U.S. patent application number 15/406732 was filed with the patent office on 2019-09-05 for systems, methods and metrics for wafer high order shape characterization and wafer classification using wafer dimensional geomet.
The applicant listed for this patent is KLA-Tencor Corporation. Invention is credited to Haiguang Chen, Sergey Kamensky, Jaydeep Sinha, Sathish Veeraraghavan, Pradeep Vukkadala.
Application Number | 20190271654 15/406732 |
Document ID | / |
Family ID | 50486102 |
Filed Date | 2019-09-05 |
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United States Patent
Application |
20190271654 |
Kind Code |
A1 |
Chen; Haiguang ; et
al. |
September 5, 2019 |
SYSTEMS, METHODS AND METRICS FOR WAFER HIGH ORDER SHAPE
CHARACTERIZATION AND WAFER CLASSIFICATION USING WAFER DIMENSIONAL
GEOMETRY TOOL
Abstract
Systems and methods for improving results of wafer higher order
shape (HOS) characterization and wafer classification are
disclosed. The systems and methods in accordance with the present
disclosure are based on localized shapes. A wafer map is
partitioned into a plurality of measurement sites to improve the
completeness of wafer shape representation. Various site based HOS
metric values may be calculated for wafer characterization and/or
classification purposes, and may also be utilized as control input
for a downstream application. In addition, polar grid partitioning
schemes are provided. Such polar grid partitioning schemes may be
utilized to partition a wafer surface into measurement sites having
uniform site areas while providing good wafer edge region
coverage.
Inventors: |
Chen; Haiguang; (Mountain
View, CA) ; Sinha; Jaydeep; (Livermore, CA) ;
Kamensky; Sergey; (Campbell, CA) ; Veeraraghavan;
Sathish; (Santa Clara, CA) ; Vukkadala; Pradeep;
(Newark, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
KLA-Tencor Corporation |
Milpitas |
CA |
US |
|
|
Family ID: |
50486102 |
Appl. No.: |
15/406732 |
Filed: |
January 15, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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13656143 |
Oct 19, 2012 |
9546862 |
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15406732 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01N 21/9501 20130101;
G06F 17/00 20130101; G06T 7/60 20130101; G01B 11/24 20130101; G06K
9/6267 20130101; G01B 2210/56 20130101; G06T 2207/20021 20130101;
G06T 7/0004 20130101; G06T 2207/30148 20130101; H01L 22/12
20130101; H01L 22/20 20130101 |
International
Class: |
G01N 21/95 20060101
G01N021/95; G01B 11/24 20060101 G01B011/24; G06T 7/00 20060101
G06T007/00; G06T 7/60 20060101 G06T007/60; G06K 9/62 20060101
G06K009/62 |
Claims
1.-14. (canceled)
15. A polar grid partitioning method for partitioning a wafer
surface, the method comprising: specifying a number of sectors and
a number of zones required for the polar grid partitioning;
calculating, with one or more processors, a sector angular span
based on the number of sectors specified; calculating, with one or
more processors, a radial span for each of the number of zones,
wherein the radial span for a first zone having a first radial
distance to the center of the wafer is different from the radial
span for a second zone having a second radial distance to the
center of the wafer; partitioning, with one or more processors, the
wafer surface into a plurality of sites based on the sector angular
span and the radial span for each zone to improve accuracy of wafer
shape analysis performed on the wafer, wherein the plurality of
sites have uniform site areas; calculating, with one or more
processors, one or more measurement metrics based on the
partitioning of the wafer surface into the plurality of sites based
on the sector angular span and the radial span for each zone; and
providing, with one or more processors, the one or more measurement
metrics to control a process of one or more process tools.
16. The polar grid partitioning method of claim 15, wherein the
radial span for the first zone is greater than the radial span for
the second zone when the first radial distance is smaller than the
second radial distance.
17. The polar grid partitioning method of claim 15, wherein the
radial span for the i.sup.th radial zone is defined as the span
between boundaries: r.sub.i= {square root over (i)}L and r.sub.i-1=
{square root over (i-1)}L, =1,2,3, . . . K wherein L = R K ,
##EQU00009## and R is the radius of the wafer and K is the number
of zones.
18. A polar grid partitioning method for partitioning a wafer
surface, the method comprising: specifying a number of zones K
required for the polar grid partitioning and a number of angular
segments M in a center region of the wafer; calculating, with one
or more processors, a radial zone length L based on the number of
zones specified; calculating, with one or more processors, an
angular span .theta..sub.i for the i.sup.th radial zone, wherein
i=1, 2, 3, . . . K; partitioning, with one or more processors, the
wafer surface into a plurality of sites based on the radial zone
length L and the angular span for each radial zone to improve
accuracy of wafer shape analysis performed on the wafer, wherein
the plurality of sites have uniform site areas; calculating, with
one or more processors, one or more measurement metrics based on
the partitioning of the wafer surface into the plurality of sites
based on the radial zone length L and the angular span for each
radial zone; and providing, with one or more processors, the one or
more measurement metrics to control a process of one or more
process tools.
19. The polar grid partitioning method of claim 18, wherein the
angular span .theta..sub.i is less than the angular span
.theta..sub.i-1 for i>1.
20. The polar grid partitioning method of claim 19, wherein the
angular span .theta..sub.i for the i.sup.th radial zone is
calculated according to equation: .theta. i = 1 2 i - 1 2 .pi. M ,
i = 1 , 2 , 3 , K . ##EQU00010##
21. The method of claim 15, wherein the one or more measurement
metrics includes at least one of: a plurality of surface shape
metrics; and a plurality of deviation metrics.
22. The method of claim 21, wherein the surface shape metrics
includes at least one of: an average slope of a measurement site in
x-direction; an average slope of a measurement site in y-direction;
a magnitude of a measurement site slope; a magnitude of a second
order surface component for a measurement site; a radial slope of a
measurement site; or a tangential slope of a measurement site.
