Photoconductivity in macroporous silicon with regular structure of macropores
The effects of the increase of photoconductivity in periodic macroporous silicon structures depending on the size and period of cylindrical macropores are investigated. It is obtained that the ratio of macroporous silicon photoconductivity to bulk silicon photoconductivity achieves a maximum at t...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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irk-123456789-1183362017-05-30T03:06:09Z Photoconductivity in macroporous silicon with regular structure of macropores Ivanov, V.I. Karachevtseva, L.A. Karas, N.I. Lytvynenko, O.A. Parshin, K.A. Sachenko, S.A. The effects of the increase of photoconductivity in periodic macroporous silicon structures depending on the size and period of cylindrical macropores are investigated. It is obtained that the ratio of macroporous silicon photoconductivity to bulk silicon photoconductivity achieves a maximum at the distance between macropores equal to two thicknesses of the Schottky layer, which corresponds to the experimental data. The increase of photoconductivity is due to both the large total surface area of macropores and the existence of Schottky layers in the near-surface region of cylindrical macropores. 2007 Article Photoconductivity in macroporous silicon with regular structure of macropores / V.I. Ivanov, L.A. Karachevtseva, N.I. Karas, O.A. Lytvynenko, K.A. Parshin, A.V. Sachenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 4. — С. 72-76. — Бібліогр.: 9 назв. — англ. 1560-8034 PACS 71.25.Rk, 81.60.Cp http://dspace.nbuv.gov.ua/handle/123456789/118336 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The effects of the increase of photoconductivity in periodic macroporous
silicon structures depending on the size and period of cylindrical macropores are
investigated. It is obtained that the ratio of macroporous silicon photoconductivity to
bulk silicon photoconductivity achieves a maximum at the distance between macropores
equal to two thicknesses of the Schottky layer, which corresponds to the experimental
data. The increase of photoconductivity is due to both the large total surface area of
macropores and the existence of Schottky layers in the near-surface region of cylindrical
macropores. |
| format |
Article |
| author |
Ivanov, V.I. Karachevtseva, L.A. Karas, N.I. Lytvynenko, O.A. Parshin, K.A. Sachenko, S.A. |
| spellingShingle |
Ivanov, V.I. Karachevtseva, L.A. Karas, N.I. Lytvynenko, O.A. Parshin, K.A. Sachenko, S.A. Photoconductivity in macroporous silicon with regular structure of macropores Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Ivanov, V.I. Karachevtseva, L.A. Karas, N.I. Lytvynenko, O.A. Parshin, K.A. Sachenko, S.A. |
| author_sort |
Ivanov, V.I. |
| title |
Photoconductivity in macroporous silicon with regular structure of macropores |
| title_short |
Photoconductivity in macroporous silicon with regular structure of macropores |
| title_full |
Photoconductivity in macroporous silicon with regular structure of macropores |
| title_fullStr |
Photoconductivity in macroporous silicon with regular structure of macropores |
| title_full_unstemmed |
Photoconductivity in macroporous silicon with regular structure of macropores |
| title_sort |
photoconductivity in macroporous silicon with regular structure of macropores |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118336 |
| citation_txt |
Photoconductivity in macroporous silicon with regular structure of macropores / V.I. Ivanov, L.A. Karachevtseva, N.I. Karas, O.A. Lytvynenko, K.A. Parshin, A.V. Sachenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 4. — С. 72-76. — Бібліогр.: 9 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT ivanovvi photoconductivityinmacroporoussiliconwithregularstructureofmacropores AT karachevtsevala photoconductivityinmacroporoussiliconwithregularstructureofmacropores AT karasni photoconductivityinmacroporoussiliconwithregularstructureofmacropores AT lytvynenkooa photoconductivityinmacroporoussiliconwithregularstructureofmacropores AT parshinka photoconductivityinmacroporoussiliconwithregularstructureofmacropores AT sachenkosa photoconductivityinmacroporoussiliconwithregularstructureofmacropores |
| first_indexed |
2025-07-08T13:50:12Z |
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1837086920637677568 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 4. P. 72-76.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
72
PACS 71.25.Rk, 81.60.Cp
Photoconductivity in macroporous silicon
with regular structure of macropores
V.I. Ivanov, L.A. Karachevtseva, N.I. Karas, O.A. Lytvynenko,
K.A. Parshin, and A.V. Sachenko
V. Lashkaryov Institute of Semiconductor Physics, 45, prospect Nauky, 03028 Kyiv, Ukraine
Phone: 525 9815, fax: 525 8243, e-mail: lakar@isp.kiev.ua
Abstract. The effects of the increase of photoconductivity in periodic macroporous
silicon structures depending on the size and period of cylindrical macropores are
investigated. It is obtained that the ratio of macroporous silicon photoconductivity to
bulk silicon photoconductivity achieves a maximum at the distance between macropores
equal to two thicknesses of the Schottky layer, which corresponds to the experimental
data. The increase of photoconductivity is due to both the large total surface area of
macropores and the existence of Schottky layers in the near-surface region of cylindrical
macropores..
