The spectral dependence of the photoluminescence (PL) decay kinetics at room temperature have been
studied in porous nc-Si-SiOx nanostructures. Investigated samples were obtained by oblique evaporation of
SiO with following annealing at 975 C in vacuum and treating in the HF vapor at 50 C. PL decay in these
structures described by a stretched exponential and the average lifetime of the PL decrease exponentially
with increasing energy of photons. PL lifetime values is in microsecond range that point out on phonon
participation in radiative recombination. Dispersion parameter do not depend on emission energy and
tends to 1 with increasing porosity, which is consistent with the model of noninteracting nc-Si. It was established,
that the absorption cross section σ of the nc-Si particles increase with decreasing of nc-Si dimensions
and increasing of emission energy.
This result is consistent with the quantum confinement effects, where the smaller nc-Si with larger
energy gaps are characterized by a short radiative lifetime and the corresponding radiative recombination
process take place within the individual nc-Si.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3501

Danko, V.A.

Indutnyi, I.Z.

Michailovska, K.V.

Shepeliavyi, P.E.

SocioEconomic Challenges Journal (Sumy State University)

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE NANOMATERIALS: APPLICATIONS AND PROPERTIES 
Vol. 1 No 3, 03TF13(4pp) (2012) 
 
 
2304-1862/2012/1(3)03TF13(4) 03TF13-1  2012 Sumy State University 
Absorption Cross Section and Photoluminescence Lifetime of Silicon-Based Light-Emitting 
nc-Si-SiOx Structures 
 
V.A. Dan’ko*, K.V. Michailovska, I.Z. Indutnyi, P.E. Shepeliavyi 
 
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 41, prospect Nauky, 03028 Kyiv, Ukraine,  
 
(Received 18 June 2012; published online 22 August 2012) 
 
The spectral dependence of the photoluminescence (PL) decay kinetics at room temperature have been 
studied in porous nc-Si-SiOx nanostructures. Investigated samples were obtained by oblique evaporation of 
SiO with following annealing at 975 C in vacuum and treating in the HF vapor at 50 C. PL decay in these 
structures described by a stretched exponential and the average lifetime of the PL decrease exponentially 
with increasing energy of photons. PL lifetime values is in microsecond range that point out on phonon 
participation in radiative recombination.  Dispersion parameter  do not depend on emission energy and 
tends to 1 with increasing porosity, which is consistent with the model of noninteracting nc-Si. It was es-
tablished, that the absorption cross section σ of the nc-Si particles increase with decreasing of nc-Si dimen-
sions and increasing of emission energy. 
 This result is consistent with the quantum confinement effects, where the smaller nc-Si with larger 
energy gaps are characterized by a short radiative lifetime and the corresponding radiative recombination 
process take place within the individual nc-Si. 
 
Keywords: Si nanocrystals, Photoluminescence, Decay time. 
 
 PACS numbers: 78.55.Mb, 79.60.Jv, 81.40.Ef 
 
 
                                                          
*danko-va@ukr.net  
1. INTRODUCTION 
 
The creation of light-emitting structures on the 
basis of developed silicon technology for advanced 
electronic and optoelectronic devices is actual problem 
now. Porous silicon [1], Si nanoclusters (nc-Si) em-
bedded in the SiO2 matrix [2, 3], Si/SiO2 superlattices 
[4], etc. structures of the most intensively investigat-
ed in recent years. On the basis of nano-silicon has 
created electronic and optoelectronic devices (lasers, 
photodetectors, etc.) [5, 6], now it is a promising can-
didate for next-generation flash memory silicon tech-
nology [7]. 
Some of the most promising silicon light-emitters 
are structures containing Si nanoclusters (nc-Si) em-
bedded in the SiOx matrix. Recently we have devel-
oped new porous light-emitting nanocomposite nc-Si-
SiOx structures obtained by thermal evaporation of 
silicon monooxide and oblique deposition with follow-
ing high temperature annealing in a vacuum [8-10]. 
HF vapor treatment of such structures results in sig-
nificant (more than 100 time) photoluminescence (PL) 
intensity increasing and essential shift (up to 210 nm) 
of PL maximum from infrared to visible spectral 
range, that can explained  by modification of nc-Si 
and nanocluster-SiOx matrix interface. But, mecha-
nism of photoluminescence (PL) in such structures is 
discussed yet. 
The present paper continues investigations of PL 
properties of thin films porous nc-Si-SiOx  structures, 
where nc-Si clusters are situated in suboxide SiOx 
columns (e.i. on the surface or near surface area). The 
main objective of this work is the elucidation of the 
mechanism of recombination of excited carriers in 
these structures by studying the kinetics of lumines-
cence decay. 
 
