U.S. patent application number 11/058099 was filed with the patent office on 2005-09-08 for fine force control of actuators for chemical mechanical polishing apparatuses.
Invention is credited to Novak, W. Thomas, Watson, Douglas C., Yang, Pai-Hsueh, Yuan, Bausan.
Application Number | 20050197045 11/058099 |
Document ID | / |
Family ID | 35800568 |
Filed Date | 2005-09-08 |
United States Patent
Application |
20050197045 |
Kind Code |
A1 |
Novak, W. Thomas ; et
al. |
September 8, 2005 |
Fine force control of actuators for chemical mechanical polishing
apparatuses
Abstract
An actuator assembly (432) for positioning a pad (48) includes a
first actuator assembly (440), a second actuator subassembly (442)
and a control system (524). In one embodiment, the first actuator
subassembly (440) includes a first core (502), and a conductor
(504) secured to the first core (502), and the second actuator
subassembly (442) includes a second core (506) spaced apart a
component gap (444) from the first core (502). Further, the control
system (524) directs current to the conductor (504) to attract the
second core (506) to the first core (502). In one embodiment, the
amount of current directed to the conductor (504) is calculated
without measuring the component gap (444).
Inventors: |
Novak, W. Thomas;
(Hillsborough, CA) ; Watson, Douglas C.;
(Campbell, CA) ; Yang, Pai-Hsueh; (Palo Alto,
CA) ; Yuan, Bausan; (San Jose, CA) |
Correspondence
Address: |
THE LAW OFFICE OF STEVEN G ROEDER
5560 CHELSEA AVE
LA JOLLA
CA
92037
US
|
Family ID: |
35800568 |
Appl. No.: |
11/058099 |
Filed: |
February 14, 2005 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
11058099 |
Feb 14, 2005 |
|
|
|
10722090 |
Nov 24, 2003 |
|
|
|
6855032 |
|
|
|
|
60621399 |
Oct 22, 2004 |
|
|
|
Current U.S.
Class: |
451/5 |
Current CPC
Class: |
B24B 37/042 20130101;
B24B 37/30 20130101; B24B 37/005 20130101; B24B 41/068
20130101 |
Class at
Publication: |
451/005 |
International
Class: |
B24B 049/00 |
Claims
What is claimed is:
1. A polishing apparatus for polishing a device, the polishing
apparatus comprising: a polishing pad positioned near the device; a
first attraction only actuator including a first core, a conductor
secured to the first core, and a second core spaced apart a
component gap from the first core, the second core being coupled to
the polishing pad; and a control system that controls the first
attraction only actuator.
2. The polishing apparatus of claim 1 wherein the first core is
somewhat "C" shaped.
3. The polishing apparatus of claim 1 wherein the first core is
somewhat "E" shaped.
Description
RELATED APPLICATION
[0001] The application is a continuation-in-part of application
Ser. No. 10/722,090 filed on Nov. 24, 2003, which is currently
pending. This application also claims priority on pending
Provisional Application Ser. No. 60/621,399 filed on Oct. 22, 2004.
As far as is permitted, the contents of application Ser. No.
10/722,090 and Provisional Application Ser. No. 60/621,399 are
incorporated herein by reference.
FIELD OF THE INVENTION
[0002] The present invention relates to a method for maintaining
fine force control between a polishing pad and a wafer that is
being polished by the pad. The present invention also relates to an
apparatus that utilizes actuators to perform fine force control
without the need of gap measurement.
BACKGROUND
[0003] Chemical mechanical polishing apparatuses (CMP apparatuses)
are commonly used for the planarization of silicon wafers. In one
type of CMP apparatus, a rotating pad is placed in contact with a
rotating wafer and the pad is moved back and forth laterally
relative to the rotating wafer. Additionally, a polishing slurry is
forced into a gap between the wafer and the pad. The slurry is
typically an aqueous solution that carries a high concentration of
nanoscale abrasive particles. The slurry can play a number of
critical roles in the polishing of the wafer. For example, the
chemical composition of the slurry can alter the surface properties
of the wafer, soften the wafer surface and make it amenable to
material removal. Further, the abrasive particles in the slurry
remove material from the wafer surface by cutting nanoscale grooves
in the wafer surface. Some in the industry believe that most of the
material removal occurs when pad asperities on the pad are in
contact with the wafer, trapping slurry particles between them. The
asperities push the particles into the wafer surface and drag them
along so the abrasive particles act as nanoscale cutting tools.
[0004] Designers are constantly trying to improve the accuracy and
efficiency of CMP apparatuses. For example, if the force applied by
the pad against the wafer is not uniform, the material removal rate
will not be uniform. Additionally, if the force applied by the pad
against the wafer is not precisely controlled, the planarity of the
wafer and accuracy of the CMP apparatus will be diminished.
SUMMARY
[0005] The present invention is directed to an actuator assembly
including a first attraction only actuator and a control system. In
one embodiment, the first actuator includes a first core, a
conductor secured to the first core, and a second core spaced apart
a component gap from the first core. Further, the control system
directs current to the conductor to attract the second core to the
first core.
[0006] In one embodiment, the amount of current directed to the
conductor is calculated without measuring the component gap.
[0007] In one embodiment, the control system utilizes the
simplified formula of I={square root}F to calculate the amount of
current directed to the conductor. In this embodiment, I is the
current and F is the force generated by the first actuator.
[0008] In another embodiment, the control system calculates the
component gap from at least one previous sample. The calculated
component gap is used for calculating the amount of current
directed to the conductor at a subsequent time. In another
embodiment, the control system uses calculated component gap
information from a plurality of previous samples to determine the
amount of current to direct to the conductor at a subsequent
time.
[0009] The present is also directed to a system and method for
accurately controlling the force applied by a pad against a wafer.
In some embodiments, the present invention provides a system and
method for controlling actuators without directly measuring the
component gap between components of the actuators and an actuator
assembly that can be controlled without measuring the component
gap.
