Optical and electronic properties of Si nanoclusters synthesized in inverse micelles

Article abstract of DOI:10.1103/PhysRevB.60.2704

Highly crystalline, size-selected silicon (Si) nanocrystals in the size range 2-10 nm were grown in inverse micelles and their optical absorption and photoluminescence (PL) properties were studied. High resolution TEM and electron diffraction results show

Full text of DOI:10.1103/PhysRevB.60.2704

PHYSICAL REVIEW B
VOLUME 60, NUMBER 4
15 JULY 1999-II
Optical and electronic properties of Si nanoclusters synthesized in inverse micelles
J. P. Wilcoxon, G. A. Samara, and P. N. Provencio
Sandia National Laboratories, Albuquerque, New Mexico 87185-1421
͑
Received 10 December 1998; revised manuscript received 31 March 1999͒
Highly crystalline, size-selected silicon ͑Si͒ nanocrystals in the size range 2–10 nm were grown in inverse
micelles and their optical absorption and photoluminescence ͑PL͒ properties were studied. High resolution
TEM and electron diffraction results show that these nanocrystals retain their cubic diamond structures down
to sizes ϳ4 nm in diameter, and optical absorption data suggest that this structure and bulklike properties are
retained down to the smallest sizes produced ͑ϳ1.8 nm diameter containing about 150 Si atoms͒. High pressure
liquid chromatography techniques with on-line optical and electrical diagnostics were developed to purify and
separate the clusters into pure, monodisperse populations. The optical absorption revealed features associated
with both the indirect and direct band-gap transitions, and these transitions exhibited different quantum con-
finement effects. The indirect band-gap shifts from 1.1 eV in the bulk to ϳ2.1 eV for nanocrystals ϳ2 nm in
diameter and the direct transition at ⌫(⌫ Ϫ⌫ ) blueshifts by 0.4 eV from its 3.4 eV bulk value over the same
25
15
size range. Tailorable, visible, room temperature PL in the range 700–350 nm ͑1.8–3.5 eV͒ was observed from
these nanocrystals. The most intense PL was in the violet region of the spectrum ͑ϳ365 nm͒ and is attributed
to direct electron-hole recombination. Other less intense PL peaks are attributed to surface state and to indirect
band-gap recombination. The results are compared to earlier work on Si clusters grown by other techniques and
to the predictions of various model calculations. Currently, the wide variations in the theoretical predictions of
the various models along with considerable uncertainties in experimental size determination for clusters less
than 3–4 nm, make it difficult to select among competing models. ͓S0163-1829͑99͒02328-0͔
I. INTRODUCTION
To understand the origin of visible PL and other elec-
tronic properties of Si nanoclusters, it is necessary to study
size-selected nanoclusters and to assess the role of surface
recombination. Definitive experimental results will be key to
future scientific progress and practical utilization of this ma-
terial. From a physics perspective, such studies should lead
to a better understanding of quantum confinement of elec-
trons and holes in indirect band-gap semiconductors. Quan-
tum confinement in direct gap semiconductors such as GaAs
Because it is an indirect band-gap semiconductor, silicon
Si͒ has a major drawback: its inability to emit light effi-
͑
ciently, and, furthermore, its weak emission is in the near IR.
There is presently a large research effort aimed at exploring
physical and chemical means to break silicon’s lattice sym-
metry and mix different momentum ͑k͒ states in order to
induce a useful level of luminescence and optical gain. The
approaches include1 ͑1͒ impurity-induced luminescence
e.g., S, B, Be, Er͒, ͑2͒ alloy-induced luminescence ͑e.g.,
Si-Ge-C͒, ͑3͒ porous silicon, and ͑4͒ quantum wires and dots
or nanosize clusters͒. The first two of these approaches are
plagued by, among other things, relatively low luminescence
intensity at low temperature which becomes vanishingly
weak at room temperature, whereas the last two, which may
be mechanistically related via quantum confinement, have
considerable potential but have remained largely uncon-
trolled and poorly understood. Success in this endeavor is
obviously a major challenge to materials science, one that
could have profound technological implications.
and CdSe is fairly well understood, but much less is known
about confinement in indirect gap materials.1
0–11
The bulk
͑
excitonic radius for Si is ϳ4 nm which suggests that quan-
tum confinement effects should be observed for nanocrystals
smaller than this size.
We have developed a synthesis method based on using
inverse micelles as reaction vessels12 to produce useful quan-
tities of size-selected clusters and have used this method to
͑
synthesize a variety of metal and compound semiconductor
clusters.1
3–15
These clusters have been remarkable in their
size monodispersity and the sharpness and richness of their
spectral features which have demonstrated strong quantum
confinement effects. In this paper we apply our inverse mi-
cellar synthesis method to produce size-selected Si nanoclus-
ters and to study their size-dependent optical absorption and
photoluminescence ͑PL͒. We shall first discuss the synthesis
and characterization of these nanoclusters and then present
and discuss their optical properties including comparison
with earlier work and theoretical predictions.
Because visible photoluminescence ͑PL͒ has been ob-
1
served from Si nanoclusters, these clusters and their poten-
tial are a subject of current interest. Si nanoclusters have
2
3
been produced by aerosol techniques, plasma deposition,
4
5
6
sputtering, spark ablation and grown as colloids, or in
7
–9
glass matrices by a variety of approaches
including ion
9
implantation followed by high temperature annealing; how-
ever, all of these techniques produce a large distribution of
cluster sizes resulting in very broad optical absorption and
PL features which limit usefulness and make definitive inter-
pretation in terms of quantum confinement and other mecha-
nisms difficult.
II. SYNTHESIS AND CHARACTERIZATION
Size-selected nanosize Si clusters were grown by a ge-
neric process described in detail elsewhere.1
2,13
Controlled
0
163-1829/99/60͑4͒/2704͑11͒/$15.00
PRB 60
2704
©1999 The American Physical Society

