U.S. patent application number 13/777953 was filed with the patent office on 2014-08-28 for optical model with polarization direction effects for comparison to measured spectrum.
This patent application is currently assigned to Applied Materials, Inc.. The applicant listed for this patent is Applied Materials, Inc.. Invention is credited to Jeffrey Drue David.
Application Number | 20140242880 13/777953 |
Document ID | / |
Family ID | 51388605 |
Filed Date | 2014-08-28 |
United States Patent
Application |
20140242880 |
Kind Code |
A1 |
David; Jeffrey Drue |
August 28, 2014 |
OPTICAL MODEL WITH POLARIZATION DIRECTION EFFECTS FOR COMPARISON TO
MEASURED SPECTRUM
Abstract
A method of controlling a polishing operation includes storing
an optical model for a layer stack having a plurality of layers.
The optical model has a plurality of input parameters, the
plurality of input parameters including a first parameter and a
second parameter. The second parameter is a polarization angle or a
relative contribution between two orthogonal polarizations. A
spectrum reflected from the substrate is measured with an
in-sequence or in-situ monitoring system to provide a measured
spectrum. The optical model is fit to the measured spectrum, or a
plurality of reference spectra are calculated using the optical
model and a best matching reference spectrum from the plurality of
reference spectra is determined.
Inventors: |
David; Jeffrey Drue; (San
Jose, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Applied Materials, Inc. |
Santa Clara |
CA |
US |
|
|
Assignee: |
Applied Materials, Inc.
Santa Clara
CA
|
Family ID: |
51388605 |
Appl. No.: |
13/777953 |
Filed: |
February 26, 2013 |
Current U.S.
Class: |
451/5 ;
451/6 |
Current CPC
Class: |
B24B 49/12 20130101;
B24B 37/013 20130101 |
Class at
Publication: |
451/5 ;
451/6 |
International
Class: |
B24B 49/12 20060101
B24B049/12; B24B 37/013 20060101 B24B037/013 |
Claims
1. A method of controlling a polishing operation, comprising:
storing an optical model for a layer stack having a plurality of
layers, the optical model having a plurality of input parameters,
the plurality of input parameters including a first parameter and a
second parameter, wherein the second parameter is a polarization
angle or a relative contribution between two orthogonal
polarizations; measuring a spectrum reflected from the substrate
with an in-sequence or in-situ monitoring system to provide a
measured spectrum; fitting the optical model to the measured
spectrum, the fitting including finding a first value of the first
parameter and a second value of the second parameter that provides
a minimum difference between an output spectrum of the optical
model and the measured spectrum; polishing the substrate with the
polishing apparatus; and adjusting a polishing endpoint or a
polishing parameter of the polishing apparatus based on the first
value associated with the best matching reference spectrum.
2. The method of claim 1, wherein measuring the spectrum is
performed with the in-line monitoring system before or after the
polishing of the substrate.
3. The method of claim 1, wherein measuring the spectrum is
performed with an in-situ monitoring system during the polishing of
the substrate.
4. The method of claim 1, wherein measuring the spectrum comprises
directing polarized light onto the substrate.
5. The method of claim 4, wherein the second parameter comprises a
polarization angle.
6. The method of claim 1, wherein measuring the spectrum comprises
directing ostensibly unpolarized light onto the substrate.
7. The method of claim 6, wherein the second parameter comprises
the relative contribution between two orthogonal polarizations.
8. The method of claim 1, wherein the first parameter comprises a
thickness of an outermost layer.
9. A method of controlling a polishing operation, comprising:
storing an optical model for a layer stack having a plurality of
layers, the optical model having a plurality of input parameters,
the plurality of input parameters including a first parameter and a
second parameter, wherein the second parameter is a polarization
angle or a relative contribution between two orthogonal
polarizations; storing data defining a plurality of first values
for the first parameter and a plurality of second values for the
second parameter; for each combination of a first value from the
plurality of first values and a second value from the plurality of
second values, calculating a reference spectrum using the optical
model based on the first value and the second value, to generate a
plurality of reference spectra; measuring a spectrum reflected from
the substrate with an in-sequence or in-situ monitoring system to
provide a measured spectrum; determining a best matching reference
spectrum from the plurality of reference spectra that provides a
best match to the measured spectrum; determining the first value
associated with the best matching reference spectrum; polishing the
substrate with the polishing apparatus; and adjusting a polishing
endpoint or a polishing parameter of the polishing apparatus based
on the first value associated with the best matching reference
spectrum.
10. The method of claim 9, wherein measuring the spectrum is
performed with the in-line monitoring system before or after the
polishing of the substrate.
11. The method of claim 9, wherein measuring the spectrum is
performed with an in-situ monitoring system during the polishing of
the substrate.
12. The method of claim 9, wherein measuring the spectrum comprises
directing polarized light onto the substrate.
13. The method of claim 12, wherein the second parameter comprises
a polarization angle.
14. The method of claim 9, wherein measuring the spectrum comprises
directing ostensibly unpolarized light onto the substrate.
15. The method of claim 14, wherein the second parameter comprises
the relative contribution between two orthogonal polarizations.
16. The method of claim 9, wherein the first parameter comprises a
thickness of an outermost layer.
Description
TECHNICAL FIELD
[0001] The present disclosure relates to polishing control methods,
e.g., during chemical mechanical polishing of substrates.
BACKGROUND
[0002] An integrated circuit is typically formed on a substrate by
the sequential deposition of conductive, semiconductive, or
insulative layers on a silicon wafer. A variety of fabrication
processes require planarization of a layer on the substrate. For
example, for certain applications, e.g., polishing of a metal layer
to form vias, plugs, and lines in the trenches of a patterned
layer, an overlying layer is planarized until the top surface of a
patterned layer is exposed. In other applications, e.g.,
planarization of a dielectric layer for photolithography, an
overlying layer is polished until a desired thickness remains over
the underlying layer.
[0003] Chemical mechanical polishing (CMP) is one accepted method
of planarization. This planarization method typically requires that
the substrate be mounted on a carrier head. The exposed surface of
the substrate is typically placed against a rotating polishing pad.
The carrier head provides a controllable load on the substrate to
push it against the polishing pad. A polishing liquid, such as
slurry with abrasive particles, is typically supplied to the
surface of the polishing pad.
