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SEMI E141-0705 © SEMI 2005 8 NOTE 6: The reference samples are typically certified thickness standards using reference m aterials. For thickness measurements typical samples are thermal oxides on silicon ra ngi ng from 4…

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SEMI E141-0705 © SEMI 2005 7
7.4 material and layer definition — the optical properties of a material determine how the complex refractive index
N
i
is given as a function of wavelength and environmental parameters (e.g., temperature). A layer consists of a
single material or a combination of several materials with a metric thickness t
i
. This definition also applies to
complex structures as index gradients, interfaces, and roughness that can be modeled as a series of layers.
7.5 substrate medium — Lowest (see ¶7.2.1) material involved in the reflection with a complex refractive index N
s
.
A sample has only one substrate material, which is treated as semi-infinite.
7.6 Ellipsometric Measurand (raw data set)
5, 6, 7, 8, 9
7.6.1 r
p
= E
rp
/E
ip
— Complex amplitude reflection coefficient parallel to the plane of incidence.
7.6.2 r
s
= E
rs
/E
is
— Complex amplitude reflection coefficient perpendicular to the plane of incidence.
7.6.3
= r
p
/r
s
= tan
e
j
— Ratio of the complex amplitude reflection coefficients.
7.6.4
p
— Phase shift of E
rp
relative to E
ip.
7.6.5
s
— Phase shift of E
rs
relative to E
is.
7.6.6
=
p
-
s
— Phase shift between p and s components of the electric field strength.
7.6.7 tan
= |r
p
|
/|r
s
| — Ratio of the absolute values of the amplitude reflection coefficients.
7.6.8 S
x
— Stokes parameters (x = 0, 1, 2, 3).
NOTE 4: The four Stokes parameters describe the polarization ellipse using the physical dimension of energy. The four Stokes
parameters involve three independent parameters that are necessary to describe the polarization ellipse. For totally polarized light,
the Stokes parameters describe a sphere with the radius S
0
and represent the parameters
and
in a Cartesian coordinate
system: S
0
2
= S
1
2
+ S
2
2
+ S
3
2
. The parameter S
0
is proportional to the energy of the light wave. For elliptically and totally
polarized light, the Stokes parameters are calculated from the parameters
and
as follows: S
1
= – S
0
cos 2
, S
2
= S
0
sin 2
cos
, and S
3
= S
0
sin 2
sin
. The Stokes vector, consists of four vector components, which are the Stokes parameters.
7.6.9 s
x
= S
x
/S
0
— normalized Stokes parameters (x = 1, 2, 3).
NOTE 5: The normalized Stokes parameters are calculated from the Stokes parameters as follows: s
1
= S
1
/S
0
, s
2
= S
2
/S
0
, and s
3
=
S
3
/S
0
.
7.6.10 The results are typically given as [
,
](
0
,

), [tan
, cos
](
0
,

), [s1, s2, s3](
0
,

) dependent
on the measurement angle of incidence
0
, and the wavelength

see ¶3.4) The parameter array
provides all
environmental conditions (influence quantities) relevant for the measurement. All relevant parameters shall be
provided in SI units. At least the sample temperature must be specified, but additional parameters (e.g. ambient
pressure, measurement time, sample orientation, the measurement position
10
, composition, and strain) may have to
be added.
7.7 Qualification of Ellipsometric Data
7.7.1 The qualification of an ellipsometer is verified by measuring certified reference samples and test procedures
11, 12, 13, 14
.
5 Born, M.; Wolf, E.: “Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light”, Cambridge
University Press, ISBN 0521642221.
6 Azzam, R. M. A., Bashara, N. M.: "Ellipsometry and Polarized Light", Elsevier Science Publishers B. V., ISBN 0444870164.
7 Tompkins, H. G.; McGahan W.A.: "Spectroscopic Ellipsometry and Reflectometry: A User's Guide”, Wiley-Interscience, ISBN 0471181722.
8 Muller, R. H.: "Definitions and Conventions in Ellipsometry", Surface Science Vol. 16 (1969), pp. 14-33.
9 Röseler, A.: Infrared Spectroscopic Ellipsometry, Akademie Verlag Berlin, ISBN 3-05-500623-2.
10 See SEMI M20.
11 See SEMI E89-1104E.
12 See SEMI MF576.
13 Metrology Tool Gauge Study Procedure for the International 300 mm Initiative (I300I), Technology Transfer # 97063295A-XFR,
International 300 mm Initiative, June 15, 1997.
14 Eastman, S. A.: Evaluating Automated Wafer Measurement Instruments. Technology Transfer # 94112638A-XFR; SEMATECH February 28,
1995.
SEMI E141-0705 © SEMI 2005 8
NOTE 6: The reference samples are typically certified thickness standards using reference materials. For thickness
measurements typical samples are thermal oxides on silicon ranging from 4 nm to 800 nm. For refractive index measurements,
the reference sample thickness is typically in the range from 80 nm to 500 nm.
NOTE 7: SEMI MF576-01 was originally published by ASTM International as ASTM F 576-78. It was formally approved by
ASTM balloting procedures and adhered to ASTM patent requirements. Though ownership of this standard has been transferred
to SEMI, it has not been formally approved by SEMI balloting procedures and does not adhere either to SEMI Regulations
dealing with patents or to SEMI Editorial Guidelines. It was available at www.semi.org, last published by ASTM International as
ASTM F 576-01. Hence in SEMI MF576-01, the notation for parameters required in data acquisition and modeling is aligned but
could not retroactively be fully harmonized with the definitions specified in the presented guide. This does not constitute any
constraints since these few parameters may easily be superseded by the newer definitions provided.
7.7.2 Whenever the thickness and refractive index measurement (if performed) is within specified limits for the
reference sample, the ellipsometer is defined as qualified and hence capable of measuring the respective type of
sample.
7.7.3 The qualification status of an ellipsometer is defined and must be specified by providing the following
parameters: (1) the relevant parameters for sample identification, (2) the relevant optical parameters of the sample,
(3) the expected measurement result, (4) the actual measurement result, (5) the tolerated deviation between the
actual and the expected measurement result, (6) all relevant parameters of the ellipsometer system (e.g. all relevant
parameters of the positions of the optical components) the angle of incidence, and (7) all relevant environmental
parameters.
7.7.4 Recommended Units and Symbols — The units as listed in Table 1 are recommended for the description of the
listed parameter.
Table 1 Recommended Units
Physical Quantity Symbol Unit(s)
Metric thickness t µm, nm, Å
Wavelength
µm, nm, Å
Photon energy E eV
Wave number
cm
-1
Angles
,
,
0
,
p
,
c
,
PEM
,
A
° or deg (360° are a full circle)
Electric field vectors E
ip
, E
is
, E
rp
, E
rs
V/m
Optical parameters (refractive indices) N, n, k
no unit
Complex dielectric function
no unit
Pseudo <
>
no unit
#1
See SEMI E30.5 for the preferred thickness unit (Å).
#2
The pseudo dielectric constant <> is calculated from the raw data set using a sample model consisting of only the ambient and substrate
without layers.
SEMI E141-0705 © SEMI 2005 9
NOTE: The P C S A configuration is shown for a single-wavelength ellipsometer. For other configurations, see
¶6.4.1.
Figure 1
Schematic of an Ellipsometer System
Layer 1: N
1
: n
1
, k
1
Layer 2: N
2
: n
2
, k
2
Substrate medium: N
s
: n
s
, k
s
Layer i: N
i
: n
i
, k
i
Ambient medium: N
a
: n
a
, k
a
Figure 2
Illustration of the Layer Counting Principle