, since the table is eight in. thick, this does not pose a
significant problem and the latter method is recommended over the one detailed in the
section 7.1.
78
8
Platen Assembly
As was mentioned before, the rotary configuration involves two rotating bodies,
consisting of the pad and the wafer, that are lapped against each other. The pad is
attached on to a rotating platen, which rotates inside the platen spindle assembly. The
platen assembly consists primarily of the platen; the drive system, which includes the
motor, encoder, and torque transfer components of the spindle; the bearings; and the
capsule, which holds the spindle bearings and motor stator. The platen assembly must
satisfy certain design requirements in order to provide for the necessary process
parameters. The first and perhaps most important design parameter is to insure a uniform
velocity profile across the wafer surface, and to insure a specific, desired magnitude for
the relative polish velocity. To achieve the first, the platen must rotate at the same speed
as the wafer as can be seen from Eq. 2, and to achieve the latter both the platen and the
wafer must rotate at a specific desired velocity. As a result the platen and wafer drive
systems must provide both precise (repeatable) and accurate rotational velocities.
Another design consideration is to insure that the polishing force is constant during each
stage of the polishing process. However, any axial runout in the platen spindle, can cause
variations in the polishing force. Furthermore, any axial or radial runout of the platen
spindle can induce vibrations in the entire machine. As a result, another design
requirement for the platen assembly is to minimize the axial and radial runouts of the
bearings used in the spindles. In addition, the machine requires an optical endpoint
detection mechanism to be used to indicate the end of the process. This device is intended
to measure reflected light from the wafer surface as a means of detecting the presence of
copper. Therefore, another requirement for the platen assembly is to provide the
79
necessary space for embedding such a device and all of its supporting components inside
the platen. And finally, to provide the machine with the necessary flexibility of a research
tool, it will be equipped with the option to supply slurry to the pad through the platen or
over the top.
9
Torque and Speed Considerations
The main purpose for the spindle is to provide the rotary motion necessary for
polishing to occur. The spindle must provide this motion while resisting the friction force
that due to contact of the wafer with the pad under the exerted normal load. Since the
wafer platen centers are offset, the force due to the friction exerts a torque that the spindle
motor must overcome. To quantify this torque it is desired to know the coefficient of
kinetic friction pu between the wafer and the pad. However, data from the supporting
research group shows that p is not constant. This data shows that p is a function of both
relative polish velocity and polish pressure. More specifically, it is assumed that g is a
function of the ratio of velocity over pressure denoted from here on by R. The following
graph shows the relationship between and R obtained from data from experiments carried
under a constant pressure of 7 psi and varying velocity.
80
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.2
0.4
0.6
1
0.8
PaX
R__
M/s
104
Figure 45. Coefficient of kinetic friction as a function of the ratio ofpolish pressure over
polish velocity for 7psi pressure.
The latter data was used to calculate M as a function of polish velocity and
pressure. Since there are only six data points in the provided data, it was necessary to
curve fit the data to obtain values of. However, curve fitting the data with a seconddegree polynomial results in a curve that does not match the data well. Fitting the data
with higher order polynomials matches the data better, but it is impossible to justify that
the actual behavior should follow a high order polynomial behavior. As a result, the data
was fitted by a piece wise linear fit between each consecutive two points exactly as
shown in the previous figure. The following figure shows P as a function of polish
pressure and velocity based on the latter stated relationship.
81
0.3
0.2030.1
3
6
Velocity (rr/s)
0
0
4
2 Pressure (Pa)
X1
Figure 46. Coefficient of kineticfriction as a function of polish pressure and velocity.
A gross assumption has been made here that can not be verified because of a lack of
data. As was mentioned previously the data that is available is from experiments carried
out at a polish pressure of 7 psi. As a result this data is only truly valid for 7 psi and is not
a truly taken as a function of two variables but rather as a function of only the velocity at
a given pressure value. However, general research done in this field suggests that the
amount of material removal during the polish process is a function of R. Specifically, it is
proposed that the amount of material removal is given by the following equation, also
know as the Preston equation where k is the Preston constant.
(Eq. 15)
pressure
Material Removal Rate = k - velocity
.eoct
Material removal occurs partly because of the transverse force that the pad exerts on the
wafer surface. The fact that the material removal rate under a constant normal load drops
as the velocity increases suggests that the value of y might also drop with increased
82
velocity. In addition, since the pad is a compliant material with a rough surface it is also
assumed that increased pressure will increase the engagement of the pad and wafer
surface elements. Thus for the purposes of obtaining the motor torque and power
requirement p will be assumed to be the same function of R for any pressure as it is for
7psi. Once y is obtained for the required polish velocity and pressure ranges, the torque
and power requirements for the motor are then calculated using the following functions
where smax is the maximum wafer offset distance that can occur during wafer sweep.
Torque = y -(s.
(Eq. 16)
)- Polish Pressure-Wafer Surface Area
Power = Toque -Relative PolishVelocity
(Eq. 17)
The following two figures show the required motor torque and power as a function of
relative polish velocity and polish pressure.
200
150
Torque (Nm)
100,
50,e..- -
3
2
-6
Velocity (ni/s)
X 4 4
2
Pressure (Pa)
x 10
00
Figure 47. Required motor torque as afunction ofpolish pressureand velocity.
83
Power (W)
3
Velocity (mis)
1.
4
2
0
Pressure (Pa)
0
Figure 48. Required motor power as a function of polish pressure and velocity.
These calculations were done for speeds up to 3m/s. While it is desirable to operate
the machine at speeds as high as 4m/s as well, to save cost and space, the motors are
chosen to have a nominal maximum speed that achieves 3m/s. When necessary they can
be overdriven for short periods of time to achieve 4m/s. Considering that the nominal
polishing speed that machine will be operated at, most of the time, is around 0.7m/s it is
not justifiable to use large expensive motors that can operate at 4m/s for longer periods of
time.
10 Chosen Motor
There are several methods to drive the platen spindles. The first method is to use a
belt drive to drive the platens. A belt drive system can be used to drive both platens using
one motor, as shown in Figure 6, or it can be used to drive each platen separately.
84
Another method, is to use a gear mechanism to drive the platens. This method can also be
implemented such that a single motor drives both platens. The third and last method is to
drive the platens using frameless motors where the rotor is attached to the platen and the
stator is attached to the capsule. No drive train is used with the latter method. The latter
method also requires that each platen have its own motor. The following table shows the
advantages and disadvantages of each of the three methods.
Advantages and
Belt Driven System
Gear Driven System
0
0
-1
-1
-1
1
-2
-1
0
-1
-1
-1
0
-4
System
Disadvantages
Quite Operation
Speed Control
Maintenance
Space Requirements
Particle Generation
Cost
Total:
Frameless Motor
1
1
1
1
1
-1
4
Table 3. Tabularassessment of advantagesand disadvantagesof the three different drive
systems.
It is clear from Table 3, that the frameless motor design is the best option out of
the three. It provides the quietest operation since it does not contain any torque transfer
mechanisms or drive train. In addition, the absence of any rolling and sliding parts
eliminates the possibility of particle generation. The lack of the drive train components
also allows for the frameless motor to take the least amount of space among all of the
options. This is a crucial advantage considering the platen design must allow room for the
components of the end point detection mechanism.
There are many choices for companies that manufacture frameless motors.
However, several key design constraints narrowed these choices down to one
85
manufacturer, Motion Control Systems(MCS). The first and most fundamental
constraints are to provide the necessary rotational speed to achieve the desired relative
polish velocity and the necessary torque to resist the torque exerted on the platen by the
polish friction force. As mentioned before, for this purpose, a range of 0.7m/s-4m/s for
the relative polishing velocity and a range of 4psi-20psi were chosen. Using these values,
the requirement for wafer sweep, and taking into account the footprint of the machine, the
minimum and maximum values for the platen to wafer offset were calculated to be
3in.(0.0762m) and 7in.(0.1778m) respectively. The analysis for this calculation is
detailed in sections 5.2 and 12.
The MCS brushless motors are DC motors that employ a permanent magnet rotor
inside a stator made of coil magnets. The rotation of the rotor relative to the stator is
achieved by commutation of the stator coil magnets. In order to know the required state
of the commutation it is necessary for the motor controller to know of the position of the
rotor relative to the stator. This is achieved by mounting an encoder on the rotor.
Although this type of motor requires the addition of an encoder, it does eliminate brush
contacts and any particle generation that may result from them. Furthermore, a rotormounted encoder is necessary for measuring and controlling the rotational speed of the
platen, regardless of the type of motor that is used. Thus the incorporation of an encoder
is a necessary design requirement anyway and is not considered as a disadvantage due to
the use of the MCS motor. MCS already provides a servo amplifier that uses the encoder
pulse counts to adjust the motor commutation to provide a specific torque. This serves as
a torque control system that can then be used by another control system to control the
speed of the platen.
86
There are several options for mounting a frameless brushless DC motor onto the
platen and capsule. The first is to clamp the rotor and stator as shown in the following
figure.
laten
Stator
Rotor
Figure 49. Schematic of Rotor and Stator clampedfits.
In the latter design, running-fits (R1) are used for the mounting of the platen to
the rotor and the capsule to the stator. Special retaining rings are then used to hold the
rotor and stator onto the platen and capsule, respectively. These rings are bolted into the
platen and capsule as shown in the figure above. Since running fits can not transmit
torque, the only means of transmitting torque between the capsule and platen is through
the retaining rings and the contact surfaces opposite them. With this design the use of a
key-way may be necessary to transmit the required torque.
Another way to mount the motor is to press-fit the rotor and stator into their
respective housings as shown in the following figure.
87
Stator
Platen
\Rotor
Figure 50. Schematic of Rotor and Statorfits
In this design no clamps are used to hold the rotor and stator in their respective
housings. Instead, the friction from the press-fit(F1) is relied upon to keep the rotor and
stator in place and to transmit the necessary torque. A press-fit is achieved by designing
for interference between the two mating parts. The degree of interference is designed
such that the parts can be pressed together with a reasonable force. In addition, care must
be taken to insure that the parts do not deform as a result of the forces induced during the
press-fit process and thereafter due to presence of the press-fit. For this purpose the
values for the required interference were obtained form appropriate charts based on the
diameter of the mating surface. Furthermore, the walls of the platen and capsule would
have to be made thick enough to withstand the necessary forces.
88
Yet another design is to shrink fit the rotor and stator into their respective
housings. This design is very similar to the press fit design shown in Figure 50 and
differs only in the manner in which the two parts are assembled. As with a press-fit
design, the mating parts are designed with desired amount of interference. However,
instead of forcing the two parts together, the parts are heated or cooled to specific
temperatures to allow them to slide into on another with the ease of a running-fit.
Thereafter, once the temperatures of the parts equalize to ambient temperature, the same
tight fit as that of a press-fit is achieved. If the two parts are of the same material, then the
inner parts is cooled and outer part is heated for the shrink fit. In this manner, the inner
part will contract and the outer part will expand according to their coefficients of thermal
expansion. Then the two parts are assembled rather quickly before their temperatures
have a chance to equalize. Once their temperatures have equalized to ambient
temperature, the inner part expands and the outer part retracts to achieve a tight fit
between the two parts. Disassembly without risk of damage to either the motor or the
housing is not possible with this option.
If the two mating parts are made of different material with different coefficients
of thermal expansion a different method is used for the shrink fit. If the inner part's
material has higher coefficient of expansion than the outer part's material, then both parts
are cooled down below their ambient operation temperature. When this is done, both
parts will contract. However, the inner part, which has a higher coefficient of expansion
will contract more than outer part. As a result, the inner part will slide easily into the
outer part at the cooler temperature, even though the two parts are designed to have an
interference fit at their ambient operation temperature. Once the two parts warm back up
89
to their operating temperature, they will achieve a tight interference fit. If the outer part
has a higher coefficient of thermal expansion than the inner parts, then the two parts are
heated to some temperature above their ambient operating temperature. This causes the
outer part to expand more than the inner parts and allows for the inner part to simply slide
in place. Again, once the operating temperature is reached a tight interference fit is
achieved. As with the press-fit and running-fit, there are charts that can be used to obtain
the right amount of interference, for all of the shrink fit types mentioned, based on the
diameter of the contact surface and the temperatures involved. This latter option also
allows for the possibility of disassembly without damage to either the motor or housing.
