Out-of-plane optical transmittance of 2D photonic macroporous silicon structures
Optical transmission spectra of 2D photonic macroporous silicon structures are investigated. The absolute bandgap for high values of the out-of-plane component kz is situated between the second and third photonic bands. Essential reduction in the transmittance of electromagnetic radiation and the...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2007
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| Цитувати: | Out-of-plane optical transmittance of 2D photonic macroporous silicon structures / L.A. Karachevtseva, A.E. Glushko, V.I. Ivanov, O.O. Lytvynenko, V.F. Onishchenko, K.A. Parshin, O.J. Stronska // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 2. — С. 51-57. — Бібліогр.: 26 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1178932025-06-03T16:25:27Z Out-of-plane optical transmittance of 2D photonic macroporous silicon structures Karachevtseva, L.A. Glushko, A.E. Ivanov, V.I. Lytvynenko, O.O. Onishchenko, V.F. Parshin, K.A. Stronska, O.J. Optical transmission spectra of 2D photonic macroporous silicon structures are investigated. The absolute bandgap for high values of the out-of-plane component kz is situated between the second and third photonic bands. Essential reduction in the transmittance of electromagnetic radiation and the step formation are observed for wavelengths less than the optical period of structures due to directed and decay optical modes formed by macroporous silicon as a short waveguide. The absorption in the macroporous silicon structure is determined by a maximum of the longitudinal component of electromagnetic waves, its interaction with 2D surface oscillations, and the appearance of polaritonic resonances. We would like to acknowledge STCU (Science and Technology Center of Ukraine) for the financial support through Project 2444. 2007 Article Out-of-plane optical transmittance of 2D photonic macroporous silicon structures / L.A. Karachevtseva, A.E. Glushko, V.I. Ivanov, O.O. Lytvynenko, V.F. Onishchenko, K.A. Parshin, O.J. Stronska // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 2. — С. 51-57. — Бібліогр.: 26 назв. — англ. 1560-8034 PACS 71.25.Rk, 81.60.Cp https://nasplib.isofts.kiev.ua/handle/123456789/117893 en Semiconductor Physics Quantum Electronics & Optoelectronics application/pdf Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Optical transmission spectra of 2D photonic macroporous silicon structures are
investigated. The absolute bandgap for high values of the out-of-plane component kz is
situated between the second and third photonic bands. Essential reduction in the
transmittance of electromagnetic radiation and the step formation are observed for
wavelengths less than the optical period of structures due to directed and decay optical
modes formed by macroporous silicon as a short waveguide. The absorption in the
macroporous silicon structure is determined by a maximum of the longitudinal
component of electromagnetic waves, its interaction with 2D surface oscillations, and the
appearance of polaritonic resonances. |
| format |
Article |
| author |
Karachevtseva, L.A. Glushko, A.E. Ivanov, V.I. Lytvynenko, O.O. Onishchenko, V.F. Parshin, K.A. Stronska, O.J. |
| spellingShingle |
Karachevtseva, L.A. Glushko, A.E. Ivanov, V.I. Lytvynenko, O.O. Onishchenko, V.F. Parshin, K.A. Stronska, O.J. Out-of-plane optical transmittance of 2D photonic macroporous silicon structures Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Karachevtseva, L.A. Glushko, A.E. Ivanov, V.I. Lytvynenko, O.O. Onishchenko, V.F. Parshin, K.A. Stronska, O.J. |
| author_sort |
Karachevtseva, L.A. |
| title |
Out-of-plane optical transmittance of 2D photonic macroporous silicon structures |
| title_short |
Out-of-plane optical transmittance of 2D photonic macroporous silicon structures |
| title_full |
Out-of-plane optical transmittance of 2D photonic macroporous silicon structures |
| title_fullStr |
Out-of-plane optical transmittance of 2D photonic macroporous silicon structures |
| title_full_unstemmed |
Out-of-plane optical transmittance of 2D photonic macroporous silicon structures |
| title_sort |
out-of-plane optical transmittance of 2d photonic macroporous silicon structures |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2007 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/117893 |
| citation_txt |
Out-of-plane optical transmittance of 2D photonic macroporous silicon structures / L.A. Karachevtseva, A.E. Glushko, V.I. Ivanov, O.O. Lytvynenko, V.F. Onishchenko, K.A. Parshin, O.J. Stronska // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 2. — С. 51-57. — Бібліогр.: 26 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-11-28T09:23:14Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 51-57.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
51
PACS 71.25.Rk, 81.60.Cp
Out-of-plane optical transmittance
of 2D photonic macroporous silicon structures
L.A. Karachevtseva, A.E. Glushko, V.I. Ivanov, O.O. Lytvynenko,
V.F. Onishchenko, K.A. Parshin, O.J. Stronska
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 45, prospect Nauky, 03028 Kyiv, Ukraine
Phone: 525 9815, fax: 525 8243, e-mail: lakar@isp.kiev.ua
Abstract. Optical transmission spectra of 2D photonic macroporous silicon structures are
investigated. The absolute bandgap for high values of the out-of-plane component kz is
situated between the second and third photonic bands. Essential reduction in the
transmittance of electromagnetic radiation and the step formation are observed for
wavelengths less than the optical period of structures due to directed and decay optical
modes formed by macroporous silicon as a short waveguide. The absorption in the
macroporous silicon structure is determined by a maximum of the longitudinal
component of electromagnetic waves, its interaction with 2D surface oscillations, and the
appearance of polaritonic resonances.