[0004] One problem in CMP is determining whether the polishing
process is complete, i.e., whether a substrate layer has been
planarized to a desired flatness or thickness, or when a desired
amount of material has been removed. Variations in the initial
thickness of the substrate layer, the slurry composition, the
polishing pad condition, the relative speed between the polishing
pad and the substrate, and the load on the substrate can cause
variations in the material removal rate. These variations cause
variations in the time needed to reach the polishing endpoint.
Therefore, it may not be possible to determine the polishing
endpoint merely as a function of polishing time.
[0005] In some systems, a substrate is optically monitored in-situ
during polishing, e.g., through a window in the polishing pad. In
some optical monitoring processes, a spectrum is measured in-situ,
i.e., during a polishing process of CMP. However, existing optical
monitoring techniques may not satisfy increasing demands of
semiconductor device manufacturers.
SUMMARY
[0006] One approach to deriving endpoint data from a spectrum
measured in-situ during polishing is to fit a function, e.g., an
optical model, to the measured spectrum. The optical model is a
function with multiple parameters, e.g. the thickness, index of
refraction and extinction coefficient of each layer in the stack.
The optical model generates an output spectrum based on the
parameters. By fitting the optical model to the measured spectrum,
the parameters are selected, e.g., by regression techniques, to
provide an output spectrum that closely matches the measured
spectrum.
[0007] Another approach to use the optical model to generate a
library with a plurality of reference spectra. The measured
spectrum is compared to the reference spectra in the library, and
the best matching reference spectrum is identified. Parameters that
generated the reference spectrum can be identified.
[0008] In some situations, the light that illuminates the substrate
may be partially polarized, e.g., due to interaction with optical
components between the light source and the substrate. Even if the
monitoring system is ostensibly designed to illuminate the
substrate with unpolarized light, some polarization effects can
occur. Thus, the polarization may be unintentional (in which case
the light will likely be partially polarized), or intentional (in
which case the light will likely be completely polarized).
[0009] A device wafer is typically patterned. This pattern can
generate diffraction effects, which can depend on the polarization
of the light. However, since the orientation of the substrate may
not be known, and the polarization may be unintentional, an optical
model which assumes a known polarization (or assumes unpolarized
light) may not be accurate, and consequently the endpoint
determination may be unreliable. A technique is for the model to
include the polarization angle as an input parameter that is varied
when fitting or generating the reference spectra.
[0010] In one aspect, a method of controlling a polishing operation
includes storing an optical model for a layer stack having a
plurality of layers. The optical model has a plurality of input
parameters, the plurality of input parameters including a first
parameter and a second parameter. The second parameter is a
polarization angle or a relative contribution between two
orthogonal polarizations. A spectrum reflected from the substrate
is measured with an in-sequence or in-situ monitoring system to
provide a measured spectrum. The optical model is fit to the
measured spectrum. The fitting includes finding a first value of
the first parameter and a second value of the second parameter that
provides a minimum difference between an output spectrum of the
optical model and the measured spectrum. The substrate is polished
with the polishing apparatus, and a polishing endpoint or a
polishing parameter of the polishing apparatus is adjusted based on
the first value associated with the best matching reference
spectrum.
[0011] In another aspect, a method of controlling a polishing
operation includes storing an optical model for a layer stack
having a plurality of layers. The optical model having a plurality
of input parameters, the plurality of input parameters including a
first parameter and a second parameter. The second parameter is a
polarization angle or a relative contribution between two
orthogonal polarizations. Data is stored defining a plurality of
first values for the first parameter and a plurality of second
values for the second parameter. For each combination of a first
value from the plurality of first values and a second value from
the plurality of second values, a reference spectrum is calculated
using the optical model based on the first value and the second
value, to generate a plurality of reference spectra. A spectrum
reflected from the substrate is measured with an in-sequence or
in-situ monitoring system to provide a measured spectrum. A best
matching reference spectrum from the plurality of reference spectra
that provides a best match to the measured spectrum is determined.
The first value associated with the best matching reference
spectrum is determined. The substrate is polished with the
polishing apparatus, and a polishing endpoint or a polishing
parameter of the polishing apparatus is adjusted based on the first
value associated with the best matching reference spectrum.
[0012] Implementations of either aspect may include one or more of
the following features. Measuring the spectrum may be performed
with the in-line monitoring system before or after the polishing of
the substrate. Measuring the spectrum may be performed with an
in-situ monitoring system during the polishing of the substrate.
Measuring the spectrum may include directing polarized light onto
the substrate. The second parameter may be a polarization angle.
Measuring the spectrum may include directing ostensibly unpolarized
light onto the substrate. The second parameter may be the relative
contribution between two orthogonal polarizations. The first
parameter may be a thickness of an outermost layer.
[0013] In another aspect, a non-transitory computer program
product, tangibly embodied in a machine readable storage device,
includes instructions to carry out the method.
[0014] Certain implementations may include one or more of the
following advantages. An optical model may account for either
unintended polarization effects or the orientation of the substrate
By looking at different polarization angles, additional information
may be obtained. For example, by looking at TE and TM polarized
light, two spectra (as opposed to one spectrum in the case of
unpolarized light) that carry different information can be
obtained. The system now has two spectra to which the model can be
fit, thus increasing fit confidence. Also, there may be more (or
better information) contained in a particular polarization angle.
For example, if one polarization state contains good signal
information and the other polarization state does not, it is
possible to rely only on the former for parameter information.
Reliability of the endpoint system to detect a desired polishing
endpoint may be improved, and within-wafer and wafer-to-wafer
thickness non-uniformity (WTWNU and WTWNU) may be reduced.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] FIG. 1 illustrates a schematic cross-sectional view of an
example of a polishing station.
[0016] FIG. 2 illustrates a schematic top view of a substrate
having multiple zones.
[0017] FIG. 3 illustrates a top view of a polishing pad and shows
locations where in-situ measurements are taken on a substrate.
[0018] FIG. 4 illustrates a schematic cross-sectional view of an
example of an in-line monitoring station.
[0019] FIG. 5 illustrates a measured spectrum from the in-situ
optical monitoring system.
[0020] FIG. 6 illustrates a model of a portion of the substrate
using a 1-dimensional model of layers of the stack.
[0021] FIG. 7 illustrates a model of a portion of the substrate
using a 2-dimensional model of layers of the stack.