For disassembly, the motor and housing is either heated or cooled to the temperature at
which it was assembled and the parts are taken apart.
Finally, another novel way to mount the rotor and stator into their respective
housings, is to use a sliding fit with the use of an adhesive agent to hold the two pieces
together. With this method, the two mating parts are designed to have a tight sliding fit.
This fit is tighter than a running fit but has no interference between the mating parts. In
order, to hold the rotor and stator in place and to transmit the required torque an adhesive
agent is used. In this case, locktite would be used since it provides the necessary adhesion
to transmit the required torque.
Each of the methods detailed above poses its own advantages and disadvantages.
The clamping method offers the possibility of easy disassembly at the expense of greater
design complexity and poorer alignment. Although frequent and easy disassembly of
nearly all of the platen assembly components is desired, in particular there is no foreseen
90
need for the disassembly of the rotor from the platen or the stator from the capsule for
this machine. As a result, the extra design complexity of this method is not justified.
While the press-fit method provides for very precise alignment between mating
parts it also poses certain risk of damage for the mounting of the stator into the capsule.
The MCS stators are made of sheets of steel that have been laminated together and have
coils of wire wrapped around them. According to the manufacturer, there is a risk that the
sheets of steel will delaminate as a result of the sheering force exerted upon them by the
capsule wall during the press-fit. Since these motors cost $5,914.00 each, and since the
bulk of that cost is for the production of the stators, the extra risk posed by the use of a
press-fit does not justify the precise alignment that it offers. As a result, a shrink fit was
considered to strike a compromise between the clamped-fit and press-fit options.
However, a shrink fit of two materials of different coefficients of expansion is not really
possible in this case since the platen and capsule have to be made of stainless steel in
order to withstand the corrosive properties of the slurries that they will be exposed to. A
shrink-fit procedure for parts with the same material can be used in this case. However,
the shrink-fit procedure must be carried out fast enough in order to prevent the
temperatures of the two parts from equalizing to each other. If the temperatures of the
mating parts do equalize to each other in the middle of the procedure, then the two parts
will be permanently stuck to each other. In such a case, even if both parts are not
damaged beyond repair, most likely, one of the parts will have to be sacrificed to save the
other. In addition, the B44-38 motor chosen has a diameter of 17.500 in. and a stator
height of 1.500in. This is a very wide and relatively short motor with a diameter to height
ratio of 11.67. If the stator is not introduced into the capsule with the two axis of rotation
91
aligned perfectly parallel, then there is a high risk that the stator may tilt sideways and get
caught inside the capsule, part of the way through. This situation is very similar to that of
a self-energizing break where any further forward motion of the stator inside the capsule
will cause it to tilt even more. As a result, the shrink fit option is of particularly high risk
for this motor and the adhesive-fit seems to be the best option of all five for mounting the
motor. Since it incorporates a very tight sliding fit, it offers a precision in alignment that
is comparable to that of the press-fit. At the same time it offers none of the risks of a
press-fit or a shrink-fit. In addition, since locktite can be melted at 600'F, the adhesion-fit
also offers the possibility of disassembly similar to that of a shrink-fit between two
different material. The overall advantages and disadvantages of all of the five methods
have been listed and rated in the following table.
Advantages and
Clamp-fit
Press-fit
Disadvantages
Precise alignment
Ease of assembly
Possibility of
disassembly
Risk of damage
during assembly
Degree of
damage
Complexity of
Shrink-fit
Shrink-fit
(Partswith
different
coefficients of
thermal
expansion)
(Partswith the
same coefficients
of thermal
expansion)
Adhesive-fit
-1
1
3
1
0
-1
1
-1
2
1
-1
-1
0
1
1
1
-1
1
-2
1
1
-1
1
-2
0
-3
3
0
1
3
2
1
4
-4
6
design
Total:
Table 4. Tabular assessment of advantagesand disadvantagesof the four different
methods for mounting the rotorand stator into their respective housings.
92
11 Bearing Selection and Design
The kinematic requirements for the bearings of this spindle are very simple. Like
most other spindles, the bearings of this spindle design should allow for only one
rotational degree of freedom about the spindle axis. This basic requirement can be
achieved in a multiple number of ways, each of which offers certain advantages and
disadvantages. In certain cases, where the loads on the system are not very large, this
basic requirement can be satisfied by the use of one ball bearing as shown in the
following figure.
Shaft
Outer Race
Ii/z
Inner Race
Figure 51. Schematic of a shaft supported by a radialball bearing.
In the above figure it is assumed that the bearing has been mounted onto the shaft
such that it can support axial loads from the shaft. A press-fit or a clamped-fit can
93
achieve this. In such a case, the contour of the inner and outer raceways where the rolling
elements sit, are shaped such that the ball bearing can take some amount of axis loading
as well. This type of configuration can withstand the large radial loads that are exerted by
the friction between the wafer and pad during wafer sweep. However, it can not
withstand the large axial loads resulting from the polish force. In general, when the axial
loads are not very small, this type of bearing configuration should not be used. Instead, it
is best to use an axial ball bearing in conjunction with the radial ball bearing as shown in
the following figure.
Shaft
Radial Bearing
a2
Axial Bearing
Figure 52. Schematic of a shaft supported by one radialand one axial ball bearing
configuration.
94
Although the bearing configuration above provides a more complete support than that of
Figure 51, it does not offer much support for large moment loads. In the design of this
machine, the center of the wafer is offset from the center of the platen. As a result, the
polish pressure force from the wafer will exert large moments on the platen spindle.
Therefore a second radial ball bearing needs to be incorporated as shown in the following
figure, in order to withstand the necessary moments exerted.
Shafta
adial Bearing
B
ro"""xial
Bearing
Figure 53. Schematic of a shaft supported by two radialand one axial ball bearing
configuration.
The ball bearing configuration shown in the above figure can support large axial, radial,
and moment loads. It is important to mention that there are many types of rolling element
axial and radial bearings that can be used in the above configuration to provide the
95
necessary support for the loads exerted. In addition, the design of the spacing and
orientation of the bearings will affect things such as spindle stiffness and location of
thermal center and is thus much more detailed than the one shown above.
Another type of bearing that can be used for this application is a hydrostatic
bearing. These bearing have no contact elements and use a thin film of fluid, in this case
water, to provide lubrication between the two moving parts. In order to maintain a
constant thickness fluid layer, the fluid is continuously pumped into the gap between the
two parts. A general concept schematic of this type of design is shown in the following
figure. It is important to mention that the design of these types of bearings and the
regions in contact with the fluid layer is specific to the type of application and the relative
velocities and loads present.
Rotating
Compone
Flow of
Water
Stationar
Component
Figure 54. Schematic of a single direction axial hydrostatic bearing.
96
As with the contact element ball bearing, it is desired to have two separated regions of
radial constraint and one region of axial constraint in order to support the radial, axial,
and moment loads exerted. A possible design for such a configuration is shown in the
following figure.
Radial
Bearings
Rotating
compon
Axial
Bearing
Figure 55. Schematic of single direction axial, radial,and moment supporting
hydrostatic bearing configuration.
The bearing configuration shown in the figure above is no different than the one shown in
Figure 53. However, hydrostatic bearings, in general, do not have as high a stiffness as
regular contact element bearings. This is partly due to the fact that the thickness of fluid
in the fluid gap can vary depending on the loads that are exerted on the bearing.
Hydrostatic bearings can be made stiffer by pumping the fluid through the sequence of
97
gaps in a specific order as to create what is called a self-compensating hydrostatic
bearing. A concept schematic of such a bearing is shown in the following figure.
Magnified Area
Rotating
component
tationary
component
Figure 56. Schematic of an axial self-compensating hydrostatic bearing.
The bearing shown above is a simple schematic of an axial hydrostatic bearing. The
green lines represent the fluid source for the bearing. The blue lines show the part of the
flow that is supplied to the lower fluid pocket which supports downward load, and the red
lines show the part of flow which supplies the upper fluid pocket which supports upward
load. A magnified portion of this schematic is sown in the following figure.
98
Stationar
component
Rotating
Fluid Gap
component
Flow Source
Figure 57. Magnified section of an axial self-compensating hydrostatic bearing.
There are two additional fluid gaps in the magnified schematic above. These gaps
are not bearing pockets but rather pass through gaps that allow the fluid to pass through
them. These pass through gaps have smaller surface area than the bearing pockets and are
not intended to support large loads. As can be seen from the preceding figure, the flow
that supplies the lower fluid pocket (shown in blue) does not do so directly and rather
passes through the smaller fluid gap on the upper bearing surface. Similarly, the flow that
on the
supplies the upper flow pocket (shown in red) passes through the pass through gap
lower surface of the bearing. Notice also that when either of the smaller gaps is closed, it
will restrict the flow that is passing through it. In addition, because of its small surface
load. In this
area, the pass through gaps can be closed off without resisting any significant
it will
manner if the load on the rotating component is large enough to push it down,
In this
close the lower pass through gap, which supplies the upper bearing pocket.
the lower
manner, the flow rate in the upper bearing will drop and causes the flow in
99
bearing to increase since they share the same constant flow source. This will in turn
create a difference in bearing force that is opposite that of the load and will push up on
the rotating component. Similarly, if an upward load is large enough to push the rotating
component upward it will restrict flow to the lower bearing thus creating a difference in
bearing force that will compensate and push the rotating component back down (To be
brief, a more analytical explanation involving the modeling of the flow resistance at each
junction has not been included in this document). In this manner, a self-compensating
hydrostatic bearing can be made stiffer than a regular one. Although axial deflection of
the spindle bearing does not pose a problem in this application, lateral and angular
deflections can affect the rotor and stator alignment of the frameless motors. However, a
self compensating bearing in the configuration shown in Figure 55 can be made stiff
enough to be used for this spindle without large deviations under the polish load.
Yet another type of bearing that can be used is a cross-roller bearing. The crossroller bearing is also a contact element bearing like a ball bearing but uses cylindrical
rolling elements instead of spheres. In addition, the axis of each consecutive is
perpendicular to the one before. This is shown in the following rendered view figure.
Figure 58. Rendered cut-away view of a cross roller bearing.
100
The following schematic figure shows the general shape and orientation of the roller
elements. The rollers have a diameter to height ratio that is more than one. This is
necessary to insure
that each
roller contacts
the raceways
on their rolling
(circumferencial) surfaces only and does not rub on the other raceways.
First Roller Element
Next Roller Element
Figure 59. Schematic of the roller element alignment in a cross roller bearing.
As can be seen in the preceding figures, each consecutive roller axis is perpendicular to
the one before it. In this manner, a cross roller element bearing restricts all degrees of
freedom except rotation about the bearing axis. Furthermore, unlike the ball bearing
shown in Figure 51, a cross roller bearing can support large amounts of axial, radial, and
moment loads. In addition, THK, the company that makes this bearing uses a grinding
process to machine the rolling elements and the raceways. This way the bearing
components can be machined with higher precision than rolling and other machining
techniques used in the production of regular contact element bearings. THK offers these
bearings in a regular class, which has radial and axial runout values of 5gm, and also an
Ultra Super Precision (USP) class, which is made using more precise manufacturing
techniques and has radial and axial runout values of 2.5gm.
101
All of the three bearing options detailed in the preceding section have been used
by different manufactures in the design of spindles. More commonly however, ball
bearings are not used in the design of high precision spindles since in general the other
two options offer better axial and radial runout values. Hydrostatic bearings, on the other
hand, which are often used in high precision applications, can also withstand very large
loads. In addition, because hydrostatic bearing do not involve the use of any rolling
elements they do not suffer from the wear and tear that contact element bearings do.
However, the design and implementation of hydrostatic bearings is more complex than of
either of the contact element bearing options. Usually the design and implementation of
hydrostatic bearings is specific to each application and is therefore more costly since they
are not off the shelf items. In addition, since hydrostatic bearings involve the continuous
flow of a fluid into the open atmosphere, there is a risk the bearing fluid might
contaminate the polish process. From a commercial standpoint, this machine must be able
to operate in a designated clean environment without risk of contamination. As a result, it
is critical that care be taken to seal the bearing fluid from the rest of the machine, which
is possible but adds yet further design complexity to the hydrostatic bearing option. The
cross roller bearing option on the other hand, is the simplest and most compact of all
three. Cross roller bearings are commercial, off the shelf items that can be purchased and
thus do not require the design and production effort that hydrostatic bearings would. In
addition, only one cross roller bearing needs to be used to provide the total support that
would require at least 3 ball bearings to achieve. Finally, the cross roller bearing option is
the most compact design option of the three. In order for this machine to be an effective
commercial tool, it and all of its components must be as compact as possible. Both as a
102
research tool and as a commercial tool, the spindles of the machine must provide for
precise motions without risk of contamination of the wafer surface. Considering that the
THK cross roller bearing option offers the best compromise between design cost and
complexity, durability, precise motion, and contamination risk, it is clearly the best
option of the three to be used in the spindle design. The following table details the
advantages and disadvantages of the three bearing options.