Keywords: 2D macroporous silicon, photonic band, polaritonic resonance.
Manuscript received 04.04.07; accepted for publication 24.04.07; published online 19.10.07.
1. Introduction
Macroporous silicon can be considered as an ideal 2D
and 3D photonic crystal due to high aspect ratios of
macropores and a periodic variation of the
photoelectrochemical etching parameters [1-3]. The
lattice constants can be varied in the range from 8000
down to 500 nm, resulting in complete bandgaps in a
wavelength range between 20 and 1.3 µm. Point defects,
3D photonic crystals, microchips in a photonic crystal
based on macroporous silicon were characterized in [4-
10]. Sharp resonances were recorded in the bandgap of
photonic crystals with defects, in excellent agreement
with the results of numerical simulations by applying a
tight-binding model [4, 5]. Extended 3D photonic
crystals based on macroporous silicon are prepared due
to a periodic variation of the illumination during
photoelectrochemical etching [6] and subsequent
focused-ion-beam drilling [7]. All-optical transistor
action in photonic bandgap silicon materials doped with
active atoms was described in [8]. The concept of a
hybrid 2D-3D photonic bandgap silicon heterostructure,
which enables the planar light-wave propagation in
engineered wavelength-scale microcircuits, was
introduced in [9]. The incorporation of semiconductor
quantum dots as internal emitters into 2D photonic
crystals of macroporous silicon was reported in [10]. In
addition, a spectral modification of the emission by the
surrounding photonic crystal was demonstrated for
mercury telluride quantum dots, when the emission
coincides with the photonic bandgap of the silicon
photonic crystal.
Diffraction efficiency, birefringence, and
polaritonic and structural gaps on the silicon-based
photonic crystals were studied in [11-13]. A 2D photonic
crystal can exhibit spectral regions of very small
diffraction efficiency [11], while the diffraction
efficiency is near unity in other regions. The
experimental results agree well with the corresponding
numerical calculations and highlight the prominent role
of the surface termination, an aspect which cannot be
described by the photonic band structure alone. Such
additional spectral filters have possible applications in
Raman and photoluminescence spectroscopy. The
experimental and theoretical studies of the birefringence
of two-dimensional silicon photonic crystals in the
spectral region below the first photonic bandgap were
reported in [12]. The measured birefringence was
defined as the difference in the effective refractive
indices of the electric fields polarized in parallel and
perpendicularly to the cylinder axis and reached a
maximum value of 0.366 near the first photonic band
edge. The results demonstrate the potential use of two-
dimensional photonic crystals for highly birefringent
optically integrated devices. The coexistence and
interaction of polaritonic and structural gaps are studied
in [13] on one-dimensional photonic crystals Si/SiO2,
SiO2/Si, and SiO2/air. The calculated results verify the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 51-57.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
52
a
b
17 19 21 23 25
0
8
16
24
32
p90
p0
Wavelength, micron
A
bs
or
ba
nc
e,
a
rb
. u
n.
c
17 19 21 23 25
0
8
16
24
32
p90
p0A
bs
or
ba
nc
e,
a
rb
. u
n.
Wavelength, micron
d
Fig. 1. Periodic (a) and arbitrary (b) macroporous silicon structures. Optical absorption of electromagnetic waves propagated in
periodic (c) and arbitrary (d) macroporous silicon.
presence of a polaritonic gap in photonic crystals Si/SiO2
for thicknesses much lower than the wavelength for the
cases SiO2/Si and SiO2/air.
