U.S. patent application number 10/388857 was filed with the patent office on 2004-09-30 for ellipsometry methods and apparatus using solid immersion tunneling.
This patent application is currently assigned to Regents of the University of Minnesota. Invention is credited to Leger, James R., Zhan, Qiwen.
Application Number | 20040189992 10/388857 |
Document ID | / |
Family ID | 29715130 |
Filed Date | 2004-09-30 |
United States Patent
Application |
20040189992 |
Kind Code |
A9 |
Zhan, Qiwen ; et
al. |
September 30, 2004 |
Ellipsometry methods and apparatus using solid immersion
tunneling
Abstract
A solid immersion tunneling ellipsometer and methods relating
thereto may include a solid immersion apparatus (e.g., a prism or
an objective lens in combination with a solid immersion lens) that
facilitates optical tunneling and provide information that can be
used in the determination of one or more characteristics (e.g.,
thickness, index of refraction, etc.) of samples (e.g., thin films,
ultrathin films, etc.).
Inventors: |
Zhan, Qiwen; (Centerville,
OH) ; Leger, James R.; (Plymouth, MN) |
Correspondence
Address: |
MUETING, RAASCH & GEBHARDT, P.A.
P.O. BOX 581415
MINNEAPOLIS
MN
55458
US
|
Assignee: |
Regents of the University of
Minnesota
Minneapolis
MN
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 0227623 A1 |
December 11, 2003 |
|
|
Family ID: |
29715130 |
Appl. No.: |
10/388857 |
Filed: |
March 14, 2003 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
10388857 |
Mar 14, 2003 |
|
|
|
09691346 |
Oct 18, 2000 |
|
|
|
6693711 |
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60364475 |
Mar 15, 2002 |
|
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Current U.S.
Class: |
356/369 |
Current CPC
Class: |
G01N 21/211 20130101;
G01J 4/00 20130101 |
Class at
Publication: |
356/369 |
International
Class: |
G01J 004/00 |
Claims
What is claimed is:
1. An ellipsometry method comprising: receiving one or more
ellipsometric signals corresponding to at least one ray of
polarized light provided at an angle greater than a critical angle
of a solid immersion apparatus, wherein the solid immersion
apparatus comprises a surface located adjacent a thin film of a
sample; determining one or more measured ellipsometric parameters
as a function of the one or more ellipsometric signals for the at
least one ray of the polarized light provided at an angle greater
than the critical angle; and determining at least one
characteristic of the thin film by fitting the one or more measured
ellipsometric parameters to a model, wherein the model provides a
relationship between the at least one characteristic for thin films
and model ellipsometric parameters corresponding to the one or more
measured ellipsometric parameters.
2. The method of claim 1, wherein the model provides a relationship
between the at least one characteristic for thin films having a
thickness less than 100 angstroms and model ellipsometric
parameters corresponding to the one or more measured ellipsometric
parameters.
3. The method of claim 1, wherein the solid immersion apparatus
comprises one of a hemispheric lens and a stigmatic lens.
4. The method of claim 1, wherein the one or more measured
ellipsometric parameters comprise .PSI. and .DELTA. for the at
least one ray of the polarized light provided at an angle greater
than the critical angle.
5. The method of claim 1, wherein fitting the one or more measured
ellipsometric parameters to a model comprises providing a greater
weight to the measured ellipsometric parameter .PSI. than the
measured ellipsometric parameter .DELTA. when determining the at
least one characteristic.
6. The method of claim 1, wherein the at least one characteristic
comprises at least one of thickness and index of refraction of one
or more thin films.
7. The method of claim 1, wherein the method further comprises:
receiving one or more ellipsometric signals corresponding to at
least one ray of polarized light provided at an angle less than the
critical angle of the solid immersion apparatus; and determining
one or more ellipsometric parameters as a function of the one or
more ellipsometric signals for the at least one ray of the
polarized light provided at an angle less than the critical angle,
wherein the method further comprises determining at least one
characteristic for the thin film based on one or more measured
ellipsometric parameters determined for the at least one ray of the
polarized light provided at an angle less than the critical angle
and one or more measured ellipsometric parameters determined for
the at least one ray of the polarized light provided at an angle
less than the critical angle.
8. The method of claim 7, wherein determining the at least one
characteristic for the thin film comprises: fitting the one or more
measured ellipsometric parameters determined for the at least one
ray of the polarized light provided at an angle greater than the
critical angle to a model that provides a relationship between the
at least one characteristic for thin films having a thickness less
than 100 angstroms and model ellipsometric parameters corresponding
to the one or more measured ellipsometric parameters; fitting the
one or more measured ellipsometric parameters determined for the at
least one ray of the polarized light provided at an angle less than
the critical angle to a model that provides a relationship between
the at least one characteristic for thin films of any thickness and
model ellipsometric parameters corresponding to the one or more
measured ellipsometric parameters; and determining the at least one
characteristic using both the results of the model fitting of the
one or more measured ellipsometric parameters determined for the at
least one ray of the polarized light provided at an angle greater
than the critical angle and of the one or more measured
ellipsometric parameters determined for the at least one ray of the
polarized light provided at an angle less than the critical
angle.
9. The method of claim 8, wherein the one or more measured
ellipsometric parameters comprise .PSI. and .DELTA. for the at
least one ray of the polarized light provided at an angle greater
than the critical angle and for the at least one ray of the
polarized light provided at an angle less than the critical
angle.
10. The method of claim 9, wherein the at least one characteristic
is determined using a fitting method utilizing only .PSI. values
determined for the at least one ray of polarized light provided at
an angle greater than the critical angle and .DELTA. values
determined for the at least one ray of polarized light provided at
an angle less than the critical angle.
11. The method of claim 1, wherein the solid immersion apparatus
comprises a prism, wherein the prism comprises the surface located
adjacent the thin film of the sample and the critical angle.
12. The method of claim 1, wherein the solid immersion apparatus
comprises an objective lens and a solid immersion lens, wherein the
solid immersion lens comprises the surface located adjacent the
thin film of the sample and the critical angle, and wherein the
method further comprises: providing polarized light incident normal
to the thin film of the sample; focusing the polarized light on the
solid immersion lens using the objective lens; and collecting
elliptically polarized reflected light from the sample.
13. The method of claim 12, wherein providing the polarized light
further comprises providing radially symmetric polarized light.
14. The method of claim 12, wherein the elliptically polarized
light comprises at least elliptically polarized light corresponding
to at least one ray of the polarized light provided at an angle
greater than the critical angle of the solid immersion lens, and
further wherein the method comprises detecting the elliptically
polarized light resulting in one or more ellipsometric signals for
use in determining one or more ellipsometric parameters for the at
least one ray of the polarized light provided at an angle greater
than the critical angle of the solid immersion lens.
15. The method of claim 12, wherein the surface of the solid
immersion lens is adjacent the thin film but separated therefrom by
a substrate upon which the thin film is provided, wherein the solid
immersion lens comprises an abbreviated hemispheric lens, wherein
the abbreviated hemispheric lens has a height less than a
hemisphere, and further wherein the polarized light is incident on
the thin film through the substrate.
16. The method of claim 1, wherein the surface of the solid
immersion apparatus is separated from the sample by a distance.
17. The method of claim 1, wherein the surface of the solid
immersion apparatus is positioned in contact with the sample.
18. An ellipsometer apparatus comprising: an interface apparatus
operable to receive one or more ellipsometric signals corresponding
to at least one ray of polarized light provided at an angle greater
than a critical angle of a solid immersion apparatus, the solid
immersion apparatus comprising a surface adapted to be positioned
adjacent a thin film of a sample; and a processing apparatus
operable to: determine one or more measured ellipsometric
parameters as a function of the one or more ellipsometric signals
for the at least one ray of the polarized light provided at an
angle greater than the critical angle; and determine at least one
characteristic of the thin film by fitting the one or more measured
ellipsometric parameters to a model, wherein the model provides a
relationship between the at least one characteristic for thin films
and model ellipsometric parameters corresponding to the one or more
measured ellipsometric parameters.
19. The apparatus of claim 18, wherein the model provides a
relationship between the at least one characteristic for thin films
having a thickness less than 100 angstroms and model ellipsometric
parameters corresponding to the one or more measured ellipsometric
parameters.
20. The apparatus of claim 18, wherein the one or more measured
ellipsometric parameters comprise .PSI. and .DELTA. for the at
least one ray of the polarized light provided at an angle greater
than the critical angle.
21. The apparatus of claim 18, wherein the at least one
characteristic comprises at least one of thickness and index of
refraction of one or more films.
22. The apparatus of claim 18, wherein the interface apparatus is
further operable to receive one or more ellipsometric signals
corresponding to at least one ray of polarized light provided at an
angle less than the critical angle of the solid immersion
apparatus, and wherein the processing apparatus is further operable
to: determine one or more measured ellipsometric parameters as a
function of the one or more ellipsometric signals for the at least
one ray of the polarized light provided at an angle less than the
critical angle; and determine at least one characteristic for the
thin film based on one or more measured ellipsometric parameters
determined for the at least one ray of the polarized light provided
at an angle less than the critical angle and one or more
ellipsometric parameters determined for the at least one ray of the
polarized light provided at an angle less than the critical
angle.
23. The apparatus of claim 22, wherein the processing apparatus is
further operable, when determining the at least one characteristic
for the thin film, to: fit the one or more measured ellipsometric
parameters determined for the at least one ray of the polarized
light provided at an angle greater than the critical angle to a
model that provides a relationship between the at least one
characteristic for thin films less than 100 angstroms and model
ellipsometric parameters corresponding to the one or more measured
ellipsometric parameters; fit the one or more measured
ellipsometric parameters determined for the at least one ray of the
polarized light provided at an angle less than the critical angle
to a model that provides a relationship between the at least one
characteristic for thin films of any thickness and model
ellipsometric parameters corresponding to the one or more measured
ellipsometric parameters; and determine the at least one
characteristic using both the results of the model fitting of the
one or more measured ellipsometric parameters determined for the at
least one ray of the polarized light provided at an angle greater
than the critical angle and the model fitting of the one or more
measured ellipsometric parameters determined for the at least one
ray of the polarized light provided at an angle less than the
critical angle.
24. The apparatus of claim 23, wherein the one or more measured
ellipsometric parameters comprise .PSI. and .DELTA. for the at
least one ray of the polarized light provided at an angle greater
than the critical angle and for the at least one ray of the
polarized light provided at an angle less than the critical
angle.
25. The apparatus of claim 18, wherein the solid immersion
apparatus comprises a prism, wherein the prism comprises the
surface adapted to be located adjacent the thin film of the sample
and the critical angle.
26. The apparatus of claim 18, wherein the solid immersion
apparatus comprises one of a hemispheric lens and a stigmatic
lens.
27. The apparatus of claim 18, wherein the surface of the solid
immersion apparatus is positioned in contact with the sample.
28. The apparatus of claim 18, wherein the surface of the solid
immersion apparatus is separated from the sample by a distance.
