Optics: measuring and testing – By polarized light examination – Of surface reflection
Reexamination Certificate
2000-04-14
2002-11-19
Stafira, Michael P. (Department: 2877)
Optics: measuring and testing
By polarized light examination
Of surface reflection
Reexamination Certificate
active
06483584
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to an ellipsometer for measuring the complex refractive index and thin film thickness of a sample.
2. Description of the Related Art
Currently, only ellipsometer widely applied in semiconductor, optical and chemical industries can measure the complex refractive index and thin film thickness of a sample with better precision and higher resolution. Ellipsometer which has been developed over 100 years includes null ellipsometer, rotating-polarizer ellipsometer, rotating-analyzer ellipsometer, rotating-compensator ellipsometer, phase-modulation ellipsometer, small-modulation ellipsometer, dual-modulation ellipsometer, analyzer-shifting ellipsometer, compound-splitting ellipsometer, phase-shifting ellipsometer, and phase-analysis ellipsometer.
The principle of the ellipsometer is based on the ellipsomeric polarizing optics. Typically, a planar wave electric field E can be divided into two electric fields E
p
and E
s
. That is, the planar wave electric field E can be expressed by:
{right arrow over (E)}={right arrow over (E)}
p
+{right arrow over (E)}
s
(1)
With Jones' vector, the electric field E can also be expressed by:
E
⇀
=
[
E
p
E
s
]
=
[
E
op
ⅇ
j
(
ω
t
-
kz
-
φ
p
)
E
os
ⅇ
j
(
ω
t
-
kz
+
φ
s
)
]
∝
[
E
op
ⅇ
jΔ
E
os
]
(
2
)
wherein E
op
and E
os
represent the amplitudes of the electric fields E
p
and E
s
respectively, j={square root over (−1)}, and &Dgr;=&phgr;
p
−&phgr;
s
. The traveling direction of the electric field E is along the z axis. If two polarized electric fields E
ip
and E
is
are inputted, two outputted electric fields E
rp
and E
rs
can be measured after the two inputted electric fields E
ip
and E
is
pass through a sample. Therefore, the related reflection coefficients can be given by:
r
p
=
E
rp
E
ip
=
ρ
p
ⅇ
jΔ
p
(
3
)
r
s
=
E
rp
E
ip
=
ρ
s
ⅇ
jΔ
s
(
4
)
wherein &Dgr;
p
represents the phase shift of the reflected electric field E
p
, and &Dgr;
s
represents the phase shift of the reflected electric field E
s
. Thus, the polarization transfer function F (ellipsomeric function p) of the sample can be defined by:
F
=
ρ
=
E
rP
E
rs
E
ip
E
is
=
E
rp
E
ip
E
rs
E
is
=
r
p
r
s
=
ρ
p
ⅇ
jΔ
p
ρ
s
ⅇ
jΔ
s
=
tan
Ψⅇ
jΔ
(
5
)
wherein
tan
Ψ
=
ρ
p
ρ
s
and &Dgr;=&Dgr;
p
−&Dgr;. The tan &psgr; and &Dgr; are called ellipsomeric parameters.