23. The method of claim 15, wherein the one or more measurement
metrics are calculated based on surface coefficients obtained
utilizing at least one of: a polynomial fitting process or a
pixel-based shape-slope computation process.
24. The method of claim 15, wherein the one or more measurement
metrics are utilized for controlling at least one of: a Chemical
Mechanical Planarization or Polishing (CMP) process, a wafer
specification development process, an unpatterned wafer geometry
control process, or a wafer uniformity control process.
25. The method of claim 18, wherein the one or more measurement
metrics includes at least one of: a plurality of surface shape
metrics; and a plurality of deviation metrics.
26. The method of claim 25, wherein the surface shape metrics
includes at least one of: an average slope of a measurement site in
x-direction; an average slope of a measurement site in y-direction;
a magnitude of a measurement site slope; a magnitude of a second
order surface component for a measurement site; a radial slope of a
measurement site; or a tangential slope of a measurement site.
27. The method of claim 18, wherein the one or more measurement
metrics are calculated based on surface coefficients obtained
utilizing at least one of: a polynomial fitting process or a
pixel-based shape-slope computation process.
28. The method of claim 18, wherein the one or more measurement
metrics are utilized for controlling at least one of: a Chemical
Mechanical Planarization or Polishing (CMP) process, a wafer
specification development process, an unpatterned wafer geometry
control process, or a wafer uniformity control process.
Description
PRIORITY
[0001] The present application claims the benefit under 35 U.S.C.
.sctn. 120 (pre-AIA) of U.S. patent application Ser. No.
13/656,143, filed Oct. 19, 2012, issued as U.S. Pat. No. 9,546,862,
which is incorporated herein by reference.
TECHNICAL FIELD
[0002] The disclosure generally relates to the field of wafer
surface metrology, and particularly to systems and methods for
wafer high order shape characterization and wafer
classification.
BACKGROUND
[0003] Thin polished plates such as silicon wafers and the like are
a very important part of modern technology. A wafer, for instance,
may refer to a thin slice of semiconductor material used in the
fabrication of integrated circuits and other devices. Other
examples of thin polished plates may include magnetic disc
substrates, gauge blocks and the like. While the technique
described here refers mainly to wafers, it is to be understood that
the technique also is applicable to other types of polished plates
as well. The term wafer and the term thin polished plate may be
used interchangeably in the present disclosure.
[0004] Generally, certain requirements may be established for the
flatness and thickness uniformity of the wafers. The semiconductor
industry uses the two global wafer shape metrics, bow and warp, to
describe the overall wafer shape. Global surface fitting using the
Zernike polynomials or Taylor polynomials have also been used to
describe the wafer shape components.
[0005] However, the two global wafer shape metrics, bow and warp,
do not have the required spatial resolution and sensitivity for the
local wafer shape characterization. Methods based on the whole
wafer surface fitting cannot provide the information about the
location of wafer local higher order shape components and often do
not have good shape sensitivity even with very high polynomial
fitting orders.
[0006] Therein lies a need for systems, methods and metrics for
wafer high order shape characterization and wafer classification
without the aforementioned shortcomings.
SUMMARY
[0007] The present disclosure is directed to a method for
inspecting a wafer. The method may include: defining a wafer
partitioning scheme; obtaining a wafer surface image; partitioning
the wafer surface image into a plurality of measurement sites
according to the wafer partitioning scheme; calculating a plurality
of measurement metrics for each of the plurality of measurement
sites based on the acquired wafer surface image; and reporting the
plurality of measurement metrics calculated for each of the
plurality of measurement sites in a graphical representation.
[0008] A further embodiment of the present disclosure is directed
to a system for inspecting a wafer. The system may include an
optical system configured for obtaining a wafer surface image. The
system may also include a site based high order wafer shape
analysis module in communication with the optical system. The site
based high order wafer shape analysis module may be configured for:
defining a wafer partitioning scheme; partitioning the wafer
surface image into a plurality of measurement sites according to
the wafer partitioning scheme; calculating a plurality of
measurement metrics for each of the plurality of measurement sites
based on the acquired wafer surface image; and reporting the
plurality of measurement metrics calculated for each of the
plurality of measurement sites in a graphical representation.
[0009] An additional embodiment of the present disclosure is
directed to polar grid partitioning method for partitioning a wafer
surface. The method may include: specifying a number of sectors and
a number of zones required for the polar grid partitioning;
calculating a sector angular span based on the number of sectors
specified; calculating a radial span for each of the number of
zones, wherein the radial span for a first zone having a first
radial distance to the center of the wafer is different from the
radial span for a second zone having a second radial distance to
the center of the wafer; and partitioning the wafer surface into a
plurality of sites based on the sector angular span and the radial
span for each zone, wherein the plurality of sites have uniform
site areas.
[0010] An additional embodiment of the present disclosure is
directed to polar grid partitioning method for partitioning a wafer
surface. The method may include: specifying a number of zones K
required for the polar grid partitioning and a number of angular
segments M in a center region of the wafer; calculating a radial
zone length L based on the number of zones specified; calculating
an angular span .theta..sub.i for the i.sup.th radial zone, wherein
i=1, 2, 3, . . . K; and partitioning the wafer surface into a
plurality of sites based on the radial zone length L and the
angular span .theta. for each radial zone, wherein the plurality of
sites have uniform site areas.
