U.S. patent application number 12/820542 was filed with the patent office on 2010-10-14 for method for obtaining force combinations for template deformation using nullspace and methods optimization techniques.
This patent application is currently assigned to MOLECULAR IMPRINTS, INC.. Invention is credited to Anshuman Cherala, Byung-Jin Choi, Sidlgata V. Sreenivasan, Ecron D. Thompson.
Application Number | 20100259745 12/820542 |
Document ID | / |
Family ID | 46327650 |
Filed Date | 2010-10-14 |
United States Patent
Application |
20100259745 |
Kind Code |
A1 |
Cherala; Anshuman ; et
al. |
October 14, 2010 |
METHOD FOR OBTAINING FORCE COMBINATIONS FOR TEMPLATE DEFORMATION
USING NULLSPACE AND METHODS OPTIMIZATION TECHNIQUES
Abstract
The present invention is directed towards a method for
determining deformation parameters that a patterned device would
undergo to minimize dimensional variations between a recorded
pattern thereon and a reference pattern, the method including,
inter alia, comparing spatial variation between features of the
recorded pattern with respect to corresponding features of the
reference pattern; and determining deformation forces to apply to
the patterned device to attenuate the dimensional variations, with
the forces having predetermined constraints, wherein a summation of
a magnitude of the forces is substantially zero and a summation of
moment of the forces is substantially zero.
Inventors: |
Cherala; Anshuman; (Austin,
TX) ; Sreenivasan; Sidlgata V.; (Austin, TX) ;
Choi; Byung-Jin; (Austin, TX) ; Thompson; Ecron
D.; (Round Rock, TX) |
Correspondence
Address: |
MOLECULAR IMPRINTS
PO BOX 81536
AUSTIN
TX
78708-1536
US
|
Assignee: |
MOLECULAR IMPRINTS, INC.
Austin
TX
BOARD OF REGENTS, THE UNIVERSITY OF TEXAS SYSTEM
Austin
TX
|
Family ID: |
46327650 |
Appl. No.: |
12/820542 |
Filed: |
June 22, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11695469 |
Apr 2, 2007 |
7768624 |
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12820542 |
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11143076 |
Jun 2, 2005 |
7535549 |
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11695469 |
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60788811 |
Apr 3, 2006 |
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60788812 |
Apr 3, 2006 |
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60576570 |
Jun 3, 2004 |
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Current U.S.
Class: |
355/77 |
Current CPC
Class: |
G03F 7/0002 20130101;
B82Y 10/00 20130101; G03F 7/70633 20130101; B82Y 40/00 20130101;
G03F 9/7092 20130101; G03F 7/70783 20130101; G03F 9/7003 20130101;
G03F 7/703 20130101 |
Class at
Publication: |
355/77 |
International
Class: |
G03B 27/32 20060101
G03B027/32 |
Goverment Interests
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
[0002] The United States government has a paid-up license in this
invention and the right in limited circumstance to require the
patent owner to license others on reasonable terms as provided by
the terms of 70NANB4H3012 awarded by National Institute of
Standards (NIST) ATP Award and N66001-06-C-2003 awarded by
Nanoimprint Lithography Manufacturing Scale (NIMS) Award.
Claims
1. A method for determining deformation parameters that a patterned
device would undergo to minimize dimensional variations between a
recorded pattern thereon and a reference pattern, said method
comprising: comparing spatial variations between features of said
recorded pattern with respect to corresponding features of said
reference pattern; generating distortion vectors from location
differences between said features in said recorded pattern and said
corresponding features of said reference pattern; and determining
deformation forces as a linear operation minimizing computational
power; applying said forces to the patterned device to attenuate
the dimensional variations, with the forces having predetermined
constraints, wherein a summation of a magnitude of the forces is
substantially zero and a summation of moment of the forces is
substantially zero.
2. The method as recited in claim 1 wherein said patterned device
lies in a plane having a first and a second axis, said first axis
being orthogonal to said second axis, with said summation of said
magnitude of said forces being substantially zero with respect to
said first and second axis and a summation of said moment of said
forces is substantially zero with respect to a third axis, said
third axis being orthogonal to said first and said second axis.
3. The method as recited in claim 1 wherein said patterned device
comprises first and second opposed sides and third and fourth
opposed sides, with a distance between said first and second
opposed sides and a distance between said third and further opposed
sides having a predetermined magnitude with a tolerance of 0.05
mm.
4. The method as recited in claim 3 wherein an angle between any
two sides of said first, second, third, and fourth sides has a
predetermined magnitude with a tolerance of 1E-3 Radians.
