JOURNAL OF APPLIED PHYSICSVOLUME 90, NUMBER 9

1 NOVEMBER 2001

Resonant excitation of Er3¿ by the energy transfer from Si nanocrystals
Kei Watanabe
Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan

Minoru Fujiia) and Shinji Hayashi
Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University, Rokkodai,
Nada, Kobe 657-8501, Japan

共Received 2 October 2000; accepted for publication 13 August 2001兲
Photoluminescence 共PL兲 properties of SiO2 films containing Si nanocrystals (nc-Si) and Er werestudied. The average size of nc-Si was changed in a wide range in order to tune the exciton energyof nc-Si to the energy separations between the discrete electronic states of Er3⫹. PL from exciton
recombination in nc-Si and the intra-4 f shell transition of Er3⫹ were observed simultaneously. At
low temperatures, periodic features were observed in the PL spectrum of nc-Si. The period agreed
well with the optical phonon energy of Si. The appearance of the phonon structure implies thatnc-Si which satisfy the energy conservation rule during the energy transfer process can resonantly
excite Er3⫹. For the PL from Er3⫹, a delay was observed after the pulsed excitation of nc-Si hosts.
The rise time of the PL showed strong size dependence. The effects of the quantum confinement of
excitons in nc-Si on the energy transfer process are discussed. © 2001 American Institute ofPhysics. 关DOI: 10.1063/1.1409572兴

I. INTRODUCTION

Recently, Er-doped Si has been attracting a lot of attention, because Er3⫹ ions incorporated into Si produce stable
sharp luminescence from the intra-4 f shell transition ( 4 I 13/2
to 4 I 15/2兲 at around 0.81 eV, which corresponds to the absorption minimum in silica-based glass fibers. Electroluminescence devices operating at room temperature have beenrealized,1–5 and many attempts have been made to improve
the quantum efficiency. The excitation mechanism of Er3⫹ ina bulk-Si crystal is generally explained as follows.5 First, anelectron-hole pair generated in Si is trapped at an Er-related
level about 0.15 eV below the bottom of the conduction
band. The recombination energy of the trapped electron-hole
pair is then transferred to Er3⫹ 共energy transfer兲, and the 4 fshell is excited. A drawback to use a bulk Si crystal as a hostof Er3⫹ is the large temperature quenching of the 0.81 eVluminescence. The temperature quenching arises from thedissociation of an electron-hole pair bound to the Er-related
level before the energy is transferred to Er3⫹ and the deexcitation of an excited Er3⫹ by forming an electron-hole
pair at the Er-related level 共energy back transfer兲.5– 8 The
temperature quenching can drastically be reduced by using
Si nanostructures such as porous Si and Si nanocrystals(nc-Si) as a host of Er.5,9–19 The band gap widening of Si
nanostructures arising from the confinement of an electronhole pair in a small volume 共quantum size effects兲 is considered to be responsible for the observed small temperature
quenching.
In our previous work,12–14 we have studied photoluminescence 共PL兲 from SiO2 films containing nc-Si and Er anddiscussed the excitation mechanism of Er3⫹ via nc-Si. Thea兲

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

0021-8979/2001/90(9)/4761/7/$18.00

4761

samples exhibited strong 0.81 eV PL at room temperature aswell as 1.5 eV PL due to the recombination of excitons in
nc-Si. The correlation between the intensities of the two PL
peaks was studied. We found that the 0.81 eV peak becomesstrong as the Er concentration increases, while the 1.5 eVpeak becomes weak. These results combined with the excitation spectra of the two PL peaks suggest that the excitationof Er3⫹ is made by the energy transfer from nc-Si.
The energy transfer process has been discussed in detailon the basis of the time kinetics of the PL bands and rateequations, and some different models are proposed.16,17,19,20
However, no spectroscopic evidences which indicate thestrong coupling between nc-Si and Er3⫹ have been obtained.
Since the electronic states of Er3⫹ are discrete and the band
gap of nc-Si changes with the size, nc-Si with some specificsizes can resonantly excite Er3⫹. Observation of such resonant nature offers direct evidence of the energy coupling andgives useful information to understand the energy transfer
mechanism. Furthermore, the energy transfer rate has notbeen estimated; it is not known whether or not the energy
transfer rate depends on the size. Since the energy transfer
rate is an important parameter which determines the luminescence efficiency, an estimation of the rate and the evaluationof the size dependence is indispensable to fully understandthe energy transfer mechanism and to further improve theluminescence efficiency of Er-doped Si nanostructures.
In this work, we studied PL and PL decay dynamics of
SiO2 films containing nc-Si and Er. The average size ofnc-Si was changed in a wide range in order to tune theexciton energy of nc-Si to the energy separations between
the discrete electronic states of Er3⫹. This wide tunability
provides valuable information to understand the energy
transfer mechanism. We will demonstrate that phononrelated periodic features appear on the PL spectra of nc-Si.
The appearance of the features implies the existence of a
© 2001 American Institute of Physics