[0011] It is to be understood that both the foregoing general
description and the following detailed description are exemplary
and explanatory only and are not necessarily restrictive of the
present disclosure. The accompanying drawings, which are
incorporated in and constitute a part of the specification,
illustrate subject matter of the disclosure. Together, the
descriptions and the drawings serve to explain the principles of
the disclosure.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] The numerous advantages of the disclosure may be better
understood by those skilled in the art by reference to the
accompanying figures in which:
[0013] FIG. 1 is a flow diagram illustrating a site based high
order shape analysis method;
[0014] FIG. 2 is an illustration depicting a Cartesian grid
partition scheme;
[0015] FIG. 3 is an illustration depicting a polar grid partition
scheme;
[0016] FIG. 4 is an illustration depicting a polar grid partition
scheme configured for providing uniform measurement site areas;
[0017] FIG. 5 is an illustration depicting another polar grid
partition scheme configured for providing uniform measurement site
areas;
[0018] FIG. 6 is an illustration depicting site image shape data
obtained for each measurement site;
[0019] FIG. 7 is an illustration depicting a site shape image, two
surface fitting images and the corresponding deviation (residue)
images;
[0020] FIG. 8A is an illustration depicting an exemplary wafer
shape image;
[0021] FIG. 8B is an illustration depicting the X profile of the
exemplary wafer shape image of FIG. 8A;
[0022] FIG. 9 are illustrations depicting various graphical
representations of the site based high order shape analysis in
accordance with the present disclosure;
[0023] FIG. 10A is an illustration depicting a deviation map for
site based high order shape analysis;
[0024] FIG. 1013 is an illustration depicting a second order
coefficient derived map for site based high order shape
analysis;
[0025] FIG. 11A is an illustration depicting another exemplary
wafer shape image;
[0026] FIG. 11B is an illustration depicting the profile of the
exemplary wafer shape image of FIG. 11A in -45.degree.
orientation;
[0027] FIGS. 12-13 are illustrations depicting various graphical
representations of the site based high order shape analysis in
accordance with the present disclosure;
[0028] FIG. 14 is an illustration depicting various graphical
representations of the site based high order shape analysis,
presented in polar space, in accordance with the present
disclosure;
[0029] FIG. 15A is an illustration depicting high order shape
metrics obtained using a pixel-based shape-slope computation
process;
[0030] FIG. 15B is an illustration depicting high order shape
metrics obtained using a polynomial fitting process;
[0031] FIG. 16 is a flow diagram illustrating an intra-field data
analysis method;
[0032] FIG. 17 is an illustration depicting a number of
pre-determined target locations within a lithography field and
across multiple fields within a wafer;
[0033] FIG. 18 is an illustration depicts a wafer lithography
process relative to a timeline;
[0034] FIG. 19 is an illustration depicting the relationship
between the amount of nitride thinning experienced as the magnitude
of wafer lip increases;
[0035] FIG. 20 is a flow diagram illustrating utilizing the site
based high order shape analysis to control a Chemical Mechanical
Planarization or Polishing (CMP) process;
[0036] FIG. 21 is an illustration depicting contact gap(s) before
and after chucking;
[0037] FIG. 22 is an illustration depicting the observed
correlation between contact gap and site based shape curvature
metrics;
[0038] FIG. 23 is a flow diagram illustrating utilizing the site
based high order shape analysis for specification development;
[0039] FIG. 24 is a flow diagram illustrating utilizing the site
based high order shape analysis for an unpatterned wafer geometry
control process;
[0040] FIG. 25 is a flow diagram illustrating utilizing the site
based high order shape analysis for process uniformity control;
[0041] FIG. 26 is a block diagram illustrating a system for
inspecting a wafer in accordance with the present disclosure;
[0042] FIG. 27 is a flow diagram illustrating a polar grid
partitioning method in accordance with the present disclosure;
and
[0043] FIG. 28 is a flow diagram illustrating another polar grid
partitioning method in accordance with the present disclosure.
DETAILED DESCRIPTION
[0044] Reference will now be made in detail to the subject matter
disclosed, which is illustrated in the accompanying drawings.
[0045] The present disclosure is directed to systems and methods
for improved results of wafer higher order shape (HOS)
characterization and wafer classification based on localized
shapes. In accordance with the present disclosure, a wafer map is
partitioned into a plurality of measurement site areas to improve
the completeness of wafer shape representation. This method may
therefore be referred to as the site based high order shape
analysis method.
[0046] FIG. 1 is a flow diagram illustrating the major steps of the
site based high order shape analysis method 100 in accordance with
the present disclosure. Data acquisition and HOS recipe may be
created in step 102. Data acquisition and HOS recipe may specify
how various wafer surface maps will be partitioned in later steps.
Step 104 may acquire the wafer surface images directly utilizing
wafer dimensional geometry tools such as the WaferSight metrology
system from KLA-Tencor. It is contemplated, however, that the wafer
shape image, wafer front and back surface shape images or the like
may also be constructed indirectly using other metrology tools as
well. Subsequently, step 106 may partition the wafer map into a
plurality of measurement site areas and step 108 may calculate HOS
metrics for each of the plurality of measurement site areas based
on the wafer shape information (e.g., wafer shape, front and/or
back surface, image maps or the like) obtained in step 104. Step
110 may then report the site based HOS metrics and may also
group/classify sites and wafers according to automatic or manually
set thresholds.
[0047] More particularly, the recipe for site based high order
shape may be created based on Cartesian grid partition or polar
grid partition. FIG. 2 is an illustration depicting a Cartesian
grid partition. It is contemplated that different site sizes and
shifts of the site array may be selected according to requirements
of desired spatial resolution and alignment with other measurement
or process setup. As illustrated in the figure, all sites in the
Cartesian wafer surface partition have the same site area, except
the partial sites at wafer edge regions.
[0048] Alternatively, the wafer surface may also be partitioned
into polar grid for HOS analysis. Polar grid partition provides a
better wafer edge region coverage. FIG. 3 is an illustration
depicting an exemplary polar grid partition having 6 zones and 6
sectors. In this partition scheme, all polar sites have the same
radial zone length L and the same sector angular span .theta.. The
zone boundaries of the i.sup.th zone may be determined by
equation:
r.sub.1=iL and r.sub.i-1=(i-1)L,i=1,2,3, . . . K
[0049] For instance, the first zone is a circular-shaped zone with
radius r.sub.1=L, the second zone is a ring-shaped zone defined by
an outer region having an outer radius r.sub.2=2L and excluding an
inner region having an inner radius r.sub.1=L and so on.