[0022] FIG. 8 illustrates an index trace.
[0023] FIG. 9 illustrates an index trace having a linear function
fit to index values collected after clearance of an overlying layer
is detected.
[0024] FIG. 10 is a flow diagram of an example process for
controlling a polishing operation.
[0025] Like reference numbers and designations in the various
drawings indicate like elements.
DETAILED DESCRIPTION
[0026] One optical monitoring technique for controlling a polishing
operation is to measure a spectrum of light reflected from a
substrate, either in-situ during polishing or at an in-line
metrology station, and fit a function, e.g., an optical model, to
the measured spectra. Another technique is to compare the measured
spectrum to a plurality of reference spectra from a library, and
identify a matching reference spectrum.
[0027] As noted above, even if the monitoring system is ostensibly
designed to illuminate the substrate with unpolarized light, some
polarization effects can occur. The optical model can include the
polarization angle as an input parameter. This permits the
polarization angle to be varied when fitting the function, or when
generating reference spectra for the library. Thus, the
polarization may be unintentional (in which case the light will
likely be partially polarized), or intentional (in which case the
light will likely be completely polarized).
[0028] A substrate can include a first layer (that will undergo
polishing) and a second layer disposed under the first layer. Both
the first layer and the second layer are at least semi-transparent.
Together, the second layer and one or more additional layers (if
present) provide a layer stack below the first layer. Examples of
layers include an insulator, passivation, etch stop, barrier layer
and capping layers. Examples of materials in such layers include
oxide, such as silicon dioxide, a low-k material, such as carbon
doped silicon dioxide, e.g., Black Diamond.TM. (from Applied
Materials, Inc.) or Coral.TM. (from Novellus Systems, Inc.),
silicon nitride, silicon carbide, carbon-silicon nitride (SiCN), a
metal nitride, e.g., tantalum nitride or titanium nitride, or a
material formed from tetraethyl orthosilicate (TEOS).
[0029] Chemical mechanical polishing can be used to planarize the
substrate until a predetermined thickness of the first layer is
removed, a predetermined thickness of the first layer remains, or
until the second layer is exposed.
[0030] FIG. 1 illustrates an example of a polishing apparatus 100.
The polishing apparatus 100 includes a rotatable disk-shaped platen
120 on which a polishing pad 110 is situated. The platen is
operable to rotate about an axis 125. For example, a motor 121 can
turn a drive shaft 124 to rotate the platen 120. The polishing pad
110 can be a two-layer polishing pad with an outer polishing layer
112 and a softer backing layer 114.
[0031] The polishing apparatus 100 can include a port 130 to
dispense polishing liquid 132, such as a slurry, onto the polishing
pad 110 to the pad. The polishing apparatus can also include a
polishing pad conditioner to abrade the polishing pad 110 to
maintain the polishing pad 110 in a consistent abrasive state.
[0032] The polishing apparatus 100 includes one or more carrier
heads 140. Each carrier head 140 is operable to hold a substrate 10
against the polishing pad 110. Each carrier head 140 can have
independent control of the polishing parameters, for example
pressure, associated with each respective substrate.
[0033] In particular, each carrier head 140 can include a retaining
ring 142 to retain the substrate 10 below a flexible membrane 144.
Each carrier head 140 also includes a plurality of independently
controllable pressurizable chambers defined by the membrane, e.g.,
three chambers 146a-146c, which can apply independently
controllable pressurizes to associated zones 148a-148c on the
flexible membrane 144 and thus on the substrate 10 (see FIG. 3).
Referring to FIG. 3, the center zone 148a can be substantially
circular, and the remaining zones 148b-148c can be concentric
annular zones around the center zone 148a. Although only three
chambers are illustrated in FIGS. 1 and 2 for ease of illustration,
there could be one or two chambers, or four or more chambers, e.g.,
five chambers.
[0034] Returning to FIG. 1, each carrier head 140 is suspended from
a support structure 150, e.g., a carousel or track, and is
connected by a drive shaft 152 to a carrier head rotation motor 154
so that the carrier head can rotate about an axis 155. Optionally
each carrier head 140 can oscillate laterally, e.g., on sliders on
the carousel 150; by rotational oscillation of the carousel itself,
or by motion of a carriage 158 (see FIG. 4) on along the track. In
operation, the platen is rotated about its central axis 125, and
each carrier head is rotated about its central axis 155 and
translated laterally across the top surface of the polishing
pad.
[0035] While only one carrier head 140 is shown, more carrier heads
can be provided to hold additional substrates so that the surface
area of polishing pad 110 may be used efficiently. Thus, the number
of carrier head assemblies adapted to hold substrates for a
simultaneous polishing process can be based, at least in part, on
the surface area of the polishing pad 110.
[0036] In some implementations, the polishing apparatus includes an
in-situ optical monitoring system 160, e.g., a spectrographic
monitoring system, which can be used to determine whether to adjust
a polishing rate or an adjustment for the polishing rate as
discussed below. An optical access through the polishing pad is
provided by including an aperture (i.e., a hole that runs through
the pad) or a solid window 118. The solid window 118 can be secured
to the polishing pad 110, e.g., as a plug that fills an aperture in
the polishing pad, e.g., is molded to or adhesively secured to the
polishing pad, although in some implementations the solid window
can be supported on the platen 120 and project into an aperture in
the polishing pad.
[0037] In some implementation, illustrated in FIG. 4, the polishing
apparatus of includes an in-sequence optical monitoring system 160
having a probe 180 positioned between two polishing stations,
between a polishing station and a transfer station, or in the
transfer station. The probe 180 of the in-sequence monitoring
system 160 can be supported on a platform 106, and can be
positioned on the path of the carrier head.
[0038] The probe 180 can include a mechanism to adjust its vertical
height relative to the top surface of the platform 106. In some
implementations, the probe 180 is supported on an actuator system
182 that is configured to move the probe 180 laterally in a plane
parallel to the plane of the track 128. The actuator system 182 can
be an XY actuator system that includes two independent linear
actuators to move probe 180 independently along two orthogonal
axes.
[0039] Referring to FIGS. 1 and 4, in either the in-situ or
in-sequence embodiments, the optical monitoring system 160 can
include a light source 162, a light detector 164, and circuitry 166
for sending and receiving signals between a remote controller 190,
e.g., a computer, and the light source 162 and light detector 164.
