JOURNAL OF APPLIED PHYSICSVOLUME 95, NUMBER 1

1 JANUARY 2004

Coexistence of two different energy transfer processes
in SiO2 films containing Si nanocrystals and Er
Minoru Fujii,a) Kenji Imakita, Kei Watanabe, and Shinji Hayashi
Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University, Rokkodai,
Nada, Kobe 657-8501, Japan

共Received 3 July 2003; accepted 14 October 2003兲
The mechanism of energy transfer from silicon nanocrystals 共nc-Si兲 to erbium ions (Er3⫹ ) in SiO2
films containing nc-Si and Er was studied by analyzing delayed infrared luminescence from Er3⫹ .
It was found that, to theoretically reproduce the rising part of the time-dependent luminescenceintensity, two different energy transfer processes, i.e., fast and slow processes, should be considered.
From the fitting of the delayed luminescence to a model, the ratio of the two energy transfer
processes and the energy transfer rate of the slow process were estimated. The ratio exhibited a clear
dependence on the luminescence peak energy of Si nanocrystals, which act as photosensitizers for
Er3⫹ , indicating that the ratio depends on the size of nc-Si. The ratio of slow to fast processes
increased with the decrease in size; this observation is a strong indication that the fast process is the
direct inheritance of the process in bulk Si:Er systems, and the slow process is a characteristic
process occurring only in nc-Si:Er systems. The energy transfer rate of the slow process was foundto depend on the recombination rate of excitons in nc-Si. © 2004 American Institute of Physics.
关DOI: 10.1063/1.1631072兴

I. INTRODUCTION

action between nc-Si and Er3⫹ . One standard approach inanalyzing the interaction is to construct a set of rate equations by taking into account all possible transitions in andbetween nc-Si and Er3⫹ , fitting the experimental data to themodel, and extracting parameters describing the energy exchange processes. This approach has worked very well, andall experimental results have been explained consistently.16
Furthermore, by extending this approach, a guideline to realizing an optical amplifier from nc-Si:Er systems has been
given.16
In these previous studies, the coupling between nc-Si
and Er is assumed to be very strong. However, this assumption is not always applicable. In our previous work on SiO2
films containing nc-Si and Er,14 we demonstrated that, after
excitation of nc-Si by a pulse laser with a 5 ns pulse width,
the photoluminescence 共PL兲 intensity of Er3⫹ rises very fast
up to about 70% of the maximum intensity, and then starts torise slowly until reaching the maximum. The observed delay
time was distributed from several microseconds to several
hundredths of a microsecond, depending on the sample
preparation conditions. The observation of the long PL delaysuggests that, in addition to the strong coupling that is usually considered, a weak coupling process exists, although it
might play a minor part in the whole energy transfer process.
Another point not discussed in detail so far is the size
dependence of the interaction properties. In previous models,nc-Si:Er systems have been treated as an independent systemthat is essentially different from Er-doped bulk Si 共bulkSi:Er兲 systems, that is, no continuity from bulk-Si:Er to ncSi:Er systems has been discussed. This distinction seems to
be reasonable by considering different exciton transport
properties between the two systems; in nc-Si:Er systems, excitons can interact only with Er3⫹ staying nearby each nanocrystal, while in bulk-Si:Er systems, excitons can migrate

The electronic structure of silicon nanocrystals 共nc-Si兲 isstrongly modified from that of bulk Si crystals due to theconfinement of electrons and holes in a space smaller thanthe exciton Bohr radius of bulk Si crystals.1,2 The modification of the electronic structure provides nc-Si with functions
which do not occur in bulk Si crystals. For example, one
function is as a photosensitizer for optically inactive materials. Recently, nc-Si were demonstrated to act as photosensitizers for molecular oxygen3,4 and several kinds of rare earth
ions.5–18 In particular, erbium ions (Er3⫹ ) can be excitedvery efficiently by the energy transfer from nc-Si; the effective absorption cross section of the intra-4 f shell transitionof Er3⫹ is enhanced by 2– 4 orders of magnitude because of
the large absorption cross section of nc-Si in a visible range
and because of the efficient energy transfer from nc-Si to
Er3⫹ . 5–15 This sensitized excitation of Er3⫹ provides large
benefits in a number of fields which utilize near-infraredemission of Er3⫹ . One application which takes advantage ofthe enhanced absorption cross section is a planer-waveguide
optical amplifier operating at 1.54 ␮m. With a simple ridgetype waveguide structure 共1 cm long, 9 ␮m wide, and 0.5
␮m high兲 consisting of SiO2 films containing nc-Si and Er
excited from the top, a net gain of 7 dB/cm at 1.535 ␮m has
been obtained.19,20 By employing similar materials as a gate
oxide of a metal–oxide–semiconductor structure, electroluminescence devices operating at room temperature with thequantum efficiency of 1%21 and 10%22 have been reported.
Because of these possible applications, great efforts havebeen devoted to understanding the mechanism of the intera兲

Author to whom correspondence should be addressed; electronic mail:fujii@eedept.kobe-u.ac.jp

0021-8979/2004/95(1)/272/9/$22.00

272© 2004 American Institute of Physics

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Fujii et al.