Furthermore, the area A of the polar site may be determined by
equation:
A i = .theta. 2 ( r i 2 - r i - 1 2 ) = .theta. 2 ( i 2 - ( i - 1 )
2 ) L 2 , i = 1 , 2 , 3 , K ##EQU00001##
where K is the number of zones in the polar partition and KL=R is
the wafer radius.
[0050] While this exemplary polar grid partition may be utilized
for HOS analysis, it is clear that the site areas defined by this
partition scheme may vary greatly. For example, in the scheme shown
in FIG. 3, the ratio of the site areas in the wafer edge and in the
wafer center is 11. Such variations in site areas can result in the
big spread in the HOS measurement values and affect the accurate
wafer shape characterization.
[0051] The present disclosure therefore provides new polar grid
partition schemes that are able to partition the wafer surface into
uniform areas. The first polar grid partition scheme in accordance
with the present disclosure adopts the non-uniform radial span and
defines the partition and defines the site zone boundaries of the
i.sup.th zone as:
r.sub.i= {square root over (i)}L and r.sub.i-1= {square root over
(i-1)}L,i=1,2,3, . . . K
where L is determined by the wafer radius R and the maximum zone
number K in the partition as:
L = R K ##EQU00002##
[0052] In accordance with the polar grid partition scheme described
above, the sector angular span .theta. remains constant and the
radial span for each zone may vary to keep the site areas uniform.
For example, for the same numbers of the sectors and zones as
depicted in FIG. 3, the polar sites created according to this new
partition scheme are illustrated in FIG. 4. It is noted that all
polar sites now have the same areas and can be used to improve the
accuracy of the wafer shape analysis.
[0053] Alternatively, the second polar grid partition scheme in
accordance with the present disclosure may adjust the angular span
.theta. of the site in each zone radius to obtain the uniform site
area while keeping the radial length constant. In this case, the
angular span for the i.sup.th radial zone band may be determined
utilizing equation:
.theta. i = 1 2 i - 1 2 .pi. M , i = 1 , 2 , 3 , K ##EQU00003##
where M is the number of the angular segments in the wafer center
region (identified as region 502 in FIG. 5) and K is the number of
the zones.
[0054] Using the second partition scheme for the case M=6 and K=6,
the polar site partition with uniform site areas can be obtained as
shown in FIG. 5, which has good wafer edge region coverage, good
site spatial resolution and provides area uniformity.
[0055] It is contemplated that similar to the two schemes described
above where uniform site area is maintained by either keeping the
radial length constant and varying the angular span or vice-versa,
uniform site area polar partition may also be obtained by varying
both the radial length and the angular span simultaneously.
Furthermore, the polar grid partitions having 6 zones and 6 sectors
as described in the example above are used merely for illustrative
purposes. It is contemplated that the number of zones and the
number of sectors may vary without departing from the spirit and
scope of the present disclosure.
[0056] As illustrated in FIG. 1, once the wafer map is partitioned
and the wafer shape information is obtained, step 108 may calculate
HOS metrics for each of the plurality of uniform measurement site
areas based on the obtained wafer shape information. More
specifically, given the site image shape data, I(x,y), in the
Cartesian wafer partition as shown in FIG. 6A, the following best
fitting surfaces of orders 0 to 2 may be calculated as defined by
the following three equations, where N is the number of valid
pixels in the given site image and the surface coefficients C(i,j)
in these equations may be determined by the least mean squared
error (LMS) method. For instance, the mean level of site image may
be calculated as:
L c = ( x , y ) I ( x , y ) N ##EQU00004##
[0057] In addition, the first order best-fit surface of site image
may be calculated as:
P.sub.c(x,y)=C(0,0)+C(1,0)x+C(0,1)y
[0058] And the second order best-fit surface of site image may be
calculated as:
S.sub.c(x,y)=C(0,0)+C(1,0)x+C(0,1)y+C(2,0)x.sup.2+C(1,1)xy+C(0,2)y.sup.2
[0059] It is contemplated that higher order best-fit surface of
site image (order greater than 2) may be calculated to characterize
the complex wafer surface geometry. In addition, the corresponding
non-correctable shape components for different surface fitting
orders may also be computed to correlate to higher order process
parameters.
[0060] For example, the deviations of the input site image, I(x,y),
from the site level L.sub.c and two best fit surfaces, P.sub.c(x,y)
and S.sub.c(x,y), may be calculated as:
D.sub.0(x,y)=I(x,y)-L.sub.c
D.sub.1(x,y)=I(x,y)-P.sub.c(x,y)
D.sub.2(x,y)=I(x,y)-S.sub.c(x,y)
[0061] These deviation images (D.sub.0, D.sub.1 and D.sub.2) are
obtained by subtracting the polynomial-fit surface from the
original surface of each measurement site. They represent the
higher order shape components which cannot be described by the
corresponding zero order, first order and second order surface
equations, and therefore cannot be corrected by the corresponding
zero order, first order and second order surface correction
processes. These various deviation metrics may also be referred to
as residues or shape residues, and various deviations/residues may
be obtained by varying the order of the fitting polynomial.
Together with the surface coefficients, these deviation images
provide rich information about the wafer shape and can be used to
characterize and sort the wafers effectively.