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4762

J. Appl. Phys., Vol. 90, No. 9, 1 November 2001

Watanabe, Fujii, and Hayashi

FIG. 1. PL spectra of SiO2 films containing nc-Si and Er at room temperature. The size of nc-Si is varied from 2.7 to 5.5 nm, and the Er concentration (C Er) is fixed at 0.11 at. %. The energy position of the first ( 4 I 13/2),
second ( 4 I 11/2), and third ( 4 I 9/2) excited states of Er3⫹ measured from theground state is shown.

resonant energy transfer process. We will also show that the
4 f shell PL of Er3⫹ exhibits a delay after the pulsed excitation of nc-Si hosts, and the rise time depends strongly on thesize of nc-Si. The effects of the quantum confinement of
excitons in nc-Si on the efficient PL of Er3⫹ are discussed.
II. EXPERIMENT

SiO2 films containing nc-Si and Er were prepared by aco-sputtering method. Details of the preparation proceduresare described in our previous papers.12,13 In this work, theaverage size of nc-Si (d Si) was changed from 2.7 to 5.5 nm.
PL spectra were measured using a single grating monochromator and a near-infrared photomultiplier with a InP/InGaAs
photocathode. This near-infrared-sensitive fast photomultiplier allows us to measure time response of PL from Er3⫹
with the time resolution of less than 10 ns. The excitation
source was the 457.9 nm line of an Ar-ion laser. For all the
spectra, the spectral response of the detection system wascorrected by the reference spectrum of a standard tungsten
lamp. For the time response measurements, the 532.0 nm
line of a Nd:yttrium–aluminum–garnet laser was used as an
excitation source. The pulse width was 5 ns and the repetition frequency was 20 Hz. A multichannel scalar was used in
obtaining decay curves. The time resolution of the system
was about 40 ns.
III. RESULTS
A. PL spectra

Figure 1 shows PL spectra at room temperature. All thesamples show two peaks. The low-energy one 共0.81 eV兲 corresponds to the intra-4 f shell transition of Er3⫹ ( 4 I 13/2 to4
I 15/2兲 共Er3⫹ PL兲,5 while the high-energy one to the recombination of excitons confined in nc-Si 共nc-Si PL兲.12,13,21 The
PL from nc-Si depends strongly on the size. The PL peak isshifted from 1.2 to 1.5 eV as the size decreases from 5.5 to
2.7 nm. Although not shown here, the intensity ratio of thetwo PL peaks depends strongly on the Er concentration and

FIG. 2. 共a兲 PL spectra in the range between 1.0 and 1.75 eV at 5 K and 共b兲
the first derivative. Vertical lines are drawn with the period of 64 meV. Theenergy position of the second ( 4 I 11/2) and third ( 4 I 9/2) excited states of Er3⫹
measured from the ground state is shown.

the excitation power.12 The Er3⫹ PL becomes intense with Erconcentration, while the nc-Si one becomes weak.
Figure 2共a兲 shows the PL spectra at 5 K. Only the spectral range between 1.0 and 1.75 eV is shown. In contrast to
the featureless spectral shape at room temperature, periodic
features can clearly be distinguished, i.e., the spectra are periodically suppressed, and dips appear periodically. In particular, for the sample with d Si⫽5.5 nm, the higher energy
part of the spectrum is strongly suppressed. It should be
noted here that without Er doping, the spectra are featurelesseven at 5 K. The first derivatives of the spectra are shown in
Fig. 2共b兲. In all the spectra, the features in the derivative
spectra appear at the same energy. The energy separations
between the three features in the low-energy side as well as
those in the high-energy side are almost the same. The vertical lines are drawn at every 64 meV, and correspond well to
the features in the derivative spectra. Besides periodic dips, asmall peak is seen at 1.26 eV 共indicated by arrows兲. This
peak is due to the transition between the second excited( 4 I 11/2) and ground states ( 4 I 15/2) of Er3⫹. This peak is observed only when relatively small nc-Si are co-doped, i.e.,
when the PL energy of nc-Si is larger than the energy separation between the third excited state ( 4 I 9/2) and the groundstate ( 4 I 15/2).
B. PL decay dynamics