5. The method as recited in claim 4 wherein said patterned device
comprises fifth side, said fifth side being orthogonal to said
first, second, third, and fourth sides, said patterned device
further comprising an edge surface between said fifth side and said
first, second, third, and fourth sides, with a width of said edge
surface having a predetermined magnitude with a tolerance of 0.2
mm.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] The present application is a continuation of U.S.
application Ser. No. 11/695,469 filed Apr. 2, 2007, which claims
priority to U.S. provisional application No. 60/788,811 filed on
Apr. 3, 2006 and to U.S. provisional application No. 60/788,812
filed on Apr. 3, 2006; and is also a continuation-in-part of U.S.
patent application Ser. No. 11/143,076 filed on Jun. 2, 2005, which
in turn claims priority to U.S. provisional application No.
60/576,570 filed on Jun. 3, 2004. All of the aforementioned
applications are incorporated herein by reference.
BACKGROUND INFORMATION
[0003] Nano-fabrication involves the fabrication of very small
structures, e.g., having features on the order of nanometers or
smaller. One area in which nano-fabrication has had a sizeable
impact is in the processing of integrated circuits. As the
semiconductor processing industry continues to strive for larger
production yields while increasing the circuits per unit area
formed on a substrate, nano-fabrication becomes increasingly
important. Nano-fabrication provides greater process control while
allowing increased reduction of the minimum feature dimension of
the structures formed. Other areas of development in which
nano-fabrication has been employed include biotechnology, optical
technology, mechanical systems and the like.
[0004] An exemplary nano-fabrication technique is commonly referred
to as imprint lithography. Exemplary imprint lithography processes
are described in detail in numerous publications, such as U.S.
patent publication no. 2004/0065976 (filed as U.S. application Ser.
No. 10/264,960), entitled "Method and a Mold to Arrange Features on
a Substrate to Replicate Features having Minimal Dimensional
Variability"; U.S. patent publication 2004/0065252 (filed as U.S.
application Ser. No. 10/264,926), entitled "Method of Forming a
Layer on a Substrate to Facilitate Fabrication of Metrology
Standards"; and U.S. Pat. No. 6,936,194, entitled "Functional
Patterning Material for Imprint Lithography Processes," all of
which are assigned to the assignee of the present invention and
incorporated herein by reference.
[0005] The imprint lithography technique disclosed in each of the
aforementioned U.S. patent publications and U.S. patent includes
formation of a relief pattern in a polymerizable layer and
transferring a pattern corresponding to the relief pattern into an
underlying substrate. The substrate may be positioned upon a stage
to obtain a desired position to facilitate patterning thereof. To
that end, a mold is employed spaced-apart from the substrate with a
formable liquid present between the mold and the substrate. The
liquid is solidified to form a patterned layer that has a pattern
recorded therein that is conforming to a shape of the surface of
the mold in contact with the liquid. The mold is then separated
from the patterned layer such that the mold and the substrate are
spaced-apart. The substrate and the patterned layer are then
subjected to processes to transfer, into the substrate, a relief
image that corresponds to the pattern in the patterned layer.
BRIEF DESCRIPTION OF THE DRAWINGS
[0006] FIG. 1 is a simplified side view of a lithographic system
having a template spaced-apart from a substrate;
[0007] FIG. 2 is a simplified side view of the substrate shown in
FIG. 1, having a patterned layer positioned thereon;
[0008] FIG. 3 is a simplified plan view of a holder for the
template, both shown in FIG. 1, in accordance with the present
invention;
[0009] FIG. 4 is a simplified plan view of the template shown in
FIG. 1, having a plurality of alignment marks;
[0010] FIG. 5 is a simplified plan view showing distortion vectors
determined in accordance with the present invention;
[0011] FIG. 6 is a top down view of the template shown in FIG.
1;
[0012] FIG. 7 is a side view of the template shown in FIG. 1;
and
[0013] FIG. 8 is a exploded view of a portion of the template shown
in FIG. 7.
DETAILED DESCRIPTION
[0014] Referring to FIG. 1, a system 10 to form a relief pattern on
a substrate 12 is shown. Substrate 12 may be coupled to a substrate
chuck 14. Substrate chuck 14 may be any chuck including, but not
limited to, vacuum, pin-type, groove-type, or electromagnetic, as
described in U.S. Pat. No. 6,873,087 entitled "High-Precision
Orientation Alignment and Gap Control Stages for Imprint
Lithography Processes," which is incorporated herein by reference.