Keywords: macroporous silicon, photoconductivity, Schottky layer.
Manuscript received 04.05.07; accepted for publication 19.12.07; published online 13.02.08.
1. Introduction
Two-dimensional photonic structures based on
macroporous silicon are perspective for their use in the
infrared region due to an increase of the optical
absorption [1], a high photoconductivity in the intrinsic
absorption region [2], and the presence of additional
bands of photoconductivity [3]. The existence of deep
macropores periodically arranged in the n-type silicon
matrix provides a large effective surface area (Fig. 1),
which determines the optical and electrophysical
properties of structures. Increasing the light absorption
in macroporous silicon structures by two orders of
magnitude with respect to that of bulk silicon was
measured for the wavelengths shorter than the optical
period of a structure [1]. The dependence of
photoconductivity on the incidence angle and the light
absorption higher than the reflection in macroporous
silicon are explained by the interaction of optical modes
with surface oscillators on the macropore surface and the
generation of optical polaritons [2]. The absolute
maximum of photoconductivity is measured at the
distance between macropores equal to 2 µm. The
dependences of conductivity, concentration, and
mobility of electrons on the sizes and the concentration
of macropores were measured on a two-layer structure
“macroporous silicon–silicon” [4]. The obtained results
were explained by the formation of a near-surface region
around macropores with a thickness of 1 µm after the
electrochemical and chemical etching. It was established
that the microstructure of a macropore surface and the
built-in field depend on parameters of the
electrochemical process such as voltage and current
density [5]. The value of the built-in field on a
macropore surface is defined by the surface
concentration of Si-О and Si-Н bonds [6]. In addition,
the sign of the main maximum in the spectra of
electroreflectance and the dependence of its magnitude
on the applied constant bias correspond to the formation
of inversion layers (Schottky layers) on the macropore
surface. In the present article, we will determine the
conductivity and photoconductivity of macroporous
silicon structures for various sizes and periods of
cylindrical macropores, by taking the Schottky layers in
the silicon matrix into account.
2. Methodology
The starting material consisted of n-type silicon with
orientation [100] and 4.5-Ohmּcm resistivity (n0 =
1015 cm−1). The periodic structures were anisotropically
etched in a 10 % solution of KOH after the
photolithography procedure with formation of periodic
pits. Macropores were formed due to the generation and
transfer of nonequilibrium holes to the electrochemically
treated surface of n-Si as a result of the backside optical
band-to-band electron-hole generation [7, 8]. According
to the optical microscope study, macropores were
formed with diameters Dp = 1–10 µm and periods a =
3.5–14 µm.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 4. P. 72-76.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
73
8 µm
Fig. 1. Optical microscope photo of a two-dimensional
macroporous silicon photonic structure with cylindrical
macropores of 4 µm in period and 1.8 µm in diameter.
