semi合集-English.pdf - 第1032页
SEMI E141-0705 © SEMI 2005 5 6.4.2.4 electric field vector (E is ) — Elect ric field strengt h of the incident beam perpendicul ar to the plane of incidence and perpendicular to the wa ve vector of the incid ent beam. 6.…
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6.3.1.2 rotating polarizer (RP) — Component that transmits light with a preferred polarization axis (typically
linearly polarized) and that is rotating during measurement.
6.3.1.3 compensator (retarder) (C) — Component that can add a phase shift between the components of the electric
field (i.e. the field component parallel to the plane of incidence and perpendicular to the beam direction and the field
component perpendicular to the plane of incidence and to the beam direction, respectively) (see ¶6.4.2.3–¶6.4.2.6).
6.3.1.4 rotating compensator (retarder) (RC) — A rotating component that can add a phase shift between the
components of the electric field (i.e., the field component parallel to the plane of incidence and perpendicular to the
beam direction and the field component perpendicular to the plane of incidence and to the beam direction,
respectively) (see ¶6.4.2.3–¶6.4.2.6).
6.3.1.5 birefringence modulator (BM) — Component that can add a time-modulated phase shift between the
components of the electric field (i.e. the field component parallel to the plane of incidence and perpendicular to the
beam direction and the field component perpendicular to the plane of incidence and to the beam direction,
respectively) (see ¶6.4.2.3–¶6.4.2.6). The photoelastic modulator (PEM) is a component of this type.
NOTE 1: A PEM is an electro-optical modulator made of a suitable birefringent material. By applying an external electric field
to this material, its refractive index changes anisotropically, thus resulting in a phase shift of a transmitting light wave. By driving
the electric field resonantly, the phase of one polarization component of the transmitting light wave will be delayed periodically.
6.3.1.6 analyzer (A) — Component that transmits light with a preferred polarization axis (typically linearly
polarized).
6.3.1.7 rotating analyzer (RA) — Component that transmits light with a preferred polarization axis (typically
linearly polarized) and that is rotating during measurement.
6.3.1.8 sample (S) — Material or layer system to be analyzed. The sample is the reflecting component that changes
the state of polarization in a characteristic manner (typically, light is elliptically polarized after reflection) and that is
to be evaluated.
6.4 Ellipsometer Equipment Definition (see Figure 1)
6.4.1 sequence of ellipsometer components — The first item to be described for the definition of ellipsometer
equipment is the sequence of optical components beginning with the first component in the polarizer module after
the light source and including all the optical components to the analyzer module before the detector element. For this
definition, optical elements that do not intentionally affect the state of light polarization (e.g. the light source, the
detector, or the spectrometer) are not listed.
6.4.1.1 The most commonly applied ellipsometer equipment is listed below.
6.4.1.1.1 P C S A and P S C A — Null Ellipsometer.
6.4.1.1.2 P (C) S RA and P S (C) RA — Rotating Analyzer Ellipsometer (with) without Compensator.
6.4.1.1.3 RP (C) S A and RP S (C) A — Rotating Polarizer Ellipsometer (with) without Compensator.
6.4.1.1.4 P RC S A, P S RC A, and P RC S RC A — Rotating Compensator Ellipsometer.
6.4.1.1.5 P BM S A and P S BM A — Birefringence Modulation Ellipsometer (sample configuration: P PEM S A or
P S PEM A).
6.4.2 position of ellipsometer components — The second item to be described for the definition of ellipsometer
equipment is the position of the optical components within this coordinate system. The ellipsometer setup uses a
coordinate system defined by the sample surface and the light beam (see Figure 1).
6.4.2.1 definition of the optical system of coordinates — The optical system of coordinates is defined by the
electromagnetic field components, described as complex numbers, and the wave vector.
6.4.2.2 wave vector (k
) — The vector indicates the propagation direction of a light beam. The magnitude is given by
|k
| = 2
/
, with
being the wavelength of the light beam. The wave vector of the incident beam is k
i
and that of the
reflected beam is k
r
.