29. The apparatus of claim 18, wherein the solid immersion
apparatus comprises an objective lens and a solid immersion lens,
wherein the solid immersion lens comprises the surface adapted to
be located adjacent the thin film of the sample and the critical
angle, and further wherein the apparatus comprises: a light source
to provide polarized light incident normal to the thin film of the
sample, wherein the objective lens is adapted to focus the
polarized light on the solid immersion lens and collect
elliptically polarized reflected light from the sample; and a
detector operable to detect the elliptically polarized light
resulting in one or more ellipsometric signals for the at least one
ray of the polarized light provided at an angle greater than the
critical angle of the solid immersion lens.
30. The apparatus of claim 29, wherein the light source is operable
to provide radially symmetric polarized light.
31. The apparatus of claim 29, wherein the surface of the solid
immersion lens is adapted to be located adjacent the thin film but
separated therefrom by a substrate upon which the thin film is
provided, wherein the solid immersion lens comprises an abbreviated
hemispheric lens, wherein the abbreviated hemispheric lens has a
height less than a hemisphere, and further wherein the polarized
light is incident on the thin film through the substrate.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This is a Continuation-in-Part of U.S. patent application
Ser. No. 09/691,346 filed on Oct. 18, 2000 entitled "Ellipsometer
Using Radial Symmetry", and claims the benefit of U.S. Provisional
Patent Application No. 60/364,475, filed Mar. 15, 2002, which are
hereby incorporated by reference.
BACKGROUND OF THE INVENTION
[0002] The present invention relates generally to ellipsometry.
More particularly, the present invention pertains to ellipsometric
methods and apparatus using solid immersion tunneling.
[0003] Ellipsometry is an optical technique that uses polarized
light to probe the properties of a sample. The most common
application of ellipsometry is the analysis of thin films. Through
the analysis of the state of polarization of the light that
interacts with the sample, ellipsometry can yield information about
such films. For example, depending on what is already known about
the sample, the technique can probe a range of properties including
the layer thickness, index of refraction, morphology, or chemical
composition.
[0004] Generally, optical ellipsometry can be defined as the
measurement of the state of polarized light waves. An ellipsometer
measures the changes in the polarization state of light when it
interacts with a sample. The most common ellipsometer configuration
is a reflection ellipsometer, although transmission ellipsometers
are sometime used. If linearly polarized light of a known
orientation is reflected or transmitted at oblique incidence from a
sample surface, then the resultant light becomes elliptically
polarized. The shape and orientation of the ellipse depends on the
angle of incidence, the direction of the polarization of the
incident light, the wavelength of the incident light, and the
Fresnel properties of the surface. The polarization of the light is
measured for use in determining characteristics of the sample. For
example, in one conventional null ellipsometer, the polarization of
the reflected light can be measured with a quarter-wave plate
followed by an analyzer. The orientation of the quarter-wave plate
and the analyzer are varied until no light passes though the
analyzer, i.e., a null is attained. From these orientations and the
direction of polarization of the incident light, a description of
the state of polarization of the light reflected from the surface
can be calculated and sample properties deduced.
[0005] Two characteristics of ellipsometry make its use
particularly attractive. First, it is a nondestructive technique,
such that it is suitable for in situ observation. Second, the
technique is extremely sensitive. For example, it can measure small
changes of a film down to sub-monolayer of atoms or molecules. For
these reasons, ellipsometry has been used in physics, chemistry,
materials science, biology, metallurgical engineering, biomedical
engineering, etc.
[0006] As mentioned above, one important application of
ellipsometry is to study thin films, e.g., in the fabrication of
integrated circuits. In the context of ellipsometry, a thin film
includes films over a variety of thickness. The sensitivity of an
ellipsometer is such that a change in film thickness of a few
angstroms can usually be detected. From the measurement of changes
in the polarization state of light when it is reflected from a
sample, an ellipsometer can measure the refractive index and the
thickness of thin films, e.g., semi-transparent thin films. The
ellipsometer relies on the fact that the reflection at a material
interface changes the polarization of the incident light according
to the index of refraction of the interface materials. In addition,
the polarization and overall phase of the incident light is changed
depending on the refractive index of the film material as well as
its thickness.
[0007] Generally, for example, a conventional reflection
ellipsometer apparatus, such as shown in FIG. 1, includes a
polarizer arm 12 and an analyzer arm 14. The polarizer arm 12
includes a light source 15 such as a laser (commonly a 632.8 nm
helium/neon laser or a 650-850 nm semiconductor diode laser) and a
polarizer 16, which provides a state of polarization for the
incident light 18. The polarization of the incident light may vary
from linearly polarized light to elliptically polarized light to
circularly polarized light. The incident light 18 is reflected off
the sample 10 or layer of interest and then analyzed with the
analyzer arm 14 of the ellipsometer apparatus. The polarizer arm 12
of the ellipsometer apparatus produces the polarized light 18 and
orients the incident light 18 at an angle 13 with respect to a
sample plane 11 of the sample 10 to be analyzed, e.g., at some
angle such as 20 degrees with respect to the sample plane 11 or 70
degrees with respect to the sample normal.
[0008] The reflected light 20 is examined by components of the
analyzer arm 14, e.g., components that are also oriented at the
same fixed angle with respect to the sample plane 11 of the sample
10. For example, the analyzer arm 14 may include a quarter wave
plate 22, an analyzer 24 (e.g., a polarizer generally crossed with
the polarizer 16 of the polarizer arm 12), and a detector 26. To
measure the polarization of the reflected light 20, the operator
may change the angle of one or more of the polarizer 16, analyzer
24, or quarter wave plate 22 until a minimal signal is detected.
For example, the minimum signal is detected if the light 20
reflected by the sample 10 is linearly polarized, while the
analyzer 24 is set so that only light with a polarization that is
perpendicular to the incoming polarization is allowed to pass. The
angle of the analyzer 24 is therefore related to the direction of
polarization of the reflected light 20 if the minimum condition is
satisfied. The instrument is "tuned" to this null (e.g., generally
automatically under computer control), and the positions of the
polarizer 16, the analyzer 24, and the incident angle 13 of the
light relative to the sample plane 11 of the sample 10 are used to
calculate the fundamental quantities of ellipsometry: the so called
(psi (.PSI.), delta (.DELTA.)) pair given by: 1 r p r s tan ( j
)
[0009] where r.sub.p and r.sub.s are the complex Fresnel reflection
coefficients for the transverse magnetic and transverse electrical
waves of the polarized light, respectively. For example, from the
ellipsometry pair (.PSI., .DELTA.), the film thickness and index of
refraction can be determined. It will be recognized that various
ways of analyzing the reflected light may be possible. For example,
one alternative is to vary the angle of the quarter wave plate and
analyzer to collect polarization information.
[0010] Advances in microelectronics fabrication are rapidly
surpassing current capabilities in metrology. In order to enable
future generations of microelectronics, advanced specific metrology
capabilities must be developed. Key among these metrology
capabilities is the ability to measure the properties of ultra-thin
films over sub-micron lateral dimensions. As used herein, ultrathin
film refers to a film having a thickness of less than 100
angstroms.
[0011] Currently available ellipsometric techniques that measure
material properties generally measure them over a large area. In
other words, polarization measurements have been traditionally used
to determine the thickness and refractive index of homogeneous
films over a relatively large area. However, in many cases
determining the thickness and refractive index of homogeneous films
over a relatively large area is inadequate for exceedingly
small-featured structures. Since the polarization state is affected
significantly by diffraction from sub-micron features, the shape of
such sub-micron features (e.g., critical dimensions of lateral or
transverse structures such as gate dielectrics for transistor
structures) may be difficult to measure using current ellipsometric
techniques that determine thickness and refractive index over
relatively large areas. For example, the smallest spot that a
conventional ellipsometer can measure is generally determined by
the beam size, usually on the order of hundreds of microns. This
essentially limits the application of conventional ellipsometers to
samples with large and uniform interface characteristics.
[0012] Existing ellipsometers have difficulties in measuring
characteristics (e.g., index of refraction, thickness, etc.) for
ultrathin films. This may be due, at least in part, to the fact
that conventional ellipsometry models do not provide adequate
accuracy when such ultrathin films are being characterized (e.g.,
when ellipsometric measurements are being processed). For example,
a small error in a .PSI. measurement from a conventional
ellipsometer apparatus can skew determination of the refractive
index significantly when such models are used. Thus, conventional
ellipsometers may, in many cases, be unsuitable to measure
characteristics, such as refractive index, for films that are
thinner than 100 angstroms.
SUMMARY OF THE INVENTION
[0013] The present invention provides an ellipsometer apparatus and
methods that can be used for accurately measuring properties of
thin films. In one embodiment, such apparatus and methods are
particularly advantageous where the thin film is an ultrathin film
having a thickness of less than 100 angstroms.
[0014] The present invention exploits the use of a solid immersion
apparatus (e.g., a prism or an objective lens in combination with a
solid immersion lens) that facilitates optical tunneling, which
provides accurate ellipsometric measurements for thin films,
particularly for ultrathin films having a thickness of less than
100 angstroms. One or more embodiments of the present invention
provide additional capabilities including the use of solid
immersion tunneling to measure ultrathin films with improved
spatial resolution (e.g., on the order of 100 nanometers). The
present invention also includes modeling and model fitting
techniques for processing ellipsometric signals to provide enhanced
capabilities and improved measurement accuracy. Further, in one or
more embodiments, the present invention may provide enhanced
accuracy by using a technique during model fitting (e.g., using
regression analysis) in which one or more ellipsometric parameters
are given more weight than other ellipsometric parameters. The
present invention may also provide an ellipsometric technique that
can measure some thin film sample characteristics over a wide range
of film thickness (e.g., ultrathin films and those films having a
greater thickness than ultrathin films).
[0015] An ellipsometry method according to the present invention
includes receiving one or more ellipsometric signals corresponding
to at least one ray of polarized light provided at an angle greater
than a critical angle of a solid immersion apparatus. The solid
immersion apparatus includes a surface located adjacent a thin film
of a sample. The method further includes determining one or more
measured ellipsometric parameters as a function of the one or more
ellipsometric signals for the at least one ray of the polarized
light provided at an angle greater than the critical angle and then
determining at least one characteristic (e.g., thickness or index
of refraction) of the thin film by fitting the one or more measured
ellipsometric parameters to a model. The model provides a
relationship between the at least one characteristic for thin films
and model ellipsometric parameters corresponding to the one or more
measured ellipsometric parameters.
[0016] In one embodiment of the method, the model may provide a
relationship between the at least one characteristic for thin films
having a thickness less than 100 angstroms and model ellipsometric
parameters corresponding to the one or more measured ellipsometric
parameters.
[0017] In another embodiment of the method, the solid immersion
apparatus may include a hemispheric lens or a stigmatic lens.
[0018] In another embodiment, the one or more measured
ellipsometric parameters may include .PSI. and .DELTA. for the at
least one ray of the polarized light provided at an angle greater
than the critical angle.
