Simulating the diffraction grating reflectivity using effective medium theory
The features of optical radiation interaction with surface of gratings are investigated. The diffraction grating is proposed to be used in the effective medium model to test nanostructured surfaces. This object allows obtaining simultaneous visualization of different spatial frequencies and estim...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2013
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| Cite this: | Simulating the diffraction grating reflectivity using effective medium theory / A.A. Goloborodko, N.S. Goloborodko, Ye.A. Oberemok, S.N. Savenkov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2013. — Т. 16, № 2. — С. 128-131. — Бібліогр.: 8 назв. — англ. |
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Goloborodko, A.A. Goloborodko, N.S. Oberemok, Ye.A. Savenkov, S.N. 2017-05-26T09:06:42Z 2017-05-26T09:06:42Z 2013 Simulating the diffraction grating reflectivity using effective medium theory / A.A. Goloborodko, N.S. Goloborodko, Ye.A. Oberemok, S.N. Savenkov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2013. — Т. 16, № 2. — С. 128-131. — Бібліогр.: 8 назв. — англ. 1560-8034 PACS 42.25.Gy, 42.79.Dj, 81.70.Fy https://nasplib.isofts.kiev.ua/handle/123456789/117679 The features of optical radiation interaction with surface of gratings are investigated. The diffraction grating is proposed to be used in the effective medium model to test nanostructured surfaces. This object allows obtaining simultaneous visualization of different spatial frequencies and estimation of both structure and surface features of 3D-objects. It was shown that the effective medium model could be used to predict the reflectivity of nanostructured surfaces by using diffraction gratings with different depths of profile. Computer simulations show that the filling factor of composite systems could be an angle dependent function. So, the correct solution of the inverse problem of finding surface characteristics, such as refraction indices and absorption coefficients, is related with the angle dependence of filling factor. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Simulating the diffraction grating reflectivity using effective medium theory Article published earlier |
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Simulating the diffraction grating reflectivity using effective medium theory Goloborodko, A.A. Goloborodko, N.S. Oberemok, Ye.A. Savenkov, S.N. |
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Simulating the diffraction grating reflectivity using effective medium theory |
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simulating the diffraction grating reflectivity using effective medium theory |
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Goloborodko, A.A. Goloborodko, N.S. Oberemok, Ye.A. Savenkov, S.N. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The features of optical radiation interaction with surface of gratings are
investigated. The diffraction grating is proposed to be used in the effective medium
model to test nanostructured surfaces. This object allows obtaining simultaneous
visualization of different spatial frequencies and estimation of both structure and surface
features of 3D-objects. It was shown that the effective medium model could be used to
predict the reflectivity of nanostructured surfaces by using diffraction gratings with
different depths of profile. Computer simulations show that the filling factor of
composite systems could be an angle dependent function. So, the correct solution of the
inverse problem of finding surface characteristics, such as refraction indices and
absorption coefficients, is related with the angle dependence of filling factor.
|
| issn |
1560-8034 |
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https://nasplib.isofts.kiev.ua/handle/123456789/117679 |
| citation_txt |
Simulating the diffraction grating reflectivity using effective medium theory / A.A. Goloborodko, N.S. Goloborodko, Ye.A. Oberemok, S.N. Savenkov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2013. — Т. 16, № 2. — С. 128-131. — Бібліогр.: 8 назв. — англ. |
| work_keys_str_mv |
AT goloborodkoaa simulatingthediffractiongratingreflectivityusingeffectivemediumtheory AT goloborodkons simulatingthediffractiongratingreflectivityusingeffectivemediumtheory AT oberemokyea simulatingthediffractiongratingreflectivityusingeffectivemediumtheory AT savenkovsn simulatingthediffractiongratingreflectivityusingeffectivemediumtheory |
| first_indexed |
2025-11-25T20:29:34Z |
| last_indexed |
2025-11-25T20:29:34Z |
| _version_ |
1850521353318301696 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 2. P. 128-131.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
128
PACS 42.25.Gy, 42.79.Dj, 81.70.Fy
Simulating the diffraction grating reflectivity
using effective medium theory
A.A. Goloborodko, N.S. Goloborodko, Ye.A. Oberemok, S.N. Savenkov
Taras Shevchenko Kyiv National University, Department of Radiophysics,
64, Volodymyrska str., 01601 Kyiv, Ukraine
E-mail: angol@univ.kiev.ua
Abstract. The features of optical radiation interaction with surface of gratings are
investigated. The diffraction grating is proposed to be used in the effective medium
model to test nanostructured surfaces. This object allows obtaining simultaneous
visualization of different spatial frequencies and estimation of both structure and surface
features of 3D-objects. It was shown that the effective medium model could be used to
predict the reflectivity of nanostructured surfaces by using diffraction gratings with
different depths of profile. Computer simulations show that the filling factor of
composite systems could be an angle dependent function. So, the correct solution of the
inverse problem of finding surface characteristics, such as refraction indices and
absorption coefficients, is related with the angle dependence of filling factor.