Advantages and
Ball Bearing
Disadvantages
Hydrostatic
Cross Roller
Bearing
Bearing
Design Complexity
0
-1
1
Design Cost
1
-1
0
Contamination
1
-1
1
Precise Motion
-1
1
1
Total:
1
-2
3
12 Design of the Platen
The main design goal for the platen is to provide a top surface for the detachable
section, and thereof the pad to sit on. The diameter of this surface is determined by the
diameter of the wafer, the minimum center to center offset between the platen and the
wafer, and the wafer sweep amplitude. The wafer sweep action serves two main
purposes. The first is to distribute the waste that is generated by the polishing process
over a larger area as to not overload the pad. The second purpose is to distribute the heat
generated by the polishing process over a larger area as well. Temperature is an important
factor in the polish process. Distributing the heat over a larger area will reduce the
103
amount by which the temperature of any section of the pad will increase within each run,
and from one run to the next. This increases uniformity of polish results within each
wafer and from one wafer to another. The exact amplitude for wafer sweep can not be
determined theoretically. In addition, since the research team currently does not have
information on wafer sweep, this remains a possible focus for future research. As a result,
the amplitude of wafer sweep was chosen to be 4in., which is higher than that used by
most commercial tools already on the market. This was done to allow for the ability to
experiment with a wide range of amplitudes for added research flexibility. It must be
noted, however, that the cost of this added flexibility is a larger machine size, which
compromises the machine's competitiveness as a commercial tool. From the calculation
from the machine configuration section, the optimum minimum center to center offset
was calculated to be 3.0 in. In addition, it was desired to have the edge of the platen well
outside of the wafer surface area at all times, since edge pressure distributions are higher
than that of the rest of the contact plane. As a result a 1.5-inch margin was allowed for, to
insure that edge effects would not create an uneven pressure distribution on the wafer.
104
Platen
Wafer
--
3"
4"'
1.5
4" --
Center to Center
Spacing
afer Swee
afer Radius
Figure 60. Schematic showing the resulting platen diameter
As can be seen from the previous figure, the diameter of the platen adds up to be
25in. Initially, a thickness of 3in. is chosen for the top platen surface. This is done to
insure that the platen is stiff enough to withstand the polish load with minimal deflection.
Later on, this will be made thinner, and stiffening ribs will be added as the design is
optimized. Therefore, the initial step in the platen design is a simple flat circular plate, as
shown in the following figure.
105
3.000
Figure 61. Rendered view of the top platen section.
The next feature on the platen is a shaft for the B44-38 motor rotor to mount on.
This shaft has an outside diameter of 3in. to fit inside the rotor and an inside diameter of
11.5in. to provide space for through the platen slurry supply and endpoint detection
components. This feature of the platen is shown in the following figure.
106
Figure 62. Rendered view of the platen rotor shaft
In the above figure, the outer diameter of the shaft is chosen such that it provides a
sliding fit with the inner diameter of the rotor as is necessary for the locktite fit discussed
previously. While this is sufficient, it does not provide for easy assembly of the rotor onto
the platen. As a result a step is placed in the shaft diameter to act as hard stop for the
assembly of the rotor. By providing a similar hard stop for the stator on the capsule,
proper alignment of the rotor inside the stator can be achieved without any extra
assembly effort. These steps are simply used as positioning guides. The step, which is
shown in the above figure, is created by starting out with a shaft diameter of 13.500in.
and then machining the portion that the rotor mounts onto down to 13.000in.
107
Figure 63. Rendered view of the positioning step on the rotorshaft
Next the features that are necessary for the mounting of the cross roller bearing
are created. The cross roller bearing that was chosen was the minimum diameter THK
UCP cross roller bearing that provided enough room for the rotor shaft. The inner
diameter of the outer race of this bearing, however, is not large enough to clear the
platen. In order to prevent the surface underneath the platen from rubbing against the
outer bearing raceways, this surface is displaced from the top surface of the bearing by a
hollow cylindrical feature shown in the following figure.
108
Figure 64. Rendered view of bearing displacementfeature
This feature sits over the inner bearing raceways and is not thick enough to touch the
outer raceway. Next another cylindrical feature is created to locate the bearing such that
its center axis is aligned with that of the platen, thus making sure that two are concentric.
This feature is shown in sectioned view in the following figure.
109
Displacemenjt
Feature
Centering
Feature
Figure 65. Rendered view of bearing locationfeature.
Notice that the latter feature also has 12 equally spaced holes drilled into it. These holes
are tapped and are there for a lower retaining ring to screw onto. As will be seen later in
section 14, this retaining is there to prevent the platen from being pulled out up and out of
the capsule. A section view of the assembly of the bearing to the platen is shown in the
following figure. For clarity, the bearing and bearing retaining ring are shown in blue and
green respectively. Notice again, that both the platen and retaining ring touch the inner
bearing raceway only.
110
Figure 66. Rendered view showing the assembly of the bearing and lower retainingring.
The platen design shown in the previous figure, is a functional but not yet
optimized. Although a 3in. thick top circular plate is strong enough to withstand the
polish loads, it is heavier than it needs to be. The extra mass of the platen increases its
rotational inertia, which in turn increases the time it takes for the platen to reach a desired
rotational velocity. In order for the machine to have the ability to maintain constant
polish velocity during wafer sweep the rotational velocity of the platen must be
continuously and quickly adjusted to compensate for the difference in the center to center
offset distance (Refer to equation 1). As a result, it is necessary to modify the design to
111
achieve a high structural rigidity while at the same time minimizing the rotational inertia
of the platen. To this end, the design shown in the previous figure is first modified by
making the section of the platen that is inside the bearing radius thinner and rounding the
sharp corners of the cavities in order to prevent stress concentrations.
Top plate
Figure 67. Rendered section view of platen cavity features.
While the latter modifications make the platen lighter, they also increase the amount by
which it will deflect under polish loads. In order to make the platen much stiffer without
adding much weight, 12 equally spaced stiffening ribs are added as shown.
112
Figure 68. Rendered view of stiffening rib structures.
The following figure shows the deflections of the platen structure under the polish load
before it was made thinner (See Figure 65). In order to take into account the worst case
scenario, the analysis is carried out as if the wafer were being polished on a pad fixed
directly onto the platen and the Detachable Section(See Figure 79) is excluded. If the
detachable section is used, as it should be, it will only add more stiffness to the system.
113
p3-k:: Staic Displacemert
Unts: m
URES
.416e-007
.632e-007
7.847e-007
7.062e-007
6.278e-007
.493e-007
.708e-007
.923e-007
.1 39e-007
.354e-007
1.569e-007
7.847e-008
1.000e-033
Figure 69. DisplacementFEA resultsfor platen structure with thick top plate under
polish load.
To compare the following figure shows the deflections of the platen as shown in Figure
68 under the same loading conditions.
114
P2-:: Static Displacement
Units: m
URES
.289e-006
.932e-006
575e-006
3.217e-006
.860e-006
.502e-006
.1 45e-006
1.787e-006
I .430e-006
I.072e-006
7.149e-007
.575e-007
11.000e-033
Figure 70. DisplacementFEA results of platen structure with rib section underpolish
load.
Although the structure with the ribs experiences more deflection under the same load, the
deflections are still very small and well within tolerances. For example, the 2.8 pm or
.0001 in. sideways deflection of the rotor shaft is well under the 0.0005 cylindrical runout
value that the shaft is machined to. In addition, the 4.3pm vertical deflection under the
wafer is also acceptable considering the compliance of the pad that would sit on top of
the platen. In order to better demonstrate the effectiveness of the rib structures, stress
FEA plots of both designs have been included in the Appendix Section.
115
Welding these rib structures inside the tight space provided between the rotor and
bearing shafts is not easy. In addition, such extensive welding requires stress relieving in
order to avoid deformations in the platen in the future. As a result, it is perhaps best to
cast the platen with these structures and to then machine critical surfaces such as the
outer surface of the rotor and bearing shafts.
As was mentioned previously, the slurry that is used during the polish process is
usually both chemically and mechanically corrosive. As a result, despite the fact that
cross roller bearings are sealed, it is best to prevent the slurry from contacting the bearing
since it may wear the seal on the bearing and compromise its components. As a result a
splashguard is used to isolate the top surface of the platen from the bearing and other
components. The specific design of the splashguard can best be seen in Figure 90 and
Figure 91 in the platen assembly section. In order for the platen to interface with the
splashguard, more specifically the inner lip of the splashguard, a groove is machines into
the outer section of the platen for the inner lip to sit within. This approach was chosen
prevent the slurry from splash over the inner lip and onto the bearing below.
116
Figure 71. Rendered view of splashguardand platen interface.
13 Design of the Capsule
The goals for the design capsule are to provide the necessary features for the
proper mounting of the bearing outer race and the motor stator; and the mounting of the
platen assembly onto the rest of the machine. Since capsule is exposed to the same
corrosive environment as the platen it also has to be made of stainless steel. As with the
platen design, and just about every other component of this machine, the capsule design
must also be as compact as possible.
117
The first feature of the capsule is the bearing seat. This feature is designed
according to the g7 bearing fit recommended by THK. The depth of the seat is equal to
the thickness of the bearing. Thus the top bearing surface and the top surface of the
capsule are flush. In this manner, the height of the top surface of the platen above the
capsule is determined by the way the bearing is mounted onto the platen and cylindrical
displacement feature shown in Figure 65. This feature also controls the amount of space
that is left between the platen and the capsule for the splashguard. The start of the capsule
thus far is as shown in the following figure.
Figure 72. Rendered view of the bearing seat on the capsule.
The lower surface of the cylindrical feature shown above rests on the top surface of the
granite. The height of the bearing seat above this surface will determine the height of the
top surface of the platen above the granite table. Ideally, the top surface of the platen
should be no taller than waste height in order to allow for convenient access during pad
change and other maintenance.
The following figure, which shows the cross roller
bearings in blue, shows a section view of the bearing assembly inside the capsule.
118
Contact surface for the
capsule and granite table
Figure 73. Rendered view of the bearing assembly inside the capsule.
As with the bearing seat on the platen, the corners of the bearing seat have a
radius of 2 mm, as indicated by the bearing manufacturer. In addition, THK recommends
that four equally spaced holes be provided for periodic lubrication of the bearing. Since
this bearing is to be used in a configuration where the outer race is stationary, lubrication
will be provided through these holes and into holes manufactured in the outer race. The
height of these holes above the bearing seat is 20 mm, so that they are aligned with the
holes in the bearing.
119
Lubrication hole
Figure 74. Rendered view of bearing lubricationholes.
Although there is no force that will pull the bearing out of the capsule, it is still
recommended practice by the manufacturer to provide a means of securing the position of
the bearing. At the very minimum this, together with the lower retaining ring shown in
Figure 66, will insure that platen remains secure inside the capsule as the entire platen
assembly is placed in and taken out of the rest of the machine for various maintenance
purposes. There are several ways to achieve the latter. One way is to use another upper
retaining ring, similar to the lower retaining ring shown in Figure 66. This, however,
would require additional space between the lower surface of the splashguard and the top
surface of the capsule in order to provide adequate room to fasten the bolts of the
retaining ring (See Figure 91). The latter in turn would require the top section of the
platen to be raised with respect to the capsule and would increase the height of the pad
120
surface above waste height. To prevent this, it is desirable to have a retaining ring that
fastens from the sides rather than the top. To achieve this two half rings, each like the one
shown in the following figure are used.
Figure 75. Rendered view of half ring retainingrings.
In addition, to receive these rings, the top rim of the bearing seat is modified as shown.
Figure 76. Rendered view showing retainingring interfacefeature
In this manner, the two retaining rings can be placed around the top rim of the bearing
seat and fastened to each other. In this position, the two rims clamp down on the outer
race of the bearing as shown in the following figure.