6.4.2.3 electric field vector (E
ip
) — Electric field strength of the incident beam parallel to the plane of incidence and
perpendicular to the wave vector of the incident beam.
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6.4.2.4 electric field vector (E
is
) — Electric field strength of the incident beam perpendicular to the plane of
incidence and perpendicular to the wave vector of the incident beam.
6.4.2.5 electric field vector (E
rp
) — Electric field strength of the reflected beam parallel to the plane of incidence
and perpendicular to the wave vector of the reflected beam.
6.4.2.6 electric field vector (E
rs
) — Electric field strength of the reflected beam perpendicular to the plane of
incidence and perpendicular to the wave vector of the reflected beam.
6.4.2.7 handedness of the coordinate system — The vectors E
ip
, E
is
, and the wave vector k
i
of the incident beam as
well as the vectors E
rp
, E
rs
, and the wave vector k
r
of the reflected beam span a right-handed coordinate system (see
Figure 1).
6.4.2.8 description of the component position — The positions of the ellipsometer components are described by the
following angles, which are specified counterclockwise relative to E
ip
and E
rp
, respectively.
6.4.2.8.1 polarizer azimuth (
P
) — Angle between the plane of incidence and the polarization axis of the light
emerging the polarizer (see Figure 1).
6.4.2.8.2 compensator azimuth (
C
) — Angle between the plane of incidence and the fast axis of the compensator
crystal. If a compensator consists of multiple anisotropic crystals, the axis is defined as the effective axis when the
output is modeled by a single anisotropic crystal (see Figure 1).
6.4.2.8.3 PEM azimuth (
PEM
)
— The PEM azimuth denotes the same angle as
C
for an electronically phase
modulated compensator.
6.4.2.8.4 analyzer azimuth (
A
)
— The analyzer azimuth denotes the angle between the plane of incidence and the
polarization axis of the light emerging the analyzer (see Figure 1).
6.4.3 description of the angle of incidence — The third item to be described for the definition of ellipsometer
equipment is the number of angles of incidence.
6.4.3.1 single-angle ellipsometer (SAE) — With the single-angle ellipsometer, the ellipsometric measurement is
performed at a single angle of incidence.
6.4.3.2 multiple-angle ellipsometer (MAE) — With the multiple-angle ellipsometer, the ellipsometric measurement
is performed at different angles of incidence.
6.4.4 description of measurement wavelength (
— The fourth item to be described for the definition of
ellipsometer equipment is the number of wavelengths used for measurement.
6.4.4.1 single-wavelength ellipsometer (SWE) — With the single-wavelength ellipsometer, one discrete wavelength
is used in the measurement.
6.4.4.2 multiple-wavelengths ellipsometer (MWE) — With the multiple-wavelengths ellipsometer, several discrete
wavelengths are used in the measurement.
6.4.4.3 spectroscopic ellipsometer (SE) — With the spectroscopic ellipsometer many (at least 10) different
wavelengths are used in the measurement.
6.4.5 description of the data acquisition method — The fifth item to be described for the specification of
ellipsometer equipment is the data acquisition method.
6.4.5.1 scanning data acquisition — In scanning data acquisition, the state of polarization is measured wavelength
by wavelength for different positions of one or more optical components.
6.4.5.2 parallel data acquisition — In parallel data acquisition, the state of polarization is measured by
simultaneously varying one or more parameters of the ellipsometer equipment for a defined position of one or more
optical components, e.g. simultaneously measuring the state of polarization for different wavelengths or at different
angles of incidence.
NOTE 2: In the literature, the terms TM (transverse magnetic) and TE (transverse electric) are also used to denote p and s
polarizations, respectively. The TM polarization denotes that the magnetic field vector is perpendicular to the plane of incidence,
while the TE polarization denotes that the electric field vector is perpendicular to the plane of incidence.