Substrate 12 and substrate chuck 14 may be supported upon a stage
16. Further, stage 16, substrate 12, and substrate chuck 14 may be
positioned on a base (not shown). Stage 16 may provide motion about
the x and y axes.
[0015] Spaced-apart from substrate 12 is a template 18 having first
and second opposed sides 20 and 22. Positioned on first side 20 of
template 18 is a mesa 24 extending therefrom towards substrate 12
with a patterning surface 26 thereon. Further, mesa 24 may be
referred to as a mold 24. Mesa 24 may also be referred to as a
nanoimprint mold 24. In a further embodiment, template 18 may be
substantially absent of mold 24. Template 18 and/or mold 24 may be
formed from such materials including but not limited to,
fused-silica, quartz, silicon, organic polymers, siloxane polymers,
borosilicate glass, fluorocarbon polymers, metal, and hardened
sapphire. In a further embodiment, template 18 and mold 24 may be
commonly referred to as patterned device 28. As shown, patterning
surface 24 comprises features defined by a plurality of
spaced-apart recesses 30 and protrusions 32. However, in a further
embodiment, patterning surface 24 may be substantially smooth
and/or planar. Patterning surface 24 may define an original pattern
that forms the basis of a pattern to be formed on substrate 12.
[0016] Template 18 may be coupled to a template chuck (not shown),
the template chuck (not shown) being any chuck including, but not
limited to, vacuum, pin-type, groove-type, or electromagnetic, as
described in U.S. Pat. No. 6,873,087 entitled "High-Precision
Orientation Alignment and Gap Control Stages for Imprint
Lithography Processes." Template 18 may be coupled to an imprint
head 34 to facilitate movement of template 18 and mold 26. In a
further embodiment, the template chuck (not shown) may be coupled
to imprint head 34 to facilitate movement of template 18 and mold
26.
[0017] System 10 further comprises a fluid dispense system 36.
Fluid dispense system 36 may be in fluid communication with
substrate 12 so as to deposit a polymeric material 38 thereon.
System 10 may comprise any number of fluid dispensers and fluid
dispense system 36 may comprise a plurality of dispensing units
therein. Polymeric material 38 may be positioned upon substrate 12
using any known technique, e.g., drop dispense, spin-coating, dip
coating, chemical vapor deposition (CVD), physical vapor deposition
(PVD), thin film deposition, thick film deposition, and the like.
As shown, polymeric material 38 may be deposited upon substrate 12
as a plurality of spaced-apart droplets 40. Typically, polymeric
material 38 is disposed upon substrate 12 before the desired volume
is defined between mold 24 and substrate 12. However, polymeric
material 38 may fill the volume after the desired volume has been
obtained.
[0018] Referring to FIGS. 1 and 2, system 10 further comprises a
source 42 of energy 44 coupled to direct energy 44 along a path 46.
Imprint head 34 and stage 16 are configured to arrange mold 24 and
substrate 12, respectively, to be in superimposition and disposed
in path 46. Either imprint head 34, stage 16, or both vary a
distance between mold 24 and substrate 12 to define a desired
volume therebetween such that mold 24 contacts polymeric material
38 and the desired volume is filled by polymeric material 38. More
specifically, polymeric material 38 of droplets 40 may ingress and
fill recesses 30 of mold 24. After the desired volume is filled
with polymeric material 38, source 42 produces energy 44, e.g.,
broadband ultraviolet radiation that causes polymeric material 38
to solidify and/or cross-link conforming to the shape of a surface
48 of substrate 12 and patterning surface 26, defining a patterned
layer 50 on substrate 12. Patterned layer 50 may comprise a
residual layer 52 and a plurality of features shown as protrusions
54 and recessions 56. System 10 may be regulated by a processor 58
that is in data communication with stage 16, imprint head 34, fluid
dispense system 36, and source 42, operating on a computer readable
program stored in memory 60.
[0019] Referring to FIGS. 1 and 3, system 10 further comprises an
actuator system 62 surrounding patterned device 28 to facilitate
alignment and overlay registration. To that end, actuation system
62 includes a plurality of actuators 64 coupled between a frame 66
and patterned device 20. Each of actuators 64 are arranged to
facilitate generation of a force on one of the four sides 70, 72,
74 and 76 of patterned device 28.