Figure 3共a兲 shows the nc-Si PL decay curves detected at
the maximum of nc-Si PL in Fig. 1 at room temperature. The

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J. Appl. Phys., Vol. 90, No. 9, 1 November 2001

Watanabe, Fujii, and Hayashi

4763

FIG. 4. A typical decay curve of Er3⫹ PL. The decay curve did not strongly
depend on Er concentration.

FIG. 3. 共a兲 Decay curves of photoluminescence from nc-Si measured at the
maximum of the spectra in Fig. 1. 共b兲 Er concentration dependence of the
decay curves for the sample with d Si⫽2.7 nm. The Er concentration is varied from 0 to 0.11 at. %.

decay curves are nonexponential. The PL lifetime becomesshorter as the size decreases. Figure 3共b兲 shows Er concentration dependence of the nc-Si PL decay curves for the
sample with d Si⫽2.7 nm. As the Er concentration increases,
the lifetime becomes shorter. The decay curves were wellfitted by the modified stretched exponential function, whichis generally used to analyze the decay curves of porous Si.22
The lifetime obtained for the sample not containing Er isabout 79 ␮s, while that for the sample with the largest Er
concentration is about 47 ␮s. The shortening of the lifetimeof the host (nc-Si) PL with increasing Er concentration implies that the energy transfer is mediated by photogenerated
excitons, i.e., not due to the absorption of light emitted by
nc-Si. In other words, energy transfer to Er3⫹ is a preferential nonradiative recombination channel for nc-Si. As will be
discussed later, the shortening of the lifetime is mainly due to‘‘nonresonant’’ energy transfer. The contribution of ‘‘resonant’’ energy transfer is rather small.
In Fig. 3共b兲, the reduction of the decay time by Er doping is rather small. It is worth nothing that the small reduction does not mean that the energy transfer to Er occurs on atimescale similar to that of the radiative exciton recombination process. If the decay curve reflects only the radiative
exciton recombination process, this argument seems to becorrect. However, PL decay curves of pure nc-Si in Fig. 3
reflect not only the radiative exciton recombination process
but also non-radiative recombination processes. Therefore,
only from the nc-Si decay curves, the timescale of the energy
transfer cannot simply be discussed. As will be shown later,
the energy transfer time can be estimated from PL rise time,and is much shorter than the estimated radiative exciton recombination time even at room temperature.
In previous PL studies of similar samples, the decay timeof nc-Si PL was reported to be insensitive to Er
concentration.17,18 The reason for this contradiction is notclear at present. However, we measured nc-Si PL decay
curves for several series of samples, and the shortening of
the lifetime with increasing Er concentration was observed
for all the series.
The Er3⫹ PL decay curve detected at 0.81 eV is shown in
Fig. 4 for the sample with d Si⫽5.5 nm. The lifetime is about
5 ms. The lifetime became slightly long with decreasing thesize 共as listed in Table I兲. However, it is not clear whether itis really a size effect or it is related to sample preparation
parameters, e.g., Si concentration and annealing temperature,
which are changed to control the size. The lifetime was almost independent of the Er concentration.
The Er3⫹ PL decay curves at 0.81 eV immediately after
pulsed excitation of nc-Si hosts are shown in Fig. 5. The
pulse width is 5 ns. We can clearly see the PL delay for all
samples. The PL delay becomes remarkable as the size ofnc-Si increases. We roughly estimated the rise time ␶ rise by
the following procedure. The slow decay part (400 ␮ s⬍t⬍1 ms) of the data was first fitted by a single exponentialfunction, and then the fitted function is subtracted from theexperimental decay curve. The resultant data were not asingle-exponential function. We thus tried to fit the curve
again by a stretched exponential function, I Er(t)⫽1⫺I o exp兵⫺(t/␶rise) 其 ␤ . The data could be well fitted by thefunction. Although there is no theoretical model which indicates that the rising part will be a stretched-exponential function, it is convenient to quantitatively estimate the size dependence of the rise time. The possible reason for thedeviation of the rising part from a single-exponential funcTABLE I. Radiative recombination time of excitons in nc-Si( ␶ R ), lifetimeof the lowest excited state of Er3⫹ ( ␶ Er), rise time of Er3⫹ PL after pulsed
excitation of nc-Si hosts ( ␶ rise), and energy transfer time ( ␶ Tr).
d Si 共nm兲␶ R 共␮s兲␶ Er 共␮s兲␶ rise 共␮s兲

