# US 7,612,891 B2 · Measurement of thin films using fourier amplitude

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- Number: US 7,612,891 B2
- Document ID: US7612891B2
- Status: Granted
- Kind: B2
- Application number: 11/300,945
- Filed: 2005-12-15
- Published: 2007-06-21
- Granted: 2009-11-03
- Earliest claimed: 2005-12-15
- Assignees: Veeco Instruments Inc.
- Inventors: Der-Shen Wan
- Web page: https://patentgrep.com/patent/US7612891B2

## CPC

- G01B 11/0675: {using interferometry}
- G01B 9/02057: {by using common path configuration, i.e. reference and object path almost entirely overlapping}
- G01B 9/02072: {by calibration or testing of interferometer}
- G01B 9/02084: {Processing in the Fourier or frequency domain when not imaged in the frequency domain}
- G01B 9/0209: Low-coherence interferometers
- G01N 21/45: using interferometric methods; using Schlieren methods
- G01N 21/8422: {Investigating thin films, e.g. matrix isolation method}
- G01B: MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- 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

Thin-film thickness and refractive index are measured using the Fourier amplitude of a broadband interferometric spectrum. Due to the smooth nature of the Fourier amplitude as a function of wavelength, as compared to the fast varying Fourier phase conventionally used to measure thickness, increased stability and repeatability of measurement are achieved. As a result, measurements of ultra-thin films with thickness below 100 nm are possible with reliable results.

## Claims

### Claim 1

A method for determining a property of a thin film placed over a substrate, comprising the following steps:
producing a test correlogram of said thin film over the substrate;
generating a test linear transform of the test correlogram and extracting a test transform amplitude from the test linear transform;
deriving a test-beam amplitude component of said test transform amplitude by removing a reference amplitude function, wherein the reference amplitude function comprises the product of the amplitude components contributed by the light source and the reference beam; and
finding a value of said property of the thin film by comparing said test-beam amplitude component to a model test-beam amplitude function.

### Claim 2 (depends on 1)

The method of claim 1, wherein said reference amplitude function is obtained by calibration using a reference substrate having a known reflectivity over a predetermined waveband.

### Claim 3 (depends on 2)

The method of claim 2, wherein said calibration comprises the steps of:
generating a calibration correlogram with a broadband light source included within said predetermined waveband;
generating a calibration linear transform of the calibration correlogram;
extracting a calibration transform amplitude from the calibration linear transform; and
establishing said reference amplitude function from said calibration transform amplitude and said known reflectivity of the reference substrate, said reference amplitude function representing light-source and reference-beam amplitude components of the calibration transform amplitude.

### Claim 4 (depends on 3)

The method of claim 3, wherein said known reflectivity of the reference substrate is substantially constant over said predetermined waveband.

### Claim 5 (depends on 3)

The method of claim 3, wherein said reference amplitude function is established by dividing said calibration transform amplitude by a spectral amplitude of a test beam reflected from said reference substrate during said calibration steps.

### Claim 6 (depends on 1)

The method of claim 1, wherein said test-beam amplitude component is calculated by dividing the test transform amplitude by said reference amplitude function.

### Claim 7 (depends on 1)

The method of claim 1, wherein said finding step is carried out by defining an error function equal to a difference between said test-beam amplitude component and said model test-beam amplitude function, and by minimizing said error function with respect to said property of the thin film.

### Claim 8 (depends on 1)

The method of claim 1, wherein said model test-beam amplitude function is derived from a theoretical expression modeling a reflection from said thin film over the substrate.

### Claim 9 (depends on 8)

The method of claim 8, wherein said theoretical expression is
ρ
⁡
(
k
,
d
)
=
r
01
+
r
12
⁢
exp
⁡
(
-
ⅈ2δ
)
1
+
r
01
⁢
r
12
⁢
exp
⁡
(
-
ⅈ2δ
)
=
b
′
⁢
⁡
(
k
,
d
)
⁢
exp
⁡
[
ⅈϕ
⁡
(
k
,
d
,
θ
)
]
,
where ρ(k,d) is a coefficient of total reflection, r01 is a Fresnel coefficient of reflection at an incident-medium to film boundary, r12 is a Fresnel coefficient of reflection at a film to substrate boundary, δ=2 knd cos θ is a phase difference between consecutive reflections off the film, n is an index of refraction of the film at wavenumber k, θ is a refractive angle in the film, d is a film thickness, and b′(k,d) is said theoretical test-beam amplitude function.

### Claim 10 (depends on 1)

The method of claim 1, wherein said reference amplitude function is derived from an optical model.

### Claim 11 (depends on 1)

The method of claim 1, wherein said linear transform is a Fourier transform.

### Claim 12 (depends on 3)

The method of claim 3, wherein said linear transform is a Fourier transform.

### Claim 13 (depends on 1)

The method of claim 1, wherein said property is a thickness of the thin film.

### Claim 14 (depends on 3)

The method of claim 3, wherein said property is a thickness of the thin film.

### Claim 15 (depends on 1)

The method of claim 1, wherein said property is an index of refraction of the thin film.

### Claim 16 (depends on 3)

The method of claim 3, wherein said property is an index of refraction of the thin film.

### Claim 17 (depends on 3)

The method of claim 3, wherein said linear transform is a Fourier transform; said property is a thickness of the thin film; said reference amplitude function is established by dividing said calibration transform amplitude by a spectral amplitude of a test beam reflected from said reference substrate during the calibration steps; said test-beam amplitude component is calculated by dividing the test transform amplitude by said reference amplitude function; said finding step is carried out by defining an error function equal to a difference between said test-beam amplitude component and said theoretical test-beam amplitude function, and by minimizing said error function with respect to said thickness of the thin film; and said model test-beam amplitude function is derived from a theoretical expression modeling a reflection from said thin film over the substrate.

### Claim 18 (depends on 3)

The method of claim 3, wherein said linear transform is a Fourier transform; said property is an index of refraction of the thin film; said reference amplitude function is established by dividing said calibration transform amplitude by a spectral amplitude of a test beam reflected from said reference substrate during the calibration steps; said test-beam amplitude component is calculated by dividing the test transform amplitude by said reference amplitude function; said finding step is carried out by defining an error function equal to a difference between said test-beam amplitude component and said theoretical test-beam amplitude function, and by minimizing said error function with respect to said index of refraction of the thin film; and said model test-beam amplitude function is derived from a theoretical expression modeling a reflection from said thin film over the substrate.

### Claim 19 (depends on 13)

The method of claim 13, further including the step of determining a profile of said substrate using said thickness of the thin film.

### Claim 20 (depends on 19)

The method of claim 19, wherein said step of determining a profile of the substrate includes utilizing phase information extracted from said test correlogram.

### Claim 21 (depends on 1)

The method of claim 1, wherein said thin film includes multiple layers, said property is a thickness of each layer, and said thickness of each layer is determined using a corresponding model test-beam amplitude function.

### Claim 22 (depends on 1)

The method of claim 1, wherein said steps are repeated using light of different polarization to identify a bi-refringent thin film.