[0020] As shown, actuator system 62 comprises sixteen actuators
64a-62p coupled to patterned device 20. More specifically, coupled
to side 70 of template 18 are actuators 64a-64d; coupled to side 72
of template 18 are actuators 64e-64h; coupled to side 74 of
template 18 are actuators 64i-64l; and coupled to side 76 of
template 18 are actuators 64m-64p. In a further embodiment,
template 18 may have any number of actuators 64 coupled thereto and
may have differing number of actuators 64 coupled to each side of
template 18. Template 18 may have any configuration and number of
actuators 64 positioned on sides 70, 72, 74, and 76 thereof.
Actuation system 62 may be in data communication with processor 58,
operating on a computer readable program stored in memory 60, to
control an operation thereof, and more specifically, generate
control signals that are transmitted to actuators 64 of actuation
system 62.
[0021] Actuation system 62 facilitates alignment and overlay
registration by selectively deforming patterned device 20. This
facilitates correcting various parameters of the pattern shape,
i.e., magnification characteristics, skew/orthogonality
characteristics, and trapezoidal characteristics. Magnification
characteristics may be magnification error, such as where the
overall pattern changes from a square shape to a rectangular shape.
Skew/orthogonality characteristics may be skew/orthogonality error
where adjacent edges form an oblique or obtuse angle with respect
to one another instead of an orthogonal angle. Trapezoidal
characteristics may be trapezoidal error where as in where a
square/rectangular assumes the shape of a trapezium, with trapezium
including a trapezoid. To control the pattern shape, patterned
device 20 may be selectively deformed by actuators 64 to minimize,
if not cancel, the distortions present, thereby reducing overlay
errors. To that end, patterned device 20 is inspected employing
known image placement or image registration systems, e.g., LMS
IPRO3 available from Leica Microsystems of Bannockburn, Ill.
[0022] Referring to FIGS. 1, 3 and 4, measured information 78
concerning the location of the features on patterned device 20
would be mapped into memory 60. The features that measured
information 78 represents are reference marks present on patterned
device 20 to facilitate overlay and alignment techniques. The
features may include any known alignment mark, such as box-in-box;
cross-in-cross and/or vernier scale marks, referred to as overlay
features. The overlay features are usually positioned at differing
regions of patterned device 20 as room permits and are arranged in
a polygonal, if not rectangular grid. As shown in FIG. 4, alignment
marks 80 are positioned in the corners of mold 24.
[0023] Referring to FIGS. 1 and 3, loaded into memory 60 would be
reference information 82 against which measured information 78
would be compared. Reference information 82 would include
information concerning an optimal, or desired, location of overlay
features and, therefore, the pattern on patterned devices 20. This
information may be obtained from an existing reference patterned
device (not shown) that may be employed as a standard against which
patterned device 20 is measured. Alternatively, reference
information 82 may be obtained from a GDS file that is employed to
form the pattern on patterned device 20. Considering that errors,
or distortion, in the pattern on the patterned device 20 may be
attributed to the writing and etch processes used to form patterned
device 20, computer data of the type employed in computer aided
design software may provide reference information 82 with the most
accurate reflection of the optimal pattern. Exemplary computer data
is that employed by CATS.TM. software sold by Synopsis, Inc., of
Mountain View, Calif.
[0024] Referring to FIGS. 3 and 5, also stored in memory 60 is a
routine 84 that facilitates comparison of measured information 78
with reference information 82. Routine 84 includes X and Y
positional variations between features in measured information 78
with respect to corresponding features in reference information 82
and generates image placement variation data shown in below in
Table 1:
TABLE-US-00001 TABLE 1 Image Placement Variation Point X (.mu.m) Y
(.mu.m) 1 0.01 -0.012 2 0 -0.003 3 -0.003 -0.001 4 0.013 -0.013 5
0.016 -0.016 6 0.018 -0.014 7 0.012 -0.012 8 -0.001 -0.001 9 -0.012
-0.004 10 -0.001 -0.007 11 0.005 -0.014 12 0.009 -0.013 13 -0.004
-0.004 14 -0.017 0.005 15 -0.02 0.01 16 -0.01 -0.002 17 -0.007
-0.008 18 0 -0.007 19 -0.008 0.007 20 -0.022 0.013 21 -0.024 0.017
22 -0.011 0.012 23 -0.005 0 24 0.001 0 25 0.01 -0.001 26 -0.006
0.006 27 -0.006 0.012 28 0.003 0 29 0.012 -0.006 30 0.016 -0.005 31
0.011 -0.01 32 0.002 -0.001 33 -0.005 0.004 34 0.011 -0.003 35
0.016 -0.011 36 0.019 -0.006
[0025] From the data in Table 1, distortion vectors 86 are
generated. Distortion vectors 86 are vectorized representations of
the differences in spatial location of the overlay features
associated with measured information 78 with respect to
corresponding overlay features associated with reference
information 82. As a result, distortions vectors 86 comprise data
88, mapped into memory 60, concerning a set of spatial locations 90
of features of the pattern on patterned device 20. An exemplary
distortion vector 86 generated from image placement variation data
would be mapped into memory as a series starting with feature 1 and
ending with feature 36 as identifying the x and y variations of
each of the features as follows: {0.01, -0.012, 0, -0.003, . . .
