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SCANNING MICROWAVE ELLIPSOMETER
AND PERFORMING SCANNING:
MICROWAVE ELLIPSOMETRY

CROSS REFERENCE TO RELATED,
APPLICATIONS

The application claims priority to U.S. Provisional Patent
Application Ser, No. 62/841,612 filed May 1, 2019, the
disclosure of which is incorporated herein by reference in its
entirety.

STATEMENT REGARDING FEDERALLY,
SPONSORED RESEARCH

‘This invention was made with United States Government
support from the National Institute of Standards and Tech-
nology (NIST), an agency of the United States Department
of Commerce. The Government has certain rights in the
invention. Licensing inquiries may be directed to the Tech-
nology Partnerships Office, NIST, Gaithersburg, Md.
20899; voice (301) 301-975-2573; email tpo@nist. gov; ref-
erence NIST Docket Number 19-040USI.

BRIEF DESCRIPTION

Disclosed is a scanning microwave ellipsometer compris
ing: a microwave ellipsometry test head comprising: a
polarization controller that receives an input electrical sig-
nal, produces a polarization-controlled microwave radiation
from the input electrical signal, receives reflected micro-
wave radiation resulting from the polarization-controlled
microwave radiation, and produces output electrical signal
from reflected microwave radiation; a transmission line in
communication with the polarization controller and that
receives the polarization-controlled microwave radiation
from the polarization controller, produces transmitted
microwave radiation from the polarization-controlled micro-
wave radiation, receives sensor-received microwave radia-
tion resulting from the transmitted microwave radiation, and
produces a reflected microwave radiation from the sensor-
received microwave radiation; and a sensor in communica-
tion with the transmission line and that receives the tran:
mitted microwave radiation from the transmission line,
produces sensor microwave radiation from the transmitted
microwave radiation, subjects a sample to the sensor micro-
wave radiation, receives a sample-reflected microwave
radiation from the sample that results from subjecting the
sample with sensor microwave radiation, and produces a

sensor-received microwave radiation from the sample-re- 5

flected microwave radiation, wherein a polarization of the
sensor microwave radiation is controlled by the polarization
controller; an electrical signal measurement system in elec-
trical communication with the microwave ellipsometry test

head and that produces the input electrical signal, commu- 5

nicates the input electrical signal to the microwave ellip-
sometry test head, receives the output electrical signal from
the microwave ellipsometry test head, produces an electric:
readout signal from the output electrical signal such that a
magnitude of reflection coefficient T and an angle of reflec-
tion coefficient I’ of the sample reflected microwave radia-
tion reflected from the sample is determined from the
electrical readout signal, and produces a position control
signal; and a position controller in communication with the
electrical signal measurement system and that receives the
position control signal from the electrical signal measure-
ment system, adjusts a relative position of the sensor and the

20

&

&

2

sample based on the position control signal, and moves the
sensor relative to the sample so that the sensor scans a
surface of the sample.

Disclosed is a microwave ellipsometer calibrant to cali-
brate a scanning microwave ellipsometer, the microwave
ellipsometer calibrant comprising: a substrate and a plurality
of sectors disposed on the substrate, wherein each sector
provides a known material and known positional anisotropy
of microwave reflection coeflicient I, wherein the plurality
of sectors comprises: a first sector that comprises a first
material disposed as first stripes and a second material
disposed as second stripes such that the first stripes and the
second stripes are alternatingly disposed to provide a first
anisotropic sheet resistivity; a second sector that comprises
a third material disposed as third stripes and a fourth
material disposed as fourth stripes such that the third stripes
and the fourth stripes are alternatingly disposed to provide a
second anisotropic sheet resistivity; a third sector that com-
prises a fifth material disposed to provide a first isotropic
sheet resistivity; and a fourth sector that comprises a sixth
material disposed to provide a second isotropic sheet resis-
tivity.

Disclosed is a process for performing scanning micro-
wave ellipsometry with the scanning microwave ellipsom-
eter, the process comprising: receiving, by the polarization
controller, the input electrical signal; producing, by the
polarization controller, the polarization-controlled micro-
wave radiation from the input electrical signal; receiving, by
the polarization controller, the reflected microwave radiation
resulting from the polarization-controlled microwave radia-
tion; producing, by the polarization controller, the output
electrical signal from the reflected microwave radiation;
receiving, by the transmission line, the polarization-con-
trolled microwave radiation from the polarization controller;
producing, by the transmission line, transmitted microwave
radiation from the polarization-controlled microwave radia-
tion; receiving, by the transmission line, the sensor-received
microwave radiation resulting from the transmitted micro-
wave radiation; producing, by the transmission line, the
reflected microwave radiation from the sensor-received
microwave radiation; receiving, by the sensor, the transmit-
ted microwave radiation from the transmission line; produc-
ing, by the sensor, the sensor microwave radiation from the
transmitted microwave radiation; controlling the polariza-
tion of the sensor microwave radiation by the polarization
controller; subjecting the sample to the sensor microwave
radiation; receiving, by the sensor, the sample-reflected
microwave radiation from the sample that results from
subjecting the sample with the sensor microwave radiation;
producing, by the sensor, the sensor-received microwave
radiation from the sample-reflected microwave radiation;
producing, by the electrical signal measurement system, the
input electrical signal; communicating, by the electrical
signal measurement system, the input electrical signal to the
microwave ellipsometry test head; receiving, by the electri-
cal signal measurement system, the output electrical signal
from the microwave ellipsometry test head; producing, by
the electrical signal measurement system, the electrical
readout signal from the output electrical signal; producing,
by the electrical signal measurement system, the position
control signal; receiving, by the position controller, the
position control signal from the electrical signal measure-
ment system; adjusting the relative position of the sensor
and the sample based on the position control signal; and
scanning over the surface of the sample with the sensor



U.S. Patent Mar. 29,2022 Sheet 52 of 53 US 11,287,366 B2

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relative to one another for scanning sensor microwave
radiation 34 from sensor 6 over sample 7.

Tn an embodiment with reference to FIG. 17 through FIG.
20, a process for performing microwave ellipsometry
includes characterizing the S-parameters of the test head as
a function of polarization. The S-parameters of the test head
asa function of polarization are characterized by performing
a first-tier one-port coaxial calibration (e.g., a Short-Open-
Load calibration) at the end of a coaxial cable that carries an
input electrical signal 10 to the test head and carries an
output electrical signal 11 from the test head, followed by a
second-tier rectangular-waveguide calibration (¢.g., a Short-
Open-Load calibration) at the end of waveguide aperture 13
for each polarization. The S-parameters of test head 2 are
directly obtained from the second-tier calibration error box,
This step is performed once for a given test head 2 and is not
required every time waveguide ellipsometry is performed if
the S-parameters of the test head do not drift appreciably and
are retained for future use.

Tn an embodiment, with reference to FIG. 17 through FIG.
20, the process for performing microwave ellipsometry
includes performing a first-tier one-port coaxial calibration
(e.g., a Short-Open-Load calibration) at the end of a coaxial
cable that carries an input electrical signal 10 to the test head
and carries an output electrical signal 11 from the test head,
followed by cascading the S-parameters of the test head
obtained in the first step with the first-tier calibration error
box. This step can be repeated to correct for drift in the
systematic errors introduced by electrical signal measure-
ment system 1. This step includes installation of an elec-
tronic calibration unit at the end of a coaxial cable that
carries an input electrical signal 10 to the test head and
carries an output electrical signal 11 from the test head.

Inan embodiment, with reference to FIG. 17 through FIG.
20, the process for performing microwave ellipsometry
includes placing the sample between the waveguide flange
and the dielectric spacer (e.g., Rohacell) (FIG. 19) and
aligning microwave ellipsometry test head 2 normal to
sample 7. The dielectric spacer can be optional but can
simplify implementation of the absorber in simulations,
making it advantageous to include for simulations to be
performed.

In an embodiment, with reference to FIG. 17 through.
FIG. 20, the process for performing microwave ellipsometry
includes measuring a raw complex reflection coefficient at a
polarization and with a distance between sensor 6 and
sample 7, at a location on sample 7. A raw complex
reflection coefficient is error corrected with the first-tier
error box of the prior step cascaded with the S-parameters of

the test head from step 1 to obtain an error-corrected 5

magnitude of reflection coefficient I’ and an angle of reflec-
tion coefficient P for the material under test.

In an embodiment, with reference to FIG. 17 through FIG.
20, the process for performing microwave ellipsometry

includes an optional step of repeating the immediate prior 5

two steps for a plurality of sectors of calibrant 20.

Inan embodiment, with reference to FIG. 17 through FIG.
20, the process for performing microwave ellipsometry
includes an optional step of optimizing a finite element
simulation to match the measurements of calibrant 20.
Optimized parameters can include a distance between the
sample 7 and the waveguide aperture 13, a thickness and
complex permittivity of the dielectric spacer, and a boundary
condition corresponding to the absorber under the dielectric
spacer.

Inan embodiment, with reference to FIG. 17 through FIG.
20, the process for performing microwave ellipsometry

20

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10

optionally includes implementing the sample in a finite-
element simulation and the material properties of the simu-
lated material-under-test are varied until the simulated error-
corrected magnitude of reflection coefficient T’ and an angle
of reflection coeflicient T for the material under test match
the corresponding measured quantities.

Scanning microwave ellipsometer 200 has numerous
advantageous and unexpected benefits and uses. In an
embodiment, with reference to Example 1, Example 2, and
Example 3, a process for performing scanning microwave
ellipsometry with scanning microwave ellipsometer 200
includes: receiving, by polarization controller 4, input elec-
trical signal 10; producing, by polarization controller 4,
polarization-controlled microwave radiation 30 from input
electrical signal 10; receiving, by polarization controller 4,
reflected microwave radiation 31 resulting from polariza-
tion-controlled microwave radiation 30; producing, by
polarization controller 4, output electrical signal 11 from
reflected microwave radiation 31; receiving, by transmission
line 5, polarization-controlled microwave radiation 30 from
polarization controller 4; producing, by transmission line 5,
transmitted microwave radiation 32 from polarization-con-
trolled microwave radiation 30; receiving, by transmission
line 5, sensor-received microwave radiation 33 resulting
from transmitted microwave radiation 32; producing, by
transmission line 5, reflected microwave radiation 31 from
sensor-received microwave radiation 33; receiving, by sen-
sor 6, transmitted microwave radiation 32 from transmission
line 5; producing, by sensor 6, sensor microwave radiation
34 from transmitted microwave radiation 32; controlling
polarization of sensor microwave radiation 34 by polariza-
tion controller 4; subjecting sample 7 to sensor microwave
radiation 34; receiving, by sensor 6, sample-reflected micro-
wave radiation 35 from sample 7 that results from subjecting
sample 7 with sample-reflected microwave radiation 35:
producing, by sensor 6, sensor-received microwave radia-
tion 33 from sample reflected microwave radiation 35;
producing, by electrical signal measurement system 1, input
electrical signal 10; communicating, by electrical signal
measurement system 1, input electrical signal 10 to micro-
wave ellipsometry test head 2; receiving, by electrical signal
measurement system 1, output electrical signal 11 from
microwave ellipsometry test head 2; producing, by electrical
signal measurement system 1, electrical readout signal 12
from output electrical signal 11; producing, by electrical
signal measurement system 1, position control signal 9;
receiving, by position controller 8, position control signal 9
from electrical signal measurement system 1; adjus
relative position of sensor 6 and sample 7 based on pos
control signal 9; and scanning over surface of sample 7 with
sensor microwave radiation 34 from sensor 6 as sensor 6 is
moved relative to sample 7 to perform scanning microwave
ellipsometry of sample 7.

‘The process further can include determining, from elec-
trical readout signal 12, the polarization of reflected micro-
wave radiation 31, magnitude of reflection coefficient T, and
angle of reflection coeflicient of sample reflected micro-
wave radiation 35 from sample 7. The process can include
adjusting, by position controller 8, relative position by
moving sensor 6 relative to sample 7 selectively along three
orthogonal linear directions and in three independent angu-
lar coordinates.

In an embodiment, the process includes calibrating scan-
ning microwave ellipsometer 200 with microwave ellipsom-
eter calibrant 20 by scanning sensor 6 over sectors over
microwave ellipsometer calibrant 20 as microwave ellip-
someter calibrant 20 is subjected to sensor microwave



US 11,287,366 B2

17

waveguide and the plastic holder on the test-head. We did
not import the 3D model of the aluminum motor (pictured in
FIG. 30) because its features were complex to mesh. Instead,
we defined a box of aluminum approximately equal in size
to the motor in (&, $) (FIG. 29) to capture its effect on the
electromagnetic fields. Next, we defined a wave port and
excited the fundamental TE,, mode (with a Z,,, power-
voltage characteristic impedance [25]) at one port of the
rectangular waveguide and de-embedded the excitation port
by the length of the waveguide. In this case, de-embedding
means correcting for the phase and attenuation of the
simulated signal. The result is to change the reference plane
of the simulation to match the same plane in the measure-
ment.

The simulated waveguide was at a height, h, above the
MUT, which had a thickness, tye and assigned material
properties (e.g., conductivity, permittivity). In simulation
and measurement, we varied h to understand the impact on
our measurements. When we simulated the test wafers, we
included a 500 jum thick piece of fused silica under the MUT
layer (simulated separately because it was not part of the
composite). Behind the fused silica layer, we had an air
volume whose thickness was equal to the thickness of the
Rohacell slab. Rohacell is highly porous and can be treated
as air at these frequencies and measurement conditions.
After the air volume, we included the absorber (FIG. 19) and
the planarizing table (FIG. 19) in the measurement setup,
modeling them as a volume of air and conducting boundary
condition, respectively. We set the convergence criteria to be
a fractional S-parameter error of 1% and specified the
maximum mesh size to be b/10, where b is the smaller
dimension of the WR-42 waveguide.

Our MUTs were either isotropic (film of uniform mate-
rial) or anisotropic (gold stripes on a less-conductive thin
film). The isotropic materials were simple to simulate
because they had isotropic conductivity (e.g., gold) or per-
mittivity (e.g., fused silica), hence results were not depen-
dent on the angle, 6, of the E-field polarization. For these
uniform samples we simulated the S-parameters as a func-
tion of height offset (h) and matched them to measurement
to define the parameters: distance between the waveguide
flange and the material surface, Rohacell and absorber
thickness, and permittivity of fused silica wafer (FIG. 29).

