Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique
Si crystal surface after chemical etching was studied using ellipsometry, atomic force microscopy and scanning tunneling microscopy. The ellipsometric parameters as functions of light incidence angles at two light wavelengths 546.1 and 296.7 nm were measured. The calculations based on equations for...
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| Опубліковано в: : | Semiconductor Physics Quantum Electronics & Optoelectronics |
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| Дата: | 2015 |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2015
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| Цитувати: | Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique / T.S. Rozouvan, L.V. Poperenko, I.A. Shaykevich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 1. — С. 26-30. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859863597623017472 |
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| author | Rozouvan, T.S. Poperenko, L.V. Shaykevich, I.A. |
| author_facet | Rozouvan, T.S. Poperenko, L.V. Shaykevich, I.A. |
| citation_txt | Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique / T.S. Rozouvan, L.V. Poperenko, I.A. Shaykevich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 1. — С. 26-30. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | Si crystal surface after chemical etching was studied using ellipsometry, atomic force microscopy and scanning tunneling microscopy. The ellipsometric parameters as functions of light incidence angles at two light wavelengths 546.1 and 296.7 nm were measured. The calculations based on equations for the plane surface have shown that the refractive index and absorption coefficient values are different from those determined earlier. Two models for surface layers were developed. After etching, the upper layer contains chemical compounds and the lower layer characterizes the sample roughness. By applying Airy’s formula to ellipsometric data, optical constants and thicknesses of the layers were obtained. The calculated values of bulk Si optical constants wholly correspond to the data from literature. The calculated thickness of the lower layer is similar to that obtained through scanning tunneling microscopy measurements. Calculations based on Maxwell-Garnett and Bruggeman equations were performed to determine the content of silicon particles within the lower rough layer.
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| first_indexed | 2025-12-07T15:47:10Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 26-30.
doi: 10.15407/ spqeo18.01.026
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
26
PACS 68.37.Ef
Influence of the surface roughness and oxide surface layer
onto Si optical constants measured by the ellipsometry technique
T.S. Rozouvan, L.V. Poperenko, I.A. Shaykevich
Taras Shevchenko Kyiv National University, Department of Physics,
4, prospect Glushkova, 03187 Kyiv, Ukraine
E-mail: tamara_rozouvan@yahoo.ca
Abstract. Si crystal surface after chemical etching was studied using ellipsometry,
atomic force microscopy and scanning tunneling microscopy. The ellipsometric
parameters as functions of light incidence angles at two light wavelengths 546.1 and
296.7 nm were measured. The calculations based on equations for the plane surface have
shown that the refractive index and absorption coefficient values are different from those
determined earlier. Two models for surface layers were developed. After etching, the
upper layer contains chemical compounds and the lower layer characterizes the sample
roughness. By applying Airy’s formula to ellipsometric data, optical constants and
thicknesses of the layers were obtained. The calculated values of bulk Si optical
constants wholly correspond to the data from literature. The calculated thickness of the
lower layer is similar to that obtained through scanning tunneling microscopy
measurements. Calculations based on Maxwell-Garnett and Bruggeman equations were
performed to determine the content of silicon particles within the lower rough layer.
Keywords: Si nanoislands, scanning tunneling microscopy, spectral ellipsometry.
Manuscript received 12.08.14; revised version received 02.12.14; accepted for
publication 19.02.15; published online 26.02.15.
1. Introduction
Ellipsometric experimental techniques are most
commonly used for measurements of such optical
constants as refractive and absorption indices inherent to
metals or semiconductors within a strong absorption
spectral band [1, 2]. It’s also known that the equations
used to calculate optical constants based on
experimentally obtained ellipsometric data are obtained
for geometrically ideal plane surface of the sample. At
the same time, the polished surface of the samples is
rough, and there is a covering layer of oxide and other
molecules [2, 3]. The latter influences the ellipsometric
studies and respective values of the calculated optical
constants. The problem of simultaneous consideration of
the influence of surface roughness and the interface layer
influence on the results of ellipsometric measurements is
quite complex. Most of researches in the following
works either determines the latter factor [3-7] or the
former one [3, 8-12]. While we managed to
simultaneously establish the influence of the interface
layer and the roughness on the optical constants of Si
sample obtained by ellipsometry experiments.