0.019, and -0.006}. Distortion vectors 86 may further represent,
inter alia, magnification errors, orthogonal errors, and other
errors.
[0026] Spatial locations 90 represent the spatial location of the
overlay features on patterned device 20. Data 88 includes
directional and magnitude characteristics of the differences
between measured information 78 and reference information 82.
Specifically, data 88 includes information concerning the distance,
along two orthogonal axes, between spatial locations 90 of each of
the overlay features on patterned device 20 with respect to spatial
locations of the corresponding overlay feature of the
optimal/desired pattern.
[0027] To that end, actuator system 62 facilitates alignment and
overlay registration by selectively deforming patterned device 20
by applying forces upon patterned device 20 by actuators 64. The
forces upon patterned device 20 by actuators 64 must satisfy the
following equilibrium and moment conditions:
.SIGMA.F.sub.x=0; (1)
.SIGMA.F.sub.y=0; and (2)
.SIGMA.M.sub.z=0; (3)
[0028] where F.sub.X are forces in the x direction, F.sub.y are
forces in the y direction and M.sub.z are moments about the z axis.
To that end, equations (1), (2), and (3) may be modeled as
follows:
[K].times.{f}={0} (4)
[0029] Matrix [K] may be determined by the spatial relationship
between actuators 64 and patterned device 20. In the present
example,
[ K ] = [ x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 1 0 x 11 x 12 x 13
x 14 x 15 x 16 y 1 y 2 y 3 y 4 y 5 y 6 y 7 y 8 y 9 y 1 0 y 11 y 12
y 13 y 14 y 15 y 16 m 1 m 2 m 3 m 4 m 5 m 6 m 7 m 8 m 9 m 1 0 m 11
m 12 m 13 m 14 m 15 m 16 ] ( 5 ) ##EQU00001##
[0030] where x.sub.i, y.sub.i, and m.sub.i are the co-efficients of
f.sub.i in equations (1), (2), and (3), respectively. To that end,
in the present example, the matrix [K] may be defined as
follows:
[ K ] = [ 1 1 1 1 0 0 0 0 - 1 - 1 - 1 - 1 0 0 0 0 0 0 0 0 1 1 1 1 0
0 0 0 - 1 - 1 - 1 - 1 - 3 - 1 1 3 - 3 - 1 1 3 - 3 - 1 1 3 - 3 - 1 1
3 ] ( 6 ) ##EQU00002##
[0031] The force vector {f} is the forces associated with actuators
64. In the present example, the force vector {f} may be defined as
follow:
{f}={f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12, f13, f14,
f15, f16}.sup.T (7)
[0032] where f1 is the force associated with actuator 64a; f2 is
the force associated with actuator 64b; f3 is the force associated
with actuator 64c; f4 is the force associated with actuator 64d; f5
is the force associated with actuator 64e; f6 is the force
associated with actuator 64f; f7 is the force associated with
actuator 64g; f8 is the force associated with actuator 64h; f9 is
the force associated with actuator 64i; f10 is the force associated
with actuator 64j; f11 is the force associated with actuator 64k;
f12 is the force associated with actuator 64l; f13 is the force
associated with actuator 64m; f14 is the force associated with
actuator 64n; f15 is the force associated with actuator 64o; and
f16 is the force associated with actuator 64p.