Keywords: diffraction grating, effective medium, refraction index, absorption
coefficient.
Manuscript received 15.01.13; revised version received 22.02.12; accepted for
publication 19.03.12; published online 25.06.12.
1. Introduction
Nowadays, nondestructive, multiple parameters, express
detection of structures local features become more
necessary with nanotechnologies improvement. For the
most widespread layered film structures the main
features are: the layer thickness and basical optical
features such as refraction index n [1] and absorption
coefficient κ [2]. It should be mentioned that
dependences n(d) and κ(d) for nanostructured surfaces,
obtained for one wavelength, can vary with the
wavelengths change [3, 4]. Thus, using the value of
some parameter from tables or literature data can be
inaccurate or can lead to essential errors in diagnosing
the other features.
So, the solution of this problem is in determination
of a set of bound parameters within a unified method and
one measuring system that allow defining a set of
features in one measurement. However, currently optical
methods that allow simultaneous determination of
refraction index, absorption coefficient and thickness for
absorbing and nonabsorbing media are developed
insufficiently. Widespread angular methods [5] were
applied only to bulk samples for determining only two
parameters – n and κ.
Big success in nanostructures investigation was
achieved for porous silicon [6], which consists of silicon
nanocrystals separated by air. If the characteristic sizes
of pores and nanocrystals are much smaller than the
irradiation wavelength, then such a semiconductor can
be considered as homogeneous optical medium, which
has some effective refraction index and absorption
coefficient. These characteristics differ from
characteristics of bulk samples that form the
nanostructure. In this case, the model of effective
medium for defining the characteristics of
nanostructured objects should be discussed. The
electrostatic approximation is frequently used in the
model of effective medium for optical problems. This
approximation requires both small sizes of the
nanoparticles and a short distance between them as
compared to the optical wavelength in the medium [7].
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 2. P. 128-131.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
129
In the other case, there arises the problem of taking into
account the scattering on particles that form the
nanocomposite medium and interference of reflected
waves. Thus, the aim of this paper was to create the
optical scheme suitable for visualization and
investigation of polarization characteristics of diffraction
grating and effective medium model verification for
reflected light characteristics description.
2. Ellipsometric investigation of ordinary grating
The diffraction gratings are often used as tested objects
for calibration of optical devices. And usage of
diffraction gratings with appearance of nanostructured
composite materials (inhomogeneity size values of
which are about the wavelength λ of scanning beam)
needs an additional investigation. Thus, the medium
model based on diffraction gratings with the period d =
1 μm and variable height h from 12 up to 300 nm with
the step 12 nm are considered in this work. These
gratings were produced using the electron beam
lithography method on photoresist (electron-sensitive
PMMA resist). A reconstructed 3D image received with
a scanning electron microscopy (SEM) method is shown
in Fig. 1.
The optical scheme shown in Fig. 2 was used for
experiment. This scheme includes the probing (Laser, P,
L1, L2) and receiving (L3, L4, WP1, WP2, PhD1,
PhD2) channels. Coherent radiation from a He–Ne laser
with λ = 0.63 μm, which was used as a source, was
formed into converging beams by the long-focus system
L2-L1 illuminating the grating entirely. After reflection
from the grating, the main maximum in the mirror
reflection direction and a great number of secondary
orders were observed. This scheme allows suitable
observation of diffraction orders from a grating with
submicron relief dimensions that were upright spacing
from the main order. The photodetectors PhD1 and
PhD2 were used to register the diffraction maximum
intensities and were situated on the goniometry arms.
