US 2024/0011894 Al

[0056] When unpolarized radiation beam 104a enters
polarizer 112, the Stokes vector transmitting through polar-
izer 112 and compensator 114 and emerging as radiation
beam 104g when compensator 114 is rotated an angle o
from polarizer 112, is

R(-O)M(8,, MO, )MO5,DR()ME,,1)MB>,0M
(8,105,

[0057] where M(@, i) is obtained from Equation (4) using
Equations (1) and (2), and R(o) is the rotation matrix

1 0 0 0 o
0 costa sina 0
0 -sin2a cosda 0
oo O18

R@=

[0058] FIG. 8 shows an ellipsometer 800 in accordance
with a second embodiment of the present invention. Ellip-
someter for probing a sample artifact includes a sample
holder 802, a radiation source 804, polarization state gen-
erator 806 and a polarization state analyzer 808 and a
processor 810 arranged in a manner as shown in FIG. 8.
Radiation source 804 is similar to radiation source 104, as
shown in FIG. 1, which emits radiation beam 804a to
polarization state generator 806. Polarization state generator
806 includes a Brewster mirror 812 and a compensator 814.
Brewster mirror 812 is positioned to receive radiation beam
804a from radiation source 804 and reflect a s-polarized
radiation beam 804b to compensator 814 while no p-polar-
ized radiation beam enters and exits Brewster mirror 812.
[0059] Compensator 814 is similar to compensator 116, as
shown in FIGS. 1 and 4, and receives radiation beam 804b
reflected from Brewster mirror 812. All other disclosed
embodiments of compensator 116 could also apply to com-
pensator 814. Compensator 814 includes mirrors 814a,
814b, and 814c, as shown in FIG. 8, positioned to receive
radiation beam 804 reflected from Brewster mirror 812 and
redirect radiation beam 804e reflected from mirrors 814a-c
along an optical axis that aligns with the optical axis of
radiation beam 8045, as further shown in FIG. 8. Compen-
sator 814 is capable of rotating about an axis that aligns with
the optical axes of radiation beams 804b and 804e.

[0060] Radiation beam 804e exiting compensator 814 is
directed to sample artifact positioned on sample holder 802.
Sample holder 802 is positioned such that radiation beam
804e exiting compensator 814 is incident on a surface of
sample artifact. Sample holder 802 can be rotated such that
radiation beam 804e is incident on sample artifact front
surface at a predetermined incident angle. In one embodi-
ment, sample holder 802 can be rotated azimuthally about its
surface normal. Radiation beam 804e incident on sample
artifact front surface is reflected as radiation beam 804f into
polarization state analyzer 808.

[0061] Polarization state analyzer 808 includes a compen-
sator 816, a Brewster mirror 818 and a detector 820 and
rotates about an axis passing through the location where
radiation beam 804e strikes the front surface of the sample
artifact positioned on sample holder 802, as further shown in
FIG. 8. Compensator 816 is similar to compensator 116, as
shown in FIGS. 1 and 4, and receives radiation beam 804/
reflected from sample artifact front surface. All other dis-
closed embodiments of compensator 116 could also apply to
compensator 816. Compensator 816 includes mirrors 816a,

Jan. 11, 2024

816, and 816c, as shown in FIG. 8, positioned to receive
radiation beam 804f reflected from sample artifact front
surface and redirect radiation beam 804i reflected from
mirrors 816a-c along an optical axis that aligns with the
optical axes of radiation beam 804/, as further shown in FIG.
8. Compensator 816 is capable of rotating about an axis that
aligns with the optical axes of radiation beams 804f and
804i. Radiation beam 804i from compensator 816 is trans-
mitted to Brewster mirror 818 and Brewster mirror 818
reflects primarily s-polarized radiation beam 804j to detector

820.

[0062] Detector 820 is similar to detector 120, and is
positioned to detect s-polarized radiation beam 804j
reflected by Brewster mirror 818, as further shown in FIG.
8. Detector 820 measures signals for N rotation angles of
compensator 814 of polarization state generator 806 and M
rotation angles of compensator 816 of polarization state
analyzer 808. Processor 810 determines a MxN matrix
corresponding to N rotation angles of compensator 814 and
M rotation angles of compensator 816. Processor 810 further
determines a Mueller matrix for reflection by sample artifact
as a function of the angle radiation beam 804f exiting
compensator $14 and incident upon sample artifact. For
anisotropic media or periodic nanostructures, it is also a
function of azimuthal rotation of sample artifact about its
surface normal.

[0063] Ellipsometers in accordance with the present
invention, as shown in FIGS. 1 and 8, can be calibrated using
an arrangement of optical elements as shown in FIG. 9 and
eigenvalue calibration methods known in the art to obtain
the matrices A and W, as shown in Equation (5), and data
reduction matrices A~! and W~', as shown in Equation (6).
The arrangement of optical elements shown in FIG. 9 is
similar to the arrangement of optical elements shown in FIG.
8 with sample artifact and sample holder 802 removed such
that polarization state analyzer 908 is positioned to directly
measure radiation beam 902h transmitted by rotating com-
pensator 914 of polarization state generator 904. An addi-
tional rotating compensator 906 is positioned between the
polarization state generator 904 and polarization state ana-
lyzer 908, as shown in FIG. 9. For each of at least two
rotations of compensator 906, detector 920 measures signals
corresponding to N rotation angles of compensator 914 of
polarization state generator 904 and M rotation angles of
compensator 916 of polarization state analyzer 908. Proces-
sor 910 determines a MxN matrix corresponding to N
rotation angles of compensator 914 and M rotation angles of
compensator 916. The additional compensator 906 exhibits
net diattenuation and retardance to yield a suitable calibra-
tion. Detector 920 further measures signals corresponding to
N rotation angles of compensator 914 and M rotation angles
of compensator 916 in an arrangement without including
compensator 906, and processor 910 determines an addi-
tional MxN matrix corresponding to the N rotation angles of
compensator 914 and the M rotation angles of compensator
916.

[0064] In embodiments wherein radiation beam from a
radiation source is naturally polarized, a polarizer is optional
in a polarization state generator for the operation of an
ellipsometer in accordance with the present invention and,
as shown in FIG. 10, a polarization state generator need only
include a compensator and the naturally polarized radiation
beam from radiation source can be transmitted directly to the
compensator. FIG. 10 shows an ellipsometer 1000 in accor



US 2024/0011894 Al

reflected radiation beam comprises a second phase retar-
dance; a fifth mirror positioned to reflect the third reflected
radiation beam incident on the fifth mirror as a fourth
reflected radiation beam, wherein the fourth reflected radia-
tion beam comprises a third phase retardance; and a sixth
mirror positioned to reflect the fourth reflected radiation
beam incident on the sixth mirror as the second polarized
radiation beam having the first phase retardance; a sample
holder for positioning a first surface of the sample to receive
the second polarized radiation beam from the first rotating
compensator, wherein the first surface of the sample reflects
a third polarized radiation beam; a second rotating compen-
sator for altering the third polarized radiation beam to a
fourth polarized radiation beam having a fourth phase retar-
dance, wherein an optical axis of the fourth polarized
radiation beam is substantially aligned with the optical axis
of the third polarized radiation beam, wherein the second
compensator is rotated about an axis substantially aligned
with the optical axes of the third and the fourth polarized
radiation beams, wherein the second compensator includes:
a seventh mirror positioned to reflect the third polarized
radiation beam incident on the seventh mirror as a fifth
reflected radiation beam, wherein the fifth reflected radiation
beam comprises a fifth phase retardance; an eighth mirror
positioned to reflect the fifth reflected radiation beam inci-
dent on the eighth mirror as a sixth reflected radiation beam,
wherein the sixth reflected beam comprises a sixth phase
retardance; and a ninth mirror positioned to reflect the sixth
reflected radiation beam incident on the ninth mirror as the
fourth polarized radiation beam having the fourth phase
retardance; a second polarizer for modifying the fourth
polarized radiation beam to a fifth polarized radiation beam,
wherein an optical axis of the fifth polarized radiation beam.
is substantially aligned with an optical axis of the fourth
polarized radiation beam, wherein the second polarizer
includes: a tenth mirror positioned to reflect the fourth
polarized radiation beam incident on the tenth mirror as a
seventh reflected radiation beam; an eleventh mirror posi-
tioned to reflect the seventh reflected radiation beam inci-
dent on the eleventh mirror as an eighth reflected radiation
beam; and a twelfth mirror positioned to reflect the eighth
reflected radiation beam incident on the twelfth mirror as the
fifth polarized radiation beam; a detector for measuring a
plurality of first signals for a plurality of first rotation angles
of the first rotating compensator and a plurality of second
signals for a plurality of second rotation angles of the second
rotating compensator; and a processor for determining a
Mueller matrix from the plurality of the first rotation angles
of the first rotating compensator and the plurality of the
second rotation angles of the second rotating compensator.

[0016] In one embodiment of the present invention, the
first polarizer further comprises a thirteenth mirror posi-
tioned to receive one of the non-polarized radiation beam,
the first reflected radiation beam and the second reflected
radiation beam, and wherein the first, the second, the third
and the thirteenth mirrors are positioned to modify the
non-polarized radiation beam to the first polarized radiation
beam. In another embodiment of the present invention, the
second polarizer further comprises a thirteenth mirror posi-
tioned to receive one of the fourth polarized radiation beam,
the seventh reflected radiation beam and the eighth reflected
radiation beam, and wherein the tenth, the eleventh, the
twelfth and the thirteenth mirrors are positioned to modify
the fourth polarized radiation beam to the fifth polarized

Jan. 11, 2024

radiation beam. In yet another embodiment of the present
invention, the first polarizer further comprises a thirteenth
mirror positioned to receive a ninth reflected radiation beam
from the third mirror, and wherein the thirteenth mirror is
positioned to reflect the ninth reflected radiation beam
incident on the thirteenth mirror as the first polarized radia-
tion beam, and wherein the second polarizer further com-
prises a fourteenth mirror positioned to receive a tenth
reflected radiation beam from the twelfth mirror, and
wherein the fourteenth mirror is positioned to reflect the
tenth reflected radiation beam incident on the fourteenth
mirror as the fifth polarized radiation beam.

[0017] Another embodiment of the present invention
relates to an ellipsometer for investigating a sample, said
ellipsometer including a radiation source for generating a
non-polarized radiation beam; a polarization state generator
for modifying the non-polarized radiation beam to a first
polarized radiation beam having a first phase retardance,
wherein the polarization state generator includes: a first
mirror positioned to reflect the non-polarized radiation beam.
incident on the first mirror as a first reflected radiation beam;
a second mirror positioned to reflect the first reflected
radiation beam incident on the second mirror as a second
reflected radiation beam; a third mirror positioned to reflect
the second reflected radiation beam incident on the second
mirror as a third reflected radiation beam; a fourth mirror
positioned to reflect the third reflected radiation beam inci-
dent on the third mirror as a fourth reflected radiation beam;
and a first rotating compensator for altering the fourth
reflected radiation beam to the first polarized radiation beam,
having the first phase retardance, wherein an optical axis of
the first polarized radiation beam is substantially aligned
with the optical axis of the non-polarized radiation beam,
wherein the first compensator is rotated about an axis
substantially aligned with the optical axis of the first polar-
ized radiation beam; a sample holder for positioning a first
surface of the sample to receive the first polarized radiation
beam from the polarization state generator, wherein the first
surface of the sample reflects a second polarized radiation;
a polarization analyzer including: a second rotating com-
pensator for altering the second polarized radiation beam to
a third polarized radiation beam having a second phase
retardance, wherein an optical axis of the third polarized
radiation beam is substantially aligned with the optical axis
of the second polarized radiation beam, wherein the com-
pensator is rotated about an axis substantially aligned with
the optical axes of the second and the third polarized
radiation beams; and a polarizer for modifying the third
polarized radiation beam to a fourth polarized radiation
beam, wherein an optical axis of the fourth polarized radia-
tion beam is substantially aligned with an optical axis of the
third polarized radiation beam; a detector for measuring a
plurality of first signals for a plurality of first rotation angles
of the polarization state generator and a plurality of second
signals for a plurality of second rotation angles of the
rotating compensator; and a processor for determining a
Mueller matrix from the plurality of the first rotation angles
of the polarization state generator and the plurality of the
second rotation angles of the rotating compensator.