[0019] In yet another embodiment of the method, the method includes
receiving one or more ellipsometric signals corresponding to at
least one ray of polarized light provided at an angle less than the
critical angle of the solid immersion apparatus and determining one
or more ellipsometric parameters as a function of the one or more
ellipsometric signals for the at least one ray of the polarized
light provided at an angle less than the critical angle. The at
least one characteristic is then determined based on one or more
measured ellipsometric parameters determined for the at least one
ray of the polarized light provided at an angle less than the
critical angle and one or more measured ellipsometric parameters
determined for the at least one ray of the polarized light provided
at an angle less than the critical angle.
[0020] In various embodiments, the solid immersion apparatus may
include a prism or, for example, an objective lens and a solid
immersion lens (e.g., a solid immersion lens adjacent the thin film
but separated therefrom by a substrate upon which the thin film is
provided, a solid immersion lens having a surface separated from
the sample by a distance, or a surface of the solid immersion lens
being positioned in contact with the sample).
[0021] An ellipsometer apparatus according to the present invention
includes an interface apparatus operable to receive one or more
ellipsometric signals corresponding to at least one ray of
polarized light provided at an angle greater than a critical angle
of a solid immersion apparatus. The solid immersion apparatus
includes a surface adapted to be positioned adjacent a thin film of
a sample. The apparatus further includes a processing apparatus
operable to determine one or more measured ellipsometric parameters
as a function of the one or more ellipsometric signals for the at
least one ray of the polarized light provided at an angle greater
than the critical angle and determine at least one characteristic
of the thin film by fitting the one or more measured ellipsometric
parameters to a model. The model provides a relationship between
the at least one characteristic for thin films and model
ellipsometric parameters corresponding to the one or more measured
ellipsometric parameters.
[0022] Various embodiments may include one or more features for
carrying out one or more methods or processes described herein. For
example, the apparatus may include a model that provides a
relationship between the at least one characteristic for thin films
having a thickness less than 100 angstroms and model ellipsometric
parameters corresponding to the one or more measured ellipsometric
parameters; a prism that includes a surface adapted to be located
adjacent the thin film of the sample; a hemispheric lens or a
stigmatic lens; a surface of a solid immersion apparatus that is
positioned in contact with the sample or one that is separated from
the sample by a distance; etc.
[0023] The above summary of the present invention is not intended
to describe each embodiment or every implementation of the present
invention. Advantages, together with a more complete understanding
of the invention, will become apparent and appreciated by referring
to the following detailed description and claims taken in
conjunction with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0024] FIG. 1 is a diagram of a conventional ellipsometer.
[0025] FIG. 2 is one illustrative general diagram of a solid
immersion tunneling ellipsometer system according to the present
invention.
[0026] FIG. 3A and FIG. 3B illustrate an example trajectory diagram
associated with a conventional ellipsometer and an example
trajectory diagram associated with a solid immersion tunneling
ellipsometer system such as shown generally in FIG. 2.
[0027] FIG. 4 shows one illustrative diagram of an embodiment of
the solid immersion tunneling ellipsometer system shown generally
in FIG. 2, using a solid immersion prism, according to the present
invention.
[0028] FIG. 5 is a processing flow diagram illustrating one
embodiment of a general flow of processing performed in a system
such as shown generally in FIG. 2.
[0029] FIG. 6 shows one illustrative diagram of an embodiment of
the solid immersion tunneling ellipsometer system shown generally
in FIG. 2, using an objective lens focusing polarized light on a
solid immersion lens, according to the present invention.
[0030] FIG. 7 shows one illustrative diagram of an embodiment of
the solid immersion tunneling ellipsometer system shown generally
in FIG. 2, using radially symmetric light and a solid immersion
lens, according to the present invention.
[0031] FIG. 8 shows a more detailed diagram of the solid immersion
lens configuration of the ellipsometer system shown in FIG. 7.
[0032] FIG. 9 is a processing flow diagram illustrating one
embodiment of a portion of the general flow of processing to
generate trajectories for use in the processing apparatus of the
system such as shown generally in FIG. 2.
[0033] FIG. 10 is a processing flow diagram illustrating one
embodiment of a portion of the general flow of processing shown
generally in FIG. 5, to determine at least one characteristic of a
sample (e.g., thickness of an ultrathin film).
[0034] FIG. 11 is a processing flow diagram illustrating one
embodiment of a portion of the general flow of processing shown
generally in FIG. 5, where one model associated with incident light
greater than the critical angle is used.
[0035] FIG. 12 is a processing flow diagram illustrating one
embodiment of a portion of the general flow of processing shown
generally in FIG. 5, where two models associated with incident
light greater than the critical angle and less than the critical
angle are used.
[0036] FIGS. 13A, 13B, 13C, and 13D show a setup and associated
trajectories for illustrating the use of ellipsometric measurements
in the determination of the sidewall shape of a line.
DETAILED DESCRIPTION OF THE EMBODIMENTS
[0037] Solid immersion tunneling ellipsometer methods and apparatus
shall be described herein with reference to FIGS. 2-13. In the
following detailed description of the embodiments, reference is
made to the drawings that form a part thereof, and in which are
shown by way of illustration specific embodiments in which the
invention may be practiced. It is to be understood that other
embodiments may be utilized, as structural or process changes may
be made without departing from the scope of the present
invention.
[0038] FIG. 2 shows a general illustration of a solid immersion
tunneling ellipsometer system 30 operable for carrying out one or
more ellipsometry methods according to the present invention with
respect to a sample 36. The sample 36 includes a thin film 37 to be
characterized provided on a substrate 38.
[0039] The solid immersion tunneling ellipsometer system 30 is
operable to determine one or more characteristics of various thin
films and/or structures. Examples of characteristics that may be
measured include: thickness and index of refraction of a single
film; thickness and indexes of refraction of multiple films; index
of refraction of a substrate; absorption of a thin film;
absorptions of multiple films; stress of thin films; surface
roughness; material composition; and magnetic properties.
[0040] One skilled in the art will recognize that the present
invention may be used to characterize different types of films
provided on a substrate. Furthermore, the present invention may be
used to characterize one or more thin films on a substrate or a
thin film that may include one or more layers. Examples of the
types of films that may be characterized are biological samples,
metallic films, and dielectric films.
[0041] In one embodiment, the sample 36 may include a thin film
formed on the substrate 38. In another embodiment, the sample 36
may include an ultrathin film formed on the substrate 38. Yet in
another embodiment, the sample may include a dielectric thin film
provided on the substrate 38. Yet in another embodiment, the sample
may include a high dielectric constant thin film provided on the
substrate 38. Yet further, in another embodiment, the sample 36 may
include a gate oxide (e.g., silicon oxide, silicon oxynitride,
silicon nitride, etc.) formed on a substrate (e.g., silicon
substrate.
[0042] The solid immersion tunneling ellipsometer system 30
includes an ellipsometer apparatus 32 and a processing apparatus 34
(e.g., a computer executing suitable software). The ellipsometer
apparatus 32 performs physical measurements on the sample 36, and
the results, in the form of ellipsometric signals 55, are provided
to the processing apparatus 34 for processing. In this application,
ellipsometric signals are defined as any signals or information
that is provided by the ellipsometer apparatus 32 to the processing
apparatus 34 for use in determining one or more characteristics of
the sample. For example, an illumination apparatus 40 of the
ellipsometer apparatus 32 may provide information including the
wavelength and polarization of the incident light, and the angle of
incidence. As a further example, an analyzer apparatus 46 of the
ellipsometer apparatus 32 may provide information including the
intensity of the reflected light in a specific state of
polarization, and the nulling positions and angles related to the
reflected light. The processing apparatus 34 uses the ellipsometric
signals 55 to determine one or more ellipsometric parameters (e.g.,
.PSI. and .DELTA.) which are then used to determine one or more
characteristics of the film 37 (e.g., index of refraction,
thickness, etc.).
[0043] As shown generally in FIG. 2, the ellipsometer apparatus 32
includes the illumination apparatus 40, an optional optical
apparatus 44, the analyzer apparatus 46, and a solid immersion
apparatus 50 (e.g., a prism or an objective lens in combination
with a solid immersion lens). Such a general configuration will be
apparent to one skilled in the art when viewed with reference to
more detailed embodiments shown in FIGS. 2, 6, and 7.
[0044] Generally, polarized light 52 is provided to the solid
immersion apparatus 50 from the illumination apparatus 40. With the
solid immersion apparatus 50 having a surface 51 located adjacent
the film 37, tunneling occurs for incident light provided at an
angle greater than a critical angle of the solid immersion
apparatus 50. Elliptically polarized light 54 is provided as the
reflected light from the film 37. The elliptically polarized light
54 is provided to the analyzer apparatus 46. Upon operation of the
analyzer apparatus 46, ellipsometric signals 55 representative of
the reflected light are provided to the processing apparatus 34.
The optional optical apparatus 44, for example, may be a beam
splitter configuration such as described with reference to FIG. 7
or may not be required such as with use of a prism in the
ellipsometer apparatus configuration of FIG. 4.
[0045] Generally, the method of determining the one or more
characteristics of the thin film 37 of sample 36 is based on
associating the measured ellipsometric parameters (e.g., determined
using measurements from ellipsometer apparatus 32) with a
mathematical model based on the same ellipsometric parameters
generated using a model of an event. An event, as used herein,
refers to a physical measurement performed using the ellipsometer
apparatus 32 (e.g., incident light at greater than the critical
angle and the measurement of the reflected light with the result of
the event being measured ellipsometric signals; incident light at
less than the critical angle and the measurement of the reflected
light with the result of the event being measured ellipsometric
signals, etc.).
[0046] A model, as used herein, refers to a mathematical
description of an event, and trajectories that are generated from
the mathematical description. Trajectories, as used herein, refer
to information (e.g., a set of graphs, a lookup table, etc.)
generated using the mathematical description which provide the
relationship between one or more ellipsometric parameters (e.g.,
.PSI., .DELTA.) and one or more characteristics (e.g., thickness)
of the thin films to be characterized. Thus, the processing
apparatus 34 uses the measured ellipsometric parameters, along with
modeled ellipsometric parameters (e.g., a set of trajectories or
some other relational information), to determine at least one
characteristic of the sample 36 (e.g., index of refraction of the
film 37, thickness of the film 37, etc.).