The isotropic gold behaved as a short circuit reflect,
however it was not a perfect reflect (ITI=1) because there
was a gap between the waveguide flange and the materials.
This gap allows some of the reflected wave to scatter away
from the waveguide flange, but a gap is necessary to make

non-contact measurements of the MUT. We measured the 5

gap with shims and verified the physical measurement by
parameterizing the offset in the simulation. We parameter-
ized the simulation to verify the physical measurement
because the measurement had a large uncertainty associated
with
absorber and simulated it as a volume of air backed by a
conductive boundary (conductivity of aluminum). Like our
procedure for gold, we parameterized this air thickness to
verify the physical measurement. Finally, we measured a
bare fused silica wafer and parameterized the permittivity in
simulation to match measurement. Once these physical
parameters were set, we set up the simulation for our
anisotropic MUTs.

We parameterized the orientation (6) of the conductivity
tensor of the MUT, where o, and o,, were obtained from 3D
DC composite simulation and circuit analysis in the previous
section. Since these results were so close, we show simu-

. Next, we measured the thickness of Rohacell and s

20

&

&

18

lations performed with the effective-medium conductivities
from composite theory. We compare the simulated S-param-
eters with the measured S-parameters in the results (Section
IV).

We tested the waveguide ellipsometry method with the
following step-by-step procedure: 1. Measure short-open-
load calibration standards at both a coaxial reference plane
before the rotation joint and at the waveguide probe refer-
ence plane, then extract the S-parameters of the test-head.
This step is only performed once. 2. Measure short-open-
load calibration standards at the coaxial reference plane
before the rotation joint to calibrate the VNA. This step is
performed before each measurement campaign. Set standard
sweep parameters for the measurements. All measurements
are over 16 (x, y)-positions, 5 heights (h), 73 angles (6, 5°
steps), and 51 frequency points spaced linearly between 18
GHz and 26.5 GHz. The 16 (x, y)-positions were distributed
over the sample and far enough from all edges to minimize
edge effects. 3. Place the MUT in the measurement setup
between the waveguide flange and the absorptive material
(FIG. 19). 4. Measure the one-port S-parameters of the four
test wafers and their quadrants. 5. Calibrate the raw mea-
surements to the WR-42 reference plane with the S-param-
eters extracted in steps (1) and (2). 6. Average the calibrated
S-parameters over the 16 different (x, y)-positions for each
sample. 7. Match the measurement and simulation for the
isotropic MUTs as a function of height offset between
waveguide and MUT and frequency. We started with iso-
tropic gold, absorber, and fused silica measurements. In
simulation, we parameterized the following variables to
assign values to physical parameters. (a) height offset from
the gold measurement, (b) absorber and Rohacell height
from the absorber measurement, and (c) permittivity of the
fused silica from the fused silica wafer measurement. 8. Run
the full-wave 3D simulation with a 200 nm thick MUT, and.
parameterize the conductivity over 10° S/m to 10° S/m with
10 points at each decade. 9. Create a mapping function
between the simulated S-parameters and the sheet resistance
of the material. 10. Convert from measured S-parameters to
sheet resistance with the mapping function. 11. Calculate the
conductivity tensor components with a 3D composite simu-
lation and/or circuit analysis then compare to results of
mapping function. 12. Run the full-wave 3D simulation with
conductivity tensor components obtained from 3D compos-
ite theory and circuit analysis and compare to measurement.

The calibration for waveguide ellipsometry moved the
reference plane from somewhere inside the VNA to the end
of the WR-42 waveguide for each angle position. The
calibration procedure was a two-tier calibration (FIG. 30).
The first-tier was a standard short-open-load (SOL) coaxial
calibration to move the reference plane to the coaxial
connector before the test-head. The second-tier was a
WR-42 SOL calibration that rolled the reference plane to the
end of the test-head as a function of angle, to account for any
affects from the rotary joint on the robot arm that rotated the
waveguide. We divided the calibration into two-tiers
because measuring the WR-42 SOL standards required
dismantling the test-head for each measurement.

Before each material measurement, we performed the
first-tier calibration with a 2.4 mm coaxial short-open-load
(SOL) calibration. The robot was in the same (x,y,z)-
position for each calibration and the first MUT measurement
position. Next, we rolled the reference plane from the
first-tier reference plane to the WR-42 waveguide flange
with the test-head’s S-parameters. To obtain the S-param-
eters of the test-head, we measured WR-42 SOL compo-
nents for each of the 73 angle positions and corrected them



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stripes such that the third stripes and the fourth stripes
are alternatingly disposed to provide a second aniso-
tropic sheet resistivity;

a third sector that comprises a fifth material disposed to

provide a first isotropic sheet resistivity; and

a fourth sector that comprises a sixth material disposed to

provide a second isotropic sheet resistivity.

15. A process for performing scanning microwave cllip-
sometry with the scanning microwave ellipsometer of claim
1, the process comprising:

receiving, by the polarization controller, the input elec-

trical signal;

producing, by the polarization controller, the polarizatio:

controlled microwave radiation from the input electr
cal signal;

receiving, by the polarization controller, the reflected

microwave radiation resulting from the polarization
controlled microwave radiation;
producing, by the polarization controller, the output elec-
trical signal from the reflected microwave radiatio1

receiving, by the transmission line, the polarization-con-
trolled microwave radiation from the polarization con-
troller;

producing, by the transmission line, transmitted micro-

wave radiation from the polarization-controlled micro-
wave radiation;

receiving, by the transmission line, the sensor-received

microwave radiation resulting from the transmitted
microwave radiation;

producing, by the transmission line, the reflected micro-

wave radiation from the sensor-received microwave
radiation;

receiving, by the sensor, the transmitted microwave radia-

tion from the transmission line;

producing, by the sensor, the sensor microwave radiation

from the transmitted microwave radiation;

controlling the polarization of the sensor microwave

radiation by the polarization controller;

subjecting the sample to the sensor microwave radiation;
by the sensor, the sample reflected microwave
ion from the sample that results from subjecting

the sample with the sample reflected microwave radia-

tion;

producing, by the sensor, the sensor-received microwave
radiation from the sample reflected microwave radia-
tion;

producing, by the electrical signal measurement system,
the input electrical signal;

communicating, by the electrical signal measurement
system, the input electrical signal to the microwave
ellipsometry test head;

receiving, by the electrical signal measurement system,
the output electrical signal from the microwave ellip-
sometry test head;

producing, by the electrical signal measurement system, 5

the electrical readout signal from the output electrical
signal:

producing, by the electrical signal measurement system,
the position control signal:

receiving, by the position controller, the position control
signal from the electrical signal measurement system;

adjusting the relative position of the sensor and the
sample based on the position control signal; and

scanning over the surface of the sample with the sensor
microwave radiation from the sensor as the sensor is
moved relative to the sample to perform scanning
microwave ellipsometry of the sample.

0

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36

16. The process of claim 15, further comprising deter-
mining, from the electrical readout signal, the magnitude of
reflection coefficient and the angle of reflection coefficient
T of the sample reflected microwave radiation from the
sample.

17. The process of claim 15, further comprising adjusting,
by the position controller, the relative position by moving
the sensor relative to the sample selectively along three
orthogonal linear directions and in three independent angu-
lar coordinates.

18. The process of claim 15, further comprising:

calibrating the scanning microwave ellipsometer with a
microwave ellipsometer calibrant that comprises:

a substrate and a plurality of sectors disposed on the
substrate, wherein each sector provides a known
material and known positional anisotropy of micro-
wave reflection coefficient T,

wherein the plurality of sectors comprises:

a first sector that comprises a first material disposed as
first stripes and a second material disposed as second
stripes such that the first stripes and the second
stripes are alternatingly disposed to provide a first
anisotropic sheet resistivity;

a second sector that comprises a third material disposed
as third stripes and a fourth material disposed as
fourth stripes such that the third stripes and the
fourth stripes are alternatingly disposed to provide a
second anisotropic sheet resistivity;

a third sector that comprises a fifth material disposed to
provide a first isotropic sheet resistivity; and

a fourth sector that comprises a sixth material disposed
to provide a second isotropic sheet resistivity,

by:

scanning the sensor over the sectors over the microwave
ellipsometer calibrant as the microwave ellipsometer
calibrant is subjected to the sensor microwave radia-
tion;

acquiring the sample reflected microwave radiation from
the microwave ellipsometer calibrant; and

determining the angle of reflection coefficient I and the
magnitude of reflection coefficient T for the input
electrical signal acquired from the output electrical
signal for the sample reflected microwave radiation
from the microwave ellipsometer calibrant to produce
correction factors to apply to an arbitrary output elec-
trical signal acquired from a sample.

19. A microwave ellipsometer calibrant to calibrate a
scanning microwave ellipsometer, the microwave ellipsom-
eter calibrant comprising:

a substrate and a plurality of sectors disposed on the
substrate, wherein each sector provides a known mate-
rial and known positional anisotropy of microwave
reflection coefficient I,

wherein the plurality of sectors comprises:

a first sector that comprises a first material disposed as
first stripes and a second material disposed as second
stripes such that the first stripes and the second stripes
are alternatingly disposed to provide a first anisotropic
sheet resistivity;

a second sector that comprises a third material disposed as.
third stripes and a fourth material disposed as fourth
stripes such that the third stripes and the fourth stripes
are alternatingly disposed to provide a second aniso-
tropic sheet resistivity;

a third sector that comprises a fifth material disposed to
provide a first isotropic sheet resistivity; and



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US 11,287,366 B2

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wire or multiple coils of wire in proximity to a material-
under-test (MUT). In this case, the coil is treated as a
lumped-element. This approximation breaks down as the
wavelength of the probing radiation approaches the size of
the probe coil, limiting the technique to lower frequencies
(~100 MHz).

‘The scanning microwave ellipsometer herein character-
izes conduetively anisotropic materials, including compos-
ites, which we called waveguide ellipsometry and probes the
conductive anisotropy of the MUT by measuring the reflec-
tion coeflicient of a linearly polarized electric field (E-field)
incident on the MUT. The magnitude and phase of the
reflected electromagnetic wave depend on the relative ori-
entation of the anisotropic MUT and the polarization of the
incident wave. Sweeping the incident polarization direction
allows us to probe the material’s bulk conductivity tensor
(and potentially the permittivity or permeability for broader
impact). The test-head includes a rotation joint to control the

incident polarization direction. Finite-element simulation 2

and composite theory analysis are employed to compute the
waveguide fields in lieu of analytic expressions. The mea-
surements and analysis are automated as a function of angle.

Waveguide ellipsometry is a non-contact, electromagnetic

characterization technique (FIG. 19) to characterize material 2;

properties.

We designed, fabricated, and measured four different test
wafers with quadrants designed to mimic both ideal isotro-
pic and ideal anisotropic materials (FIG. 27). The test wafer
substrates were 150 mm diameter fused silica wafers. The
metal layers on top of the fused silica were gold (Au) and
molybdenum disilicide (MoSi,). We chose gold for its high
conductivity and we chose MoSi, because the range of
thicknesses available in our cleanroom produced a suitable
range of sheet resistances. These sheet resistances were
targeted to maximize the coverage of a smith chart relative
to the TE,, waveguide impedance.

Each test wafer had four quadrants of different conductor
geometries (FIG. 27). Quadrant #1 had (10.020.5) um wide
continuous gold stripes on MoSi, on a fused silica substrate,
quadrant #2 had (10.020.5) um continuous gold stripes
deposited on the fused silica substrate, quadrant #3 was a
continuous layer of MoSi, with no gold stripes, quadrant #4
was a continuous layer of gold. The gold stripes had a
center-to-center distance of (20.020.5) um and were aligned
to the defined §-direction. These gold stripes served as an
idealized representation of the conductive fibers in a com-
posite material. Each of the four test fers had the same
four quadrant pattern, however, the thickness of the MoSi,,

both under the stripes (quadrant #1) and by itself (quadrant s

#3) ranged from 185 nm to 20 nm to achieve linearly spaced
values of the magnitude of the reflection coefficient (I'l)
between the test wafers (FIG. 27).

We fabricated the test wafers in a Class-100 cleanroom.

All four test wafers used a two-layer deposition process,

where layer one was MoSi, and layer two was Au. We
started with a fused silica wafer that was cleaned with an O,
plasma to remove organic contaminants from the surface.
Next, we spun on a | um lift-off resist (LOR) and 1 pm
negative image resist stack to reduce fencing. We then
exposed the photoresist with the pattern for layer one
(MoSi,) with a maskless aligner (MLA) and developed the
resist in an auto-developer to remove resist in the regions for
deposition. We deposited the first layer (MoSi,) with a
sputtering tool to have better control over deposition thick-
ness compared to other available tools. Next, we performed
a standard lift-off process including a wafer wash and a 60

&

0

14

s plasma clean before the deposition of the second layer.
Before adding the photoresist, exposing the pattern, and
developing the resist for second layer, we spun on a thin
layer of adhesion promoter, We note that the plasma clean
and adhesion promoter were critical for adhesion of photo-
resist to MoSi,. The second layer consisted of a thin layer
(205) nm of titanium (Ti) for adhesion and a thicker layer
(approximately 200+10) nm of gold (FIG. 27). The gold was
deposited with an electron beam evaporation tool. FIG. 27
lists measured values for the MoSi, thickness, the MoSi,
sheet resistance, and the second layer (Au and Ti) thickness
with the standard deviation for six measurements taken at
different locations over the wafers.

The test wafers were designed to mimic the electrical
behavior of real composites. In a fiber-reinforced composite
the gold stripes are akin to the conducting fibers and the
MoSi, is akin to a combination of conducting fibers that are
misaligned, an electrical percolation network between
aligned or misaligned fibers, and the conductivity of the
matrix material. For the WR-42 waveguide aperture in this
work, the smallest dimension of the waveguide is approxi-
mately 4.3 mm. This dimension is much larger than the fiber
diameter in many conductive-fiber composites and also
much larger than the width of the gold stripes in our test
wafers. Since the fibers are small compared to the sampled
volume, it is reasonable to average out these small features
and treat the whole composite as an effective medium with
an eflective anisotropic conductivity tensor.

‘As implemented, our technique measured the complex
reflection coefficient (S,,) as a function of angle for a
conductive MUT. We used DC composite theory and finite-
element simulations to verify the measurement with known
material properties. For both the DC composite theory and
the finite element modeling, we represented the MUT as a
bulk effective medium with an anisotropic conductivity
tensor. The effective medium was defined over a volume that
included the gold stripes, the space between the stripes, and
a thickness of MoSi, (FIG. 28).