Fig. 3 shows experimental dependences of the
intensity inherent to the main and first diffraction orders
for gratings with different profile heights in the case of
normal incidence.
As one can see, behavior of these dependences
shows their anticorrelation and illustrates the energy
redistribution between diffraction maxima (from the
main to higher orders). Thereby, next calculations
require taking into account the intensities redistribution
in the maxima with the relief depth changing. In
addition, the curves in Fig. 3 lead to the conclusion that
there is no interference for gratings with profile depths
less than 84 nm, so the model of effective medium may
be applied to them. Contribution of the first diffraction
orders for a deeper depth of the grating profile becomes
more substantial, and the model with effective refraction
index requires some corrections for the further
theoretical calculations.
Fig. 1. 3D SEM image of the grating.
Fig. 2. Optical setup for simultaneous visualization of different
spatial frequencies.
Fig. 3. Intensities of the main (0 Max) and first (±1 Max)
diffraction orders for various depths of the grating profile.
Fig. 4. Experimental and theoretically calculated angular
dependences of the reflection coefficient of photoresist surface
on the chrome – glass substrate.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 2. P. 128-131.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
130
Fig. 5. Angular dependences of the reflection coefficient.
Dependences for orthogonal components of the
reflection coefficients for the plane surface of
photoresist on the glass substrate with chrome coating
(5 μm) are shown in Fig. 4. Taking into account the
dependence type and value of reflection coefficients, the
refraction coefficient of the photoresist was nPMMA =
1.515+j0.0019 and thickness of the photoresist layer
dPMMA = 0.5 μm. These values were used for determining
the effective refraction coefficients of the gratings.
3. Effective medium model for the grating
Bruggeman and Maxwell–Garnett effective medium
models are based on the Lorentz local field concept [7].
For the Maxwell–Garnett model, the effective
permittivity εeff of composite medium that consists of
dotted dissemination of material with the permittivity
εb = (nb+iκb)
2 in dielectric matrix εm = (nm+iκm)2 is
determined as [8]:
mb
mb
meff
meff
LLLL
11
, (1)
where η is the volume filling factor, L – depolarization
factor. The drawback of the Maxwell–Garnett model is
the fact that components, which form the
nanocomposite, are unequal and the filling factor
η < 0.3.
The Bruggeman model is based on the fact that
particles with permittivities εb and εm are placed into
medium with the permittivity εeff. Taking into account
field averaging within the sample volume, one can
receive the following equation for the permittivity:
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 2. P. 128-131.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
131
0
bbeff
beff
b
mmeff
meff
m LL
, (2)
where ηm+ηb = 1. It should be mentioned that there is a
necessity to consider the filling factors changing in
different media for angular investigations of optical
illumination characteristics. Calculation of the filling
factors is done in the single scattering approximation for
some simplification. Thus, taking into account shading
the different areas of the grating, the filling factors can
be given as:
inbm
inmmnew
m nn
n
sin5.01
sin5.0
,
inbm
inbbnew
b nn
n
sin5.01
sin5.0
, (3)
where φin is the angle of beam incidence on structured
medium. Thus, changing the filling factor should be
taken into account when solving the inverse problem to
define the effective refraction coefficient.
The influence of the filling factor changing on
angular dependences of the reflection coefficient is
shown in Fig. 5. As one can see, for the relief depth less
than 12 nm, the model of medium with the effective
refraction index allows precise description of angular
dependences for the reflection index (the error is less
than 3%). When increasing the diffraction grating relief
depth up to 24 nm, the error of the model is increased to
8%. The further increase (h = 24 nm) of the relief depth
leads to the error increase up to 15%.
In case of using the variable filling factor, the depth
increase up to 72 nm leads to insignificant error
increasing (the error increased from 2% for h = 12 nm
up to 4% for h = 72 nm). It should be mentioned that
usage of variable filling factor allows application of the
effective medium model for approximation of angle
dependences for heights up to h = 120 nm, although
diffraction appears under these conditions (Fig. 3).