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OPTICAL AND ELECTRONIC PROPERTIES OF Si . . .
2705
FIG. 1. Coplot of optical absorbance at 250 nm ͑dashed line͒
and PL ͑emission detector at 400 nm excitation at 250 nm, solid
line͒ vs elution time for a solution containing two sizes of Si nano-
crystals. Chromatography conditions were a ODS200-c18 ͑c18-
terminated reverse phase͒ column with 120 Å pores, using acetoni-
trile as a mobile phase at 0.5 ml/min flow.
nucleation and growth of the nanoclusters occurs in the inte-
rior of nanosize surfactant aggregates called inverse micelles.
An anhyrous ionic salt ͑e.g., SiX , where XϭCl, Br, or I is
4
dissolved in the hydrophilic interior of a solution of micelles.
Since the ionic salts are completely insoluble in the continu-
ous oil medium used ͑e.g., octane͒, nucleation and growth of
Si is restricted to the micelle interior which can be varied
from 1–10 nm. The anhydrous salt dissolves to form a trans-
parent ionic solution but with a complete absence of water;
in a sense the salt is ‘‘hydrated’’ by the micelle. The absence
FIG. 2. HRTEM images of a 2 nm Si crystal ͑upper left͒, 8–10
nm crystals ͑upper right͒, and a SAD pattern for 8–10 nm crystals.
dation of the Si nanoclusters. However, upon exposure to
oxygen, a yellowing of the solution occurs presumably due
to surface oxidization.
of water prevents simple hydrolysis to form SiO which is
2
why this synthesis must be performed in water-free oils like
octane or decane, and using a controlled atmosphere glove
box. Similarly, the surfactants used, both nonionic aliphatic
polyethers, or alternatively quaternary ammonium cationic
surfactants, must be dissolved in anhydrous THF and dried
over Na metal to remove any small traces of water.
HPLC separation and elution peak spectral data were ob-
tained using apparatus with automated fraction collection.
Previous HPLC experiments on Si/SiO nanoclusters synthe-
2
sized in the gas phase showed a broad range of elution
times2 which is in contrast with our results where the Si
peak is of comparable width to that from the other molecular
constituents of the solution. Figure 1 illustrates separation of
two sizes of Si nanoclusters. Using the PL detector we can
identify which size of cluster has significant room tempera-
ture PL, and also make sure that no impurity organic chemi-
cals could be giving rise to the PL signal. Only the absor-
bance peak corresponding to the more numerous population
of small, 2.0 nm clusters coincides with a strong visible PL
signal. We also obtained the complete absorbance and PL
wavelength dependences for each size Si nanoclusters as will
be shown in Sec. III. Inductively coupled plasma/mass spec-
troscopy of the collected Si fractions showed that nearly 80%
of the total Si was recovered by HPLC and the only inor-
ganic detected was Si. Gas chromatography/mass spectros-
copy showed the only significant organic chemical in the
collected fractions was the mobile phase solvent. In particu-
lar, no surfactant was detected.
,10
We next reduce Si͑IV͒ to Si͑0͒ using an anhydrous metal
hydride, ͑usually 1 M LiAlH in THF͒. The reduction is
4
rapid with vigorous bubbling as H gas is released, electrons
2
are transferred to the Si͑IV͒ and the light yellow solution
becomes clear ͑for the smallest clusters formed͒. One can
determine the correct stoichiometry of the reaction by fol-
lowing the disappearance of the Si͑IV͒ charge transfer peaks
from the precursor solution. Control over cluster size is
achieved by variation of the micelle size, intermicellar inter-
actions and reaction chemistry. Clusters with diameters be-
tween 1.8 and ϳ10 nm were produced. Spectroscopy and
high pressure liquid chromatography ͑HPLC͒ with on-line
spectroscopy, conductivity and refractive index diagnostics
were used to demonstrate 100% reduction of the Si͑IV͒ to
the final Si͑0͒ nanocluster form. All solvents and surfactants
used were HPLC grade and completely dust free to prevent
inhomogeneous nucleation.
Since there is no source of oxygen in the reaction mixture,
and anhydrous metal hydrides are used as reducing agents, it
is likely that the Si cluster surface is terminated by hydrogen
from the metal hydride, although we currently have no direct
proof of this. When kept in the glove box under Ar, there
appears to be no long term ͑i.e., 6 month to 1 year͒ degra-
Other characterization tools employed were x-ray diffrac-
tion, selected area electron diffraction ͑SAD͒, and high-
resolution transmission electron microscopy ͑HRTEM͒. Fig-
ure 2 shows HRTEM images of a 2 nm crystal ͑upper left͒,
8–10 nm crystals ͑upper right͒ and a SAD pattern from 8–10
nm crystals. The high crystalline quality is evident.