With a suitable choice of axes, the bulk conductivity
tensor can always be represented as a diagonal matrix,

aw

where o,, 0,, and @, are the &, 9, and % components of the
conductivity tensor respectively. However, in the waveguide
ellipsometry measurements, the direction of the electric field
changes as the test head spins. To represent the orientation
of the of the test wafer with respect to the test head, the
conductivity tensor must be rotated by applying a rotation
matrix. Afier applying a rotation matrix around the z-axis by
some angle 6, the new conductivity tensor o,,, is,

AF O
FBO
00

Q)

where A, B, and F are functions of the conductivity tensor
components o,, and oy, and 0 is the relative angle between the

incident E-field polarization and the fiber direction. These
coefficients have the form:


| a



U.S. Patent Mar. 29,2022 Sheet 31 of 53 US 11,287,366 B2

Gold, ©

: Moai,
-- gold fiber on MoSi, (20 nm, 40 nm, 8G nm, °

(¢) (0)

FIG. 34


US 11,287,366 B2

27

similar alignment values compared to the uncertainty. We
observed that Sample #3, which has a middle layer rotated
by 5°, has a comparable alignment value to the control and
Sample #1, which is identical to the control.

Even in this preliminary configuration the uncertainty in
the alignment values from waveguide ellipsometry is small
compared to the variance of the alignment value over the
nominally aligned samples (Sample #1, Sample #2). This
fact is important to note because it implies that alignment as
measured by waveguide ellipsometry, can inform process
control.

FIG. 43. Absolute values for the average alignment for
control and four blind samples. Side A and Side B corre-
sponded to the top-facing and bottom-facing sides, respec-
tively. The number of measurements on each sample was
N=5 for the control, Sample #2, and Sample #4. For Sample
#1 and Sample #3, the number of measurements on each
sample was N=10. The measurement frequency was 18
GHz.

Accordingly, we demonstrated quantitative measurements
of alignment and orientation of short fiber composites by
microwave ellipsometry. Next-generation processing tech-
niques can involve in-line quality assurance tools for real-
time feedback of processing variables, and formed parts
require in situ characterization as the material is laid up to
improve quality and process control. We showed that by
acquiring the relative reflected power as a function of angle
at 18 GHz we quantified alignment and orientation for
in-line process control and for formed parts.

We measured four samples whose nominal misalignment
was unknown at the time of test. After we applied the
microwave ellipsometry technique, we successfully identi-
fied the alignment of each sample. By measuring both sides
of each sample, we were able to speculate about which side
of the sample had the nominally misaligned layer. We can
integrate robotics to create three dimensional images of
alignment and orientations. Additional efforts include the
development of real-time scanning systems. Finally, we
developed an uncertainty analysis and concluded that the
uncertainties in the initial alignment of the sample relative to
the waveguide flange was the dominant source of error.

Example 3. Application of Waveguide Ellipsometry
to Carbon Fiber Composites

We show measurement results from two different types of
composites in this paper. The first set of materials are test
wafers fabricated and designed to emulate the carbon fiber
composites used to help develop a mapping function

between the measured S-parameters and the material prop- 5

erties of the carbon fiber composites. They are fabricated
with well-known materials and uniform anisotropy. Once
the test wafers were characterized and a mapping function
was created, the second set of composites were four different

carbon fiber composites samples. These included a single ;

layer short carbon fiber composites (SCFC), multiple layer
SCFC, a single layer continuous carbon fiber composite
(CCFC), and a multiple layer CCFC.

We designed and fabricated four test wafers that were
designed to mimic the geometry of the carbon fiber com-
posites and develop a mapping function between measured
S-parameters and sheet resistance. Each fused silica wafer
had four quadrants (FIG. 45): quadrant (1) was (10.020.5)
jun wide continuous gold stripes on molybdenum disilicide
(MoSi,), quadrant (2) was (10.020.5) jum continuous gold
stripes deposited similarly on a fused silica substrate, quad-
rant (3) was a layer of MoSi, with no gold stripes, and

&

45

28

quadrant (4) was a continuous layer of gold. The gold stripes
were spaced with a center-to-center distance of (20.020.5)
jm and aligned in what we defined as the y-direction. These
gold stripes serve as an idealized representation of the
conductive fibers in a composite material. Each of the four
calibration wafers had the same four quadrant pattern,
however, the thickness of the MoSi, both under the stripes
(quadrant (1)) and by itself (quadrant (3)) ranged from 185
nm to 20 nm to achieve linearly spaced values of ID]
between the four layer thicknesses.

The first set of samples were loose short carbon fibers
(FIG. 45) that were aligned. Each layer had carbon fibers
chopped to approximately 5.0+0.1) mm in length. The
second set of samples were all made from the loose short
carbon fiber samples and then impregnated with the ther-
moplastic polymer (FIG. 45). Then each layer was aligned
by hand ona light table with a protractor and the layers were
consolidated in a four-layer ply (40 um to 60 um thick) over
4 hours at 2-10° Pa and 335° C. There is one control sample
where all four layers were aligned relative to one another
and oriented to 0°. The four other samples had unknown and.
alignment and orientation when they were initially given to
us. We did know that one sample would be the same as the
control, one sample would have the four layers aligned

“relative to one another and oriented to 5°, one sample would

have one of the middle four layers misaligned by 5°, and the
final sample would have one of the middle four layers
misaligned by 15°,

The second set of samples was a commercial one-layer
continuous IM7 fiber composite (FIG. 45) aligned and
impregnated with an 8552 prepreg (FIG. 45) and a sample
with multiple layers of the commercially available one-layer
continuous IM7 carbon fiber composite (FIG. 45). The
layers were laid up and put into a vacuum bag at 15 psig of
pressure. It was then heated at (-16.1 to -15.0) ° C/min to
107.2° C. and held for 30 to 60 min. The pressure was raised
to 85-100 psig so that the vacuum pressure reaches 30 psig.
‘The sample was put into an autoclave at 30 psig and held at
176.7° C. for (12510) minutes. It was then cooled at (16.7
to -15.0) ° C/min to 65.6° C. and vented.

These four samples are an overview of a typical manu-
facturing processes, carbon fiber right after alignment and
before impregnation with a matrix (single layer SCFC), a
single layer of carbon fiber impregnated with a matrix
(single layer CCFC), and multiple layers of carbon fiber
aligned to make thinner and thicker ply (multiple layer
SCFC and CCFC respectively).

Waveguide ellipsometry rotates a probe over an MUT so
that the relative angle, 0, between the fiber orientation and
linearly polarized E-field changes. Given a linearly polar-
ized electric field incident on an MUT, the reflection coef-
ficient can be expressed as a function of the characteristic
impedance at the reference plane (Z,.) and the impedance of
the MUT (Zager)

pa Zuer=2
Zuur + Zo"

w

where Zygor Zo, and [can be complex numbers. This
relationship defines how the reflection coefficient will
change as the relative angle between the fibers and the
linearly polarized E-field changes as well as defining some
constraints on the measurement technique. When Zyger is
too close to the impedance of the waveguide or too far away
from the impedance of the waveguide, the magnitude of the


US 11,287,366 B2

31

where a, b, c, and d are fit parameters. When the mapping
function was applied to the carbon fiber composite samples,
we get a similar shape as the real(I(0)), where smaller
values of R (:(0)) correspond to smalll values of R, and visa
versa (FIG. 47). The carbon fiber composites are now
defined as R,(@), where R,(@) can be calculated using Ohm’s
law:

(icra

(7 — 0, sin(8)c0s(9) I E | 6)

(ox = oy)sin@cos(9) 7, sin*9 + o,cos*O Jt Ey

If we only take the E-field excited in the x-direction that
couples back into the fundamental mode of the rectangular
waveguide, we simplify the expression to express the bulk
sheet resistance with five fit parameters a, b, 0,,R,.,and R,,:

R,(0)-a(R,, c0s?(0-0, +R, sin?(0-0)))+6(Re-R,)
sin(00,)cos(0-6,). )

The sheet resistance for the carbon fiber composites was
fit (FIG, 48) using this physical model to extract parameters
6,, R,. and R,,. Each spatial position on the carbon fiber
composites has an orientation, @,, and an alignment factor
related to the sheet resistance in the x and y directions
R,JR,,- Both factors are important to characterize the mate-
rial and recognize points of structural weakness.

The scanning microwave ellipsometer electromagneti-
cally detected four different carbon fiber samples. We devel-
‘oped a phenomenological mapping function between mea-
sured S-parameters and sheet resistance, derived a physical
fit for R,(®) and, measured and mapped four different carbon
fiber composites. FIG. 49 shows the fit function R (6) vs
R,(8) with points at R,(0°) and R,(90°) for each of the
carbon fiber composites. The measured sheet resistance
along the conductive fibers was ill-conditioned, and the
sheet resistance was sensitive to offset height on the order of
tens of microns, smaller than the step size of the robotic arm.
Future work could include a way to track the height and a
height dependent mapping function. Given these constraints,
we measured each carbon fiber composite and extracted the
fit parameters 0,, R,,, and R,,, (FIG. 44).

The first composite we measured was single layer SCFC.
The carbon fiber was aligned but not embedded within a
matrix with a thickness between 10 and 15 jm thick and
about a 30% carbon fiber density (FIG. 50). This carbon
fiber composite is the first step in the fabrication procedure
for any carbon fiber composite. The alignment, R,,/R,,. is
uniform over the sample, while the orientation, 6,, has some

nonuniformity (FIG. 50). Compared to the other three s

samples, the range of R(@)) (FIG. 49) is well within the
measure-able sheet resistance. The non-uniformity of the
samples could point to a weakness of this setup for this
composite sample. Perhaps for carbon fiber composites

where there is low density conductive fiber, a larger aperture

would give a better average over spatial position and
decrease the nonuniformity of the orientation.

The second composite was a (40 to 60) jum thick com-
posite where the carbon fibers were embedded in an ultem
matrix and the layers were aligned by hand. There is less
uniformity (FIG. 51) of both alignment and orientation
compared to the single layer SCFC, suggesting that some-
where between the initial alignment and the layup of four
layers individual clumps of fiber get disoriented. The align-
ment is low (FIG. 51), which also suggests that the layers are
not well aligned relative to one another compared to the
alignment of the initial single layer SCFC. The test wafers

&

32

were designed to look like this geometry, and the shape of
the original data (FIG. 46) supports this. This means for
future work we can use the percolation network fabricated
with the different MoSi, layers to better understand how the
fibers could align better

The third sample was a single layer CCFC approximately
80 to 100 jum thick with tightly packed fibers. The fit (FIG.
52) is not the typical shape we have seen with the other
samples. The ellipse is more compact, suggesting that even
at angles not along or across the fibers, there is some current
excited along the densely packed fibers. The alignment and
orientation of the continuous carbon fiber composite is more
uniform than the two previous short carbon fiber samples.
This sample is thicker than the skin depth of carbon fiber
conductivity along the fibers, making the sheet resistance
along the fibers (R,,) potentially inaccurate. Despite this, the
fit is good, and the extracted parameters have some infor-
mation.

The final sample was a multiple layer CCFC fabricated
out of multiple single layer CCFCs and aligned by hand to
be approximately 1 mm thick. The alignment is overall
slightly smaller than the single layer CCFC, following the
trend of the SCFC and suggesting that there is some mis-
alignment that occurs during the multiple layer alignment
process for both sets of composites.

‘We demonstrated non-contact electromagnetic character-
ization on four different carbon fiber composite samples,
measured carbon fiber composites, and extracted material
properties directly related to strength. To achieve this our
analysis included the introduction of a mapping function
between measured data (Real(I'(6)) and a material charac-
teristic (R,(0)), a physical fit for R,(), and the extraction of
orientation and alignment. We compared the measurements
of four different carbon fiber composite samples and ana-
lyzed the effectiveness of the measurement technique for
each.

While one or more embodiments have been shown and
described, modifications and substitutions may be made
thereto without departing from the spirit and scope of the
invention. Accordingly, it is to be understood that the present
invention has been described by way of illustrations and not
limitation. Embodiments herein can be used independently
or can be combined.

All ranges disclosed herein are inclusive of the endpoints,
and the endpoints are independently combinable with each
other. The ranges are continuous and thus contain every
value and subset thereof in the range. Unless otherwise
stated or contextually inapplicable, all percentages, when
expressing a quantity, are weight percentages. The suffix
“(s)” as used herein is intended to include both the singular
and the plural of the term that it modifies, thereby including
at least one of that term (e.g., the colorant(s) includes at least
one colorants). “Optional” or “optionally” means that the
subsequently described event or circumstance can or cannot
occur, and that the description includes instances where the
event occurs and instances where it does not. As used herein,
“combination” is inclusive of blends, mixtures, alloys, reac-
tion products, and the like.

As used herein, “a combination thereof” refers to a
combination comprising at least one of the named constitu-
ents, components, compounds, or elements, optionally
together with one or more of the same class of constituents,
components, compounds, or elements.

All references are incorporated herein by reference.

The use of the terms “a” and “an” and “the” and similar
referents in the context of describing the invention (espe-
cially in the context of the following claims) are to be



US 11,287,366 B2

33

construed to cover both the singular and the plural, unless
otherwise indicated herein or clearly contradicted by con-
text. “Or” means “and/or.” It should further be noted that the
terms “first,” “second,” “primary,” “secondary,” and the like
herein do not denote any order, quantity, or importance, but
rather are used to distinguish one element from another. The
modifier “about” used in connection with a quantity is
inclusive of the stated value and has the meaning dictated by
the context (e.g., it includes the degree of error associated
with measurement of the particular quantity). The conjune-
tion “or” is used to link objects of a list or alternatives and
is not disjunctive; rather the elements can be used separately
or can be combined together under appropriate circum-
stances.

What is claimed is:
1. A scanning microwave ellipsometer comprising:
a microwave ellipsometry test head comprising:
a polarization controller that receives an input electrical

signal, produces a polarization-controlled micro- 2

wave radiation from the input electrical signal,
receives reflected microwave radiation resulting
from the polarization-controlled microwave radia-
tion, and produces output electrical signal from
reflected microwave radiation;
transmission line in communication with the polar-
ization controller and that receives the polarization-
controlled microwave radiation from the polarization
controller, produces transmitted microwave radiation
from the polarization-controlled microwave radia-
tion, receives sensor-received microwave radiation
resulting from the transmitted microwave radiation,
and produces a reflected microwave radiation from
the sensor-received microwave radiation; and
a sensor in communication with the transmission line
and that receives the transmitted microwave radia-
tion from the transmission line, produces sensor
microwave radiation from the transmitted micro-
wave radiation, subjects a sample to the sensor
microwave radiation, receives a sample reflected
microwave radiation from the sample that results
from subjecting the sample with the sensor micro-
wave radiation, and produces a_sensor-received
microwave radiation from the sample reflected
microwave radiation, wherein a polarization of the
sensor microwave radiation is controlled by the
polarization controller;
an electrical signal measurement system in electrical
communication with the microwave ellipsometry test

®

head and that produces the input electrical signal, s

communicates the input electrical signal to the micro-
wave ellipsometry test head, receives the output elec-
trical signal from the microwave ellipsometry test head,
produces an electrical readout signal from the output

electrical signal such that a magnitude of reflection s

coefficient T and an angle of reflection coefficient T of
the sample reflected microwave radiation reflected
from the sample is determined from the electrical
readout signal, and produces a position control signal:
and

position controller in communication with the electrical
signal measurement system and that receives the posi-
tion control signal from the electrical signal measure-
ment system, adjusts a relative position of the sensor
and the sample based on the position control signal, and
moves the sensor relative to the sample so that the
sensor scans a surface of the sample.

a

&

&

at

34

2. The scanning microwave ellipsometer of claim 1,
wherein position controller adjusts the relative position by
moving the sensor relative to the sample selectively along
three orthogonal linear directions or in three independent
angular coordinates.