J. Appl. Phys., Vol. 95, No. 1, 1 January 2004

and interact with any Er3⫹ . However, it is not plausible thatthe mechanism of the energy-exchange itself is completely
different between the two systems. The electronic structureof nc-Si is modified only slightly from that of bulk Si crystals, and the electronic structure changes continuously fromthe bulk structure with decreasing size.1,2 As a result, theoptical property of nc-Si is a small modification of those ofbulk Si crystals, and all parameters 共e.g., band gap energy,
exciton lifetime, degree of electron-hole exchange interaction, and so on兲 change continuously from the bulk values. It
is well-established from experimental and theoretical studies
that all these changes are the results of spatial confinement ofelectrons and holes, or excitons in a small space 共i.e., thequantum size effect兲.1,2 The exciton Bohr radius of a bulk Si
crystal is about 5 nm. The quantum size effect thus becomesprominent for nanocrystals smaller than about 10 nm in diameter, and larger nanocrystals can be regarded as bulk fromthe point of view of electronic structures. Therefore, if thestrong interaction between nc-Si and Er3⫹ is a consequenceof quantum size effects, we should observe continuouschanges of the interaction properties from bulk-Si:Er-like tonc-Si:Er-like in the size range less than 10 nm.
The purpose of this work is to have experimental accessto these problems. To do so, we extended our previous workon SiO2 films containing nc-Si and Er.14 We have studied thetime development of Er3⫹ PL intensity after pulsed excitation of nc-Si hosts. The rising part of Er3⫹ PL intensity contains valuable information concerning the energy transfer
mechanism. We will demonstrate that, in order to quantitatively reproduce the observed rising part, two different energy transfer processes 共fast and slow兲 should be considered.
From the fitting of observed curves to a model, the ratio of
the two processes and the energy transfer rate of the slow
process are extracted. It will be shown that the ratio depends
greatly on the size of nc-Si and changes continuously in awide size range; this continuous change indicates that there
is no distinct border from bulk Si to nc-Si in the sense ofenergy exchange with Er3⫹ . The observed size dependence
implies that the slow energy transfer process is a characteristic process occurring only in nc-Si:Er systems, thus becoming more important with decreasing size. It will be shownthat the energy transfer rate of the slow process is determinedby the recombination rate of excitons in nc-Si.
II. EXPERIMENTAL DETAILSSiO2 films containing nc-Si and Er (SiO2 :nc-Si:Er)
were prepared by a cosputtering method. Details of the
preparation procedures are described in our previous
papers.6,7 Si, SiO2 , and Er2 O3 were simultaneously sputter
deposited in argon 共Ar兲 gas, and the deposited films 共about 1
␮m in thickness兲 were annealed in a nitrogen (N2 ) gas
共99.999%兲 atmosphere for 30 min at temperatures between
1100 and 1250 °C. Si nanocrystals were grown in films of the
mixture of SiO2 and Er2 O3 during the annealing. In thismethod, the size of nc-Si can be controlled by changing theconcentration of Si in the films or changing the annealing
temperature. The average size of nc-Si was estimated bycross-sectional transmission electron microscopic observa-

273

FIG. 1. Photoluminescence spectra of SiO2 films containing Si nanocrystals
and Er at room temperature. A broadband at about 1.55 eV is due to recombination of excitons in Si nanocrystals and a sharp peak at 0.81 eV arises
from intra-4 f shell transition of Er3⫹ .

tions. In this work, the average size of nc-Si (d Si) waschanged from 2.7 to 5.5 nm. Er concentration was fixed to
0.11 at. % for all the samples. PL spectra were measured
using a single grating monochromator and a near-infrared
photomultiplier with an InP/InGaAs photocathode. The excitation source for taking the spectra was the 457.9 nm line of
an Ar-ion laser 共0.3 W/cm2兲. In this wavelength, Er3⫹ is notdirectly excited. For all the spectra, the spectral response of
the detection system was corrected by the reference spectrumof a standard tungsten lamp. For the time response measurements, a 532.0 nm line of a Nd:Yttritium–aluminum–garnet
共YAG兲 laser was used as the excitation source 共pulse energy
0.65 mJ, pulse width 5 ns, repetition frequency 20 Hz, andspot size 2 mm兲. A multichannel scalar was used in obtaining
the decay curves. The overall time resolution of the system
was better than 100 ns. All measurements were performed atroom temperature.
III. RESULTS AND DISCUSSION
A. Analysis of PL decay curves