[0018] In one embodiment of the present invention, the
first rotating compensator includes a fifth mirror positioned
to reflect the fourth reflected radiation beam incident on the
fifth mirror as a fifth reflected radiation beam, wherein the
fifth reflected radiation beam comprises a third phase retar-


US 2024/0011894 Al

15. The ellipsometer of claim 14, wherein the wavelength
of the non-polarized radiation beam is from about 10 nm to
about 30 nm.

16. The ellipsometer of claim 14, wherein the wavelength
of the non-polarized radiation beam is from about 30 nm to
about 240 nm.

17. The ellipsometer of claim 14, wherein the second
compensator and the second polarizer are rotated about an
axis passing through a location the second polarized radia-
tion beam is received on the first surface of the sample
positioned on the sample holder, wherein the sample holder
rotates the sample about the axis passing through the loca-
tion the second polarized radiation beam is received on the
first surface of the sample positioned on the sample holder,
wherein the rotation of the sample is about one-half of the
rotation of the polarization state analyzer, and wherein the
rotating the polarization state analyzer adjusts an angle of
incidence of the second polarized radiation beam on the first
surface of the sample positioned on the sample holder and an
angle of reflection of the third polarized radiation beam.

18. The ellipsometer of claim 14, wherein the sample
holder rotates the sample in an azimuthal direction about an
axis normal to the first surface of the sample.

19. The ellipsometer of claim 14, wherein the first polar-
izer further comprises a thirteenth mirror positioned to
receive one of the non-polarized radiation beam, the first
reflected radiation beam and the second reflected radiation
beam, and wherein the first, the second, the third and the
thirteenth mirrors are positioned to modify the non-polarized
radiation beam to the first polarized radiation beam.

20. The ellipsometer of claim 14, wherein the second
polarizer further comprises a thirteenth mirror positioned to
receive one of the fourth polarized radiation beam, the
seventh reflected radiation beam and the eighth reflected
radiation beam, and wherein the tenth, the eleventh, the
twelfth and the thirteenth mirrors are positioned to modify
the fourth polarized radiation beam to the fifth polarized
radiation beam.

21. The ellipsometer of claim 14, wherein the first polar-
izer further comprises a thirteenth mirror positioned to
receive a ninth reflected radiation beam from the third
mirror, and wherein the thirteenth mirror is positioned to
reflect the ninth reflected radiation beam incident on the
thirteenth mirror as the first polarized radiation beam, and
wherein the second polarizer further comprises a fourteenth
mirror positioned to receive a tenth reflected radiation beam.
from the twelfth mirror, and wherein the fourteenth mirror is
positioned to reflect the tenth reflected radiation beam
incident on the fourteenth mirror as the fifth polarized
radiation beam.

22. An cllipsometer for investigating a sample, said
ellipsometer comprising:

aradiation source for generating a non-polarized radiation
beam;

‘a polarization state generator for modifying the non-
polarized radiation beam to a first polarized radiation
beam having a first phase retardance, wherein the
polarization state generator comprises:

a first mirror positioned to reflect the non-polarized
radiation beam incident on the first mirror as a first
reflected radiation beam;

a second mirror positioned to reflect the first reflected
radiation beam incident on the second mirror as a
second reflected radiation beam:

Jan. 11, 2024

a third mirror positioned to reflect the second reflected
radiation beam incident on the second mirror as a
third reflected radiation beam;

a fourth mirror positioned to reflect the third reflected
radiation beam incident on the third mirror as a
fourth reflected radiation beam; and
first rotating compensator for altering the fourth
reflected radiation beam to the first polarized radia-
tion beam having the first phase retardance, wherein
an optical axis of the first polarized radiation beam is
substantially aligned with the optical axis of the
non-polarized radiation beam, wherein the first com-
pensator is rotated about an axis substantially aligned
with the optical axis of the first polarized radiation
beam;

a sample holder for positioning a first surface of the
sample to receive the first polarized radiation beam
from the polarization state generator, wherein the first
surface of the sample reflects a second polarized radia-
tion;

a polarization analyzer comprising:

a second rotating compensator for altering the second
polarized radiation beam to a third polarized radia-
tion beam having a second phase retardance, wherein
an optical axis of the third polarized radiation beam
is substantially aligned with the optical axis of the
second polarized radiation beam, wherein the com-
pensator is rotated about an axis substantially aligned
with the optical axes of the second and the third
polarized radiation beams; and

a polarizer for modifying the third polarized radiation
beam to a fourth polarized radiation beam, wherein
an optical axis of the fourth polarized radiation beam

is substantially aligned with an optical axis of the

third polarized radiation beam;

a detector for measuring a plurality of first signals for a
plurality of first rotation angles of the polarization state
generator and a plurality of second signals for a plu-
rality of second rotation angles of the rotating compen-
sator; and

a processor for determining a Mueller matrix from the
plurality of the first rotation angles of the polarization
state generator and the plurality of the second rotation
angles of the rotating compensator.

23. The ellipsometer of claim 22, wherein the non-
polarized radiation beam has a wavelength in vacuum ultra-
violet region of an electromagnetic spectrum.

24. The ellipsometer of claim 22, wherein the non-
polarized radiation beam has a wavelength in extreme
ultraviolet region of an electromagnetic spectrum,

25. The ellipsometer of claim 22, wherein the first rotating
compensator comprises:

a fifth mirror positioned to reflect the fourth reflected
radiation beam incident on the fifth mirror as a fifth
reflected radiation beam, wherein the fifth reflected
radiation beam comprises a third phase retardance;
sixth mirror positioned to reflect the fifth reflected
radiation beam incident on the sixth mirror as a sixth
reflected radiation beam, wherein the fifth reflected
beam comprises a fourth phase retardance; and
a seventh mirror positioned to reflect the sixth reflected

radiation beam incident on the seventh mirror as the

first polarized radiation beam having the first phase
retardance.

»

ey


Patent Application Publication Jan. 11,2024 Sheet 4 of 10 US 2024/0011894 Al

116b

Figure 4



US 2024/0011894 Al

dance with an alternate embodiment of the present invention
for probing a sample artifact. Ellipsometer 1000 includes a
sample holder 1002, a radiation source 1004, polarization
state generator 1006, a polarization state analyzer 1008 and
a processor 1010 arranged ina manner as shown in FIG. 10.
Radiation source 1004 emits radiation beam 1004a that is
naturally polarized to polarization state generator 1006.
Polarization state generator 1006 includes a compensator
1012 positioned to receive radiation beam 1004a from
radiation source 1004 and reflect a radiation beam 1004d
having a phase retardance to sample artifact positioned on
sample holder 1002.

[0065] Compensator 1012 is similar to compensator 116,
as shown in FIGS. 1 and 4, and receives radiation beam
1004a from radiation source 1004. All other disclosed
‘embodiments of compensator 116 could also apply to com-
pensator 1012. Compensator 1012 includes mirrors 1012a,
10125, and 1012c, as shown in FIG. 10, positioned to
receive radiation beam 1004a from radiation source 1004
and redirect radiation beam 1004d reflected from mirrors
1012a-c along an optical axis that aligns with the optical axis
of radiation beam 1004a, as further shown in Figure Com-
pensator 1012 is capable of rotating about an axis that aligns
with the optical axes of radiation beams 1004a and 10044.
[0066] Radiation beam 1004d exiting compensator 1012 is
directed to sample artifact positioned on sample holder
1002. Sample holder 1002 is positioned such that radiation
beam 1004d exiting compensator 1012 is incident on a
surface of sample artifact. Sample holder 1002 can be
rotated such that radiation beam 1004d is incident on sample
artifact front surface at a predetermined incident angle. In
one embodiment, sample holder 1002 can be rotated azi-
muthally about its surface normal. Radiation beam 1004d
incident on sample artifact front surface is reflected as
radiation beam 1004e into polarization state analyzer 1008.
[0067] Polarization state analyzer 1008 includes a com-
pensator 1014, a polarizer 1016 and a detector 1018, and
rotates about an axis passing through the location where
radiation beam 1004d strikes the front surface of the sample
artifact positioned on sample holder 1002, as further shown.
in FIG. 10. Compensator 1014 is similar to compensator
116, as shown in FIGS. 1 and 4, and receives radiation beam
1004¢ reflected from sample artifact front surface. All other
disclosed embodiments of compensator 116 could also apply
to compensator 1014. Compensator 1014 includes mirrors
1014a, 1014, and 1014c, as shown in FIG. 10, positioned
to receive radiation beam 1004e reflected from sample
artifact front surface and redirect radiation beam 1004h
reflected from mirrors 1014a-c along an optical axis that
aligns with the optical axis of radiation beam 1004e, as
further shown in FIG. 10, Compensator 1014 is capable of
rotating about an axis that aligns with the optical axes of
radiation beams 1004e and 1004h. Radiation beam 1004h
from compensator 1014 is transmitted to polarizer 1016.
Polarizer 1016 is similar to polarizer 118, and is positioned
to reflect primarily s-polarized radiation beam 1004k to
detector 1018.

[0068] Detector 1018 is similar to detector 120, and is
positioned to detect s-polarized radiation beam 1004k
reflected by polarizer 1016, as further shown in FIG. 10.
Detector 1018 measures signals for N rotation angles of
compensator 1012 of polarization state generator 1006 and
M rotation angles of compensator 1014 of polarization state
analyzer 1008. Processor 1010 determines a MxN matrix

Jan. 11, 2024

corresponding to N rotation angles of compensator 1012 and
M rotation angles of compensator 1014. Processor 1010
further determines a Mueller matrix for reflection by sample
artifact as a function of the angle radiation beam 1004d
exiting compensator 1012 and incident upon sample artifact.
For anisotropic media or periodic nanostructures, it is also a
function of azimuthal rotation of sample artifact about its
surface normal.

[0069] It should be understood that arrangement of optical
elements in ellipsometers, as shown herein, are not exhaus-
tive and that other optical elements can be utilized as well
before, after, or between any of the illustrated optical
elements.
[0070] Ellipsometers in accordance with embodiments of
the present invention can operate at VUV and EUV wave-
lengths and enable measurements of the Mueller matrix
associated with the reflection of radiation in VUV and EUV
wavelengths, which can be used to determine optical con-
stants of materials, the thickness and optical constants of
thin films, and the dimensions (such as height, width, side
wall angle) of periodic microstructures. Ellipsometers in
accordance with embodiments of the present invention has
several advantages over previous ellipsometers. Scatterom-
etry, or the use of spectroscopic ellipsometry for the mea-
surement of the dimensions of nanopatterned structures, is a
critical process control technology used by the semiconduc-
tor industry. Ellipsometers in accordance with embodiments
of the present invention provide paths toward implementing
scatterometry in wavelengths shorter than about 150 nm,
and in particular, in the deep ultraviolet or extreme ultra-
violet spectral regions. Ellipsometers in accordance with
embodiments of the present invention can be used to char-
acterize high-quality multilayer optical systems to provide
complete knowledge of the polarization properties, such as
the change in phase at the interfaces of a multilayer, which
is necessary for the optical imaging in EUV-lithography and
currently is simulated from coating models. Mueller matrix
formalism can describe reflection from disordered materials,
such as patterns with roughness that cause depolarization.
As industrial processes become more complex, ellipsom-
eters in accordance with embodiments of the present inven-
tion operating at VUV or EUV wavelengths can be used to
improve the characterization of nanostructured materials
with roughness.