2. EXPERIMENT 
 
Investigated samples were obtained by thermal 
evaporation of silicon monooxide SiО (Cerac Inc.,  
99.9 % purity) in a vacuum (residual pressure 1-2∙10 – 3 
Pa) and oblique deposition onto two-side polished sili-
con substrate. The angle ( ) between the vapor stream 
and the substrate normal was 60  and 75  for different 
samples (samples I and II, correspondently). The rate 
of deposition was controlled by the calibrated quarts 
monitor. The film thicknesses measured with the use of 
an MII-4 microinterferometer after deposition were 
400–600 nm. Because of additional oxidation by resid-
ual gases during evaporation of SiO, the compositional-
ly nonstoichiometric SiOx (x  1) films were deposited 
in the vacuum chamber. 
The structure of the obliquely deposited SiOx films 
was studied by transmission electron microscopy (TEM) 
with the use of a ZEISS EVO 50XVP high-resolution 
electron microscope. The film structure presents well-
defined columns characterized by a certain orientation of 
growth; the column diameter varies in the range 10–
100 nm. The dimensions of the columns, their orienta-
tion, and the porosity (the relative volume of pores) of 
the films depend on the angle of deposition. The porosity 
of the film (specific pore volume) for deposition angles 
60  and 75 , calculated from the change of its thickness 
in comparison with that of normally deposited film [9], 
was 34 and 53 %, respectively. Due to the presence of 
free space (pores) between the oxide columns, porous 
films of SiOx easily amenable to chemical treatment, and 
additional oxidation in air compared with the same solid 
SiOx films, which allowed to specifically change the lu-
minescence properties of these structures by modifying 
the interface nc-Si/oxide matrix [8] . 
After the deposition the porous SiOx films were an-
nealed in vacuum chamber at 975  C for 15 min. For 
 V.A. DAN’KO, K.V. MICHAILOVSKA, I. Z. INDUTNUI, P.E, SHEPELIZVYI PROC. NAP 1, 03TF13 (2012) 
 
 
03TF13-2 
such annealing the thermally stimulated formation of 
the nc-Si occurs in the SiOx columns thus forming nc-
Si-SiOx structures. Before PL measuring annealed nc-
Si–SiOx samples were treated in the HF vapor at 50  C 
and than they were maintain for a month in air atmos-
phere for characteristic stabilization. 
Time-resolved PL was investigated at room temper-
ature under exitation of a pulsed nitrogen laser 
(337 nm). The excitation photon flux density was 3∙1022 
cм – 2s – 1 and can was changed by using of optical aper-
ture and neutral density filters. PL signal was ana-
lyzed by monochromator and was detected by a photo-
multiplier in conjunction with a pulse oscillograph. 
Time-resolution of our system was 0.5 s. Obtained PL 
spectra were corrected on setup spectral sensitivity. 
 