[0033] To that end, from equation (4), the nullspace basis vectors
may be determined. In the present example, there are 16 independent
forces from actuators 64 and there are 3 equilibrium conditions,
resulting in 13 independent force vectors. To that end, employing
equations (6) and (7) with equation (4), the orthonormal basis of
the matrix [K] may be determined using well-known linear algebraic
methods and may be defined as follows:
[ nK ] = [ 1 2 1 2 3 - 2 - 1 0 1 3 - 2 - 1 0 - 2 - 3 - 1 - 2 - 3 3
2 1 0 3 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 - 1 - 1 - 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ] ( 8 )
##EQU00003##
[0034] To that end, each column of the matrix [nK] is an
independent force vector and may referred to as .lamda..sub.1,
.lamda..sub.2, . . . , .lamda..sub.13. Force vectors .lamda..sub.1,
.lamda..sub.2, . . . , .lamda..sub.13 may be referred to as the
nullspace basis vectors of equation (4). More specifically, the
matrix [nK] may be defined as follows:
[nK].sub.16.times.13=[.lamda..sub.1, .lamda..sub.2, .lamda..sub.3,
.lamda..sub.4, .lamda..sub.5, .lamda..sub.6, .lamda..sub.7,
.lamda..sub.8, .lamda..sub.9, .lamda..sub.10, .lamda..sub.11,
.lamda..sub.12, .lamda..sub.13, .lamda..sub.14, .lamda..sub.15,
.lamda..sub.16] (9)
[0035] As a result, any force vector {f} may be defined as
follow:
{f}={p.sub.1.lamda..sub.1+p.sub.2.lamda..sub.2+p.sub.3.lamda..sub.3+p.su-
b.4.lamda..sub.4+p.sub.5.lamda..sub.5+p.sub.6.lamda..sub.6+p.sub.7.lamda..-
sub.7+p.sub.8.lamda..sub.8+p.sub.9.lamda..sub.9+p.sub.10.lamda..sub.10+p.s-
ub.11.lamda..sub.11+p.sub.12.lamda..sub.12+p.sub.13.lamda..sub.13+p.sub.14-
.lamda..sub.14+p.sub.16.lamda..sub.16} (10)
[0036] wherein p.sub.1, p.sub.2, p.sub.3, p.sub.4, p.sub.5,
p.sub.6, p.sub.7, p.sub.8, p.sub.9, p.sub.10, p.sub.11, p.sub.12,
p.sub.13, p.sub.14, p.sub.15, and p.sub.16 are the scalar
co-efficients of .lamda..sub.1, .lamda..sub.2, .lamda..sub.3,
.lamda..sub.4, .lamda..sub.5, .lamda..sub.6, .lamda..sub.7,
.lamda..sub.8, .lamda..sub.9, .lamda..sub.10, .lamda..sub.11,
.lamda..sub.12, .lamda..sub.13, .lamda..sub.14, .lamda..sub.15, and
.lamda..sub.16, respectively.
[0037] Referring to FIGS. 3 and 5, to that end, processor 58
operates on routine 84 to process data concerning distortion
vectors 86 and generate signals that are sensed by actuators 64 to
selectively deform patterned device 20 and attenuate, if not
abrogate, differences between measured information 78 and reference
information 82, thereby minimizing overlay variations between the
pattern on patterned device 20 with respect to the optimal/desired
pattern. The distance between the overlay features associated with
measured information 78 from the corresponding overlay features
associated with reference information 82 is minimized by creating
translational movement of spatial locations 90. To that end,
routine 84 determines the loads to be applied by actuators 64 in
order to selectively deform patterned device 20 solving an inverse
transform function as follows:
[A]{p}={u}, (11)
[0038] where [A] represents the compliance matrix to be specified
for patterned device 20; {p} comprises weighting coefficients for
the force vectors .lamda..sub.1, .lamda..sub.2, . . . ,
.lamda..sub.13; and {u} represents spatial translation of features
associated with measured information 78 must undergo in order to
match the spatial location of the corresponding feature in
reference information 82, i.e., {u} represents an additive inverse
of the distortion vectors 86.
[0039] One manner in which to determine the compliance matrix [A]
employs finite element analysis (FEA). To that end, an FEA model of
patterned device 20, referred to as modeled device 96 is generated
and stored in memory 60, using any known modeling technique, such
as software sold under the trade name Pro/Engineer.TM. 2001 and
finite element solver software sold under the trade name
Pro/Mechanica.TM. 2001.
[0040] Employing FEA, obtained are measurements of the spatial
displacement of each of a plurality of data points 98 of the
modeled device 96 in response to simulated loading of force vectors
.lamda..sub.i by actuators 64. Data points 98 represent the spatial
location of the overlay features of the pattern on modeled device
96. To obtain useful information, the overlay features with which
data points 98 are associated correspond to same features of
patterned device 20 that are associated with spatial locations 90.
In the present example, each of data points 98 is associated with
one of spatial locations 90, such that each of data points 98
corresponds to one of spatial locations 90 that differs from the
spatial locations 90 associated with the remaining data points 98.