[0062] For instance, wafer shape information (may be referred to as
surface shape metrics) that can be calculated for each measurement
site based on the surface coefficients may include: X Slope=C(1,0),
which represents the average site image slope in x direction with
unit nm/mm; Y Slope=C(0,1), which represents the average site image
slope in y direction with unit nm/mm;
T 1 = C 2 ( 1 , 0 ) + C 2 ( 0 , 1 ) 2 , ##EQU00005##
which represents the magnitude of the site image slope with unit
nm/mm; and
T 2 = C 2 ( 2 , 0 ) + C 2 ( 1 , 1 ) + C 2 ( 0 , 2 ) 2 ,
##EQU00006##
which represents the magnitude of the second order surface
components with unit nm/mm.sup.2. It is noted that the magnitude of
the first order polynomial fit coefficients is the magnitude of the
shape-slope, and the magnitude of the second order polynomial fit
coefficients is the magnitude of shape-curvature or simply
shape-curvature. It is contemplated that magnitude of other
higher-order polynomial fit coefficients may be derived in a
similar manner.
[0063] Additional site slope metrics may also be derived from the
surface coefficients and the site position angle .PHI. (as depicted
in FIG. 2) determined by the site center position on the wafer
surface. For instance, the radial slope of the measurement site may
be calculated as Radial
Slope=C(1,0).times.cos(.PHI.)+C(0,1).times.sin(.PHI.) with unit
nm/mm, and the tangential slope of the measurement site may be
calculated as Tangential
Slope=-C(1,0).times.sin(.PHI.)+C(0,1).times.cos(.PHI.) with unit
nm/mm.
[0064] While the magnitudes of the shape slope and the shape
curvature are defined in equations above, it is contemplated that
if more detailed second order components are required, they may be
obtained from the three surface components C(2,0), C(1,1) and
C(0,2), which provide the second order shape curvature descriptions
about the local shape. For instance, the curvature in x direction
may be obtained as X Curvature=C(2,0), the curvature in y direction
may be obtained as Y Curvature=C(0,2), and the curvature in the
(x=y) direction may be obtained as XY Curvature=C(1,1).
[0065] Furthermore, the following deviation metrics may also be
constructed from the deviation images with unit nm:
PD 0 = max [ D 0 ( x , y ) ] ; VD 0 = min [ D 0 ( x , y ) ] ; PVD 0
= PD 0 - VD 0 ; MD 0 = ( x , y ) D 0 ( x , y ) N PD 1 = max [ D 1 (
x , y ) ] ; VD 1 = min [ D 1 ( x , y ) ] ; PVD 1 = PD 1 - VD 1 ; MD
1 = ( x , y ) D 1 ( x , y ) / N PD 2 = max [ D 2 ( x , y ) ] ; VD 2
= min [ D 2 ( x , y ) ] ; PVD 2 = PD 2 - VD 2 ; MD 2 = ( x , y ) D
2 ( x , y ) / N ##EQU00007##
[0066] It is contemplated that these deviation metrics provide the
information about the wafer shape after certain correction
procedures. For example, the metric PD.sub.0 tells the maximum
positive error after the site leveling operation, the metric
MD.sub.1 denotes the average deviation error after the piston/tilt
correction, which may be carried out by the stepper/scanner in
auto-focus process, and MD.sub.2 gives the information about the
surface components higher than the second order.
[0067] FIG. 7 illustrates one original site shape image I(x,y) and
its corresponding two deviation images D.sub.1(x,y) and
D.sub.2(x,y) where the distributions of the shape components in the
original shape image can be clearly seen from two deviation images.
It is noted that if the original shape image has only shape
components of the first order, D.sub.1(x,y) will be an all zero
plane. Similarly, if the original image has only the shape
components up to the second order, then the second order deviation
image D.sub.2(x,y) will be an all zero plane.
[0068] It is contemplated that the HOS metrics calculated for each
of the measurement site areas in step 108 may be utilized to
group/classify the site areas for reporting purposes in step 110.
In addition, automatic or manually set thresholds may be utilized
to visualize the site based high order shape analysis results. For
example, FIG. 8 shows a wafer shape image and its X profile. This
wafer has high shape slope at the wafer edge region and has higher
order components than linear terms at the wafer radius of 40 mm
region. The X slope metric map, the Y slope metric map, the radial
slope map and the tangential slope map may be calculated according
to the equations described above and the calculated site metric
values may be presented for each measurement site in a
corresponding map as shown in FIG. 9. Alternatively/additionally,
the calculated shape metrics and the classification results may
also be reported in measurement result files (e.g., a text-based or
machine-readable result file).
[0069] In the maps shown in FIG. 9, each site may be shaded (or
colored based on the specific implementation) according to the
calculated site metric values and shading/coloring rules. For
instance, a site may be shaded/colored in a first manner if its
metric value is below a lower threshold, in a second manner if its
metric value is between the lower threshold and an upper threshold,
or in a third manner if its metric value is above the upper
threshold. It is contemplated that the lower and upper thresholds
may be set manually by the user to classify the sites and wafers.
Alternatively, the thresholds may be determined automatically. For
instance, a median value of absolute metric values of all sites may
be calculated first and used as the lower threshold. The upper
threshold may be defined subsequently as twice the lower threshold.
It is understood, however, that utilizing two thresholds is merely
exemplary. The number of thresholds utilized for
grouping/classifying the measurement sites may vary without
departing from the spirit and scope of the present disclosure.
Furthermore, the threshold values may also be determined
differently as described above.
[0070] It is clear that the four slope maps shown in FIG. 9
describe the wafer shape slope in different orientations and
provide comprehensive wafer shape information. The radial slope map
and the tangential slope map indicate that wafer shape has bigger
slope in the wafer edge region than the interior region and that
the wafer shape has very smooth shape profile in the tangential
direction. Furthermore, to obtain shape information of higher order
components, the metrics from the first order deviation map, such as
PVD.sub.1, or the metrics from the second order fitting
coefficients, such as T.sub.2, may be utilized. FIG. 10 shows the
deviation PVD.sub.1 map and the second order coefficient derived
T.sub.2 map. Both of them characterize the wafer shape components
higher than the first order and they both show that there are
bigger higher order components in wafer radius of 40 mm
neighborhood region. T.sub.2 metric map also indicates that there
are higher order shape components in wafer edge sites.