3. RESULTS AND DISCUSSION  
 
Fig. 1 shown normalized room temperature PL spec-
tra of nc-Si-SiOx structures (curves 1 and 2 correspond 
on samples obtained at α  60  and 75 ). There is a broad 
band in the spectral range of 1.25 – 2.0 eV and the band 
shapes are similar for both types of samples. PL band 
maximum are situated at 1.44 and 1.51 eV, and their 
widths on half of maximum consists of 0.4 and 0.37 eV, 
correspondently. 
 
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
0.0
0.2
0.4
0.6
0.8
1.0
 
 
P
L
 i
n
te
n
si
ty
, 
a
rb
. 
u
n
it
s
Photon energy, eV
1 - 60
0
2 - 75
0
1
2
 
 
Fig. 1 – PL spectra of porous nc-Si-SiOx structures (curves 1 
and 2 correspond on samples deposited at   60  and 75 ) 
 
The comparison of obtained PL spectra with early 
known literature data [11, 12] allows to suggest that PL 
of nc-Si-SiOx structure is connected with silicon nano-
particles. The short-wavelength shift of PL maximum in 
75  sample (curve 2) is explained by nanoparticles Si size 
decreasing (are forming during high temperature an-
nealing) with increasing of deposition angle. Such size 
decreasing depend on (in the first line) changing of film 
composition (x rise when α increase).  
Fig. 2. shows experimental PL decay for sample de-
posited at   60  measured at registration energies 
1.48, 1.59, 1.72 and 1.87 eV (curves 1, 2, 3, and 4, corre-
spondently). PL relaxation is more quickly for more 
short-wavelength emission. It correlates with probability 
rise of radiative recombination in smaller Si nanoparti-
cles. In consistent with the quantum confinement effect 
(e.g. size dependent phenomena), when  nc-Si size de-
crease then nc-Si energy gap increase and radiative re-
combination rate growths [13, 14].  
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0
 
 
P
L
 i
n
te
n
si
ty
, 
a
rb
. 
u
n
it
s
Decay time, s
E
em
1 - 1.48 eV
2 - 1.59 eV
3 - 1.72 eV
4 - 1.87 eV
1
2
34
 
 
Fig. 2 – PL decay time for nc-Si-SiOx structure deposited at 
  600 
 
Decay PL curves (and their main characteristics) for 
the samples deposited at   75  are qualitatively simi-
lar to curves shown on Fig. 2. 
In order to analyze the kinetics of PL decay we have 
fitted the experimental date (Fig. 2) to a stretched-
exponential decay function that is frequently used to 
describe dispersive processes in disordered systems with 
a distribution of relaxation times [15, 16]:  
 
 IPL(t)  I0 exp[ – (t/ ) ], (3.1) 
 
where  – is the PL average decay time, IPL(t) and I0- are 
current and at t  0 PL intensity values, 0    1 is the 
dispersion exponent.  
We used our experimental data and eq. (3.1) to calcu-
late  and  of investigated samples. The least-squares 
fit of the eq. (3.1) to experimental data brings values of τ 
and . Fig. 3 presents the dependence of average decay 
time  of PL from emission energy Еem in semilogarith-
mic plot.  
It may seen that the τ obtained for sample (II) (at the 
same emission energies) are smaller in comparison with 
the one for sample (I), that, given the smaller size of nc-
Si in them, consistent with the results [8, 14, 17]. More-
over, as in the most structures, contained silicon nano-
particles, our experimental dependence τ on photon en-
ergy (Еem) can be described by exponential function: 
  1/k ∞ exp(-Eem/E0). The experimental line slope (1/Е0) 
allowed to determine a value of characteristic energy Е0. 
For sample (I) value Е0=0.33 eV almost coincide with 
difference between energy position of PL maximum and 
massive silicon gap (Ес  0.31 eV). Rather well correla-
tion is observed between these values (Е0  0.36 eV and 
Ес  0.39 eV) in sample (II) too.  
Dispersion parameter  do not depend on emission 
energy Еem (within experimental errors) in both  samples 
(I and II) and its average values are equal to 0.85 (I) and 
0.90 (II). As was pointed out, increasing of deposition 
angle is accompanied by growth of obtained SiOx film 
porosity, decreasing of silicon content and the nc-Si con-
centration after high temperature annealing. So nc-Si-
SiOx structures formed on the base of SiOx films with 
smaller silicon content may be consider as a ensemble of 
non interacting nc-Si. In that case parameter β increas-
ing ( 1) is typical, and its behavior characterize the 
local properties of oxide matrix surrounded nanoincludi-
 ABSORPTION CROSS SECTION AND PHOTOLUMINESCENCE… PROC. NAP 1, 03TF13 (2012) 
 