One or more optical fibers can be used to transmit the light from
the light source 162 to the optical access in the polishing pad,
and to transmit light reflected from the substrate 10 to the
detector 164. For example, a bifurcated optical fiber 170 can be
used to transmit the light from the light source 162 to the
substrate 10 and back to the detector 164. The bifurcated optical
fiber an include a trunk 172 positioned in proximity to the optical
access, and two branches 174 and 176 connected to the light source
162 and detector 164, respectively. The probe 180 can include the
trunk end of the bifurcated optical fiber.
[0040] The light source 162 can be operable to emit white light. In
one implementation, the white light emitted includes light having
wavelengths of 200-800 nanometers. In some implementations, the
light source 162 generates unpolarized light. A suitable light
source is a xenon lamp or a xenon mercury lamp.
[0041] In some implementations, the light source 162 and optical
components between the light source 162 and substrate 10 are
ostensibly configured to direct unpolarized light onto the
substrate 10, e.g., there are no polarization filters or the like
in the path of the light between the light source 162 and the
substrate 10. Nevertheless, defects in the optical components may
cause the light beam that reaches the substrate to be partially
polarized. In other implementations, optical components between the
light source 162 and substrate 10 are configured to deliberated
direct polarized light onto the substrate, e.g., a polarization
filter 178 (illustrated in FIG. 4, although it can be used in the
in-situ system of FIG. 2) can be positioned between the light
source 162 and the substrate 10.
[0042] The light detector 164 can be a spectrometer. A spectrometer
is an optical instrument for measuring intensity of light over a
portion of the electromagnetic spectrum. A suitable spectrometer is
a grating spectrometer. Typical output for a spectrometer is the
intensity of the light as a function of wavelength (or frequency).
FIG. 4 illustrates an example of a measured spectrum 300.
[0043] In some in-situ implementations, the top surface of the
platen can include a recess 128 into which is fit an optical head
168 that holds one end of the trunk 172 of the bifurcated fiber.
The optical head 168 can include a mechanism to adjust the vertical
distance between the top of the trunk 172 and the solid window
118.
[0044] The output of the circuitry 166 can be a digital electronic
signal that passes through a rotary coupler 129, e.g., a slip ring,
in the drive shaft 124 to the controller 190 for the optical
monitoring system. Similarly, the light source can be turned on or
off in response to control commands in digital electronic signals
that pass from the controller 190 through the rotary coupler 129 to
the optical monitoring system 160. Alternatively, the circuitry 166
could communicate with the controller 190 by a wireless signal.
[0045] As noted above, the light source 162 and light detector 164
can be connected to a computing device, e.g., the controller 190,
operable to control their operation and receive their signals. The
computing device can include a microprocessor situated near the
polishing apparatus, e.g., a programmable computer. With respect to
control, the computing device can, for example, synchronize
activation of the light source with the rotation of the platen
120.
[0046] In some in-situ implementations, the light source 162 and
detector 164 of the in-situ monitoring system 160 are installed in
and rotate with the platen 120. In this case, the motion of the
platen will cause the sensor to scan across each substrate. In
particular, as the platen 120 rotates, the controller 190 can cause
the light source 162 to emit a series of flashes starting just
before and ending just after the optical access passes below the
substrate 10. Alternatively, the computing device can cause the
light source 162 to emit light continuously starting just before
and ending just after each substrate 10 passes over the optical
access. In either case, the signal from the detector can be
integrated over a sampling period to generate spectra measurements
at a sampling frequency.
[0047] In operation, the controller 190 can receive, for example, a
signal that carries information describing a spectrum of the light
received by the light detector for a particular flash of the light
source or time frame of the detector.
[0048] As shown by in FIG. 3, if the detector is installed in the
platen, due to the rotation of the platen (shown by arrow 204), as
the window 108 travels below a carrier head, the optical monitoring
system making spectra measurements at a sampling frequency will
cause the spectra measurements to be taken at locations 201 in an
arc that traverses the substrate 10. For example, each of points
201a-201k represents a location of a spectrum measurement by the
monitoring system (the number of points is illustrative; more or
fewer measurements can be taken than illustrated, depending on the
sampling frequency). The sampling frequency can be selected so that
between five and twenty spectra are collected per sweep of the
window 108. For example, the sampling period can be between 3 and
100 milliseconds.
[0049] As shown, over one rotation of the platen, spectra are
obtained from different radii on the substrate 10. That is, some
spectra are obtained from locations closer to the center of the
substrate 10 and some are closer to the edge. Thus, for any given
scan of the optical monitoring system across a substrate, based on
timing, motor encoder information, and optical detection of the
edge of the substrate and/or retaining ring, the controller 190 can
calculate the radial position (relative to the center of the
substrate being scanned) for each measured spectrum from the scan.
The polishing system can also include a rotary position sensor,
e.g., a flange attached to an edge of the platen that will pass
through a stationary optical interrupter, to provide additional
data for determination of which substrate and the position on the
substrate of the measured spectrum. The controller can thus
associate the various measured spectra with the controllable zones
148b-148e (see FIG. 2) on the substrates 10a and 10b. In some
implementations, the time of measurement of the spectrum can be
used as a substitute for the exact calculation of the radial
position.
[0050] Over multiple rotations of the platen, for each zone, a
sequence of spectra can be obtained over time. Without being
limited to any particular theory, the spectrum of light reflected
from the substrate 10 evolves as polishing progresses (e.g., over
multiple rotations of the platen, not during a single sweep across
the substrate) due to changes in the thickness of the outermost
layer, thus yielding a sequence of time-varying spectra. Moreover,
particular spectra are exhibited by particular thicknesses of the
layer stack.
[0051] If the probe of the in-line monitoring system is used, the
probe can moved relative to the substrate due to rotation of the
carrier head, lateral motion of the carrier head, or lateral motion
of the probe, to measure multiple spectra situation along a path on
the substrate.