[0071]  Ellipsomet in accordance with one or more
embodiments of the present invention can be adapted to a
variety of configurations. It is thought that ellipsometers in
accordance with various embodiments of the present inven-
tion and many of its attendant advantages will be understood
from the foregoing description and it will be apparent that
various changes may be made without departing from the
spirit and scope of the invention or sacrificing all of its
material advantages, the form hereinbefore described being
merely a preferred or exemplary embodiment thereof.
[0072] Those familiar with the art will understand that
embodiments of the invention may be employed, for various
specific purposes. without departing from the essential sub-
stance thereof. The description of any one embodiment
given above is intended to illustrate an example rather than
to limit the invention. This above description is not intended
to indicate that any one embodiment is necessarily preferred
over any other one for all purposes, or to limit the scope of
the invention by describing any such embodiment, which
invention scope is intended to be determined by the claims,



US 2024/0011894 Al Jan. 11, 2024
16

41. The ellipsometer of claim 36, wherein the polarizer
further comprises a tenth mirror positioned to receive a
seventh reflected radiation beam from the ninth mirror, and
wherein the tenth mirror is positioned to reflect the seventh
reflected radiation beam incident on the tenth mirror as the
fifth polarized radiation beam.

ee eee


US 2024/0011894 Al
12

10. The ellipsometer of claim 6 or 7, wherein the fourth
plurality of mirrors further comprises a fourteenth mirror
positioned to receive one of the fourth polarized radiation
beam, the seventh reflected radiation beam and the eighth
reflected radiation beam, wherein the tenth, the eleventh, the
twelfth and the fourteenth mirrors modify the fourth polar-
ized radiation beam to the fifth polarized radiation beam.

AL. The ellipsometer of claim 1, wherein the first rotating
compensator is rotated about an axis substantially aligned
with the optical axes of the first and the second polarized
radiation beams, and wherein the second compensator is
rotated about an axis substantially aligned with the optical
axes of the third and the fourth polarized radiation beams.

12. The ellipsometer of claim 1, wherein the polarization
state analyzer is rotated about an axis passing through a
location the second polarized radiation beam is received on
the first surface of the sample positioned on the sample
holder, wherein the sample holder rotates the sample about
the axis passing through the location the second polarized
radiation beam is received on the first surface of the sample
positioned on the sample holder, wherein the rotation of the
sample is about one-half of the rotation of the polarization
state analyzer, and wherein the rotating the polarization state
analyzer adjusts an angle of incidence of the second polar-
ized radiation beam on the first surface of the sample
positioned on the sample holder and an angle of reflection of
the third polarized radiation beam.

13. The ellipsometer of claim 1, wherein the sample
holder rotates the sample in an azimuthal direction about an
axis normal to the first surface of the sample.

14. An cllipsometer for investigating a sample, said
ellipsometer comprising:

aradiation source for generating a non-polarized radiation
beam having a wavelength from about 10 nm to about
240 nm;

a first polarizer for modifying the non-polarized radiation
beam to a first polarized radiation beam, wherein an
optical axis of the first polarized radiation beam is
substantially aligned with an optical axis of the non-
polarized radiation beam, wherein the first polarizer
comprises:

a first mirror positioned to reflect the non-polarized
radiation beam incident on the first mirror as a first
reflected radiation beam;

a second mirror positioned to reflect the first reflected
radiation beam incident on the second mirror as a
second reflected radiation beam; and

a third mirror positioned to reflect the second reflected
radiation beam incident on the third mirror as the
first polarized radiation bean

a first rotating compensator for altering the first polarized
radiation beam to a second polarized radiation beam
having a first phase retardance, wherein an optical axis
of the second polarized radiation beam is substantially
aligned with the optical axis of the first polarized
radiation beam, wherein the first compensator is rotated
about an axis substantially aligned with the optical axes
of the first and the second polarized radiation beams,
wherein the first rotating compensator comprises:

a fourth mirror positioned to reflect the first polarized
radiation beam incident on the fourth mirror as a
third reflected radiation beam, wherein the third
reflected radiation beam comprises a second phase
retardance;

Jan. 11, 2024

a fifth mirror positioned to reflect the third reflected
radiation beam incident on the fifth mirror as a fourth
reflected radiation beam, wherein the fourth reflected
radiation beam comprises a third phase retardance;
and

s

sixth mirror positioned to reflect the fourth reflected

radiation beam incident on the sixth mirror as the

second polarized radiation beam having the first
phase retardance;

a sample holder for positioning a first surface of the
sample to receive the second polarized radiation beam
from the first rotating compensator, wherein the first
surface of the sample reflects a third polarized radiation
beam;

a second rotating compensator for altering the third polar-
ized radiation beam to a fourth polarized radiation
beam having a fourth phase retardance, wherein an
optical axis of the fourth polarized radiation beam is
substantially aligned with the optical axis of the third
polarized radiation beam, wherein the second compen-
sator is rotated about an axis substantially aligned with
the optical axes of the third and the fourth polarized
radiation beams, wherein the second compensator com-
prises:

a seventh mirror positioned to reflect the third polarized
radiation beam incident on the seventh mirror as a
fifth reflected radiation beam, wherein the fifth
reflected radiation beam comprises a fifth phase
retardance;

an eighth mirror positioned to reflect the fifth reflected

radiation beam incident on the eighth mirror as a

sixth reflected radiation beam, wherein the sixth

reflected beam comprises a sixth phase retardance;
and

ninth mirror positioned to reflect the sixth reflected

radiation beam incident on the ninth mirror as the

fourth polarized radiation beam having the fourth
phase retardance;

a second polarizer for modifying the fourth polarized
radiation beam to a fifth polarized radiation beam,
wherein an optical axis of the fifth polarized radiation
beam is substantially aligned with an optical axis of the
fourth polarized radiation beam, wherein the second
polarizer comprises
a tenth mirror positioned to reflect the fourth polarized

radiation beam incident on the tenth mirror as a

seventh reflected radiation beam;

2

an eleventh mirror positioned to reflect the seventh

reflected radiation beam incident on the eleventh

mirror as an eighth reflected radiation beam; and
twelfth mirror positioned to reflect the eighth
reflected radiation beam incident on the twelfth
mirror as the fifth polarized radiation beam;

a detector for measuring a plurality of first signals for a
plurality of first rotation angles of the first rotating
compensator and a plurality of second signals for a
plurality of second rotation angles of the second rotat-
ing compensator; and

»

processor for determining a Mueller matrix from the
plurality of the first rotation angles of the first rotating
compensator and the plurality of the second rotation
angles of the second rotating compensator.


US 2024/0011894 Al

azimuthally about its surface normal. Radiation beam 104g
incident on the front face of a sample artifact is reflected as
radiation beam 104h into polarization state analyzer 108.

[0042] Polarization state analyzer 108 includes a compen-
sator 116, a polarizer 118 and a detector 120, as shown in
FIGS. 1 and 4. Polarization state analyzer 108 rotates about
an axis passing through the location where radiation beam
114g strikes the front surface of the sample artifact posi-
tioned on sample holder 102 such that the angle of incidence
of radiation beam 104g on a front face of the sample artifact
varies with the rotation of polarization state analyzer 108. In
one embodiment, sample holder 102 is rotated about an axis
that aligns with the axis polarization state analyzer 108
rotates about the front surface of the sample artifact posi-
tioned on sample holder 102 and sample holder 102 is
rotated about half as fast as polarization state analyzer 108.
In another embodiment, sample holder 102 is rotated in an
azimuthal direction about its surface normal. In some
embodiments, sample holder 102 is tilted about an axis
parallel to its surface. Compensator 116 includes mirrors
116a, 1165, and 116c, as shown in FIG. 4, positioned to
receive radiation beam 104/ reflected from the front surface
of a sample artifact positioned on sample holder 102 and
introduces a relative phase delay between a pair of mutually
orthogonal polarized optical beam components of radiation
beam 104i. Mirrors 116a-c can be made from silicon, gold,
platinum, and the like. Ellipsometer 100 operating at the
shorter wavelengths, such as from about 10 nm to about 30
nm, may include mirrors 116a-c having multilayer stacks
applied to optimize the reflectance and phase change. Mir-
rors 116a-c are rigidly arranged in a housing such that the
optical axis of incoming radiation beam 104/ reflected from
the sample artifact front surface aligns with the optical axis
of radiation beam 104k exiting compensator 116. Mirror
116a is configured such that radiation beam 104A is incident
upon mirror 116q at an incident angle 65. Mirror 116q is
configured to reflect incident radiation beam 104h such that
radiation beam 104j reflected from mirror 116a is incident
upon mirror 1166 at an incident angle @,=20.-90°. Mirror
116¢ is configured to reflect incident radiation beam 104/
such that radiation beam 104j reflected from mirror 116d is
incident on mirror 116¢ at the incident angle 6. Mirror 116c
is configured to reflect incident radiation beam 104) such
that radiation beam 104k reflected from mirror 116 exits
compensator 116 as radiation beam 104k along an optical
axis that aligns with the optical axis of radiation beam 104h.
Any number of mirrors can be used in compensator 116 such
that the optical axis of an incoming radiation beam and that
of an outgoing radiation beam are aligned and unchanged. In
an alternate embodiment of the present invention, compen-
sator 116 includes four mirrors arranged in a manner as
shown in FIG. 5. Compensator 116 is capable of rotating at
an angular velocity about an axis that aligns with the optical
axes of radiation beams 104h and 104k. In some embodi-
ments of the present invention, compensator 116 is capable
of rotating in steps about an axis that aligns with the optical
axes of radiation beams 104h and 104k.

[0043] Radiation beam 104k from compensator 116 is
directed to polarizer 118 and polarizer 118 imparts diattenu-
ation and phase retardance to radiation beam 104k. In one
embodiment of the present invention, polarizer 118 includes
mirrors 118a, 1184, and 118c, as shown in FIG. 4, positioned
to receive radiation beam 1044 from compensator 116 to
apply diattenuation and phase retardance. Mirrors 118a-c are

Jan. 11, 2024

rigidly arranged in a housing such that the optical axis of
incoming radiation beam 104k received by polarizer 118
aligns with the optical axis of radiation beam 104n exiting
polarizer 118. Mirror 118a is configured such that radiation
beam 104k is incident upon mirror 1184 at an incident angle
6,. Mirror 118a is configured to reflect incident radiation
beam 104k such that radiation beam 104/ reflected from
mirror 18a is incident upon mirror 1184 at an incident angle
,=20,-90°. Mirror 118d is configured to reflect incident
radiation beam 104/ such that radiation beam 104m reflected
from mirror 118d is incident on mirror 118¢ at the incident
angle 6,. Mirror 118¢ is configured to reflect incident
radiation beam 104m such that radiation beam 104n
reflected from mirror 118c exits polarizer 118 as radiation
beam 1047 along an optical axis that aligns with the optical
axes of radiation beams 104/ and 104k. Mirrors 118a-c can
be made from silicon, gold, platinum, and the like. Ellip-
someter 100 operating at the shorter wavelengths, such as
from about 10 nm to about 30 nm, may include mirrors
118a-c having multilayer stacks applied to optimize the
reflectance and phase change.