 
03TF13-3 
ons nc-Si. This conclusion is proved by value   0,76 for 
samples obtained at deposition angle   45   (results on 
these films not shown). 
 
1.4 1.5 1.6 1.7 1.8 1.9
10
-5
2x10
-5
3x10
-5
4x10
-5
 
 
,s
Photon energy, eV
2
 exp(-E
em
/ E
0
) 1
 
 
Fig. 3 – Spectral dependence of average PL decay time τ. 
Curves 1 and 2 correspond on samples deposited at   60  
(sample I) and 75  (sample II) 
 
Assuming the nc-Si can be represented by a quasi-
level system, the following rate equation can be written:  
 
 dN*/dt  Ф(N – N*) – N*/ ,  (3.2) 
 
where N, N* ,  and Ф are the total number of the nc-
Si, the number of the nc-Si in the exited state, the nc-Si 
absorption cross section at 3.68 eV (wavelength of excita-
tion), the lifetime of the nc-Si excited state, and the exci-
tation photon flux, respectively. If the PL intensity is 
defined by Ipl   N*/τrad , where rad is the nc-Si radiative 
lifetime, solving (1) for steady state conditions gives the 
following expression of the PL intensity:  
 
 Ipl(Eem)  Aσ(Eem)τ(Eem)Ф/1  σ(Eem)τ(Eem)Ф, (3.3) 
 
where A is constant.  
Fig. 4 presented of the dependence of the PL intensity 
from the excitation flux at the different emission energy 
Eem. The data are normalized with respect to the PL in-
tensity measured at the maximum of the laser power 
used. The lines represent the fit of the experimental data 
by expression (3.3). Using the obtained data we have cal-
culated absorption cross section σ on one nc-Si particle. It 
was established that σ increase from 5·10 – 18 to 1.34·10 – 17 
сm2 when the emission energy varies from 1.48 to 2.06 eV. 
Since σ is defined as the product of electron states 
density and oscillator force of optical transition then we 
observed monotonic rise σ when Eem increase. It is mean, 
that the increase of the oscillator force, when the size of 
emitting nc-Si decrease, predominate over the reduction 
of electronic state density in little particles. 
 
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.2
0.4
0.6
0.8
1.0
 
 
N
o
rm
a
li
z
e
d
 P
L
 i
n
te
n
s
it
y
Photon flux, 10
22
 cm
-2
s
-1
1
2
3
4
1 - 1,48 eV
2 - 1,59 eV
3 - 1,77 eV
4 - 2,06 eV
 
 
Fig. 4 – PL intensity dependence on photon flux for sample 
(I). Curves 1, 2, 3, and 4, correspond to registration energies 
1.48, 1.59, 1.77 and 2.06 eV. 
 
4. CONCLUSIONS  
 
In this work we carried out investigation of photo-
luminescence decay kinetics of the samples of porous 
nc-Si-SiOx nanostructures obtained by oblique deposi-
tion (at angles of 60  and 75 ) and annealed in vacuum 
followed by treatment with HF vapor at 50  C. At room 
temperature photoluminescence decay kinetics in these 
structures described by a stretched exponential and the 
average lifetime of the PL decrease exponentially with 
increasing energy of photons. The parameter β tends to 
1 with increasing porosity, which is consistent with the 
model of noninteracting nc-Si. It was established, that 
the absorption cross section σ of the nc-Si particles in-
crease with decreasing of nc-Si dimensions and increas-
ing of emission energy. 
The results of spectral and kinetics investigations 
allowed suppose that PL of porous light-emitting nc-Si-
SiOx structures in the 1.25-2.0 eV region is originated 
from radiative recombination of carriers (excitons). The 
recombination take place in nc-Si, moreover emission 
energy depend on nc-Si sizes. The room temperature 
PL lifetime values are in microsecond range that point 
out on phonon participation in radiative recombination. 
 