␶ Tr 共␮s兲

2.7
3.3
4.1
5.5

107
298
747
990

7100
5800
5500
5000

4.1
6.4
11
38

11
21
39
115

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4764

J. Appl. Phys., Vol. 90, No. 9, 1 November 2001

FIG. 5. Decay curves of Er3⫹ PL just after the pulsed excitation of nc-Si
hosts. The size of nc-Si is varied from 2.7 to 5.5 nm and the Er concentration is fixed at 0.11 at. %.

Watanabe, Fujii, and Hayashi

process.23 In the following discussion, to simplify the problem and to extract important parameters from the observed
decay curves, we will make the following assumptions: 共i兲excitation pulse is so short that no energy transfer occurs
during the pulsed excitation, 共ii兲 excitation pulse is so weakthat most of the Er atoms are not directly excited, 共iii兲 that
nonlinear effects do not occur in nc-Si, and 共iv兲 there is noenergy back transfer process. The first assumption is valid
because the pulse width 共5 ns兲 is apparently much shorter
than the observed PL delay. The second assumption is also
valid because in the same experimental condition Er3⫹ PL
was not observed for the sample not containing nc-Si. Furthermore, the intensity of nc-Si PL was in proportion to theexcitation power. The last assumption is also possible, because we observed almost no temperature quenching of Er3⫹
PL.
In the present samples, nc-Si are isolated from the others by SiO2 barriers 4 –5 nm in thickness.24 Thus, diffusionof carriers between nc-Si does not occur. In this situation,nc-Si can be classified into two categories, i.e., nc-Si withno nonradiative centers and those with at least one such center. The PL lifetime of the former nc-Si is equal to the radiative recombination time ( ␶ R ) of excitons in nc-Si, whilethat of the latter one is expressed as 1/(1/␶ R ⫹1/␶ NR), where␶ NR is the lifetime of nonradiative recombination of excitonsin nc-Si and is generally much smaller than ␶ R . The numberof excited nc-Si having no nonradiative recombination centers 关 N Si⫺R (t) 兴 and that having nonradiative recombination
centers 关 N Si⫺NR(t) 兴 can be expressed as

再 冉 冊冎
再 冉 冊冎

0
N Si⫺R 共 t 兲 ⫽N Si⫺R
exp ⫺tion will be discussed in the next subsection. The estimatedvalues of ␶ rise are listed in Table I.
The PL delay was observed for all the samples containing both nc-Si and Er. Within the present sample preparation
condition, the delay time depended only on the size of nc-Si,
but did not depend on the Er concentration. This Er concentration insensitiveness seems to suggest that, on average,
each nanocrystal can interact with less than one Er3⫹ even in
the sample with the highest Er concentration. If Er concentration is further increased, the number of Er3⫹ which caninteract with one nanocrystal will exceed one. This mightchange the properties of the interaction, and the effect should
appear on the rise time. Detailed theoretical consideration isrequired to further discuss this problem. However, this is outof the scope of this article.
In all the spectra, we can see a very fast component after
the pulsed excitation; this component is faster than the system response time. The component was observed for the
sample not containing Er, suggesting that the component is
not related to Er and is a background signal. A very similar
fast decay component was observed for the PL decay curveof Er-doped bulk Si,8 but the origin of the fast component
was not identified.
C. Analysis of the PL decay curves

Here, we analyze the observed PL decay curves. The
time evolution of Er3⫹ luminescence is a very complicated

1
t ,
␶R

0
exp ⫺
N Si⫺NR共 t 兲 ⫽N Si⫺NR

共1兲

1
1
⫹
t ,
␶ R ␶ NR共2兲00and N Si⫺NR
are the number of excited nc-Si at
where N Si⫺Rt⫽0. The nc-Si PL intensity is