[0047] Conventional ellipsometers, in many instances, have
difficulties in measuring characteristics such as the index of
refraction of ultrathin films. This is due, at least in part, to
the fact that (.PSI., .DELTA.) trajectories used for determining
the index of refraction are not well separated in the ultrathin
regime, as illustrated in FIG. 3A. FIGS. 3A and 3B show examples of
trajectories in a graphic format that can be used to express the
relationship between the one or more sample characteristics (e.g.,
thickness and index of refraction) and the ellipsomatic parameters
(e.g., .PSI. and .DELTA.). The x-axis corresponds to the .PSI.
value and y-axis corresponds to the .DELTA. value, thus any value
of a .PSI., .DELTA. pair indicates a point on the graph. Note that
each curve on the graph corresponds to a particular value of the
index of refraction, and that along each curve, the individual dots
indicate the thickness of the sample, where each dot along the
curve represents a thickness change of 10 angstroms. Note the
difference between FIG. 3A and FIG. 3B. In FIG. 3A, the thinnest
films are at the bottom left, and the thickness increases as the
curve goes to the upper right; for FIG. 3B, the thinnest films are
at the upper left, and the thickness increases as the curve goes to
the lower left. To determine a sample characteristic, the measured
.PSI., .DELTA. pair is used to select a point on the graph, from
which the sample characteristics can be determined by selecting the
closest curve (which determines the index of refraction) and then
on that curve, finding the closest dot (which determines the
thickness). Note that fitting can be performed in the case of a
.PSI., .DELTA. pair that is between curves and/or between dots.
Note that for this example, the ellipsometric system is able to
determine both the index of refraction and thickness
simultaneously.
[0048] As shown in FIG. 3A, in region 80 (i.e., the region
corresponding to film thickness less than or equal to 100
angstroms), the separation between curves representing different
indexes of refraction is minimal, making it difficult to make an
accurate measurement. In region 82, corresponding to film thickness
of 800 angstroms to 1000 angstroms, the separation is clearer, and
more accurate measurements can be made. Thus, when using a
conventional ellipsometer to measure ultrathin films, a small error
in the .PSI. value, due to measurement error, can skew the results
(e.g., a thickness measurement) significantly. Therefore,
conventional ellipsometers are, in many cases, unsuitable to
measure the refractive index of ultrathin films. As previously
indicated, ultrathin films are films having a thickness of less
than 100 angstroms.
[0049] The present invention includes a solid immersion tunneling
ellipsometric technique that is capable of overcoming the problems
of conventional ellipsometric systems such that characteristics of
ultrathin films (e.g., thickness and refractive index) can be
measured effectively. Such characteristics, like refractive index
and thickness, may be determined simultaneously. Moreover, a
near-field ellipsometric method using a solid immersion tunneling
technique provides accurate thickness and index of refraction
measurements with very high spatial resolution. High quality images
of the ultrathin films can therefore be obtained through scanning
(e.g., as opposed to providing such characteristics for a small
spot). Any suitable scanning apparatus may be used to provide
measurements over a larger area for providing an image.
[0050] To accurately measure, for example, a refractive index, it
is advantageous to separate the (.PSI., .DELTA.) trajectories along
the .PSI. direction. In other words, one wants to choose an event
type that corresponds to trajectories in which the (.PSI., .DELTA.)
trajectories along the .PSI. direction provide good separation. To
achieve this, a technique and apparatus was developed that utilizes
optical tunneling. Such optical tunneling provides a desired
.PSI.-resolution enhancement that will be apparent from the
description herein, particularly the description with reference to
the following FIG. 4.
[0051] FIG. 4 shows an illustrative diagram of one embodiment of a
portion of the ellipsometer system shown generally in FIG. 2. The
solid immersion tunneling ellipsometer apparatus 100 shown in FIG.
4 utilizes a solid immersion prism 118. The ellipsometer apparatus
100 is operable to provide ellipsometric signals that may be
processed according to the present invention to determine at least
one characteristic of thin film 122 provided on substrate 124 of
sample 120.
[0052] In comparison to the ellipsometry apparatus generally shown
in FIG. 2, the solid immersion apparatus 50 includes the prism 118,
and the optional optical apparatus 44 is not present. The prism 118
includes an incident surface 115 through which incident light 110
may be received, and a reflection surface 119 through which
reflected light 108 may be provided to an analyzer apparatus (not
shown). Further, the prism includes a tunneling surface 117
positioned adjacent an upper surface 127 of film 122.
[0053] In one embodiment, the sample 120 (e.g., substrate assembly)
is in contact with tunneling surface 117 of the prism 118. In
another embodiment, the thin film 122 may be separated from the
tunneling surface 117 by a narrow gap 126 (e.g., air gap).
[0054] In one embodiment, the incident polarized light 110
illuminates the thin film 122 through a high refractive index prism
118. For example, a high refractive index material such as GaP
(n=3.4) may be used. However, one skilled in the art will recognize
that any prism providing a suitable tunneling surface 117 and a
critical angle 116 (as shown relative to normal 112) may be used
according to the present invention.
[0055] One will recognize that incident light 110 as shown in FIG.
4 is provided at an angle greater than the critical angle 116 of
the prism 118. However, incident light may also be provided at less
than the critical angle 116 as shown by incident light 114.
[0056] With the polarized light 110 incident on the prism 118 at an
angle greater than the critical angle 116, an evanescent wave is
generated at the prism tunneling surface 117. The evanescent wave
can be coupled into a propagating wave, thus causing a decrease in
reflectivity from the film 122 back into the prism 118. Such
tunneling provides the desired .PSI.-resolution enhancements
mentioned above and further described herein, particularly with
reference to FIG. 3B below.
[0057] FIG. 3B shows illustrative model ellipsometric parameter
(.PSI., .DELTA.) trajectories for a tunneling ellipsometer using a
solid immersion configuration with an exemplary 10 angstrom air
gap. The trajectories in Region 84, which corresponds to ultrathin
films, clearly show the .PSI.-resolution enhancement between
different refractive indexes. Another characteristic of this near
field technique is that, for films thicker than approximately 100
angstroms, the separation of the trajectories gets smaller as the
films get thicker, as shown in region 86. This indicates that solid
immersion tunneling ellipsometry is more suitable for ultrathin
films and is less suitable for thicker films.
[0058] In view of the above, it is recognized that more accurate
characteristics may be determined for ultrathin films using the
near field solid immersion tunneling aspects of the present
invention with measurements taken for incident light greater than
the critical angle of the solid immersion configuration (e.g.,
critical angle of prism 118 or as described further herein the
critical angle of a solid immersion lens). Likewise, it is also
recognized that more accurate characteristics may be determined for
films thicker than ultrathin films using techniques similar to
conventional ellipsometry with measurements taken for incident
light less than the critical angle of the solid immersion
apparatus.
[0059] By combining techniques similar to conventional ellipsometry
(e.g., using light incident at less than the critical angle of a
solid immersion apparatus) with the solid immersion tunneling
technique, where incident light at greater than the critical angle
is used, an ellipsometry system can provide highly accurate results
across a wide range of thin film thickness values. In other words,
with further reference to the ellipsometry configuration of FIG. 4,
for the incident ray 114 at an angle less than the critical angle,
the evanescent fields disappear and the measurement is more similar
to a conventional ellipsometer. On the other hand, for the incident
ray 110 at an angle greater than the critical angle, a near-field
measurement is obtained. Thus, a variable angle solid immersion
ellipsometer will be able to accurately measure sample
characteristics (e.g., thickness and refractive index) for films
with varied thickness as further described herein.
[0060] At least in one embodiment, the sample characteristic can be
determined by performing a fit of measured ellipsometric parameters
(e.g., determined from one or more ellipsometric signals of an
ellipsometry apparatus) to a model trajectory or relational
information generated from a model of an event (e.g., the model
trajectory providing the relationship between one or more sample
characteristics and ellipsometric parameters, such as for ultrathin
films, based on incident light provided at greater than the
critical angle of a solid immersions apparatus of a solid immersion
tunneling ellipsometer apparatus).
[0061] In one embodiment, a regression algorithm can be used to
perform this fitting. The regression process can be any standard
regression algorithm. When performing the regression, a merit
function can be defined. With some experimental measurements
available, for example, (.PSI., .DELTA.) pairs, one can use the
regression process to find out the best guess for the actual
parameters of the sample, such as thickness, index of refraction
etc. Normally, the regression algorithm takes a guess of these
parameters at the beginning, then uses these parameters and a
certain optical model (e.g., an event model as described herein) to
calculate the corresponding output parameters (.PSI., .DELTA.)
pairs. Then it compares the output parameters with the experimental
using the merit function and sees how close they are. If it is not
close enough, the next estimation of the sample parameters is
calculated, and the above process is repeated until a satisfactory
estimation of the sample parameters is obtained. The output of the
regression process is used as the best estimation of the actual
sample parameters.
[0062] In some embodiments, the solid immersion apparatus is placed
adjacent to the sample surface, and there is a gap between the
adjacent surface of the solid immersion apparatus and the surface
of the sample thin film. The size of the gap may be included as a
model parameter or model fitting parameter. For example, in one
embodiment, the gap may be measured using interferometry techniques
and the measurement provided for use as a parameter of the model.
In another embodiment, the present invention can be used to
determine the size of the gap with the gap size being an unknown
model fitting parameter. When used as a model fitting parameter,
priori knowledge of the spacing is not necessary. In other words,
the gap can be considered in the modeling process by either
performing the gap measurement and providing the value to the model
fitting process or treating the size of the gap as an unknown and
determining the size during the model fitting process.
[0063] An example of a merit function, Merit Function 1, applicable
for use with the present invention is: 2 M = i = 1 N [ ( i - ( x )
) 2 + ( i - ( x ) ) 2 ]
[0064] where (.PSI..sub.i, .DELTA..sub.i) are the measured data
corresponding to the I.sup.th incident angle, {right arrow over
(x)} is a vector inclusive of the model parameters,
.sigma..sub..DELTA. and .sigma..sub..PSI. are the standard
deviations of the (.PSI., .DELTA.) measurement, and .DELTA.({right
arrow over (x)}) and .PSI.({right arrow over (x)}) are the
calculated data points using the optical model and the model
parameters. During regression, this merit function is minimized to
find the optimum results. This merit function has been used to
compare conventional ellipsometry with the solid immersion
tunneling ellipsometry of the present invention. One example
computer simulation based on this merit function showed a
refractive index resolution of +/-0.01 for the solid immersion
tunneling ellipsometry of the present invention, as compared to
+/-0.15 for conventional ellipsometry. This merit function is
applicable to any scenario in which there are multiple
measurements.
[0065] Even though solid immersion tunneling ellipsometry provides
enhanced results compared to conventional ellipsometry for films
less than 100 angstroms, its resolution of refraction index
degrades for films thinner than 20 angstroms. The (.PSI., .DELTA.)
trajectories of ultrathin films illustrate a complementary behavior
between solid immersion tunneling ellipsometry and conventional
ellipsometry.