REFERENCES 
 
1. L.T. Canham, Appl. Phys. Lett. 57 No10, 1046 (1990). 
2. A.V. Kabashin, J.-P. Sylvestre, S. Patskovsky, 
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Optical properties of semiconductor quantum dots. (St. Pe-
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P.E. Shepelyavyi, and V. A. Dan’ko, Semiconductors, 41 
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V.I. Min’ko, P.E. Shepelyavyi, Optoelectronics and Semi-
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conductors Technics 39, 65 (2004). 
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V.I. Min’ko, P. E. Shepelyavyi, Optoelectronics and Semi-
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14171 (1992). 
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Appl. Phys. Lett. 69, 1241 (1996). 
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English

Absorption Cross Section and Photoluminescence Lifetime of Silicon-Based Light-Emitting nc-Si-SiOx Structures

Electronic Sumy State University Institutional Repository

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE NANOMATERIALS: APPLICATIONS AND PROPERTIES Vol. 1 No 3, 03TF13(4pp) (2012)   2304-1862/2012/1(3)03TF13(4) 03TF13-1  2012 Sumy State University Absorption Cross Section and Photoluminescence Lifetime of Silicon-Based Light-Emitting nc-Si-SiOx Structures  V.A. Dan’ko*, K.V. Michailovska, I.Z. Indutnyi, P.E. Shepeliavyi  V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 41, prospect Nauky, 03028 Kyiv, Ukraine,   (Received 18 June 2012; published online 22 August 2012)  The spectral dependence of the photoluminescence (PL) decay kinetics at room temperature have been studied in porous nc-Si-SiOx nanostructures. Investigated samples were obtained by oblique evaporation of SiO with following annealing at 975 C in vacuum and treating in the HF vapor at 50 C. PL decay in these structures described by a stretched exponential and the average lifetime of the PL decrease exponentially with increasing energy of photons. PL lifetime values is in microsecond range that point out on phonon participation in radiative recombination.  Dispersion parameter  do not depend on emission energy and tends to 1 with increasing porosity, which is consistent with the model of noninteracting nc-Si. It was es-tablished, that the absorption cross section σ of the nc-Si particles increase with decreasing of nc-Si dimen-sions and increasing of emission energy.  This result is consistent with the quantum confinement effects, where the smaller nc-Si with larger energy gaps are characterized by a short radiative lifetime and the corresponding radiative recombination process take place within the individual nc-Si.  Keywords: Si nanocrystals, Photoluminescence, Decay time.   PACS numbers: 78.55.Mb, 79.60.Jv, 81.40.Ef                                                             *danko-va@ukr.net  1. INTRODUCTION  The creation of light-emitting structures on the basis of developed silicon technology for advanced electronic and optoelectronic devices is actual problem now. Porous silicon [1], Si nanoclusters (nc-Si) em-bedded in the SiO2 matrix [2, 3], Si/SiO2 superlattices [4], etc. structures of the most intensively investigat-ed in recent years. On the basis of nano-silicon has created electronic and optoelectronic devices (lasers, photodetectors, etc.) [5, 6], now it is a promising can-didate for next-generation flash memory silicon tech-nology [7]. Some of the most promising silicon light-emitters are structures containing Si nanoclusters (nc-Si) em-bedded in the SiOx matrix. Recently we have devel-oped new porous light-emitting nanocomposite nc-Si-SiOx structures obtained by thermal evaporation of silicon monooxide and oblique deposition with follow-ing high temperature annealing in a vacuum [8-10]. HF vapor treatment of such structures results