Once compliance matrix [A] is determined, vector {p} is determined
from equation (11), and thus force vector {f} is determined from
equation (10). Signals are generated by processor 58 to cause
actuators 64 to apply the requisite loads to patterned device 20
that are a function of the force vector {f}. In this fashion,
distortions in the patterned device 20 are minimized, if not
abrogated.
[0041] For each of data points 98 a displacement along the x and y
axes may be defined as follows:
X.sub.n=p.sub.1x.sub.1n+p.sub.2x.sub.2n+ . . . +p.sub.mx.sub.mn;
and (12)
Y.sub.n=p.sub.1y.sub.1n+p.sub.2y.sub.2n+ . . . +p.sub.mY.sub.mn;
(13)
[0042] where p.sub.i is the scalar co-efficient from force vector
.lamda..sub.i, n denotes the data point and x.sub.in, y.sub.in
represents the movement of a data point n along x, y directions in
terms of millimeters/Newtons in response to loading with force
vector In the present example, n is an integer from 1 to 4 and i is
an integer from 1 to 8. An exemplary compliance matrix [A] based
upon the conditions set forth in equations 1-3 and 12-13 for 4
overlay features is as follows:
A = le - 5 .times. [ - 0.0350 - 0.3316 - 0.6845 - 0.4965 0.4924
0.2550 0.2025 - 0.5387 0.4923 0.2551 0.2028 - 0.5388 - 0.0349 -
0.3316 0.6845 - 0.4957 0.0311 0.3313 0.6848 0.4965 0.5387 - 0.2034
- 0.2557 - 0.4926 0.4930 0.2550 0.2026 - 0.5389 - 0.4989 - 0.6846 -
0.3310 - 0.0323 - 0.4992 - 0.6846 - 0.3310 - 0.0329 0.4931 0.2549
0.2025 - 0.5388 0.5385 - 0.2033 - 0.2556 - 0.4925 0.0313 0.3313
0.6848 0.4973 0.4938 0.6847 0.3318 0.0333 0.5393 - 0.2036 - 0.2560
- 0.4925 0.5393 - 0.2034 - 0.2559 - 0.4927 0.4941 0.6846 0.3319
0.0338 ] ( 14 ) ##EQU00004##
[0043] Knowing compliance matrix [A], routine 84 may determine the
magnitude of the forces to be generated {f} by actuators by solving
for {p}.
Specifically, routine 84 solves the force vector {p} from equation
(11) as follows:
{p}=[A].sup.-1{u}, (15)
[0044] were [A] a square matrix. Were [A] not a square matrix,
equation (15) is expressed as follows:
{p}={A.sup.TA}.sup.-1A.sup.T{u}, (16)
[0045] where A.sup.T is the transpose matrix of compliance matrix
[A].
[0046] To solve for {p} over the infinity norm, equation (11) may
be reforumulated as follows:
[A]{p}-{u}={e}. (17)
[0047] Hence the problem becomes finding {p} such that the error
vector {e} is minimized. [A] is the compliance matrix described
above. Routine 84 may minimize the error vector {e} over the
infinity norm given by the following:
max(|[A]{p}-{u}|) (18)
[0048] The reason for selecting to minimize the infinity norm is
that it is believed that the magnitude of the absolute value of
overlay error that determines a pattern layer's usefulness. As
mentioned above, the maximum overlay error is believed to be less
than 1/3.sup.rd the minimum feature size of the pattern, for the
pattern layer to be functional. Hence, it is desired to have
routine 84 minimize this maximum absolute error, i.e., the infinity
norm as follows:
Min(max |[A]{p}-{u}|). (19)
[0049] Objective function (19) is convex piecewise linear in terms
of the decision variables, i.e. p.sub.i. A convex piecewise linear
function is, by definition, non-linear. The domain of differences
among the set may, therefore, include several local minima. To that
end, routine 84 may be required to undertake several iterations
with a range of trial/guess starting vectors and to implement a
directional search routine. A typical iterative procedure in
accordance with the present invention commences from an initial
point where a function value is calculated. The procedure proceeds
to solutions in which the function has lower values. This results
in routine 48 computing information concerning the function until
convergence is identified. Routine 48 ends the procedure at a
minimum value where no further reduction in the functional value is
identified within the tolerance.
[0050] Any known iterative directional search techniques like
Newton-Raphson Methods, Conjugate Gradient methods, Quasi-Newton
Methods may be employed to get the optimum {p}. One manner in which
to implement these techniques is with Microsoft EXCEL.RTM., stored
in memory 60 and operated on by processor 40 using standard
operating systems such as WINDOWS.RTM., available from Microsoft
Corporation. The data obtained from the finite element analysis,
discussed above, is collated in a matrix form and entered, and the
appropriate relationships between the matrices are established,
e.g., in accordance with equation (11).