I Si共 t 兲 ⬀⫺
⬀

冋

册

␦
1/␶ R
N Si⫺R 共 t 兲 ⫹
N
共t兲 ,
␦t
1/␶ R ⫹1/␶ NR Si⫺NR

冋

共3兲

1
0
exp
N Si⫺R1/␶
R
00
N Si⫺R ⫹N
1/␶ R ⫹1/␶ NR Si⫺NR冉
再 冉 冊冎
⫺

冊

再冉

冊 冎册

1
1
1
0
t ⫹N Si⫺NR
exp ⫺
⫹
t
␶R
␶ R ␶ NR

. 共4兲In Er-doped samples, a new nonradiative recombination
process, i.e., the energy transfer process, should be added.
The energy transfer time ( ␶ Tr) is considered to be muchlarger than ␶ NR , because the sum of the intensities of the two
PL peaks 共nc-Si PL and Er3⫹ PL兲 is almost independent of
Er concentration; if ␶ Tr⭐ ␶ NR , the total intensity should increase with Er concentration. Furthermore, ␶ Tr is smaller
than ␶ R , because the energy transfer is the preferential recombination channel for excitons in Si nanocrystals. Therefore, the following relation holds between the three parameters:

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J. Appl. Phys., Vol. 90, No. 9, 1 November 2001

Watanabe, Fujii, and Hayashi␶ NRⰆ ␶ Tr⬍ ␶ R .

Equation 共5兲 indicates that nc-Si which originally do nothave nonradiative recombination centers can transfer energy
to Er, and those having nonradiative recombination centers
do not participate in the energy transfer process. Under thissimple approximation, the number of excited nc-Si whichshows exciton recombination PL 关 N Si⫺R (t) 兴 and which cantransfer energy to Er3⫹ 关 N Si⫺Er(t) 兴 can be expressed as00⫺N Si⫺Er兲⫹
共 N Si⫺R

冋

冉

1

冊
再 冉 冊冎
再 冉 冊 冎册I Si共 t 兲 ⬀0⫹N Si⫺NR
exp ⫺

冉

1
1
⫹
t
␶ R ␶ NR

再冉

1
t ,
␶ Er

共9兲

1
1
1
1
⫹
⫹
␶ R ␶ Tr ␶ Er冊冎再冉
再 冉 冊 冎冎
1
1
1
⫹
⫹
t
␶ R ␶ Tr ␶ Er

1
1
exp ⫺
t
␶ Er
␶ Er

共7兲

冊

.

冊冎

共8兲

where ␶ Er is the lifetime of the lowest excited state of Er3⫹.
The derivative of this equation gives the decay curve of Er3⫹
PL

⫹

1
1
⫹
t ,
␶ R ␶ Tr共6兲0is the number of excited nc-Si which will
where N Si⫺Ertransfer energy to Er3⫹. The nc-Si PL intensity is.

再 冉 冊冎

0⫺N Si⫺Er共 t 兲兴 exp ⫺N Er共 t 兲 ⫽ 关 N Si⫺Er⫻exp ⫺0exp ⫺N Si⫺Er共 t 兲 ⫽N Si⫺Er

1
t ,
␶R

1
1
1
0
t ⫹N Si⫺Er
exp ⫺
⫹
t
␶R
␶ R ␶ TrIn this equation, we can see that, with increasing Er concentration, the contribution of the second term increases, resulting in the shortening of the nc-Si PL lifetime. This isconsistent with the experimental results shown in Fig. 3共b兲.
In Eq. 共8兲, only the second term is related to the excitation
process of Er3⫹. If one nc-Si excites one Er3⫹, the numberof excited Er3⫹ will be