Figure 1 shows the typical PL spectra of SiO2 films containing Si nanocrystals and Er at relatively low Er concentration ranges 共⬃0.11 at. %兲. Two emission bands due to theexciton recombination in nc-Si and intra-4 f shell transitionof Er3⫹ are observed. The intensities of these bands competewith each other; with increasing Er concentration, the Er3⫹
PL band becomes stronger, while the exciton PL band isquenched. The ratio of the increase in Er3⫹ PL intensity
共integrated intensity兲 to the loss of nc-Si PL one was about
0.7 at low excitation power. The excitation spectrum of theEr3⫹ PL is very similar to that of the exciton PL, indicatingthat excitation of Er3⫹ is due mainly to the energy transferfrom Si nanocrystals.7
More evidence of the energy transfer is obtained in thetime transient of Er3⫹ PL.14 Figure 2 shows the time dependence of PL intensity just after excitation by the frequencydoubled pulsed Nd:YAG laser with a pulse width of 5 ns.
The time resolution of the detection system is better than 100

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274

Fujii et al.

J. Appl. Phys., Vol. 95, No. 1, 1 January 2004

perature 共1150 °C兲 are fixed and the excess Si concentrationis changed. By changing the excess Si concentration from
2.43 to 11.1 vol %, the PL peak energy is shifted from 1.52 to
1.36 eV 共see Table I兲, corresponding to the size change of
3.2– 4.6 nm. We can see that with increasing the size, the PLdelay becomes slightly longer. In contrast to Fig. 2共a兲, in Fig.
2共b兲 the annealing temperature is changed and the other parameters are fixed. In this case, the PL peak energy ischanged in a smaller energy range, i.e., from 1.41 to 1.30 eV,corresponding to the size change of 4.2–5.2 nm. Although
the change in size is smaller than that in Fig. 2共a兲, the variation of the delay time is much larger. It is clear that a higher
annealing temperature results in a longer PL delay, even if
the size of nc-Si, i.e., the PL peak energy, is the same. Therefore, in addition to a size, there exists another parameter that
affects the energy transfer rate.
In order to discuss this in more detail, we quantitatively
analyze the observed data. In the present Er and nc-Si concentration range, we can assume that one nanocrystal interacts with one Er3⫹ . Under this assumption, in the simplest
model, Er3⫹ PL intensity is expressed as
I 共 t 兲 ⬀exp共 ⫺w Ert 兲 ⫺exp关 ⫺ 共 w Tr⫹w Si兲 t 兴 ,FIG. 2. PL time transient at 0.81 eV just after 5 ns pulsed excitation. Symbols are experimental results, and curves are results of model fittings. 共a兲
Annealing temperature and Er concentration are fixed at 1150 °C and 0.11
at. %, respectively, and excess Si concentration is changed. 共b兲 Excess Si
concentration and Er concentration are fixed at 9.28 vol % and 0.11 at. %,and annealing temperature is changed.

ns. We can clearly see that PL intensity rises slowly after
finishing the excitation, and the delay time depends strongly
on the samples. The observation of the delayed PL is the
direct evidence that Er3⫹ is excited indirectly by the energy
transfer from nc-Si.
It is worth noting that, although excitation of Er3⫹ is due
mainly to the energy transfer, at the present excitation wavelength 共532 nm兲, the direct excitation of Er3⫹ is also partiallypossible. In order to know the extent of the contribution of
direct excitation, we compared PL intensities of the present
samples to other samples without nc-Si but with the sameamount of Er3⫹ (SiO2 :Er). The PL intensity obtained for the
SiO2 :Er samples was less than 5% of the PL intensity of the
SiO2 :nc-Si:Er samples, suggesting that the contribution of
direct excitation is negligibly small in SiO2 :nc-Si:Er
samples.
In the present sample preparation method, the size ofnc-Si can be controlled by two independent parameters, i.e.,
excess Si concentration and annealing temperature. In Fig.
2共a兲, the Er concentration 共0.11 at. %兲 and annealing tem-

共1兲

where w Si , w Er , and w Tr are the recombination rates of excitons in nc-Si and Er3⫹ , and the energy transfer rate, respectively. In this equation, both the rising and decaying parts ofthe curves are expressed with a single exponential function.
However, as can be seen in Fig. 2共b兲, the intensity rises very
fast until reaching about 70% of the maximum intensity andthen starts to rise slowly. This behavior is apparently different from Eq. 共1兲.
To reproduce the observed decay curves, we have toconsider at least two different energy transfer processes occurring simultaneously; one process is faster than our time
resolution 共100 ns兲, and the other is slower and depends
strongly on the samples. We define the number of Er3⫹ ionswhich interact very strongly with nc-Si and contribute to theffast process as N Er
, and the number of Er3⫹ ions whichs.
interact weakly and contribute to the slow process as N Erfs,
The energy transfer rate of each process is w Tr and w Tr
respectively. Under the assumption that one nanocrystal inf
teracts with one Er3⫹ , N Er
is equal to the number of nc-Si
fs), and N Er
is equal tointeracting strongly with Er3⫹ (N Sisthose weakly interacting with Er3⫹ (N Si). After pulsed excitation, the number of excited nc-Si that can transfer energy to
Er3⫹ isffexp关 ⫺ 共 w Tr
⫹w Si兲 t 兴
N Si共 t 兲 ⫽N Si
0