in sig-nificant (more than 100 time) photoluminescence (PL) intensity increasing and essential shift (up to 210 nm) of PL maximum from infrared to visible spectral range, that can explained  by modification of nc-Si and nanocluster-SiOx matrix interface. But, mecha-nism of photoluminescence (PL) in such structures is discussed yet. The present paper continues investigations of PL properties of thin films porous nc-Si-SiOx  structures, where nc-Si clusters are situated in suboxide SiOx columns (e.i. on the surface or near surface area). The main objective of this work is the elucidation of the mechanism of recombination of excited carriers in these structures by studying the kinetics of lumines-cence decay.  2. EXPERIMENT  Investigated samples were obtained by thermal evaporation of silicon monooxide SiО (Cerac Inc.,  99.9 % purity) in a vacuum (residual pressure 1-2∙10 – 3 Pa) and oblique deposition onto two-side polished sili-con substrate. The angle ( ) between the vapor stream and the substrate normal was 60  and 75  for different samples (samples I and II, correspondently). The rate of deposition was controlled by the calibrated quarts monitor. The film thicknesses measured with the use of an MII-4 microinterferometer after deposition were 400–600 nm. Because of additional oxidation by resid-ual gases during evaporation of SiO, the compositional-ly nonstoichiometric SiOx (x  1) films were deposited in the vacuum chamber. The structure of the obliquely deposited SiOx films was studied by transmission electron microscopy (TEM) with the use of a ZEISS EVO 50XVP high-resolution electron microscope. The film structure presents well-defined columns characterized by a certain orientation of growth; the column diameter varies in the range 10–100 nm. The dimensions of the columns, their orienta-tion, and the porosity (the relative volume of pores) of the films depend on the angle of deposition. The porosity of the film (specific pore volume) for deposition angles 60  and 75 , calculated from the change of its thickness in comparison with that of normally deposited film [9], was 34 and 53 %, respectively. Due to the presence of free space (pores) between the oxide columns, porous films of SiOx easily amenable to chemical treatment, and additional oxidation in air compared with the same solid SiOx films, which allowed to specifically change the lu-minescence properties of these structures by modifying the interface nc-Si/oxide matrix [8] . After the deposition the porous SiOx films were an-nealed in vacuum chamber at 975  C for 15 min. For  V.A. DAN’KO, K.V. MICHAILOVSKA, I. Z. INDUTNUI, P.E, SHEPELIZVYI PROC. NAP 1, 03TF13 (2012)   03TF13-2 such annealing the thermally stimulated formation of the nc-Si occurs in the SiOx columns thus forming nc-Si-SiOx structures. Before PL measuring annealed nc-Si–SiOx samples were treated in the HF vapor at 50  C and than they were maintain for a month in air atmos-phere for characteristic stabilization. Time-resolved PL was investigated at room temper-ature under exitation of a pulsed nitrogen laser (337 nm). The excitation photon flux density was 3∙1022 cм – 2s – 1 and can was changed by using of optical aper-ture and neutral density filters. PL signal was ana-lyzed by monochromator and was detected by a photo-multiplier in conjunction with a pulse oscillograph. Time-resolution of our system was 0.5 s. Obtained PL spectra were corrected on setup spectral sensitivity.  3. RESULTS AND DISCUSSION   Fig. 1 shown normalized room temperature PL spec-tra of nc-Si-SiOx structures (curves 1 and 2 correspond on samples obtained at α  60  and 75 ). There is a broad band in the spectral range of 1.25 – 2.0 eV and the band shapes are similar for both types of samples. PL band maximum are situated at 1.44 and 1.51 eV, and their widths on half of maximum consists of 0.4 and 0.37 eV, correspondently.  