[0010] The present invention is also directed to a CMP apparatus, a
method for controlling an actuator assembly, and a method for
making a CMP apparatus. Additionally, the present invention is
directed to an object or wafer that has been polished by the
methods or apparatuses provided herein.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] The novel features of this invention, as well as the
invention itself, both as to its structure and its operation, will
be best understood from the accompanying drawings, taken in
conjunction with the accompanying description, in which similar
reference characters refer to similar parts, and in which:
[0012] FIG. 1 is a schematic illustration of an apparatus having
features of the present invention;
[0013] FIG. 2 is a perspective view of a portion of a polishing
station of the apparatus of FIG. 1;
[0014] FIG. 3A is a side illustration of a substrate holder, a
substrate, a pad holder, a pad, and a fluid supply having features
of the present invention with the pad in a first lateral position
relative to the substrate;
[0015] FIG. 3B is a side illustration of a substrate holder, a
substrate, a pad holder, a pad, and a fluid supply with the pad in
a second lateral position relative to the substrate;
[0016] FIG. 4A is a perspective view of a polishing head assembly
having features of the present invention;
[0017] FIG. 4B is a cut-away view of the polishing head assembly of
FIG. 4A;
[0018] FIG. 4C is a top plan view of the polishing head assembly of
FIG. 4A;
[0019] FIG. 5A is a perspective view of an actuator assembly having
features of the present invention;
[0020] FIG. 5B is a side illustration of a portion of the actuator
assembly of FIG. 5A;
[0021] FIG. 5C is a side illustration of another embodiment of a
portion of an actuator assembly that can be used in the polishing
head assembly of FIG. 4A;
[0022] FIG. 6 is a graph that illustrates the functions of the
control system;
[0023] FIG. 7 is a graph that illustrates the measured forces at a
plurality of time steps; and
[0024] FIG. 8 is a graph that illustrates force versus voltage;
[0025] FIGS. 9A-9F are alternative graphs that illustrate features
of the present invention; and
[0026] FIGS. 10A-10E are alternative graphs that illustrate
features of the present invention.
DESCRIPTION
[0027] FIG. 1 illustrates a top plan illustration of a precision
apparatus 10 having features of the present invention. For example,
the apparatus 10 can be used for the preparation, cleaning,
polishing, and/or planarization of a substrate 12. The design of
the apparatus 10 and the type of substrate 12 can vary. In the
embodiment illustrated in FIG. 1, the apparatus 10 is a Chemical
Mechanical Polishing system that is used for the planarization of a
semiconductor wafer 12. Alternatively, for example, the apparatus
10 can be used to clean and/or polish another type of substrate 12,
such as bare silicon, glasses, a mirror, or a lens.
[0028] In FIG. 1, the apparatus 10 includes a frame .about.14, a
loading station 16, a cleaning station 18, a polishing station 20,
a receiving station 22, and a control system 24. The frame 14
supports the other components of the apparatus 10.
[0029] The loading station 16 provides a holding area for storing a
number of substrates 12 that have not yet been prepared for their
intended purpose. For example, the substrates 12 can be
unplanarized and unpolished. The substrates 12 are transferred from
the loading station 16 to the receiving station 22. The substrate
12 is then transferred to the polishing station 20 where the
substrate 12 is planarized and polished to meet the desired
specifications. After the substrate 12 has been planarized and
polished, the substrate 12 is then transferred through the
receiving station 22 to the cleaning station 18. The cleaning
station 18 can include a rotating brush (not shown) that gently
cleans a surface of the substrate 12. After the cleaning procedure,
the substrate 12 is transferred to the loading station 16 from
where it can be removed from the apparatus 10 and further
processed.
[0030] In the embodiment illustrated in FIG. 1, the polishing
station 20 includes a polishing base 26, two transfer devices 28,
29, three polishing systems 30, and a fluid source 32.
Alternatively, for example, the polishing station 20 can be
designed with more than three polishing systems 30 or less than
three polishing systems 30 or more than one fluid source 32.
[0031] The polishing base 26 is substantially disk shaped and is
designed to be rotated in either a clockwise or counterclockwise
direction about a centrally located axis. As shown in FIG. 1, the
polishing base 26 can be designed to rotate in a clockwise
direction about the axis to progressively and stepwise move the
substrate 12 from a load/unload area 34 to each of three polishing
areas 36 and then back to the load/unload area 34. The polishing
base 26 can also referred to as an index table.
[0032] In FIG. 1, the polishing base 26 includes four holder
assemblies 38 that each retain and rotate one substrate 12. Each
holder assembly 38 includes a vacuum chuck or gimbaled substrate
holder 40 that retains one substrate 12 and a substrate rotator 42
(illustrated in phantom) that rotates the substrate holder 40 and
the substrate 12 about a substrate axis of rotation during
polishing. Additionally, the polishing base 26 includes a "+"
shaped divider that separates the substrate holders 40.
[0033] The substrate rotator 42 can be designed to rotate the
substrate 12 in the clockwise direction or the counter clockwise
direction. In one embodiment, the substrate rotator 42 includes a
motor that selectively rotates the substrate 12 between
approximately negative 400 and 400 revolutions per minute.
[0034] In FIG. 1, each holder assembly 38 holds and rotates one
substrate 12 with the surface to be polished facing upward.
Alternatively, for example, the polishing station 20 could be
designed to hold the substrate 12 with the surface to be polished
facing downward or to hold the substrate 12 without rotating the
substrate 12 during polishing.
[0035] The transfer device 29 transfers the substrate 12 to be
polished from the receiving station 22 to the substrate holder 40
positioned in the load/unload area 34. Subsequently, the transfer
device 28 transfers a polished substrate 12 from the substrate
holder 40 positioned in the load/unload area 34 through the
receiving station 22 to the cleaning station 18. The transfer
devices 28 and 29 can include a robotic arm that is controlled by
the control system 24.
[0036] The polishing station 20 illustrated in FIG. 1 includes
three polishing systems 30, each of the polishing systems 30 being
designed to polish the substrate 12 to a different set of
specifications and tolerances. By using three separate polishing
systems 30, the apparatus 10 is able to deliver improved planarity
and step height reduction, as well as total throughput. The desired
polished profile can also be changed and controlled depending upon
the requirements of the apparatus 10.
[0037] The design of each polishing system 30 can be varied. In
FIG. 1, each polishing system 30 includes a pad conditioner 46; a
polishing pad 48 (illustrated in FIG. 3A) having a polishing
surface; a pad holder 50; a pad rotator 52 (illustrated in
phantom); a lateral mover 54 (illustrated in phantom); a polishing
arm 56 that moves the polishing pad 48 between the pad conditioner
46 and a location above the substrate 12 on the polishing base 26;
a pad vertical mover assembly 58 (illustrated in phantom in FIG.
1); and a detector (not shown) that monitors the surface flatness
of the substrate 12. In this embodiment, each polishing system 30
holds the polishing pad 48 so that the polishing surface faces
downward. However, the apparatus 10 could be designed so that the
polishing surface of one or more of the polishing pads 48 is facing
upward.