[0052] For either in-situ or in-line monitoring, the controller,
e.g., the computing device, can be programmed to fit a function,
e.g., an optical model, to the measured spectrum. The function has
multiple input parameters, and generates an output spectrum
calculated from the input parameters. The input parameters include
at least a parameter that can be used to control the polishing
endpoint or which can be used to adjust a polishing process, e.g.,
the thickness of the first layer, However, the parameter from which
the polishing endpoint can readily be determined could also be a
thickness removed, or more generic representation of the progress
of the substrate through the polishing process, e.g., an index
value representing the time or number of platen rotations at which
the spectrum would be expected to be observed in a polishing
process that follows a predetermined progress.
[0053] In some in-situ implementations, the function is fit to each
spectra in the sequence, thereby generating a sequence of fitted
parameter values, e.g., a sequence of fitted thickness values.
[0054] The optical model at least partially accounts for
diffraction effects generated by a repeating feature on the
substrate. At least one of the input parameters represents a
characteristic of the repeating feature. As shown in FIG. 6, the
repeating feature can be represented with a 1-dimensional model
(e.g. repeating lines and spaces). In this case, the diffracted
light resulting from the repeating feature can be optically modeled
with a "1-D" diffraction grating, and the input parameter can be a
line width or a line pitch. This model may be appropriate for
regions of the substrate having multiple parallel conductive
traces.
[0055] Alternatively, referring to FIG. 7, the repeating feature
can be represented with a 2-dimensional model (e.g. repeating
shapes). In this case, the diffracted light resulting from the
repeating feature can be optically modeled with a "2-D" diffraction
grating, and the input parameter can be the feature dimension
and/or the feature pitch in either or both dimensions. This model
may be appropriate for regions of the substrate with repeating
cells, e.g., DRAM structures. The 2-D model includes a unit cell
300 that includes a portion 310 of one material (with first optical
characteristics) and a portion 320 of a different material (with
different optical characteristics). Although FIG. 7 illustrates a
simple 2-D parallelepiped volume of different material than the
surrounding, the repeating feature can be more complex and can
include multiple sub-features.
[0056] Other input parameters of the optical model can include the
thickness, index of refraction and/or extinction coefficient of
each of the layers.
[0057] An additional input parameter of the optical model is either
the polarization, or a relative weighting between two orthogonal
polarizations.
[0058] The diffraction effects can be calculated using rigorous
coupled waveform analysis. In particular, rigorous coupled waveform
analysis (RCWA) can be used to model and calculate the diffraction
effects. RCWA equations can be used to generate a reflectance R for
each wavelength, and then to determine a diffraction efficiency at
each wavelength.
[0059] Details of RCWA are laid out "Formulation for stable and
efficient implementation of the rigorous coupled-wave analysis of
binary gratings" by Moharam et. al, and "Stable implementation of
the rigorous coupled-wave analysis for surface-relief gratings:
enhanced transmittance matrix approach" by Moharam et. al., each of
which is incorporated by reference.
[0060] For example, for optically modeling of a "1-D" diffraction
grating, equations 24-26 from "Stable implementation of the
rigorous coupled-wave analysis for surface-relief gratings:
enhanced transmittance matrix approach" can be used to generate R
for each wavelength, and the diffraction efficiency can be
determined at each wavelength via equations 25 and 45 from
"Formulation for stable and efficient implementation of the
rigorous coupled-wave analysis of binary gratings."
[0061] The diffraction efficiency is normalized to the diffraction
efficiency of blanket silicon to match the reflectance spectra of
the in-situ monitoring system, which also is normalized to silicon
to get rid of lamp, pad, and process effects. The
silicon-normalized diffraction efficiency is then compared to the
measured spectra.
[0062] Modeling diffracted light for a 2-D structure is more
complicated, but similar in technique, extrapolated from a 1-D line
to a 2-D plane.
[0063] The method described above is not the only way and not
necessarily the fastest or most accurate way to determine the
diffraction efficiency of a 1-D or 2-D structure. There are
alternative techniques, e.g., described in "Multilayer modal method
for diffraction gratings of arbitrary profile, depth, and
permittivity" by Lifeng Li. But in these various techniques, the
model includes diffraction caused by the repeating structure.
[0064] For at least two of the parameters, parameters values are
calculated that provide a minimum difference between an output
spectrum of the optical model and the measured spectrum. A first of
the at least two parameters includes the parameter from which the
polishing endpoint can readily be determined, e.g., the thickness
of the first layer. A second of the at least two parameters can be
an input parameter that represents a dimensional characteristic of
the repeating feature. For example, the second of the at least two
parameters can be a linewidth of the repeating feature. Other
possibilities for the second of the at least two parameters include
the line pitch, the area density of a material of the feature (e.g.
how much of the area of the device being modeled is consumed by a
given material), or the vertical shape and depth of structures
(e.g. is a copper line best modeled as square, or is it tapered
with depth).
[0065] In an example, to account for an array of traces on the
substrate, the input parameters include the angle of incidence of
the light, (e.g. zero degrees), the pitch of the traces, the number
of layers modeled, the thickness of each layer, the linewidth of
the traces, the n and k values of the input and output planes, the
n and k values of the feature(s) and the region(s) outside the
feature(s) (e.g., the ridge and groove) for each layer, and the
wavelength range analyzed. The values for the thickness of the
outermost layer and the linewidth that provide the minimum
difference between an output spectrum of the optical model and the
measured spectrum is determined.
[0066] Some of the input parameters can have fixed values. Some of
the input parameters can be permitted to vary; these are the
parameters for which values will be determined as part of the
fitting process. Those input parameters for which values are
determined as part of the fitting can be limited to variation
between predetermined ranges. The ranges for the input parameters
can be chosen to 1) avoid degenerative fits, and 2) to keep
calculation time at a reasonable level. If the allowed range for a
value of an input parameter is too great, the likelihood a
degenerative fit increases. A user can input into the model the
nominal parameter values for some of the parameters (e.g. line
width, expected thickness, and index of refraction and extinction
coefficient for various materials). The user can also input into
the model the permitted ranges for some of the parameter values.
These nominal values and ranges can be based on the user's
knowledge of the device/layer being polished.
[0067] As noted above, some boundary conditions can be imposed on
the parameters. For example, the thickness t for a layer j can be
permitted to vary between a minimum value T.sub.MINj and a maximum
value T.sub.MAXj. Similar boundary conditions can be imposed on the
parameters that are material properties, e.g., index of refraction
(n), extinction coefficient (k), and/or on parameters that are
structural properties, e.g., the line width. The boundary values
can be input by the operator based on knowledge of variation within
the fabrication process.