2. Experimental and results
In our experiments, the chosen n-type phosphorus-doped
silicon substrate with the surface plane [111] was similar
to those used in solar batteries. It was etched in chemical
solution based on the mixture of HNO3-HF, Na2Cr2O7,
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 26-30.
doi: 10.15407/ spqeo18.01.026
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
27
HNO3 and HF in order to make the sample surface
smoother. These chemical compounds are usually used
to polish Si plates, although in our case it diminished
roughness of our sample surface.
The sample surface studies were performed using
the INTEGRA NT-MDT atomic force microscope that
allows to perform both atomic force and scanning
tunneling microscopy measurements. Ellipsometric
experiments were made using the Beattie technique [2].
Parameters, such as the amplitude component ψ and the
phase difference Δ, were measured for various angles of
incidence at two wavelengths 546.1 and 296.7 nm.
These wavelengths were chosen within the spectral
region of strong interband transitions for Si. The
ellipsometric measurements are most effective in these
spectral regions. Being based on the obtained data, the
sample optical constants – refractive index n and
absorption index k – were calculated.
The well-known theoretical relations for these
calculations [1, 2] were applied. In order to determine
the roughness and the interface oxide layer influences on
the final results, the sample was modeled as that having
two layers on its surface (Fig. 1).
A light beam propagates from air 1 (n = 1) and then
through the oxide layer 2, roughness layer 3 and finally
reaches the bulk Si plate 4. Multiple beam interference
occurs in these layers, which can be described by
applying Airy’s formula [13]. The layer 3 is structured
with Si surface irregularities (shaded in Fig. 1) and filled
gaps by upper layer 2 substance. The layer 3 is
considered in the model as the homogenous plane-
parallel one with an effective refractive index n3.
The thicknesses of layers and their refractive
indices were calculated using the measured dependences
tan(ψ) and cos(Δ) on the angle of incidence f, applying
Eq. (1). For the layer 3, we obtain an effective refractive
index. All the obtained values for refractive indices are
complex n + ik:
i
ii
i
ii
i ig
psps
ig
psps
ps
eRr
eRr
R
2
,,
2
,,
,
1
1
1
, (1)
Fig. 1. Schematic cross-section of the sample. Air (1) and
oxide (2), interface layers of roughness (3) on the sample
surface (4).
here i – indices mark the layers (reflection between i and
i + 1 layers)
ipsr , , in Eq. (1) – amplitude Fresnel
reflection coefficients related to the interface between i
and i + 1 layers:
,
)cos()cos(
)cos()cos(
,
)cos()cos(
)cos()cos(
11
11
11
11
iiii
iiii
p
iiii
iiii
s
fnfn
fnfn
r
fnfn
fnfn
r
i
i
(2)
ni and fi are the complex refractive index and light
incidence angle, respectively. gi – i layer phase thickness
taken as iiii fdng cos
2
, where di is the i layer
thickness and λ – light wavelength.
ipsR , – amplitude
reflection coefficient from the previous layer, calculated
similarly using Eq. (1), or equal to the Fresnel
coefficient for the last layer 4. Finally, we calculated the
rest of the parameters from the equation
exptan/ 11 sp RR (3)
checking the fit between the experimental and
theoretical data.
3. Discussion
The surface of our Si sample was first studied by the
atomic force microscopy technique. The results of the
experiments are presented in Fig. 2. As one can see, the
surface is covered by irregular pyramid-shaped parts
with the micron order of magnitude difference in their
height and size. The faces of the pyramidal parts are not
parallel to the sample surface plane, so we were not able
to perform the ellipsometric experiments with such a
surface. Therefore, the sample surface was etched, which
resulted in a radical smoothing of the surface. The
surface profile after etching is presented in Figs. 3 and 4.