再00
N Si⫺R 共 t 兲 ⫽ 共 N Si⫺R
⫺N Si⫺Er兲 exp ⫺

1/␶ R
1/␶ R
0
N Si⫺Er⫹
N0
1/␶ R ⫹1/␶ Tr
1/␶ Tr⫹1/␶ NR Si⫺NR

00⫻ 共 N Si⫺R
⫺N Si⫺Er兲 exp ⫺

0I Er共 t 兲 ⬀N Si⫺Er⫺

再 冉 冊冎
再 冉 冊冎

共5兲

4765

共10兲

The first term of Eq. 共10兲 expresses the increase in theintensity of the PL after pulsed excitation with the time constant 1/␶ rise⫽1/␶ R ⫹1/␶ Tr⫹1/␶ Er , and the second term expresses the intensity decrease with the time constant ␶ Er . The
term ␶ Tr can thus be estimated from ␶ rise , ␶ R and ␶ Er .
As discussed in the previous subsection, the rising partof the decay curves could not be fitted by a singleexponential function. In this respect, Eq. 共10兲 does not properly express the experimental data. This discrepancy seems
to arise from size distributions of nc-Si. 24 Since the rise timedepends on the size of nc-Si as clearly demonstrated in Fig.

5, the observed data are the superposition of the data fromdifferent sizes of nc-Si. Therefore, even if each process isexpressed by a single-exponential function, the actual data
should deviate from a single-exponential function.
To roughly estimate ␶ Tr , we adopt ␶ rise in Table I. The
values of ␶ R are obtained from the slopes in the tail region of
the decay curves in Fig. 3共a兲, because the first term of Eq. 共8兲
decays very slowly. The values of ␶ Er can easily be estimatedfrom decay curves. The estimated values of ␶ rise , ␶ R , ␶ Er and␶ Tr are listed in Table I. We can see that ␶ Tr becomes smallerwith decreasing the size. Furthermore, ␶ Tr is always muchsmaller than ␶ R .
Although not shown here, the energy transfer time wasalmost independent of temperature. On the other hand, radiative recombination time of excitons in nc-Si increased withdecreasing the temperature.24,25 Therefore, in the whole temperature range studied in this work, energy transfer is thepreferential process for excitons in nc-Si.
It is noted here that ␶ Tr is the sum of the energy transfer
time and the time necessary to relax from the higher excitedstates ( 4 I 11/2 or 4 I 9/2兲 of Er3⫹ to the lowest excited state( 4 I 13/2). We tried to extract the relaxation time by directly
exciting the third excited state ( 4 I 9/2). However, the time wasshorter than our instrumental limit. Therefore, ␶ Tr estimatedin the above purely reflects the energy transfer time.
IV. DISCUSSION

Before discussing the observed PL properties, we summarize PL properties of bulk Si crystal and nc-Si not containing Er. Bulk Si crystal is an indirect gap semiconductor
with the conduction band minima in the vicinity of the X
points of the Brillouin zone 共⌬ minima兲. Momentumconserving phonons thus participate in the optical transition.
In general, TO phonon-assisted transition is the most dominant in the PL, and the nonphonon 共NP兲 transition probabil-