Theoretical and experimental results obtained
during last years demonstrate the potential use of
silicon-based photonic crystals for active and passive
optically integrated devices [14]. 2D photonic crystals
on the basis of macroporous silicon are perspective for
use in the infrared range of electromagnetic waves due
to the effective transformation of a spectrum of
electromagnetic radiation. The presence of periodically
located cylindrical pores divided by silicon columns
provides the big effective surface of a sample which
determines the optical and electrophysical
characteristics of macroporous silicon structures [15].
In this paper, the out-of-plane optical transmission
spectra of 2D photonic macroporous silicon structures
have been investigated with the purpose of a definition
of new opportunities for applications of such structures.
The incidence direction of electromagnetic radiation in
parallel to macropores is more technological for planar
technologies. The basic researches of optical
characteristics have been concentrated also on this
variant. The dependences of photoconductivity and
Raman scattering on the angle of incidence of the
electromagnetic radiation were observed by taking into
account the comparative analysis of a surface of
macroporous silicon by methods of electron
microscopy, infrared absorption, and the modulation
spectroscopy of electroreflection
2. Methodology
The starting material consisted of n-type silicon (100)
with a resistivity of 4.5 Ohm⋅cm. Macropores were
formed with diameters Dp = 1-10 µm due to the
generation and transfer of nonequilibrium holes to the n-
Si electrochemically treated surface as a result of the
optical band-to-band electron-hole generation [16].
Periodic structures as well as structures with arbitrary
distribution of macropores have been fabricated (Fig. 1a
and b). Optical transmittance was measured using an IR
Fourier spectrometer IFS-113 and an IR spectro-
photometer Specord M85.
3.Results
3.1. Photonic bandgap
For the out-of-plane light propagation, a sharp increase
in absorption and the photonic bandgap formation is
observed at wavelengths between one and two optical
periods λa < λ < 2λa of the macroporous silicon structure
(λa is equal to (a - Dp)ε1/2 + Dp); a –the structure period,
and Dp – the diameter of macropores). Thus, the absolute
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 51-57.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
53
5 6
0.25
0.30
0.35
0.40
ω
a/
(2
πc
)
kza
Upper gap edge
Lower gap edge
Fig. 2. The dependence of the bandgap edge position on the
kz component.
1000 2000 3000 4000
0.0
0.1
0.2
0.3
0.4
0.5
0.2
0.4
0.6
0.8
1.0
(a-Dp)nSi
Dp
R
ef
le
ct
an
ce
, a
rb
.u
n.
Tr
an
sm
itt
an
ce
, a
rb
.u
n.
Wavenumber, cm-1
Dp 1
2
4
3
(a-Dp)nSi
Fig. 3. Transmittance spectra of macroporous silicon
structures with parameters: 1 – Dp > (a -Dp) nSi; 2 –
Dp ≈ (a -Dp) nSi; 3 – Dp< (a -Dp) nSi; reflectance spectra of
monocristalline silicon (4).
photonic bandgap was measured for the light direction
parallel to macropores for planar technologies at λ = 1.2-
1.5λa. One photonic bandgap is formed for periodic
structures (Fig. 1c), and the narrow peaks of the density
of states are formed for the structure with arbitrary
macropore distribution (Fig. 1d).
Optical transmittance of 2D periodic structures
was investigated for the out-of-plane direction in
[17, 18]. Within the plane-wave method, Maradudin and
McGurn in [17] had calculated the dispersion curves of
electromagnetic wave propagation in a two-dimensional
periodic structure. The structure studied numerically
possesses a bandgap between 3 and 4 zones common to
waves of both E- and H-polarizations propagating in the
plane parallel to the rods. In [18], the transmission of
electromagnetic waves propagating in 2D photonic
crystals for the out-of-plane incident angle as high as 85°
was studied. There is a full calculated photonic bandgap
for both E- and H-polarizations for the ratio of dielectric
constants higher than 12.25. Our calculations of the out-
of-plane propagation of electromagnetic waves through a
square-lattice photonic crystal by the plane-wave method
show that the absolute bandgap appears for high values
of the out-of-plane component kz. In our case, the
bandgap opens up for kza > 4.5 and is situated between
the second and third bands (Fig. 2). As it obvious, the
gap width increases and its edges shift sufficiently to
higher frequencies. Our experimental results (Fig. 1c)
correspond to kza = 5 and ωa/2πc = 0.32-0.35.