s
s
⫹N Si
exp关 ⫺ 共 w Tr
⫹w Si兲 t 兴 ,0共2兲

where w Si is the recombination rate of excitons in nc-Si, andfsand N Sidenote the number of nc-Si excited at t⫽0. If
N Si
00we ignore direct excitation of Er3⫹ , the excitation rate ofEr3⫹ can befff
G 共 t 兲 ⫽w Tr
N Si
exp关 ⫺ 共 w Tr
⫹w Si兲 t 兴
0

s
s
s
⫹w Tr
N Si
exp关 ⫺ 共 w Tr
⫹w Si兲 t 兴 ,0

共3兲

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Fujii et al.

J. Appl. Phys., Vol. 95, No. 1, 1 January 2004

275

TABLE I. List of samples studied in this work. Er concentration is fixed to 0.11 at. % for all the samples.
Recombination rates of nc-Si (w Si) and Er (w Er) are obtained from PL decay curves. The ratio of slow to fasts
fsenergy transfer processes (N Er/N Er) and the energy transfer rate of the slow process (w Tr) are obtained by fittings*experimental decay curves to a model. w Tr is obtained by subtracting the time necessary for Er3⫹ to relax froms
higher excited states to the first excited state from 1/w Tr
共see Ref. 23兲.
Ta
共°C兲

Si
共vol %兲

PL peak energy
共eV兲

w Si
共s⫺1兲

w Er
共s⫺1兲

s
f
N Er
/N Er

s
w Tr
3 ⫺1
(10 s )

s
*
w Tr
3 ⫺1
(10 s )

1150
1200
1250

2.43
2.43
2.43

1.52
1.43
1.35

8692
5931
3927

255
165
125

0.80
0.64
0.53

191
42.4
14.4

366
47.4
14.9

1100
1150
1200
1250

4.08
4.08
4.08
4.08

1.52
1.46
1.37
1.35

11515
7795
5061
3927

291
318
184
173

0.76
0.62
0.53
0.30

265
176
49.7
17.6

785
314
56.8
18.4

1100
1150
1200
1250

6.66
6.66
6.66
6.66

1.46
1.40
1.36
1.33

10870
6897
4916
3631

367
320
178
163

0.81
0.58
0.49
0.34

269
139
35.2
21.2

821
213
38.6
22.4

1100
1150
1200
1250

9.28
9.28
9.28
9.28

1.41
1.38
1.31
1.30

10322
6598
4191
3188

447
305
189
199

0.51
0.47
0.50
0.40

222
96.4
24.6
17.1

499
127
26.2
17.9

1100
1150
1200
1250

11.1
11.1
11.1
11.1

1.35
1.36
1.34
1.30

9688
6299
4626
3188

465
318
254
248

0.37
0.42
0.37
0.37

130
70.5
38.8
18.2

193
85.6
43.0
19.1

f
N Er

s
w Tr

N Er

s
w Tr
⫹w Si⫺w Er

and the number of Er3⫹ ions in the excited state is
I共 t 兲⬀N Er共 t 兲 ⫽

f
f
w Tr
N Si
0
f
w Tr
⫹w Si⫺w Er

兵 exp共 ⫺w Ert 兲

f⫺exp关 ⫺ 共 w Tr
⫹w Si兲 t 兴 其 ⫹

⫺
s
s
w Tr
N Si
0

s
w Tr
⫹w Si⫺w Ers⫻ 兵 exp共 ⫺w Ert 兲 ⫺exp关 ⫺ 共 w Tr
⫹w Si兲 t 兴 其 .

共4兲

As can be seen in Fig. 2共b兲, the fast process is faster than ourtime resolution, and is also faster than the lifetimes of nc-Si
PL 共100 ␮s–1 ms兲 and Er3⫹ PL 共⬃5 ms兲. Therefore, Eq. 共4兲
can be approximated ass
N Er共 t 兲 ⫽N Si
0

⫺

再冉

f
N Si

0

s
N Si

0

⫹

s
w Tr
s
w Tr
⫹w Si⫺w Er

s
w Tr
s
w Tr
⫹w Si⫺w Er

冉

冊

exp共 ⫺w Ert 兲冎sexp关 ⫺ 共 w Tr
⫹w Si兲 t 兴 .

⫹
s

s
w Tr
s
w Tr
⫹w Si⫺w Er

冊

exp共 ⫺w Ert 兲sexp关 ⫺ 共 w Tr
⫹w Si兲 t 兴 .