[0066] While the .PSI. resolution is worse for conventional
ellipsometry than for tunneling ellipsometry, the .DELTA.
resolution is usually better due to the multiple reflections, which
are absent in the tunneling case. Thus, an improved merit function,
which contains only .DELTA. values from measurements less than the
critical angle and .PSI. values from measurements greater than the
critical angle, is more immune to noise (e.g., provides more
accurate measurements of sample characteristics). This improved
merit function, Merit Function 2, which may be used according to
the present invention is: 3 M = j ( i - ( x ) ) 2 + j ( i - ( x ) )
2
[0067] where j denotes incident angles that are less than the
critical angle and i denotes incident angles greater than the
critical angle. Merit Function 2 is only applicable in the scenario
where there are multiple measurements, where at least one
measurement corresponds to incident light greater than the critical
angle of the solid immersion apparatus, and at least one
measurement corresponds to incident light at less than the critical
angle of the solid immersion apparatus. Merit Function 2 can be
considered a subset of Merit Function 1. If in Merit Function 1,
.sigma..sub..DELTA. goes to infinity (because the .DELTA. error
gets very large for measurements at angles greater than the
critical angle) then this term goes to zero. Similarly, if in Merit
Function 1, .sigma..sub..PSI., goes to infinity (because the .PSI.
error gets very large for measurements at angles less than the
critical angle) then this term goes to zero. Example simulations
using this merit function have shown regression results for
determining the index of refraction for films as thin as 10
angstroms with a resolution of +/-0.003.
[0068] The regression analysis can provide an optimization process
for a variety of measurement scenarios. For example, where there
are multiple measurements and multiple models (e.g., models for
greater than and less than the critical angle), an optimization
step may be performed to determine the desired sample
characteristics by minimizing the total error across all the
measurements (which can be based on different models). In addition,
during the optimization, a weighting of the ellipsometric
parameters can be done to improve the accuracy of results. For
example, the weight of parameters that contain significant noise
may be reduced.
[0069] The solid immersion ellipsometry technique shown in FIG. 4
can be applied to measure a homogeneous film. Its spatial
resolution is determined by the incident beam size, which is
usually on the order of hundreds of micrometers. For thin films
with patterns, it is desirable to be able to characterize the
sample with high spatial resolution.
[0070] FIG. 5 is a processing flow diagram generally illustrating
the operation of the system 30 shown generally in FIG. 2. FIG. 5
includes a data processing flow 60 along with a physical
measurement flow 70. Physical measurement flow 70 provides a
general illustration of the operation of the ellipsometer apparatus
32. One embodiment of the sequence of events of the ellipsometer
apparatus 32 includes light 52 incident on the sample 36 at a
specified angle (block 72). The incident light reflects off the
sample as elliptically polarized light (block 74). The light is
measured and detected (block 76) resulting in a set of measurement
data 78. The measurement data is provided to the data processing
flow 60 in the form of ellipsometric signals 67.
[0071] As shown in FIG. 5, the data processing flow 60 generally
includes, at least in one embodiment, two components: a modeling
component 61 that includes the generation of trajectories 62 and
the set of trajectories 64; and a sample characteristic
determination component 57 that computes the sample
characteristic(s) from the measurement data 78. Sample
characteristic determination 57 includes ellipsometric parameter
determination 66 and model fitting block 68.
[0072] The generate trajectories block 62 includes defining one or
more mathematical equations describing the model trajectories for
ellipsometric parameters corresponding to those determined or
measured using block 66 (e.g., .PSI., .DELTA., etc.). Processing
one or more equations produces the various model trajectories
resulting in the set of model trajectories (block 64). These model
trajectories are utilized during the process of determining one or
more sample characteristic(s) for the sample 36.
[0073] The determine ellipsometric parameters block 66 receives the
ellipsometric signals 67 and uses the information to determine
ellipsometric parameters 63 representative of the reflected light
54. The ellipsometric parameters 63 and set of model trajectories
64 are used to determine the desired sample characteristics (e.g.,
thickness). In one embodiment, the measured ellipsometric
parameters 63 are fit to a selected model trajectory by regression
analysis to provide a resulting desired sample characteristic
69.
[0074] The data processing flow 60 may include for example,
processing such as generate trajectories 62, determine
ellipsometric parameters 66, and model fit by regression analysis
68. One or more of the processing functions performed within data
processing flow 60 may be provided using one or more media
types.
[0075] In one embodiment of the processing flow 60 for a solid
immersion tunneling ellipsometer method and apparatus, the
ellipsometric signals 67 are determined from at least one reflected
ray corresponding to an incident ray at greater than the critical
angle. The reflection from the incident ray at greater than the
critical angle is influenced by optical tunneling, and is processed
using a set of trajectories 64 generated as part of a tunneling
model; the tunneling model providing a relationship between the
sample characteristic to be determined and one or more model
ellipsometric parameters for, preferably, ultrathin films having a
thickness less than 100 angstroms.
[0076] In another embodiment of the processing flow 60 for a solid
immersion tunneling ellipsometer method and apparatus, the
ellipsometric signals 67 are determined from at least one reflected
ray corresponding to an incident ray at less than the critical
angle and greater than the critical angle. The reflection from the
incident ray at greater than the critical angle is influenced by
optical tunneling, and the reflection from the incident ray at less
than the critical angle which is not influenced by optical
tunneling, is processed using one or more sets of trajectories 64
generated as part of one or more models.
[0077] FIG. 6 shows one illustrative diagram of an embodiment of
the solid immersion tunneling ellipsometer system 30 shown
generally in FIG. 2, using polarized light and a solid immersion
lens, according to the present invention. With reference to FIG. 2,
the optional optical apparatus 44 is a beam splitter 136 in the
FIG. 6 configuration and the solid immersion apparatus 50 is a
microscope objective lens 148 and a solid immersion lens 150 in the
FIG. 6 configuration.
[0078] Solid immersion tunneling ellipsometer system 130 shown in
FIG. 6 is used to characterize the thin film 158 provided on
substrate 159 of sample 157. The ellipsometer system 130 includes a
light source 132 and polarizer 134 used to create incident
polarized light 146. However, one of skill in the art will
recognize that any manner of providing the polarized light may be
used.
[0079] The beam splitter directs the polarized light 146 onto the
objective lens 148 which focuses the light onto the SIL 150
resulting in a focused spot 145 (e.g., on the bottom tunneling
surface 153 of the SIL 150). The hemispherical SIL 150 is placed at
the focal plane of the objective lens 148. The existence of the SIL
150 provides higher spatial resolution and optical tunneling for
ellipsometric measurement. A spherical surface 151 of the SIL 150
matches the wave front of the focused incident beam. The incident
beam is focused to a very small spot at the bottom tunneling
surface 153 of the SIL 150 and reflected back from the SIL/sample
interface. Optical tunneling will occur for those rays that have
incident angles greater than the critical angle 156.
[0080] One or more various types of SILs may be used according to
the present invention. For example, SILs that are suitable for the
present application are the standard SIL (hemispherical lens) and
the super SIL (stigmatic lens). These two types of SILs produce
non-aberrated spots at the focus point. The SIL shown in FIG. 6 has
a hemispherical surface 151 and a planar tunneling surface 153.
However, for example, one or more different SILs and super SILs are
described in the following references: M. Born and E. Wolf,
Principles of Optics, 4.sup.th Edition, Pergamon Press, Oxford,
1970; Ichimura, et al., "High-density optical recording using a
solid immersion lens," Applied Optics, v.36 n. 19, pp 4339-4348
(Jul. 1, 1997); Qian et al., "Imaging with solid immersion lenses,
spatial resolution, and applications," Proceedings of the IEEE, Vol
88, Issue: 9, pp. 1491-1498 (September 2000); and T. D. Milster,
"Near-field optics: a new tool for data storage," Proceedings of
the IEEE, Vol. 88, Issue: 9, pp. 1480-1490 (September 2000).
[0081] Further, for example, because the incident light 146 is
focused to a very small spot 145, the size of the tunneling surface
need not be very large. In fact, such a surface may take the form
of a probe or more pointed tip. All that is necessary is that the
surface be able to couple the evanescent wave to the film to be
characterized.
[0082] Yet further, the substrate may be used to form a part of the
SIL such that the measurements being made for a film on the
substrate can be made with the SIL positioned in contact with the
back side of the substrate. In this manner, with the SIL and
substrate being generally of the same material or at least having
similar index of refraction, the substrate actually becomes a part
of the SIL 150 and tunneling occurs at the interface between the
substrate surface and the thin film to be characterized. In other
words, the surface of the solid immersion lens is adjacent the thin
film but separated therefrom by a substrate upon which the thin
film is provided. In this configuration, the solid immersion lens
may include an abbreviated hemispheric lens, wherein the term
abbreviated hemispheric lens refers to a lens that has a height
less than a hemisphere (i.e., a hemisphere being half of a sphere).
As a consequence, in this embodiment, the polarized light is
incident on the thin film through the substrate.
[0083] It is well known that the field at the back focal plane and
the field at the front focal plane are related through a Fourier
transform. Thus, each point at the back focal plane corresponds to
one ray with a specific incident angle from the front focal plane.
By measuring the state of polarization at the back focal plane,
ellipsometric signals representative of the SIL/sample interface
associated with different incident angles can be provided. The use
of the objective lens 148 and SIL 150 creates light incident on the
sample at both greater than and less than the critical angle
simultaneously, and therefore is capable of providing ellipsometric
signals that contain information from both types of angles with a
single measurement.
[0084] The light reflected from the thin film 158 is directed by
the SIL 150 to the objective lens 148. The reflected elliptically
polarized light 144 is directed into the beam splitter apparatus
136 and directed to the analyzer 138. The analyzer 138 determines
the polarization properties of the reflected light 144. For
example, the analyzer 138 may include waveplates, polarizers,
polarization rotators, modulators, or any other number of elements
as described in R. M. A Azzam and N. M. Bashara, Ellipsometry and
polarized light, North Holland Publishing Company, New York
(1977).
[0085] The light is then received by the detector 140, which
measures the intensity of the light and creates a signal
proportional to the light intensity. The detector may be a CCD
array, a ring CCD, or any other type of light detector that is
capable of separating reflected light based on incident light
provided greater than the critical angle from reflected light based
on incident light provided less than the critical angle. For
example, in one embodiment, a ring CCD may be able to provide
detection of light returned based on light incident at greater than
the critical angle. Further, a CCD array may perform detection of
all of the light reflected and then processing may perform a
selection of measurements made for reflected light corresponding to
the incident light provided at greater than the critical angle.
Further, for example, as shown optionally in FIG. 6, a spatial
filter 141 may be used to provide reflected light based on the
incident light greater than the critical angle (e.g., a spatial
filter that allows only an annular ring of reflected light to
pass). The above detection would also apply to providing detection
of reflected light corresponding to incident light at less than the
critical angle.
[0086] The analyzer 138 and detector 140 provide information as
described herein (e.g., such as intensity of the reflected light in
a specific state of polarization, or the nulling positions and
angles related to the reflected light.) in the form of
ellipsometric signals that are then sent to the processing
apparatus 142 to determine at least one characteristic of the
sample.
[0087] FIG. 7 shows one illustrative diagram of another embodiment
of the solid immersion tunneling ellipsometer system 30 shown
generally in FIG. 2. The ellipsometer configuration of FIG. 7 uses
radially symmetric techniques and a solid immersion lens
configuration.
