# US 5,706,088 A · Polarizer-sample-analyzer intensity quotient ellipsometry

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- Number: US 5,706,088 A
- Document ID: US5706088A
- Status: Granted
- Kind: A
- Application number: 08/603,779
- Filed: 1996-02-20
- Granted: 1998-01-06
- Earliest claimed: 1996-02-20
- Assignees: National Science Council
- Inventors: Yu-Faye Chao; Chi-Shing Wei; Wen-Chi Lee
- Web page: https://patentgrep.com/patent/US5706088A

## CPC

- G01N 21/211: {Ellipsometry (optical thickness measurement G01B11/06)}
- 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

A polarizer-sample-analyzer intensity quotient ellipsometer and ellipsometric technique is disclosed which includes: a polarized light source, including a light source and a polarizer, for providing polarized light; and a detecting device, including an analyzer and a photodetector. The ellipsometer successively measures three intensities of polarized light emitted by the polarized light source and reflected by the sample being measured with the azimuth angle of the polarizer rotated to .+-.45.degree. with respect to a plane of incidence and the azimuth angle of the analyzer successively rotated to 0.degree.,60.degree., and 120.degree.. With these three measurements, the ellipsometric parameters .psi. and .DELTA. can be deduced. The invention also calculates deviations in the azimuth angles of the polarizer and analyzer with respect to a plane of incidence by utilizing two intensity quotients under two incident angles to be equal after roughly adjusting azimuth angles of the polarizer and the analyzer.

## Claims

### Claim 1

A method for measuring ellipsometric parameters of a sample by using a polarizer-sample-analyzer intensity quotient, comprising the steps of:
(i) providing a sample to be measured;
(ii) providing a polarizer and an analyzer above the sample;
(iii) projecting a light beam through the polarizer to obtain a linearly polarized light beam;
(iv) reflecting the linearly polarized light beam off of the sample;
(v) projecting the reflected light beam through the analyzer;
(vi) systematically aligning the polarizer and the analyzer to an aligned position corresponding to a plane of incidence of the sample;
(vii) rotating an azimuth angle of the polarizer to 45.degree. with respect to the plane of incidence;
(viii) measuring the intensity of the polarized light beam that has passed through the analyzer;
(ix) rotating an azimuth angle of the analyzer to 60.degree.;
(x) measuring the intensity of the polarized light beam that has passed through the analyzer;
(xi) rotating the azimuth angle of analyzer to 120.degree.;
(xii) measuring the intensity of the polarized light beam that has passed through the analyzer;
(xiii) deducing ellipsometric parameters .psi. and .DELTA. of the simple according to the following process by utilizing the intensities measured in steps (viii), (x) and (xii), wherein the ellipsometric parameters .psi. and .DELTA. can be defined as
tan .psi.e.sup.i.DELTA. =r.sub.p /r.sub.s
where r.sub.p and r.sub.s are reflection coefficients of p polarized and s polarized light, respectively, and the intensities measured in steps (viii), (x) and (xii) are represented as
J(A)=0.5I.sub.0 › sin .sup.2 A+tan .sup.2 .psi. cos .sup.2 A+tan .psi. cos .DELTA. sin 2A!
and as
J(A)=L cos .sup.2 (A-.beta..sub.0)+T sin .sup.2 (A-.beta..sub.0),
where A represents a rotation angle of the analyzer and I.sub.0 is the intensity being measured and .beta..sub.0 is an auxiliary angle between a major axis L and the plane of incidence,
wherein R=(L-T)/(L+T) where R is a normalized ratio between the major axis L and a minor axis T,
substituting the three intensities respectively measured in the steps (viii), (x) and (xii) to the following equations,
tan 2.beta..sub.0 =.sqroot.3›J(60)-J(120)!/›2J(0)-J(60)-J(120)!
and
R cos 2.beta..sub.0 =›2J(0)-J(60)-J(120)!/›J(0)+J(60)+J(120)!
then, after calculating R and .beta..sub.0, substituting R and .beta..sub.0 into the following equations to calculate the ellipsometric parameters .DELTA. and .psi.
tan 2.beta..sub.0 =-cos .DELTA. tan .psi.
and
tan 2.psi.=(1-R cos 2.beta..sub.0)/(1+R cos 2.beta..sub.0).