共6兲

f
s
s
In Eq. 共6兲, N Er
/N Er
and w Trare unknown parameters and w Er
and w Si can be obtained experimentally from the decay
curves of Er3⫹ and nc-Si PL. The decay time of nc-Si PL
was obtained by fitting the tail part of the decay curves with
f
s
s
/N Er
and w Trasa single exponential function. By using N Er
fitting parameters, we fitted all of the experimental curves
and extracted the values. The solid curves in Fig. 2 are theresults of the fitting. The model can reproduce all the observed data with very good accuracy. The parameters used
for and obtained from the fittings are summarized in Table I.

B. Ratio of slow to fast energy transfer processes

共5兲

Equation 共5兲 multiplied by w Er results in the PL intneisty.
Since the excitation rate of nc-Si does not depend on whether
f
s
f
s
/N Si
⫽N Si
/N Si
, and
the energy transfer is fast or slow, N Si
00
from the assumption that one nanocrystal interacts with onefsfs
Er3⫹ , N Si
/N Si
⫽N Er
/N Er
. Therefore, PL intensity will be

In Fig. 3, the ratio of slow to fast energy transfer prosf
/N Er
) is plotted as a function of the peak energy
cesses (N Er
of nc-Si PL. Since the PL spectrum of nc-Si is determined byits size distribution, the abscissa of Fig. 3 can be converted tothe average size of nc-Si. We can see a good correlation
between the two parameters, allowing us to conclude that
s
f
/N Er
is the function of nc-Si size. In Fig. 3, in all the PL
N Er
s
f
/N Er
is smaller than 1, indipeak energy ranges studied, N Er
cating that the fast energy transfer process always dominates
the whole energy transfer process. The straight line in Fig. 3

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276

Fujii et al.

J. Appl. Phys., Vol. 95, No. 1, 1 January 2004

FIG. 3. The ratio of slow to fast processes estimated from curve fittings as
a function of luminescence peak energy of Si nanocrystals. The dashed lineis the result of least-squares fitting of the data. Excess Si concentrations are
2.43 共䊐兲, 4.08 共䊊兲, 6.66 共䉭兲, 9.28 共䉮兲, and 11.1 vol % 共〫兲.

As a result, the energy of excitons trapped at Er-related centers will not be high enough to excite Er3⫹ to higher excitedstates, and the energy transfer is made only to the first excited state of Er3⫹ .
In bulk-Si:Er systems, dissociation of excitons from Errelated trap levels and energy back-transfer from excited
Er3⫹ to the level is considered to be responsible for the observed strong temperature quenching of the PL. Bothquenching processes require absorption of phonons to meetthe energy conservation rule. In nc-Si:Er systems, even if the
Er-related trap levels are not strongly affected by size, bothconduction and valence band edges are shifted to higher andlower energies. These shifts prevent the dissociation of excitons, and also slightly increase the energy of the trapped
excitons, although it is not high enough to excite the second
excited state of Er3⫹ , resulting in very small temperature
quenching.

D. Slow energy transfer process

is obtained by the least-squares fitting of all the data. Theintercept of the line to the x axis is about 1.13 eV, which isvery close to the band gap energy of bulk Si crystals. Although this coincidence might be accidental, it is clear that,for the samples consisting of very large nc-Si, only the fast
energy transfer process occurs, suggesting that the fast transfer process is a direct inheritance of the process in bulk-Si:Er
systems, and the slow process is a characteristic process occurring only in nc-Si:Er systems.
C. Fast energy transfer process

In the above model, the energy transfer time includes
pure energy transfer time and the time necessary for excited
Er3⫹ to relax to the first excited state 共⬃2.5 ␮s兲,23 if it isexcited to higher excited states. The transfer time of the fast
process, which is shorter than our time resolution, is much
shorter than the relaxation time. This suggests that the energy
transfer is made only to the first excited state ofEr3⫹ ( 4 I 13/2), independent of the size of the nanocrystals.
The fact that the energy transfer is made to the firstexcited state despite the enlargement of the band gap of nc-Si
supports the above conclusion that the fast energy transfer
process is bulk-Si:Er-like, i.e., a trap-mediated energy transfer. In bulk-Si:Er systems, energy transfer is considered to be
mediated by Er-related trap levels at about 150 meV below
the conduction band of nc-Si; excitons are trapped at thatlevel and the recombination energy of excitons is transferred
to Er3⫹ by an Auger-like process.24,25
In general, the energy levels of localized states in nc-Si
are not strongly modified by quantum size effects because
they are localized in space.26,27 In fact, the size-dependent
shift of the dangling-bond-related PL of nc-Si observed at
low temperatures is about half of that of the exciton PL,
suggesting that the trap level is almost unaffected by size andthe observed small shift reflects that of either a conduction orvalence band edge.2,28 –30 Similarly, the energy of the Errelated trap level measured from the vacuum level is notexpected to be strongly affected by the quantum size effects.