[0038] The pad conditioner 46 conditions and/or roughens the
polishing surface of the polishing pad 48 so that the polishing
surface has a plurality of asperities and to ensure that the
polishing surface of the polishing pad 48 is uniform.
[0039] The pad rotator 52 rotates the polishing pad 48. The
rotation rate can vary. In one embodiment, the pad rotator 52
includes a rotator motor (not shown) that selectively rotates the
polishing pad 48 at between approximately negative 800 and 800
revolutions per minute.
[0040] In one embodiment, the difference in relative rotational
movement of the pad rotator 52 and the substrate rotator 42 is
designed to be relatively high, approximately between negative 800
and 400 revolutions per minute. In this embodiment, the high speed
relative rotation, in combination with relatively low pressure
between the polishing pad 48 and the substrate 12 helps to enable
greater precision in planarizing and polishing the substrate 12.
Further, the polishing pad 48 and the substrate 12 can be rotated
in the same or opposite direction.
[0041] The pad lateral mover 54 selectively moves and sweeps the
pad 48 back and forth laterally, in an oscillating motion relative
to the substrate 12. This allows for uniform polishing across the
entire surface of the substrate 12. In one embodiment, the pad
lateral mover 54 moves the polishing pad 48 laterally a distance of
between approximately 30 mm and 80 mm and at a rate of between
approximately 1 mm/sec and 200 mm/sec. However, other rates are
possible.
[0042] The pad vertical mover assembly 58 moves the polishing pad
48 vertically and at least partly controls the force that the
polishing pad 48 applies against the substrate 12. In one
embodiment, the pad vertical mover assembly 58 applies between
approximately 0 and 10 psi between the polishing pad 48 and the
substrate 12. The pad vertical mover assembly 58 further provides
forces to help maintain the force between the polishing pad 48 and
the substrate 12 at a substantially equal level across the
cross-section of the polishing pad 48. In one embodiment, the pad
vertical mover assembly 58 maintains the force at a substantially
equal level across the cross-section of the polishing pad 48 above
the substrate 12 regardless of whether the polishing pad 48 is
positioned entirely above the surface of the substrate 12 or
whether the polishing pad 48 extends beyond the outer edge of the
substrate 12. The pad vertical mover assembly 58 is described in
greater detail below.
[0043] The fluid source 32 provides a pressurized polishing fluid
60 (illustrated as circles) into a gap 64 (illustrated in FIG. 3A)
between the polishing pad 48 (illustrated in FIG. 3A) and the
substrate 12. The type of fluid 60 utilized can be varied according
to the type of substrate 12 that is polished. In one embodiment,
the fluid 60 is a slurry that includes a plurality of nanoscale
abrasive particles dispersed in a liquid. For example, the slurry
used for chemical mechanical polishing can include abrasive
particles comprised of metal oxides such as silica, alumina,
titanium oxide and cerium oxide of a particle size of between about
10 and 200 nm in an aqueous solution. Slurries for polishing metals
typically require oxidizers and an aqueous solution with a low pH
(0.5 to 4.0). However, when planarizing an oxide layer, an alkali
based solution (KOH or NH4OH) with a pH of 10 to 11 can be
used.
[0044] In another embodiment, the slurry can include non-abrasive
particles and/or abrasive-free particles.
[0045] In one embodiment, the chemical solution in the slurry can
create a chemical reaction at the surface of the substrate 12 which
makes the surface of the substrate 12 susceptible to mechanical
abrasion by the particles suspended in the slurry. For example,
when polishing metals, the slurry may include an oxidizer to
oxidize the metal because metal oxides polish faster compared to
the pure metal. Additionally, the fluid 60 can also include a
suspension agent that is made up of mostly water plus fats, oils or
alcohols that serve to keep the abrasive particles in suspension
throughout the slurry.
[0046] The rate of fluid flow and the pressure of the fluid 60
directed into the gap 64 can also vary. In one embodiment, the
fluid 60 is directed into the gap 64 at a flow rate of between
approximately 50 ml/sec and 300 ml/sec and at a pressure of between
approximately 0 and 10 psi.
[0047] The control system 24 controls the operation of the
components of the apparatus 10 to accurately and quickly polish the
substrates 12. For example, the control system 24 can control (i)
each substrate rotator 42 to control the rotation rate of each
substrate 12, (ii) each pad rotator 52 to control the rotation rate
of each polishing pad 48, (iii) each pad lateral mover 54 to
control the lateral movement of each polishing pad 48, (iv) each
pad vertical mover assembly 58 to control the force applied by each
polishing pad 48, and (v) the fluid source 32 to control the fluid
flow in the gap 64.
[0048] The control system 24 can include one or more conventional
CPU's and data storage systems. In one embodiment, the control
system 24 is capable of high volume data processing.
[0049] FIG. 2 illustrates a perspective view of a portion of the
polishing station 20 of FIG. 1 and three substrates 12. More
specifically, FIG. 2 illustrates the polishing base 26 and a
portion of three polishing systems 30. In this embodiment, each of
the pad holders 50 and polishing pads 48 are rotated as indicated
by arrows 200 and moved laterally relative to the surface of the
substrate 12 as indicated by arrows 202 and each substrate 12 is
rotated as indicated by arrows 204.
[0050] FIG. 3A is a side illustration of the substrate holder 40,
the substrate 12, the pad holder 50, the pad 48, and the fluid
source 32 with the pad 48 in a first lateral position relative to
the substrate 12. FIG. 3A also illustrates the gap 64 (which is
greatly exaggerated) and the fluid 60 (which is greatly
exaggerated) in the gap 64. In the first lateral position, the pad
48 is completely positioned over the substrate 12.
[0051] In this embodiment, the polishing pad 48 is relatively small
in diameter compared to the substrate 12. This can facilitate high
speed rotation of the polishing pad 48. Additionally, the
relatively small size of the polishing pad 48 results in a
polishing pad 48 that is lightweight, with less pad deformity,
which in turn allows for improved planarity. Alternatively, for
example, the polishing pad 48 can have an outer diameter that is
greater than the outer diameter of the substrate 12.
[0052] The fluid 60 supplied under pressure into the gap 64 by the
fluid source 32 generates hydrostatic lift under the polishing pad
48 that reduces the load applied to the asperities of the polishing
surface of the polishing pad 48.