[0071] FIG. 11 shows another exemplary wafer shape image and its
profile in -45.degree. orientation. The corresponding four slope
metric maps are shown in FIG. 12. As indicated in FIG. 12, the high
shape slope in the south-east wafer edge region is well detected by
these slope metric maps. In addition, the tangential slope map
shows that this wafer has higher tangential slope components in the
3 o'clock and 6 o'clock wafer edge regions than other wafer edge
regions. Furthermore, FIG. 13 shows the PVD.sub.1 map, T.sub.2 map
and PVD.sub.2 map, where the PVD.sub.2 map clearly shows that the
deep shape valley in the wafer center region has the shape
components higher than the second order. It is contemplated that
providing the ability for the user to visualize the information as
depicted in FIGS. 12 and 13 is appreciated in various situations.
However, it is also contemplated that such information may be
reported in a classification result file (e.g., a text-based or
machine-readable result file) without departing from the spirit and
scope of the present disclosure.
[0072] While the surface fitting coefficients and deviation images
discussed above are defined on the Cartesian (x,y) image site
partitions, the principles and methods can be extended to polar
(r,.beta.) partitions as well. For instance, if polar position is
used for the HOS characterization, the acquired wafer image maps
(usually in Cartesian space) may be converted/transformed into
polar space first. The entire wafer polar image may then be
partitioned into rectangular polar space data blocks I(r,.beta.),
as shown in FIG. 6B. The boundaries of these polar space data
blocks are defined by the particular partition scheme selected
(e.g., from the schemes described in FIG. 3, 4 or 5). That is, the
polar site image in FIG. 6B corresponds to a site area in FIG. 3, 4
or 5 based on the partition scheme selected, and the polar sites
shown in Cartesian space in FIGS. 3, 4 and 5 becomes rectangular
data blocks in the polar space depicted in FIG. 6B.
[0073] The surface fitting and deviation image calculation may now
be calculated as follows:
L p = ( r , .beta. ) I ( r , .beta. ) N P p ( r , .beta. ) = C ( 0
, 0 ) + C ( 1 , 0 ) r + C ( 0 , 1 ) .beta. S p ( r , .beta. ) = C (
0 , 0 ) + C ( 1 , 0 ) r + C ( 0 , 1 ) .beta. + C ( 2 , 0 ) r 2 + C
( 1 , 1 ) r .beta. + C ( 0 , 2 ) .beta. 2 ##EQU00008##
[0074] Similarly, the deviations of the input site image, I(r,
.beta.), from the site level L.sub.p and two best fit surfaces,
P.sub.p(x,y) and S.sub.p(r, .beta.), may be calculated as:
D.sub.0(r,.beta.)=I(r,.beta.)-L.sub.p
D.sub.1(r,.beta.)=I(r,.beta.)-P.sub.p(r,.beta.)
D.sub.2(r,.beta.)=I(r,.beta.)-S.sub.p(r,.beta.)
[0075] Additional site slope metrics may also be derived from the
surface coefficients. For instance, the radial slope of the
measurement site may be calculated as Radial Slope=C(1,0), which
represents the average site image shape slope in r direction, and
the tangential slope of the measurement site may be calculated as
Tangential Slope=C(0,1), which represents the average site image
shape slope in .beta. direction. Furthermore, the X shape slope and
Y shape slope values in the polar space partition may be calculated
from the radial shape slope, tangential shape slope and the site
center angle .OMEGA. (as depicted in FIG. 5). For instance, the X
shape slope may be calculated as X Slope=Radial
Slope*cos(.OMEGA.)-Tangential Slope*sin(.OMEGA.) and the Y shape
slope may be calculated as Y Slope=Radial
Slope*sin(.OMEGA.)+Tangential Slope*cos(.OMEGA.). Other metrics
such as T.sub.1 and T.sub.2 may also be calculated in a similar
manner as described above. T.sub.1 and T.sub.2 provide the
magnitude of the shape slope and the magnitude of the second order
shape components or shape curvature components.
[0076] Similar to the Cartesian space described above, the HOS
metrics calculated for each of the measurement site areas in the
polar space may also be utilized to group/classify the site areas
for reporting purposes. For example, FIG. 14 shows the X slope
metric map, the Y slope metric map, the radial slope map and the
tangential slope map for an exemplary wafer partitioned utilizing
polar partitioning. It is understood that the polar space
partitioning scheme depicted in FIG. 14 is merely exemplary. The
uniform site area partitioning scheme depicted in FIGS. 4 and 5 may
also be utilized for reporting purposes without departing from the
spirit and scope of the present disclosure. Furthermore, it is
contemplated that polar partition may provide better wafer shape
characterization and better correlation with the process
information in certain applications.
[0077] Alternative to calculating the HOS metrics based on fitting
first order polynomials across sites/polar-sectors as described
above, another technique for shape slope computation is to compute
the X slope, the Y slope, the radial slope and the tangential slope
(may be jointly referred to as x/y/radial/tangential components) at
every pixel location via numerical methods such as forward
difference, backward difference, and central difference methods.
For instance, subsequently to capture local shape-slope effects
efficiently and report to the user in the form of images and
text-based data output, the pixel-based shape-slope maps
(x/y/radial/tangential components) may be segmented into
sites/polar-sectors and a mean value of shape-slopes
(x/y/radial/tangential components) may be reported for each
site/polar-sector. Similarly max/min/range and other values may be
reported per site/polar-sector. For illustration purpose a contour
image of the mean radial shape slope for a wafer segmented by sites
is shown in FIG. 15A. This is also compared to slope computation by
way of polynomial fitting described earlier in and as shown in FIG.