[0044] Any number of mirrors can be used in polarizer 118
such that the optical axis of an incoming radiation beam and
that of an outgoing radiation beam are aligned and
unchanged. Figure illustrates an alternate polarizer 500 as
used in an ellipsometer in accordance with an embodiment
of the present invention. Polarizer 500 includes mirrors
500a, 5005, 500c, and 500d positioned to receive radiation
beam 104k from compensator 116. Mirrors 500a-d are
rigidly arranged in a housing such that the optical axis of
incoming radiation beam 104k received by polarizer 500
aligns with the optical axis of radiation beam 104o exiting
polarizer 500. Mirror 500a is configured such that radiation
beam 104k is incident upon mirror 500a. Mirror 500 is
configured to reflect incident radiation beam 104k such that
radiation beam 104/ reflected from mirror 500q is incident
upon mirror 5005. Mirror 5005 is configured to reflect
incident radiation beam 104/ such that radiation beam 104m
reflected from mirror 5006 is incident on mirror 500c.
Mirror 500c is configured to reflect incident radiation beam
104m such that radiation beam 104n reflected from mirror
500c is incident on mirror 500d. Mirror 500d is configured
to reflect incident radiation beam 104n such that radiation
beam 1040 reflected from mirror 500c exits polarizer 500 as
radiation beam 104o along an optical axis that aligns with
the optical axis of radiation beams 104h and 104k.

[0045] Fewer reflective elements in polarization state ana-
lyzer 108 may be used to reduce the losses incurred at each
mirror reflection. In some embodiments of the present
invention, polarizers 112 or 118 may be replaced with
Brewster mirrors. FIG. 6 illustrates a polarization state
analyzer 600 in accordance with an alternate embodiment of
the present invention, which includes a compensator 602,
Brewster mirror 604, and a detector 606. Compensator 602
is similar to compensator 116, as shown in FIGS. 1 and 4,
and receives radiation beam 104h reflected from sample
artifact front surface positioned on sample holder 102. All
other disclosed embodiments of compensator 116 could also
apply to compensator 602. Compensator 602 includes mir-
rors 602a, 6025, and 602c, as shown in FIG. 6, positioned
to receive radiation beam 104h reflected from sample arti-
fact 102 front surface and redirect as radiation beam 104k
along an optical axis that aligns with the optical axis of
radiation beam 104h after reflections from mirrors 602a-c,



Patent Application Publication Jan. 11,2024 Sheet 9 of 10 US 2024/0011894 Al

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Patent Application Publication Jan. 11,2024 Sheet 6 of 10 US 2024/0011894 Al

600 ~

Figure 6


Patent Application Publication Jan. 11,2024 Sheet 5 of 10 US 2024/0011894 Al

500

104k

500d \ 500a

Figure 5


US 2024/0011894 Al

as further shown in FIG. 6. Compensator 602 is capable of
rotating about an axis that aligns with the optical axes of
radiation beams 104h and 104k. Radiation beam 104k from
compensator 602 is transmitted to Brewster mirror 604 and
Brewster mirror 604 reflects primarily s-polarized radiation
beam 104/ to detector 606. Brewster mirror 604 can be made
from silicon, gold, platinum, and the like. Ellipsometer 100
operating at the shorter wavelengths, such as from about 10
nm to about 30 nm, may include mirrors 604 having
multilayer stacks applied to optimize the reflectance.
[0046] Referring back to FIGS. 1 and 4, detector 120 is
positioned along an axis that aligns with the optical axes of
radiation beams 104h, 104k and 104n, as further shown in
FIG. 1, to detect radiation beam 104n exiting polarizer 118.
Detector 120 measures signals for N rotation angles of
compensator 114 of polarization state generator 106 and M
rotation angles of compensator 116 of polarization state
analyzer 108. Processor 110 determines a MxN matrix
corresponding to N rotation angles of compensator 114 and
M rotation angles of compensator 116. Processor 110 further
determines a Mueller matrix for reflection by sample artifact
102 using Equation (6) provided below. The Mueller matrix
is a function of the angle of radiation beam 104g exiting
compensator 114 and incident upon a front surface of a
sample artifact positioned on sample holder 102. For aniso-
tropic media or periodic nanostructures, the Mueller matrix
is also a function of azimuthal rotation of sample artifact
about its surface normal.

[0047] Optical reflection from an isotropic medium can be
described by two complex-valued, wavelength-dependent
coeflicients r, and r,, that represent the ratios of the electric
field amplitudes upon reflection for s and p polarized light,
respectively. Here, s polarization refers to optical radiation
with an electric field perpendicular to the plane of incidence,
p polarization refers to optical radiation with an electric field
parallel to the plane of incidence. Coefficients r, and r,, can
be determined from Fresnel’s equations for any incident
angle @ for materials whose complex-valued indices of
refraction fi=n+ik are known, where n and K are referred to
as optical constants:

1/2 cy)

cos@ - (a? — sin’)

cos + (a? - sin?)

2

3 —

HP cost + (9? — sin?)

[0048] The square of the complex-valued index of refrac-
tion is referred to as the dielectric function. Other expres-
sions for the coefficients r, and r, can be used when the
material has multiple interfaces, such as with thin films, or
when the indices are graded.

[0049] Quantities that describe optical radiation intensity
can be represented polarimetrically by a Stokes vector,

(<P) + (Ep?) 8)
(EP) - (EP)

(2Re[ 4%)

ime.)

Jan. 11, 2024

(0050] where E, and E,, represent the s and p components
of the electric field, respectively. The first component rep-
resents the total intensity, the second and third components
represent linear polarization, and the fourth component
represents circular polarization. Reflection from a surface
can be represented by a Mueller matrix, representing the
linear relationship between the incoming and outgoing
Stokes vectors, which for a surface having reflection coef-
ficients r, and r,, is

(nP-IrPV2 0 0 co)
(ee + rpP V2 0 0

0 (Relrsr5)) (lim(rsr5))
0 o =(Imfrsr3)) (Re(r.r))

[0051] For anisotropic materials and for periodic struc-
tures, the Mueller matrix has fewer elements that are zero
than those shown in Equation (2). For a single interface
between vacuum and a material having a complex-valued
index of refraction Ai, the reflection coefficients are given by
Equations (1) and (2) above.

[0052] Ellipsometer 100 operates by impinging a series of
Stokes vectors generated by polarization state generator 106
onto the unknown sample under test and sensing the
reflected light with a series of Stokes vector sensitivities
analyzed by polarization state analyzer 108. The measure-
ment matrix can be represented by

P=AMW 6)

[0053] where W is a 4xN matrix whose rows include the
N Stokes vectors applied to the sample and A is a Mx4
matrix whose columns include the M Stokes vector sensi-
tivities. P is a MXN matrix that contains the measurements
for each combination of incident and sensed polarization.
The unknown sample matrix M can then be determined from

M=A"'PW"! ©

[0054] A~! and W~' can be determined from A and W in
Equation (5) provided A and W are well-conditioned. As
used herein, the term “well-conditioned” refers to a matrix
having a condition number not substantially larger than Y3
and that the inverse of such matrix can be calculated with
reasonable accuracy. The condition number is defined as the
ratio of maximum singular value to the minimum singular
value in a singular value decomposition and provides a
metric for a Stokes polarimeter’s behavior. A preferred
polarimeter has a condition number of V3.

(0055] FIG. 7 shows an exemplary plot for calculated
condition number for polarizer 112 shown in FIG. 1,
wherein each of mirrors 112a-c and 114a-c are platinum
mirrors and positioned with @,=67.5 deg. (such that 0,=45
deg.), 6,=82 deg. (such that 6,=74 deg.), and compensator
114 is rotated from 0 deg. (where the planes of incidence of
all six reflections coincide) to 157.5 deg. with increments of
5 deg. The condition number for this configuration of
platinum mirrors is less than 10 for wavelengths longer than
36 nm. Other mirror materials, or combinations of different
materials for each mirror, used with varying angles 6, and 0,
(and thus, 8, and @,) can yield different condition numbers
and improved condition numbers or increase the throughput
of polarization state generator 106.



US 2024/0011894 Al

Jan. 11,2024 Sheet 8 of 10

Patent Application Publication

g ons



US 2024/0011894 Al

26. The ellipsometer of claim 22, wherein the second
rotating compensator comprises:

a fifth mirror positioned to reflect the second polarized
radiation beam incident on the fifth mirror as a fifth
reflected radiation beam, wherein the fifth reflected
radiation beam comprises a third phase retardance:
sixth mirror positioned to reflect the fifth reflected
radiation beam incident on the sixth mirror as a sixth
reflected radiation beam, wherein the sixth reflected
beam comprises a fourth phase retardance; and

a seventh mirror positioned to reflect the sixth reflected
radiation beam incident on the seventh mirror as the
third polarized radiation beam having the second phase
retardance.

27. The ellipsometer of claim 22, wherein the polarizer

comprises

a fifth mirror positioned to reflect the third polarized
radiation beam incident on the fifth mirror as a fifth
reflected radiation beam;

a sixth mirror positioned to reflect the fifth reflected
radiation beam incident on the sixth mirror as a sixth
reflected radiation beam; and

a seventh mirror positioned to reflect the sixth reflected
radiation beam incident on the seventh mirror as the
fourth polarized radiation beam.

28. The ellipsometer of claim 22, wherein the polarizer

comprises

a fifth mirror positioned to reflect the third polarized
radiation beam incident on the fifth mirror as a fifth
reflected radiation beam;
sixth mirror positioned to reflect the fifth reflected
radiation beam incident on the sixth mirror as a sixth
reflected radiation beam; and

a seventh mirror positioned to reflect the sixth reflected
radiation beam incident on the seventh mirror as a
seventh reflected radiation beam; and

an eighth mirror positioned to receive the seventh
reflected radiation beam incident on the eighth mirror
as the fourth polarized radiation beam.

29. The ellipsometer of claim 22, wherein the polarization
state analyzer is rotated about an axis passing through a
location the second polarized radiation beam is received on
the first surface of the sample positioned on the sample
holder, wherein the sample holder rotates the sample about
the axis passing through the location the second polarized
radiation beam is received on the first surface of the sample
positioned on the sample holder, wherein the rotation of the
sample is about one-half of the rotation of the polarization
state analyzer, and wherein the rotating the polarization state
analyzer adjusts an angle of incidence of the second polar-
ized radiation beam on the first surface of the sample
positioned on the sample holder and an angle of reflection of
the third polarized radiation beam.

30. The ellipsometer of claim 22, wherein the sample
holder rotates the sample in an azimuthal direction about an
axis normal to the first surface of the sample.

