# US 11,906,604 B2 · Method for extracting a transverse magneto-optic effect signal

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- Number: US 11,906,604 B2
- Document ID: US11906604B2
- Status: Granted
- Kind: B2
- Application number: 17/514,351
- Filed: 2021-10-29
- Published: 2022-02-17
- Granted: 2024-02-20
- Earliest claimed: 2019-04-30
- Assignees: AsociacióN Centro De InvestigacióN Cooperativa En Nanociencias, Cic Nanogune
- Applicants: AsociacióN Centro De InvestigacióN Cooperativa En Nanociencias “Cic Nanogune”
- Inventors: Eva Oblak; Patricia Riego Saavedra; Andreas Berger; Aitor García Manso; Ane Martínez De Guereñu Elorza; Fernando Arizti; Andoni Irizar Picón
- Web page: https://patentgrep.com/patent/US11906604B2

## CPC

- G01R 33/0325: {using the Kerr effect}
- G01R 33/12: Measuring magnetic properties of articles or specimens of solids or fluids (involving magnetic resonance G01R33/20)
- G01N 21/211: {Ellipsometry (optical thickness measurement G01B11/06)}
- G01R 33/02: Measuring direction or magnitude of magnetic fields or magnetic flux (G01R33/20 takes precedence)
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)

## Abstract

An apparatus to detect and measure a T-MOKE signal includes a first linear polarizer located on the optical path between a light source and a reflecting surface of a sample, a device to produce a magnetic field at the sample location, the device being configured to direct the magnetization perpendicularly to the optical plane of incidence and to reverse the direction of the magnetic field, a rotatable quarter-wave plate located after the reflecting surface on the optical path of the reflected light, a second linear polarizer that is rotatable and is located after the quarter-wave plate on the optical path of the reflected light, and a photo-detector located after the second linear polarizer on the optical path of the reflected light, the photo-detector being configured to measure the intensity of the light. A method for extracting a T-MOKE signal in an ellipsometric measurement procedure employs such an apparatus. The method includes a polarization detection scheme to ascertain that a T-MOKE signal (and not a noise signal) is indeed detected.

## Claims

### Claim 1

A method for extracting a transverse magneto-optic Kerr effect (T-MOKE) signal in an ellipsometric measurement procedure upon a sample, the method employing an apparatus comprising a light source intended to emit a light beam that is to follow an optical path, the sample having a reflecting surface arranged to reflect, at least partially, the light beam in an optical plane of incidence, the apparatus further comprising:
a first linear polarizer having an axis and being located on the optical path between the light source and the reflecting surface;
a device to produce a magnetic field at a sample location, the device being configured to direct the magnetic field perpendicularly to the optical plane of incidence and to reverse the direction of the magnetic field;
a rotatable quarter-wave plate having an axis and being located after the reflecting surface on the optical path of the reflected light beam;
a second linear polarizer that is rotatable and is located after the quarter-wave plate on the optical path of the reflected light beam, the quarter-wave plate having an axis;
a photo-detector located after the second linear polarizer on the optical path of the reflected light beam, the photo-detector being configured to measure an intensity of the light beam that reaches it; and
the sample is represented by a Jones reflection matrix of the form
[
r
s
0
0
r
p
+
β
]
,
where rs is a complex Fresnel reflection coefficient for s-polarization, rp is the complex Fresnel reflection coefficient for p-polarization and β is a complex coefficient that represents the component of light reflected on the reflecting surface due to the magnetic-field induced magnetization of the sample in a direction perpendicular to the optical plane of incidence, whereby {tilde over (β)}=β/rp is a relative T-MOKE coefficient;
the method comprising the steps of:
a) defining a grid of at least six angle pairs, each angle pair being formed by an orientation angle φ for the quarter-wave plate and a polarization angle θ for the second linear polarizer, the orientation angle φ being an angular distance between the quarter-wave plate axis and the optical plane of incidence, and the polarization angle θ being an angular distance between the second linear polarizer axis and the optical plane of incidence;
b) setting the first linear polarizer at a fixed polarization angle α that is neither 0° nor 90°, the fixed polarization angle α being the angular distance between the first linear polarizer axis and the optical plane of incidence;
c) setting the quarter-wave plate at the orientation angle φ of an angle pair;
d) setting the second linear polarizer at the polarization angle θ of the same angle pair of step (c);
e) testing the set angle pair by making the light source to emit the light beam along the optical path, whereby the light beam is transmitted through the first linear polarizer, is reflected, at least partially, by the reflecting surface of the sample, is transmitted through the quarter-wave plate, is transmitted through the second linear polarizer and reaches the photo-detector;
f) recording a measurement of the light intensity from the photo-detector;
g) recording a measurement of the light intensity from the photo-detector upon a magnetic-field reversal with respect to the measurement of step (f);
h) computing and recording a relative change in the light intensity (ΔI/I) due to magnetization reversal upon the magnetic-field reversal of step (g);
i) setting the quarter-wave plate at the orientation angle of another angle pair;
j) setting the second linear polarizer at the polarization angle of the same angle pair of step (i),
k) repeating steps (e) to (j) until at least six of the angle pairs of the grid have been tested; and
l) determining numerical values of real free fit parameters B1, B2, B3, B4, B5 and B6 by matching the collection of the recorded relative changes in the light intensity to equation ΔI/I=f(α, φ, θ, B1, B2, B3, B4, B5, B6), where f is a function mathematically derived for the relative change in the light intensity.