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4766

J. Appl. Phys., Vol. 90, No. 9, 1 November 2001

Watanabe, Fujii, and Hayashi

ity is negligibly small. This fundamental property of Si ispreserved even for particles smaller than 10 nm. In
nanometer-sized crystals, excitons are confined in a spacecompatible or smaller than the Bohr radius of free excitonsin bulk Si crystal. This confinement increases the uncertaintyof their quasimomentum, thus allowing NP optical transitions. The ratio of the NP to phonon-assisted transition is
studied as a function of a confinement energy.26 The ratio is
estimated to be around several % for the sample with d Si
⫽5.5 nm, and around several tens of % for d Si⫽2.7 nm. The
increase in the NP transition rate with respect to the phononassisted one results in the shortening the radiative lifetime ofnc-Si. 24,26,27
PL spectra under the nonresonant excitation are verybroad and featureless. This inhomogeneous broadening of
the PL band is mainly caused by the nanocrystal size andshape variation. The inhomogeneous broadening can belifted by resonant PL spectroscopy; only the particles having
the excitation threshold at the near-infrared laser energy are
selectively excited. In pure nc-Si, resonant PL spectroscopy
has been widely used to study the nearly homogeneous spectral shape, and some features corresponding to TO and TA
momentum-conserving phonons are observed.25 Similarly,
by a hole burning technique, only the particles having theexcitation threshold larger than the pump laser energy are
selectively suppressed. The suppressed spectrum is demonstrated to coincide with the resonant PL spectrum.28
The features observed in Fig. 2 can be regarded as a kindof hole burning spectroscopy. PL from nc-Si with some particular sizes are suppressed by exciting Er3⫹ by the energy
transfer. First we analyze the features around 1.3 eV. The
positions of the features are close to the energy separation
between the second excited state ( 4 I 11/2) and the ground state( 4 I 15/2) of Er3⫹ (⌬E 11/2– 15/2⫽1.26 eV). This suggests thatthe energy transfer is made to the second excited state. However, the value of ⌬E 11/2– 15/2 is slightly larger than the onsetof the lowest energy PL feature, i.e., the lowest energy negative peak in the derivative spectra 共1.2 eV, see Fig. 2兲. This
discrepancy can be explained by considering the indirect
band gap nature of nc-Si. As mentioned in the above, thedominant radiative recombination process of nc-Si as large
as 5 nm in diameter is the TO phonon emission one. Since
TO phonon energy at ⌬ minima 关 E ⌬(TO) 兴 is 57 meV, thefeature at 1.20 eV corresponds to the exciton with the recombination energy of 1.257 eV. This value agrees well with thatof ⌬E 11/2– 15/2 . Therefore, the appearance of the dip at 1.20
eV implies that the exciton with the recombination energy of
1.257 eV recombines and resonantly excites the 4 I 11/2 state.
The PL features appear periodically with a period of
about 64 meV, which corresponds to the optical phonon energy of Si at the ⌫ point 关 E ⌫(O) 兴 . This indicates that excitons
with the recombination energies of 1.26 eV⫹E ⌫(O) ⫻n (n⫽0,1,2) can also resonantly excite Er3⫹ with the assistanceof the ⌫ point optical phonons 关 ⌫(O) 兴 to satisfy the energy
conservation rule. Therefore, periodic features appear at theenergies of
1.26 eV⫹E ⌫ 共 O 兲 ⫻n⫺E ⌬ 共 TO兲 .

共11兲

The fact that the suppression of the spectra starts at 1.2 eV

共not at 1.26 eV兲 implies that, in contrast to the radiative
recombination of excitons, momentum conserving phonons
do not participate in the energy transfer process. In otherwords, photoexcited excitons recombine without emitting amomentum conserving phonon and transfer the recombination energy to Er3⫹. Only phonons in the center of the Brillouin zone can participate in the process to satisfy the energy
conservation rule.
Similar to the excitation to the second excited state, thatto the third excited state ( 4 I 9/2) is possible. In that case, thePL features appear at⌬E 9/2– 15/2⫹E ⌫ 共 O 兲 ⫻n⫺E ⌬ 共 TO兲 ,共12兲

where ⌬E 9/2– 15/2 is the energy separation between the third
excited state and the ground state. The energy position of theperiodic features in Fig. 2 can be reproduced by the formulaif ⌬E 9/2– 15/2 is 1.53 eV, which is close to the value reported
for Er-doped glasses.29–31 Compared to the energy transfer tothe second excited state, the PL features are ill defined. The
size of particles emitting light in this region is smaller thanthose around 1.26 eV. The smaller size leads to the larger
probability of NP recombination of excitons. This means
that, in addition to the spectral positions that satisfy Eq. 共12兲,features would appear at ⌬E 9/2– 15/2⫹E ⌫(O) ⫻n. The overlapof these features and the broadening of the phonon structuresby the size effects 共phonon confinement effects兲 are considered to be responsible for the ill-defined structures.
It is worth noting that the PL spectra of nc-Si become
weak in a whole spectral range with increasing Er concentration, i.e., not only the spectral positions that satisfy Eqs.
共11兲 and 共12兲 but also other regions in broad PL bands ofnc-Si are quenched.12,13 Furthermore, the area of the observed dips was less than ⬃1% of that of Er PL at 5 K. These
indicate that there is a dominant nonresonant energy transfer
process in addition to the resonant one. The energy conservation rule during the energy transfer is satisfied not only byemitting ⌫(O) but also by emitting various combinations of
optical and acoustic phonons with the total momentum ofzero. However, the observation of clear ⌫(O)-related dips
indicates that, among various processes, ⌫(O) emission one
is the most dominant in the energy transfer process.
In Er-doped bulk Si crystal, the excitation of Er3⫹ ismade to the first excited state ( 4 I 15/2). Since the lifetime ofthe state is very long, the relaxation of excited Er3⫹ by thephonon-assisted re-excitation of host Si 共energy back transfer兲 is possible at relatively high temperatures and is one of
the major nonradiative relaxation processes at room temperature. In the present samples, excitation of Er3⫹ is made to thesecond or third excited states due to the large band gap. Er3⫹
excited to these higher states is considered to relax promptly
to the lowest excited state ( 4 I 13/2) before the energy backtransfer occurs. The probability of the back transfer from thelowest excited state to nc-Si is negligibly small even at room
temperature due to the large energy mismatch. This may result in the extremely small temperature quenching of the PL
observed previously.12
Free excitons in bulk Si crystal cannot recombine without emitting/absorbing momentum-conserving phonons due
to its indirect band gap nature. In the case of Er-doped bulk