31. An ellipsometer for investigating a sample, said
ellipsometer comprising:

aradiation source for generating a non-polarized radiation
beam;

a polarization state generator comprising:

a first Brewster mirror for modifying the non-polarized
radiation beam to a first polarized radiation beam,

»

2

14

Jan. 11, 2024

wherein the first polarized radiation beam comprises
a first parallel optical component and a first orthogo-
nal optical component;

a first rotating compensator comprising a first plurality
of mirrors for altering the first polarized radiation
beam to a second polarized radiation beam having a
first phase retardance, wherein an optical axis of the
second polarized radiation beam is substantially
aligned with an optical axis of the first polarized
radiation beam, wherein the first rotating compen:
tor is rotated about an axis substantially aligned with
the optical axes of the first and the second polarized
radiation beams;

a sample holder for positioning a first surface of the
sample to receive the second polarized radiation beam
from the first rotating compensator, wherein the first
surface of the sample reflects a third polarized radiation
beam;

a polarization analyzer comprising:

a second rotating compensator comprising a second
plurality of mirrors for altering the third polarized
radiation beam to a fourth polarized radiation beam
having a second phase retardance, wherein an optical
axis of the fourth polarized radiation beam is sub-
stantially aligned with an optical axis of the third
polarized radiation beam, wherein the second com-
pensator is rotated about an axis substantially aligned

axes of the third and the fourth

polarized radiation beams; and

a second Brewster mirror for modifying the fourth
polarized radiation beam to a fifth polarized radiation
beam, wherein the fifth polarized radiation beam
comprises a second parallel optical component and a
second orthogonal optical component, wherein an
optical axis of the fifth polarized radiation beam is
substantially aligned with the optical axis of the
fourth polarized radiation beam,

wherein the polarization state analyzer is rotated about
an axis passing through a location the second polar-
ized radiation beam is received on the first surface of
the sample positioned on the sample holder, wherein
the sample holder rotates the sample about the axis
passing through the location the second polarized
radiation beam is received on the first surface of the
sample positioned on the sample holder, wherein the
rotation of the sample is about one-half of the
rotation of the polarization state analyzer, and
wherein the rotating the polarization state analyzer
adjusts an angle of incidence of the second polarized
radiation beam on the first surface of the sample
positioned on the sample holder and an angle of
reflection of the third polarized radiation beam;

a detector for measuring a plurality of first signals for a

plurality of first rotation angles of the first rotating

compensator and a plurality of second signals for a

plurality of second rotation angles of the second rotat-

ing compensator; and

processor for determining a Mueller matrix from the

plurality of the first rotation angles of the first rotating

compensator and the plurality of the second rotation
angles of the second rotating compensator.

32. The ellipsometer of claim 31, wherein the non-

polarized radiation beam has a wavelength in vacuum ultra-

violet region of an electromagnetic spectrum.

»



as) United States

0240011894A1

a2) Patent Application Publication co) Pub. No.: US 2024/0011894 Al

Germer

(43) Pub. Date: Jan. 11, 2024

(54) MUELLER MATRIX ELLIPSOMETER

(71) Applicant: Government of the United States of
America, as represented by the
Secretary of Commerce, Gaithersburg,
MD (US)

(72) Inventor: Thomas Avery Germer, Montgomery
Village, MD (US)

(21) Appl. No.: 18/218,692

(22) Filed: Jul. 6, 2023

Related U.S. Application Data

(60) Provisional application No. 63/358,717, filed on Jul.

6, 2022.

Publication Classification

(51) Int. Cl.

GOIN 21/21 (2006.01)

(52) U.S. CL
CPC ..... GOIN 21/211 (2013.01); GOIN 202.
(2013.01); GOIN 2021/214 (2013.01):
2201/126 (2013.01)

(57) ABSTRACT

Embodiments of the present invention relate to an ellipsom-
eter that includes a combination of a plurality of reflective
devices to measure a Mueller matrix reflectance of a mate-
rial in the VUV and EUV region. Ellipsometer in accordance
with embodiments of the present invention relate to an
ellipsometer that includes a multi-mirror polarization state
generator combined with a multi-mirror polarization state
analyzer and a detector to realize a Mueller matrix ellip-
someter. Embodiments of the present invention utilize two
rotating assemblies with each assembly including multiple
mirrors that combine to act as amplitude and phase retarders.

oN

114

\ 104d a



US 2024/0011894 Al

MUELLER MATRIX ELLIPSOMETER

CROSS-REFERENCE TO RELATED,
APPLICATION

[0001] | This application claims the benefit of priority from
US. Provisional Patent Application Ser. No. 63/358,717,
filed on Jul. 6, 2022, the disclosure of which is incorporated
herein by reference in its entirety.

STATEMENT REGARDING FEDERAL RIGHTS,

[0002] The invention described herein was made with
United States Government support from the National Insti-
tute of Standards and Technology (NIST), an agency of the
United States Department of Commerce. The United States
Government has certain rights in the invention.

FIELD OF THE INVENTION

[0003] The present invention relates generally to optical
analyzers, and more particularly toa Mueller matrix ellip-
someter.

BACKGROUND OF THE INVENTION

[0004] Spectroscopic ellipsometry is a measurement tech-
nique often used for measuring the dielectric function of
materials, the thicknesses and dielectric functions of films,
and/or the dimensions and dielectric functions of complex
periodic structures. This technique measures the change in
polarization state of optical radiation upon reflection from
the sample as a function of the wavelength of the optical
radiation, and dielectric functions and dimensions are
inferred from the measurement data through inverse elec-
tromagnetic modeling. Spectroscopic ellipsometry can also
be used to determine the dimensions and dielectric functions
ina period structure, and such applications are often referred
to as scatterometry or optical critical dimension metrology.
[0005] Ellipsometry requires control of the polarization of
the incident radiation and analysis of the polarization of the
reflected radiation. While measurements from isotropic
materials and thin films only require a subspace of incident
and analyzed polarization states, measurements from aniso-
tropic materials and structures benefit from a full spanning
of incident and analyzed polarization states, in what is
referred to as Mueller matrix ellipsometry. Typical polariza-
tion control and/or analysis is performed using optical
devices that act either as polarizers or as phase retarders. A
preferred polarizer exhibits a diattenuation, such that one
polarization is transmitted or reflected with little attenuation
while the orthogonal polarization is attenuated. A preferred
phase retarder, often referred to as a wave plate or a
compensator, is a device that alters the phase of one polar-
ization with respect to its orthogonal polarization but with-
out changing its amplitude. These devices can be combined
to perform polarization control and analysis. If a source
generating unpolarized radiation is followed first by a fixed
polarizer and then by a rotating phase retarder, the exiting
radiation will include polarization spanning all degrees of
freedom. Similarly, in reverse, complete polarization analy-
sis of radiation can be performed by passing the radiation
first through a rotating phase retarder then through a fixed
polarizer before striking a detector. A complete analysis of
the reflection properties of a sample (what is known as the

Jan. 11, 2024

Mueller matrix) can be achieved using a complete polariza-
tion state generator together with a complete polarization
state analyzer.

[0006] Ellipsometers have been constructed for operation
in the terahertz, infrared, visible, and ultraviolet spectral
regions, having a minimum wavelength of about 140 nm.
Extending such devices into the vacuum ultraviolet (VUV)
and extreme ultraviolet (EUV) regions of the electromag-
netic spectrum have been impeded because nearly all mate-
rials are opaque in these regions. Therefore, these devices
will need to rely upon reflection from surfaces instead of
transmission through materials. While a reasonable polarizer
may be possible for this purpose, constructing an ideal phase
retarder is difficult because reflection from a surface gener-
ally yields both diattenuation and retardance of the two
natural polarization states with respect to each other. This
difficulty increases with the need for an ideal phase retarder
over a broad spectral range.

[0007] Accordingly, there is a need for an ellipsometer
having polarization state analyzer and polarization state
generator capable of operating in the VUV and EUV regions
of the electromagnetic spectrum to determine a Mueller
matrix reflectance of a material.

SUMMARY OF THE INVENTION

[0008] Embodiments of the present invention relate to an
ellipsometer that includes a combination of a plurality of
reflective devices to measure a Mueller matrix reflectance of
a material in the VUV and EUV region. Embodiments of the
present invention relate to an ellipsometer that includes a
multi-mirror polarization state generator combined with a
multi-mirror polarization state analyzer and a detector to
realize a Mueller matrix ellipsometer.

[0009] Embodiments of the present invention also relate to
an ellipsometer for investigating a sample, said ellipsometer
including a radiation source for generating a non-polarized
radiation beam; a polarization state generator including a
first polarizer comprising a first plurality of mirrors posi-
tioned to modify the non-polarized radiation beam to a first
polarized radiation beam, wherein an optical axis of the first
polarized radiation beam is substantially aligned with an
optical axis of the non-polarized radiation beam; and a first
rotating compensator comprising a second plurality of mir-
rors for altering the first polarized radiation beam to a second
polarized radiation beam having a first phase retardance,
wherein an optical axis of the second polarized radiation
beam is substantially aligned with the optical axis of the first
polarized radiation beam: a sample holder for positioning a
first surface of the sample to receive the second polarized
radiation beam from the first rotating compensator, wherein
the first surface of the sample reflects a third polarized
radiation beam; a polarization state analyzer including a
second rotating compensator comprising a third plurality of
mirrors for altering the third polarized radiation beam to a
fourth polarized radiation beam having a second phase
retardance, wherein an optical axis of the fourth polarized
radiation beam is substantially aligned with the optical axis
of the third polarized radiation beam; and a second polarizer
comprising a fourth plurality of mirrors for modifying the
fourth polarized radiation beam to a fifth polarized radiation
beam, wherein an optical axis of the fifth polarized radiation,
beam is substantially aligned with an optical axis of the
fourth polarized radiation beam; a detector for measuring a
plurality of first signals for a plurality of first rotation angles



US 2024/0011894 Al

Jan. 11,2024 Sheet 10 of 10

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US 2024/0011894 Al

properly construed, including all subject matter encom-
passed by the doctrine of equivalents as properly applied to
the claims.

What is claimed is:

1. An ellipsometer for investigating a sample, said ellip-
someter comprising:

aradiation source for generating a non-polarized radiation
beam;

a polarization state generator comprising:

a first polarizer comprising a first plurality of mirrors
positioned to modify the non-polarized radiation
beam to a first polarized radiation beam, wherein an
optical axis of the first polarized radiation beam is
substantially aligned with an optical axis of the
non-polarized radiation beam; and
first rotating compensator comprising a second plu-
rality of mirrors for altering the first polarized radia-
tion beam to a second polarized radiation beam
having a first phase retardance, wherein an optical
axis of the second polarized radiation beam is sub-
stantially aligned with the optical axis of the first
polarized radiation beam;
sample holder for positioning a first surface of the
sample to receive the second polarized radiation beam
from the first rotating compensator, wherein the first
surface of the sample reflects a third polarized radiation
beam;

a polarization state analyzer comprising:

second rotating compensator comprising a third plu-
rality of mirrors for altering the third polarized
radiation beam to a fourth polarized radiation beam
having a second phase retardance, wherein an optical
axis of the fourth polarized radiation beam is sub-
stantially aligned with the optical axis of the third
polarized radiation beam; and

second polarizer comprising a fourth plurality of
mirrors for modifying the fourth polarized radiation
beam to a fifth polarized radiation beam, wherein an
optical axis of the fifth polarized radiation beam is
substantially aligned with an optical axis of the
fourth polarized radiation beam;

a detector for measuring a plurality of first signals for a
plurality of first rotation angles of the first rotating
compensator and a plurality of second signals for a
plurality of second rotation angles of the second rotat-
ing compensator; and

‘a processor for determining a Mueller matrix from the
plurality of the first rotation angles of the first rotating
compensator and the plurality of the second rotation
angles of the second rotating compensator.