3. The scanning microwave ellipsometer of claim 1,
wherein the position controller is in mechanical communi-
tion with the microwave ellipsometry test head through
disposition of the microwave ellipsometry test head on the
position controller,

4. The scanning microwave ellipsometer of claim 1
wherein the position controller is in mechanical communi
cation with the sample through disposition of the sample on
the position controller.

5. The scanning microwave ellipsometer of claim 1,
wherein the sample is disposed on a first position controller,
and the microwave ellipsometry test head is disposed on a
second position controller,

wherein the first position controller and the second posi-
tion controller are independently controlled by the
electrical signal measurement system respectively via a
first position control signal and a second position
control signal.

6. The scanning microwave ellipsometer of claim 1,
wherein a shape of the sample comprises a planar surface, a
regular three-dimensional surface, or an irregular three-
dimensional surface that is subject to the sensor microwave
radiation from the sensor.

7. The scanning microwave ellipsometer of claim 1,
further comprising the sample.

8. The scanning microwave ellipsometer of claim 1,
wherein the sensor comprises a waveguide aperture, a wave-
guide hor antenna, a waveguide spot-focusing or gaussian-
beam antenna, or a combination comprising at least one of
the foregoing sensors.

9. The scanning microwave ellipsometer of claim 1,
wherein the polarization controller comprises an orthomode
transducer, a waveguide rotary joint, or a combination
comprising at least one of the foregoing sensors.

10. The scanning microwave ellipsometer of claim 1,
wherein the position controller comprises a roller on which
the sample is disposed, wherein the roller rotates to move the
sample relative to the sensor of the microwave ellipsometry
test head.

11. The scanning microwave ellipsometer of claim 1,
wherein the position controller comprises a robotic arm on
which the sensor is disposed, wherein the robotic arm moves
the sensor relative to the sample.

12. The scanning microwave ellipsometer of claim 1,
further comprising a microwave ellipsometer calibrant in
communication with the sensor from which the scanning,
microwave ellipsometer is calibrated.

13. The scanning microwave ellipsometer of claim 12,
wherein the microwave ellipsometer calibrant comprises a
substrate and a plurality of sectors disposed on the substrate,
wherein each sector provides a known material and known
positional anisotropy of microwave reflection coeflicient I.

14. The scanning microwave ellipsometer of claim 13,
wherein the plurality of sectors comprises:

a first sector that comprises a first material disposed as
first stripes and a second material disposed as second
stripes such that the first stripes and the second stripes
are alternatingly disposed to provide a first anisotropic
sheet resistivity;

a second sector that comprises a third material disposed as
third stripes and a fourth material disposed as fourth



US 11,287,366 B2

Sheet 28 of 53

Mar. 29, 2022

U.S. Patent

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SOW y X1S0Hy SOW y

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U.S. Patent Mar. 29,2022 Sheet 5 of 53 US 11,287,366 B2

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and linear motions



US 11,287,366 B2

Sheet 4 of 53

Mar. 29, 2022

U.S. Patent

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U.S. Patent Mar. 29,2022 Sheet 17 of 53 US 11,287,366 B2

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Relative rotational 7
and linear motions

FIG. 17


U.S. Patent Mar. 29, 2022

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U.S. Patent Mar. 29,2022 Sheet 23 of 53 US 11,287,366 B2

FIG. 23


a2) United States Patent
Long et al.

(10) Patent No.:
(45) Date of Patent:

US 11,287,366 B2
Mar. 29, 2022

(54) SCANNING MICROWAVE ELLIPSOMETER (58) Field of Clas n Search
AND PERFORMING SCANNING. CPC wren . GOIN 21/211
MICROWAVE ELLIPSOMETRY (Continued)

. 56 Ref Cited
(71) Applicant: Government of the United States of 66) eferences ©
America, as represented by the US, PATENT DOCUMENTS
Secretary of Commerce, Gaithersburg,
MD (US) 5,886,534 A 3/1999 Bakhtiari et al
7,453,562 BL* 11/2008 Kaack GOIN 21/33,
‘. 356/237.2
(72) Inventors: Christian John Long, Westminster, CO —
(US); Nathan Daniel Orloff, Louisville, FORFIGN ort CUMENTS
CO (US); Nina Popovie Basta, 4
Boulder, CO (US); Edward Joseph WO — WO-2008006825 Al * 1/2008 GOLV 3/12
Garboezi, Arvada, CO (US)
cous vet oe ne repre OTHER PUBLICATIONS
(73) Assignee: GOVERNMENT OF THE UNITED ‘Yurgartis, S.W., “Measurement of Small Angle Misalignments in
STATES OF AMERICA, AS Continuous Fiber Composites”, Composites Science and Technol-
REPRESENTED BY THE ogy, loa p. 279-293, vol. 30.
papain is . ., “Multi-functional flexible carbon fiver composites
SECRETARY OF COMMER’ ih contcolled’ fiber alignment usiag additive manulnetaras”
Gaithersburg, MD (US) Additive Manufacturing, 3018, p. 360-367, vol. 22.
Li, Z., et al., “Principles and Applications of Microwave Testing for
(*) Notice: Subject to any disclaimer, the term of this Ne at en ee an eeoe wal oom
patent is extended or adjusted under 35 (Continued)
USC. 154(b) by 139 days.
Primary Examiner — Tarifur R Chowdhury
(21) Appl. No.: 16/864,466 Assistant Examiner — Omar H Nixon
. (74) Attorney, Agent, or Firm — Office of Chief Counsel
(22) Filed: May 1, 2020 for National Institute of Standards and Technology
(65) Prior Publication Data 67) ABSTRACT
‘A scanning microwave ellipsometer includes: a microwave
US 2020/0348224 Al Nov. 5, 2020 ellipsometry test head including: a polarization controller; a
transmission line; and a sensor that produces sensor micro-
wave radiation, subjects a sample to the sensor microwave
Related U.S. Application Data radiation, receives a sample reflected microwave radiation
. : from the sample that results from subjecting the sample with

(60) Provisional application No. 62/841,612, filed on May the sample reflected microwave radiation, and produces a

1, 2019. sensor-received microwave radiation from the sample
; reflected microwave radiation, wherein a polarization of the

(51) Int. Cl. sensor microwave radiation is controlled by the polarization
GOIN 21/21 (2006.01) controller; an electrical signal measurement system that
GOIN 22/02 (2006.01) produces an electrical readout signal such that a magnitude

(52) of reflection coeficient F and an angle of reflection coefli-

GOIN 21/211 (2013.01); GOIN 22/02 cient T’ of the sample reflected microwave radiation is
(2013.01) (Continued)
. [=—— |
- i ie
este i i y
Sion j 3



US 11,287,366 B2

Sheet 46 of 53

Mar. 29, 2022

U.S. Patent

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radiation 34; acquiring sample reflected microwave radia-
tion 35 from microwave ellipsometer calibrant 20; and
determining angle of reflection coefficient ’ and magnitude
of reflection coefficient I for input electrical signal 10
acquired from output electrical signal 11 for sample reflected
microwave radiation 35 from microwave ellipsometer cali-
brant 20 to produce correction factors to apply to an arbitrary
output electrical signal 11 acquired from a sample 7.

Scanning microwave ellipsometer 200 and processes dis-
closed herein have numerous beneficial uses, including
real-time process control and quality control for composite
manufacturing, non-destructive imaging, sub-surface defect
detection, and quantitative characterization of anisotropic
electrical sheet resistance. These capabilities provide char-
acterizing alignment and orientation of short conductive
fibers in composite materials. Composites containing short
conductive fibers (e.g., carbon fibers and carbon nanotubes)
are involved in next-generation automotive and aerospace
applications, where they offer improved mechanical and
electrical performance and reduced weight. Unfortunately,
the structural and electrical integrity of composite parts
containing short conductive fibers can be limited by vari:
tion in the quality of the feedstock with which they are built.
‘To avoid catastrophic failure, engineers can assume a worst-
case performance for a batch of composite material. Mate-
rial-screening provided by scanning microwave ellipsometer
200 is beneficial to tighten tolerance on composite feedstock
and formed parts and provide lower cost, lower rate of
catastrophic failure, or tighter tolerance for high-perfor-
mance parts.

A conventional characterization technique for composites
is eddy-current inspection that may not operate at high
frequencies where the size of the eddy-current-excitation
coil becomes comparable to the wavelength of the probing
radiation. Increasing measurement frequency above the
eddy-current excitation limit can be favorable when the
thickness of a material under test is much less than the skin
depth at the upper-frequency-limit of the eddy current tech-
nique. Scanning microwave ellipsometer 200 overcomes
this frequency limitation, offering access to an advantageous
frequency range. In addition, the sensitivity of an eddy-
current technique decreases rapidly as the distance between
an eddy-current-probe coil and a material-under-test
increases. In an embodiment of scanning microwave ellip-
someter 200 where sensor 6 is waveguide spot-focusing or
gaussian-beam antenna 15, the distance between sensor 6
and sample 7 can be large compared to the distances
available in an eddy-current technique, overcoming the
sample-distance limitation.

Another conventional practice characterizing short-car- 5

bon-fiber composites is to image the material on a light
table, but light table imaging does not provide quantitative
sheet resistance data for analysis and light table imaging can
fail when the host matrix is not optically transparent or if the

material is too dense, which scanning microwave ellipsom-

eter 200 overcomes.

Scanning microwave ellipsometer 200 and proce:
herein unexpectedly facilitate evaluation of composite mate-
rials and formed composite parts. This evaluation includes
qualitative information about the alignment and orientation
of conducting fibers in an insulating host matrix and quan-
titative evaluation of anisotropic electromagnetic materials
properties. The capability to perform a unique combination
of spatially-resolved, anisotropic electrical conductivity
measurements, at microwave frequencies, with the option to
incorporate a substantial standoff distance between the test
head and a material under test, while also allowing for

0

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12

complex formed parts represents a novel departure from
conventional processes. Moreover, the measurement speed
of scanning microwave ellipsometer 200 is compatible with
real-time composite manufacturing techniques, enabling
real-time process optimization.

The articles and processes herein are illustrated further by
the following Examples, which are non-limiting.

EXAMPLES

Example 1. Microwave Measurements for
Anisotropic Materials Measurement

Applications of anisotropic composite materials range
from construction composites to electric circuit boards.
Anisotropic conductivity is one of the many important
measurands for anisotropic composites for identifying mis-
alignment. However, there are only a few non-destructive,
non-contact techniques available. Here, we explore wave-
guide ellipsometry, a new electromagnetic characterization
technique, and its application to conductive anisotropic
composites. We demonstrate waveguide ellipsometry and
discuss the design and implementation of a novel rotation
test-head on a robotic arm. To validate our technique, we
designed and fabricated test wafers with ideal anisotropic
composites consisting of gold stripes on materials with
varying sheet resistances. Finally, we map the measured
scattering (S-) parameters to simulated S-parameters with
help from composite theory and circuit modeling. Broader
impacts of microwave ellipsometry include in-line measure-
ment and conductivity imaging of large-scale and three-
dimensional parts for nondestructive evaluation.

Typical anisotropic composites include two or more
phases where the final material may have a blend of the
properties (chemical, mechanical, or electrical) of the origi-
nal constituents or even a property that is not present in
either of the constituent materials (e.g., metamaterials).
Narrowing the scope, there are several examples of thin
conducting anisotropic composites, which include sheets of
aligned carbon fibers, sheets of aligned carbon nanotubes,
and metasurfaces. In these composites, the electrical con-
ductivity can carry critical information about the anisotropic
mechanical and thermal properties, making electrical char-
acterization a useful engineering and quality control tool.
More broadly, electromagnetic characterization is applicable
when at least one material property (e.g., permittivity, per-
meabilit wr conductivity) is directional.

Specific electromagnetic characterization techniques for
anisotropic materials include far-field free-space measure-
ments and electromagnetic probing. Perhaps the first
example of electromagnetic characterization applied to
directionally dependent materials is microwave polarimetry.
Microwave polarimetry is a radar technique where a trans-
mitter or receiver rotates and results in an image of the
environment (eg., precipitation) between the two antennas.
After microwave polarimetry, free-space techniques are
extensive in literature, including work on two-port measure-
ments, oblique incidence reflection measurements, one-port
frequency shift measurements, and non-destructive inspec-
tion. There are reports of applications with non-destructive
rectangular waveguide probing on uniaxial anisotropic
dielectric materials, and biaxial anisotropic materials where
both the permittivity and permeability are tensors.

More specific to thin conducting anisotropic composites,
much of scientific literature focuses on eddy-current tech-
niques. These techniques characterize anisotropic conduc-
tive composites by measuring the impedance of a coil of



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Our experimental setup used a rotation stage, a foam
dielectric spacer, a WR-42 rectangular waveguide flange, a
translation stage, and a VNA. We connected the VNA to the
waveguide flange with a coaxial cable and contacted the
waveguide flange to the material-under-test via a microma-
nipulator. Afier positioning the flange over the axis of
rotation, we rotated the material-under-test to different fixed
angles. At each angle, we measured T’ (Eq. 1) with the VNA
cover the fundament mode of the waveguide (18 GHz to 26.5
GHz). All data shown is at 18 GHz. This was repeated over
several position on each sample to give an idea of local vs.
global alignment for each sample. The number of measure-
ments on each sample was N=5 for the control, Sample #2,
and Sample #4. For Sample #1 and Sample #3, the number
of measurements on each sample was N=10.

We show a schematic of the measurement setup in FIG. 3a
and a photograph of the measurement setup in FIG. 37. In
the next section, we provide a detailed step-by-step experi-
mental procedure.