15B.
[0078] It is observed that the two methods of slope computation
(i.e., based on fitting first order polynomials, or alternatively,
based on numerical methods) produce very similar results. It is
therefore contemplated that step 108 may utilize either method to
calculate metrics for the measurement sites. It is further
contemplated that other alternative computation methods may also be
utilized to compute the various metrics described above. The
specific equations and/or method utilized may vary without
departing from the spirit and scope of the present disclosure.
[0079] It is also observed that the metrics described above provide
metric values for each field/site. These metric values by
definition are suitable for performing inter-field (field-to-field
variations) data analysis, but may not be optimal for performing
intra-field (within field variations) data analysis. It is
contemplated, however, that the method in accordance with the
present disclosure may be adapted to provide metrics for multiple
data points (may be referred to as targets) per measurement site.
Providing metrics for multiple data points for each site will
therefore support intra-field data analysis, which may be
appreciated in various wafer measurement applications.
[0080] FIG. 16 describes a new methodology for performing
intra-field data analysis. Step 1602 may receive the wafer shape
data as input and step 1604 may compute the shape slope data by
pixel level computation or by polynomial fitting computation method
as described above. Using the example of lithography overlay
variation, overlay errors are typically measured at a number of
pre-determined target locations within a lithography field and
across multiple fields within a device wafer. This is shown in FIG.
17. These target locations across the wafer 1702 may be fed back to
the wafer geometry tool in order to be used as sampling locations
for shape-slope metric or shape-slope residual metric measurement.
The development and usage of shape-slope residual metric is
described in: Overlay and Semiconductor Process Control Using a
Wafer Geometry Metric, P. Vukkadala et al., U.S. patent application
Ser. No. 13/476,328, which is herein incorporated by reference in
its entirety. Furthermore, the feed-back loop 1802 for feeding
process measure locations to the wafer geometry tool 1804 is
illustrated in FIG. 18, which depicts a wafer lithography process
relative to a timeline.
[0081] Step 1606 may then obtain the shape slope data and other
higher-order shape (HOS) data for certain user specified target
locations and step 1608 may utilize the shape slope data at these
target locations to study intra-field lithography process variation
such as overlay variation. The HOS values measured at these target
locations may then be utilized to perform intra-field data analysis
in step 1610. For instance, step 1610 may compare the HOS values
measured at these target locations to process data such as overlay
errors (using visual color maps or statistical correlation
analysis) in order to identify the correlation between HOS values
and process variation. Such analysis can be used to assess the
impact of HOS on intra-field process variation.
[0082] It is contemplated that alternative approaches may also be
utilized for assessing the impact of HOS on inter-field process
variations. For instance, the process data such overlay data
(measured at several targets per field and at multiple fields
across the wafer) may be partitioned and re-formatted into sites
(fields) and sectors exactly similar to the partitioning scheme
used with the corresponding wafer geometry data. Thus metrics such
as mean overlay, peak-to-valley overlay and the like may be
computed per field/sector for multiple fields/sectors across the
wafer. This may then be compared to site-based or sector-based
wafer geometry metrics to assess the impact of wafer geometry
variation (HOS) on inter-field process variation.
[0083] It is also contemplated that the site based high order shape
analysis method and system in accordance with the present
disclosure may be appreciated in various other wafer analysis
applications. For example, the various HOS metrics described above
may be utilized to control a Chemical Mechanical Planarization or
Polishing (CMP) process.
[0084] More specifically, modeling simulation results reported in
P.
[0085] Vukkadala et al., "Impact of Wafer Geometry on CMP for
Advanced Nodes," Journal of Electrochemical Society (JES), Vol.
158, No. 10, pp. H1002-H1009, 2011, shows that the uniformity of
CMP processes such as Shallow Trench Isolation (STI) are highly
dependent on the higher order components of the shape of a wafer.
This is illustrated in FIG. 19, which shows increasing amount of
nitride thinning experienced as the magnitude of wafer lip (a
higher order shape component) increases. A typical method for
measuring nitride thinning during a CMP process is by measuring the
STI step height. The process data such as STI step height variation
are typically measured at finite number of points on the surface of
the wafer. To assess the correlation between the process data and
the wafer geometry metrics, the process data needs to be formatted
appropriately. The methodology for formatting the process data is
dependent on the format of the wafer geometry metrics. For example,
for comparing the sector metrics the process data will be grouped
into various sectors and relevant metrics will be computed on the
process data.
[0086] Consequently experiments were conducted to assess the impact
of higher order shape on CMP removal uniformity. It was determined
that the Radial Shape-Slope metric (both sites/polar-sector based)
correlated well with the STI step height variation process data.
Hence the Radial Shape Slope metric of an unpatterned/filmed wafer
may be used to control the uniformity of CMP processes such as STI.
This may be achieved by having an inline monitor for Radial Shape
Slope to assess the amount of CMP non-uniformity an incoming wafer
may exhibit down the line after a CMP process.
[0087] This is illustrated in FIG. 20 where the wafer geometry
(including HOS) is measured at the bare/unpatterned wafer level as
well as several process steps later but right before the wafer is
subjected to CMP. This way two things may be determined: (i) by
computing the difference in higher order shape between the two
wafer geometry measurements gives an indication of the amount of
higher order shape induced by wafer processing; and (ii) by
correlating higher order shape (e.g., Radial Shape Slope) to CMP
removal variation across the wafer a model may be developed for
predicting the amount of CMP variation that may be caused by a
given wafer higher order shape. Proper thresholds for the wafer
high order shapes may be developed to limit the amount of CMP
variation to an acceptable level. Thus an inline wafer geometry
(higher order shape) monitor may be used to: (i) accept/reject a
wafer for a particular process, (ii) identify process steps that
induce larger higher order shape for further root-cause-analysis,
and (iii) sort incoming wafers into technology node specific
bins.