### Claim 2 (depends on 1)

The method for measuring ellipsometric parameters as claimed in claim 1, further comprising the step of:
replacing the equation for J(A), by the following equation
J(A)=0.5I.sub.0 { sin .sup.2 A+tan .sup.2 .psi. cos .sup.2 A.+-.›( sin .sup.2 A-tan .sup.2 .psi. cos .sup.2 A) sin 2.alpha.+tan .psi. cos .DELTA. sin 2A cos 2.alpha.!}
for P=.+-.45.degree.+.alpha., wherein .alpha. is a deviation of azimuth angle of the polarizer, therefore, while P=45.degree.+.alpha.
tan .sup.2 .psi.=(1-sin 2.alpha.)(1-R cos 2.beta..sub.0)/(1-sin 2.alpha.)(1+R cos 2.beta..sub.0) (9)
and while P=45.degree.+.alpha.
tan .sup.2 .psi.=(1+sin 2.alpha.)(1-R' cos 2.beta.')/(1-sin 2.alpha.)(1+R cos 2.beta.') (10)
wherein R' and .beta.' correspond to factors R and .beta..sub.0 in the equation J(A)=L cos .sup.2 (A-.beta..sub.0)+T sin .sup.2 (A-.beta..sub.0), thereafter taking .beta..sub.av =(180-.beta.'+.beta..sub.0)/2, and
substituting .beta..sub.0 with .beta..sub.av to calculate the ellipsometric parameters.

### Claim 3 (depends on 2)

The method for measuring ellipsometric parameters as claimed in claim 2 wherein, said step (vi) systematically aligning the polarizer and the analyzer to the plane of incidence of the sample further includes the sub-steps of:
measuring an intensity I.sub.a1 at a first incident angle while the polarizer azimuth angle P is rotated to 45.degree. and the analyzer azimuth angle A is at the aligned position,
measuring an intensity I.sub.a2 at the first incident angle while the polarizer azimuth angle A is rotated to 45.degree. and the analyzer azimuth angle A is rotated to 90.degree.,
measuring an intensity I.sub.b1 at the first incident angle while the polarizer azimuth angle P is rotated to -45.degree. and the analyzer azimuth angle A is at the aligned position,
measuring an intensity I.sub.b2 at the first incident angle while the polarizer azimuth angle P is rotated to -45.degree. and the analyzer azimuth angle is rotated to 90.degree.,
obtaining the azimuthal deviations .alpha. and .beta. of the polarizer and the analyzer azimuth angles, respectively by deducing the positions of the polarizer and the analyzer corresponding to the plane of incidence according to intensity quotients .GAMMA..sub.a and .GAMMA..sub.b, respectively defined by
.GAMMA..sub.a =I.sub.a1 (.pi./4.alpha.,.beta.)/I.sub.a2 (.pi./4.alpha.,.pi./2+.beta.).apprxeq.tan .sup.2 .psi.-2›2 tan .sup.2 104 .multidot..alpha.-sec .sup.2 .psi..multidot.tan .psi..multidot.cos .DELTA..multidot..beta.)
.GAMMA..sub.b =I.sub.b1 (-.pi./4+.alpha.,.beta.)/I.sub.b2 (-.pi./4+.alpha.,.pi./2+.beta.).apprxeq.tan .sup.2 .psi.+2›2 tan .sup.2 .psi..multidot..alpha.-sec.sup.2 .psi..multidot.tan .psi..multidot.cos .DELTA..multidot..beta.)
hence, while .GAMMA..sub.a =.GAMMA..sub.b,
›2 tan .sup.2 .psi..multidot..alpha.-sec.sup.2 .psi..multidot.tan .psi..multidot.cos .DELTA..multidot..beta.!=0
repeating said measuring steps and said obtaining the azimuthal deviations .alpha. and .beta. step for a second incident angle, so that .alpha. and .beta. can be calculated by solving simultaneous equations for the first and second incident angles.