A. process
includes performing a 1-port coaxial calibration (Short-
Open-Load) at the end of the cable that connects to the
waveguide flange: performing a waveguide calibration at the
end of the waveguide flange; levelling the waveguide flange
with a reference flat (FIG. 38); validating that the waveguide
flange is at the center of the axis of rotation; performing a
waveguide calibration at the end of the waveguide flange:
place a sample on the dielectric spacer; aligning the sample
to the edge of graph paper aflixed to the dielectric spacer
(FIG. 38). The graph paper is aligned to the sample with a
reference edge we assumed to be cut at 0°; rotating the
sample (FIG. 38); measuring T; repeating step 6 through
step 9 for the chosen number of angles between 0° and 360°;
flipping sample and repeat step 10 for the other side of the
sample-under-test; squaring the measured values to compute
the relative reflected power; fitting the data from step 9 to a
squared-ellipse model; computing the alignment and orien-
tation; and moving to a different position on the sample and
repeat step 1 through step 8.

‘We performed scanning microwave ellipsometry on four
blind samples and a control sample (FIG. 39). The four blind
samples had an unknown sample orientation and alignment
at the time of measurement. Each sample consisted of four
layers of aligned short carbon fibers. For an individual layer,
we used IM7* carbon fiber that had been chopped to an
average length of approximately (5.00.1) mm.

All blind samples were fabricated using the same method.
First, an individual layer was fabricated. Second, these
individual layers were consolidated to make a sample. To

make the sample, we aligned each layer on a light table, 5

controlling the layer-to-layer alignment with a protractor.
Once we aligned the fibers, we impregnated and consoli-
dated the sample with a thermoplastic polymer (polyether-
imide—Ultem 1000*) in autoclave for 4 hours at 2x10° Pa

and 335 C. For the control sample, we aligned each layer to

minimize the light transmitted through the sample, which we
aligned and measured by eye. For the blind samples, Sample
#1 was identical to the control, Sample #2 had all the layers
rotated by 5°, Sample #3 had the second of four layers
rotated by 5°, and Sample #4 had the second of four layers
rotated by 15°. FIG. 39 shows the control and blind samples.
Each sample was approximately 10 emx7 cm.

Before we measured the blind samples, we measured two
controls: no sample, and a laminated aluminum sheet. We
took the ‘no sample’ measurement by placing the waveguide
flange in direct contact with the dielectric spacer. We took
the ‘aluminum’ measurement by placing the waveguide

for performing microwave ellipsometry 2

&

&

26

flange in direct contact with a laminated aluminum sheet
placed on top of the dielectric spacer. We expected that the
‘no sample’ case would look like a circle on the microwave
ellipsometry graph with a smaller radius (FIG. 40), because
the signal propagated and was absorbed or radiated out the
sides of the dielectric spacer before a fraction of the power
was reflected into the waveguide flange. We expected that
the ‘aluminum’ case would also look like a circle on the
microwave ellipsometry graph with a radius close to one
(FIG. 40), because the signal was immediately reflected into
the waveguide flange and more of the signal was reflected.
In contrast with these isotropic samples, Sample #2 (FIG.
40) shows a rotated squared-ellipse, which is consistent with
an aligned carbon fiber sample with a 5° orientation.

Here we note that (2) was true for the measurement
configuration used for this work (FIG. 40), where the
backing plane consisted of a dielectric and a metal plate. We
can use a microwave absorber in lieu of the dielectric spacer,
which requires a Cassini oval model in lieu of a squared
ellipse model. Either approach can measure the alignment
and orientation, but in the latter case the signal-to-noise is
bigger.

After validating our measurements with the test cases, we
measured all the blind samples, and the control sample. We

5 then fit the microwave ellipsometry data to the model in (2).

extracting the orientation (0,) and alignment (y,,). We
computed uncertainty in the orientation (@,) and alignment
(Cas) bY propagating the error via a numeric Jacobian
incorporating the measurement uncertainty and fit residuals.
Unfortunately, the error in the orientation included the
uncertainty of placing the sample on the dielectric spacer by
hand, which added in quadrature to approximately #1°. This
contribution to the uncertainty was very large compared to
the other sources of error. Table 1 shows a summary of our
results.

From FIG. 42, we determined that Sample #1 (blue) was
identical to the control. Based on the orientation data, we
also determined that Sample #2 had all layers rotated by 5°,
and Sample #4 had one middle layer rotated by 15°. If the
error in the orientation had been less than +1°, we could have
also concluded that Sample #3 had one middle layer rotated
by 5°. Based on the volume of the ply misoriented by 5° (a
quarter of the sample), we expected the overall misorienta-
tion to be 1.25°. This is consistent with the value obtained
for Sample #3 Side A, however it is not true for Side B.
Based on this discrepancy we speculate that this microwave
technique can determine which layer is misaligned. How-
ever, this data is inconclusive based on the large uncertain-
ties. In future work we will decrease the uncertainty and pair
measurement with simulation. Likewise, for Sample #4, a
quarter of 15°, 3.75°, is also consistent with the value
obtained for Sample #4 Side B. For Sample #4, we hypoth-
esize that layer rotated by 5° was also closer to Side B.
Although this is a more reasonable hypothesize given the
uncertainty values, future work will include more extensive
measurements with lower uncertainties to confirm this
hypothesis.

From FIG. 43, Sample #2 had the highest alignment value
(2) compared to the other blind samples in the test. Sample
#4 had the lowest alignment value compared to the other
blind samples in the test. Based on FIG. 42, we expected that
Sample #4 should have the lowest alignment, because this
sample had a middle layer rotated by 15°. This sample
shows that orientation and alignment become convolved
when measuring multiple layers. From the perspective of the
electric field (FIG. 35), the carbon fibers in this sample
appeared more uniformly distributed. The other samples had



U.S. Patent Mar. 29,2022 Sheet 6 of 53 US 11,287,366 B2

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from polarization-controlled microwave radiation 30,
receives sensor-received microwave radiation 33 resulting
from transmitted microwave radiation 32, and produces
reflected microwave radiation 31 from sensor-received
microwave radiation 33; and sensor 6 in communication
with transmission line 5 and that receives transmitted micro-
wave radiation 32 from transmission line 5, produces sensor
microwave radiation 34 from transmitted microwave radia-
tion 32, subjects sample 7 to sensor microwave radiation 34,
receives sample-reflected microwave radiation 35 from
sample 7 that results from subjecting sample 7 with sensor
microwave radiation 34, and produces sensor-received
microwave radiation 33 from sample-reflected microwave
radiation 35, wherein a polarization of sensor microwave
radiation 34 is controlled by polarization controller 4; elec-
trical signal measurement system 1 in electrical communi-
cation with microwave ellipsometry test head 2 and that
produces input electrical signal 10, communicates input
electrical signal 10 to microwave ellipsometry test head 2,

receives output electrical signal 11 from microwave ellip- 2

sometry test head 2, produces electrical readout signal 12
from output electrical signal 11 such that the polarization,
magnitude of reflection coefficient I’, and angle of reflection
coefficient of sample-reflected microwave radiation 35
reflected from sample 7 is determined from electrical read-
out signal 12, and produces position control signal 9; and
position controller 8 in communication with electrical signal
measurement system 1 and that receives position control
signal 9 from electrical signal measurement system 1,
adjusts a relative position of sensor 6 and sample 7 based on
position control signal 9, and moves sensor 6 relative to
sample 7 so that sensor 6 scans a surface of sample 7.

In an embodiment, position controller 8 adjusts the rela-
tive position by moving sensor 6 relative to sample 7
selectively along three orthogonal linear directions and in
three independent angular coordinates. According to an
embodiment, position controller 8 is in mechanical commu-
nication with microwave ellipsometry test head 2 through
disposition of microwave ellipsometry test head 2 on posi-
tion controller 8. In an embodiment, position controller 8 is
in mechanical communication with sample 7 through dis-
position of sample 7 on position controller 8. In some
embodiments, sample 7 is disposed on first position con-
troller 8.1, and microwave ellipsometry test head 2 is
disposed on second position controller 8.2, wherein first
position controller 8.1 and second position controller 8.2 are
independently controlled by electrical signal measurement
system 1 respectively via first position control signal 9.1 and
second position control signal 9.2.

Sample 7 can be an arbitrary sample such as metal, 5

plastic, glass, ceramic, polymer, alloy, liquid, and the like.
Sample 7 can be a single material, or it can be a composite
of multiple materials in an arbitrary arrangement. A shape of
sample 7 can include a planar surface, a regular three-

dimensional surface (e.g., a sphere, parallelepiped, icosahe-

dron, truncated shape, and the like), or an irregular three-
dimensional surface that is subject to sensor microwave
radiation 34 from sensor 6.

In an embodiment, sensor 6 includes waveguide aperture
13, waveguide hor antenna 14, waveguide spot-focusing or
gaussian-beam antenna 15, or a combination of at least one
of the foregoing sensors 6. In an embodiment, polarization
controller 4 includes an orthomode transducer 16, wave-
guide rotary joint 17, or a combination of at least one of the
foregoing sensors 6. In an embodiment, position controller
8 includes roller 18 on which sample 7 is disposed, wherein
roller 18 rotates to move sample 7 relative to sensor 6 of

&

&

8

microwave ellipsometry test head 2. In an embodiment,
position controller 8 includes robotic arm 19 on which
sensor 6 is disposed, wherein robotic arm 19 moves sensor
6 relative to sample 7.

According to an embodiment, scanning microwave ellip-
someter 200 includes microwave ellipsometer calibrant 20
in communication with sensor 6 from which scanning
microwave ellipsometer 200 is calibrated. Microwave ellip-
someter calibrant 20 includes: substrate 21 and a plurality of
sectors disposed on substrate 21. Fach sector provides a
known material and known positional anisotropy of micro-
wave reflection coeflicient I. The plurality of sectors
includes: first sector 22 that includes a first material disposed
as first stripes 26 and a second material disposed as second
stripes 27 such that first stripes 26 and second stripes 27 are
alternatingly disposed to provide a first anisotropic sheet
resistivity; second sector 23 that includes a third material
disposed as third stripes 28 and a fourth material disposed as
fourth stripes 29 such that third stripes 28 and fourth stripes
29 are alternatingly disposed to provide a second anisotropic
sheet resistivity; third sector 24 that includes a fifth material
disposed to provide a first isotropic sheet resistivity; and
fourth sector 25 that includes a sixth material disposed to
provide a second isotropic sheet resistivity.

In an embodiment, electrical signal measurement system
1 includes a microwave source and a microwave detector,
wherein input electrical signal 10 and output electrical signal
11 are microwave radiation. In an embodiment, electrical
signal measurement system 1 includes a vector network
analyzer, and input electrical signal 10 and output electrical
signal 11 are microwave radiation. In an embodiment,
electrical signal measurement system 1 includes a scalar
network analyzer, and input electrical signal 10 and output
electrical signal 11 are microwave radiation. In an embodi-
ment, the electrical signal measurement system 1 includes a
computer that controls a vector network analyzer, scalar
network analyzer, microwave source, or microwave detec-
tor.

In an embodiment, transmission line 5 supports multiple
polarizations. Transmission line 5 supports polarized micro-
wave radiation and can be an arbitrary transmission line,
eg. circular waveguide, rectangular waveguide, ridge
waveguide, and the like.

‘As used herein, “microwave” refers to a frequency in
from 300 Hz to 3 THz. In an embodiment, microwave
radiation is above a cutoff frequency for waveguides in test
head 2 and below a frequency at which any waveguide in
test head 2 supports more than one propagating mode.

Scanning microwave ellipsometer 200 can be made in
various ways. In an embodiment, a process for making
scanning microwave ellipsometer 200 includes providing
sensor 6; connecting transmission line 5 to sensor 6; con-
necting polarization controller 4 to transmission line 5 so
that sensor 6 is in communication with polarization control-
ler 4 via transmission line 5; connecting polarization con-
troller 4 to electrical signal measurement system 1 so that
electrical signal measurement system 1 and polarization
controller 4 are in communication; connecting electrical
signal measurement system 1 to position controller 8 so that
electrical signal measurement system 1 and position con-
troller 8 are in communication; optionally disposing sensor
6 proximate to sample 7 so that sensor 6 can subject sample
7 to sensor microwave radiation 34 and so that sensor 6 can
receive sample reflected microwave radiation 35 form
sample 7; and optionally disposing sensor 6 or sample 7 on
a position manipulator so that sensor 6 and sample 7 move



US 11,287,366 B2

21

(gold lines in FIG. 31) have a maximum at the gold
boundary (90°), move toward a resonance at approximately
45°, and finally converge to the fused silica boundary at 0°,

The data in FIG. 31 is useful for relative measurements.
For example, one would expect a composite with well-
aligned conductive fibers to have a high electrical anisot-
ropy. Such a composite would be expected to behave like the
gold stripes without MoSi,. In contrast, a composite with

random fiber orientations would likely look more isotropic, 1

like one of the blanket films of gold or MoSi,.

While qualitative comparisons might find applications in
quality assurance or process control for composite manu-
facturing, it is preferable to map these relative measurements
to material properties. To verify our measurement with
known material properties, we combined full-wave simula-
tion and composite theory. The simulation section outlined
how we matched the isotropic MUTs, gold, fused silica, and
absorber as a function of height (FIG. 29) to decrease the

number of unknown parameters in the measurement setup. 2

Next, we defined a MUT with a conductivity tensor with
tensor components 0, and o,, from 3D composite simulation
and circuit models. Because the values for the tensor com-
ponents are so similar, we show the simulation with the 3D
composite simulation results. We converted these conduc-
tivity tensor components to bulk sheet resistance R,, and
R,,- which are easier to compare over MUTs of different
thicknesses (Table 2). The uncertainties were calculated
based on the measurement uncertainty of the MoSi, thick-
ness (rounded to the nearest nm for the simulation) (FIG.
27).

Looking at (FIG. 33) the three composites showed a
reasonable match between measurement and simulation. We
calculated the vector magnitude, the magnitude between the
measurement and simulation defined by their real and imagi-
nary parts, (FIG. 33). As the conductivity of the MoSi, layer
decreases, the match between simulation and measurement
gets worse. The worst case is gold stripes on bare fused
silica. There are three possible reasons why there is a
difference between simulation and measurement. The first is
the conductivity tensor calculated from composite theory
was calculated at DC and did not take frequency into
account. The second reason is the DC simulation and circuit
analysis do not take any capacitance between the fibers or
inductance along the fibers into account. The final source of
error is that the measurement is sensitive to the orientation
of the wafer, which is oriented relative to the waveguide by
hand. Mis-orientation of this nature was not part of the

simulation and would affect the gold stripes on fused silica 5

the most, because there is the largest angle-dependent di
ference in the S-parameters for the most anisotropic
samples.