4. Conclusions
The obtained results show that submicron structural
changes of reflective surfaces can be defined by means
of multiangular ellipsometry in the optical range. It is
shown that multiangular ellipsometry allows
determining the changes in the relief height of structured
media with the step 12 nm on the example of light
reflection from diffraction gratings. Besides, it has been
shown that the model of the effective medium with a
variable filling factor allows describing the angular
dependences of reflection coefficients with error values
less than 5% for the inhomogeneity heights less than
120 nm. It should be noted that there is some critical
height for which application of the medium model with
the effective refraction index becomes impossible
because of diffraction phenomena.
Development of the offered method can be
considered as a perspective way for obtaining the
macroscopic characteristics, which describe general
properties of investigated materials.
References
1. S.C. Russev, M.I. Boyanov, J.-P. Drolet, R.M.
Leblanc, Analytical determination of the optical
constants of a substrate in the presence of a
covering layer by use of ellipsometric data // J.
Opt. Soc. Am. A, 16(6), p. 1496-1500 (1999).
2. S.H. Chen, H.W. Wang, T.W. Chang, Absorption
coefficient modelling of microcrystalline silicon
thin film using Maxwell–Garnett effective medium
theory // Opt. Express, 20(S2), p. A197-A204
(2012).
3. J.R. Power, T. Farrell, P. Gerber, S. Chandola, P.
Weightman, J.F. McGilp, The influence of
monolayer coverages of Sb on the optical
anisotropy of vicinal Si(001) // Surf. Sci. 372,
p. 83-90 (1997).
4. S.A. Kovalenko, M.P. Lisitsa, Thickness
dependences of optical constants for thin layers of
some metals and semiconductors // Semiconductor
Physics, Quantum Electronics & Optoelectronics,
4(4), p. 352-357 (2001).
5. R.C. van Duijvenbode, E.A. van der Zeeuw, G.J.M.
Koper, High precision scanning angle ellipsometry
// Rev. Sci. Instrum. 72(5), p. 2407-2414 (2001).
6. W. Theiß, Optical properties of porous silicon //
Surf. Sci. Repts. 29(3-4), pp. 91-93, 95-192 (1997).
7. W.S. Weiglhofer, A. Lakhtakia, B. Michel,
Maxwell-Garnett and Bruggeman formalisms for a
particulate composite with bianisotropic host
medium // Microwave and Opt. Technol. Lett.
15(4), p. 263-266 (1997).
8. L.A. Golovan, V.Yu. Timoshenko, P.K.
Kashkarov, Optical properties of porous-system
based nanocomposites // Uspekhi Fizicheskikh
Nauk, 177(6), p. 619-638 (2007), in Russian.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 2. P. 128-131.
PACS 42.25.Gy, 42.79.Dj, 81.70.Fy
Simulating the diffraction grating reflectivity
using effective medium theory
A.A. Goloborodko, N.S. Goloborodko, Ye.A. Oberemok, S.N. Savenkov
Taras Shevchenko Kyiv National University, Department of Radiophysics,
64, Volodymyrska str., 01601 Kyiv, Ukraine
E-mail: angol@univ.kiev.ua
Abstract. The features of optical radiation interaction with surface of gratings are investigated. The diffraction grating is proposed to be used in the effective medium model to test nanostructured surfaces. This object allows obtaining simultaneous visualization of different spatial frequencies and estimation of both structure and surface features of 3D-objects. It was shown that the effective medium model could be used to predict the reflectivity of nanostructured surfaces by using diffraction gratings with different depths of profile. Computer simulations show that the filling factor of composite systems could be an angle dependent function. So, the correct solution of the inverse problem of finding surface characteristics, such as refraction indices and absorption coefficients, is related with the angle dependence of filling factor.
Keywords: diffraction grating, effective medium, refraction index, absorption coefficient.
Manuscript received 15.01.13; revised version received 22.02.12; accepted for publication 19.03.12; published online 25.06.12.
1. Introduction
Nowadays, nondestructive, multiple parameters, express detection of structures local features become more necessary with nanotechnologies improvement. For the most widespread layered film structures the main features are: the layer thickness and basical optical features such as refraction index n [1] and absorption coefficient κ [2]. It should be mentioned that dependences n(d) and κ(d) for nanostructured surfaces, obtained for one wavelength, can vary with the wavelengths change [3, 4]. Thus, using the value of some parameter from tables or literature data can be inaccurate or can lead to essential errors in diagnosing the other features.