### Claim 2 (depends on 1)

The method according to claim 1, comprising the step of computing the relative T-MOKE coefficient {tilde over (β)} as a derived function of B1 and B2.

### Claim 3 (depends on 2)

The method according to claim 2, wherein the relative T-MOKE coefficient {tilde over (β)} is computed as {tilde over (β)}=B1+iB2.

### Claim 4 (depends on 1)

The method according to claim 1, wherein the recorded relative change in the light intensity is computed as
Δ
⁢
I
/
I
=
2
⁢
(
I
/
(
H
)
-
I
/
(
-
H
)
)
I
/
(
H
)
+
I
/
(
-
H
)
,
where I(H) is the intensity of the light beam that reaches the photo-detector when the magnetic field at the sample location is H, and I(−H) is the intensity of the light beam that reaches the photo-detector when the magnetic field at the sample location is −H.

### Claim 5 (depends on 1)

The method according to claim 1, wherein the recorded measurement of the light intensity I is computed as a mean value of the measurement of the light intensity at the photo-detector, and the change in the light intensity ΔI is computed as twice the amplitude of the first harmonic of the light beam.

### Claim 6 (depends on 5)

The method according to claim 5, wherein the first harmonic is obtained by Fast Fourier Transform analysis of the recorded measurement of the light intensities, using sinusoidal magnetic field modulation.

### Claim 7 (depends on 1)

The method according to claim 1, wherein the mathematical function for the relative change in the light intensity is derived as
Δ
⁢
I
/
I
=
4
⁢
B
1
⁢
sin
2
⁢
α
⁢
h
2
+
cos
⁢
αsinα
[
(
B
1
⁢
B
3
+
B
2
⁢
B
4
)
⁢
h
3
-
(
B
1
⁢
B
4
-
B
2
⁢
B
3
)
⁢
h
4
]
+
1
2
⁢
B
6
(
B
3
2
+
B
4
2
)
⁢
cos
2
⁢
α
⁢
h
1
+
sin
2
⁢
α
⁢
h
2
+
2
⁢
cos
⁢
αsinα
⁡
(
B
3
⁢
h
3
-
B
4
⁢
h
4
)
+
1
2
⁢
B
5
,
where
2h1=cos2(2φ−θ)+cos2(θ),2h2=sin2(2φ−θ)+sin2(θ),4h3=sin(4φ−2θ)+sin(2θ),2h4=sin(2φ−2θ).

### Claim 8 (depends on 7)

The method according to claim 7, wherein B3 is the real part of rs/rp.

### Claim 9 (depends on 7)

The method according to claim 7, wherein B4 is the imaginary part of rs/rp.

### Claim 10 (depends on 8)

The method according to claim 8, wherein B4 is the imaginary part of rs/rp.

### Claim 11 (depends on 7)

The method according to claim 7, wherein B5 represents optical or electronic imperfections in the apparatus.

### Claim 12 (depends on 8)

The method according to claim 8, wherein B5 represents optical or electronic imperfections in the apparatus.

### Claim 13 (depends on 9)

The method according to claim 9, wherein B5 represents optical or electronic imperfections in the apparatus.

### Claim 14 (depends on 7)

The method according to claim 7, wherein B6 represents background noise.

### Claim 15 (depends on 8)

The method according to claim 8, wherein B6 represents background noise.

### Claim 16 (depends on 9)

The method according to claim 9, wherein B6 represents background noise.

### Claim 17 (depends on 10)

The method according to claim 10, wherein B6 represents background noise.

### Claim 18 (depends on 1)

The method according to claim 1, wherein the fixed polarization angle α is set at 45°.

### Claim 19 (depends on 18)

The method according to claim 18, wherein the mathematical function for the relative change in the light intensity is derived as
Δ
⁢
I
/
I
=
4
⁢
B
1
⁢
sin
2
⁢
α
⁢
h
2
+
cos
⁢
αsinα
[
(
B
1
⁢
B
3
+
B
2
⁢
B
4
)
⁢
h
3
-
(
B
1
⁢
B
4
-
B
2
⁢
B
3
)
⁢
h
4
]
+
1
2
⁢
B
6
(
B
3
2
+
B
4
2
)
⁢
cos
2
⁢
α
⁢
h
1
+
sin
2
⁢
α
⁢
h
2
+
2
⁢
cos
⁢
αsinα
⁡
(
B
3
⁢
h
3
-
B
4
⁢
h
4
)
+
1
2
⁢
B
5
,
where
2h1=cos2(2φ−θ)+cos2(θ),2h2=sin2(2φ−θ)+sin2(θ),4h3=sin(4φ−2θ)+sin(2θ),2h4=sin(2φ−2θ).

### Claim 20 (depends on 1)

The method according to claim 1, wherein the matching of the collection of the recorded relative changes in the light intensity to equation (α, φ, θ; Bj), where j=1, 2, 3, 4, 5, 6, is effected by means of a least-squares fit in which all Bj are free fit parameters.