From the conductivity tensor components (FIG. 32) and

the match between measurement and simulation (FIG. 33), 5

it is clear that the measurement is sensitive to anisotropy in
the conductivity tensor. It is also clear that it is possible to
estimate the conductivity tensor of an MUT by sweeping the
conductivity in a FEM simulation and comparing to mea-
surements. With the simulation setup that emulated the
measurement setup, we simulated a range of isotropic MUTs
with a thickness of 200 nm and parameterized the isotropic
conductivity between 10° (S/m) and 10-° (S/m) with 10
points for each decade (120 points in total) (gray line FIG.
34). We fit a phenomenological function with four fitting
parameters a, b, c, and d to map between the sheet resistance
and the real part of the reflection coefficient:

&

22

a (13)
RO= aR

where o=1.14, b=8.69*10“Q"', c=0.15, and d=-0.11.

From FIG, 34, we note that the measurement is not
sensitive to significant changes to the conductivity tensor
when the conductivity 0, is above ~10° Wm. For the
thicknesses and conductivities of these materials, the sheet
resistance is small compared to the waveguide impedance
(FIG. 34). In this regime the materials all act like short-
circuit reflects, making them diflicult to distinguish. Because
larger conductivities (smaller sheet resistances) are ill-con-
ditioned, we only used the mapping function (FIG. 34) to
extract the sheet resistance across the stripes, R,, (Table 2)
as well as the uncertainty in the measurement as the test-
head rotates (e.g., 0°, 180°, and 360°). The sheet resistance
between the three different techniques were all within the
uncertainty for the first three wafers. As noted earlier, the
circuit model and DC simulation do not take capacitance or
inductance into account as a function of frequency. This
frequency dependence becomes more apparent as we
increase the sheet resistance (decrease the thickness of the
MoSi,) and compare the theoretical results to the mapping
function. For wafer #4 and bare gold stripes on fused silica,
the theoretical values are larger than the mapping function,
suggesting that the DC simulation does not account for
additional parasitic circuit elements at high frequencies,
such as capacitance between the gold stripes.

We can also characterize materials such as carbon fiber
composites with a sheet resistance mapping function devel-
oped from the test wafers developed here. For example,
compact circuit models might replace the full-wave electro-
magnetic simulation, which might simplify the analysis and
increase the utility of our technique.

We demonstrated a non-contact electromagnetic charac-
terization technique that we called waveguide ellipsometry.
Our analysis verified the measured reflection coefficient with
composite theory and simulation using the calculated effec-
tive conductivity tensor of thin conducting anisotropic com-
posites. We automated our measurements of the complex
reflection coefficient by developing a motorized test-head to

change the angle of the F.-field with respect to the MUT. We
explained how to relate our complex reflection coefficient as
a function of angle to composite theory. To validate the
technique, we designed, fabricated, and measured several
test wafers that included both isotropic and anisotropic
materials. Next, we validated the effective material proper-
ties obtained from waveguide ellipsometry against those
from composite theory and circuit modeling. We found that
the bulk sheet resistance components extracted with circuit
model theory, DC composite simulations, and the mapping
function agreed over all four test wafers. However, we also
concluded that the measurement is not sensitive to signifi-
cant changes to the conductivity tensor when the sheet
resistance of the sample is below ~10Q/Q, which is a
limitation of this particular setup.

We tested a microwave ellipsometer for measuring thin
conducting anisotropic composites and related our measure-
ments to conductivity through a combination of simulations
and composite theory. Such tools will be useful for nonde-
structive testing, inline process control, and quantitative
imaging of conducting sheets used in next-generation com-
posites manufacturing.



U.S. Patent Mar. 29,2022 Sheet 37 of 53 US 11,287,366 B2

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U.S. Patent Mar. 29,2022 Sheet 53 of 53 US 11,287,366 B2

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U.S. Patent Mar. 29,2022 Sheet 26 of 53 US 11,287,366 B2

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US 11,287,366 B2

5

FIG. 39 shows four-layer short carbon fiber samples for
testing the microwave ellipsometry measurement. (a) Con-
trol sample with each layer aligned to minimize the light
transmitted through the ply. (b) Sample #1 was identical to
the control. (c) Sample #2 had all the layers rotated by 5°.
(d) Sample #3 had the second of four layers rotated by 5°,
(e) Sample #4 had the second of four layers rotated by 15°;

FIG. 40 shows microwave ellipsometry data at 18 GHz
for no sample, an aluminum sheet, and Sample #2. (a) ‘no
sample’ case measurements (blue circles) appears as a circle,
has a radius less than one, and fits an isotropic model (red
circle). (b) Aluminum case measurements (blue circles)
appears as a circle, has a radius close to one, and fits an
isotropic model (red circle). (c) Sample #3 measurements
(blue circles) appears as an ellipse, has an orientation close
to 5°, and fits an anisotropic model (red circle);

FIG. 41 shows data for blind samples results for orienta-
tion (@,) and alignment for (y,,). Uncertainties were
rounded up;

FIG. 42 shows absolute values for the average orientation
for control and four blind samples. Side A and Side B
corresponded to the top-facing and bottom-facing sides,
respectively. The number of measurements on each sample
was N=5 for the control, Sample #2, and Sample #4. For
Sample #1 and Sample #3, the number of measurements on
each sample was N=10. The measurement frequency was 18
GHz;

FIG. 43 shows absolute values for the average alignment
for control and four blind samples. Side A and Side B
corresponded to the top-facing and bottom-facing sides,
respectively. The number of measurements on each sample
was N=S for the control, Sample #2, and Sample #4. For
Sample #1 and Sample #3, the number of measurements on
each sample was N=10. The measurement frequency was 18
GHz;

FIG. 44 shows data for carbon fiber composite samples
with extracted parameters;

FIG. 45 shows samples measured for (a) a fabricated ideal
sample and (b) a single-layer short carbon fiber, (c) a
multiple layer short carbon fiber, (d) a single layer continu-
ous fiber, and (¢) multiple layer continuous fiber:

FIG. 46 shows R(T(8)) for (a) test wafers with gold stripes
on different thickness of MoSi, and (b) short carbon fiber
composites (SCFC) and continuous carbon fiber composites
(CCFC);

FIG. 47 shows (a) a mapping function between R (I) and
R,(Q/O) with the simulated data, measured data from the

test wafers, and the phenomenological fit (black line). (b) 5

‘The implementation of the mapping function of one spatial
position and two different carbon fiber composites. The
left-hand plot is R (1(@)) while the right-hand plot is R,(6)
on a log scale;

FIG. 48 shows R,(@)(Q/C) for (a) single layer short s

carbon fiber composite (SCFC), (b) multiple layer SCFC, (c)
single ‘bon fiber composite (CCFC
(@) multiple layer CCFC. Graphs are for one s;
and a fit (solid line) over mapped data (dots);

FIG. 49 shows R() versus R, including the fit (black
line) and measurements for the different carbon fiber com-
posites. Data points are colored based on the composite. The
points at the lower end correspond to (0°) and T(90°) for
each of the samples;

FIG. 50 shows a single layer SCFC with (a) the mapped
data with fit for one spatial position, (b) the percent error as
a function of angle for the same spatial position (c) a plot of

20

&

&

6

the orientation for each spatial position and (d) a plot of the
ratio between the sheet resistance across and along the fibers
(Re/Ryy)s

FIG. 51 shows multiple layer SCFC with (a) the mapped
data with fit for one spatial position, (b) the percent error as
a function of angle for the same spatial position, (c) a plot
of the orientation for each spatial position, and (d) a plot of
the ratio between the sheet resistance across and along the
fibers (R,/R,,):

FIG. 52 shows a single layer CCFC with (a) the mapped
data with fit for one spatial position, (b) the percent error as
a function of angle for the same spatial position, (c) a plot
of the orientation for each spatial position, and (d) a plot of
the ratio between the sheet resistance across and along the
fibers (R,,/R,,); and

FIG. 53 shows a multiple layer CCFC with (a) the mapped
data with fit for one spatial position, (b) the percent error as
a function of angle for the same spatial position, (c) a plot
of the orientation for each spatial position, and (d) a plot of
the ratio between the sheet resistance across and along the
fibers (R,/R,,)-

DETAILED DESCRIPTION,

A detailed description of one or more embodiments is
presented herein by way of exemplification and not limita-
tion.

New strong, light, and compact formed carbon fiber
components involve short, high-aspect ratio carbon fibers.
Short carbon fibers are aligned to provide a desired tensile
strength. Conventional tools fail to accurately characterize
carbon fiber alignment for inline quality assurance or for
verification of alignment in 3D parts. Advantageously, a
scanning microwave ellipsometer overcomes this problem
by providing scanning microwave ellipsometry. The scan-
ning microwave ellipsometer provides a polarized electric
microwave field and measures reflection of the polarized
electric microwave field from a sample as a function of
angle. Resulting reflected power plotted versus measured
angle on a polar plot has an elliptical shape. The scanning
microwave ellipsometer includes a test head that rotates the
electric microwave field relative to the sample. The test head
is rastered over the sample, e.g., by a 6-axis robotic arm or
other motion manipulator. A process for performing micro-
wave ellipsometry acquires data, fits the microwave ellip-
sometry data, and produces discrete measurands that can be
plotted as a function of position in three dimensions, two
dimensions, or one dimension. The discrete measurands can
include a maximum value, a minimum value, an alignment
value, and an orientation value. Scanning microwave ellip-
sometry is broadly applicable where large-scale imaging of
material properties is useful as well as single testing cases.

Tt has been discovered that scanning microwave ellipsom-
eter 200 subjects a sample to scanning microwave ellipsom-
etry. In an embodiment with reference to FIG. 1 to FIG. 20,
scanning microwave ellipsometer 200 includes scanning
microwave ellipsometer 200 including: microwave ellip-
sometry test head 2 including: polarization controller 4 that
receives input electrical signal 10, produces polarization-
controlled microwave radiation 30 from input electrical
signal 10, receives reflected microwave radiation 31 result-
ing from polarization-controlled microwave radiation 30,
and produces output electrical signal 11 from reflected
microwave radiation 31; transmission line 5 in communica-
tion with polarization controller 4 and that receives polar-
ization-controlled microwave radiation 30 from polarization
controller 4, produces transmitted microwave radiation 32



US 11,287,366 B2

23

Example 2. Nondestructive, Noncontact
Quantification of Carbon Fiber Alignment and
Orientation by Microwave Ellipsometry

Short-fiber composites facilitate the manufacture of tai-
lorable feedstock for small formed parts. In these compos-
ites, the alignment and orientation of the short fibers must be
controlled to achieve the desired composite properties. To
realize this control, process engineers need a fast, nonde-
structive, noncontact in-line measurement technique that
quantifies alignment and orientation as the material is pro-
duced for on-the-fly feedback. Such a technique would
enable real-time control of processing variables, resulting in
higher quality composites. Here, we describe high-speed
microwave ellipsometry to measure alignment and orienta-
tion. To evaluate our approach, we measured five short-fiber
composites samples made from a four-layer stack of carbon-
fiber mats. These samples included one known control
sample and four blind samples that were unknown at the

time of testing. ‘The four blind samples were known to be 2

either a control, a sample with all layers rotated by 5°, a
sample with a single unknown layer rotated by 5°, or a
sample with a single unknown layer rotated by 15°. Our
results demonstrated effectiveness of this technique and
discuss a path for real-time, large-scale imaging of fiber
alignment and orientation.

To realize commercial tailorable feedstock, materials
engineers need to produce highly aligned layers of fibers and
they need to control the orientation of each layer in the ply
feedstock. This implies that there are at least two process
variables of interest: fiber alignment and fiber orientation.

In this Example, alignment is a measurand that quantifies
the average alignment of each carbon fiber in a layer relative
to each other. A relative alignment with a value of one means
that all the carbon fibers in a layer are parallel to one and
another. A relative alignment with a value of zero means that
all the carbon fibers are uniformly distributed by angle
relative to each other. Likewise, we define orientation as the
orientation of a layer relative to the direction of the electric
field in the measurement (FIG. 35). A relative orientation is
an angle that describes which direction the carbon fibers in
all the layers point to relative to some applied electric field
orientation. When multiple layers form a ply, the alignment
and orientation values from each layer combine.

Imaging a ply on a light table is a common technique. To
get spatial information, an image can be segmented. This
optical technique can be fast, leveraging advances in real-
time image processing (e.g., OpenCV). This optical tech-
nique is also transmission-based. As such, it does not work

for samples that cannot pass light, cannot differentiate s

between layers, and it is difficult to implement for three
dimensional samples. Yet another technique uses eddy cur-
rent sensors. This eddy current approach has some trade-
offs, which include operating in the near-field with a small

working distance and requiring the composite to have a ;

conductivity within a specific range.

Microwave ellipsometry uses the relative reflected power
of a microwave signal measured as a function of the angle
between the carbon fibers and the polarized incident micro-
wave radiation. When the electric field is parallel to the
carbon fibers, the electric field moves charge along the
length of the fiber. The current flow in this case is much the
same as it would be in a conducting sheet, resulting in a
combination of reflection and absorption of the electrical
signal. When the electrical field is perpendicular to the
carbon fibers, the electric field cannot move charge in the
fiber as far, and instead charges must capacitively couple

24

from fiber to fiber through the host matrix in the ply. In this
case, the ply acts more like an insulator than a conductor,
and there is a higher amount of transmission through the ply,
in addition to some reflection and absorption. Later, we will
show that the resultant relative reflected power versus mul-
tiple angles creates a squared-ellipse model on a polar graph,
which can then be related to the alignment and orientation.
The microwave ellipsometry approach can work on thick
samples, it is comparatively easy to implement in three
dimensions, it can work in the far field, and it can potentially
work with a wide range of conductivities.

Microwave ellipsometry uses the relative reflected power,
which is measured with a vector network analyzer (VNA).
The VNA measures a relative reflection coeflicient (I),
which is related to the reference impedance of the port (Z,)
and the impedance of the sample (Zjampie). The resultant
reflection coeflicient is given as,

Error!
Bookmark

‘not
defined(1)

© 7+ Zoanote

The relative reflected power is simply the square of the
reflection coefficient. After we measured (1), we found that
the general form of a squared ellipse modeled the relative
reflected power as,

Enort
a-b Bookmark
cos (0 = 0) + sin 85) defined)

where a is the minor axis, b is the major axis, and the
orientation is described by 6, From (2), we define the
orientation as 0,, and the alignment as (FIG. 36),

Error!
Bookmark
defined (3)

For a highly aligned, very conducting sample, when the
electric field is aligned with b then b is close to one, and a
is close to zero. Any nonzero value of a is then due to
electrical conduction through the matrix of the ply, capaci-
tive coupling between fibers and any reflection from the
isotropic substrate material, which would tend to be the
same for any angle. In this case, the value of x,, in (3) is
close to 1. Conversely, for a sample that has highly con-
ducting fibers that are uniformly distributed throughout the
layer at random angles, the value of ,,, is close to zero, since
ais similar in value to b. This former case represents a layer
(or ply) that is aligned, and the latter case represents a layer
(or ply) that is not aligned. The value calculated is not
absolute, at this point, we can only say that for a weakly
conducting matrix an alignment closer to one indicates a
more aligned sample. Samples with known alignments could
calibrate this alignment value, allowing us to quantify align-
ments across different processes. That said, we assert that the
alignment value calculated without calibration samples suf-
fice for process control. FIG. 36 shows the squared-ellipse
function as the blue solid line, and the minor and major axes
are labeled with the orientation.