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J. Appl. Phys., Vol. 90, No. 9, 1 November 2001

Si crystal, recombination energy of free excions is not directly transferred to Er3⫹, but the energy transfer is mediatedby Er-related trap centers.5– 8 An exciton generated in Si is
first trapped at an Er-related level about 0.15 eV below thebottom of the conduction band. The localization of an exciton in a small space partially breaks the momentum conservation rule and makes the direct recombination of the exciton
possible. The recombination energy of the trapped exciton isthen transferred to Er3⫹, and the 4 f shell is excited.
In contrast to Er-doped bulk Si crystal, the existence ofsuch a trap level is not experimentally shown in the present
samples and also in Er-doped porous Si. In the present
samples, Er3⫹ responsible for energy transfer are considered
to be not doped in nc-Si, but exist in the vicinity of
nc-Si. 17,19 Therefore, it might be possible that energy transfer is not mediated by Er-related trap states. Under this assumption, we propose the following model to explain thesize dependence of the energy transfer rate.
As mentioned in the above, NP recombination of free
excitons is partially allowed in nanocrystals, although for
nc-Si exhibiting PL at around 1.2 eV, the probability of NP
transition is much smaller than that of the phonon-assisted
one because of the relatively large size and resulting weak
confinement. Similarly, the energy transfer is considered tobe restricted by the momentum conservation rule and the rateis small. As the size decreases, the overlap of the electron
and hole wave functions becomes larger. This may increase
the probability of the NP radiative recombination as well as
the energy transfer rate. We believe that the energy transfer
rate is mainly determined by the degree of the breakdown of
the k-conservation rule during the optical transition in nc-Si
induced by the quantum confinement effects.
The probability of the quasidirect recombination of excitons in nc-Si depends not only on the size but also on the
crystallinity. A disorder in the translation invariance of thecrystalline lattice brings about a breakdown of thek-conservation rule, and makes the probability of NP transition large. It seems to be very interesting to study the effects
of disorder on the energy transfer rate.
V. CONCLUSION

The present results demonstrate the first spectroscopic
evidence of the strong coupling between nc-Si and Er3⫹.
The observation of phonon-related periodic features in broadnc-Si PL band is the direct evidence of the existence ofresonant energy transfer processes. The observed periodic
features indicate that excitons in nc-Si interact with the second or third excited states of Er3⫹. We also observed a delayof Er3⫹ PL after the pulsed excitation of host nc-Si. From
the observed size dependence of the delay time, it is foundthat the smaller the nc-Si, the larger the energy transfer rate.
The present results strongly suggest that two major aspects of the quantum size effects of nc-Si, i.e., widening of
the band gap and the increase in the quasidirect recombination of excitons, play crucial roles for the efficient luminescence of Er3⫹. The excitation to the higher excited states andthe prompt relaxation to the first excited state make the en-

Watanabe, Fujii, and Hayashi

4767

ergy back transfer process small, resulting in the small temperature quenching of the PL. Furthermore, the increase in
the uncertainty in the crystal momentum relaxes the momentum conservation rule during the energy transfer process andrealizes the higher energy transfer rate.
ACKNOWLEDGMENTS

The authors are grateful to Hiroyuki Tamaoka for his
valuable assistance in this work. This work was supported by
a Grant-in-Aid for Science Research from the Ministry of
Education, Science and Culture, Japan, and a Grant for Research for the Future Program from the Japan Society for the
Promotion of Science 共JSPS-RFTF-98P-0120兲. One of authors 共K.W.兲 would like to thank the Japan Society for the
Promotion of Science for financial support.
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