The In/monocrystal n-Si and In/macroporous n-Si
contacts were formed by thermal evaporation of indium
in the atmosphere of hydrogen in the same 4-probe
configuration at the 4-mm distance between contacts
with a transient resistance of 4-10 Ohmּcm2. The
electrical parameters (conductivity, charge carrier
concentration, and mobility) were obtained by the 4-
probe method at 300 K. The photoconductivity spectra
were measured at the normal light incidence on the
macroporous silicon structure with screening contacts at
light wavelengths λ = 0.8–1.5 µm by using a
spectrometer IRS-31. Photoconductivity of macroporous
silicon structures as a function of the illumination
intensity was measured at 0.95 µm using a light diode
3L130A.
3. Parameters of the inversion potential on the
macropore surface
For the macroporous silicon structures under study, we
calculated the dependence of the dimensionless surface
potential on the surface level concentration (Fig. 2).
There are the inversion potentials for surface level con-
centrations between 1011 and 1012 cm−2. For surface level
concentrations less than 1011 cm−2, the inversion poten-
tial transforms to a depleted one and sharply diminishes
with a reduction of the surface level concentration.
The thickness of a Schottky layer on the macropore
surface is determined by the formula [9]
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
)(
ln2
10
300
182.0 0
5.0
0
15
Tn
n
n
T
w
i
, (1)
where T is the absolute temperature, n0 and ni(T) are the
equilibrium electron concentration in a silicon matrix
and the intrinsic charge carrier concentration in silicon,
respectively. Fig. 3 shows the theoretical dependences of
the Schottky layer thickness on temperature according
to (1). The observed decrease of the Schottky layer
thickness with increase in temperature is due to a
decrease of the intrinsic charge carrier concentration.
Thus, for the investigated macroporous silicon
structures, the Schottky layer thicknesses are equal to
w = 0.9 – 1.15 µm at 77 – 300 K (n0 = 1015 cm−1) and
determine the dark resistance of the silicon matrix for
the structures with the distance between macropores a –
Dp ≈ 0.6–3.6 µm.
1011 1012
-30
-20
-10
0
2
1
3y s,
kT
/e
Nt, cm-2
Fig. 2. Dependence of the surface potential in silicon on the
surface level concentration at room temperature (n0 =
1015 сm−3). Values of the parameter n0 are as follows: 1 − 1015,
2 − 3·1015, 3 − 3·1014 cm−3.
75 150 225 300
0.5
2.0
1.5
1.0
1
2
3
w
, µ
m
T, K
Fig. 3. Dependence of the Schottky layer thickness (in µm) on
temperature. Values of the parameter n0 are as follows: 1 −
3·1014, 2 − 1015, 3 − 3·1015 cm−3.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 4. P. 72-76.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
74
4. Dependence of conductivity on the geometry of
pores in macroporous silicon structures
To find the dark conductivity and photoconductivity, we
consider macroporous silicon with a regular structure of
cylinder macropores with period a. The elementary cell
consists of four adjacent cells with the macropore
diameter Dp and the distance between pores a – Dp
(Fig. 4). The ratio of the area of macropores to that of
the crystal surface is equal to
2
2
0 2
)2(
a
wD
S
S pp +π
= , (2)
taking the Schottky layers of thickness w around a
macropore into account. Here, S0 is the area of the
elementary cell surface limited to lines between the
centers of macropores, and Sp is the part of S0 occupied
by macropores.
The dark resistance of a crystal with regular
structure of cylinder macropores was determined as two
series resistances of the silicon matrix (1) with area
S0 − Sp and length h, and (2) with area S0 and length
d − h. This gives
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−−
+
−
=
p
dp SS
S
hd
h
d
hdRR
0
0
0 1 , (3)
where R0 is the dark resistance of a crystal without pores.