121
Figure 77. Rendered view showing how the half ring retainingrings clamp down on the
outer race of the bearing.
There are several details in the design of the half rings that will insure a tight clamping
force when two rings are fastened together. As can be seen from the following figure, the
inner cylindrical surface of the half rings has a slightly larger diameter than the outer
cylindrical surface of the capsule. In addition the lower edge of the ring is also not
touching the capsule.
122
I
Conical surface
k'---
~1
Lower edge of
retaining ring.
Figure 78. Schematic bearing retainingrings.
Furthermore, each of the half rings extends only 174 degrees around instead of 180
degrees. In this manner, as the bolts that fasten the two rings are tightened, there is room
for the two half rings to stretch circumferencially and come together. Because of the
inclined conical surfaces on the rings and the capsule the rings are pulled down as they
are squeezed together by the bolts. As a result, the rings will keep pressing harder and
harder on the bearing as the bolts that fasten them to each other are tightened. The final
result is a retaining ring that exerts and evenly distributed and adjustable force over the
bearing with two fasteners that are located on the outer perimeter of the capsule instead
of the top.
123
14 Design of the Platen Spindle Assembly
14.1 Assembly Procedure of Major Components
The latter sections described the major design features of the platen and capsule,
which are the two main components of the platen assembly. What is to follow, is a
description of how these two parts, along with the many other parts that form the platen
assembly are put together. This section will also include additional modifications that are
made to the platen and capsule for the purpose of attachment of other components. The
order in which the following material is presented is in the same order the components
should be assembled. To provide a better understanding of the platen assembly and
assembly order, a rendered view figure of the assembly is shown with some of the
components labeled.
Endpoint Detection
Sensor
Detachable Section
Figure 79. Rendered section view of the platen assembly.
124
First, the rotor is attached to the platen using the locktite fit detailed in the
previous sections. The stator is also attached to the capsule using the very same process.
This still a rather risky process and should is ideally carried out by the motor
manufacturer.
Figure 80. Rendered view of splashguardin the platen assembly.
As can be seen form the previous figure, the outer diameter of the outer bearing race is
larger than the inner diameter of the splashguard. As a result the splashguard must be
inserted loosely in its designated groove in the platen before the bearing is attached.
Otherwise the bearing outer race will not allow the splashguard to be assembled onto the
125
platen. Next, the large THK cross roller bearing is attached to the platen. It is placed in its
seat on the platen and then secured to the platen via the "lower retaining ring" shown in
Figure 66. Once this is completed, the platen, with the bearing and splashguard attached,
is lowered inside the capsule as shown in the following figure.
Figure 81. Rendered view platen and capsule subassemblies as they are assembled
together.
Finally, the two "half retaining rings" are placed around the top lip of the capsule.
They are fastened together using two pairs of bolts and nuts, which are tightened to clamp
down on the outer race of the bearing inside the capsule.
126
Figure 82. Rendered section view of the platen assembly with the all retainingrings
attached.
At this point, the rotary electrical coupling that supplies power to the endpoint
detection sensor is bolted onto the inside of the platen as shown.
127
Figure 83. Rendered view of the rotary electricalcoupling in the assembly.
This coupling has a hollow shaft for the passage of the slurry fluid lines. The
supply lines for slurry are then threaded through the assembly as completed thus far. Next
the appropriate ends of the fluid lines are attached to the rotary union that supplies the
three channels of slurry and the rotary union is bolted onto the end of the rotary electrical
coupling as shown.
Figure 84. Rendered view of the rotaryfluid union in the assembly.
At this point it is necessary to fix the stationery sections of both the rotary
electrical coupling and the rotary fluid union such that they do not rotate due to the
128
friction between the stationary and rotating components. To some extent this can be
achieve by the mere attachment of the supply lines. However, this method would rely on
the stiffness of the supply line tubes to keep that stationary section from rotating. If the
friction forces are too large this may cause the supply line to wrap around and possibly
break. As a result some type of a bracket is necessary to fix the stationary components. At
the same time however, care must be taken to not over constrain the platen assembly.
Thus far, the platen's motions with respect the capsule are constrained only by the cross
roller bearings only. Adding another 5 degree of freedom constraint through the bearings
of the rotary coupling and rotary union would require perfect tolerance on all involved
components in order to insure that the over constrains are identical and thus do not
require deformations of the parts to be satisfied. Since perfect tolerances are impossible,
another approach is to allow one of the over constraining components to deform easily
without exerting any significant forces. To achieve this, the stationary components of the
rotary coupling and rotary union are fixed to the platen using a very flexible bracket. This
intentional compliance will allow the cross roller bearings to constrain and uniquely
define the motions of the platen while the bracket deforms readily to match these
motions. The latter condition is true regardless of the tolerances of the parts involved.
This bracket and the manner in which it is attached to the rotary coupling, the rotary
union, and the capsule is shown in the following figure. For clarity, none of the other
assembly components are shown.
129
Figure 85. Rendered view showing the bracket in the platen assembly.
Up to this point, the order in which the latter components are assembled has been
critical. However, the order of the assembly of the components to be described in the
following sections is not critical. In fact, they can be assembled in any order, even before
the components mentioned in the previous sections. The order in which they are
assembled should be determined at the time of assembly based on the time of availability
of each component and the order that appears most convenient in practice.
130
14.2 Assembly of the Detachable Section
The next major component in the assembly is the detachable section. The main
purposes of this section as mentioned before, is to provide for easy and quick change over
between processes that require different pads and slurries. Another advantage of having a
multiple detachable sections is the ability to have and test sections with different fluid
passageway patterns. As such, the design of the passageway patterns of each section is
unique to that detachable section and is not covered in this document. Rather the design
of a general detachable section with the correct kinematic coupling to the platen and with
the ability to receive fluid from the fluid supply is detailed. The first such section to be
used will be solid. It will be attached to the platen using two pins for alignment. The first
pin will sit against a sideways v slot and the other will stop against a flat surface to define
a unique alignment. The following figure shows a schematic of the coupling method.
Note that the pins are attached to the top plate of the platen and the slots machined into
the underside of the detachable section.
131
Step 2
Step I
Step 3
Figure 86. Schematic showing the relation between the pins and the underside grooves of
the Detachable Section (Bottom View).
As the previous figure shows, first the detachable section is lowered onto the platen such
that the two pins sit inside the triangular and ring section slots. Next, the detachable
section is pushed up on the platen until the left pin is tangent to the two side edges of the
triangle. At this point the detachable section is turned clockwise, while still pushing up,
until the right pin sits against the horizontal edge of the ring section. In this manner, the
location of the Detachable Section with respect to the platen is defined in the two 2-D
plane. In addition from Figure 2 it can be seen that the platen rotates counterclockwise.
Therefore, any loads that the platen will exert on the detachable section will also be
counterclockwise. Any counterclockwise moment exerted on the detachable section by
132
the platen will further push the two pins in their seating inside the detachable section and
thus provide appropriate nesting force for the kinematic coupling. In this manner, the
load is taken entirely by the two pins, and there are no load trying to open up the
coupling. As a result only a single bolt, inserted from the bottom through the top platen
plate and threaded into the detachable section, is used to secure the two parts together.
The friction force generated by the tightening of the bolt is relied upon, solely, to insure
that the detachable section does not rotate counterclockwise with respect the platen. Since
there are no appreciable loads that would cause the latter the used of a single bolt is
sufficient and provides ease of assembly.
14.3 Assembly of the Endpoint Detection Components
Next, the endpoint detection sensor assembly is attached inside the platen right
under the top platen plate. Three appropriately threaded holes are provided inside this
plate for the sensor assembly to bolt onto from the bottom as shown.
133
Figure 87. Rendered sectioned view of the endpoint detection sensor in the assembly.
In addition, the sensor requires an amplifier to transmit the power from the rotary
electrical coupling. Because this amplifier is too large to fit in between the stiffening rib
structures under the top plate, it is attached to the inner wall of rotor shaft instead. The
underside of the amplifier, which is shown in the following figure is flat. As a result, an
adapter section is used in between the amplifier and the platen to appropriately mate the
two parts.
134
SAdapter
Amlifier
Plate
Figure 88. Rendered view of the amplifier and adapterplate.
The following figure shows the arrangement of these components inside the platen. Note
that the amplifier rotates with the platen and receives its supply lines from the rotating
component of the electrical coupling.
135
Figure 89. Rendered view of amplifier and adapterplate in assembly.
The entire assembly as it would exist before it is assembled onto the granite table
and the rest of the machine, is shown in the following figures in multiple views.
136
Figure 90. Rendered view of the overallplaten assembly.
137
Figure 91. Rendered section view of the overall platen assembly.
138
Figure 92. Rendered view of the overallplaten assembly showing the components inside
the platen rotor shaft.
In addition, again for increased flexibility the platen will be equipped with a detachable
face onto which the pad is attached. The latter will allow for different supporting material
to be used under the pad. Furthermore, the detachable section will allow for easy and
quick change over between different pads which can save time and cost in a commercial
fab where process change over is frequent. The mechanisms necessary to achieve these
two functions will also be incorporated into the platen assembly.
139
15 Head Gimbal Design
As was mentioned before, CMP is a lapping process where silicon wafers are
polished against a pad surface. In the chosen rotary configuration that was detailed
earlier, the wafer is held inside a wafer a carrier that rotates the wafer at the same speed
as the pad while applying the necessary polishing pressure against it. In order to allow for
and provide the necessary rotation, the wafer carrier is attached to a head spindle that
consists of bearings and a motor. Another requirement of the polishing process is to apply
uniform pressure against over the entire wafer surface. To achieve this the wafer must sit
flat against the pad surface during the process. If this is not the case the edges of the
wafer will experience a higher polishing pressure than the middle as shown in the
following figure and will be polished faster as a result.
Application of
Polishing Force
*wp
ft)
aaer
Wafer
Carrier
Pad
Platen
Figure 93. Schematic of an exaggeratedwafer vs. pad spindle axes misalignment.
140
In order to prevent edge fast polishing, the wafer surface must be aligned parallel
to the pad surface within a very tight tolerance. It must be noted at this point, that the
back surface of the wafer is not always parallel to its front surface (the surface to be
polished). Furthermore, the degree to which the two surfaces are not parallel is not
uniform and varies with each wafer. In addition, as was mentioned in the "design goals"
section, this machine should have easy and repeatable assembly. As a result, parallel
alignment of the wafer and pad surfaces can not and should not be achieved through
precision assembly requirements. Thus a gimbaled mechanism is necessary for the wafer
spindle to allow its alignment to conform to that of the pad surface during the polishing
process.
The simplest design for such a gimbaled mechanism is to use a universal joint. A
common and basic design for such a mechanism is shown below.
Pivot
Intermediate
Grounded
Coupler
Figure 94. Schematic of the kinematic configurationof a universaljoint.
141
In the above figure the yellow elements are pivot elements, or hinges. These pivots have
an object connected to each end and allow for relative rotations between these two
objects along the pivot's longitudinal axis. The two outer pivots allow for the blue
intermediate ring to rotate with respect to the gray ground ring. The two inner pivots
allow for the red coupler ring to rotate with respect to the blue ring. The axis of rotation
of the inner pivots always remains perpendicular to that of the outer pivots. As such the
two axis of rotation of the coupler ring will always be orthogonal to each other. In this
manner, they form a linearly independent set that spans the space of rotations of the
coupler ring for all rotations other than rotations about its own axis (The spindle axis).
There are two ways that a simple universal joint can be used in the head design in
order to allow the wafer orientation to conform to that of the pad. The first is to mount
the wafer carrier onto the coupler ring and then mount ground ring onto the rotor of the
motor. In this manner, the axis of the head spindle will remain fixed but the wafer
orientation will conform to sit flat against the pad. In this design, however, the
components of the gimbaled mechanism will undergo a cyclic motion to maintain the
wafer vs. pad orientation during each spindle rotation. Since the gimbaled mechanism is
bearing the load of the polishing force, cyclic motions of its components under this load
can cause unnecessary ware and tare on the bearings and fatigue the structural elements
of the mechanism. Another design is to mount the entire head spindle on to the coupler
ring and then mount the ground link to the gantry structure. In this manner as the wafer is
lowered onto the pad the components of the gimbaled mechanism will move once to
achieve wafer vs. pad orientation. Thereafter the components will undergo small cyclic
motions to compensate for the run-out of the platen and head spindles.