[0068] In some implementations, the input parameters are fed
directly into equations of the optical model. However, in some
implementations the input parameters can be used to generate a
plurality of pixel grids. Each layer of the device that has a
different 2-D pattern is modeled with its own pixel grid, so that
the 3-D device is represented by a stack of pixel grids. Each pixel
grid in the stack can be assigned its own thickness. The grid is a
user-defined size in the x and y directions, and the scale of the
pixels can also be user-defined. Each pixel in a grid is assigned a
refractive index and an extinction coefficient based on the
material in the pixel. The diffraction is then calculated based on
the array of pixels. By combining the a series of grid slices, one
can model any device in 3 dimensions.
[0069] For example, to model a region of repeating lines, the input
parameters could include the linewidth and pitch of the lines, and
the material composition of the lines and the material composition
of the region between the lines. A pixel array would then be
generated; a determination of whether the pixel is part of the line
or part of the region between the lines is made based on the
linewidth and pitch. If the pixel is part of the line, then it
would be assigned index of refraction and extinction coefficient
values for the material composition of the line. If the pixel is
not part of the line, then it would be assigned index of refraction
and extinction coefficient values for the material composition of
the region between the lines.
[0070] In some implementations, the optical model models the
presence of a metal line. However, a metal liner material, e.g.,
Tantalum, can be used to model the metal contribution instead of
the material of the metal line, e.g., copper. Although it may be
possible to completely model both the liner and the copper which
lies below or next to the liner, this may be too complicated or
computationally intensive; the model can be simplified and
computation time reduced if the liner material only is used.
[0071] Some in-line monitoring systems illuminate a substrate with
polarized light beams at multiple different angles of incidence,
although unpolarized light can also be used. Some in-situ
monitoring systems illuminate the substrate with unpolarized light,
although polarized light can also be used. In addition, the
unpolarized light can be at a single angle of incidence.
[0072] In some implementations, which can fit well with intentional
use of polarized light, a polarization angle is used as an input
parameter of the optical model. That is, the polarization angle is
simply treated as a parameter to vary when optimizing the fit
between the model and the measured spectrum.
[0073] In some implementations, which can fit well with
unintentional use of polarized light, calculation of the output
spectrum can include calculation of a first spectrum for a first
polarization of light and calculation of a second spectrum for a
second polarization of light. In this case, the relative
contribution between the first polarization and the second
polarization is used as an input parameter of the optical model.
The relative contribution is treated as a parameter to vary when
optimizing the fit between the model and the measured
substrate.
[0074] For example, the calculation of the model M can be
represented as
M=X*S.sub.1+(1-X)*S.sub.2
where S.sub.1 the first spectrum generated using the first
polarization of light, S.sub.2 is the second spectrum generated
using the second polarization of light, and X is the relative
contribution.
[0075] The calculation of the first spectrum and the second
spectrum can otherwise be conducted with identical values for the
input parameters. The first polarization can be s-polarization and
the second polarization can be p-polarization.
[0076] In some implementations, the optical model can include
multiple optical sub-models. Each optical sub-model operates as the
optical model described above, e.g., with various input parameters,
but the different sub-model represent regions of different
patterning on the substrate. Since the patterning is different, the
effect of diffraction will be different, and the resulting spectrum
will be different. Each sub-model can generate an intermediate
spectrum, and the intermediate spectra can combined to generate the
output spectrum. The relative weight, e.g., percentage
contribution, of each intermediate spectrum can be one of the
parameters that is calculated as part of the fitting process.
[0077] This permits the optical model to account for the
possibility that the light beam will illuminate regions with
different patterns on the substrate. Thus the model can provide one
output spectrum that would be generated if the light happened to be
collected from two structures simultaneously, e.g. if the light
spot rested halfway on one structure and halfway on a different
structure. For example, if the light spot was halfway on a 1-D
grating that had a pitch A and the other half of the light spot was
halfway on a structure of pitch B, then the proper model for such a
reflectance spectrum would be one that was a combination of each
with equal weighting for both.
[0078] In fitting the optical model to the measured spectrum, the
parameters are selected to provide an output spectrum that is a
close match to the measured spectrum. A close match can be
considered to be the calculation of a minimum difference between
the output spectrum and the measured spectrum, given the available
computational power and time constraints. The thickness of the
layer being polished can then be determined from the thickness
parameter.
[0079] Calculation of a difference between the output spectrum and
the measured spectrum can be a sum of absolute differences between
the measured spectrum and the output spectrum across the spectra,
or a sum of squared differences between the measured spectrum and
the reference spectrum. Other techniques for calculating the
difference are possible, e.g., a cross-correlation between the
measured spectrum and the output spectrum can be calculated.
[0080] Fitting the parameters to find the closest output spectrum
can be considered an example of finding a global minima of a
function (the difference between the measured spectrum and the
output spectrum generated by the function) in a multidimensional
parameter space (with the parameters being the variable values in
the function). For example, where the function is an optical model,
the parameters can include the thickness, the index of refraction
(n) and extinction coefficient (k) of the layers.
[0081] Regression techniques can be used to optimize the parameters
to find a local minimum in the function. Examples of regression
techniques include Levenberg-Marquardt (L-M)--which utilizes a
combination of Gradient Descent and Gauss-Newton; Fminunc( )--a
matlab function; lsqnonlin( )--matlab function that uses the L-M
algorithm; and simulated annealing. In addition, non-regression
techniques, such as the simplex method, can be used to optimize the
parameters.
[0082] Certain parameter values may be thrown out based on the
polarization angle. For example, it may be known that s or p
polarization (0 or 90) does not contain useful information as the
device size is shrunk.
[0083] A potential problem with using regression or non-regression
techniques alone to fine a minimum is that there may be multiple
local minima in the function. If regression is commenced near the a
local minima that is not the global minima, then the wrong solution
may be determined as regression techniques will only go "downhill"
to the best solution. However, if multiple local minima are
identified, regression could be performed on all of these minima
and the best solution would be identified by the one with the least
difference. An alternative approach would be to track all solutions
from all local minima over a period of time, and determine which is
the best one over time. Examples of techniques to identify global
minima include genetic algorithms; multi-start (running the
regression techniques from multiple starting points with parallel
computing); global search--a Matlab function; and pattern
searching.
