US 5,706,088 AGranted

Polarizer-sample-analyzer intensity quotient ellipsometry

AssigneeNational Science Council

InventorsYu-Faye Chao, Chi-Shing Wei, Wen-Chi Lee

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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.

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.3J(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).

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Abstract

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