[0053] In one embodiment, the polishing pad 48 is made of a
relatively soft and wetted material such as blown polyurethane or
similar substance. For example, the polishing pad 48 can be made of
felt impregnated with polyurethane. The polishing surface of the
polishing pad 48 is roughened to create a plurality of asperities
on the polishing surface of the polishing pad 48.
[0054] In one embodiment, the polishing pad 48 is flat, annular
shaped and has an outer diameter of between approximately 260 mm
and 150 mm and an inner diameter of between approximately 80 mm and
40 mm. Polishing pads 48 within this range can be used to polish a
wafer having a diameter of approximately 300 mm or 200 mm.
Alternatively, the polishing pad 48 can be larger or smaller than
the ranges provided above.
[0055] Additionally, in one embodiment, the polishing surface of
the polishing pad 48 includes a plurality of grooves 300 positioned
in a rectangular shaped grid pattern. Each of the grooves 300 has a
groove depth and a groove width. The grooves 300 cooperate to form
a plurality of spaced apart plateaus on the polishing surface of
the polishing pad 48. The grooves 300 reduce pressure and
hydrostatic lift in the gap 64. It should be noted that the groove
shape and pattern can be changed to alter the polishing
characteristics of the polishing pad 48. For example, each groove
300 can be a depth and a width on the order of between
approximately 0.1 mm and 1.5 mm. Also, the grooves 300 may be in a
different pattern and shape. For example, a set of radial grooves
combined with a set of circular grooves also could be utilized.
[0056] Alternatively, a polishing pad 48 without grooves can be
used in one or more of the polishing systems 30. Still
alternatively, the polishing pad 48 could be another type of
substrate.
[0057] FIG. 3B is a side illustration of the substrate holder 40,
the substrate 12, the pad holder 50, and the pad 48, with the pad
48 in a second lateral position relative to the substrate 12. In
the second lateral position, the pad 48 is only partly positioned
over the substrate 12.
[0058] As an overview, in one embodiment, the control system 24
(illustrated in FIG. 1) controls the pad vertical mover assembly 58
to maintain the force at a substantially equal and uniform level
across the cross-section of the polishing pad 48 above the
substrate 12 regardless of whether the polishing pad 48 is
positioned entirely above the surface of the substrate 12 or
whether the polishing pad 48 extends beyond the outer edge of the
substrate 12. The pad vertical mover assembly 58 is described in
greater detail below.
[0059] FIG. 4A is a perspective view a polishing system 30
including the pad holder 50, the polishing pad 48, a portion of the
pad rotator 50, a fluid conduit 400, and the vertical mover
assembly 58 that can be used in the apparatus 10 of FIG. 1. The
design of each of these components can be varied to suit the design
requirements of the apparatus.
[0060] FIG. 4B is a cut-away view of the polishing system 30 of
FIG. 4A. In this embodiment, the pad holder 50 is generally disk
shaped and retains the polishing pad 48. In one embodiment, the pad
holder 50 uses vacuum pressure to hold the polishing pad against
the pad holder. The pad holder 50 is also referred to herein as a
stage.
[0061] The pad rotator 52 includes a rotator shaft 402 that is
coupled to and rotated about a central axis by the rotator motor
(not shown). In FIG. 4B, the rotator shaft 402 has a substantially
circular cross-section and is coupled to the pad holder 50 so that
rotation of the rotator shaft 402 results in rotation of the pad
holder 50.
[0062] The fluid conduit 400 is used to transfer fluid between the
fluid source 32 (illustrated in FIG. 1) and the gap 64 (illustrated
in FIG. 3A). In FIG. 4B, the fluid conduit 400 is a tube that
extends through rotator shaft 402, the vertical mover assembly 58,
and the pad holder 50. In one embodiment, the fluid conduit 400
allows for relative motion between the pad holder 50 and the
rotator shaft 402. In FIG. 4B, the fluid conduit 400 includes a
fluid outlet 404 positioned near the polishing pad 48. However, the
number and location of the fluid outlets 404 can be varied. For
example, the fluid conduit 400 can include a plurality of spaced
apart fluid outlets 404.
[0063] The vertical mover assembly 58 couples and secures the pad
holder 50 to the rotator shaft 402. Additionally, the vertical
mover assembly 58 is used to control the force of the pad 48
against the substrate 12 (illustrated in FIG. 3A) and the position
of the pad 48 relative to the substrate 12. In one embodiment, the
vertical mover assembly 58 includes a first pad mover 406 and a
second pad mover 408. In one embodiment, the first pad mover 406 is
used to make a relatively coarse adjustment to the position of the
pad 48 relative to the substrate 12 and coarse force adjustment;
and the second pad mover 408 is used to make a relatively fine
adjustment to the position of the pad 48 relative to the substrate
12 and fine force adjustment. Alternatively, the first pad mover
406 can be designed to make a relatively fine adjustment to the
position of the pad 48 relative to the substrate 12 and the second
pad mover 408 can be designed to make a relatively coarse
adjustment to the position of the pad 48 relative to the substrate
12.
[0064] In FIG. 4B, the first pad mover 406 includes a mover housing
410, a mover drive ring 412, and a mover fluid source 414. In this
embodiment, the mover housing 410 is somewhat bell shaped and
includes a disk shaped top section 416 and a generally annular
shaped side wall 418 that extends downward from the top section
416. In this embodiment, the wall 418 includes a first section 420F
having a first inner diameter and a second section 420S having a
second inner diameter that is greater than the first inner
diameter. In this embodiment, the top section 416 is fixedly
secured to the rotator shaft 402.
[0065] The mover drive ring 412 is generally disk shaped and is
secured to the bottom of the side wall 418 of the mover housing
410. A bottom of the mover drive ring 412 is secured to the top of
the pad holder 50. In one embodiment, the mover drive ring 412 is
made of a magnetic material such as iron, silicon steal or Ni--Fe
Steel. In this embodiment, the mover drive ring 412 transfers
rotational force from the rotator shaft 402 to the pad holder 50.
The mover housing 410 and the mover drive ring 412 cooperate to
define a mover chamber 422.
[0066] The mover fluid source 414 directs a fluid 424 (illustrated
as triangles) into the mover chamber 422 to adjust the position of
the mover drive ring 412, and pad holder 50 relative to the rotator
shaft 402. As the pressure of the pressurized fluid inside the
mover chamber 422 increases, the mover drive ring 412 will move
downward so as to slightly increase the volume inside the mover
chamber 422. Conversely, as the pressure of the pressurized fluid
inside the mover chamber 422 decreases, the mover drive ring 412
will deform and move upward so as to slightly decrease the volume
inside the mover chamber 422. As the mover drive ring 412 moves so
as to slightly increase or decrease the volume inside the mover
chamber 422, the mover drive ring 412 transfers the pressure from
inside the mover chamber 422 toward the polishing pad 48 to
influence the force that the polishing pad 48 applies against the
substrate 12.