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7 Definitions for Modeling the Reflection from a Sample Surface
7.1 Analysis of Ellipsometric Measurements
7.1.1 For the analysis of ellipsometric measurements an optical model describing the optical parameters and layer
thickness values of the sample must be provided. The optical model is regarded as part of the necessary substrate
data set
4
. The objective of the ellipsometric measurement is to determine the value of at least one parameter within
the optical model such that the measurand calculated from the optical model is in optimum consistency with the
measurand (raw data value
1
) determined in the measurement. For a correct optical model and in the absence of
measurement errors, the measurand calculated from the optical model coincides with the measurand (raw data
value
1
) determined in the measurement.
7.1.2 The set of adjusted parameter values is the measurement result (i.e. the converted measurement data
1
determined by the ellipsometric measurement). In some special cases the measurement result can be calculated from
the measurands or raw data analytically.
7.1.3 Typically, in ellipsometry the analysis is performed by calculating the expected value of the measurand (i.e.
raw data value from the parameter values provided in the optical model). The parameter values of interest within the
optical model are then intentionally adjusted in a manner such that optimum consistency between the calculated and
measured value of the measurand (i.e. the raw data value is obtained). The adjusted parameter values are the
measurement result (i.e. the converted measurement data).
7.2 Definition of the Optical Parameters — The optical parameters are used as substrate data set and the optimized
parameter values after measurement and analysis denote the measurement result (i.e. the converted measurement
data).
7.2.1 layer index (i) — The layer index i identifies the layer for remote access. The index i = ‘a’ describes the
ambient medium (n
a
, k
a
). The index i = ‘s’ describes the substrate medium (n
s
, k
s
). The intermediate layers are
numbered in the direction from the substrate to the ambient (i.e. i = 1 denotes the first layer on the substrate) (see
Figure 2).
7.2.2 n
i
— Denotes the refractive index of layer i being a positive real number.
7.2.3 k
i
— Denotes the extinction coefficient of layer i. The value of the extinction coefficient k
i
must be set as a
positive number |k
i
| for better readability in programs and printouts, independently of the notation of the complex
refractive index and complex dielectric function (see ¶¶7.2.4, 7.2.6, and 7.2.7).
NOTE 3: The extinction coefficient k describes absorbing media if |k| > 0 and transparent media if |k| = 0. The absorption
coefficient
and the absorption index
are also two common optical parameters used for describing absorbing media. The
extinction coefficient k is related to the absorption coefficient
by
= 4k/
and to the absorption index
by
= k/n.
7.2.4 N
i
— Denotes the complex refractive index of layer i. Depending on the physical notation the complex
refractive index is calculated by N
i
= n
i
– j k
i
or N
i
= n
i
+ j k
i
(see ¶7.2.3).
7.2.5
i
= N
i
2
— Complex dielectric function of layer i.
7.2.6
1i
=
n
i
2
– k
i
2
— Real part of the dielectric function of layer i.
7.2.7
2i
— Imaginary part of the dielectric function of layer i. Depending on the physical notation, the imaginary
part of the dielectric function is calculated by
2i
= −2n
i
k
i
or
2i
= 2n
i
k
i
(see ¶7.2.4, ¶7.2.5). The value of the
imaginary part of the dielectric function
2i
must be set as a positive number |
2i
| for better readability in programs
and printouts, independently of the notation of the complex refractive index and complex dielectric function (see
¶¶7.2.3, 7.2.4, and 7.2.5).
7.2.8 t
i
— Metric thickness of the layer i. The method for counting is identical as for the refractive indices, but no
thickness is provided for the ambient and the substrate.
7.3 ambient medium — The modeling always requires a semi-infinite space (or material) for the incident and the
reflected beam that is not part of the sample. The ambient is the propagation medium immediately before and after
reflection at the sample surface. In many cases the ambient medium is air or vacuum with n
a
= 1 and k
a
= 0.
4 Terminology here is as defined in SEMI E127.