[0051] One manner in which to improve the calculation of {p} is by
converting the non-linear formulation (19) into a linear problem.
To that end, equation (17) is substituted into equation (19). This
allows routine 84 to express equation (19) for the series of data
88, as follows:
Minimize(Maximum(|e.sub.1|, |e.sub.2| . . . |e.sub.n|)), (20)
[0052] where, e.sub.i are the elements of error vector {e}. By
routine 84 expanding equation (20), obtained is the following:
Minimize(Maximum(e.sub.1, -e.sub.1, e.sub.2, -e.sub.2, . . .
e.sub.n, -e.sub.n)). (21)
[0053] By routine 84 substituting a variable w for (Maximum
e.sub.1, -e.sub.1, e.sub.2, -e.sub.2, . . . , e.sub.n, -e.sub.n),
equation (21) may be defined as follows:
Minimize(w). (22)
[0054] Providing the following constraints:
w.gtoreq.e.sub.i (23)
w.gtoreq.-e.sub.i. (24)
[0055] That is, routine 84 may solve non-linear equation (19)
formulated as equation (22) with the following constraints:
w.gtoreq.[A]{p}-{u}; and (25)
w.gtoreq.{u}-[A]{p}. (26)
[0056] An advantage with reformulating equation (19) as a linear
problem is that the linear problem is likely to converge to the
global minimum in a finite number of steps, under pseudo-polynomial
algorithms like the Simplex method. This minimizes the
computational power required to have routine 84 determine the
global minimum. Iterative search techniques can however still be
used. Also, most often non-linear programming techniques converge
to the local optima, unless careful checks are implemented. This
was noticed to happen when EXCEL tried to solve the non-linear
problem. As a result, reformulated equation (19) as a linear
problem facilitates obtaining the minimum among the set of data 88
while minimizing the computational power required.
[0057] Referring to FIGS. 6-8, patterned device 20 is shown. To
that end, it may be desired for patterned device 20 to have
dimensions to facilitate magnification and distortion thereof, with
the dimensions for geometric parameters of patterned device 20
shown below in Table 2.
TABLE-US-00002 TABLE 2 Geometric Specifications for Patterned
Device Geometric Parameter Target Tolerance L.sub.1 64.95 mm
.+-.0.05 L.sub.2 64.95 mm .+-.0.05 Q.sub.1 90.degree. .+-.1E-3
Radians Q.sub.2 0.degree. .+-.1E-3 Radians w.sub.1 0.4 mm .+-.0.2
mm w.sub.2 0.4 mm .+-.0.2 mm d.sub.1-d.sub.2 0 mm .+-.0.05 mm
d.sub.3-d.sub.4 0 mm .+-.0.05 mm T 6.35 mm .+-.0.1 mm R 1.5 mm
.+-.1 mm
[0058] The geometric parameters may be defined as follows: L1 may
be defined between side 70 and 74; L2 may be defined between side
72 and 76; Q1 may be defined as the angle between any two sides of
sides 70, 72, 74, and 76; Q2 may be defined as the angle between
any side of sides 70, 72, 74, and 76 and a plane 100 perpendicular
to a plane 102 in which patterned device 20 lays; w1 may be defined
as the width of a first edge surface 106 defined between first
surface 20 and a side of sides 70, 72, 74, and 76; w2 may be
defined as the width of a second edge surface 108 defined between
second surface 22 and a side of sides 70, 72, 74, and 76; d1-d4 may
be defined between mold 24 and a side of sides 70, 72, 74, and 76;
T may be defined as the thickness of template 18 between first and
second opposed sides 20 and 22; and R may be defined as the radius
of curvature of template 18 between any two sides of sides 70, 72,
74, and 76.
[0059] The embodiments of the present invention described above are
exemplary. Many changes and modifications may be made to the
disclosure recited above, while remaining within the scope of the
invention. For example, the method described above is discussed
with respect to attenuating, if not eliminating overlay error
resulting from both image placement and other characteristics, such
as magnification, orthogonality and trapezoidal errors in the case
of imprint lithography. Were magnification, orthogonality and/or
trapezoidal not present or corrected by other methods, for example
in the case of optical lithography, the invention described above
can be used to minimize the uncorrected overlay errors. The scope
of the invention should, therefore, not be limited by the above
description, but instead should be determined with reference to the
appended claims along with their full scope of equivalents.
* * * * *