Optics: measuring and testing – By polarized light examination – Of surface reflection
Reexamination Certificate
2001-06-25
2004-10-05
Smith, Zandra V. (Department: 2877)
Optics: measuring and testing
By polarized light examination
Of surface reflection
Reexamination Certificate
active
06801312
ABSTRACT:
TECHNICAL FIELD
The present invention relates to characterization of optically thick material systems, and more particularly is a method of simultaneously evaluating mathematical model parameters including Euler angles, and directions and magnitudes of complex components of orthogonally related dielectric functions or refractive indicies in an optically thick material system which presents with an optical axis oriented either in-plane or out-of-plane with respect to an alignment surface thereof. The present invention method, while not limited thereto, is particularly applicable in investigating optically thick material systems which are at least uniaxial in that magnitudes of corresponding real, and magnitudes of corresponding imaginary, components of at least two orthogonally related optically thick material system characterizing diagonalized tensor:
ϵ
_
(
E
)
=
[
ϵ
sc
0
0
0
ϵ
sc
0
0
0
ϵ
pc
]
complex dielectric functions or refractive indicies are equal.
BACKGROUND
Ellipsometry is a well known means by which to monitor optical and physical properties of material systems, (eg. a substrate which possibly comprises thin films on a surface thereof). In brief, ellipsometry provides that a polarized beam of electromagnetic radiation of one or more wavelengths is caused to impinge upon a material system along one or more angles of incidence and interact, (eg. reflect from or transmit through), therewith. Beams of electromagnetic radiation can be considered as comprised of two orthogonal components, (ie. “P” and “S”), where “P” identifies a plane which contains both an incident beam of electromagnetic radiation, and a normal to an investigated alignment surface of a material system being investigated, and where “S” identifies a plane perpendicular to the “P” plane and parallel to said alignment surface of said material system. A change in polarization state in a polarized beam of electromagnetic radiation caused by said interaction with a material system, is representative of properties of said material system. (Note that Polarization State basically refers to a magnitude of a ratio of orthogonal component magnitudes in a polarized beam of electromagnetic radiation, and a phase angle therebetween, although absolute values for orthogonal components and “handedness”, and even percent of polarization are further full polarization state determining factors). Generally two well known angles, (PSI and DELTA), which characterize a material system at a given Wavelength and Angle-of-Incidence, are determined by analysis of data which represents change in polarization state. PSI is a ratio of the “P” and “S” component magnitudes, and DELTA is the phase angle therebetween.
For general interest, it is noted that spectrophotometer systems do not provide data regarding DELTA related phase angle, and often provide absolute, rather than PSI (&psgr;) type ratio, intensity values. For instance, utilizing a transmission Jones matrix:
[
Epo
Eso
]
=
=
[
Tpp
Tsp
Tps
Tss
]
[
Epi
Esi
]
to represent mathematically how a material system affects a polarized electromagnetic beam, with Epi and Esi orthogonal components, and which is caused to interact therewith, it is to be appreciated that an ellipsometer/polarimeter system might return an on-diagonal ratio:
(
Tpp
/
Tss
)
=
Tan
(
ψ
pp
ss
)
(
ⅇ
ⅈ
Δ
pp
ss
)
;
and off-diagonal ratios
(
Tsp
/
Tss
)
=
Tan
(
ψ
sp
ss
)
(
ⅇ
ⅈ
Δ
sp
ss
)
;
(
Tps
/
Tss
)
=
Tan
(
ψ
p
s
ss
)
(
ⅇ
ⅈ
Δ
p
s
ss
)
;
(
Tsp
/
Tpp
)
=
Tan
(
ψ
sp
pp
)
(
ⅇ
ⅈ
Δ
sp
pp
)
;
(
Tps
/
Tpp
)
=
Tan
(
ψ
p
s
pp
)
(
ⅇ
ⅈ
Δ
p
s
pp
)
;
as a function of a selection from the group consisting of:
angle-of-incidence;
wavelength; and
material system rotation about a normal to said alignment surface.