142
Figure 94 above is a simple schematic of the kinematic configuration of a
universal joint and does not detail the actual implementation of such a design. However,
it can be observed from diagram Figure 94 that the axes of rotation for the four pivots
must always lie inside the volume occupied by the mechanism. Therefore in practice, the
center of rotation of the coupler ring, which is at the intersection of the two axes of
rotation, can not lie outside the boundaries of the mechanism. In addition, in both of the
previously suggested head designs that incorporate a universal joint, the joint is placed at
a distance above the wafer vs. pad contact surface (Here on referred to as the contact
plane). Since friction is clearly present between the two contacting surfaces and since the
force due to the friction acts in the contact plane it will exert a moment about the center
of rotation of the wafer as shown in the figure below.
Center of rotation of coupler ring
imbaled Mechanism
W/-2afer
Moment Arm
Wafer Carrier
Direction of
travel of pad
to friction
\Pad
Figure 95. Schematic showing the moment exerted about the center of rotation of the
wafer by thefrictionforce.
143
As can be seen from Figure 95, the moments exerted about the center of rotation of the
coupler ring will force the entire wafer and wafer carrier mechanism that is mounted on
to it, to rotate counterclockwise about that center. As a result the left edge of the wafer
will be pushed into the pad. Since the pad is traveling from the left to the right, the entire
system shown in Figure 95 will behave similar to a self-energizing brake mechanism.
This will clearly produce an uneven polishing pressure across the wafer surface and is
unacceptable.
To alleviate the problem detailed above, ideally the center of rotation of the
coupler ring must be moved to a location in the contact plane. Alternatively, and
somewhat less desirable, is to move the center of rotation below the contact plane, where
the force due to friction still exerts a moment about the center of rotation but the
mechanism does not act as a self-energizing brake. Both of the latter suggestions would
require a gimbaled mechanism with a center of rotation that lies outside of the boundaries
of the mechanism itself, since clearly, the mechanism has to be above the contact plane
and the center of rotation must be within or below the contact plane.
One suitable mechanism that can be used in the design of such a gimbaled
mechanism is the four-bar linkage such as the one shown in the following figure. The
advantage of the four-bar linkage is that it can be designed such that the center of rotation
of its coupler link is at a desired location for a given configuration of the linkage.
Although the location of this instant center of rotation will change as the configuration of
the four-bar linkage changes, the linkage can be designed such that for a given range of
angular deflections of the coupler link, the loci of the instant centers of rotation (The
centrode curve) remain within an acceptable or desired range.
144
A
B
Coupler Link
Follower Lin
02
Ground Link
0
Z
0
Figure 96. Simple four-bar linkage.
In the above linkage system point A is the pivot point of the coupler link on the
driver link and is also a point common to both links. Since point A lies on the driver link,
and since the driver link is rotating about point 02, the direction of the velocity of point A
must be perpendicular to line that connects point 02 and point A, as shown in the
following figure. Similarly, point B is a point common to both the coupler link and the
follower link and the direction of its velocity must be perpendicular to the line that
connects points 04 and B. Since points A and B also lie on the coupler link, the instant
center of rotation of the coupler link must be at the point about which points A and B are
at pure rotation. An alternate definition of this point is a point whose distances to point A
and B remain fixed. Hence this point, from here on referred to as the instant center, is the
intersection of the lines that pass through points A and B and are perpendicular to their
directions of velocity. From the latter definition, these lines have to be extensions of the
lines of the driver and follower links.
145
Location of the
Instant center
0/
A-
F
Coupler Link ---
'B
Driver Link
Follower Link
O,
Ground Link
>04
Figure 97. Schematic of a four-barlinkage showing the location of the instant center of
the coupler link.
In this manner, two four-bar linkages can be designed to perform the function of a
universal
joint, while placing the center of rotation of the wafer in the contact plane. One
possible designs for such a gimbaled mechanism is shown in the following figure. Notice
that the planes of the two four-bar linkages are perpendicular to each other just as the axis
of the pivots of the universal
joint were. This is necessary in order to achieve two linearly
independent degrees of freedom for the rotations of the coupler ring. Notice also that the
intersections of the lines of the driver and follower links of both four-bar linkages are the
same. This is done to insure that the instant center of rotation of the coupler ring about
either axis of rotation is at the same location. For the sake of nomenclature, the four-bar
linkage that is immediately holding the coupler ring as its coupler link is referred to as the
primary linkage system and the four-bar linkage that contains the primary linkage system
as its coupler link is referred to as the secondary linkage system.
146
Secondary Linkage
System
Coupler Ring
Primary Linkage
System
Figure 98. Rendered view of afour-bargimbaled mechanism design.
The design of the four-bar linkage for the purposes of this machine is dictated by
the size of the head spindle, which dictates the size of the primary coupler link and the
space available in the gantry structure, which dictates the size of the secondary ground
link. With these design constraints there are an infinite number of possibilities for fourbar gimbaled mechanism design. To demonstrate this another such design is shown in the
following figure. This design uses the same primary coupler link and secondary ground
link parameters as the one shown in Figure 98 but incorporates longer driver and follower
links. It also has larger distance from the primary coupler link to the location of the
desired instant center. For clarity a rendered isometric view and a front view using hidden
lines are shown below.
147
Figure 99. Alternativefour-bargimbaled mechanism design.
As described earlier, both four-bar gimbaled mechanisms shown in Figure 98 and
provide a center of rotation for the coupler ring that is in the contact plane at this instant
only. As the coupler ring starts to rotate the location of the center about which it rotates
changes. To show why this occurs, and why a design like the one shown in Figure 99 is
better than the one shown in Figure 98, a more analytical approach is necessary.
Consider again a simple four-bar linkage with the instant center for the coupler
ring as shown in the following figure. Since the purpose of this design is to minimize the
moment of arm of the friction force about the center of rotation of the gimbaled
mechanism, the location of the desired instant center must be placed somewhere within
the contact plane. For the sake of symmetry, however, it is also aligned with wafer
148
spindle axis, and is thus the point where that head spindle axis intersects the contact
plane.
Location of
Desired
Instant Center
3
r2
r
%rF
Figure 100. Schematic of a four bar linkage system with a desired instant centerfor the
coupler link.
For the following analysis, vectors are used to define the orientation and magnitude of the
ground, driver, coupler, and follower links. In addition vectors are used to locate the
desired instant center of rotation. For the secondary linkage system, the magnitude of F
is dictated by the space available inside the gantry structure. For the primary linkage
system, the magnitude of iF is dictated by the diameter of the head spindle. Finally, the
magnitude of it is chosen to define a four-bar linkage that meets other design constraints
and certain desired characteristics.
149
In addition, for the following analysis, the complex polar notation will be used for
the book keeping of vector calculations. Using this method a vector i shown above is
expressed as:
F= rcosO +i rsin 0
In this latter case the real component is the horizontal component of the vector and the
complex component is the vertical component where 0 is the angle of the vector to the
horizontal axis.
For ease of book keeping for velocity and acceleration analysis the following equation
will also be used.
e'0 = cos6 + isin 0
The proof for the equation above comes from the sum of the Taylor series expansions of
the cos(0) and sin(iO) functions which is equal to the Taylor series expansion of the eio
function.
The methods described above can be used to analyze and obtain the necessary
link lengths and angles for the four-bar gimbaled mechanism given the location of the
desired instant center at the initial, neutral position. At the initial position both the
primary and secondary coupler and ground links are assumed to be horizontal as shown
in Figure 100.
From Figure 100, the following two vector loop equations are written:
o = rl+r
150
Using the equations above the following analysis is then carried out:
2 + F3 = F + F4
r3e 03
r2e io,+
r2 cos0 2 +r3cos0
r2
3
= reiI + r4e'4
= ricos0 1 +r4cos0 4
sin 02 + r3sin03= r,sin 0 1 + rsin0 4
01 = 03
r 2 cos0
r2
2+
=0
r = r +r 4 cos0
4
sin 02 = r 4 sin 0 4
From symmetry:
02 =180 -04
cos0 2 = cos(180 -04)= cos(180)cos(0 4 )+ sin(180)sin(0 4 )= -cos0 4
sin 02 = sin (180 -04) = cos(0 4 )sin (180)- cos(1 80)sin (04)= sin 04
r2 cos0
2
+r3 = r+rcos0
4
= r,-r 4cos0 2
ro - r
COS02 =3
r2 + r
r 2 sin
2
=
rsin0 4 = r sin (180 -
2
)=r 4 sin0 2
r2 = r
r - r
2
20
r2
2r2
=
=-re
40
0
+r4 0ei 044
151
r cos
2
= r,+ rcos04
sin 02
r
sin 04
= r,
r cos2 = r,+ r4 cos4 = r,- r cos0
cos02 =
2
r
rz + r
r, sin 62 =
r
sin 04 =r4 sin 62
r=r
cosO2-
rl
2rr
r-r
r2o
r2
3
r2
r r2
r - r3
sin 02=
r2
tanG
_
2rh
2
r - r3)r
r2)
2r2hk
-r2
Y rr2
4r
(rl
2k
)
r2
r3
(r,- r3)
(Eq. 18)
62= tan
(Eq. 19)
64= 180 - 62
(Eq. 20)
r2
r3
- r3
2cosO2
152
(Eq. 21)
r2o
o2cosO2
(Eq. 22)
r4
(Eq. 23)
=2
r'o = r2
The designated equations above give the lengths of all links and the initial angles of the
links as a function of the given and chosen design parameters.
It is desired to know the location of the instant center of both linkage systems, when the
systems are not in their neutral positions. Specifically, it is desired to know the locations
of the instant center for each system as a function of the angle of the coupler link from its
initial angle. For this purpose consider the following figure which shows the same fourbar linkage as Figure 100 with some arbitrary angle for the coupler link.
Location of
Instant Center
rA
\
B
Figure 101. Schematic of a four barlinkage system showing the location of the instant
center of the coupler link.
The values of
2
and f are already known from the previous analysis and the value of 03
153
is the given value for which the calculations are being carried out. In the above figure, the
intersection of vectors
FA
and FB is the location of the instant center. Note that vectors F-
and FB are not the same length as vectors
r2o
and F40. Only when the coupler link angle is
equal to zero, vectors F and FB are the same as vectors F20 and
F0
respectively.
Again, from the Figure 101, the following closed loop vector equations are derived.
3
4 = -F + F2 +
FA = F + FB
4 = -F
+ '2 + 3
6
r4e"04 = -re''I + r2 e 2 + r3 e
01 = 0
r4 cos0 4 = -r, + r2 cos0
2
+ r3 cos0 3
r4 sin 04 = r2 sin 02 + r3 sin 03
(r4 cos0 4
=
2+
(r2 cos0 2 f + (r cos0
3) -
2rr 2 cos0
2 -2rr
3
cos0
3
+2r 2 r3 cos0 2 cos0 3
(r4 sin0 4 7 = (r2 sin0 2) +(r 3 sin0 3 Y + 2r 2r3 sin0 2 sin0 3
2
r = r
2
2
+ r2 + r
32
-2r
-2rr
2
cosO 2
2
(Eq. 24)
r4
-2ir
2
rr
3
cos0
2
2
- r2 - r3
2r2 r3
3
+2r2r3 cos02 cos0
3
i 03
+2r 2r3 sin 02 sin
rl cos02
r-cos03 +cos(02 -0 3 )
r3
r2
154
The above equation does not have a closed form solution and is solved numerically to
obtain a value for 02.
Once 02is known,
64 = sin1 r2sin2 + r3sin
(Eq. 25)
3
r4
F=
rAe'02 =
rA cos0
2
F 1+ FB
re' + rBi94
= r,+ rB COS0
4
r 4 sin 02 = rB sin 04
_ r4 sin 02
sin 04
r + r, tan0 2
cos0 2
tan 04
(Eq. 26)
r
1
tan 02 1
tan0 4
cos0 2
Once the vector F is found, the location of the instant center is also known, where the
coordinates of the instant center in a reference frame with origin at the origin of link 1 are
rAcosO2 along the x-direction ad rAsinO2 along the y-direction.