As the size decreases, the contribution of the slow energy transfer process becomes important, suggesting that theprocess is a characteristic one in nc-Si:Er systems. Furthermore, considering the very small energy transfer rate of thisprocess, Er-related centers are not expected to be involved
and excitons may interact directly with Er3⫹ .
If excitons in nc-Si directly interact with Er3⫹ , the energy transfer should be made mainly to higher excited statesof Er3⫹ because the nc-Si PL peak energy in the present
samples is always above 1.26 eV. The evidence that Er3⫹ isexcited to higher excited states is obtained in the PL spectraof nc-Si, which are partially quenched due to the energy
transfer to Er3⫹ . 14 At room temperature, by doping Er, nc-Si
PL is quenched without changing its spectral shape verymuch and the spectra are featureless 共Fig. 1兲. On the other
hand, at low temperatures, periodic features can clearly be
distinguished, i.e., the spectra are periodically suppressed,and dips appear periodically. In particular, energy higher than
the third excited state of Er3⫹ ( 4 I 9/2) is strongly suppressed.
Periodic features appear at about the energies of the second( 4 I 11/2) and third ( 4 I 9/2) excited states of Er3⫹ measured
from the ground state, and the separation between the features is about 63 meV.
Since the energy levels of the Er3⫹ 4 f shell are discrete,
only nc-Si with specific band gap energies can transfer energy resonantly; the energy transfer rate is the highest at theresonant energy. At other energies, phonons should be emitted in nc-Si to meet the energy conservation rule. This process is the most probable for phonons having the highest
density of states, which in bulk Si are transverse opticalphonons almost at the center of the Brillioun zone with anenergy of 63 meV. If the band gap energy of nc-Si does notcoincide with the excitation energy of Er3⫹ plus an integer
number of the energy of those phonons, additional emissionof acoustic phonons is required to conserve energy. This process has a smaller probability and the efficiency of the energy transfer is reduced. Consequently, equidistant features
can be seen in quenched spectra that validate the phononassisted energy transfer. It is worth noting that, although the

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Fujii et al.

J. Appl. Phys., Vol. 95, No. 1, 1 January 2004

277

FIG. 4. Energy transfer rate of slow process is plotted as a function of 共a兲 PLpeak energy of nc-Si, i.e., the size of nc-Si, and 共b兲 inverse of PL lifetime ofnc-Si at PL peak energy, i.e., average exciton recombination rate in nc-Si.
Excess Si concentrations are 2.43 共䊐兲, 4.08 共䊊兲, 6.66 共䉭兲, 9.28 共䉮兲, and11.1 vol % 共〫兲. In the same symbols, higher-annealing temperature resultsin lower PL peak energy and smaller exciton recombination rate.

energy transfer rate is larger for some specific energies thanothers, energy transfer is possible in all energy ranges above
0.81 eV by emitting a series of phonons during the process.
Very similar but more distinct PL features have been observed in nc-Si on which oxygen molecules are adsorbed.3,4
If the energy transfer is made to higher excited states, theenergy transfer time we estimated includes the time for excited Er3⫹ to relax to the first excited state. In order to extract only the time necessary to transfer energy, we subtract
the relaxation time 共2.5 ␮s; from 4 I 11/2 to 4 I 13/2 state兲23 fromss
* . The relaxation time from further
and obtained 1/w Tr
1/w Tr4
higher states, e.g., I 9/2 – 4 I 11/2 is considered to be muchs
* are sumfaster and negligible. The estimated values of w Tr
marized in Table I.
s* as a function of the nc-Si PL
First, we plotted 1/w Tr
peak energy 关Fig. 4共a兲兴. The energy transfer rate increases
with increasing PL energy, i.e., with the decreasing size ofnanocrystals. However, the data are largely scattered, andthere seems to be another factor that also strongly affects theenergy transfer rate. Among the largely scattered data, we
can find a tendency. By comparing the energy transfer ratesof the samples exhibiting a PL peak at nearly the same en-

FIG. 5. 共a兲 PL spectra of nc-Si prepared at different annealing temperaturesand fixed excess Si concentration. PL decay curves detected at 共b兲 1.4 and共c兲 1.2 eV for the same samples in 共a兲.

ergy, the energy transfer rate is smaller for the samples annealed at higher temperatures 共see Table I兲.
E. Quality of nc-Si

To understand the implication of the data of Fig. 4, we
will consider the ‘‘quality’’ of nc-Si. The word quality israther ambiguous. However, it is sometimes useful to distinguish nc-Si grown from Si suboxide by annealing. Figure 5
shows one of the examples. In Fig. 5共a兲, PL spectra of pureDownloaded 18 Nov 2004 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp

278

J. Appl. Phys., Vol. 95, No. 1, 1 January 2004

FIG. 6. PL lifetime vs detection energy for four nc-Si samples annealed at
different temperatures.