[0084] The output of fitting process is a set of fitted parameters,
including at least the parameters which the polishing endpoint can
readily be determined, e.g., the thickness parameter of the layer
being polished. However, as noted above, the fitted parameter could
also be an index value representing the time or number of platen
rotations at which the spectrum would be expected to be observed in
a polishing process that follows a predetermined progress.
[0085] Rather than thickness, some other metric can be calculated
using one or more the parameters that represent dimensions of the
structure in the layer being polished. For example, the line width
can be one of the parameters that is fitted, i.e., the line width
is permitted to vary in the fitting process. Since the fitting is
performed for each measured spectrum, this generates a sequence of
parameter values that represent dimensions of the structure, e.g.,
a sequence of line width values.
[0086] In some implementations, for each measured spectrum, a metal
line resistivity value Rs is calculated, e.g., by multiplying the
layer thickness value by the line width value. This generates a
sequence of metal line resistivity values. The endpoint can be
determined from the sequence of metal line resistivity values.
[0087] Now referring to FIG. 8, which illustrates the results for
only a single zone of a single substrate, the sequence of fitted
endpoint parameter values, e.g., thickness values or resistance
values, generated by fitting the optical model function to the
sequence of measured spectra generates a time-varying sequence of
values 212. This sequence of values 212 can be termed a trace 210.
In general, the trace 210 can include one, e.g., exactly one, value
per sweep of the optical monitoring system below the substrate.
[0088] As shown in FIG. 9, optionally a function, e.g., a
polynomial function of known order, e.g., a first-order function
(e.g., a line 214) is fit to the sequence of values derived from
the measured spectra. The function can be fit using robust line
fitting. Other functions can be used, e.g., polynomial functions of
second-order, but a line provides ease of computation.
[0089] Optionally, the function can be fit to the values collected
after time TC. Values for spectra collected before the time TC can
ignored when fitting the function to the sequence of values. This
can assist in elimination of noise in the measured spectra that can
occur early in the polishing process, or it can remove spectra
measured during polishing of another layer.
[0090] Polishing can be halted at an endpoint time TE that the line
214 crosses a target value TT. Alternatively, polishing can be
halted simply at the time that the sequence of values cross the
target value, e.g., without fitting any function to the
sequence.
[0091] FIG. 10 shows a flow chart of a method 700 of polishing a
product substrate. The product substrate can have at least the same
layer structure as what is represented in the optical model.
[0092] The product substrate is polished (step 702), and a sequence
of measured spectra are obtained during polishing (step 704), e.g.,
using the in-situ monitoring system described above. Alternatively,
the product substrate can be transported to an in-line monitoring
system, before or after polishing, and one or more spectra can be
measured.
[0093] An optical model for a layer stack having a plurality of
layers is stored. The optical model has a plurality of input
parameters including a first parameter and a second parameter. The
second parameter is a polarization angle or a relative contribution
between two orthogonal polarizations. The first parameter can be a
layer thickness, index of refraction, or extinction coefficient of
the layer. In addition, data is stored defining a plurality of
first values for the first parameter and a plurality of second
values for the second parameter.
[0094] The optical model is fit to the measured spectrum (step
706), i.e., the input parameters are varied to find an output
spectrum of the optical model that provides a minimum difference
between the output spectrum and the measured spectrum. The fitting
including finding a first value of the first parameter and a second
value of the second parameter that provides the minimum. Since the
second parameter is a polarization angle or a relative contribution
between two orthogonal polarizations, the fitting including finding
a value for the polarization angle or a relative contribution
between two orthogonal polarizations that provides a minimum
difference between an output spectrum of the optical model and the
measured spectrum. Optionally, fitting the parameters to the
measured spectrum includes calculating the output spectrum using
diffraction effects of the repeating structure. The thickness or
other characteristic value is provided by the fitted first value of
the first parameter (step 708).
[0095] Alternatively, software can be used to automatically
calculate multiple reference spectra using the optical model
described above in order to generate a library of reference spectra
(step 701). This can occur prior to polishing of the substrate. For
each combination of a first value from the plurality of first
values and a second value from the plurality of second values,
calculating a reference spectrum using the optical model based on
the first value and the second value, to generate a plurality of
reference spectra.
[0096] The best-matching reference spectrum out of the plurality of
reference spectra is determined (step 706a). The thickness or other
characteristic value is provided by the first value of the first
parameter that was used to generate the best-matching reference
spectrum (step 708a).
[0097] Where a sequence of spectra is collected over time during
polishing, a function, e.g., a linear function, is fit to the
sequence of values for the measured spectra (step 710). Polishing
can be halted once the endpoint value (e.g., a calculated parameter
value, e.g., a thickness value, generated from the linear function
fit to the sequence of parameter values) reaches a target value
(step 712).
[0098] Although the discussion above assumes a rotating platen with
an optical endpoint monitor installed in the platen, system could
be applicable to other types of relative motion between the
monitoring system and the substrate. For example, in some
implementations, e.g., orbital motion, the light source traverses
different positions on the substrate, but does not cross the edge
of the substrate. In such cases, the collected spectra can still be
grouped, e.g., spectra can be collected at a certain frequency and
spectra collected within a time period can be considered part of a
group. The time period should be sufficiently long that five to
twenty spectra are collected for each group.
[0099] As noted above, the optical model has a plurality of input
parameters. At one input parameter is allowed to vary over a
predetermined range at a predetermined increment. In some
implementations, a reference spectrum is calculated for each
combination of values for at least two input parameters that are
allowed to vary. For each parameter that is allowed to vary, the
manufacturer can input data indicating a range (e.g., a maximum and
a minimum value) and an increment between values within the
range.
[0100] The thickness of the overlying layer can be one of the at
least two input parameters. If the reference spectra are to be used
during polishing, then the thickness can be allowed to vary over a
large range, e.g., from about the expected starting thickness to
the expected ending thickness. For example, the thickness might
vary from 0 to 3000 Angstroms in 10 Angstrom increments. On the
other hand, if the reference spectra are to be used at an
in-sequence metrology station, then the thickness can be allowed to
vary over a narrower range centered around the expected starting or
ending thickness. For example, the thickness might vary from 2700
to 2900 Angstroms in 10 Angstrom increments.