Using (1), we obtain
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎝
⎛
⋅
⋅+π
−
−
+
−
=
2
20
2
)2(
1
11
a
wDhd
h
d
hdRR
p
dp . (4)
Fig. 4. Elementary cell including 4 neighboring pores: Dp / 2 −
the pore radius, a – Dp − distance between pores, w − Schottky
layer thickness.
2 5 8 11 14 17 20
4.5
5.0
5.5
3.5
2
ρ
, O
hm
c
m
a-Dp, µm
1
4.0
Fig. 5. Dependence of the macroporous silicon resistance on the
distance between pores for the injection level of 1.3·1015 сm−3
and the Schottky layer thicknesses: 1 − 0.78 µm, 2 − 0 µm. The
used parameters are Dp = 2 µm, h = 100 µm, and d = 300 µm.
Dependences of the dark resistance on the distance
between macropores are shown in Fig. 5 in the case
where the pore diameter is equal to 2 µm. Curve 1
corresponds to the Schottky layer thickness w = 1 µm,
while curve 2 corresponds to the absence of Schottky
layers. The resistance of the crystal increases in the
presence of macropores more rapidly, when there are the
Schottky layers around pores with w = Dp / 2. The last
result corresponds to the experimental data for
macroporous silicon structures for a – Dp ≈ 2.5 µm close
to the results of theoretical calculations.
5. Dependence of photoconductivity on the pore
geometry in macroporous silicon structures
Under the estimated earlier conditions, the ratio of the
photoconductivities of a macroporous silicon structure
with highly depleted or inversed surface potential and
the bulk silicon is proportional to the ratio of the total
pore surface area spS to the structure surface area S0:
2
0 a
Dh
S
S psp π
= (5)
at a – Dp ≥ 2w. This ratio attains the value of 50-100 for
the macroporous silicon structures under study. When
the distance between macropores is less than the double
thickness of a Schottky layer (a – Dp < 2w), the resulted
depleted layer becomes thinner, and the ratio of the
photoconductivities of macroporous silicon, σph p, and
bulk silicon, σphb, diminishes
⎪
⎪
⎩
⎪⎪
⎨
⎧
<−
−π
≥−
π
≈
σ
σ
wDa
w
Da
a
Dh
wDa
a
Dh
p
pp
p
p
b
p
2for,
2
2for,
2
2
ph
ph (6)
Dp /2
a-Dp
w
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 4. P. 72-76.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
75
0 3 6 9
0
15
30
45
21 3
σ ph
p /σ
ph
b, a
rb
.u
n.
a - Dp , µm
Fig. 6. Ratio of the photoconductivities of macroporous silicon
and bulk silicon versus the distance between pores: 1 −
theoretical calculations for Dp = 2 µm, n0 = 1015 cm−3; 2 −
experimental data for a macroporous silicon structure with Dp =
0.5 – 6 µm, a – Dp = 0.65 – 4 µm, n0 = 1015; 3 – the results of
theoretical calculations and experimental data.
The sharp decrease of this ratio is due to the
overlapping of Schottky layers and a decrease of the
conductivity modulation under illumination. The
dependences of ratio (6) on the distance between pores
a – Dp are shown in Fig. 6 with a maximum value of 44
at a – Dp = 2w. It should be noted that expression (6) is
valid when macroporous silicon becomes excited
uniformly along the full depth of macropores. The
experimentally measured maximum value of the ratio of
photoconductivities is 32 at a – Dp ≈ 2 µm (Fig. 6) for a
silicon optical absorption depth of 50 µm (the absorption
coefficient is 2·102 сm−1 for λ = 0.95 µm) that
corresponds to the double thickness of a Schottky layer.
The experimental data are in good agreement with the
results of theoretical calculations.
According to the examined model, the main
contribution to the macroporous silicon
photoconductivity is made by illumination-induced
modulations of the conductivity of Schottky layers.