As the angle of the coupler link begins to change the location of the instant center
translates out of the contact plane. For relatively small changes in coupler link angle, all
forces due to friction are acting parallel to the wafer surface. This assumption holds true
155
until the coupler link angle deviations are so large that the edges of wafer begin to get
caught into the pad. Therefore, at any given instant, the moment arm of interest is the
distance from the actual instant center to the desired instant center, projected on to a line
that is perpendicular to the wafer surface. As can be seen from the following figure this
line can be conveniently taken to be the vector h0 that was used to define the location of
the desired instant center in Figure 100. Therefore, the magnitude of the moment arm for
the friction force about the actual instant center is the same as the magnitude of vector
T, in the following figure.
rP
rVP
Location of
Instant Center
Location of
Desired
Instant Center
ABp
r
r~p
p
riP
Figure 102. Schematic of afour bar linkage system showing the location of the actual
instant center of the coupler link.
From Figure 102 the following closed loop vector equation is written and solved for the
magnitude of F, . Notice the p subscripts, which denote that this four-bar linkage system
is the primary linkage system of the gimbaled mechanism. All the preceding, general
156
calculations applied to both the primary and secondary linkage systems and hence did not
have this subscript.
2
r2
e
elo2h+
(r2
-
(03p +90)
2
2~
rA
in02
+ rj
+
fi p
=rA e
pF
=r
9 e-r
e'3'
~+ rPe
rh e
(03 +90)
=( r -h)os(0 3 , +90)
cos03
P +r
OS0 2 +
(r2 -rA
hP=7 P
~
P
sin 03 = (r - h)sin(03 +90)
cos(0 3, +90)= -sin 03
sin (03 + 90)= cos0 ,
3
(r2,
rA cOS0
2
,+
(r2 rA in0 2, +
rh cos0 3 =-(r
-rA
-rr
+ rh
cos0 3 = -(r
+ r
)cOs0 2 p -{
cos-0r2
cos0
sin 0
= (r
.jcoso 3 -
2
- h)sin 0 3
-
h
s)c50
3P
(r - h, )sin 03
( ,, -h,)tan0 3
157
r,
cos0 3 =(r2 -rA)sinQ
(
sinG2
=r2 -rv P
- r, tan
(Eq. 27)
03
sin3 +hcos0 3
s
+0 2 ra rtanQP+h,
cos0
3
r rcos0
' +--tan03 +h
2
2-r-rA
cos6,, 2 p
2
r
r3,+
sir
=(r -r)
r
+
tanG 3
'-
co63,
2'
r
n
tan
3
2
03,
2
+h, tan G 3
rV=1+tan203
r2,
-
r
S
si6 cosG2 tanG6i3
0
COS03P
t 0
N
a
2
J+h(1+tan2
COSo3P
Equation 27 above gives the magnitude of moment arm as a function of the
coupler angle 03 . It was mentioned earlier that the location of the desired instant center
of rotation for both the primary and secondary linkage systems is designed to be the
same. This does not, however, mean that locations of the actual instant centers of rotation
for both the primary and secondary linkage systems will remain the same after the system
moves off of its initial, horizontal configuration. In fact, the location of the actual instant
centers will not be the same and begin to diverge as the two linkage systems move off of
their initial configurations. To show this, consider the following analysis, which
158
calculates the distance between the actual instant center of the secondary system and the
initial desired instant center.
The secondary linkage system is connected to the primary linkage system, which
is then connected to the coupler link. Since, the secondary linkage system is not
immediately connected to the coupler ring, the magnitude of its moment arm is a function
of both the primary linkage's coupler link angle and the secondary linkage's coupler
angle.
Consider the following figure, where 1, is the distance between the origin of the
secondary coupler link and the primary ground link. This distance remains fixed and is
calculated using the values obtained from equations 18 through 23, for the initial
conditions.
The orientation of the vector 1 coincides with the orientation of the primary linkage
system plane within the secondary linkage system. The origin of vector 10 is also the
origin of the ground link vector F of the primary linkage system. The vector 1, is the
distance from the secondary coupler link's instant center to the primary ground link,
projected onto the primary linkage system's plane. The vector [h is the perpendicular
component of the same distance to the plane of the primary linkage system. Notice the s
subscripts, which denote that the following linkage system is the secondary linkage
system.
159
rA.
lV
r3,-
Ys
Figure 103. Schematic of the secondary linkage system showing the location of the actual
instant center of the coupler link.
As before, from Figure 103 the following closed loop vector equation is derived:
FA, = 2,+,
rAe
5
"=
r2
e
e o+r,
2h
i3
+1+
-10e
l + H1V
(0,+90 +
e 03s
+1
rA cos2, = r2 cosO2 + r3cos3 -O cos(0 3 +90)+l cos0
2
rA sinQ2
=
r2, sin 6 2
+
-sinO
2
3
cos(03,
-10 sin (63 +90)+lh sin
3
e'(3,+)
3
+i, cos(6 3 +90)
+I sin (03 +90)
+ 90) = -sin (03,)
160
sin (63 , +90)= cos(03, )
r
rA, cos2, = r2, cos2,
+ 3,cosO3, +10 sin 03, +h COS03,
~ vsin 03,
r
rA, sin0
2,
= r2, sin 2, +
hA
iv= (r
(
s+hin13, -+l
r2,
cos
-r
2
sinO0
r
(
sin 03,
2
tan03,
2
2,+
sin 03,
C0 2 s
(Eq. 28)
2, r
COSr
sin
2
63,
r
3,
+l (r
2tanO ,
r
3,
3
=[~ tan 0 ,
2
3
I
coS
3,
h
+lo+-
2tan03,
3, +
tan03,
(1 - i,
tan 03,
lh
l v
COS03, +lhsin
(r
sin 02
r
"I sin 03,
tan03,
2tan03,
sinO2,
r COS02
sin
(,10, -__ ' )+
r
sin
03,
tan 2 03,
I
tan
3,+
+ tan 2
03,
161
Once the magnitude of TV is calculated from Eq. 28 as a function of the secondary coupler
link angle 63
,
it can then be used to calculate the perpendicular distance from the
secondary instant center to the desired instant center as follows:
rh,
Location of the
secondary actual
instant center
r2,
Figure 104. Schematic of the primary linkage system showing the location of the actual
instant center of the secondary coupler link.
In the following analysis, the vector
IVis
used to show the location of the secondary
instant center, projected onto the plane of the primary linkage system. The vector h, is
used to locate the desired instant center with respect to the coupler ring (The coupler link
162
of the primary linkage system). This distance will always remained fixed and is always in
the plane of the primary linkage system.
Again, from Figure 104, the following closed loop vector equation is written,
r2 P+
rP+3P2
r2 rOe
'P+
2
h, =
+ he i(03P+90)
0'
-2
= .lP
2 ei(O) +Iei(90)
r2p sin 0 2 +
r
-sin 0
P2
+ rV ei(3
+90
3
1Pi+
rcos(03
so+rpCS
h(Cos+90
+P
3cos6
3
22
r2 p Cos
i
-1 + , + ,,+
h,
e
+90)+ r, cosQ3,
+ h, sin (03 +90)= I, + r,, sin (03 + 90)+ rhsin 03
cos(0 3, + 90)= -sin 03,
sin (03 + 90)= cos0 3
r2 cos0 2 +
cos 3P-h
2
03
sin03 3 =
r, sin0
+rh
cos6 3
= ,, + r,, cos0 3 + r
sin 03
rip-
2
3
r
r2 sin 02 +
p
+h, cos0
2 sin 03P
03
3
163
coS0
rh
=r
2
2
os
Pcos:3P
(sin0
s\~~/2
r
'~P~Pjcos0
r3
+
r
h tan0
CO,
COS
3J
+r,
-'
-
3
tan0 3
2
2cos03P
__+_-
"
tan0 3
IVtn
___
coso 2 tan0p
cos0 3,,
sin 0 2,
[~cosQ,,J
2,3P3
2
2
r =r22, I coSQ3
( + tan2 0
3
+ -
__rata6
coSQ3
J+h
1+tan20
+ r,,
p
cos0 3,,
\
3
cos0 3 ,
COS 03,
"
')6,
tan 03P
2cosO3,,
2 COS3,
cs3
The magnitude of , is the moment arm of the friction force about secondary instant
center of rotation and is a function of both 03, and 03, , since l, is a function of 03, .
Using these equations, the following plots were obtained showing the magnitudes
of the moment arms for both linkage systems as a function of their configurations. Note
again, that the magnitude of the moment arm for the primary linkage system is not a
function of the configuration of the secondary linkage system, while the magnitude of the
moment arm for the secondary linkage system is a function of both.
The following plot shows the magnitude of the primary moment arm, the moment
arm of the friction force about the primary instant center. The plot was obtained using
164
values of 2.72 in. for the coupler link, 4.23 in. for ground link, and 7.24 in. for the
perpendicular distance from the coupler link to the desired instant center.
0.25
0.2
(a
0.15
0
Cs
E
C
0.1
a.
0.05
I
0I
3
-2
-1
0
1
2
3
Primary Link Angle in degrees
Figure 105. Magnitude of moment arm for moments about the primary instantcenter of
rotation.
The following 3-D plot shows the magnitude of the secondary moment arm, the
moment arm of the friction force about the secondary instant center. This plot was
obtained using the same parameters for primary linkage system as before and using
values of 4.82 in. for the secondary coupler link, 7.19 in. for the secondary ground link,
and 8.23 in. for the perpendicular distance from the secondary coupler link to the desired
instant center.
165
CO 0.31.0
a)
0.2,
E
a.)
0.11
E
r
0
a)
C
0,
-0.1
4
.u
e L---
-
0
2
4
PrimaryC
Angle in degrees
-4
-4
-2 Secondary Coupler Link
Angle in degrees
Figure 106. Magnitude of moment arm for moments about the secondary instant center
of rotation.
166
As can be seen in the previous section, the center of rotation of a four bar
gimbaled does not stay in the same location. Since the location of the center of rotation is
changing the magnitude of the moment arm of the polishing force that center can not
remain zero. Furthermore, as the previous figures indicate, the amount by which the
moment arm changes per degree of angle change of the coupler ring is dependent on the
geometry of the mechanism. For both the primary and secondary linkage systems this
change (deviation from zero) is less, for longer, taller systems given the same width.
Thus to minimize the moment arm of the polish force and thereof the presence of edge
effects on the wafer, it is necessary to make the gimbaled mechanism and the entire
machine taller. The latter option is very possible. In fact the equations shown in the
previous sections can be used to optimize such a design and to obtain a justifiable
compromise between polish quality and machine size. However, considering that both
machine height and polish quality are one of the highest priority design goals of either a
research or a commercial tool, it is better to consider alternative designs that would not
require such a compromise.
To this end, it is clear that a spherical cup has a permanent center of rotation at the
center of the sphere that stays fixed. A simple schematic of such a joint, also referred to
as a ball joint, is shown in the following figure.
167
Figure 107. Rendered view schematic of a simple sphericaljoint.
However, a simple spherical joint only constraints three degrees of translation freedom
and still allows for three degrees of rotation. Thus such a joint can not transmit or resist
any torque. As a result it must be used in conjunction with another coupling that provides
the torque. Such a coupling, however, would have to deliver the necessary torque without
interfering or constraining the motions of the spherical joint, as this would over define the
system. To do this the latter coupling must constraint only one degree of freedom, that of
rotation about the head spindle axis.
Consider a free floating (moving) triangle in space and a grounded triangle as
shown in the following figure. It would be the task of such a coupling to attach the two
triangles such that the moving triangle can translate anywhere and rotate about any set of
two axis passing through its center that is independent of the axis connecting the two
triangles. Only motions about the axis that connects the two triangles should be
constrained.
168
Figure 108. Schematic of the target bodies to be coupledfor the transmissionof torque.
Initially, consider a telescoping joint attached from the ground triangle to the moving
triangle.
169
Figure 109. Schematic showing the two target bodies connected by a telescopingjoint.
The triangle can now only translate along the axis of the telescoping joint. This
telescoping joint can consist of a spline that does not allow axial rotation. Next, a
universal joint is added at the moving triangle end of the telescoping joint.
170
Figure 110. Schematic showing the universaljoint configurationon the moving body.
The universal joint allows the moving triangle to rotate about any two axes that pass
through its center and that form a linearly independent set with the axis of the telescoping
joint.
Finally, in order to provide three translation degrees of freedom instead of one,
another universal joint is added at between the ground end of the telescoping joint. This
allows the other end of the telescoping joint to span the surface of a sphere that is
centered at ground. Because of the presence of the telescoping joint, the latter sphere can
vary in radius and thus spans an entire volume and provides three degrees of translation
freedom within the range of the telescoping and universal joints.