1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.00.00.20.40.60.81.0  PL intensity, arb. unitsPhoton energy, eV1 - 6002 - 75012  Fig. 1 – PL spectra of porous nc-Si-SiOx structures (curves 1 and 2 correspond on samples deposited at   60  and 75 )  The comparison of obtained PL spectra with early known literature data [11, 12] allows to suggest that PL of nc-Si-SiOx structure is connected with silicon nano-particles. The short-wavelength shift of PL maximum in 75  sample (curve 2) is explained by nanoparticles Si size decreasing (are forming during high temperature an-nealing) with increasing of deposition angle. Such size decreasing depend on (in the first line) changing of film composition (x rise when α increase).  Fig. 2. shows experimental PL decay for sample de-posited at   60  measured at registration energies 1.48, 1.59, 1.72 and 1.87 eV (curves 1, 2, 3, and 4, corre-spondently). PL relaxation is more quickly for more short-wavelength emission. It correlates with probability rise of radiative recombination in smaller Si nanoparti-cles. In consistent with the quantum confinement effect (e.g. size dependent phenomena), when  nc-Si size de-crease then nc-Si energy gap increase and radiative re-combination rate growths [13, 14].  0 10 20 30 400.00.20.40.60.81.0  PL intensity, arb. unitsDecay time, sEem1 - 1.48 eV2 - 1.59 eV3 - 1.72 eV4 - 1.87 eV1234  Fig. 2 – PL decay time for nc-Si-SiOx structure deposited at   600  Decay PL curves (and their main characteristics) for the samples deposited at   75  are qualitatively simi-lar to curves shown on Fig. 2. In order to analyze the kinetics of PL decay we have fitted the experimental date (Fig. 2) to a stretched-exponential decay function that is frequently used to describe dispersive processes in disordered systems with a distribution of relaxation times [15, 16]:    IPL(t)  I0 exp[ – (t/ ) ], (3.1)  where  – is the PL average decay time, IPL(t) and I0- are current and at t  0 PL intensity values, 0    1 is the dispersion exponent.  We used our experimental data and eq. (3.1) to calcu-late  and  of investigated samples. The least-squares fit of the eq. (3.1) to experimental data brings values of τ and . Fig. 3 presents the dependence of average decay time  of PL from emission energy Еem in semilogarith-mic plot.  It may seen that the τ obtained for sample (II) (at the same emission energies) are smaller in comparison with the one for sample (I), that, given the smaller size of nc-Si in them, consistent with the results [8, 14, 17]. More-over, as in the most structures, contained silicon nano-particles, our experimental dependence τ on photon en-ergy (Еem) can be described by exponential function:   1/k ∞ exp(-Eem/E0). The experimental line slope (1/Е0) allowed to determine a value of characteristic energy Е0. For sample (I) value Е0=0.33 eV almost coincide with difference between energy position of PL maximum and massive silicon gap (Ес  0.31 eV). Rather well correla-tion is observed between these values (Е0  0.36 eV and Ес  0.39 eV) in sample (II) too.  Dispersion parameter  do not depend on emission energy Еem (within experimental errors) in both  samples (I and II) and its average values are equal to 0.85 (I) and 0.90 (II). As was pointed out, increasing of deposition angle is accompanied by growth of obtained SiOx film porosity, decreasing of silicon content and the nc-Si con-centration after high temperature annealing. So nc-Si-SiOx structures formed on the base of SiOx films with smaller silicon content may be consider as a ensemble of non interacting nc-Si. In that case parameter β increas-ing ( 1) is typical, and its behavior characterize the local properties of oxide matrix surrounded nanoincludi- ABSORPTION CROSS SECTION AND PHOTOLUMINESCENCE… PROC. NAP 1, 03TF13 (2012)   03TF13-3 ons nc-Si. This conclusion is proved by value   0,76 for samples obtained at deposition angle   45   (results on these films not shown).  