3.2. Polaritonic absorption band
Absorption spectra of macroporous silicon with different
macropore diameters and concentrations have common
features at λ ≤ λa (Fig. 3). There is an essential reduction
in the transmittance of electromagnetic radiation as the
wavelength shortens [15]. At short wavelengths, λ < Dp,
(Fig. 3, curve 1) and at wavelengths λ < (a −Dp)nSi
(Fig. 3, curves 2, 3), the optical transmittance grows
slightly. The area of the maximal absorption of this band
depends on the difference of the macropore diameter Dp
and distances between pores, a – Dp. The maximal
absorption is measured in an interval of frequencies [(a –
Dp)nSi]-1 > ν > (Dp)-1 at Dp > (a − Dp)nSi (curve 1) and in
an interval of frequencies [(a − Dp)nSi]-1 < ν < (Dp)-1 for
Dp < (a − Dp)nSi (curve 3). Structures with a macropore
diameter comparable to the distance between pores Dp ∼
(a − Dp)nSi have the transmission minimum at ν =
= [(a − Dp)nSi]-1 ≅ (Dp)-1 (curve 2). In the first case, the
long-wave band edge is measured up to the frequencies of
transverse optical phonons (520 сm-1) that is correlated with
a reflection growth for single-crystal silicon (Fig. 3,
curve 4) due to the lattice absorption in the silicon matrix.
The transmission reduction with decrease in the lattice
absorption testifies that the phonon modes "extinguish" the
mechanism of electromagnetic energy dissipation in
macroporous silicon structures.
The transmission spectra (Fig. 3) contain steps or
oscillations, as in Fig. 4. The step frequency in the long-
wave part of the spectrum is proportional to the distance
between pores (∆νl ~ a – Dp). But, in the short-wave
region, it is proportional to the diameter of pores
(∆νs ∼ Dp). The transmission spectra of macroporous
silicon as well as the formation of the steps can be
explained by a model of directed and decay optical
modes in macroporous silicon as a short waveguide
structure [19, 20]. In the short-wave spectral region, the
directed optical modes are formed on macropores,
because the step growth of transmittance takes place for
λ ≤ Dp (Fig. 4). In the middle region Dp < λ < λa, the
formation of the directed mode for silicon waveguides
and the decay mode for macropores is possible. Such
modes are formed in the same medium (the silicon
matrix) and differ by the sign of the radius ρ only
(Table). The amplitude of the total wave in the direction
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 51-57.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
54
Table. Mode characteristics in macroporous silicon structures as in [19].
Region Propagation constant, β Mode parameter
Macropore k cosθz, 0 < β < k Up = kρ (1 – cosϑz
2)1/2 Directed optical
modes Silicon matrix knSi cosθz, k < β < knSi USi = kρSi nSi (1 – cosϑz
2)1/2
Macropore − ik nSicosθz, k2 < |β|2 < (knSi)2 Wp = kρ nSi (1 – cosϑz
2)1/2
Polaritonic modes
Silicon matrix − ik cosθz, 0 < β < k QSi = ikρSi (cosϑz
2 – 1)1/2
950 1000 10500.25
0.30
0.35
0.40
0.45
Tr
an
sm
itt
an
ce
, a
rb
.u
n
Wavenumber, cm-1
a
2500 3000 3500 4000
0.54
0.56
0.58
0.60
0.62
Tr
an
sm
itt
an
ce
, a
rb
.u
n.
Wavenumber, cm-1
b
0 1 2 3 4
20
40
60
80
∆ν
l, c
m
-1
a-Dp, µm
c
0 2 4 6 8 10 12
0
200
400
600
800
Dp, µm
∆
ν s, c
m
-1
d
Fig. 4. Long-wave steps in the transmittance spectrum (a), short-wave steps in the transmittance spectrum of macroporous
silicon (b), dependence of the long-wave step frequency ∆νl on the distance between pores a-Dp (c), dependence of the short-
wave step frequency ∆νs on the pore diameter Dp (d).
z is defined by the cylindrical functions
Jn
Si(Q)eiβz+ p
nI (-Q)e-βz. In the long-wave spectral region
λ > λa, the decay modes are formed in the silicon matrix
with the mode parameter QSi = ikρSi nSi(cos ϑz2−1)1/2.
The increase in the diameter of macropores up to
Dp > (a − Dp)nSi modifies the transmission spectrum. In
this case, the region of the directed mode formation
corresponds to λ < a – Dp and the decay modes are
formed for λ > Dp.