171
Figure 111. Schematic showing the completed coupling of the targetbodies to each other
using a telescoping constant velocity joint.
To summarize, the first universal joint constraints all three translation degrees of
freedom, and one rotational degree of freedom, but allows rotations in the two other
independent and orthogonal directions. The second universal joint that is attached to it
has the same constraints and thus allows the axis of the transmitted torque to be oriented
in any direction. Together, the two universal joints form the well known constant velocity
joint that drives the wheels of a car. The sliding or telescoping joint, in between the
universal joints, merely allows the point of application of torque to be anywhere in space.
172
AN&
A
~~71~~
Figure 112. Schematic showing the two target bodies and coupling in an arbitrary
configuration.
As was mentioned before, any such mechanism should be placed between the
ground and the stator end of the spindle and not between the rotor and the wafer carrier.
The latter option will cause the gimbaled mechanism to adjust for misalignments between
the head and platen spindles at each rotation of the wafer. This forces the gimbaled
mechanism to undergo cyclic motions at the same frequency as the rotational frequency
of the head spindle, which can be as high as 500 rotations per minute. Since such cyclic
motions will clearly wear out the mechanism faster, the gimbaled mechanism must be
placed in between the ground and the stator end of the head spindle. In this manner the
mechanism couples the head spindle carrier bracket to the head capsule which contains
the stator.
173
The mechanism must also be compact in order to fit inside confines of the gantry
structure. Fortunately, however, very small motions of the mechanism are required to
compensate for misalignment of the spindle axis due to manufacturing. The following
diagram shows a section view of the Head Spindle design, which is not covered in detail
since it is very similar to that of the Platen Spindle already covered in sections 8 through
14.
Figure 113. Rendered view diagram of the Head Spindle Assembly
The main head bracket, shown below, holds onto the head capsule and attaches to
the z-axis plate on the gantry. The gimbaled system discussed above fits in series
between the head capsule and the Main Bracket to provide gimbaling of the entire head
174
spindle(equivalent to the moving triangle in Figure 111) with respect to the rest of the
machine(equivalent to the ground triangle in Figure 111).
Figure 114. Rendered view diagram of the Main Bracket.
Notice the spherical section features shown on the Main Bracket in the previous
figure. These features along with the spherical sections shown in purple below, form a
spherical joint like the one shown in Figure 107.
175
Figure 115. Rendered view diagramshowing the Head Capsule and the spherical
sections.
The spherical section features shown in purple are add on feature which are then
bolted onto the capsule. The relation of these pieces with respect to the spherical sections
on the Main Bracket is shown in the following figure.
176
Figure 116. Rendered view diagram showing sphericaljoint assembly.
Next, a compact telescoping constant velocity joint is places in series between the
capsule and the Main Bracket. First, two pivot point brackets are fastened to the head
capsule as shown.
177
Figure 117. Rendered view diagram showing the initial components of the telescoping
constant velocity joint assembly.
Next a ring is placed in between the pivot point brackets. Dowel pins with delrin sleeves
are used to connect the ring to the pivot point brackets.
178
Figure 118. Rendered view diagram showing the secondary ring of the moving universal
joint.
This ring has anther set of holes at 90 degrees from the first two. These holes will be used
along with similar dowel pins to connect another ring that pivots inside this one. Thus far,
one of the universal joints, the one on the moving end has been completed. This joint is
exactly like the one shown in Figure 94.
179
Figure 119. Rendered view diagram showing the primary ring of moving universaljoint.
As can be seen from the figure above, the latter ring is longer than the first and has 3
slotted grooves at the top. These grooves will form a telescoping joint along with another
larger ring that contains three rectangular slots, facing towards the center of the ring. The
slots from the larger ring slide in the grooves of the inner one. A class three running fit is
used between the sliding parts for this purpose. The following figure shows this assembly
which provides the telescoping joint of the desired coupling. The outer ring of the
telescoping joint will also server as coupler ring of the grounded universal joint (Refer to
Figure 94). For this reason the outer ring also has two holes that will be used to form
pivot points using a dowel pins with delrin sleeves as before.
180
Figure 120. Rendered view diagram of the completed telescopingjoint implementation.
The latter pivot points will be used to allow the outer ring of the telescoping joint to pivot
inside yet another larger ring with matching holes. This latter ring, also has another pair
of holes at 90 degrees from the first that will allow it to pivot with respect to the Main
Bracket thus forming the final, ground, universal joint in the coupling. This coupling is
identical in principle to the one shown in Figure 111.
181
Figure 121. Rendered view diagram of the completed telescoping constant velocity joint
assembly.
The same spherical joint design shown in Figure 116 can be used with other
types of coupling to transmit the necessary torque. Another such coupling is a wide
diameter bellow. These bellows come in a variety of diameter and height arrangements.
They are made by connecting consecutive angled metal rings as shown in the following
figure.
182
Figure 122. Rendered section view of a bellow.
The rings are connected to each other using either a welding or fusion technique. The
bellows are available in Stainless Steel and are more commonly made of Type 347
Stainless Steel. The torsional strength of the connection interfaces of these bellows and
its buckling strength together define the capacity for it to transmit torque along its
cylinder axis. Larger diameter bellows can transmit a larger amount of torque without
failing in shear. Bellows that are mounted in tension can transmit a larger amount of
torque without failing due to buckling. In general, this design does not have as high a
torque capacity as the one shown in Figure 121. However, in theory the Head Spindle
must resist zero torque when both the platen and head are spinning at the same velocity.
As such, the bellows design can provide more than adequate torque for this application.
In addition, the bellows design is cheaper and simpler to implement than the telescoping
constant velocity joint option. Out of all of the options discussed, the bellows torque
coupling and spherical gimbal combination offers the desired center of rotation via a very
simple and elegant design. As such it was chosen to use this configuration in the final
183
design of the Head Assembly. The following figure shows the implementation of the
gimbal and torque coupling combination chosen for the Head Assembly.
Figure 123. Rendered section view of HeadAssembly using a bellow to transmit torque.
16 Conclusion
Most of the design of this machine was simple and strait forward. What was
unexpected was the effect that the availability of parts had on the final designs. In
particular, the design of the platen assembly reduced quite considerably in size by the use
of the cross roller bearings. The long hours that were spent searching for the types of
parts that were available were well worth the effort. In addition, conversations with
manufacturers and machine shops were also very informative and helpful. One particular
idea that resulted from one of these conversations was to use two independent air pistons
184
along with two air pistons connected with a pressure equalization line to kinematically
support the Top Table. Since this type of mounting is commonly used in self-leveling
vibration isolation optical tables, it is a promising option to explore. Even though it does
not provide as even support as the cast iron Lower Frame used, it is worth future work to
look into this option if research done with this machine leads to the design of lighter and
more compact machines. Another area for future work is to look at the possibility of
compensating for spindle bearing axial runout using the force control system on the head
to insure a constant and even polish pressure. This would relax the requirements on the
bearing and reduce cost and maintenance. To investigate this further uneven Detachable
Platen Sections can be made to be used to simulate different magnitudes of runout for the
current force control system to compensate for.
185
Appendix Section
Section A
Derivationsof the velocity equationsfor the rotary configuration:
2
Z
X,
X2
Appendix Diagram 1. Coordinatesystem for the rotary configuration.
***Note: In the diagramabove, the "1" subscript coordinatesystem is the wafer coordinate system and the
"2" subscript coordinate system is the platen coordinatesystem. The diagram above shows the platen and
wafer reference frames at t=O. In the following derivation, aO) is the rotationalvelocity of the wafer and (op
is the rotationalvelocity of the platen.
vH= V p
-
VH
In the ground referenceframe at t=O
VH
UHrsin 0
=
fp=-tpR
,
VyHrcoso
sin 0 1 +mpRcoso
sin t +W HrsinO)
=(-,R
+
i + (upRcos
-tUHrcosO)J
rsin 0 = R sin 0
rcosO = Rcoso + s
1
=
Hr sin ) I +H(q~rcos
(-uprsin 0 +
VV =
(OUH
P
+ K)rs P+H
[S
- rVHrcose)
)rcosO -FrPS] J
186
In the ground referenceframe at time t:
(r)r
y=
sifJHt +0)
[OP ~ tUH )rCOS(MHt +
-tUPS]
P0) J
In the wafer referenceframe at time t (Assuming that the wafer referenceframe is aligned with ground
referenceframe at t=O):
=MH- m,)rsinUHt+
=
+ ((w
-
UH )rcos(OhHt +0)
0)(cosPU~t)+ [('UP
(OH
-(PSICOSIHt)-
In the ground referenceframe at time t, if WH
-
(P
UH )rosOUHt + 0)
-
-
rupsKsin tfHt))
up)sin(fgHt+ 0)(sin
I
Ht)X,
(00:
VH =S-Wsj
In the wafer reference frame at time t, if (9H= o0=
,H =-tos
oG:
sintot I -osCosmot
J
187
Section B
Derivationsof the velocity equationsfor the linearconfiguration:
Y,
MH
VB
X,
XE3
Appendix Diagram 2. Coordinatesystem for the linearconfiguration.
***Note: In the diagram above, the "1" subscriptcoordinate system is the wafer coordinatesystem and the
"2" subscript coordinate system is the belt coordinate system. The diagram above shows the belt and
wafer reference frames at t=O. In the following derivation, O>H is the rotationalvelocity of the wafer and VB
is the velocity of the belt.
In the groundreferenceframe at t=O:
v
= vB
VB
VH
=
-rVTH
~
VH
VOH
sin 0 i+
ru
HCoS
j
i% = (vO + rUHsin 0) 1 - rtHcosO
j
In the ground referenceframe at time t:
V%
= [v, + r[HH
H
H
188
In the wafer referenceframe at time t(Assuming that the wafer referenceframe is aligned with ground
referenceframe at t=O):
=[v0 +
-
([v 0 + rm H
(wt+o)
HrHusin osuyt-rJH
u1Hsin
Hcos(Hut+O~intt)I
Ht+H)Hintt+rtcos(uHt +o)CostH,)
189
Section C
Detailed calculationfor the simple case of a bolt in shear between two materials undergoing diferent
thermal expansions.
BOlt
Stainless Seel
Appendix Diagram 3. Schematic diagram of a bolt being sheared between two
materials with different amounts of thermal expansion.
ail + asteel
rCy r
Etable
2
Esteel
table +
Egranite
Arailorrail =
atable Aable
2
atable
granite
Arailarail
Aable
rail -
rail
stee
E
(rail
Esteel
arail
Esteel
+
A -
table
atable
+
seel
Egranite
asteelA
=Ctable +
Egranite
+ asteelAT-
+
E,,aniie
atable
agranite
agraniteA
agranite
190
O rail
-
2
AraiGrai
ral + agraniteAT
rl + asteelAT - Erafl
E EsteelE
egble
(a
arail ~
granite -asteel
2Aa
I +
Esteel A able Egranite
Ftable
2
Arallrral
Aable
Erail =Etable =
+ asteel
atable
-
steel
__
Irail Arail
Abolt
+
a
eAT
granite
granite Agranite
2
Abolt
191
Section D
Detailedcalculationsfor the flexing bolt system. The bolt is treated as beam with no distributed load and
boundary conditions based on the rail and table plug interactions.