[0067] The type of fluid 424 utilized can be varied. In one
embodiment, the fluid 424 is air. Alternatively, for example, the
fluid 424 can be another type of gas.
[0068] As a result of this structure, the rotational movement of
the rotator shaft 402 results in rotational movement of the mover
housing 410, the mover drive ring 412, the pad holder 50, and the
polishing pad 48.
[0069] The design of the second pad mover 408 can be varied. In
FIG. 4B, the second pad mover 408 includes a first housing 426, a
bearing assembly 428, a second housing 430, and an actuator
assembly 432. The design of each of these components can be varied.
In FIG. 4B, the first housing 426 includes a generally flat ring
shaped first section 434 and an annular ring shaped second section
436 that extends downward from the first section 434.
[0070] The bearing assembly 428 secures the first section 434 of
the first housing 426 to the rotator shaft 402 and allows the
rotator shaft 402 to rotate relative to the first housing 426. In
one embodiment, the bearing assembly 428 includes a rolling type
bearing. Additionally, another structure or frame (not shown) can
be used to secure the first housing.
[0071] The second housing 430 is generally annular tube shaped and
includes a bottom end that is fixedly secured to the top of the pad
holder 50. In this embodiment, the second housing 430 rotates
concurrently with the pad holder 50, the rotator shaft 402 and the
pad 48. Further, the second housing 430 rotates relative to the
stationary first housing 426.
[0072] The actuator assembly 432 defines one or more actuators 438
that cooperate to move the second housing 430, the pad holder 50
and the pad 48 relative to the first housing 426, the rotator shaft
402, and the substrate 12. For example, in one embodiment, the
actuator assembly 432 includes a plurality of attraction only type
actuators 438. In FIG. 4B, the actuator assembly 432 includes a
plurality of spaced apart first actuator subassemblies 440 (only
one is illustrated in FIG. 4B) that are secured to the first
housing 426 and a single second actuator subassembly 442 that is
secured to the second housing 430 and rotates with the second
housing 430. The second actuator subassembly 442 is spaced apart a
component gap 444 away from each first actuator subassembly 440. In
one embodiment, during normal operation of the actuator assembly
432, the component gap 444 is in the range of between approximately
0.5 mm and 2 mm.
[0073] It should be noted that at any given time, the component gap
444 for each of the actuators 438 is different. Further, during
operation of the apparatus 10, the component gap 444 for each of
the actuators 438 usually increases as the polishing pad 48
(illustrated in FIG. 3A) wears.
[0074] FIG. 4C illustrates a top view of a portion of the polishing
system 30 of FIG. 4A. FIG. 4C illustrates that the second pad mover
408 includes three actuators 438 (illustrated in phantom),
including a first actuator 438F, a second actuator 438S, and a
third actuator 438T. In one embodiment, the actuators 438F, 438S,
438T are evenly not spaced apart. In this embodiment, the second
and third actuators 438S, 438T are spaced closer together and the
second and third actuators 438S, 438T are equal distances from the
first actuator 438F.
[0075] FIG. 5A illustrates a perspective view of one embodiment of
the actuator assembly 432 including the control system, three
spaced apart first actuator subassemblies 440 and one second
actuator subassembly 442 that is spaced apart from the first
actuator subassemblies 440 and form three spaced apart actuators
438F, 438S, 438T. Alternatively, for example, the actuator assembly
432 can include more than three or less than three first actuator
subassemblies 440. Each of the first actuator subassemblies 440 are
spaced apart component gap g.sub.1, g.sub.2, g.sub.3 from the
second actuator subassembly 442.
[0076] In this embodiment, each of the first actuator subassemblies
440 includes a sensor 500, a first core 502 and a pair of spaced
apart conductors 504. Further, the second actuator subassembly 442
is generally flat annular ring shaped and defines a second core
506.
[0077] In this embodiment, the control system 524 directs current
to the conductors 504 of each first actuator subassembly 440 to
attract the second core 506 towards the first core 502.
[0078] The sensor 500 can be a load cell, e.g. a strain guage, or
another type of sensor that measures the force that acts upon the
sensor 500. Because the sensor 500 secures the first actuator
subassembly 440 to the first housing 426 (illustrated in FIG. 4B),
each sensor 500 measures the force generated by the attraction
between the actuator subassemblies 440, 442.
[0079] Each first actuator subassembly 440 and the second actuator
subassembly 442 cooperate to form an actuator 438. Each actuator
438, in this embodiment, is an electromagnetic, attraction only
actuator. In one embodiment, the first core 502 is a C-shaped core
("C core") and the second core 506 is a ring-shaped. The second
core 506 is substantially ring-shaped and rotates with the pad
holder 50 (illustrated in FIG. 4B). As the ring-shaped second core
506 rotates, a portion of the second core 506 will be positioned
substantially directly beneath each of the first cores 502 at any
point in time. The portion of the ring-shaped second core 506 that
interacts with the first core 502 at any point in time is
substantially I-shaped. As the second core 506 continues to rotate,
the particular portion of the second core 506 that is positioned
substantially directly beneath each of the first cores 502 will
change, but at any point in time there will always be some portion
of the second core 506 that will be positioned so as to interact
with each of the first cores 502.
[0080] The first cores 502 and the second core 506 are each made of
a magnetic material such as iron, silicon steel or Ni--Fe steel.
The conductors 504 are made of an electrically conductive
material.
[0081] For the first actuator 438F, a first current I.sub.1 (not
shown) directed through the conductor(s) 504 generates an
electromagnetic field that attracts the second core 506 towards the
first core 502. This results in an attractive first force F.sub.1
across the first component gap g.sub.1. Similarly, for the second
actuator 438S, a second current I.sub.2 directed through the
conductor(s) 504 generates an electromagnetic field that attracts
the second core 506 towards the first core 502. This results in an
attractive second force F.sub.2 across the second gap 92.
Furthermore, for the third actuator 438T, a third current I.sub.3
directed through the conductor(s) 504 generates an electromagnetic
field that attracts the second core 506 towards the first core 502.
This results in an attractive third force F.sub.3 across the gap
93. The amount of current determines the amount of attraction. With
this design, the first actuator 438F urges the pad 48 with a
controlled first force F.sub.1, the second actuator 438S urges the
pad 48 with a controlled second force F.sub.2, and the third
actuator 438T urges the pad 48 with a controlled third force
F.sub.3.