Transmission spectra of macroporous silicon
structures were measured by a spectrophotometer with
an aperture of about 10°. Therefore, under the
formation of the optical mode, the multimode regime
should be realized. However, the step formation
testifies to the realization of the one-mode regime that
is related to surface oscillator fluctuations on the
macropore surface and with the surface polariton
formation. This is supported by the preferable
absorption of the р-components of the electromagnetic
radiation incident on macroporous silicon structures
(Fig. 5). In addition, the excitation of a surface
electromagnetic wave is accompanied by a reduction in
the reflected light intensity and an increase in the
absorption.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 51-57.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
55
6000 4000 2000
1
2
3
A
bs
or
ba
nc
e,
a
rb
. u
n.
2
Wavenumber, cm-1
1
Fig. 5. Absorption spectra of the р-component (1) and s-
component (2) of the electromagnetic radiation incident on
macroporous silicon.
4. Discussion
Absorption of macroporous silicon at λ ≤ λa is
determined by the longitudinal component of
electromagnetic waves in macroporous silicon structure
as a short waveguide with specific surface (Fig. 3). The
comparative analysis of the surface of macroporous
silicon by methods of electron microscopy, infrared
absorption, and modulation spectroscopy of
electroreflection was carried out in [20-22]. It was
established that the microstructure, local center structure,
and built-in electric field on a macropore surface
essentially depend on parameters of the electrochemical
process, that is, on the initial voltage and the current
density. The periodic oscillation in electroreflection
spectra (Franz-Keldysh's effect) and the effect of
increase in the built-in electric field were measured due
to a positive charge built in the oxide layer on the
macropore walls. The electric field intensity Fs on a
macropore surface varies from 4⋅105 to 9⋅105 V/cm [21].
The value of the built-in field on a cylindrical macropore
is defined by the surface concentration of Si-О and Si-Н
bonds [22]. In addition, the sign of the main maximum
in the spectra of electroreflectance and the dependence
of its magnitude on a constant voltage [21] correspond to
the formation of an inversion layer on the macropore
surface. Franz-Keldysh oscillations are a result of the
triangular potential barrier on a macropore surface and
determine two-dimensional surface carrier oscillations.
Thus, the longitudinal component of electromagnetic
waves in the macroporous silicon structure interacts
effectively with surface oscillators, and polaritonic
resonances in absorption are observed.
In addition, the photoconductivity of macroporous
silicon structure depends on an incidence angle of
electromagnetic radiation (Fig. 6). For periodic
structures, maxima of photoconductivity are formed (1)
at the normal incidence of electromagnetic radiation, (2)
in the region of the angle of total internal reflection with
respect to the macropore walls, and (3) for the grazing
incidence of light with respect to the structure surface
[23]. At the angles of incident light close to normal ones,
the directed optical modes (Fig. 3) are localized on
macropores. At the angle of total internal reflection with
respect to the macropore walls, the surface ТМ-wave
propagating along macropores is formed. At the angles
of incidence close to grazing ones, the periodic relief of
the structure transforms the incident light wave into a
surface one as a result of the m-order diffraction. Thus,
the photoconductivity maximum corresponds to a
maximum of the longitudinal component of
electromagnetic waves in analogy to light absorption.
The effect of the enhancement of Raman scattering
in the photonic structures of macroporous silicon was
measured in [24]. The band position in spectra coincides
with the position of the band for single-crystal silicon,
but its intensity strongly depends on the macropore size
and the light incidence angle. The maximal scattering
intensity was registered for the samples with the minimal
diameter of pores (about 1 µm) at an incidence angle of
25-30 degrees (Fig. 6). This maximum corresponds to
the angle of total internal reflection with respect to the
macropore walls, when the longitudinal component of
electromagnetic waves is maximal. The mechanism of
Raman scattering enhancement is determined by the
surface electromagnetic mode formation and the
scattering on it. Thus, the photoconductivity and Raman
scattering maxima are determined by the corresponding
maximum of the longitudinal component of
electromagnetic waves in the macroporous silicon
structure in analogy to light absorption.