Bolt Head
Bolt Head
S trained State
Neutral State
Rail
Rail
olt Body
Bolt Body
lug
n
DPlug
Appendix Diagram 4. 2-D schematics of the bolt bein gmodeled as afixedfixed beam in
both the neutral and strainedstates.
q(x) =0
V(x)= A
M (x) = Ax + B
(x)=v(x)=v()=D=0
D=0
6(0) = C =0
C=0
1
[Ax2-
EI
--
1 [AxI
EI
2
+Bx+C
Bx2
-+-+Cx+D]
6
2
v(L)
I
BL2-
AL 3
+
=
S(L) =-f
EI
= (Era
~ Etable )Lrail
AL +BL =0
a2 r
V(L)=A=CGrai1Arai1
192
B= -AL
2
1 AL3
EI 6
AL2]
AL3]
1[
4
EI
(Eri
8
-
12
table )Lrail
E rail +asteel AT
Erail
Esteel
CEte
Ortabl
table
+graniteAT
granite
2
Arail
rail
3
Arail6ral
ArailU rail
rail
Etable rrail
3
Urail
E l[12
ral
2
+
+
12EI
Egranite
UrailArail +
steel
(a
-
Lrail
~agranite
agranite
T Lai
ableEgranite
2A
Esteel
Aable
ETrail
Esteel
3
ULrail
= -table
rai
l
steel
a granite
T
AableEgranite
Utable
2
Arailrral
Aable
Erail
table
Trail +asteeiAT
-
=
table +a,,anitesT
steel
__
bolt
ICrailIArail
Abolt
granite
_ IUgranite Agranite
2
Abolt
193
Section E
Location of
Desired
Instant Center
r2 o
h
/
r;
r2
rF
4
Appendix Diagram 5. Schematic of a four bar linkage system with a desired instant
centerfor the coupler link
For the following analysis the complex polarnotation will be usedfor the book keeping of vector
calculations. Using this method a vector F shown above is expressed as:
F = rcosO +i rsinO
In this latter case the real component is the horizontal component of the vector and the complex component
is the vertical component.
eiO =cosO +i sin 0
The prooffor the equation above comes from the sum of the Taylor expansions of the cos(6) and sin(iO)
functions which is equal to the Taylor expansion of the e'Ofunction.
The latter methods can be used to analyze and obtain the necessary link lengths and anglesfor the four bar
gimbaled mechanism given the location of the desired instant center at the neutral position. In the neutral
position both the coupler link (the wafer carrier)and ground link are assumed to be horizontal as shown
below. The length of the coupler link is constrained by the design of the wafer carrier and is given.
Similarly, the length of the ground link is constrainedby the design of the ground link and is also given.
The location of the desired instant center is given as a distance ho relative to the center of the wafer carrier
which is the midpoint of the coupler link. This is necessary since the wafer thickness and wafer carrier
design together dictate the value of ho.
194
r2 + r3 = i + 4
'O03
io +
r2e'-' + r3e
re
+r4e
0
'e
4
r 2 cos02 + r3 cos0 3 =rcos0, + r cos0 4
r2 sin 2 + rsin 03 =r,sin 0,+ rsin0 4
01 =03
=0
r2 cos0 2 + r3 = r,+r 4 cos0 4
r2 sin 02 = rsin 0 4
From symmetry:
02=180-0 4
cos0 2 =cos(180-04)=cos(1 80)cos(0 4 ) + sin (I 80)sin (04)= -cos0
4
sin 02=sin (180-04) = cos(0 4 )sin (180)- cos(1 80)sin(04) =sin04
r2cos0
2
+ r = r + r4 cos0 4 = r -rcos02
r - r
COS02
=
3
r2 + r
r2 sin0 2 =r 4 sinG 4 = r4 sin(180-0
2
)= rsin02
r2 = r4
CO2=r - r
2r2
2
r2
r2
=r + r
e'o = rle I + r4
rz cos0
2
= r, + r4 cos0 4
r2 sin 02 = r sin 04
r%cos0
2
= r,+ r cos0 4 = r,- r cos0
cos02 =
2
r
rzo + ro
r sin
2
=
r,
sin
4
=r4 sin 02
r'o = ro
195
COS02 =
2r 20
2
r,- r3
-r-
r2
r2o
r2o =r
r2
r - r3
h
sin 02
2
r
r
2h
2r2h
2rh
tan0
(r, - 2r3
r2
rr,
r22
r3
f(r - r)
= tan
02
-
r3
=180 -02
04
r2=r,- r
42
r =
0
C
rcs0
2
2cosO2
r4 = r2
r4o = r2o
196
Location of
Instant Center
rA
r.B
r
4
F,
Appendix Diagram 6. Schematic of afour bar linkage system showing the location of
the instant center of the couplerlink
Once the initial values of 2 and 4 arefound, the location of the instant center can be found as a function
of the coupler link angle. The intersection of FA and
coupler link angle is zero FA and
4n
are r2o and
F0
FB
is the location of the instant center. When the
respectively.
F4= -4F1+
F2 + F
r4e'04 =
io
+ r3e
-reioI + r2e
0, =0
r4 cos0 4 =-r,+r2cos0
2
+r 3cos0
3
r4 sin 04 = r2sin 2 + r3sin 03
(r cos0 4 ) 2 =
(r2
+
(r sin 0 4
2
=r2 +r2
=
2
2
+3
+(r3 cos( 3 f - 2ir2 cos0
cos0 2)
=
(r2 sin
-2ir2 cos
O
14
,+r
2
2
4
r2
2r2 r3
2
cos0
3
+2rr cos0 2 cos6
3
+ (r,sinG 3) + 2r2r sin 0 2 sin 0 3
62
2-2rrrcos0+2rr
2
2 -2ir
13
3
3
cos02cosO3+2r2r
+22 3s sin
COS2CS3
2
sinG33
2
= -- cos0 2 r3
cos03 +cos(0
2
-63)
r2
The above equation does not have a closed form solution and is solved numerically.
197
04 =
sin-'
r2sin2 + r3sin03
r
8
rAe O2 = re '' + rBe i04
rA cos0
= r,+ rB COsO 4
rAsinO2 = rB sin04
2
rB
_sin 4
rB
02
sin 04
r
r tan 0 2
cos0 2
tan 04
-1
tan0 2
tan0 4
r
cos0 2
Once the vector FA is found, the location of the instant center is also known, where the coordinatesof the
instant center in a reference frame with origin at the origin of link] is rAcosO2 along the x-direction ad
rAsinO2 along the y-direction.
Once the new location of the instant center has beenfoundfor the given coupler link angle, its distance
from the location of the desired instant center can be found in the following way. Since the purpose of this
design is to minimize the moment of arm of the frictionforce at the contact surface about the axis of
rotationof the gimbaled mechanism, the location of the desired instant center is in the plane of the contact
surface. For the sake of symmetry, it is also alignedwith wafer axis of rotation, and is thus the point where
that axis intersects the contact plane.
198
hP
Location of
Instant Center
Location of
Desired
Instant Center
rBP
rAP,
r'
p
p
r~p
Appendix Diagram 7. Schematic of afourbarlinkage showing the change in the
location of the instant center.
13
P +vP
'p
r 2 ,e
P
'2P
+
2
e'0 3 +he(3
(r2 - rA
Os 2, +
(r2rAP
i
+90)
e 02
-
r
e
r
cos0 3 = (r - h )os(0
+ r
.yp+r
r
jsin 03 = (rv - h
e
3
)+
+90)
in (03 + 90)
h
cos(0 3, +90)= -sin 03,
sin(6 3 +90)= cos ,
3
r P
rA
Os0
2
+
+rh
cos 3 =-rv
-
hP)sin0 3
199
rh, cosr3
cos
in
-rA
(r 2
2
=
-
si0s3
(
-r,
r
jcOS0
-
h)sin0 3
r3
hc
3
+hnGs
+
r+rh tanP,+hp
2
cop
2
02
(r
2s6
(
(r r-rn02
ryp sin
= r2
r -h,0os%
=(
COS.
rpJ
2
v
2,
cos23 +.+sno
2P (r -h, tan
r-14)Si0
;
"cost,
sin
+r
os02 -
-r
=-(r 2r
(r 2 p
r
3
, +
)cosO2
/
_ ( o6
r
- r
tan03
'
poop 2
a
r3
LoOtan03
tan20 3 , +hp tan20 ,
3
1+ vtan2
p 3
p
{(r,r
(~p -r~p
csn
in0
coso3,2
cos0
3cos
2
an
t
coso3,
j+h,(+
p l3
tan 2 03
200
rA,
V
r3,
Appendix Diagram 8. Schematic of afourbarlinkage showing the location of the instant
center of the secondary system in the plane of the primary system.
s =
rA
raco6
e
2
= r2
e
2,
+ 6,e
+
3,+90)
1
2
cosQ3 -10 cos(0 3 +9o)+lhcoso3
= r2 cosQ2 +r2
+ IV
+I
3, -lee(O+)
2
rA. sin
2
sinG2 + 3sin
3
-lo sin(6
3
+ 90)= -sin (03,)
cos(0
3
cos5(63 +90)
vil
+ sin (63 +90)
+90)+l sin63
sin (03, +90)= cos(03,)
r, cos6
rA,
2
= r2
cos2 + 3cos03 +10sin03 +lhCOS
sin2 =r 2 sin 62
2
3
-1,sin03
+ r3sin6 3 -0cos 03 +lhsin3 +lCOS06 3
2
201
Isin 02,
r, +(10
S- (rA - r 2,(+
sin 03,
2
-
tan03,
r
cos0 2 +
+0+
3,
sin 03 , 2tanO3,
1 = r
,,)
1
h
tanG3,
V),
lh +(10 -1
tan 63,
iv
cos
= r2
sin 02
02_+ r
In+
sin 03
V +tan20[3
1+
(r,
2tan03,
(r2
-
cos02
-rA
I- sin
0 3,
r2 ,
'
r
-
sin 03, tan 03,
sin 02,
sin 03, tan03,
+
+
,
-i
_10
2_
__
2 tan 03,
tan2 03,
1+
1
tan 2 03,
)
4J
202
rh
P
h,
VP
lv
F/
P
3
Appendix Diagram 9. Schematic of a fourbar linkage showing the location of the
instant center of the secondary system relative to the desired location.
h
r2 +F2 2P~+hi, = 2~+I,,,V, +VP+F
r2 e
+
e''
P2
r2 cos02 + rcos3
2
+he(3 +90)
i(O)+
,e 9 0 )
2
+ h cos(3 +90)=
(, +90) +rh
VV
2
+ r cos(0
3
+ 90)+ rh cosO3
'3
r2
e
sin 6 2 + 2- sin 03P + h, sin (03 + 90)= l, + r, sin (03 + 90)+
r
sin 03
0
cos(0 3, +90)= -sin 03,
sin (03, +90)= cos0 ,
3
203
2
r 2 sin 0 2 +
p
,h
r'3
-Psin 03
r
co o p
+P
r;
+h +t[(3 -
'
G3 =r
ta2
r
=r
[1+
sin
2
' sinG 2
cos
3,
"~(cosG
p
p
-l + r, cosO3 + r sin 03
V
V
r,
+r
p
ta
P
0
r___
+-r--
1+
p
p
2
2
v, 2 CS3,
v, 2'[
r=
si
r sincos3
2
r
cosO2
= r2
=
nP
-hpt
cosQ3
r,
p
+ h, cosO3
2
r2
sin0
-h
r 2 cosO2 + -'cosO
2cos3h
tan 3 -
r3 tan
'
2
2
3
+IV r,, tan03P
'+h -
p
+tan2a2 3 tKrsin 2, K cos 2
l
-r
CoO
A3
rha3,
G
+fl
+h
tanG3
cosG3 ,
P
j
tanG3
vPyc , os3,J
rV + tanG3
'
cosG
+h
+ tan23)
cosG3 ,
j
3,
2cosG
1,
+ r:t
cosG 3 ,
3,
03
2cosG
3,
204
Section F
p3-k:: Static Nodal Stress
Unts: NMn^2
Von Mises
.51 7e+005
.891e+005
264e.0O5
2.34e.005
01 2e+005
.386e+005
.760e+005
.133e+005
.507e+005
.255e+005
.286e+004
.440e+002
Appendix Diagram 10. FEA stress resultsfor platen with thick top plate.
205
Platen-I:: Static Nodal Stress
Units: NnA2
Von Mises
.307e+006
.608e+006
3.007e+OO6
2.706e+006
2
405e+006
.105e+006
1.804e+006
.504e+006
1.203e+006
9.022+OO5
.01 6e+005
.009e+005
2.626e+002
Appendix Diagram 11. FEA stress resultsfor platen with rib structure.
206
Pten-4:: Static Nodai Stress
Units: NAn^2
Von Mises
.608e+006
.307e+006
.007e+006
2.706e+006
.405e+OO6
.1O5e+.O6
.804e+006
I .504e+006
.203e+DO6
.022e+005
.01 6e+005
.009e+005
.626e+002
Appendix Diagram 12. FEA stress resultsfor platen with rib structureshowing the
stresses on the ribs.
207
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for
Slocum, A.H., Precision Machine Design. 1992, Michigan: Society of Manufacturing
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Popov, E.P., Engineering Mechanics of Solids. 1990, New Jersey: Prentice-Hall Inc.
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208