2. The ellipsometer of claim 1, wherein the non-polarized
radiation beam has a wavelength in vacuum ultraviolet
region of an electromagnetic spectrum.

3. The ellipsometer of claim 1, wherein the non-polarized
radiation beam has a wavelength in extreme ultraviolet
region of an electromagnetic spectrum.

4. The ellipsometer of claim 1, wherein at least one of the
first polarizer, the second polarizer, the first compensator
and the second compensator comprise three mirrors

5. The ellipsometer of claim 1, wherein at least one of the
first polarizer, the second polarizer, the first compensator
and the second compensator comprise four mirrors.

6. The ellipsometer of claim 1, wherein the first plurality
of mirrors comprise:

»

»

s

»

11

Jan. 11, 2024

a first mirror positioned to reflect the non-polarized radia-
tion beam incident on the first mirror as a first reflected
radiation beam;

a second mirror positioned to reflect the first reflected
radiation beam incident on the second mirror as a
second reflected radiation beam; and

a third mirror positioned to reflect the second reflected
radiation beam incident on the third mirror as the first
polarized radiation beam;

wherein the second plurality of mirrors comprise:

a fourth mirror positioned to reflect the first polarized
radiation beam incident on the fourth mirror as a
third reflected radiation beam;

a fifth mirror positioned to reflect the third reflected
radiation beam incident on the fifth mirror as a fourth
reflected radiation beam; and

a sixth mirror positioned to reflect the fourth reflected
radiation beam incident on the sixth mirror as the
second polarized radiation beam having the first
phase retardance;

wherein the third plurality of mirrors comprise:

a seventh mirror positioned to reflect the third polarized
radiation beam incident on the seventh mirror as fifth
reflected radiation beam;

an eighth mirror positioned to reflect the fifth reflected
radiation beam incident on the eighth mirror as a
sixth reflected radiation beam; and

a ninth mirror positioned to reflect the sixth reflected
radiation beam incident on the ninth mirror as the
fourth polarized radiation beam having the second
phase retardance; and

wherein the fourth plurality of mirrors comprise:

a tenth mirror positioned to reflect the fourth polarized
radiation beam incident on the tenth mirror as a
seventh reflected radiation beam;

an eleventh mirror positioned to reflect the seventh
reflected radiation beam incident on the eleventh
mirror as an eighth reflected radiation beam; and

a twelfth mirror positioned to reflect the eighth
reflected radiation beam incident on the twelfth
mirror as the fourth polarized radiation beam.

7. The ellipsometer of claim 6, wherein the first plurality
of mirrors further comprises a thirteenth mirror positioned to
receive one of the non-polarized radiation beam, the first
reflected radiation beam and the second reflected radiation
beam, wherein the first, the second, the third and the
thirteenth mirrors modify the non-polarized radiation beam
to the first polarized radiation beam.

8. The ellipsometer of claim 6 or 7, wherein the second
plurality of mirrors further comprises a fourteenth mirror
positioned to receive one of the first polarized radiation
beam, the third reflected radiation beam and the fourth
reflected radiation beam, wherein the fourth, the fifth, the
sixth and the fourteenth mirrors alter the first polarized
radiation beam to the second polarized radiation beam
having the first phase retardance.

9. The ellipsometer of claim 6 or 7, wherein the third
plurality of mirrors further comprises a fourteenth mirror
positioned to receive one of the third polarized radiation
beam, the fifth reflected radiation beam and the sixth
reflected radiation beam, wherein the seventh, the eighth, the
ninth and the fourteenth mirrors alter the third polarized
radiation beam to the fourth polarized radiation beam having
the second phase retardance.


Patent Application Publication Jan. 11,2024 Sheet 3 of 10 US 2024/0011894 Al

300

104a

Figure 3


US 2024/0011894 Al

dance; a sixth mirror positioned to reflect the fifth reflected
radiation beam incident on the sixth mirror as a sixth
reflected radiation beam, wherein the fifth reflected beam
comprises a fourth phase retardance; and a seventh mirror
positioned to reflect the sixth reflected radiation beam inci-
dent on the seventh mirror as the first polarized radiation
beam having the first phase retardance.

[0019] In one embodiment of the present invention, the
second rotating compensator includes a fifth mirror pos’
tioned to reflect the second polarized radiation beam inci-
dent on the fifth mirror as a fifth reflected radiation beam,
wherein the fifth reflected radiation beam comprises a third
phase retardance; a sixth mirror positioned to reflect the fifth
reflected radiation beam incident on the sixth mirror as a
sixth reflected radiation beam, wherein the sixth reflected
beam comprises a fourth phase retardance; and a seventh
mirror positioned to reflect the sixth reflected radiation beam
incident on the seventh mirror as the third polarized radia-
tion beam having the second phase retardance.

[0020] In one embodiment of the present invention, the
polarizer includes a fifth mirror positioned to reflect the third
polarized radiation beam incident on the fifth mirror as a
fifth reflected radiation beam; a sixth mirror positioned to
reflect the fifth reflected radiation beam incident on the sixth
mirror as a sixth reflected radiation beam; and a seventh
mirror positioned to reflect the sixth reflected radiation beam.
incident on the seventh mirror as the fourth polarized
radiation beam. In another embodiment of the present inven-
tion, the polarizer includes a fifth mirror positioned to reflect
the third polarized radiation beam incident on the fifth
mirror as a fifth reflected radiation beam; a sixth mirror
positioned to reflect the fifth reflected radiation beam inci-
dent on the sixth mirror as a sixth reflected radiation beam;
and a seventh mirror positioned to reflect the sixth reflected
radiation beam incident on the seventh mirror as a seventh
reflected radiation beam; and an eighth mirror positioned to
receive the seventh reflected radiation beam incident on the
eighth mirror as the fourth polarized radiation beam.
[0021] Embodiments of the present invention also relate to
an ellipsometer for investigating a sample, said ellipsometer
including a radiation source for generating a non-polarized
radiation beam; a polarization state generator including: a
first Brewster mirror for modifying the non-polarized radia-
tion beam to a first polarized radiation beam, wherein the
first polarized radiation beam comprises a first parallel
optical component and a first orthogonal optical component:
a first rotating compensator comprising a first plurality of
mirrors for altering the first polarized radiation beam to a
second polarized radiation beam having a first phase retar-
dance, wherein an optical axis of the second polarized
radiation beam is substantially aligned with an optical axis
of the first polarized radiation beam, wherein the first
rotating compensator is rotated about an axis substantially
aligned with the optical axes of the first and the second
polarized radiation beams; a sample holder for positioning a
first surface of the sample to receive the second polarized
radiation beam from the first rotating compensator, wherein
the first surface of the sample reflects a third polarized
radiation beam; a polarization analyzer including: a second
rotating compensator comprising a second plurality of mir-
rors for altering the third polarized radiation beam to a fourth
polarized radiation beam having a second phase retardance,
wherein an optical axis of the fourth polarized radiation
beam is substantially aligned with an optical axis of the third

Jan. 11, 2024

polarized radiation beam, wherein the second compensator
is rotated about an axis substantially aligned with the optical
axes of the third and the fourth polarized radiation beams;
and a second Brewster mirror for modifying the fourth
polarized radiation beam to a fifth polarized radiation beam,
wherein the fifth polarized radiation beam comprises a
second parallel optical component and a second orthogonal
optical component, wherein an optical axis of the fifth
polarized radiation beam is substantially aligned with the
optical axis of the fourth polarized radiation beam, wherein
the polarization state analyzer is rotated about an axis
passing through a location the second polarized radiation
beam is received on the first surface of the sample positioned
‘on the sample holder, wherein the sample holder rotates the
sample about the axis passing through the location the
second polarized radiation beam is received on the first
surface of the sample positioned on the sample holder,
wherein the rotation of the sample is about one-half of the
rotation of the polarization state analyzer, and wherein the
rotating the polarization state analyzer adjusts an angle of
incidence of the second polarized radiation beam on the first
surface of the sample positioned on the sample holder and an
angle of reflection of the third polarized radiation beam; a
detector for measuring a plurality of first signals for a
plurality of first rotation angles of the first rotating compen-
sator and a plurality of second signals for a plurality of
second rotation angles of the second rotating compensator;
and a processor for determining a Mueller matrix from the
plurality of the first rotation angles of the first rotating
compensator and the plurality of the second rotation angles
of the second rotating compensator.

[0022] In some embodiments of the present invention, the
first plurality of mirrors includes a first mirror positioned to
reflect the non-polarized radiation beam incident on the first
mirror as a first reflected radiation beam; a second mirror
positioned to reflect the first reflected radiation beam inci-
dent on the second mirror as a second reflected radiation
beam; and a third mirror positioned to reflect the second
reflected radiation beam incident on the third mirror as the
first polarized radiation beam having the first phase retar-
dance. In other embodiments of the present invention, the
second plurality of mirrors includes a fourth mirror posi-
tioned to reflect the first polarized radiation beam incident
on the fourth mirror as a third reflected radiation beam; a
fifth mirror positioned to reflect the third reflected radiation
beam incident on the fifth mirror as a fourth reflected
radiation beam; and a sixth mirror positioned to reflect the
fourth reflected radiation beam incident on the sixth mirror
as the second polarized radiation beam having the second
phase retardance.

[0023] Another embodiment of the present invention
relates to an ellipsometer for investigating a sample, said
ellipsometer including a radiation source for generating a
first polarized radiation beam having a wavelength from
about 10 nm to about 240 nm in an electromagnetic spec-
trum; a first rotating compensator for altering the first
polarized radiation beam to a second polarized radiation
beam, wherein an optical axis of the second polarized
radiation beam is substantially aligned with the optical axis
of the first polarized radiation beam, wherein the first
compensator is rotated about an axis substantially aligned
with the optical axes of the first and the second polarized.
radiation beams, wherein the first rotating compensator
comprises: a first mirror positioned to reflect the first polar-



US 2024/0011894 Al

or extreme ultraviolet region of the electromagnetic spec-
trum. In one embodiment of the present invention, radiation
source 104 emits radiation beam 104q in the vacuum ultra-
violet region over a predetermined wavelength range of
from about 30 nm to about 240 nm. In another embodiment
of the present invention, radiation source 104 emits radiation
beam 104a in the extreme ultraviolet region over a prede-
termined wavelength range of from about 10 nm to about 30
nm,

[0038] Radiation beam 104a from radiation source 104 is
transmitted to polarization state generator 106, which
imparts a known polarization state to radiation beam 104a.
Polarization state generator 106 includes a polarizer 112 and
‘a rotating compensator 114. In one embodiment of the
present invention, polarizer 112 includes mirrors 112a, 1126,
and 112c, as shown in FIG. 2, positioned to receive radiation
beam 104a from radiation source 104 and change non-
polarized radiation beam 104q into linearly polarized radia-
tion beam 104d by diattenuation of non-polarized radiation
beam 104a. Diattenuation of non-polarized radiation beam.
104q is performed by taking advantage of a difference in
reflectance between s-polarized radiation beam and p-polar-
ized radiation beam and splitting the polarized light into two
mutually orthogonal components that are attenuated at dif-
ferent rates. Mirrors 112a-c can be made from silicon, gold,
platinum, and the like. Ellipsometer 100 operating at the
shorter wavelengths, such as from about 10 nm to about 30
nm, may include mirrors 112a-c having multilayer stacks
applied to optimize the reflectance and phase change. Mir-
rors 112a-c are rigidly arranged in a housing such that the
optical axis of incoming radiation beam 104a received by
polarizer 112 aligns with the optical axis of radiation beam
104d exiting polarizer 112. Mirror 112a is configured such
that radiation beam 104a is incident upon mirror 112q at an
incident angle 6,. Mirror 112a is configured to reflect
incident radiation beam 104a such that radiation beam 1046
reflected from mirror 112d is incident upon mirror 1126 at an
incident angle 6,=26,-90°. Mirror 1126 is configured to
reflect incident radiation beam 1046 such that radiation
beam 104c reflected from mirror 1126 is incident on mirror
112c at the incident angle 6,. In one embodiment of the
present invention, 6, is about 80 deg. and 6, is about 70 deg.
Mirror 112c is configured to reflect incident radiation beam
104c such that radiation beam 104d reflected from mirror
112c exits polarizer 112 as radiation beam 104d along an
optical axis that aligns with the optical axis of radiation
beam 104a.