[0088] Radially symmetric ellipsometer system 430 shown in FIG. 7
acts like a multi-channel conventional ellipsometer. Every
individual channel located at a different angular location inside a
common annular ring (along the axis of the light beam) looks
identical to others except for a phase delay. Such symmetry inside
this annular ring is referred to herein as radial symmetry. The
interference between these channels forms a high numerical aperture
cone of light at the sample plane and gives rise to high
resolution. Using this design, ellipsometric signals for use in
determining ellipsometric parameters such as a (.PSI., .DELTA.)
pair corresponding to a small spot can be measured.
[0089] Generally, the radially symmetric ellipsometer apparatus 430
uses radial symmetry to provide very high resolution in the
measuring of a very small spot 438, preferably, a spot having a
diameter less than 1 micron, of a sample 432. An illumination
apparatus 440 provides radially symmetric polarized light incident
normal to sample plane 433 of a sample 432. A beam splitter
apparatus 447 directs the polarized light 450 to the objective lens
452. The objective lens 452 focuses the light onto a solid
immersion lens 431, resulting in a focused spot 438 on the sample
plane 433 which is located at the focal plane 453 of the objective
lens 452. In other words, the sample plane 433 and the focal plane
coincide. The sample plane 433 refers to a surface of the sample
436 to be analyzed (e.g., an ultrathin film). The incident light is
normal to the sample plane 433, i.e., the incident plane of the
light is normal to the sample plane 433. The sample 432 reflects at
least a portion of the focused radially symmetric polarized light
as radially symmetric elliptically polarized light. The reflected
light is then used to generate a radially symmetric ellipsometer
signal detectable for use in determining one or more
characteristics of sample 432.
[0090] As shown in FIG. 7, the radially symmetric ellipsometer
apparatus 430 includes the illumination apparatus 440, the beam
splitter apparatus 447, the objective lens 452, and the solid
immersion lens 431, all aligned along axis 439 for use in focusing
radially symmetric polarized light to the spot 438 at the sample
plane 433 of sample 432. As described above, the radially symmetric
polarized light 450 is focused by an objective lens 452. The
hemispherical solid-immersion lens (SIL) 431 is placed at the focal
plane of the objective lens 433.
[0091] The inclusion of a solid immersion lens 431 within
ellipsometer apparatus 430 increases the resolution. Near field
optics can be employed in the near field of the sample 432 to
decrease the spot size of the ellipsometer apparatus 430 and
provide tunneling according to the present invention. FIG. 8 is a
more detailed diagram of the solid immersion apparatus including
the solid immersion lens 431 shown in FIG. 7.
[0092] As shown in FIG. 8, the solid immersion lens (SIL) 431 may
be positioned between the objective lens 452 and sample 432.
Generally, the solid immersion lens 431 is a semispherical solid
immersion lens, although other solid immersion lenses may be
feasible with modifications to the apparatus 430. As shown in the
embodiment of FIG. 8, the semispherical solid immersion lens 431
includes a lower surface 504 that is generally planar and an
opposing surface having a radius (r) 508. Preferably, the radius
508 is in the range of several millimeters.
[0093] The lower surface 504 of the SIL is positioned adjacent the
sample plane 433. The lower surface 504 may be positioned directly
adjacent and in contact with the sample 432 at sample plane 433.
However, the lower surface 504 may also be positioned with a space
or gap 507 having a height (h) in a range of less than 10
nanometers between the sample plane 433 of the sample 432 and the
lower surface 504 of the solid immersion lens 431.
[0094] The solid immersion lens 431 is generally formed of a
material having a high index of refraction. Preferably, the
refraction index may be in the range of 2 to 4. For example, the
solid immersion lens 431 may be formed of GaP that has an index of
refraction of about 3.5.
[0095] The light illuminating the objective lens 452 is focused
onto the bottom or lower surface 504 of the solid immersion lens
431. The light focused down to lower surface 504 forms a tight spot
438 thereon. The optical coupling between the light focused on the
lower surface 504 of the solid immersion lens 431 and the sample
432 produces a reflection captured by objective lens 452. For
example, the spot may be about 0.1 microns. The spot size depends,
at least in part, on the wavelength used in the apparatus.
[0096] The presence of the SIL 431 provides higher spatial
resolution and optical tunneling for ellipsometric measurement. The
spherical surface of the SIL 431 matches the wave front of the
focused incident beam. The incident beam is therefore focused to a
very small spot at the bottom tunneling surface 504 of the SIL 431
and reflected back from the SIL/sample interface. Optical tunneling
will occur for those rays that have incident angles greater than
the critical angle of the solid immersion lens 431.
[0097] The light focused down to the small spot 438 is reflected
from the sample 432 and back for collection by the objective lens
452. The SIL 431 provides incident rays at angles that are both
greater than and less than the critical angle. The SIL placed
adjacent to the sample also provides tunneling for the rays that
are incident at greater than the critical angle. The polarization
state of the incident light on sample 432 is modified by Fresnel
reflection for those rays incident at an angle less than the
critical angle, and is modified by tunneling for those rays
incident at greater than the critical angle, to provide reflected
radially symmetric elliptically polarized light that is provided
via the beam splitter apparatus 447 to an analyzer apparatus 460 of
the radially symmetric ellipsometer apparatus 430.
[0098] The analyzer apparatus 460 includes a pure polarization
rotator 462, a radial analyzer 464, and a detector 480 aligned
along optical axis 467 of the analyzer apparatus 460. The pure
polarization rotator 462 maintains the radially symmetric nature of
the reflected light representative of the spot 438 on sample 432,
which is thereafter focused to the detector 480 by the radial
analyzer 464. Through operation upon the reflected radially
symmetric elliptically polarized light, e.g., rotation of a
component of the pure polarization rotator 462, a radially
symmetric ellipsometric signal is detected at the detector 480 from
which at least one characteristic of the sample 432 may be
determined. For example, an ellipsometric pair (.PSI., .DELTA.) may
be derived based on the detected signal at detector 480 using
computer apparatus 490 electrically coupled thereto as further
described herein.
[0099] The illumination apparatus 440 may be any illumination
device suitable for providing radially symmetric polarized light
incident normal to sample plane 433 and thus normal to objective
lens 452 which is generally positioned in a parallel manner to
sample plane 433. As used herein, radially symmetric polarized
light includes, but is clearly not limited to, radially polarized
light and circularly polarized light. Any illumination that is
radially symmetric in terms of polarization state in the annular
region relative to the axis 439 may be suitable for use according
to the present invention.
[0100] As shown in FIG. 7, the illumination apparatus 440 includes
a light source 441 and a circular polarizer apparatus 442. The
circular polarizer apparatus 442 includes a polarizer 444 for
linearly polarizing light provided by light source 441 and a
quarter wave plate 446 for providing suitable polarization to
achieve circularly polarized light incident on objective lens
452.
[0101] The light source 441 may be any suitable light source at any
suitable wavelengths. With use of multiple wavelengths,
spectroscopic information may also be obtainable via detection of
reflected light and analysis by computer apparatus 490 of the
spectrum attained for the multiple wavelengths. Preferably, the
light source 441 provides collimated light incident on polarizer
444 of circular polarizer apparatus 442. More preferably, the light
source 441 is a laser beam providing precise collimated light. For
example, a collimated He--Ne laser may be used to provide the
collimated light.
[0102] The linear polarizer 444 and quarter wave plate 446 provide
circularly polarized light 450. The circularly polarized light 450
passes through a first beam splitter 448 of beam splitter apparatus
447 and is incident on objective lens 452. The beam splitter 448
may introduce some polarization modification to the circularly
polarized light provided by quarter wave plate 446. The linear
polarizer 444 and quarter wave plate 446 are adjusted to
pre-compensate for any such polarization modification introduced by
the beam splitter 448. Therefore, the light 450 illuminating the
objective lens 452 is circularly polarized such that radial
symmetry is achieved in the illumination of sample 432.
[0103] Although radially polarized light may be used according to
the present invention, preferably, the light incident on objective
lens 452 is circularly polarized light. Therefore, with respect to
the remainder of the description of this embodiment, the operation
shall be described with respect to circularly polarized light.
[0104] The circularly polarized light 450 is focused by an
objective lens 452. As described previously herein, the
hemispherical solid-immersion lens (SIL) 431 is placed at the focal
plane of the objective lens 433. The objective lens 452, and the
solid immersion lens 431, are all aligned along axis 439 for use in
focusing radially symmetric polarized light to a spot 438 at the
sample plane 433 of sample 432. The SIL 431 provides incident rays
at angles that are both greater than and less than the critical
angle. The SIL 431 placed adjacent to the sample 432 also provides
tunneling for the rays that are incident at greater than the
critical angle.
[0105] The circularly polarized light focused down to a small spot
438 on the sample 432 is then reflected there from, at least in
part, as radially symmetric elliptically polarized light. The
reflected radially symmetric elliptically polarized light is
collected by the objective lens 452 and provided to beam splitter
apparatus 447 wherefrom it is directed to the analyzer apparatus
460 of radially symmetric ellipsometer apparatus 430.
[0106] The objective lens 452 is preferably a high numerical
aperture objective lens. Preferably, the objective lens 452 has a
numerical aperture in the range of 0.5 to less than 1.0. More
preferably, the objective lens 452 has a numerical aperture in the
range of 0.8 to less than 1.0. Preferably, for example, the spot
438 is generally of a size falling in the range of 0.25 to 0.5
microns. The size depends, at least in part, on the wavelength of
the illumination source.
[0107] The reflected light collected by the objective lens 452 is
provided to the analyzer apparatus 460 of the ellipsometer
apparatus 430 by reflection in beam splitter apparatus 447. Beam
splitter apparatus 447 comprises the first beam splitter 448 which
passes the circularly polarized light from quarter wave plate 446
to the objective lens 452 for focusing upon the sample 432, and
which provides for reflection and diversion of the reflected
elliptically polarized light to analyzer apparatus 460. However,
typically, the amplitude reflectivities of the two polarization
states, r.sub.p and r.sub.s, from a beam splitter such as first
beam splitter 448, are different in amplitude and phase. As such,
the reflected light will generally pick up some additional
ellipticity from the reflection on the beam splitter interface 458
when diverted to analyzer apparatus 460. The amount of this
additional ellipticity varies for different incident polarizations.
To compensate for such added ellipticity, an identical additional
beam splitter 457 is used, as shown in FIG. 7. The additional beam
splitter 457 is identical to the beam splitter 448 but rotated in
position to provide for such compensation.
[0108] Therefore, beam splitter apparatus 447 includes both first
beam splitter 448 and second beam splitter 457. First beam splitter
448 includes an interface 458 for reflection of light collected by
objective lens 452 normal to the plane of incident light from
illumination apparatus 440, i.e., normal to the optical axis 439.