So, the solution of this problem is in determination of a set of bound parameters within a unified method and one measuring system that allow defining a set of features in one measurement. However, currently optical methods that allow simultaneous determination of refraction index, absorption coefficient and thickness for absorbing and nonabsorbing media are developed insufficiently. Widespread angular methods [5] were applied only to bulk samples for determining only two parameters – n and κ.
Big success in nanostructures investigation was achieved for porous silicon [6], which consists of silicon nanocrystals separated by air. If the characteristic sizes of pores and nanocrystals are much smaller than the irradiation wavelength, then such a semiconductor can be considered as homogeneous optical medium, which has some effective refraction index and absorption coefficient. These characteristics differ from characteristics of bulk samples that form the nanostructure. In this case, the model of effective medium for defining the characteristics of nanostructured objects should be discussed. The electrostatic approximation is frequently used in the model of effective medium for optical problems. This approximation requires both small sizes of the nanoparticles and a short distance between them as compared to the optical wavelength in the medium [7]. In the other case, there arises the problem of taking into account the scattering on particles that form the nanocomposite medium and interference of reflected waves. Thus, the aim of this paper was to create the optical scheme suitable for visualization and investigation of polarization characteristics of diffraction grating and effective medium model verification for reflected light characteristics description.
2. Ellipsometric investigation of ordinary grating
The diffraction gratings are often used as tested objects for calibration of optical devices. And usage of diffraction gratings with appearance of nanostructured composite materials (inhomogeneity size values of which are about the wavelength λ of scanning beam) needs an additional investigation. Thus, the medium model based on diffraction gratings with the period d = 1 μm and variable height h from 12 up to 300 nm with the step 12 nm are considered in this work. These gratings were produced using the electron beam lithography method on photoresist (electron-sensitive PMMA resist). A reconstructed 3D image received with a scanning electron microscopy (SEM) method is shown in Fig. 1.
The optical scheme shown in Fig. 2 was used for experiment. This scheme includes the probing (Laser, P, L1, L2) and receiving (L3, L4, WP1, WP2, PhD1, PhD2) channels. Coherent radiation from a He–Ne laser with λ = 0.63 μm, which was used as a source, was formed into converging beams by the long-focus system
L2
-
L1
illuminating the grating entirely. After reflection from the grating, the main maximum in the mirror reflection direction and a great number of secondary orders were observed. This scheme allows suitable observation of diffraction orders from a grating with submicron relief dimensions that were upright spacing from the main order. The photodetectors PhD1 and PhD2 were used to register the diffraction maximum intensities and were situated on the goniometry arms.
Fig. 3 shows experimental dependences of the intensity inherent to the main and first diffraction orders for gratings with different profile heights in the case of normal incidence.
As one can see, behavior of these dependences shows their anticorrelation and illustrates the energy redistribution between diffraction maxima (from the main to higher orders). Thereby, next calculations require taking into account the intensities redistribution in the maxima with the relief depth changing. In addition, the curves in Fig. 3 lead to the conclusion that there is no interference for gratings with profile depths less than 84 nm, so the model of effective medium may be applied to them. Contribution of the first diffraction orders for a deeper depth of the grating profile becomes more substantial, and the model with effective refraction index requires some corrections for the further theoretical calculations.
Fig. 1. 3D SEM image of the grating.
Fig. 2. Optical setup for simultaneous visualization of different spatial frequencies.
Fig. 3. Intensities of the main (0 Max) and first (±1 Max) diffraction orders for various depths of the grating profile.
Fig. 4. Experimental and theoretically calculated angular dependences of the reflection coefficient of photoresist surface on the chrome – glass substrate.
Dependences for orthogonal components of the reflection coefficients for the plane surface of photoresist on the glass substrate with chrome coating (5 μm) are shown in Fig. 4. Taking into account the dependence type and value of reflection coefficients, the refraction coefficient of the photoresist was nPMMA = 1.515+j0.0019 and thickness of the photoresist layer dPMMA = 0.5 μm. These values were used for determining the effective refraction coefficients of the gratings.