[0082] FIG. 5B is an exploded perspective view of one embodiment of
the first core 502 and conductors 504. In this embodiment, the
first core 502 is somewhat "C" shaped. One tubular shaped conductor
504 is positioned around each end bar of the C shaped core 502. The
combination of the C shaped first core 502 and the conductors 504
is sometimes referred to herein as an electromagnet.
[0083] FIG. 5C is a perspective view of another embodiment of the
first core 502C and the conductor 504C. In this embodiment, the
first core 502C is E-shaped. The conductor 504 is positioned around
the center bar of the E shaped first core 502C.
[0084] The electromagnet actuators 438 illustrated in FIGS. 5A-5C
are variable reluctance actuators and the reluctance varies with
the size of the component gap 444 (illustrated in FIG. 4B), which,
of course also varies the flux and the force applied to the second
core 502. The electromagnet actuators 438 can provide large force
with relatively small current and their physical dimensions are
much smaller than conventional actuators.
[0085] The control system 524 (i) determines the amount of current
that should be directed to the conductors 504 of the first actuator
subassemblies 440 and the amount of pressure in mover chamber 422,
(ii) controls the mover fluid source 414 to direct fluid 424 into
the mover chamber 422, and (iii) directs current to the conductors
504 of the first actuator subassemblies 440 to achieve the desired
force between the pad 48 (illustrated in FIG. 3A) and the substrate
12 (illustrated in FIG. 3A). Stated another way, the control system
24 controls the fluid 424 to the mover chamber 422 and current
level for each conductor 504 to achieve the desired resultant
forces and position the pad 48 relative to the substrate 12.
[0086] In one embodiment, the control system 524 independently
directs current to each of the conductors 504 of the second pad
mover 408 at a plurality of discrete time steps t, namely t.sub.1,
t.sub.2, t.sub.3, t.sub.4 . . . t.sub.x. At each time step, the
sensor 500 also measures the force that is generated by each of the
actuators 438F, 438S, 438T. The time interval that separates each
time step t can be varied. In alternative examples, the time
interval between time steps t is approximately 0.5, 1, 1.5, 2, 2.5
or 3 milliseconds. However, the time interval can be larger or
smaller than these values. The term time interval is also referred
to herein as sampling rate.
[0087] FIG. 6 is a schematic that illustrates the functions of the
control system 524. Initially, at each time step t, the control
system determines a total desired force F.sub.TD of the pad against
the substrate based on the desired polishing of the substrate. A
first mover force F.sub.M1 applied by the first pad mover is
subtracted from the total desired force F.sub.TD to determine (i)
the amount the first force F.sub.1 to be applied by the first
actuator 438F, (ii) the amount the second force F.sub.2 to be
applied by the second actuator 438S, and (iii) the amount the third
force F.sub.3 to be applied by the third actuator 438T. The control
law s304 prescribes the corrective action for the signal. The
feedback control law may be in the form of a PI (proportional
integral) controller, proportional gain controller or a lead-lag
filter, or other commonly known law in the art of control, for
example.
[0088] Each actuator 438F, 438S, 438T requires some kind of
commutation to globally compensate for the non linearity between
the input current and component gap to the force output. The
control system uses a commutation formula to determine the amount
of current that is to be individually directed to each of the
conductors 504 of the second pad mover to achieve the forces
F.sub.1, F.sub.2, F.sub.3 at each actuator 438F, 438S, 438T at each
time step t. Stated another way, the control system calculates a
first current I.sub.1 needed at the first actuator 438F to achieve
the desired F.sub.1 at the first actuator 438F, a second current
I.sub.2 needed at the second actuator 428S to achieve the desired
F.sub.2 at the second actuator 438S, and a third current I.sub.3
needed at the third actuator 428T to achieve the desired F.sub.3 at
the third actuator 438T. The currents I.sub.1 I.sub.2 I.sub.3 are
directed to the actuators 438F, 438S, 438T and the actuators 438F,
438S, 438T impart forces F.sub.1, F.sub.2, F.sub.3 on the pad at
each time step t.
[0089] In one embodiment, the control system 524 independently
directs current I.sub.1 I.sub.2 I.sub.3 to each of the conductors
504 of the second pad mover 408 at each time step t so that the
forces F.sub.1, F.sub.2, F.sub.3 generated by each of the actuators
438F, 438S, 438T is approximately the same. In alternative
embodiments, the control system 24 directs current to the
conductors 504 so that the forces F.sub.1, F.sub.2, F.sub.3
generated by each of the actuators 438F, 438S, 438T is within at
least approximately 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, or 100 Newtons.
Stated another way, in alternative embodiments, the control system
24 directs current to the conductors 504 so that the forces
F.sub.1, F.sub.2, F.sub.3 generated by each of the actuators 438F,
438S, 438T are within at least approximately 1, 2, 5, 10, 20, 40,
or 50 percent. Alternatively, the control system 24 can direct
current to the conductors 504 so that the force of the pad 48
against the substrate 12 is substantially uniform across the pad 48
that is against the substrate 12. In alternative embodiments, for
example, the control system 24 can direct current to the conductors
504 so that difference in force of the pad 48 against the substrate
12 at any and every two spaced apart locations is within at least
approximately 0.05, 0.075, 0.1, 0.15, 0.2, 0.5 or 1 newtons. Stated
another way, in alternative embodiments, the control system 24 can
direct current to the conductors 504 so that difference in force of
the pad 48 against the substrate 12 at any and every two spaced
apart locations is within at least approximately 0.5, 1, 2, 5, 10
or 20 percent.
[0090] As provided herein, the actual output force F.sub.1,
F.sub.2, F.sub.3 generated by one of the actuators 438F, 438S, 438T
can be expressed as follows:
F=k(I.sup.2)/(g.sup.2) equation 1
[0091] where F is in Newtons; k is an electromagnetic constant
which is dependent upon the geometries of the first core and the
second core, and the number of coil turns in the conductor(s); I is
current, measured in amperes that is directed to the conductor(s);
and g is the gap distance, measured in meters.