U.S. Patent Mar. 29,2022 Sheet 2 of 53 US 11,287,366 B2

nm

FIG. 2


U.S. Patent Mar. 29,2022 Sheet 45 of 53 US 11,287,366 B2

FIG. 45


U.S. Patent Mar. 29,2022 Sheet 43 of 53 US 11,287,366 B2

0.45
N = 5 unless noted
2 04
c
=
<
GS 0.35
<
ie]
E 0.3
&
a4
<0 25
eS S&S & &
. x 3 Rod ae
x ° ar
SY
& & 6 <

FIG. 43


US 11,287,366 B2

29

reflection coefficient is poorly defined. For an isotropic
material, as the linearly polarized E-field rotates above the
MUT, Zygor and I are therefore not function of the relative
angle, 0. For an anisotropic material, Zy-r changes and is
dependent on the effective conductivity tensor at that rela-
tive angle, 6. When the incident E-field is polarized along
the carbon fibers, the impedance is dominated by the imped-
ance of the conductive fibers, so almost all the field is
reflected to the aperture. When the incident E-field is polar-
ized across the carbon fibers, the impedance is dominated by
the impedance of the matrix, so there is less reflection and
more loss. We characterized the relationship between elec-
tromagnetic response and MUT impedance of the carbon
fibers with the help of test wafers, composite theory, and full
wave simulation.

To evaluate the carbon fiber composites, first we mea-
sured and analyzed well-known anisotropic composites on
test wafers. The test wafers were designed to mimic the

carbon fiber composites in electrical behavior as well as 2

physical geometry. The gold stripes on the test wafers are
like the IM7 carbon fibers found in the composites, and the
varying thicknesses of MoSi, mimic a combination of fiber
misalignment, an electrical percolation network, and the

conductivity of the matrix. We developed a model of the test >

wafers and represent the conductivity as an effective con-
ductivity tensor:

Q

where o,, 0,, and o. are the & 9, and 2 components of the
conductivity tensor. This is a good approximation because
the gold stripes and the IM7 fibers are significantly smaller
in fiber diameter than the size of the probe in the measure-
ment setup. Therefore average out the smaller features and
treat the whole composite as an effective medium with an
effective anisotropic conductivity tensor, 0. We applied a
rotational matrix that rotates the matrix o (2) in the (&,
$)-plane around the z-axis by some angle 0. The o,,, matrix
is a representation of the orientation of the test wafer with
respect to the test head:

7400870 +.07,sin’@ sinBcosO(ox-cy) 0 8
rot =| sinbeosA(ox- cy) oxsin?O+ oycos" 0

0 0 o

‘We computed the components of the test wafer’s effective
conductivity tensor with a 3D DC composite theory simu-

lation. From a 3D model of the composite and the conduc- s

tivity ratio between the two phases, the simulation calcu-
lated the voltage at each node and solved the current
continuity equations to satisfy the boundary conditions and
minimize the dissipated energy over the full system. To
verify the DC composite theory simulation, and to make the
analysis more available, we derived circuit models to cal-
culate the conductivity tensor [CITE]. We used the rotated
conductivity tensor to verify measurements of the test wafer
to composite theory with the help of 3D full wave finite
element method (FEM) simulation.

We connected the test-head to a 40 GHz vector network
analyzer (VNA). The test-head had to rotate relative to the

3

&

45

5

65

30

material under test, so it included a phase stable RF rota-
tional joint, a 2.4 mm coaxial to WR-42 waveguide adapter,
and a 2-inch section of waveguide left unterminated. The
test head included a rotary motor, all attached to a robotic
arm with a 3D printed connecting piece. There was a small
gap, approximately 300 jiM, between the rectangular wave-
guide and the MUT. The MUT was either the test wafer, thin
depositions of gold and MoSi, on fused silica, or carbon
fiber composites attached to bare fused silica wafers to help
with the consistency between the two samples. The MUT
was placed above a (10.2+0.5) mm thick piece of Rohacell
(€ =I) and a (18+5) mm thick piece of foam absorber (FIG.
19). Both the absorber and the Rohacell layers were much
larger in the xy-plane than the MUT. We added a stand-off
of Rohacell because absorber is difficult to simulate and
understand at near-field, by adding the Rohacell we were
able to move the absorber from the near-field to the far-field.
The absorber was secured by silicone caulking on the edges
to a planarizing table that was metallic.

After the test-head was secured to the robot and the
absorber platform was completed, there were four variables
available for each measurement: (x, y) location, angle, and
frequency. All samples were measured over 25 (x, y) posi-
tions distributed over the sample and far enough from the
edge to minimize any edge effects and a constant height z.
The robotic arm was set to an (x,y,z) coordinate with 5 jum
repeatability. Each position was measured every 5° for a
total of 73 angle positions (0° was measured twice), at one
frequency, 18 GHz. This technique is not limited to 18 GHz,
we only show this data to establish procedure and minimize
the amount of data in this paper. We made all the measure-
ments with a control program that iterated over robot
position, relative angle position, and VNA data acquisition.
The data was calibrated to the reference plane at the end of
the WR-42 waveguide. Calibration procedures are important
for electromagnetic measurements because they move the
measurement reference plane to a known position. Without
this known position, any conclusions from the measure-
ments can be incorrect or misleading. Our calibration pro-
cedure was a two-step procedure including a step that
account for the rotational angle theta.

The mapping function related the effective sheet resis-
tance to the measured reflection coefficient using the test
wafers and a full-wave FEM simulation. The full-wave FEM.
simulation modeled the measurement setup and calculated
the S-parameters defined a conductivity for the MUT. The
FEM simulation was a 3D composition of the test head
including the rectangular waveguide, plastic hold, and metal
motor components. The MUT’s sheet resistance was param-
eterized over a large range (10°? to 10°)S/m and the simu-
ation calculated Real(I(6)) (light dots FIG. 47). We took the
Real(I‘(@)) and related it to the sheet resistance which is
proportional to the Real(Z,,z,7). The relationship between
Real(T(@)) and the sheet resistance was verified using the
effective sheet resistance (along the fibers, R,,, and across the
fibers, R,,) calculated from the test wafer geometry and their
measured S-parameters (FIG. 46). We used the simulated
data for the mapping function because the test wafer did not
give us enough points for a reliable fit. The high sheet
resistance was also the thinnest deposition of MoSi,. The
mapping function between sheet resistance (R,(6)) and the
R(L(6)) had a phenomenological fit:

@)

Rio =

ae


U.S. Patent Mar. 29,2022 Sheet 13 of 53 US 11,287,366 B2

In

17

FIG. 13


US 11,287,366 B2

3

microwave radiation from the sensor as the sensor is moved
relative to the sample to perform scanning microwave
ellipsometry of the sample.

BRIEF DESCRIPTION OF THE DRAWINGS

The following description should not be considered lim-
iting in any way. With reference to the accompanying
drawings, like elements are numbered alike.

FIG. 1 shows a scanning microwave ellipsometer;

FIG. a microwave ellipsometry test head:

FIG. 3 shows a scanning microwave ellipsometer:

FIG. 4 shows a scanning microwave ellipsometer;

FIG. § shows a scanning microwave ellipsometer;

FIG. 6 shows a scanning microwave ellipsome

FIG. 7 shows a scanning microwave ellipsometer;

FIG. 8 shows a scanning microwave ellipsometer with a
sample for a two-dimensional surface of the sample in panel
A, for an irregular three-dimensional surface of the sample

in panel B, and for a regular three-dimensional surface of the 2

sample in panel C;
FIG. 9 shows a microwave ellipsometry test head;

FIG. 10 shows a microwave ellipsometry test head:

FIG. 11 shows a microwave ellipsometry test head;

FIG. 12 shows a microwave ellipsometry test head:

FIG. 13 shows a microwave ellipsometry test head:

14 shows a scanning microwave ellipsometer;

15 shows a scanning microwave ellipsometer;

16 shows a scanning microwave ellipsometer;
FIG. 17 shows a scanning microwave ellipsometer;
FIG. 18 shows an exploded view ofa scanning microwave

ellipsometer;

FIG. 19 shows a scanning microwave ellipsometer;

FIG. 20 shows a microwave ellipsometer calibrant;

FIG. 21 shows magnitude data as a function of angle for
isotropic samples, wherein panel A shows data for gold and
fused silica samples, and panel B shows data for various
MoSi, samples;

FIG. 22 shows magnitude data as a function of angle for
anisotropic samples, wherein panel A shows data for gold
stripes and fused silica samples, and panel B shows data for
various MoSi, samples;

FIG. 23 shows complex data plotted on a smith chart;

FIG. 24 shows a graph of a magnitude of reflection
coefficient I’ for output electrical signal versus sheet resis-
tance that provides a calibration curve to map reflection
coeflicient magnitude to sheet resistance;

FIG. 25 shows a graph of an angle of reflection coefficient
I’ for output electrical signal versus sheet resistance that

provides a calibration curve to map reflection coefficient 5

angle to sheet resistance;

FIG. 26 shows, in panels A and B, measurements of an
aligned and misaligned carbon fiber sample before and after
mapping to sheet resistance;

FIG. 27 shows physical properties of test wafers;

FIG. 28 shows composite theory with a (a) schematic of
the anisotropic composite where the dimensions are defined
by voxels (length in nm divided by the voxel edge length a)
The simulated volume has voxel dimensions n,=20000/a,
n,=S, and n.=200/a+t/a, where the substrate has a thickness
t. (b) The circuit model associated with the conductivity in
the ¥-direction and (c) the circuit model associated with the
conductivity in the x-direction. The resistance is dependent
on the direction of interest, the subscripts x and y indicate
that direction;

FIG. 29 shows an overview of a full wave simulation with
a (a) schematic of the full wave simulation including the

&

4

material-under-test, the waveguide, the plastic holder, and a
box representing the aluminum motor, and (b) match
between measurement (solid line with circles) and simula-
tion (dotted line with stars) for the control samples (ab-
sorber, fused silica, and gold) over 5 measured heights: (0.3,
0.8, 1.3, 1.8, 2.3) mm;

FIG. 30 shows an overview of a calibration process with
(a) a test-head with the reference planes labeled (first-tier
and second-tier) and (b) on a Smith chart with all isotropic
materials measured including the controls: gold, fused silica,
absorber, and the MoSi, on the test wafers. The symbols
indicate raw S-parameters, S-parameters calibrated to the
end of the 2.4 mm coaxial cable before the test-head
(first-tier), and the S-parameters calibrated to the edge of the

5 WR-42 waveguide (second-tier), respectively. The S-param-

eters are shown for one angle, where the change over angle
is small compared to the size of the plot markers;

FIG. 31 shows calibrated measurements for control and
test samples including the gold, fused silica, different thick-
ness of MoSi,, gold stripes on fused silica, and gold stripes
on different thickness of MoSi,. Samples were separated
into (a) isotropic gold and absorber and gold stripes on fused
silica, and (b) the isotropic MoSi, films and gold stripes on
MoSi, films. The polar plot of the magnitude of the reflec-

5 tion coefficient has uncertainties equal to the standard devia-

tion of the measurement between all 16 (x,y)-positions. The
same data are represented in (c) a Smith chart of the complex
impedances for each MUT and (d) a blown-up section of the
Smith chart for better visibility;

FIG, 32 shows sheet resistance tensor components from
circuit model analysis, 3d composite simulation, and the
mapping function;

FIG. 33 shows a comparison of measured and simulated
S-parameters (a) on a Smith chart with measured (solid line)
and simulated (dotted line) lines for three of the anisotropic
materials, gold stripes on bare fused silica, 20 nm, and 185
nm. (b) The vector magnitude between the measured and
simulated S-parameters for each angle between 0° and 360°
for all five anisotropic material

FIG. 34 shows a mapping function (a) (gray line)
extracted with simulation between complex S: eters
and a 200 nm MUT with an isotropic conductivity with 320
points between 10° (S/m) and 10-® (S/m). The stars are the
measured response of the isotropic materials gold, MoSi, of
185 nm, 80 nm, 45 nm, and 20 nm, and bare fused silica. (b)
The mapping function between R(P) and the bulk sheet
resistance (Q/D):

FIG. 35 shows how carbon fibers can be oriented relative
to the fundamental model TE, , of an electric field (arrows)
in waveguide. (a) A parallel orientation, which is defined as
0°. (b) A perpendicular orientation, which is defined as 90°.
The color bar indicates the strength of the electric field in
Vim;

FIG. 36 shows a squared ellipse that models the relative
reflected power as a function of angle, where the angle is
defined as the angle between the electric field and the
sample-under-test. The blue solid line is the squared-ellipse
fit, 0, is the orientation, a is the minor axis, and b is the major
axis;

FIG. 37 shows a microwave ellipsometry measurement
setup. (a) A schematic of the measurement setup. (b) A
photograph of the measurement setup;

FIG. 38 shows selected steps from a process that includes
(a) levelling the waveguide flange with a reference flat; (b)
aligning an edge of the sample to the edge of graph paper
that is affixed to the dielectric spacer with polyimide tape;
and (c) rotating the sample:



US 11,287,366 B2

15

A=0, c0s"(0)+0, sin” (0),

B

1 @)+0, cos*(0),
Fsin(@}cos(0)(0,-0,). co)

where 0 is the relative angle between the incident E-field
polarization and the fiber direction. This angle rotated con-
ductivity tensor allows us to validate waveguide ellipsom-
etry with full-wave modeling by simplifying the finite-
element simulations in the next section, We can also use this
form to extract the components @, and @, with DC simula-
tion and equivalent circuit modeling.

To solve for the effective medium’s conductivity tensor
with DC composite theory, we modeled our anisotropic
composite as a structure (green box in FIG. 28) with periodic
boundary conditions. The volume was divided into cubic
voxels with an edge length, a, of 5 nm. In the §-direction,
parallel to the gold stripes, there were n,=5 voxels. This
number was arbitrary, as the fields were taken to be constant
along this direction. In the &-direction, perpendicular to the

gold fibers, there were n,=4000 voxels, corresponding to 20. >

The boundary condition in the x-direction was placed in the
middle of the gold stripe, resulting in two 5 gold stripes on
either side of a 10 gap of air (FIG. 3(a)). Finally, the
z-direction had n_-40+t/a voxels, corresponding to 200 nm
of gold, and a thickness t (nm) of MoSi, (FIG. 27).