A spectrophotometer system might return Tpp, Tss, Tsp and/or Tps as a function of angle-of-incidence; wavelength; and/or material system rotation about a normal to said alignment surface. It is to be understood that a reflection Jones Matrix
[
Epo
Eso
]
=
=
[
Rpp
Rsp
Rps
Rss
]
[
Epi
Esi
]
could have also been utilized for said demonstration, and that generally the present invention method can be practiced utilizing data obtained with an ellipsometer system configured in transmission or reflection modes, and/or combinations thereof in any steps thereof, wherein functionality is preserved.
Continuing, Ellipsometer Systems generally include a source of a beam of electromagnetic radiation, a Polarizer, which serves to impose a linear state of polarization on a beam of electromagnetic radiation, a Stage for supporting a material system, and an Analyzer which serves to select a polarization state in a beam of electromagnetic radiation after it has on interacted with a material system, and prior to being passed to a Detector System for analysis. As well, one or more Compensator(s) can be present and serve to affect a phase angle between orthogonal components of a polarized beam of electromagnetic radiation. This is especially important where it is necessary to determine the “Handedness” of a polarized beam of electromagnetic radiation.
A number of types of ellipsometer systems exist, such as those which include rotating elements and those which include modulation elements. Those including rotating elements include Rotating Polarizer (RP), Rotating Analyzer (RA), Rotating Compensator (RC). It is noted that Rotating Compensator Ellipsometer Systems do not demonstrate “Dead-Spots” where obtaining data is difficult. They can read PSI (&psgr;) and DELTA (&Dgr;) of a material system over a full Range of Degrees with the only limitation being that if PSI becomes essentially zero (0.0), one can not then determine DELTA as there is not a sufficient PSI (&psgr;) Polar Vector Length to form the angle between the PSI (&psgr;) Vector and an “X” axis. In comparison, Rotating Analyzer and Rotating Polarizer Ellipsometers have “Dead Spots” at DELTA's (&Dgr;) near 0.0 or 180 Degrees and Modulation Element Ellipsometers also have “Dead Spots” at PSI (&psgr;) near 45 Degrees. The present invention method can be practiced with essentially any ellipsometer system.
A Search of Patents relevant to the present invention has identified very little of specific relevance. One Patent, to Dill, U.S. Pat. No. 4,053,232 describes a Rotating-Compensator Ellipsometer System, which operates utilizes monochromatic light. Two Patents which identify systems which utilize Polychromatic light in investigation of material systems are described in U.S. Pat. Nos. 5,596,406 and 4,668,086, to Rosencwaig et al. and Redner, respectively, were also identified. Also identified is a Patent to Woollam et al, U.S. Pat. No. 5,373,359 as it describes a Rotating Analyzer Ellipsometer System which utilizes white light. Patents continued from the 359 Woollam et al. Patent are, U.S. Pat. Nos. 5,504,582 to Johs et al. and U.S. Pat. No. 5,521,706 to Green et al. Said 582 Johs et al. and 706 Green et al. Patents describe use of polychromatic light in a Rotating Analyzer Ellipsometer System. A Patent to Bernoux et al., U.S. Pat. No. 5,329,357 is identified as it describes the use of optical fibers as input and output means in an ellipsometer system. A Patent to Chen et al., U.S. Pat. No. 5,581,350 is identified as it describes the application of regression in calibration of ellipsometer systems.
A particularly interesting Patent to Herzinger, U.S. Pat. No. 5,835,222, is identified, and incorporated hereinto by reference, as it describes an ellipsometric based method for identifying the orientation of an optical axis in a material system with respect to an alignment surface thereof. One recitation of the method of the 222 Patent method of qualifying a material system a
J.A. Woollam Co. Inc.
Smith Zandra V.
Welch James D.
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