1.4 1.5 1.6 1.7 1.8 1.910-52x10-53x10-54x10-5  ,sPhoton energy, eV2 exp(-Eem/ E0) 1  Fig. 3 – Spectral dependence of average PL decay time τ. Curves 1 and 2 correspond on samples deposited at   60  (sample I) and 75  (sample II)  Assuming the nc-Si can be represented by a quasi-level system, the following rate equation can be written:    dN*/dt  Ф(N – N*) – N*/ ,  (3.2)  where N, N* ,  and Ф are the total number of the nc-Si, the number of the nc-Si in the exited state, the nc-Si absorption cross section at 3.68 eV (wavelength of excita-tion), the lifetime of the nc-Si excited state, and the exci-tation photon flux, respectively. If the PL intensity is defined by Ipl   N*/τrad , where rad is the nc-Si radiative lifetime, solving (1) for steady state conditions gives the following expression of the PL intensity:    Ipl(Eem)  Aσ(Eem)τ(Eem)Ф/1  σ(Eem)τ(Eem)Ф, (3.3)  where A is constant.  Fig. 4 presented of the dependence of the PL intensity from the excitation flux at the different emission energy Eem. The data are normalized with respect to the PL in-tensity measured at the maximum of the laser power used. The lines represent the fit of the experimental data by expression (3.3). Using the obtained data we have cal-culated absorption cross section σ on one nc-Si particle. It was established that σ increase from 5·10 – 18 to 1.34·10 – 17 сm2 when the emission energy varies from 1.48 to 2.06 eV. Since σ is defined as the product of electron states density and oscillator force of optical transition then we observed monotonic rise σ when Eem increase. It is mean, that the increase of the oscillator force, when the size of emitting nc-Si decrease, predominate over the reduction of electronic state density in little particles.  0.0 0.5 1.0 1.5 2.0 2.5 3.00.00.20.40.60.81.0  Normalized PL intensityPhoton flux, 1022 cm-2s-112341 - 1,48 eV2 - 1,59 eV3 - 1,77 eV4 - 2,06 eV  Fig. 4 – PL intensity dependence on photon flux for sample (I). Curves 1, 2, 3, and 4, correspond to registration energies 1.48, 1.59, 1.77 and 2.06 eV.  4. CONCLUSIONS   In this work we carried out investigation of photo-luminescence decay kinetics of the samples of porous nc-Si-SiOx nanostructures obtained by oblique deposi-tion (at angles of 60  and 75 ) and annealed in vacuum followed by treatment with HF vapor at 50  C. At room temperature photoluminescence decay kinetics in these structures described by a stretched exponential and the average lifetime of the PL decrease exponentially with increasing energy of photons. The parameter β tends to 1 with increasing porosity, which is consistent with the model of noninteracting nc-Si. It was established, that the absorption cross section σ of the nc-Si particles in-crease with decreasing of nc-Si dimensions and increas-ing of emission energy. The results of spectral and kinetics investigations allowed suppose that PL of porous light-emitting nc-Si-SiOx structures in the 1.25-2.0 eV region is originated from radiative recombination of carriers (excitons). The recombination take place in nc-Si, moreover emission energy depend on nc-Si sizes. The room temperature PL lifetime values are in microsecond range that point out on phonon participation in radiative recombination.  REFERENCES  1. L.T. Canham, Appl. Phys. Lett. 57 No10, 1046 (1990). 2. A.V. Kabashin, J.-P. Sylvestre, S. Patskovsky, M. Meunier, J. Appl. Phys. 91, 3248 (2002). 3. H. Takagi, H. Ogawa, Y. Yamazaki, A. Ishizki and T. Nakagiri, Appl. Phys. Lett. 56, 2379 (1990). 4. D.J. Lockwood, Z.H. 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Absorption Cross Section and Photoluminescence Lifetime of Silicon-Based Light-Emitting nc-Si-SiOx Structures

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