[0092] The actual value of k is not exactly known because they
depend upon the geometries, shape and alignment of the first core
and the second core. In one embodiment, k=1/2N .sup.2.mu..sub.owd;
where N=the number of coil turns in the conductor(s); .mu..sub.o=a
physical constant of about 1.26.times.10.sup.-6 H/m; w=the half
width of the center of the first core, in meters; and d=the depth
of the center of the first core, in meters. In one embodiment, k is
equal to 7.73.times.10.sup.-6 kg m.sup.3/s.sup.2A.sup.2;
[0093] Equation 1 can be rewritten as follows:
I=g.times.{square root}(F/k) equation 2
g=I.times.{square root}(k/F) equation 3
[0094] However, in some embodiments, it is very difficult to
accurately measure the component gap g.sub.1 g.sub.2 g.sub.3 at
each of the actuators 438F, 438S, 438T.
[0095] In one embodiment, when the measured value of the component
gap is not available and when the component gap g.sub.1 g.sub.2
g.sub.3 does not deviate from an operational value g', then a
simplified commutation may be used. In one embodiment, the
operational value g' is within with a range of between
approximately 0.5 mm and 1.5 mm. However, the range may be larger
or smaller.
[0096] In this example, because g' and k are constant, they can be
merged to the control gain and then equation 2 can be simplified as
follows:
I={square root}F equation 4
[0097] In this embodiment, at each time step t, the control system
(i) takes the square root of the F.sub.1 to determine the current
I.sub.1 that should be directed to the first actuator 438F, (ii)
takes the square root of the F.sub.2 to determine the current
I.sub.2 that should be directed to the second actuator 438S, and
(iii) takes the square root of the F.sub.3 to determine the current
I.sub.3 that should be directed to the third actuator 438T.
[0098] In an alternative embodiment, for a system without component
gap measurement but with large deviation of the component gap
g.sub.1 g.sub.2 g.sub.3, a calculated component gap g.sub.1 g.sub.2
g.sub.3 can be calculated by the control system using information
from one or more previous samples. For example, equation 3 from
above can be rewritten as following:
g(t-1)=I(t-1).times.{square root}(k/F(t-1)) equation 5
[0099] In this embodiment, F is the actual force F.sub.1, F.sub.2,
F.sub.3 applied by the particular actuator 438F, 438S, 438T at a
previous time step t. The actual force F.sub.1, F.sub.2, F.sub.3
applied by the particular actuator 438F, 438S, 438T can be measured
by the sensor 500 of each actuator 438F, 438S, 438T.
[0100] FIG. 7 is a graph that illustrates the measured forces
F.sub.1 (solid line), F.sub.2 (solid line with triangles), and
F.sub.3 (solid line with circles) at a plurality of time steps t.
This graph is useful to understand the subsequent versions of the
invention described below.
[0101] In one embodiment, if the control-sampling rate (length of
time interval) is much faster than the rate at which the component
gap g.sub.1 g.sub.2 g.sub.3 changes, then the component gap g.sub.1
g.sub.2 g.sub.3 can be estimated by using only one earlier sample
data.
g"(t)=g(t-1)=I(t-1).times.{square root}(k/F(t-1)) equation 6
[0102] Referring to FIG. 7, in this embodiment, (i) the value of
F.sub.1 at the immediately previous time step t-1 is used to
calculate the gap g.sub.1 and subsequently the current I.sub.1 that
should be directed to the first actuator 438F at a particular time
step t, (ii) the value of F.sub.2 at the immediately previous time
step t-1 is used to calculate the gap g.sub.2 and subsequently the
current I.sub.2 that should be directed to the second actuator 438S
at a particular time step t, (iii) the value of F.sub.3 at the
immediately previous time step t-1 is used to calculate the gap 93
and subsequently the current I.sub.3 that should be directed to the
third actuator 438T at the next time step t.
[0103] As an example, in this embodiment, at time step t.sub.5, (i)
the sensor 500 measures the F.sub.1 applied by the first actuator
438F, (ii) the sensor 500 measures the F.sub.2 applied by the
second actuator 438S, and (iii) the sensor 500 measures the F.sub.3
applied by the third actuator 438T. Subsequently, during the time
interval between time step t.sub.5 and t.sub.6, the control system
(i) uses the value of F.sub.1 to determine the approximate gap
g.sub.1 and the current I.sub.1 that should be directed to the
first actuator 438F at time step t.sub.6, (ii) uses the value of
F.sub.2 to determine to determine the approximate gap g.sub.2 and
the current I.sub.2 that should be directed to the second actuator
438S at time step t.sub.6, and (iii) uses the value of F.sub.3 to
determine the approximate gap g.sub.2 and the current I.sub.3 that
should be directed to the third actuator 438T at time step t.sub.6.
This same process can be used in subsequent time steps t to
determine the appropriate for currents I.sub.1 I.sub.2 I.sub.3.
[0104] However, in an alternative embodiment, if the
control-sampling rate (length of time interval) is much slower than
the rate at which the component gap g.sub.1 g.sub.2 g.sub.3
changes, then the component gap g.sub.1 g.sub.2 g.sub.3 can be
estimated by using data from at least two earlier samples. 1 g ^ (
t ) = j = 1 N j ( t ) g ( t - j ) equation 7
[0105] The parameters .alpha.j(t) can be fixed numbers or updated
online as follows:
.alpha.j(t+1)=.alpha.j(t)+.DELTA..alpha.j(t) equation 8
.DELTA..alpha.(t)=.lambda.g(t-j)(g(t)-(t)) equation 9
[0106] The number of earlier samples utilized will vary according
to the rate at which the component gap g.sub.1 g.sub.2 g.sub.3
changes. Generally speaking, more control samples are used if the
component gap g.sub.1 g.sub.2 g.sub.3 rapidly changes than when the
component gap g.sub.1 g.sub.2 g.sub.3 does not change as rapidly.
In alternative examples, the control system can utilize 2, 3, 4, 5,
6, 8, or 10 previous control samples.
[0107] For example, in one embodiment, the control system utilizes
4 previous control steps. Referring to FIG. 7, in this embodiment,
(i) the value of F.sub.1 at the immediately previous four time
steps t-1 through t-4 are used to estimate the g.sub.1 and
subsequently calculate the current I.sub.1 that should be directed
to the first actuator 438F at a particular time step t, (ii) the
value of F.sub.2 at the immediately previous four time steps t-1
through t-4 are used to estimate g.sub.2 and subsequently calculate
the current I.sub.2 that should be directed to the second actuator
438S at a particular time step t, (i) the value of F.sub.3 at the
immediately previous four time steps t-1 through t-4 are used to
estimate g.sub.3 and subsequently calculate the current I.sub.3
that should be directed to the third actuator 438T at the next time
step t.