[0088] Another example of the application of wafer site based
higher order shape metrics is to monitor the impact of wafer shape
on lithography process. During patterning a wafer using lithography
process, the wafer is first held on a vacuum or electrostatic chuck
(based on the lithography technology) by using vacuum or
electrostatic force respectively. When the wafer is held on a chuck
using a force, the initial gap between the wafer and chuck
primarily due to the shape of the wafer is reduced. Ideally the
wafer back surface is expected to completely come in contact with
the chuck surface with zero contact gap. However, in reality the
contact gap is a function of the wafer geometry. Contact gap may
result in defocus errors and need to be monitored and controlled.
Previously, there was no metric to monitor the contact gap during
chucking.
[0089] FIG. 21 illustrates the change of the contact gap(s) as a
result of chucking. Consequently, a three-dimensional finite
element model with tens of thousands of nodes may be developed to
simulate the wafer and chuck interaction. The key input parameters
of the model may include the wafer geometry, the chuck geometry,
and the applied vacuum/electrostatic pressure. This model may be
developed assuming uniform chucking pressure over the entire
surface of the wafer. One of the key outputs of the model may
include contact gap estimation. With the pressure and chuck
geometry being constant, the impact on different wafer geometry on
contact gap may be estimated/observed. Experimental results have
indicated that contact gap is a function of the curvature of wafer
shape and a good correlation was observed between contact gap and
the site based shape curvature metric as shown in FIG. 22.
Therefore, the site based shape curvature metrics provided
utilizing the method and system of the present disclosure may be
utilized to monitor/access the impact of wafer shape on lithography
process.
[0090] In addition to utilizing the HOS metrics to control a CMP
and lithography process, it is contemplated that the HOS metrics
may be utilized for controlling other processes without departing
from the spirit and scope of the present disclosure. For instance,
FIG. 23 is a flow diagram depicting utilizing HOS metrics for
specification development, FIG. 24 is a flow diagram depicting an
unpatterned wafer geometry control process, and FIG. 25 is a flow
diagram depicting process uniformity control, all based on the HOS
metrics described in accordance with the present disclosure. It is
also contemplated that the HOS metrics may be utilized for process
control for mitigating overlay errors as well as other wafer
analysis/control applications.
[0091] FIG. 26 is a block diagram depicting a wafer inspection
system 2600 in accordance with the present disclosure. The wafer
inspection system 2600 includes an optical system 2602 configured
for obtaining a wafer surface image. As previously described, the
optical system 2602 may acquire the wafer surface images directly
utilizing wafer dimensional geometry tools such as the WaferSight
metrology system from KLA-Tencor. Alternatively, the wafer shape
image, wafer front and back surface shape images or the like may
also be constructed indirectly using other metrology tools as
well.
[0092] The wafer inspection system 2600 also includes a site based
high order wafer shape analysis module 2604 in communication with
the optical system 2602. The site based high order wafer shape
analysis module 2604 is configured for carrying out the site based
high order shape analysis method 100 as described above. The
calculated high order shape metrics may subsequently be utilized as
control input for various downstream applications 2606, including,
but not limited to, CMP processes, wafer specification development
processes, unpatterned wafer geometry control processes, wafer
uniformity control processes or the like.
[0093] FIG. 27 is a flow diagram illustrating the polar grid
partitioning method 2700 in accordance with the present disclosure.
Step 2702 may specify a number of sectors and a number of zones
required for the polar grid partitioning. Step 2704 may calculate a
sector angular span based on the number of sectors specified. Step
2706 may calculate a radial span for each of the number of zones.
In accordance with this partitioning scheme, the radial span for a
first zone having a first radial distance to the center of the
wafer is different from the radial span for a second zone having a
second radial distance to the center of the wafer. Step 2708 may
then partition the wafer surface into a plurality of sites based on
the sector angular span and the radial span for each zone. The
sites partitioned in this manner will have uniform site areas.
[0094] FIG. 28 is a flow diagram illustrating an alternative polar
grid partitioning method 2800 in accordance with the present
disclosure. Step 2802 may specify a number of zones K required for
the polar grid partitioning and a number of angular segments M in a
center region of the wafer. Step 2804 may calculate a radial zone
length L based on the number of zones specified. Step 2806 may
independently calculate an angular span .theta..sub.i for the
i.sup.th radial zone, wherein i=1, 2, 3, . . . K. Step 2808 may
subsequently partition the wafer surface into a plurality of
uniform sites based on the radial zone length L and the angular
span .theta. for each radial zone. The sites partitioned in this
manner will have uniform site areas.
[0095] It is contemplated that while the examples above referred to
wafer metrology measurements, the systems and methods in accordance
with the present disclosure are applicable to other types of
polished plates as well without departing from the spirit and scope
of the present disclosure. The term wafer used in the present
disclosure may include a thin slice of semiconductor material used
in the fabrication of integrated circuits and other devices, as
well as other thin polished plates such as magnetic disc
substrates, gauge blocks and the like.
[0096] The methods disclosed may be implemented as sets of
instructions, through a single production device, and/or through
multiple production devices. Further, it is understood that the
specific order or hierarchy of steps in the methods disclosed are
examples of exemplary approaches. Based upon design preferences, it
is understood that the specific order or hierarchy of steps in the
method can be rearranged while remaining within the scope and
spirit of the disclosure. The accompanying method claims present
elements of the various steps in a sample order, and are not
necessarily meant to be limited to the specific order or hierarchy
presented.
[0097] It is believed that the system and method of the present
disclosure and many of its attendant advantages will be understood
by the foregoing description, and it will be apparent that various
changes may be made in the form, construction and arrangement of
the components without departing from the disclosed subject matter
or without sacrificing all of its material advantages. The form
described is merely explanatory.
* * * * *