The data was obtained using atomic force microscopy
(Fig. 3) and high resolution scanning tunneling
microscopy (Fig. 4). We can see in Fig. 3 two important
features of the scanned surface. First of all, the
pyramidal structure from Fig. 2 is absent as a result of
etching. The surface is flat, though some particles, which
can be remnants of chemical reactions, are present on the
surface. Vertical lines in the figure are “shadow”
artifacts of the measurements because of finite cantilever
needle width and sharp steps in height on the sample
surface. Second, one can see straight lines a few microns
in length on the surface either as the edges of a flat
structure (left side of the picture) or just a dark straight
line (right side of the picture). The structures may reflect
crystal lattice patterns on the surface, which were
studied afterward applying high resolution scanning
tunneling microscopy (Fig. 4). Fig. 4 surface profile is
covered by nano-islands with differences in height
10 nm order of magnitude, which makes the
ellipsometry measurements possible. The sides of the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 26-30.
doi: 10.15407/ spqeo18.01.026
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
28
nanoislands are ordered forming straight lines. The
ellipsometric measurements results – dependences
tan(ψ) and cos(Δ) depending on incidence angle f at the
wavelength λ = 546.1 nm – are presented in Figs. 5 and
6. Similar measurements for the wavelength λ =
296.7 nm are also presented in Figs. 7 and 8.
Fig. 2. Surface of the sample before etching in accord with the data of
atomic force microscopy.
Fig. 3. Atomic force microscopy scans for the sample after etching.
a)
b)
Fig. 4. Scanning microscopy images for the sample after etching.
Spatial resolution (b) is five times higher than in (a).
As one can see from Figs. 5 and 6, applying the
equations (1)-(3) we calculated n2, k2, n3, k3, as well as
film thicknesses d2 and d3. The values of n4 and k4 for Si
substrate at the light wavelength 546.1 nm were taken
from the known source [14]. The values used by us were
n4 = 4.97 and k4 = 0.044. A similar procedure was made
with calculations at 296.7 nm (based on the results
presented in Figs. 7 and 8). Because of transcendental
character of Eqs. (1) and (2), we were only able to
perform numerical calculations at PC by minimizing the
difference between the experimental data and numerical
simulation results.
Fig. 5. Ellipsometric data: tan(ψ) as a function of the angle of
incidence f. The etched sample at the light wavelength 546.1 nm.
Squares – experimental data, solid line – results of calculations.
Fig. 6. Ellipsometric data: cos(Δ) as a function of the angle of
incidence f. The etched sample at the light wavelength 546.1 nm.
Squares – experimental data, solid line – results of calculations.
Fig. 7. Ellipsometric data: tan(ψ) as a function of the angle of
incidence f. The etched sample at the light wavelength 296.7 nm.
Squares – experimental data, solid line – results of calculations.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 26-30.
doi: 10.15407/ spqeo18.01.026
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
29
Fig. 8. Ellipsometric data: cos(Δ) as a function of the angle of
incidence f. The etched sample at the light wavelength 296.7 nm.
Squares – experimental data, solid line – results of calculations.
The conducted numerical simulations brought the
following outcome, by applying basic equations for
optical constants [1, 2], without taking into account
surface interface layers,
cos2sin1
2cos
tansin ffa ,
cos2sin1
sin2sin
tansin ffb ,
22222 )sin( fbakn ,
abnk , (4)
we obtained n4 = 1.61 and k4 = 0.331 at the light
wavelength 546.1 nm. These values differ from those
taken from [14]. The more drastic difference between
our numerical simulations and data of [14] take place at
the light wavelength 296.7 nm. The exact values taken
from [14] are n4 = 4.94, k4 = 4.48 and are clearly out of
the number range of the calculations by using (4) with
the values n4 = 1.38, k4 = 0.344. The results can be
explained by taking into account shorter light
wavelength of the reflected light with having more
influence on the parameters of the sample surface. The
calculations using Eqs. (1)-(3) and Figs. 5-8 data
resulted in the following plots (Fig. 7):
λ = 546.1 nm, n2 = 2.8, k2 = 0.3, n3 = 3.8, k3 = 0.1, d2 =
50 nm, d3 = 4.5 nm, n4 = 4.97, k4 = 0.044;
λ = 296.7 nm, n2 = 2, k2 = 0.384, n3 = 4.7, k3 = 1.2, d2 =
50 nm, d3 = 4.5 nm, n4 = 4.94, k4 = 4.48.
By analyzing the adduced results, we can conclude:
1. The obtained data for the substrate 4 are the same
with those taken from [14].
2. The thickness of the upper layer 2 containing
oxides and chemical compounds as a result of Si
substrate etching and the roughness layer 3
thickness are the same for the both light
wavelengths.