The cylinder consisting of a substance with
frequency-dependent dielectric permeability (l = 1)
possesses dispersive frequencies in a plane perpendicular
to the cylinder axis which satisfy the relation [25]:
Ωµ
2(q) = ωp
2{[ε∞ – ε1Iµ(ξ) µ′K Kµ(ξ)/ µ′J (ξ)Kµ(ξ)]}–1. (1)
where Iµ(ξ) and Kµ(ξ) are the µ-order cylindrical Bessel
functions; ξ, q, and p are the parameters of a mode
determined by the optical mode modulated by surface
oscillator fluctuations. In this case, the surface polariton
frequency is the lower surface plasmon frequency ωp,
and frequency-dependent dielectric permeability grows
∆ε(ω) > 0. In the opposite case (the cylinder with
constant dielectric permeability is placed in a material
with frequency dispersion in the region of surface
polariton frequencies, l = 2), we have:
Ωµ
2(q) = ωp
2{ε∞ −ε1Iµ’(ξ)Kµ(ξ)/Jµ(ξ)Kµ’(ξ)]}–1. (2)
The dependences of the resulted dispersive
frequencies on the mode parameter ξ are presented in
Fig. 7. The dependence of the surface plasmon
frequency on ξ is essential for zero-order modes at ξ <3.
The dispersion law has the classical form for ξ > 3:
Ωµ
2(q) = ωp
2(ε∞ + ε1)–1. (3)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 51-57.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
56
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oc
on
du
ct
iv
ity
, a
rb
.u
n
Incidence angle, degree
R
am
an
s
ca
tte
rin
g
in
te
ns
ity
, a
rb
.u
n
Fig. 6. Photoconductivity (∆) and Raman scattering (♦) of the
macroporous silicon structure versus the light incidence angle.
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
21
02
12
22
01
11
Mode parameter, ξ
R
el
at
iv
e
fr
eq
ue
nc
y,
Ω
µ/ω
p
Fig. 7. Dependences of frequencies on the mode parameter ξ
for µ = 0, 1, 2 and l = 1, 2.
1.5 2.0 2.5 3.0 3.5
0.2
0.4
0.6
0.8
R
el
at
iv
e
fr
eg
ue
nc
y,
a
rb
. u
n.
Mode parameter, ξ
Fig. 8. Experimental dependence of relative frequency
2πc∆νs/Ωµ versus mode parameter ξ.
The dispersion law of a surface plasmon for k >>
Ωµ /c is determined by the root dependence [26],
Ωµ = [kωpс(ε∞ + ε1)–1]1/2; (4)
The experimental dependence of the relative
frequency 2πc∆νs/Ωµ on the mode parameter ξ is shown
in Fig. 8. The frequency growth is observed with
increase in the wave vector according to relations (3)
and (4). Thus, the dispersion law of polaritonic modes in
macroporous silicon structures is determined by the root
dependence Ωµ ∼ (k)1/2 for optical modes of zero order
at the mode parameter ξ <3.
5. Conclusions
Out-of-plane optical transmission spectra of 2D photonic
macroporous silicon structures are investigated. The
absolute bandgap for high values of the out-of-plane
component kz is situated between the second and third
bands at kza = 5 and ωa /2πc = 0.32-0.35. The theore-
tically unpredicted reduction in the transmittance of
electromagnetic radiation and the step formation are
observed for wavelengths less than the optical period of
transmission of the structures due to the directed and
decay optical modes formed by macroporous silicon as a
short waveguide structure. The absorption maximum
corresponds to the directed optical mode formation. The
prevalence of absorption over reflection of light testifies
to the polaritonic type band formation. Surface polaritons
are formed on decay modes at the formation of directed
optical modes on a macropore or the silicon matrix.
The comparative analysis of the surface of
macroporous silicon by methods of electron microscopy,
infrared absorption, and modulation spectroscopy of
electroreflection is carried out. Electroreflectance
spectroscopy of the macroporous silicon surface showed
the presence of the intrinsic electric field near 106 V/cm
due to a positive charge built in the oxide layer on the
macropore walls. Franz–Keldysh oscillations confirm
the triangular surface barrier formation that results in
two-dimensional surface carrier oscillations. Thus, the
longitudinal component of electromagnetic waves in the
macroporous silicon structure interacts effectively with
surface oscillators, and polaritonic resonances in
absorption, photoconductivity, and Raman scattering are
manifested and have been measured. The dispersion law
of polaritonic modes is determined by the root
dependence Ωµ ∼ (k)1/2 for optical modes of zero order at
the mode parameter ξ <3.
We believe that devices on the base of 2D photonic
macroporous silicon structures will meet a variety of
applications in view of integrated nanophotonic circuits.
The photosensitivity enhancement and the polaritonic
mode formation will inspire the development of active
and passive elements in photonic crystal microchips and
compact highly sensitive uncooled detectors of light
radiation.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 51-57.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
57
Acknowledgements
We would like to acknowledge STCU (Science and
Technology Center of Ukraine) for the financial support
through Project 2444.
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