nc-Si in SiO2 prepared with different annealing temperatures
are plotted. The excess Si concentration is fixed for all
samples. We can see that higher temperature annealing results in a lower energy shift of the PL. This shift is due to theincrease in size. In addition to the peak shift, the annealing
temperature affects the quality of the nanocrystals. In Figs.
5共b兲 and 5共c兲, PL decay curves measured at 1.4 and 1.2 eV
are plotted. If the PL lifetime is determined only by size, thedecay curve obtained at the same energy should be the samefor all samples. However, the observed lifetime depends
strongly on the annealing temperatures, and becomes longer
at higher annealing temperatures. Furthermore, the shape ofthe decay curves depends strongly on the annealing temperatures. The decay curves of the samples annealed at higher
temperatures are nearly a single exponential function, but
those at lower temperatures largely deviated from the function. In Fig. 6, PL lifetimes obtained for four samples prepared with different annealing temperatures are plotted as afunction of the PL detection energy. In low-temperature annealed samples, the PL lifetime is almost independent of thedetection energy, while in high-temperature annealed
samples, it depends heavily on the detection energy. In aquantum confinement model, the lifetime should depend
heavily on the detection energy, because stronger confinement of excitons results in the enhancement of oscillator
strength as well as the higher energy shift of the band gap.
Therefore, higher-temperature annealed samples obey theprediction of the quantum size effects, and in this sense arehigh quality.
The different quality in samples annealed at different
temperatures can be proved by resonant PL measurements.
The PL spectra of nc-Si assemblies are always featurelessand broad, if they are excited by blue or green light, becauseof the inhomogeneous broadening caused by size distribution. The size distribution can be lifted if the PL is excited in
the low-energy tail of the luminescence band. In this method,
only a small portion of nc-Si in the size distribution is excited, and a nearly homogenous spectrum can be obtained. In
porous Si, with this method, PL peaks corresponding to theemission of momentum-conserving phonons can be ob-

Fujii et al.

served, and from the ratio of the phonon-assisted and nonphonon PL bands, the degree of the breakdown of the momentum conservation rule has been estimated.1
The same technique can be applied to synthesized nc-Si.
In the resonant PL studies of the present samples, we foundthat higher-temperature annealed samples show clearer
phonon-related structures, indicating that the indirect band
gap character of bulk Si is held. On the other hand, in lowertemperature annealed samples, the nonphonon PL band was
dominant and phonon structures were ill-defined, although
the spectral shape under nonresonant excitation was nearly
the same. This result implies that in low-temperature annealed samples, the translational symmetry of the crystal lattice is broken not only by the size effect but also by thedisorder remaining in or on the surface of the nanocrystals,
making the quasidirect optical transition more probable. This
explanation is consistent with the shorter PL lifetime observed for lower-temperature annealed samples 共Fig. 6兲. The
simultaneous occurrence of the smearing of phonon-related
structures in resonant PL spectra and the shortening of PL
lifetimes was observed by doping germanium 共Ge兲 in nc-Si(Si1⫺x Gex alloy nanocrystals兲.31 Breakdown of the translational symmetry by randomly substituting Si with Ge is considered to be responsible for the observed effects.
It is important to note here that low quality nc-Si meansthat bulk Si character is more smeared and the PL properties
cannot be explained by a simple quantum size effect. It does
not always mean lower PL quantum efficiency. In fact, in thepresent samples, PL intensity is not the highest for the
samples annealed at 1250 °C, although the quality is thehighest. Therefore, in nc-Si samples, one possible approachto obtaining higher quantum efficiency may be to introduce
proper disorder if it does not lead to the formation of nonradiative recombination channels.
The other possible explanation of the data in Figs. 5 and
6 is that the strength of particle–particle interaction ischanged by annealing temperature.15 The interaction between
nc-Si results in an energy transfer from smaller towards
larger nc-Si, leading to a deviation of the decay curves froma single-exponential function and a redshift of the PL peak.15
In this model, the deviation should be larger if we detect the
PL at the higher-energy part of the PL spectra, because theenergy transfer is made only from smaller to larger particles.
However, as can be seen in Fig. 5共c兲, the deviation becomeslarger for lower-temperature annealed samples, despite thefact that PL detection is made further from the PL peak energy for lower-temperature annealed samples. Furthermore,in our samples, the PL lifetime does not strongly depend on
the fraction of excess Si, as can be found by comparing w Siof samples with different excess Si and the same annealing
temperature in Table I. These are evidences that different PL
decay properties observed for samples annealed at different
temperatures are not due to the change of the degree ofparticle–particle interactions, but reflect changes of the quality of individual nc-Si.

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Fujii et al.