Referring to
FIG. 1
, a general PMSA type ellipsometer is shown, wherein reference numeral
15
designates a polarizer having a pass axis angle b,
22
designates a phase modulator having m as the azimuth of a fast axis,
30
designates a sample,
42
designates an analyzer having a pass axis angle a, and
45
designates a detector. As shown in
FIG. 1
, a total of
6
parameters related to the four devices is the pass axis angle coordinate b of the polarizer P designated by a numeral
15
, the azimuth angle m of the phase modulator M designated by a numeral
22
, phase delay &dgr; of a phase retarder, the ellipsomeric parameters &PSgr;, &Dgr; and pass axis angle coordinate &agr; of the analyzer A designated by a numeral
42
. They can be expressed by Jones' matrixes as follows:
P
=
[
cos
2
b
sin
b
cos
b
sin
b
cos
b
sin
2
b
]
(
6
)
M
=
[
ⅇ
i
δ
2
cos
2
m
+
ⅇ
-
i
δ
2
sin
2
m
2
i
sin
m
cos
m
sin
(
δ
2
)
2
i
sin
m
cos
m
sin
(
δ
2
)
ⅇ
-
i
δ
2
cos
2
m
+
ⅇ
i
δ
2
sin
2
m
]
(
7
)
S
=
[
tan
Ψⅇ
jΔ
0
0
1
]
(
8
)
A
=
[
cos
2
a
sin
a
cos
a
sin
a
cos
a
sin
2
a
]
(
9
)
If the detector
45
has a linear response, a signal I measured after passing through the analyzer
42
can be expressed by:
I=G{right arrow over (E)}
+
out
{right arrow over (E)}
out=
G
(
ASMP{right arrow over (E)}
in,)
+
(
ASMP{right arrow over (E)}
in) (10)
According to “Improvement of phase-modulated ellipsometry” issued on “Review of Scientific Instruents”, vol. 60, p.p. 65-77, by Acher, O., E. Bigan, formula (10) can be further expressed as:
I
(&dgr;)=
G[I+I
s
sin(&dgr;)+
I
c
cos(&dgr;)] (11)
wherein I
s
and I
c
represents the intensities of the electric fields E
p
and E
s
, respectively.
I
(
δ
)
=
G
[
(
1
-
cos
2
Ψcos2
a
)
+
cos
2
m
cos
2
(
m
-
b
)
(
cos
2
a
-
cos
2
Ψ
)
+
sin
2
a
cos
Δsin2Ψsin2
m
cos
2
(
m
-
b
)
]
(
12
)
I
s
=− sin 2&PSgr; sin 2
a
sin 2(
m−b
)sin &Dgr; (13)
I
c
=− sin 2(
m−b
)[sin 2
m
(cos 2&PSgr;− cos 2
a
)+sin 2&PSgr; cos 2
m
cos &Dgr;] (14)
Constant G is determined by the sensitivity of the detector
45
, linear circuit amplification ratio and the ellipsomeric parameters. If any one of the parameters P, M, &dgr; and A is modulated by time, then using a lock-in amplifier, the ellipsomeric parameters &psgr;, &Dgr; and G can be obtained from formula (11). The thickness of the sample can then be estimated.
The phase-shifting ellipsometer having the prior PMSA configuration employs a phase modulator to shift the phase of light to 0, &pgr;/2, and &pgr; respectively, so as to measure the ellipsomeric parameters.
The only difference between the phase-analysis ellipsometer and the phase-shifting ellipsometer is that the polarizer, phase modulator, analyzer, etc. have different angle parameters. With above mentioned angle parameters, the reflection coefficients r
p
, r
s
of the electric fields E
p
, Es can be measured directly. Meanwhile, analysis can be performed using methods well-known in prior art phase-analysis ellipsometers.
SUMMARY OF THE INVENTION
In view of the above, the invention is to provide an ellipsometer for measuring the complex refractive index and thin film thickness of a sample, which not only has all complete functions like the conventional ellipsometer, but also is small in volume, can precisely control the angle and direction of an incident light beam with respect to a sample and is easy to use. Moreover, without employing additional and details calibration procedures typically needed for traditional ellipsometers, the ellipsometer disclosed in this invention can be widely applied in semiconductor, optical and chemical industries for measuring the complex refractive index and thin film thickness of the sample.
A first ellipsometer for measuring the complex refractive index and thin film thickness of a sample according to the invention includes a linear polarized light source used to generate a measuring beam for probing the sample; a phase modulator used to control the phase of the measuring beam thereby to generate a sampling beam; a reference analyzer used to generate a reference beam according to part of the sampling beam thereby to adjust the intensity of the sampling beam; a polarization analyzer us
Chan-Ching Lin
Lee Chih-Kung
Lee Shu-Sheng
Lee Solomon J. H.
Shiue Shuen-Chen
J.C. Patents
National Science Council
Stafira Michael P.
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