Each voxel was assigned an effective conductivity based

on the ratio between gold and MoSi,. The first four aniso-
tropic materials we modeled and measured had some thick-
ness, t, of MoSi,. The conductivity of gold (6,,;/-3.95:10"
Sim) and MoSi,. was normalized by the MoSi, “conductivity
(Osg0s1,=1.3910° S/m). The conductivity of the deposited
gold was measured with an on-wafer multiline TRL tech-
nique and the conductivity of the MoSi, was measured with
a four-point probe on the blanket films of each test wafer
(quadrant #3 in FIG. 20). In the DC composite theory
simulations, we took the conductivity ratio between gold
and MoSi; to be 280:1 (6,,,:Fyy,. Fespectively).
The DC composite theory simulation computed the bulk
conductivity tensor from the model of the composite (FIG.
28) and the conductivity ratio. The simulation calculated the
voltage at each node and solved the current continuity
‘equations to satisfy the boundary conditions and minimize
the dissipated energy over the full system.

To verify the DC composite theory simulation, and to
make the analysis more available, we derived circuit models
to calculate the conductivity tensor. Although the models in
FIG. 28 were simple, they qualitatively agree with our
understanding of how the current spreads out into the

composite when the E-field is parallel and perpendicular to
the stripes.

The resistances of each material in the circuit model are ~

related to their length (1), area (A) defined by voxels (FIG.
28), and normalized material conductivity (Gyyarersat)*

L 4°

moverict A

The relationship between the circuit model resistivity and
the effective circuit conductivity in a given direction is:

UR 6)

16
where 0, y, 97 )“F'Gx40s3,» and R is the total resistance of the
circuit model. We used the dimensions defined in FIG. 28 to
find the A and I components of the circuit conductivity in the
J-direction (G,.) and simplified the expression:

papa (ect °

7%

1200000
an

+m

_ (OO) gn + (On
= 00+

Earlier, we defined Gy, 280 and Gy,,=1, therefore for
small values of t, G,.~G,,/2, while for our largest values of
1, 6,.=G,,/4. A similar approach was implemented to cal-
culate the conductivity o,. (FIG. 28), where along the
x-axis, the gold and MoSi, are first in parallel with some
parallel resistance, R,, which is in series with a section of

Rygosi: again in series with a parallel resistance, R,,

a

L
4 Rutosing + 2Rp)( =
se, +83),

21200 mp +)
© Qe 200 Fyn, )(200 +)

where the parallel circuit has a resistance R,,, based on the
physical dimensions along the x-axis:

(8)

and the MoSi, resistance (Ryyosi,) is:

Rutosing = ®

The above results are specifically for the anisotropic
materials with a layer of MoSi,. The last anisotropic mate-
rial (quadrant #2) had gold stripes on fused silica with no
MoSi,. In this case, the DC composite theory simulation
breaks down because it was based on conductivity ratios and
there was only a single material with a finite conductivity in
the simulation. For this case, we took 0, =0,,.;/2 because the
space between the Au stripes was equal to the width of the
stripes, reducing the effective conductivity by half. We also
took o,=0 S/m because the Au stripes were not electrically
connected in the x direction in the absence of MoSi, layer.
Finally, we compare measurement to theory with the help of
full-wave finite-element-method (FEM) simulation.

The full-wave FEM simulations modeled the measure-
ment setup and calculated the S-parameters from the DC
conductivity tensor (FIG. 29). The full-wave simulation
used an FEM solver to calculate the electromagnetic fields
over a specified mesh. To make the simulations as accurate
as possible, we imported a 3D model of the rectangular



US 11,287,366 B2

53

Sheet 15 of

Mar. 29, 2022

U.S. Patent

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U.S. Patent Mar. 29,2022 Sheet 1 of 53 US 11,287,366 B2

oN a

Relative rotational a
and linear motions

_ a

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FIG. 1


U.S. Patent Mar. 29,2022 Sheet 36 of 53 US 11,287,366 B2

150 /

180 |

210

240 8300
270

FIG. 36


U.S. Patent Mar. 29,2022 Sheet 24 of 53 US 11,287,366 B2

/ Validation samples

10;

0.9 | NY Measured data
| Ye

0.8 1 \

— _

O.7 | Expected uncertainty
‘Sy q- «from real samples
a

0.64 .
| ~~».

0.54

0 25 50 75 LOO 6125150
Sheet Resistance (0./0)

FIG. 24


US 11,287,366 B2
Page 2

determined from the electrical readout signal; and a position
controller that adjusts a relative position of the sensor and
the sample.

19 Claims, 53 Drawing Sheets

(58) Field of Classification Search
USPC . 356/364
ich history.

See application file for complete
(56) References Cited
U.S. PATENT DOCUMENTS

8,771,443 B2
10,099,465 B2
2003/0015493 AL*

7/2014 Clemen, Jr.
10/2018 Clemen, Jr.
1/2003 Grasshoff HOLL 21/67253,
216/59

GOIN 21/8422
356/369
GOLB 11/0641
356/369
GOLB 9/02091
356/301

HOIL 21/0271

2014/0125978 A1* 5/2014 Feiler

2015/0292866 A1* 10/2015 Sasaki ......
2016/0146722 A1* 5/2016 Koerner

2020/0401040 A1* 12/2020 Khusnatdinov

OTHER PUBLICATIONS
Heuer, H., et al., “Review on quality assurance along the CFRP
value chain—Non-destructive testing of fabrics, preforms and CFRP
by HF radio wave techniques” Composites Part B, 2015, p. 494-501,
vol. 77.
Bardl, G., et al., “Automated detection of yarn orientation in
3D-draped carbon fiber fabrics and preforms form eddy current
data”, Composites Part B, 2016, p. 312-324, vol. 96.
Gambou, F, et al., “Characterization of Material Anisotropy Using
Microwave Ellipsometry”, Microwave and Optical Technology
Letters, 2011, p. 1996-1998, vol. $3 No. 9
Sagnard, F., et al, In Situ Measurments of the Complex Permittivity
of Materials Using Reflection Ellipsometry in the Microwave Band:
Theory (Parl 1), IEEE Transactions on Instrumentation and Mea-
surement, 2005, p. 1266-1273, vol. 54 No. 3.
Sagnard, F., et al, In Situ Measurments of the Complex Permittivity
of Materials Using Reflection Ellipsometry in the Microwave Band
Theory (Parl II), IEEE Transactions on Instrumentation and Mea-
surement, 2005, p. 1274-1282, vol. 54 No. 3.
Schultz, J.W., et al., “A Comparison of Material Measurement
Accuracy of RF Spot Probes to a Lens-Based Focused Beam
System”, Proc. 2014 AMTA Symp, 2014, 2014, p. 421-427.
Compass ‘Technology Group, “SP218 CTG”, https://compasstech.
com/core-technologies/, accessed Apr. 23, 2019

* cited by examiner


U.S. Patent Mar. 29,2022 Sheet 48 of 53 US 11,287,366 B2

R,(O/0)
Frequency = 18 GHz

2Q
%

FIG. 48


US 11,287,366 B2

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Mar. 29, 2022

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U.S. Patent Mar. 29,2022 Sheet 27 of 53 US 11,287,366 B2
Wafer number} Measured | MoSi2 sheet | Measured Au
MoSi 2 resistance __ |layer thickness
thickness (nm) (Q/? ) (nm)

Wafer #1 (185.1 +5.2)| (43.9 + 1.8) | (226.5 + 5.2)
Wafer #2 (79.7 + 4.5) | (87.0 + 4.5) | (231.0 + 7.2)
Wafer #3 (45.0 + 3.8) | 172.7 + 4.7)| (279.0 + 8.6)
Wafer #4 (20.6 + 1.7) {40.4 + 11.8)] (228.3 + 3.7)

FIG. 27


U.S. Patent Mar. 29,2022 Sheet 11 of 53 US 11,287,366 B2

IN

FIG. 11


US 11,287,366 B2

19

to the 2.4 mm reference plane. The S-parameters of the
test-head are related to the model of the WR-42 calibration
devices and the measured $-parameters by:

(10)

where I”, is the reflection coefficient of a given termination,
which includes a short, matched load, and an open. Pyjeas iS
the measured reflection coeflicient for the loads corrected to
the 2.4 mm reference plane. The three terminations can be
expressed by a set of linear equations:

Tins) SO 1 Tys(O0 5) —0 (0) ab
[ =#]- Sn(0) [! Fol) Fo)
Fa I (SuSz2()~ Sf COE) FO)

where the subscripts ms, mo, and ml indicate measurements
for the short, open, and load calibration devices, respec-
tively. The subscripts s, 0, and | indicate the models for the

short, open, and load devices, respectively. S,,(8). S.2(8). ,
S,2°(0) are the components of the test-head’s S-parameters. *

Afier we calibrated the reflection coefficient to the 2.4 mm
reference plane, we translated the reference plane to the end
of the WR-42 waveguide by modifying the S-parameters as:

Tn Su)

he (2)
©* FO m— SOS + SO)

where the subscript ¢ indicates the reflection coeflicient
corrected to the end of the waveguide, the subscript m is the
measured reflection coefficient corrected to the 2.4 mm
coaxial reference plane, and the S-parameters are those of
the test-head (11). FIG. 30 shows the effect on the magnitude
and phase of the reflection coefficient for all the isotropic
materials including: gold, absorber, fused silica, and all
MoSi, thicknesses.

The calibration procedure was important for the measure-
ments because the measurements of the MUT are affected by
different systematic errors along the measurement path. We
removed these errors by calibrating the data (FIG. 30). For
example, at the first reference plane with no calibration the
data for different MUTs look very similar. After the first-tier
calibration that translates the data to the 2.4 mm reference

plane the data for the different MUTS becomes distinguish- 5

able. Taking this even further by applying the second-tier
calibration to move the reference plane to the end of the
test-head we can finally model this measured data in simu-
lation and understand the effect of anisotropic electrical
properties on the actual measurement.

To perform the measurements, we connected the test-head
to a 40 GHz vector network analyzer (VNA). The wave-
guide aperture had to rotate relative to the MUT, hence the
test head included a rotary motor, a phase-stable coaxial RF
rotary joint, a 2.4 mm coaxial to WR-42 waveguide adapter,
and a 2-inch section of waveguide that terminates in air. The
test head was attached to a robotic arm via a 3D-printed
housing (see FIG. 1).

The robotic arm was set to (x, y, Z)-coordinates with a 5
4m repeatability. The MUT was placed above a (10.2+0.5)
mum thick piece of Rohacell (€,=1) and a (18+5) mm thick
piece of foam absorber (FIG. 19). Both the absorber and the

3

&

&

s

6:

20

Rohacell layers were much larger in the (x, y)-plane than the
MUT. We added the Rohacell layer to serve as a stand-off,
because an absorber is difficult to simulate and understand in.
the near-field. The Rohacell moved the absorber into the
far-field and allowed us to simulate the setup as air on top
of the aluminum table. The absorber was secured by silicone
caulking on the edges to the metal table, whose surface was
parallel to the waveguide probe aperture.

‘After securing the test-head to the robot and completing
the absorber-Rohacell platform, there were four variables
that we tested for each measurement: (x, y)-location, (7)-
height (h), angle, and frequency, as described in the step-
by-step procedure. The measurement setup was automated,
iterating over robot position, relative angle position, and
‘VNA data acquisition. We found that as we increased the
height offset h, the change in reflection coefficient between
the most reflective (gold) and the least reflective (absorber)
decreased. Because of this, we chose to focus on the lowest
frequency (18 GHz) and the smallest height gap, though we
note that the analysis procedure would be similar for any
height or frequency.

We showed the functionality of waveguide ellipsometry
and created a mapping function with simulation between
measured S-parameters and a bulk conductivity. These out-
comes required developing a new procedure that measured
the MUT as a function of angle, calibrated the data, and used.
composite theory in conjunction with full-wave simulation
to verify the measurements and map them to material
properties.

It is useful to visualize the calibrated data of the aniso-
tropic wafers in two different ways. The first is the magni-
tude of the reflection coefficient (1I'(@)!) as a function of
angle in a polar plot (FIG. 31). This plot is an intuitive way
to visualize how the relative angle, 6, affects the measure-
ment. However, the reflection coefficient is a complex
number, so by just analyzing IT(@) we are ignoring the fact
the electrical signal changes its magnitude and phase after
reflecting off the MUT. A Smith chart allows us to visualize
both magnitude and phase information (FIG. 31), but it is
more difficult to discern the angle dependence. The isotropic
materials on our test wafers have a reflection coefficient that
does not vary with angle, which corresponds to a circle on
the polar plot (FIG. 31) and clustered points on the Smith
chart (FIG. 31). The anisotropic materials have a reflection
coeflicient that is a function of angle, which corresponds to
a non-circular shape on the polar plot and an approximate
are on the Smith chart.

Both plots include the MUTs on the four wafers with a
data point for each angle averaged over the 16 (%,¥)-plane
positions. The uncertainty (shown in FIG. 31) is the standard
deviation for each angle over these 16 positions. The upper-
boundary on the reflection coefficient is set by the gold
measurement (blue lines in FIG. 31 and blue points in FIG.
31), ITl~1 where some power was scattered away from the
waveguide flange because of the height offset. The fused
silica wafer is |T|~0.5 (pink lines in FIG. 31 and pink points
in FIG. 31), and the absorber is |T/~0.35 (gray points in FIG.
ness of the MoSi, layers is inversely propor-
‘0 that the thickest MoSi, (smaller Z,, green
points in FIG. 31) was closer to gold, and the thinnest MoSi,
(bigger Z,, brown points in FIG. 31) was closer to fused
silica, with an approximately linear spread in the value of II
between them. The anisotropic gold fiber samples have a
reflection coefficient that depends on angle. The gold stripes
‘on MoSi, (dotted lines in (FIG. 31 are elliptical on the polar
plot and are bounded by the gold(90°) and their respective
MoSi, thickness (0°). The gold stripes on the fused silica



US 11,287,366 B2

Sheet 49 of 53

Mar. 29, 2022

U.S. Patent

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U.S. Patent Mar. 29,2022 Sheet 51 of 53 US 11,287,366 B2

R(Q/D)
90°

% error

0.08 % S Se
Xess aw gs we *
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ao g 305 280 308
Angle ()
(A) (8)

FIG. 51


U.S. Patent Mar. 29,2022 Sheet 14 of 53 US 11,287,366 B2

Relative rotational
and linear motions

KE
REN

FIG. 14