The second beam splitter 457 includes an interface 459 for
reflection of the diverted light from interface 458 of first beam
splitter 448. The reflected light is diverted by the second beam
splitter 457 such that the reflected light's direction is
orthogonal to the light diverted from interface 458 and also
orthogonal to the direction of light from illumination apparatus
440 which is incident on objective lens 452. As such, the
s-component for the first beam splitter 448 becomes the p-component
for the second beam splitter 457. Similarly, the p-component for
the first beam splitter 448 changes into the s-component for the
second beam splitter 457. As a result, the combination of these two
beam splitters 448,457 has the same response to s- and p-components
as the reflected light collected at the objective lens 452. As
such, the polarization of the incident beam is maintained in the
reflected light diverted to the analyzer apparatus 460.
[0109] The reflected radially symmetric elliptically polarized
light provided to the analyzer apparatus 460 is operated upon by
the pure polarization rotator 462 and the radial analyzer 464 such
that a radially symmetric ellipsometric light is provided for
detection by detector 480 for use in determining a characteristic
of sample 432. The pure polarization rotator 462 is an angularly
independent polarization rotator. In one illustrative embodiment,
the pure polarization rotator 462 includes two half-wave plates 468
and 470.
[0110] With rotation of at least one of the half wave plates 468,
470 and with use of the radially symmetric analyzer 464 as
described below, radially symmetric ellipsometric light is provided
for detection by detector 480. The reflected intermediate
elliptically polarized light provided from the pure polarization
rotator 462 to the radial symmetric analyzer 464 is still radially
symmetric and must be maintained in such a fashion by radially
symmetric analyzer 464.
[0111] As described above, the radial analyzer 464 of the radially
symmetric ellipsometer apparatus 430 must maintain the radial
symmetry of the reflected radially symmetric elliptically polarized
light. In other words, if one looks at this ellipsometer apparatus
430 as a multiple channel ellipsometer, every channel located at
different angular locations inside a common annular region of the
radial analyzer must look identical to the others except for phase
delay.
[0112] Detector 480 of analyzer apparatus 460 is a photo detection
device such as one or more photodiodes. Further, the detector 480
may be a charge coupled device detector (CCD). Any suitable
detector for detecting the intensity of light and providing a
signal representative thereof may be used according to the present
invention. As described herein with reference to FIG. 6, the
detector may be used to only detect reflected light only
corresponding to the light provided incident at an angle greater
than the critical angle, both greater than and less than the
critical angle either separately or together, or a spatial filter
may be used to obtain a suitable signal corresponding to an
applicable event (e.g., incident light greater than or less than
the critical angle).
[0113] With further reference to FIG. 7, the computer apparatus 490
runs software that allows the user to control the ellipsometer
apparatus 430 by means of a graphical user interface (not shown)
and is generally used to control the ellipsometer apparatus 430 and
perform digital processing with respect to the ellipsometer signals
provided thereto, e.g., by detector 480. For example, the computer
apparatus 490 may be used to control rotation of any of the
components described herein (e.g., rotation of a half wave plate in
the pure polarization rotator 462), may be used to control
application of the voltages to various components, may be used to
deduce ellipsometric pairs for the signal detected by detector 480
of ellipsometer apparatus 430, or control any other components of
the apparatus 430 interfaced to the computer, such as any
microcontrollers, scanning apparatus 492, etc. For example, as
described above, the spot 438 can be scanned under control of the
computer apparatus 490 to produce polarization information with
respect to multiple spots. Such multiple spot information may be
used by the computer apparatus 490 to generate a mapped image.
[0114] Further, computer apparatus 490 includes software for
providing data visualization and analysis capabilities via user
control. For example, graphical illustrations of the thickness of a
thin layer of sample 432 may be shown graphically after digital
processing of any number of spots 438. In addition, spectroscopic
information may be available upon use of any number of different
wavelengths, as would be known to one skilled in the art.
[0115] In one illustrative manner of determining thickness and
index of refraction using an ellipsometric pair (.PSI., .DELTA.),
computer apparatus 490 includes memory having a look-up table
relating the ellipsometric pairs to thickness and index of
refraction. For example, a computer program may be used to generate
the .PSI. and .DELTA. model trajectories for various indexes of
refraction and thickness. These results are stored in a look-up
table in the computer memory of computer apparatus 490. When
ellipsometric parameters are measured for a sample 432, the
computer apparatus 490 may search the look-up table and do an
interpolation and regression computation to find a corresponding
index of refraction (n) and thickness (t). Further, alternatively,
multi-variable regression analysis may be used in determining such
parameters.
[0116] Radial symmetry, as used herein, refers to the symmetry
inside an annular region of the ellipsometer apparatus 430 about a
particular axis thereof. For example, in the provision of light
incident on the objective lens 452, the radially symmetric
polarized light from illumination apparatus 440 is radially
symmetric about optical axis 439. Likewise, reflected light
provided to the analyzer apparatus 460 is radially symmetric about
optical axis 467. To be radially symmetric, the optical response of
every different angular location within the annular region relative
to the axis, e.g., axis 439 and axis 467, is identical to the
optical responses of the other angular locations except for phase
delay.
[0117] As indicated previously, the radial symmetry according to
the present invention may be thought of in terms of a multiple
channel apparatus. In other words, multiple channels parallel to
the axes, e.g., axis 439 and axis 467, can be envisioned. Every
individual channel located at different angular locations inside a
common annular region looks identical to all the others except for
phase delay.
[0118] Also as previously indicated, in the focusing of incident
light onto the sample 432 by the combination of the objective lens
452 and the SIL 431, the interference between these channels forms
a high numerical aperture cone of light 436 (with the use of the
numerical aperture objective lens 452, e.g., a high numerical
aperture objective lens) at the sample plane 433. Such radial
symmetry and focusing of such radially symmetric light to the
sample plane 433 gives rise to the high resolution of the present
apparatus 430. Using the reflected light from the sample 432, the
ellipsometric pair (.PSI., .DELTA.) corresponding to a small spot
438 (where, as known to those skilled in the art, tan(.PSI.) is the
ratio of magnitudes of the reflection coefficients for the p-wave
and s-wave, and .DELTA. is the phase difference between the
reflection coefficients of the p-wave and s-wave) can be measured.
One or more characteristics of the sample 432, e.g., thickness or
index of refraction, may then be deduced.
[0119] The radially symmetric techniques described herein are
illustrated by FIG. 7, and are further described in U.S.
application Ser. No. 09/691,346 that is incorporated by reference
herein. However, FIG. 7 is only illustrative of one exemplary
embodiment of a radially symmetric ellipsometer apparatus 430
according to the present invention. One will recognize that various
components thereof may be modified without changing the radially
symmetric nature of the ellipsometer apparatus 430.
[0120] FIG. 9 is diagram of a processing flow 190 illustrating one
embodiment of a portion of the general process flow shown generally
in FIG. 2, primarily for use in generating trajectories. The
process flow 190 is used to create a set of model trajectories 204
(or other relational information) that can be used along with
specific measurement results (e.g., measured ellipsometric
parameters) to determine one or more sample characteristic(s). Each
type of measurement event 192 is defined in detail to create
corresponding mathematical descriptions 194. Using the mathematical
expressions 194 for a corresponding event 192, model trajectories
are generated for that event (blocks 196). For example, events may
include light incident at greater than the critical angle, light
incident at less than the critical angle, and further, for example,
a relationship between a structure parameter and one or more
ellipsometric parameters (e.g., sidewall slope of a line structure
related to the ellipsometric parameters).
[0121] For example, in one embodiment, each event relationship can
be described using a mathematical expression whereby the desired
sample characteristic is a function of .PSI. and .DELTA., along
with any other necessary parameters. For each event and from the
mathematical description, trajectories are made that relate a
measured (.PSI., .DELTA.) value to the value of the desired sample
characteristic. In some cases, an event has many trajectories that
are created by iterating some parameter of the event, for example,
the angle of incidence.
[0122] The accuracy of determining one or more characteristics of
the sample is very dependent on the use of a model that accurately
represents the measurement event and the measurement system.
[0123] FIG. 10 is a diagram of a processing flow 210 illustrating
one embodiment of a portion of the general flow of processing shown
generally in FIG. 5, to determine at least one characteristic of
the sample. The processing flow may use one or more sets of
trajectories or other relational information generated as described
with reference to FIG. 9.
[0124] The process flow 210 shown in FIG. 10 may be used with
single or multiple measurements made by an ellipsometry apparatus
such as shown generally in FIG. 2 resulting in ellipsometric
signals (i.e., measured data 212). From the measurement data 212, a
point is selected 214, and (.PSI., .DELTA.) pair is determined
(block 216). Next, the (.PSI., .DELTA.) pair is processed depending
on the relationship of the angle of incidence for the light for
which the (.PSI., .DELTA.) pair is determined to the critical angle
of the solid immersion apparatus (e.g., critical angle of SIL or
prism).
[0125] If the angle of incidence is greater than the critical
angle, an appropriate trajectory is selected (block 218) from the
set of model trajectories 220, and a fit by regression analysis
(block 218) is done with the (.PSI., .DELTA.) pair determined for
the light at greater than the critical angle, and the selected
trajectory. This results in at least one sample characteristic
being determined. In the case of a single measurement, no least
squares regression 224 is required and the result is output
226.
[0126] If there is more than one measurement, the process is
repeated, and another value for the at least one sample
characteristic is determined in block 218. These steps are repeated
for each measurement. The resulting set of values of at least one
sample characteristic are then processed through a least squares
regression 224, from which an optimized value of at least one
sample characteristic is the result and output 226.
[0127] The present invention includes a technique that further
improves the accuracy of results. This technique involves weighting
the parameters during the regression analysis as is further
described herein.
[0128] The procedure is similar for determining at least one sample
characteristic when the incident light is at an angle less than the
critical angle. If the angle of incidence is less than the critical
angle, an appropriate trajectory is selected (block 222) from the
set of model trajectories 220, and a fit by regression analysis
(block 222) is done with the (.PSI., .DELTA.) pair determined for
the light at less than the critical angle, and the selected
trajectory. This results in at least one sample characteristic
being determined. In the case of a single measurement, no least
squares regression 224 is required and the result is output
226.
[0129] If there is more than one measurement, the process is
repeated, and another value for the at least one sample
characteristic is determined in block 222. These steps are repeated
for each measurement. The resulting set of values of at least one
sample characteristic are then processed through a least squares
regression 224, from which an optimized value of at least one
sample characteristic is the result and output 226.
[0130] Whenever the flow in FIG. 10 includes more than one
measurement, the least squares regression step is performed, to
optimize across all measurements. The merit functions previously
described may be used to optimize the least squares fit. For the
flow in FIG. 10, either of the previously mentioned merit functions
(Merit Function 1 or Merit Function 2) may be applicable. Merit
Function 1 is useable in any scenario where there are multiple
measurements. Merit Function 2, which provides improved regression
analysis, is applicable to FIG. 10 provided that there is at least
one measurement from greater than the critical angle of the solid
immersion apparatus and at least one measurement from less than the
critical angle of the solid immersion apparatus. Merit Function 2
is a subset of Merit Function 1 as described herein.