[0039] Any number of mirrors can be used in polarizer 112
such that the optical axis of an incoming radiation beam and
that of an outgoing radiation beam are aligned and
unchanged. FIG. 3 illustrates an alternate polarizer 300 as
used in an ellipsometer in accordance with an embodiment
of the present invention. Polarizer 300 includes mirrors
3002, 3006, 300c, and 300d positioned to receive radiation
beam 104a from radiation source 104 and change non-
polarized radiation beam 104a into linearly polarized radia-
tion beam 104e by taking advantage of a difference in
reflectance and phase between s-polarized radiation beam
and p-polarized radiation beam. Mirrors 300a-d are rigidly
arranged in a housing such that the optical axis of incoming
radiation beam 104a received by polarizer 300 aligns with
the optical axis of radiation beam 104e exiting polarizer 300.
Mirror 300q is configured such that radiation beam 104a is
incident upon mirror 300q at an incident angle 6,. Mirror

Jan. 11, 2024

300q is configured to reflect incident radiation beam 104a
such that radiation beam 1046 reflected from mirror 300a is
incident upon mirror 3006. Mirror 3004 is configured to
reflect incident radiation beam 1046 such that radiation
beam 104c reflected from mirror 3006 is incident on mirror
300c. Mirror 300c is configured to reflect incident radiation
beam 104c such that radiation beam 104d reflected from
mirror 300c is incident on mirror 300d. Mirror 300d is
configured to reflect incident radiation beam 104d such that
radiation beam 104e reflected from mirror 300c exits polar-
izer 300 as radiation beam 104e along an optical axis that
aligns with the optical axis of radiation beam 104a.

[0040] Referring back to FIGS. 1 and 2, compensator 114
receives radiation beam 104d exiting polarizer 112. Com-
pensator 114 includes mirrors 114a, 114, and Ide, as
shown in FIG. 2, positioned to receive radiation beam 104d
exiting polarizer 112 and introduces a relative phase delay
(phase retardation) between a pair of mutually orthogonal
polarized optical beam components of radiation beam 104d.
Mirrors 114a-c can be made from silicon, gold, platinum,
and the like. Ellipsometer 100 operating at the shorter
wavelengths, such as from about 10 nm to about 30 nm, may
include mirrors 114a-c having multilayer stacks applied to
optimize the reflectance and phase change. Mirrors 114a-c
are rigidly arranged in a housing such that the optical axis of
incoming radiation beam 104d received from polarizer 112
aligns with the optical axis of radiation beam 104g exiting
compensator 114. Mirror 114a is configured such that radia-
tion beam 104d is incident upon mirror 114a at an incident
angle 03. Mirror 114a is configured to reflect incident
radiation beam 104d such that radiation beam 104e reflected
from mirror 114q is incident upon mirror 1146 at an incident
angle 0,=20,-90°. Mirror 1146 is configured to reflect
incident radiation beam 104e such that radiation beam 104f
reflected from mirror 1146 is incident on mirror 114c at the
incident angle 65. In some embodiments of the present
invention, the incident angles 6, and 0, for mirrors 114a-c
are grazing angles. In an exemplary embodiment of the
present invention, 6, is from about 75 deg. to about 85 deg.,
and 6, is from about 60 deg. to about 80 deg. Mirror 114c
is configured to reflect incident radiation beam 104f such
that radiation beam 104g reflected from mirror 114c exits
compensator 114 as radiation beam 104g along an optical
axis that aligns with the optical axes of radiation beams 104a
and 104d. Any number of mirrors can be used in compen-
sator 114 such that the optical axis of an incoming radiation
beam and that of an outgoing radiation beam are aligned and
unchanged. In an alternate embodiment of the present inven-
tion, compensator 114 includes four mirrors arranged in a
manner as shown in FIG. 3. A drive mechanism (not shown)
can be used to rotate compensator 114 about an axis that
substantially aligns with the optical axes of radiation beams
104a, 104d and 104g. As compensator 114 rotates, the
polarization state of radiation beam 104g modulates along
all three degrees of freedom necessary to act as a complete
polarization state generator.

[0041] Radiation beam 104g exiting compensator 114 is
directed to sample artifact positioned on sample holder 102,
as shown in FIG. 1. Sample holder 102 is positioned such
that radiation beam 104g exiting compensator 114 is inci-
dent on a surface of sample artifact. Sample holder 102 can
be rotated such that radiation beam 104g is incident on a
front face of the sample artifact at a predetermined incident
angle. In one embodiment, sample holder 102 can be rotated


Patent Application Publication Jan. 11,2024 Sheet 2 of 10 US 2024/0011894 Al

114b 112b S
LL

Figure 2


US 2024/0011894 Al

33. The ellipsometer of claim 31, wherein the non-
polarized radiation beam has a wavelength in extreme
ultraviolet region of an electromagnetic spectrum.

34. The ellipsometer of claim 31, wherein the first plu-
rality of mirrors comprises:

a first mirror positioned to reflect the non-polarized radia-
tion beam incident on the first mirror as a first reflected
radiation beam;

a second mirror positioned to reflect the first reflected
radiation beam incident on the second mirror as a
second reflected radiation beam; and

a third mirror positioned to reflect the second reflected
radiation beam incident on the third mirror as the first
polarized radiation beam having the first phase retar-
dance.

35. The ellipsometer of claim 34, wherein the second

plurality of mirrors comprises

a fourth mirror positioned to reflect the first polarized
radiation beam incident on the fourth mirror as a third
reflected radiation beam;
fifth mirror positioned to reflect the third reflected
radiation beam incident on the fifth mirror as a fourth
reflected radiation beam; and

a sixth mirror positioned to reflect the fourth reflected
radiation beam incident on the sixth mirror as the
second polarized radiation beam having the second
phase retardance

36. An cllipsometer for investigating a sample, said
ellipsometer comprising:

aradiation source for generating a first polarized radiation
beam having a wavelength from about 10 nm to about
240 nm in an electromagnetic spectrum;

a first rotating compensator for altering the first polarized
radiation beam to a second polarized radiation beam,
wherein an optical axis of the second polarized radia-
tion beam is substantially aligned with the optical axis
of the first polarized radiation beam, wherein the first
compensator is rotated about an axis substantially
aligned with the optical axes of the first and the second
polarized radiation beams, wherein the first rotating
compensator comprises:

a first mirror positioned to reflect the first polarized
radiation beam incident on the first mirror as a first
reflected radiation beam, wherein the first reflected
radiation beam comprises a first phase retardance:

a second mirror positioned to reflect the first reflected
radiation beam incident on the second mirror as a
second reflected radiation beam, wherein the second
reflected radiation beam comprises a second phase
retardance; and

a third mirror positioned to reflect the second reflected
radiation beam incident on the sixth mirror as the
second polarized radiation beam having a third phase
retardance;

sample holder for positioning a first surface of the

sample to receive the second polarized radiation beam

from the first rotating compensator, wherein the first
surface of the sample reflects a third polarized radiation
beam;

second rotating compensator for altering the third polar-
ized radiation beam to a fourth polarized radiation
beam, wherein an optical axis of the fourth polarized
radiation beam is substantially aligned with the optical
axis of the third polarized radiation beam, wherein the

»

»

15

Jan. 11, 2024

second compensator is rotated about an axis substan-

tially aligned with the optical axes of the third and the

fourth polarized radiation beams, wherein the second
compensator comprises:

a fourth mirror positioned to reflect the third polarized

radiation beam incident on the fourth mirror as a

third reflected radiation beam, wherein the third

reflected radiation beam comprises a fourth phase
retardance;

fifth mirror positioned to reflect the third reflected

radiation beam incident on the fifth mirror as a fourth

reflected radiation beam, wherein the fourth reflected
beam comprises a fifth phase retardance; and

sixth mirror positioned to reflect the fourth reflected

radiation beam incident on the sixth mirror as the

fourth polarized radiation beam having a sixth phase
retardance;

a polarizer for modifying the fourth polarized radiation
beam to a fifth polarized radiation beam, wherein an
optical axis of the fifth polarized radiation beam is
substantially aligned with an optical axis of the fourth
polarized radiation beam, wherein the second polarizer
comprises:

a seventh mirror positioned to reflect the fourth polar-
ized radiation beam incident on the seventh mirror as
a fifth reflected radiation beam;

an eighth mirror positioned to reflect the fifth reflected
radiation beam incident on the eighth mirror as a
sixth reflected radiation beam; and.

a ninth mirror positioned to reflect the sixth reflected
radiation beam incident on the ninth mirror as the
fifth polarized radiation beam:

a detector for measuring a plurality of first signals for a

plurality of first rotation angles of the first rotating

compensator and a plurality of second signals for a

plurality of second rotation angles of the second rotat-

ing compensator; and

processor for determining a Mueller matrix from the

plurality of the first rotation angles of the first rotating

compensator and the plurality of the second rotation
angles of the second rotating compensator.

37. The ellipsometer of claim 36, wherein the wavelength
of the non-polarized radiation beam is from about 10 nm to
about 30 nm.

38. The ellipsometer of claim 36, wherein the wavelength
of the non-polarized radiation beam is from about 30 nm to
about 240 nm.

39. The ellipsometer of claim 36, wherein the second
compensator and the polarizer are rotated about an axis
passing through a location the second polarized radiation
beam is received on the first surface of the sample positioned.
on the sample holder, wherein the sample holder rotates the
sample about the axis passing through the location the
second polarized radiation beam is received on the first
surface of the sample positioned on the sample holder,
wherein the rotation of the sample is about one-half of the
rotation of the polarization state analyzer, and wherein the
rotating the polarization state analyzer adjusts an angle of
incidence of the second polarized radiation beam on the first
surface of the sample positioned on the sample holder and an
angle of reflection of the third polarized radiation beam.

40. The ellipsometer of claim 36, wherein the sample
holder rotates the sample in an azimuthal direction about an
axis normal to the first surface of the sample.

.

2


Patent Application Publication

Jan. 11,2024 Sheet 1 of 10

x
=
Ss
zt
s
awa
a
= i
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=)
=
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US 2024/0011894 Al

Figure 1


US 2024/0011894 Al

of the first rotating compensator and a plurality of second
signals for a plurality of second rotation angles of the second
rotating compensator; and a processor for determining a
Mueller matrix from the plurality of the first rotation angles
of the first rotating compensator and the plurality of the
second rotation angles of the second rotating compensator.
More particularly, at least one of the first polarizer, the
second polarizer, the first compensator and the second
compensator include three mirrors.

[0010] In one embodiment, the non-polarized radiation
beam has a wavelength in vacuum ultraviolet region of an
electromagnetic spectrum. In another embodiment, the non-
polarized radiation beam has a wavelength in extreme
ultraviolet region of an electromagnetic spectrum.