J. Appl. Phys., Vol. 95, No. 1, 1 January 2004

F. What is the factor determining the energy transfer
rate of the slow process

As can be seen in Fig. 6, the PL lifetime of nc-Si depends both on the size and quality of nc-Si. The PL lifetime
obtained at a nc-Si PL peak energy contains information ofboth size distribution and quality. In Fig. 4共b兲, the energy
transfer rate of the slow process (w s* ) is plotted as a functionof the inverse of nc-Si PL lifetime, i.e., the recombination
rate of excitons in nc-Si (w Si). In contrast to the plot as afunction of PL peak energy shown in Fig. 4共a兲, the correlation is very good. It should be stressed that the energy transfer rate 共ordinate兲 is estimated from the fitting of the observed PL decay curves of Er-doped samples, while theexciton recombination rate 共abscissa兲 is obtained from theexciton PL of pure nc-Si samples prepared with the same
excess Si concentration and annealing temperature of the Erdoped samples. From Figs. 4共a兲 and 4共b兲, we can conclude
that the energy transfer rate of the slow process is determinedby the recombination rate of excitons in nc-Si, and the reduction of size is just one approach to realizing a larger
recombination rate of excitons.
The recombination rate of excitons in nc-Si exhibits
strong temperature dependence.1,2 At low temperatures excitons are populated in optically inactive spin-triplet states,
which are several milli-electron-volts lower in energy than
optically allowed spin-singlet states. The lifetime of the triplet states is 5–10 ms, which is almost independent of the sizeof nc-Si. On the other hand, at high temperatures, both states
are nearly equally populated and the recombination rate isdetermined by the lifetime of the singlet state. The lifetimeof the singlet state is between 1 ms to several microseconds,
depending on the size of nc-Si. In the size range of thepresent samples, the recombination rate changes more than
one order of magnitude from room temperature to liquid helium temperature, indicating that the energy transfer rate will
be drastically reduced at very low temperatures. Unfortunately, we did not succeed in experimentally proving thisphenomena. One of the obstacles is a defect-related infraredemission from nc-Si that is always observed for almost allkinds of nc-Si samples at low temperatures.2,28 –30 The lifetime of the emission is on the order of microseconds. Therefore, even if the intensity of the defect-related PL under cw
excitation is very small, under pulsed excitation, the intensity
just after excitation is much larger than that of Er3⫹ PL,
completely covering the time range we are interested in, i.e.,
the rising part.
It is important to note that, although the energy transfer
rate of the slow process is expected to be decreased at low
temperatures, energy transfer efficiency will not depend
strongly on temperature because the smaller energy transfer
rate will be compensated by the smaller radiative recombination rate of excitons 关 w Tr(T)/w Si(T)⯝constant兴 . In fact,
the intensity ratio of Er3⫹ PL and nc-Si PL does not strongly
depend on temperature.
Up to now, we avoided discussing how the fast and theslow processes are related to the sites of Er3⫹ . Unfortunately, we have no clear clue for discussing this point. However, the observed strong size dependence of the ratio of the279

two processes suggests that the bulk-Si:Er-like very fast energy transfer process is related to Er3⫹ that stays in or very
close to nc-Si because it is necessary to form an Er-related
level in the band gap of nc-Si. On the other hand, the slow
process comes from Er3⫹ that is more separated from nc-Si.
One of the promising methods to identify the sites responsible for the fast and slow processes is site-selective x-ray
absorption spectroscopy. This method has been successfully
applied to Er-doped Si thin films.32,33 By applying themethod to the two extreme samples with the largest andsmallest sizes of nc-Si, it may possible to identify independently the sites responsible for the fast and slow processes.
IV. CONCLUSION

By analyzing the time transient of PL from Er3⫹ doped
into SiO2 films containing nc-Si, two energy transfer processes 共fast and slow processes兲 were found to coexist ineach sample. The ratio of the two processes exhibited a clear
dependence on the PL peak energy of Si nanocrystals, indicating that the ratio depends on the size of the nc-Si sensitizer. The observed size dependence suggests that the fast
process is the direct inheritance of the process in bulk Si:Er
systems, and the slow process is a characteristic process occurring only in nc-Si:Er systems. The energy transfer rate of
the slow process was found to depend on the exciton recombination rate in nc-Si. Therefore, we can conclude that, inorder to realize a higher energy transfer rate, the exciton
recombination rate in nc-Si should be enhanced. This can beachieved by breaking down the translational symmetry of
crystal lattices by reducing the size of nc-Si or by introducing disorder.
The present results imply that, from the point of view ofapplication as an amplifier and a light-emitting device, perfect nc-Si that possess the indirect band gap character of bulk
Si crystals is not suitable. Defective nc-Si:Er systems such as
silicon-rich silicon dioxide, in which Si clusters smaller than
2 nm in diameter are considered to be dispersed, are moresuitable. This conclusion is already empirically known andmany reports concerning the application of similar systems
utilize defective nc-Si assemblies.19–21
ACKNOWLEDGMENTS

This work is supported by a Grant-in-Aid for Scientific
Research from the Ministry of Education, Culture, Sports,
Science and Technology, Japan, and in part by the Industrial
Technology Research Grant Program in 2002 from the New
Energy and Industrial Technology Development Organization 共NEDO兲, Japan.
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