[0131] Examination of the (.PSI., .DELTA.) trajectories of
ultrathin films reveals a complementary feature between tunneling
ellipsometry and conventional ellipsometry. While the .PSI.
resolution is worse for conventional ellipsometry than for
tunneling ellipsometry, the .DELTA. resolution is usually better
due to the multiple reflections, which are absent in the tunneling
case. Thus, if one utilizes .DELTA. values only from measurements
for lower than the critical angle, and .PSI. values only for
measurements from greater than the critical angle; the regression
is generally more immune to noise. This technique is accomplished
by weighting the .PSI. and .DELTA. parameters during the regression
analysis.
[0132] FIG. 11 is a diagram of a process flow 230 illustrating one
embodiment of a portion of the general flow of processing shown
generally in FIG. 4, where one model is used that describes the
relationship between the ellipsometric parameters and at least one
sample characteristic for ultrathin films. The processing flow 230
shown in FIG. 11 generally includes the physical measurement flow
232 and the computer processing flow 234.
[0133] Physical measurement flow 232 provides a general
illustration of the operation of the ellipsometer measurement
apparatus 32 shown generally in FIG. 2. One embodiment of the
sequence of events of the ellipsometer apparatus 32 includes
providing polarized light incident on the sample at an angle
greater than the critical angle 238. The polarized light is then
reflected from the sample 240. The reflected light is analyzed and
detected 242. The physical measurement flow must include a method
to selectively measure only reflected light corresponding to those
rays that are incident at greater than the critical angle. For
example, the measurement apparatus could include a filter mechanism
to block the incident light corresponding to light at less than the
critical angle, or a detector embodiment which implements an array
of detectors, whereby the light measured from the detectors
corresponding to the input rays at greater than the critical angle
are used. Further, ring light detectors may also be used to detect
the reflected light corresponding to incident light provided at
greater than the critical angle. The measurement data 244 is
provided as ellipsometric signals to the computer processing flow
234.
[0134] The computer processing flow 234 includes determining a
(.PSI., .DELTA.) pair (block 246), providing models 236 and
performing a model fit of the determined ellipsometric parameters
(block 252) to deduce at least one characteristic 254 of the
sample. The providing of the model (block 236), in one embodiment,
includes mathematical description process 248 and generate
trajectories process 250. Such processes have been defined
generally above. Although various details are provided herein with
regard to the generation of the models, any model no matter how
generated that provides the suitable relationship between the
sample characteristic or characteristics to be determined (e.g.,
thickness) and the ellipsometric parameters can be used. A
regression analysis 252 is performed by fitting the (.PSI.,
.DELTA.) pair to a selected model trajectory of the model, thereby
producing the result (i.e., at least one characteristic of the
sample). The method of the present invention supports a variable
number of events and event types (and therefore, model types).
[0135] The processing flow diagram shown in FIG. 11 specifically
describes the process for the case where the incident light is
incident at an angle greater than the critical angle (block 238).
The process for the case where the light is incident at an angle
less than the critical angle is similar, with the following
differences: first, block 238 would be provide polarized light at
an incident angle less than the critical angle; second, there would
be a mechanism so that the reflected light that was analyzed and
detected would only be the reflected light from the incident rays
at less than the critical angle; and third, the provide model block
236 would describe and generate trajectories for an event where the
light was incident at an angle less than the critical angle.
[0136] Whenever the flow in FIG. 11 includes more than one
measurement, the least squares regression step is performed, to
optimize across all measurements. For the flow in FIG. 11, Merit
Function 1 can be used since there is only one model, and
therefore, all the measurements are performed either with incident
light greater than the critical angle of the solid immersion
apparatus, or with incident light less than the critical angle of
the solid immersion apparatus. FIG. 12 is another processing flow
diagram 260 illustrating one embodiment of a portion of the general
flow of processing shown generally in FIG. 2. In this case, a
combination of two models is used; one for angles greater than the
critical angle and one for angles less than the critical angle.
[0137] The overall process flow 260 includes a physical measurement
flow 262 and a computer processing flow 264. Physical measurement
flow 262 provides a general illustration of the operation of the
ellipsometer measurement apparatus 32 such as shown generally in
FIG. 2. One embodiment of the sequence of events of the
ellipsometer apparatus 32 includes providing polarized light
incident on the sample at both an angle greater than the critical
angle and an angle less than the critical angle 268. The polarized
light is then reflected from the sample 270. The reflected light is
analyzed and detected 272.
[0138] The physical measurement flow 262 must include a method to
discriminate between the light corresponding to those rays that are
incident at greater than the critical angle, and the light
corresponding to those rays that are incident at an angle less than
the critical angle. For example, the measurement apparatus could
include a filter mechanism like that described herein to allow
certain light corresponding to light at less than the critical
angle and greater than the critical angle to pass to the detector,
or a detector embodiment which implements an array of detectors,
whereby the light measured from the detectors corresponding to the
input rays at greater than and less than the critical angle are
detected. Further, the method may include any other physical or
process oriented vehicle for providing such separation between
greater than critical angle and less than critical angle
information. The measurement data 274 is provided as ellipsometric
signals to the computer processing flow 264.
[0139] The computer processing flow 264 includes determining the
(.PSI., .DELTA.) pair 276, creating models 266, and performing a
fit of the data to the model 286, to produce the result (e.g., at
least one characteristic of the sample 288). The providing model
block 266, in one embodiment, includes mathematical description
process 278 and generate trajectories process 280 which creates a
set of trajectories (or other relational information) for the event
in which the light is incident at an angle greater than the
critical angle. The providing model block 266 further includes, in
one embodiment, another mathematical description process 282 and
generate trajectories process 284 which creates a set of
trajectories (or other relational information) for the event in
which the light is incident at an angle less than the critical
angle.
[0140] Although various details are provided herein with regard to
the generation of the models, any model no matter how generated
that provides the suitable relationship between the sample
characteristic or characteristics to be determined (e.g.,
thickness) and the ellipsometric parameters can be used.
[0141] A regression analysis 286 is performed by fitting the
measured (.PSI., .DELTA.) pair (e.g., determined in block 276) to
the selected model trajectory of the model, thereby producing the
result 288 (i.e., at least one characteristic of the sample). The
model fit by regression analysis (block 286) performs a fit of the
measured (.PSI., .DELTA.) (e.g., determined in block 276) to a
trajectory which is either 280 if the measured (.PSI., .DELTA.)
corresponds to light incident at greater than the critical angle,
or trajectory 284 if the measured (.PSI., .DELTA.) corresponds to
light incident at less than the critical angle.
[0142] For any particular measurement taken, the measurement data
must be associated with the correct and compatible
model/trajectory. Also, one must choose a model that is appropriate
for the specific physical system that is being measured. For
example, one must choose different models for the case of a single
thin film (of thickness and index of refraction to be determined)
on a given substrate and the case of multiple thin films on a
substrate. With multiple models, the regression analysis 286 may
include an additional step of performing a least squares fit on all
the generated results to optimize the results.
[0143] Whenever the flow in FIG. 12 includes more than one
measurement, the least squares regression step is performed, to
optimize across all measurements. The merit functions previously
described are used to optimize the least squares fit. For the flow
in FIG. 12, either of the previously mentioned merit functions
(Merit Function 1 or Merit Function 2) may be applicable. Merit
Function 1 is useable in any scenario where there are multiple
measurements. Merit Function 2, which provides improved regression
analysis, is a subset of Merit Function 1, as previously stated
herein.
[0144] The methods and apparatus of the present invention may also
include a spatially resolved ellipsometry system providing the
capability to determine critical characteristics of a structure,
such as the characterization of a sidewall shape of a line formed
on a substrate. The response of sub-wavelength structures, for
example, lines on integrated circuits, to incident light is
polarization dependent. Numerical simulation and experimental
results have shown that the polarization effect depends on the
shape of the structure, for example, the sidewall shape. In the
present invention, one can use spatially resolved ellipsometry to
extract ellipsometric information from the corresponding line
structures, to determine the sidewall shape, such as undercutting
and sidewall slope. Since the line structures are smaller than the
wavelength, a vector diffraction model that solves Maxwell's
equations rigorously is required, and the focused beam rigorous
coupled wave analysis (FB-RCWA) is utilized.
[0145] The present invention includes a modeling process to create
a model including at least trajectories that show the relationship
between ellipsometric parameters and desired sample characteristics
(e.g., slope). The present invention, in one embodiment, includes a
model for sidewall slope measurement of a line on a substrate, as a
function of the ellipsometric parameters.
[0146] An ellipsometric apparatus 600 is shown in FIG. 13A for use
in providing ellipsometric signals to determine one or more
ellipsometric parameters (e.g., (.PSI., .DELTA.)). However, any
ellipsometric signals described herein or elsewhere may be suitable
for providing ellipsometric data for determining ellipsometric
parameters (e.g., (.PSI., .DELTA.)).
[0147] In this one illustration, sample 601 is illuminated by a
Gaussian beam focused by a microscope objective 603 (NA=0.8). When
the beam illuminates the trench 605, the reflected elliptically
polarized light is analyzed and detected to provide ellipsometric
signals. With ellipsometric signals provided, ellipsometric
parameters can be determined. By using a suitable model and
trajectories showing the relationship between slope of a wall of
the trench and the ellipsometric parameters, one can determine
slope of the wall. In this case, we can determine the sidewall
slope of the trench without actually resolving its shape.
[0148] FIGS. 13B and 13C show the trajectories created using a
model of this event, i.e., measuring the sidewall slope of a line
structure. Such trajectories for different slopes have enough
separation to allow for accurate results when fitting ellipsometric
parameters to the model. FIG. 13B illustrates the magnitude ratio
(tan .PSI.) and FIG. 13C illustrates the phase delay (.DELTA.)
between two illumination conditions across the back focal plane 607
of the focusing lens 603. The curves for different sidewall slopes
are different. The sidewall shape can be distinguished by measuring
the state of polarization of one or more rays that correspond to
different spatial frequencies at the back of the focal plane 607.
FIG. 13D depicts the (tan .PSI., .DELTA.) trajectory that
corresponds to measurement by the on-axis ray.
[0149] Note that the ellipsometric apparatus used to carry out the
measurements as shown in FIG. 13A is just an example, and that any
ellipsometric apparatus, including those described in the present
invention, could be used.
[0150] It will be recognized that one or more elements or processes
described with reference to certain embodiments may be used with
other embodiments described herein as well. For example, the use of
the merit function for regression analysis described with reference
to FIGS. 3 and 4 may be used in the regression analysis described
with reference to FIG. 10. Further, for example, the type of
detector or SL used in one embodiment of an ellipsometer apparatus
may be used for other apparatus described herein as well.
[0151] All references cited herein are incorporated in their
entirety as if each were incorporated separately. This invention
has been described with reference to illustrative embodiments and
is not meant to be construed in a limiting sense. Various
modifications of the illustrative embodiments, as well as
additional embodiments of the invention, will be apparent to
persons skilled in the art upon reference to this description.
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