3. Effective medium model for the grating
Bruggeman and Maxwell–Garnett effective medium models are based on the Lorentz local field concept [7]. For the Maxwell–Garnett model, the effective permittivity εeff of composite medium that consists of dotted dissemination of material with the permittivity εb = (nb+iκb)2 in dielectric matrix εm = (nm+iκm)2 is determined as [8]:
(
)
(
)
m
b
m
b
m
eff
m
eff
L
L
L
L
e
-
+
e
e
-
e
h
=
e
-
+
e
e
-
e
1
1
,
(1)
where η is the volume filling factor, L – depolarization factor. The drawback of the Maxwell–Garnett model is the fact that components, which form the nanocomposite, are unequal and the filling factor η < 0.3.
The Bruggeman model is based on the fact that particles with permittivities εb and εm are placed into medium with the permittivity εeff. Taking into account field averaging within the sample volume, one can receive the following equation for the permittivity:
(
)
(
)
0
=
e
+
e
-
e
e
-
e
h
+
e
+
e
-
e
e
-
e
h
b
b
eff
b
eff
b
m
m
eff
m
eff
m
L
L
,
(2)
where ηm+ηb = 1. It should be mentioned that there is a necessity to consider the filling factors changing in different media for angular investigations of optical illumination characteristics. Calculation of the filling factors is done in the single scattering approximation for some simplification. Thus, taking into account shading the different areas of the grating, the filling factors can be given as:
(
)
in
b
m
in
m
m
new
m
n
n
n
j
+
-
j
-
h
»
h
sin
5
.
0
1
sin
5
.
0
,
(
)
in
b
m
in
b
b
new
b
n
n
n
j
+
-
j
-
h
»
h
sin
5
.
0
1
sin
5
.
0
,
(3)
where φin is the angle of beam incidence on structured medium. Thus, changing the filling factor should be taken into account when solving the inverse problem to define the effective refraction coefficient.
The influence of the filling factor changing on angular dependences of the reflection coefficient is shown in Fig. 5. As one can see, for the relief depth less than 12 nm, the model of medium with the effective refraction index allows precise description of angular dependences for the reflection index (the error is less than 3%). When increasing the diffraction grating relief depth up to 24 nm, the error of the model is increased to 8%. The further increase (h = 24 nm) of the relief depth leads to the error increase up to 15%.
In case of using the variable filling factor, the depth increase up to 72 nm leads to insignificant error increasing (the error increased from 2% for h = 12 nm up to 4% for h = 72 nm). It should be mentioned that usage of variable filling factor allows application of the effective medium model for approximation of angle dependences for heights up to h = 120 nm, although diffraction appears under these conditions (Fig. 3).
4. Conclusions
The obtained results show that submicron structural changes of reflective surfaces can be defined by means of multiangular ellipsometry in the optical range. It is shown that multiangular ellipsometry allows determining the changes in the relief height of structured media with the step 12 nm on the example of light reflection from diffraction gratings. Besides, it has been shown that the model of the effective medium with a variable filling factor allows describing the angular dependences of reflection coefficients with error values less than 5% for the inhomogeneity heights less than 120 nm. It should be noted that there is some critical height for which application of the medium model with the effective refraction index becomes impossible because of diffraction phenomena.
Development of the offered method can be considered as a perspective way for obtaining the macroscopic characteristics, which describe general properties of investigated materials.
References
1.
S.C. Russev, M.I. Boyanov, J.-P. Drolet, R.M. Leblanc, Analytical determination of the optical constants of a substrate in the presence of a covering layer by use of ellipsometric data // J. Opt. Soc. Am. A, 16(6), p. 1496-1500 (1999).
2.
S.H. Chen, H.W. Wang, T.W. Chang, Absorption coefficient modelling of microcrystalline silicon thin film using Maxwell–Garnett effective medium theory // Opt. Express, 20(S2), p. A197-A204 (2012).
3.
J.R. Power, T. Farrell, P. Gerber, S. Chandola, P. Weightman, J.F. McGilp, The influence of monolayer coverages of Sb on the optical anisotropy of vicinal Si(001) // Surf. Sci. 372, p. 83-90 (1997).
4.
S.A. Kovalenko, M.P. Lisitsa, Thickness dependences of optical constants for thin layers of some metals and semiconductors // Semiconductor Physics, Quantum Electronics & Optoelectronics, 4(4), p. 352-357 (2001).
5.
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Fig. 5. Angular dependences of the reflection coefficient.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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