[0108] As an example, in this embodiment, at time step t.sub.8, (i)
the sensor 500 measures the F.sub.1 applied by the first actuator
438F at t.sub.4-t.sub.7, (ii) the sensor 500 measures the F.sub.2
applied by the second actuator 438S at t.sub.4-t.sub.7, and (iii)
the sensor 500 measures the F.sub.3 applied by the third actuator
438T at t.sub.4-t.sub.7. Subsequently, during the time interval
between time step t.sub.7 and t.sub.8, the control system (i) uses
the values of F.sub.1 at t.sub.4-t.sub.7 to determine the current
I.sub.1 that should be directed to the first actuator 438F at time
step t.sub.8, (ii) uses the values of F.sub.1 to determine the
current I.sub.2 that should be directed to the second actuator 438S
at time step t.sub.8, and (iii) uses the values of F.sub.3 at
t.sub.4-t.sub.7 to determine the current I.sub.3 that should be
directed to the third actuator 438T at time step t.sub.8. This same
process can be used in subsequent time steps t to determine the
appropriate for currents I.sub.1 I.sub.2 I.sub.3.
[0109] It should be noted that in this embodiment, the slope of
measured forces F.sub.1 (solid line), F.sub.2 (solid line with
triangles), and F.sub.3 (solid line with circles) can be taken into
consideration when calculating the respective gap g.sub.1 g.sub.2
g.sub.3.
[0110] In one embodiment, as illustrated in FIG. 6, the control
system can include a stiffness compensator (K) that provides
stiffness compensation for the system. More specifically, as
provided herein, the mechanical structure, e.g. the first housing
426 and the second housing 430, of the polishing system 30 and the
pad 48 usually have finite stiffness. This stiffness contributes to
resonance of the polishing system 30. When the resonance frequency
is within the desired bandwidth of the actuators 438, the system 30
may have an oscillation problem, leading to lower bandwidth and
poorer performance of the polishing system. In this embodiment, the
control system adjusts the current to the actuators to create a
force that compensates for the stiffness of the system.
[0111] Additionally, as illustrated in FIG. 6, the control system
can include a damping enhancement (C) that damps out oscillations
of the system. The damping enhancement can be used to estimate an
artificial force that should be applied by the actuators to dampen
oscillations. Stated another way, with this design, the control
system adjusts the current to the actuators to create a force that
dampens oscillations of the system.
[0112] Damping other than the hardware setup may be provided by
feedback control of the damping enhancement. In one embodiment, in
order to do that, derivative of force output, (i.e. jerk) can be
estimated using a filter.
[0113] Simple difference
D(z.sup.-1)=1/T(1-z.sup.-1)
[0114] 3.sup.rd order filer
D(z.sup.-1)=1/T(0.3+0.1 z.sup.-1-0.1 z.sup.-20.3 z.sup.-3)
[0115] and 7.sup.th order filter
D(z.sup.-1)=1/T(0.0833+0.595 z.sup.-1+0.119 z.sup.-3-0.0119
z.sup.-40.0357 z.sup.-5-0.0595 z.sup.-6-0.0833 z.sup.-7)
[0116] Higher order estimation has smoother output with the
tradeoff of longer time delays.
[0117] FIG. 8 is a graph that illustrates the relationship between
voltage and force for one embodiment of an actuator. In this
embodiment, as voltage is increased, force generated by the
actuator is also increased.
[0118] FIGS. 9A and 9B are alternative graphs that illustrate the
closed loop frequency response of a system. In FIG. 9A, the graph
represents magnitude versus frequency for a system. Line 901
represents the response of the system if the control system does
not utilize damping enhancement and stiffness compensation and line
902 represents the response of the system if the control system
utilizes damping enhancement and stiffness compensation. In FIG.
9B, the graph represents phase versus frequency for a system. Line
903 represents the response of the system if the control system
does not utilize damping enhancement and stiffness compensation and
line 904 represents the response of the system if the control
system utilizes damping enhancement and stiffness compensation.
[0119] FIGS. 9C and 9D are alternative graphs that illustrate the
open loop frequency response of a system. In FIG. 9C, the graph
represents magnitude versus frequency for a system. Line 905
represents the response of the system if the control system does
not utilize damping enhancement and stiffness compensation and line
906 represents the response of the system if the control system
utilizes damping enhancement and stiffness compensation. In FIG.
9D, the graph represents phase versus frequency for a system. Line
907 represents the response of the system if the control system
does not utilize damping enhancement and stiffness compensation and
line 908 represents the response of the system if the control
system utilizes damping enhancement and stiffness compensation.
[0120] FIGS. 9E and 9F are alternative graphs that illustrate the
plant frequency response of a system. In FIG. 9E, the graph
represents magnitude versus frequency for a system. Line 909
represents the response of the system if the control system does
not utilize damping enhancement and stiffness compensation and line
910 represents the response of the system if the control system
utilizes damping enhancement and stiffness compensation. In FIG.
9F, the graph represents phase versus frequency for a system. Line
911 represents the response of the system if the control system
does not utilize damping enhancement and stiffness compensation and
line 912 represents the response of the system if the control
system utilizes damping enhancement and stiffness compensation.
[0121] FIG. 10A is a graph that illustrates the force step response
from 10 newtons to 11 newtons for a system if the control system
does not utilize damping enhancement and stiffness
compensation.
[0122] FIG. 10B is a graph that illustrates the force step response
from 10 newtons to 11 newtons for a system if the control system
that utilizes stiffness compensation.
[0123] FIG. 10C is a graph that illustrates the force step response
from 10 newtons to 11 newtons for a system if the control system
that utilizes first order damping enhancement and stiffness
compensation.
[0124] FIG. 10D is a graph that illustrates the force step response
from 10 newtons to 11 newtons for a system if the control system
that utilizes third order damping enhancement and stiffness
compensation.
[0125] FIG. 10E is a graph that illustrates the force step response
from 10 newtons to 11 newtons for a system if the control system
that utilizes seventh order damping enhancement and stiffness
compensation.
[0126] The graphs provided herein illustrate that with stiffness
compensation and additional software damping, the system dynamics
can be well re-shaped. Hence the resonance due to the mounting can
be completely removed.
[0127] While the particular apparatus 10 and method as herein shown
and disclosed in detail is fully capable of obtaining the objects
and providing the advantages herein before stated, it is to be
understood that it is merely illustrative of the presently
preferred embodiments of the invention and that no limitations are
intended to the details of construction or design herein shown
other than as described in the appended claims.
* * * * *