3. The thickness of the roughness layer 3 is consistent
with Fig. 4 data. The thickness does not exceed
10 nm.
4. Optical constants of the roughness layer 3 differ
from the constants of the chemical compounds in
the lower layer, which is the result of the etching
procedure, and the values are close to those of bulk
Si. The latter is pretty understandable because the
layer 3 contains particles of pure Si (Fig. 1).
The point 4 allows us to apply the Maxwell-Garnett
model [15] to determine the percentage of Si particles in
the whole layer 3 volume using the equation:
24242323 22 q , (5)
where q = VSi /
V, VSi is the Si volume in the layer 3, V –
layer 3 volume; ε = n
2
for all layers.
The results of calculations: q = 0.687 for λ =
296.7 nm, q = 0.527 for λ = 546.1 nm.
The q-numbers divergence at different light
wavelengths is the result of the pyramidal shape inherent
to the particles in the layer instead of the spherical shape
required by Maxwell-Garnett model. The Bruggeman
relation was applied to further analyze experimental data
because calculated q exceeds 0.5 [3]:
43424243 221 q . (6)
The results of calculations by using Eq. (6) are as
follows: q = 0.583 for λ = 296.7 nm and q = 0.46 for λ =
546.1 nm. The comparison between calculations with
Eq. (5) and Eq. (6) results in lower numbers for the
Bruggeman approach. The explanation is similar to the
above presented and is based on a non-spherical shape of
the particles.
4. Conclusions
1. Our studies show that the calculations based on
ellipsometric data without taking into account
surface interface layers of the Si crystal with the
etched surface produce the values of optical
constants different from those previously found for
crystalline Si.
2. We used Airy’s formula to experimental data while
applying the model of two-layered surface with the
upper layer that stems from the etching procedure
and the bottom roughness layer. The calculated
values of optical constants are similar to those
found in literature.
3. The bottom layer thickness calculated from the
ellipsometric data characterizes Si sample
roughness and is equal to 4.5 nm, which is in
agreement with the results obtained with scanning
tunneling microscopy.
4. Using the Maxwell-Garnett and Bruggeman
models, we calculated the partial ratio of Si
particles in the layer, which characterizes the
surface roughness. The calculations were based on
the obtained optical constants for two upper layers.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 26-30.
doi: 10.15407/ spqeo18.01.026
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
30
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|
| id | nasplib_isofts_kiev_ua-123456789-119992 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-12-07T15:47:10Z |
| publishDate | 2015 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Rozouvan, T.S. Poperenko, L.V. Shaykevich, I.A. 2017-06-10T17:03:17Z 2017-06-10T17:03:17Z 2015 Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique / T.S. Rozouvan, L.V. Poperenko, I.A. Shaykevich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 1. — С. 26-30. — Бібліогр.: 15 назв. — англ. 1560-8034 PACS 68.37.Ef https://nasplib.isofts.kiev.ua/handle/123456789/119992 DOI: 10.15407/spqeo18.01.026 Si crystal surface after chemical etching was studied using ellipsometry, atomic force microscopy and scanning tunneling microscopy. The ellipsometric parameters as functions of light incidence angles at two light wavelengths 546.1 and 296.7 nm were measured. The calculations based on equations for the plane surface have shown that the refractive index and absorption coefficient values are different from those determined earlier. Two models for surface layers were developed. After etching, the upper layer contains chemical compounds and the lower layer characterizes the sample roughness. By applying Airy’s formula to ellipsometric data, optical constants and thicknesses of the layers were obtained. The calculated values of bulk Si optical constants wholly correspond to the data from literature. The calculated thickness of the lower layer is similar to that obtained through scanning tunneling microscopy measurements. Calculations based on Maxwell-Garnett and Bruggeman equations were performed to determine the content of silicon particles within the lower rough layer. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique Article published earlier |
| spellingShingle | Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique Rozouvan, T.S. Poperenko, L.V. Shaykevich, I.A. |
| title | Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique |
| title_full | Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique |
| title_fullStr | Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique |
| title_full_unstemmed | Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique |
| title_short | Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique |
| title_sort | influence of the surface roughness and oxide surface layer onto si optical constants measured by the ellipsometry technique |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119992 |
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