[0101] Since there are variations in the thicknesses of the
underlying layers of the incoming substrates, the thickness of at
least one of the underlying layers can be another of the two or
more parameters. The manufacturer can input a thickness range and a
thickness increment for the at least one of the underlying layers,
e.g., for multiple underlying layers. For example, the thickness of
the underlying layer might vary from 2700 to 2900 Angstroms in 10
Angstrom increments.
[0102] In addition to variations of the layer thicknesses, the
optical model can include variations in the index of refraction
and/or the extinction coefficient of one or more layers in the
optical stack. Thus, the index of refraction and/or the extinction
coefficient of one or more layers in the optical stack can be
another of the two or more parameters. The manufacturer can input a
refractive index range and a refractive index increment for at
least one of the underlying layers, e.g., for multiple underlying
layers. The manufacturer can input a extinction coefficient range
and an extinction coefficient increment for at least one of the
underlying layers, e.g., for multiple underlying layers. For
example, the user might choose to vary the index of refraction by
modeling the dispersion coefficients with a Cauchy equation, and
varying the A and B coefficients of the Caucy equation. For
example, the user might vary the index of refraction parameter A
between 1.40 and 1.45 at 0.01 increments. The user can similarly
model extinction coefficients with the equation
k=A+exp(B-12400*(1/lambda-1/C)) with lambda in Angstroms. A might
range from 0.003 to 0.006 with increment 0.001, and B might vary
from 0.45 to 0.55 with increment 0.01.
[0103] The one or more layers can include the underlying layer
and/or the overlying layer. The one or more layers may include a
layer of silicon oxide, carbon-doped silicon oxide, silicon
carbide, silicon nitride, carbon-doped silicon nitride and/or
polysilicon. Depending on the composition and deposition method for
the layers on the substrate, some spectral measurements may be made
from substrates with a layer having a higher index of refraction or
extinction coefficient, whereas other spectral measurements may be
made from substrates with a layer having a lower index of
refraction or extinction coefficient.
[0104] As noted above, the optical model can include variations in
the polarization angle. In some implementations, the polarization
angle can be another of the two or more parameters. The
manufacturer can input a polarization range and a polarization
increment. For example, the polarization range might vary from
0.degree. (s-polarization) to 90.degree. (p-polarization) in
5.degree. increments.
[0105] Alternatively, the optical model can include relative
contribution of two polarization angles. Thus, wherein the
reference spectrum generated from the optical model is represented
by M=X*S.sub.i+(1-X)*S.sub.2, the relative contribution X can be
another of the two or more parameters. The manufacturer can input a
contribution range and a contribution increment. For example, the
polarization range might vary from 0 to 1 in 0.1 increments.
[0106] In a first example, polarized light is directed onto the
substrate at the in-line monitoring station to measure a spectrum.
The controller fits the optical model to the measured spectrum, and
the polarization angle is treated as a parameter to vary when
optimizing the fit between the model and the measured spectrum.
[0107] In a second example, ostensibly unpolarized light is
directed onto the substrate by the in-situ monitoring system. The
controller fits the optical model to the measured spectrum, and the
relative contribution between two orthogonal polarizations is
treated as a parameter to vary when optimizing the fit between the
model and the measured substrate.
[0108] In a third example, applicable to either an in-situ or
in-line monitoring system, a plurality of reference spectra are
generated from the optical model using a plurality of different
values for the relative contribution between two orthogonal
polarizations. Ostensibly unpolarized light is directed onto the
substrate to measure a spectrum. The controller searches for the
reference spectrum of the plurality of reference spectra that
provides the best match to the measured spectrum.
[0109] In a fourth example, applicable to either an in-situ or
in-line monitoring system, a plurality of reference spectra are
generated from the optical model using a plurality of different
values for polarization. Polarized light is directed onto the
substrate to measure a spectrum. The controller searches for the
best-matching reference spectrum of the plurality of reference
spectra.
[0110] In the examples above, polarized light is used when the
optical model uses polarization as an input parameter, but in other
implementations ostensibly unpolarized light is used. Similarly, in
the examples above, unpolarized light is used when the optical
model uses relative contribution of two orthogonal polarization as
an input parameter, but in other implementations polarized light is
used.
[0111] Without being limited to any particular theory, by using
polarization or relative contribution of orthogonal polarizations
as an input parameter to the model when generating reference
spectra or fitting the model, errors due to uncertainty in the
orientation of the chip structure and/or partial polarization of
ostensibly unpolarized light may be reduced.
[0112] As used in the instant specification, the term substrate can
include, for example, a product substrate (e.g., which includes
multiple memory or processor dies), a test substrate, a bare
substrate, and a gating substrate. The substrate can be at various
stages of integrated circuit fabrication, e.g., the substrate can
be a bare wafer, or it can include one or more deposited and/or
patterned layers. The term substrate can include circular disks and
rectangular sheets.
[0113] Embodiments of the invention and all of the functional
operations described in this specification can be implemented in
digital electronic circuitry, or in computer software, firmware, or
hardware, including the structural means disclosed in this
specification and structural equivalents thereof, or in
combinations of them. Embodiments of the invention can be
implemented as one or more computer program products, i.e., one or
more computer programs tangibly embodied in a non-transitory
machine readable storage media, for execution by, or to control the
operation of, data processing apparatus, e.g., a programmable
processor, a computer, or multiple processors or computers.
[0114] The above described polishing apparatus and methods can be
applied in a variety of polishing systems. Either the polishing
pad, or the carrier heads, or both can move to provide relative
motion between the polishing surface and the substrate. For
example, the platen may orbit rather than rotate. The polishing pad
can be a circular (or some other shape) pad secured to the platen.
Some aspects of the endpoint detection system may be applicable to
linear polishing systems, e.g., where the polishing pad is a
continuous or a reel-to-reel belt that moves linearly. The
polishing layer can be a standard (for example, polyurethane with
or without fillers) polishing material, a soft material, or a
fixed-abrasive material. Terms of relative positioning are used; it
should be understood that the polishing surface and substrate can
be held in a vertical orientation or some other orientation.
[0115] Although the description above has focused on control of a
chemical mechanical polishing system, the in-sequence metrology
station can be applicable to other types of substrate processing
systems, e.g., etching or deposition systems.
[0116] Particular embodiments of the invention have been described.
Other embodiments are within the scope of the following claims.
* * * * *