Here, the Schottky layer thickness is less than that in
darkness that corresponds to the additional electron
conductivity. In the case of conductivity inversion, the
Gibbs excess of electrons under illumination is given by
,
)(
ln2
)(
ln2
10
300
10182.0
00
5.0
0
15
4
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
∆−⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
×
×⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⋅=∆ −
s
ii
y
Tn
n
Tn
n
n
TN
(7)
where ∆ys is a change of the surface potential under
illumination. The value of ∆ys is found from the
electroneutrality equation that includes a surface level
charge, a non-equilibrium hole charge, and a charge of
completely ionized donors in a Schottky layer under
illumination. The surface states were approximated by
two discrete surface levels [9]. Thus, the ratio of the
photoconductivity of macroporous silicon and the dark
conductivity of bulk silicon is determined by the formula
dpph σσ / 02 2
R
w
Da
a
Dh
w
Nq pp
n
−π∆
κµ= , (8)
where µn is the electron mobility and κ is a coefficient
considerably less than unity which takes into account the
fact that Schottky layers do not fill completely the space
between pores. The ratio σph / σdp logarithmically
depends on ∆n, and the photosensitivity of a crystal with
pores is larger than the bulk silicon photosensitivity. The
dependence of ∆n on the illumination intensity I is given
by relation
LDS
In
/+
β
=∆ , (9)
where β is the quantum efficiency, S is the effective
surface recombination velocity on pores, and D and L
are the coefficient and the length of diffusion of non-
equilibrium charge carriers, respectively.
In the case of the inversion or depleted potential,
the effective surface recombination velocity can be low
[9], and its value has tendency to the reduction when the
injection level increases. Thus, the dependence of ∆n on
the illumination intensity can be either linear or ultra
linear. For D ≈ 10 сm2/s and L ≈ 10−2 сm, the value of
∆n is proportional to I with the proportionality
coefficient of about 10−3. The dependence of the
photoconductivity of a silicon crystal with regular pores
on the illumination intensity is shown in Fig. 7. In this
case, the macroporous silicon photoconductivity can
attain up to 10 % of the dark conductivity at the light
intensities 1013 – 1015 photon/(сm2s) that is ten times
larger than the bulk silicon photoconductivity. As can be
seen from (5), such an increase of the photosensitivity is
due to both the large total surface area of macropores
and the presence of the Schottky layers around pores.
1012 1013 1014 1015
0.06
0.08
0.10
0.12
3
4
2
σ ph
/σ
0 ,
ar
b.
un
.
I, quant /cm2s
1
0.04
Fig. 7. Ratio of the photoconductivity of macroporous silicon
to the dark conductivity versus the illumination intensity. The
used values of a – Dp, µm: are: 1 – 2, 2 – 3, 3 – 1, 4 – 5. The
experimental data (a – Dp equals 2 µm) are marked by dots.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 4. P. 72-76.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
76
6. Conclusions
The increase of the photoconductivity is due to the large
total surface area of macropores and the presence of
Schottky layers in the near-surface region of cylindrical
macropores.
In the present work, we have investigated the
effects of an increase of the photoconductivity in
periodic structures of macroporous silicon depending on
a size of cylindrical macropores and the inversion of
conductivity on the pore – silicon interface (Schottky
layers). The ratio of the photoconductivities of
macroporous silicon and bulk silicon attains a maximum
at the distance between macropores equal to the double
thickness of a Schottky layer that corresponds to the
experimental data. It is shown that the sharp decrease of
this ratio with decrease in the distance between pores is
due to the overlapping of Schottky layers and a decrease
of the conductivity modulation under illumination. The
calculated and experimental values of the photo-
conductivity of macroporous silicon can attain 10 % of
the dark conductivity at an illumination intensity of
1013 – 1015 quantum cm−2 s−1 that is by one order of
magnitude greater than that in bulk silicon. The increase
of the photosensitivity is due to the large total surface
area of macropores and the presence of Schottky layers
in the near-surface region of cylindrical macropores.
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