[0011] In one aspect of the present invention, the first
plurality of mirrors includes: a first mirror positioned to
reflect the non-polarized radiation beam incident on the first
mirror as a first reflected radiation beam; a second mirror
positioned to reflect the first reflected radiation beam inci-
dent on the second mirror as a second reflected radiation
beam; and a third mirror positioned to reflect the second
reflected radiation beam incident on the third mirror as the
first polarized radiation beam; the second plurality of mir-
rors include: a fourth mirror positioned to reflect the first
polarized radiation beam incident on the fourth mirror as a
third reflected radiation beam: a fifth mirror positioned to
reflect the third reflected radiation beam incident on the fifth
mirror as a fourth reflected radiation beam; and a sixth
mirror positioned to reflect the fourth reflected radiation
beam incident on the sixth mirror as the second polarized
radiation beam having the first phase retardance; the third
plurality of mirrors includes: a seventh mirror positioned to
reflect the third polarized radiation beam incident on the
seventh mirror as fifth reflected radiation beam; an eighth
mirror positioned to reflect the fifth reflected radiation beam.
incident on the eighth mirror as a sixth reflected radiation
beam; and a ninth mirror positioned to reflect the sixth
reflected radiation beam incident on the ninth mirror as the
fourth polarized radiation beam having the second phase
retardance; and the fourth plurality of mirrors includes: a
tenth mirror positioned to reflect the fourth polarized radia-
tion beam incident on the tenth mirror as a seventh reflected
radiation beam; an eleventh mirror positioned to reflect the
seventh reflected radiation beam incident on the eleventh
mirror as an eighth reflected radiation beam; and a twelfth
mirror positioned to reflect the eighth reflected radiation
beam incident on the twelfth mirror as the fourth polarized
radiation beam.

[0012] In one embodiment of the present invention, the
first plurality of mirrors further includes a thirteenth mirror
positioned to receive one of the non-polarized radiation
beam, the first reflected radiation beam and the second
reflected radiation beam, wherein the first, the second, the
third and the thirteenth mirrors modify the non-polarized
radiation beam to the first polarized radiation beam. In a
second embodiment of the present invention, the second
plurality of mirrors further comprises a fourteenth mirror
positioned to receive one of the first polarized radiation
beam, the third reflected radiation beam and the fourth
reflected radiation beam, wherein the fourth, the fifth, the
sixth and the fourteenth mirrors alter the first polarized
radiation beam to the second polarized radiation beam
having the first phase retardance. In a third embodiment of
the present invention, the third plurality of mirrors further

Jan. 11, 2024

comprises a fourteenth mirror positioned to receive one of
the third polarized radiation beam, the fifth reflected radia-
tion beam and the sixth reflected radiation beam, wherein the
seventh, the eighth, the ninth and the fourteenth mirrors alter
the third polarized radiation beam to the fourth polarized
radiation beam having the second phase retardance. In a
fourth embodiment of the present invention, the fourth
plurality of mirrors further comprises a fourteenth mirror
positioned to receive one of the fourth polarized radiation
beam, the seventh reflected radiation beam and the eighth
reflected radiation beam, wherein the tenth, the eleventh, the
twelfth and the fourteenth mirrors modify the fourth polar-
ized radiation beam to the fifth polarized radiation beam.
[0013] In one aspect of the present invention, the first
rotating compensator is rotated about an axis substantially
aligned with the optical axes of the first and the second
polarized radiation beams, and wherein the second compen-
sator is rotated about an axis substantially aligned with the
optical axes of the third and the fourth polarized radiation
beams.

[0014] In some aspects of the present invention, the polar-
ization state analyzer is rotated about an axis passing
through a location the second polarized radiation beam is
received on the first surface of the sample positioned on the
sample holder, wherein the sample holder rotates the sample
about the axis passing through the location the second
polarized radiation beam is received on the first surface of
the sample positioned on the sample holder, wherein the
rotation of the sample is about one-half of the rotation of the
polarization state analyzer, and wherein the rotating the
polarization state analyzer adjusts an angle of incidence of
the second polarized radiation beam on the first surface of
the sample positioned on the sample holder and an angle of
reflection of the third polarized radiation beam. In other
aspects of the present invention, the sample holder rotates
the sample in an azimuthal direction about an axis normal to
the first surface of the sample.

[0015] Embodiments of the present invention also relate to
an ellipsometer for investigating a sample, said ellipsometer
including a radiation source for generating a non-polarized
radiation beam having a wavelength from about 10 nm to
about 240 nm; a first polarizer for modifying the non-
polarized radiation beam to a first polarized radiation beam,
wherein an optical axis of the first polarized radiation beam
is substantially aligned with an optical axis of the non-
polarized radiation beam, wherein the first’ polarizer
includes: a first mirror positioned to reflect the non-polarized
radiation beam incident on the first mirror as a first reflected
radiation beam; a second mirror positioned to reflect the first
reflected radiation beam incident on the second mirror as a
second reflected radiation beam; and a third mirror posi-
tioned to reflect the second reflected radiation beam incident
on the third mirror as the first polarized radiation beam; a
first rotating compensator for altering the first polarized
radiation beam to a second polarized radiation beam having
a first phase retardance, wherein an optical axis of the
second polarized radiation beam is substantially aligned
with the optical axis of the first polarized radiation beam,
wherein the first compensator is rotated about an axis
substantially aligned with the optical axes of the first and the
second polarized radiation beams, wherein the first rotating
compensator includes: a fourth mirror positioned to reflect
the first polarized radiation beam incident on the fourth
mirror as a third reflected radiation beam, wherein the third



US 2024/0011894 Al

ized radiation beam incident on the first mirror as a first
reflected radiation beam, wherein the first reflected radiation
beam comprises a first phase retardance; a second mirror
positioned to reflect the first reflected radiation beam inci-
dent on the second mirror as a second reflected radiation
beam, wherein the second reflected radiation beam com-
prises a second phase retardance; and a third mirror posi-
tioned to reflect the second reflected radiation beam incident
on the sixth mirror as the second polarized radiation beam
having a third phase retardance; a sample holder for posi-
tioning a first surface of the sample to receive the second
polarized radiation beam from the first rotating compensator,
wherein the first surface of the sample reflects a third
polarized radiation beam; a second rotating compensator for
altering the third polarized radiation beam to a fourth
polarized radiation beam, wherein an optical axis of the
fourth polarized radiation beam is substantially aligned with
the optical axis of the third polarized radiation beam,
wherein the second compensator is rotated about an axis
substantially aligned with the optical axes of the third and
the fourth polarized radiation beams, wherein the second
compensator includes: a fourth mirror positioned to reflect
the third polarized radiation beam incident on the fourth
mirror as a third reflected radiation beam, wherein the third
reflected radiation beam comprises a fourth phase retar-
dance; a fifth mirror positioned to reflect the third reflected
radiation beam incident on the fifth mirror as a fourth
reflected radiation beam, wherein the fourth reflected beam.
comprises a fifth phase retardance; and a sixth mirror
positioned to reflect the fourth reflected radiation beam
incident on the sixth mirror as the fourth polarized radiation
beam having a sixth phase retardance; a polarizer for modi-
fying the fourth polarized radiation beam to a fifth polarized
radiation beam, wherein an optical axis of the fifth polarized
radiation beam is substantially aligned with an optical axis
of the fourth polarized radiation beam, wherein the second
polarizer includes: a seventh mirror positioned to reflect the
fourth polarized radiation beam incident on the seventh
mirror as a fifth reflected radiation beam; an eighth mirror
positioned to reflect the fifth reflected radiation beam inci-
dent on the eighth mirror as a sixth reflected radiation beam;
and a ninth mirror positioned to reflect the sixth reflected
radiation beam incident on the ninth mirror as the fifth
polarized radiation beam; a detector for measuring a plural-
ity of first signals for a plurality of first rotation angles of the
first rotating compensator and a plurality of second signals
for a plurality of second rotation angles of the second
rotating compensator; and a processor for determining a
Mueller matrix from the plurality of the first rotation angles
of the first rotating compensator and the plurality of the
second rotation angles of the second rotating compensator.
In some embodiments of the present invention, the polarizer
further comprises a tenth mirror positioned to receive a
seventh reflected radiation beam from the ninth mirror, and
wherein the tenth mirror is positioned to reflect the seventh
reflected radiation beam incident on the tenth mirror as the
fifth polarized radiation beam.

[0024] In one embodiment of the present invention, the
wavelength of the non-polarized radiation beam is from
about 10 nm to about 30 nm. In another embodiment of the
present invention, the wavelength of the non-polarized
radiation beam is from about 30 nm to about 240 nm.

Jan. 11, 2024

BRIEF DESCRIPTION OF DRAWINGS
[0025] FIG. 1 illustrates a schematic representation of an
ellipsometer in accordance with embodiments of the present
invention.
[0026] FIG. 2 illustrates a schematic representation of a
polarization state generator as used in an ellipsometer in
accordance with embodiments of the present invention.
[0027] FIG. 3 illustrates a schematic representation of an
alternate polarizer or compensator as used in a polarization
state generator of an ellipsometer in accordance with
embodiments of the present invention.
[0028] FIG. 4 illustrates a schematic representation of a
polarization state analyzer as used in an ellipsometer in
accordance with embodiments of the present invention.
[0029] FIG. 5 illustrates a schematic representation of an
alternate polarizer or compensator as used in a polarization
state analyzer of an ellipsometer in accordance with embodi-
ments of the present invention.
[0030] FIG. 6 illustrates a schematic representation of an
alternate polarization state analyzer as used in an ellipsom-
eter in accordance with embodiments of the present inven-
tion.
[0031] FIG. 7 illustrates an exemplary plot for calculated
condition number for polarization state generator or analyzer
shown in FIG. 1.
[0032] FIG. 8 illustrates a schematic representation of an
alternate ellipsometer in accordance with embodiments of
the present invention.
[0033] FIG. 9 illustrates a schematic representation of a
calibration assembly for an ellipsometer in accordance with
embodiments of the present invention.
[0034] FIG. 10 illustrates a schematic representation of an
alternate ellipsometer in accordance with embodiments of
the present invention.

DETAILED DESCRIPTION,

[0035] While the making and using of various embodi-
ments of the present invention are discussed in detail below,
it should be appreciated that the present invention provides
many applicable inventive concepts which can be embodied
in a wide variety of specific contexts. The specific embodi-
ments discussed herein are merely illustrative of specific
ways to make and use the invention, and do not delimit the
scope of the present invention. Reference will be made to the
drawings wherein like numerals refer to like elements
throughout.

[0036] Referring now to the drawings, and more particu-
larly, to FIG. 1, there is shown an ellipsometer, generally
designated 100 and schematically showing an embodiment
of the present invention, for measuring a Mueller matrix
reflectance of a material in the VUV and EUV region.
Ellipsometer 100 for probing a sample artifact includes a
sample holder 102, a radiation source 104, a polarization
generator 106, a polarization state analyzer 108, and a
processor 110.

[0037] Radiation source 104 emits a radiation beam 104a
having divergent rays that are isotropically non-polarized
and having a predetermined wavelength range of interest in
the vacuum or extreme ultraviolet region of the electromag-
netic spectrum. In some embodiments of the present inven-
tion, radiation source 104 emits a radiation beam 104a
having divergent rays that are naturally polarized and having
a predetermined wavelength range of interest in the vacuum