2706
J. P. WILCOXON, G. A. SAMARA, AND P. N. PROVENCIO
PRB 60
FIG. 3. The optical absorption spectrum of bulk Si at 300 K
͑
͑
after Ref. 16͒ and the band structure near the band-gap region
after Ref. 17͒.
FIG. 4. The extinction spectra of several Si nanocrystal samples
compared with the absorption spectrum of bulk Si and a Mie theory
calculation for dϭ10 nm Si taken from Ref. 10.
III. RESULTS AND DISCUSSIONS
A. Optical absorption
To better understand the optical absorption of Si clusters,
1
6
it is instructive to review the spectrum of bulk Si, which
reflect the details of the band structure17 ͑Fig. 3͒. The long
absorption tail between 1.2 and ϳ3 eV reflects the indirect
nature of the bandgap. The sharp rise in absorption with
increasing photon energy starting around 3.2 eV ͑380 nm͒ is
associated with the direct transition at the ⌫ point ͓⌫25
merely intended to reveal the shape and influence of scatter-
ing, leaving the discussion of the details of the cluster spectra
until later.
Some of our Si nanocrystal samples exhibited consider-
able structure in their absorption spectra while others had
less structure. Featureless spectra have been observed by
other workers from Si nanocrystals embedded in glass ma-
trices or from surface oxidized nanocrystals. However, subtle
features are sometimes observed. The results of Littau
et al.2 on the larger (dϭ6.5 nm) of their two samples ex-
hibit a weak hint of the direct-gap absorptions at ϳ360 nm
and at ϳ290 nm. Similarly, there is an inflection point in the
˜
⌫ ͔ whose energy is 3.4 eV ͑365 nm͒, and the second
sharp rise starting around 4 eV ͑320 nm͒ is associated with a
second direct transition, most likely the ⌫ Ϫ⌫ transition
whose energy is 4.2 eV ͑295 nm͒ or possibly the direct tran-
sition at X.
The measured optical response ͑or extinction͒ of nanoc-
rystals reflects the sum of the scattering and absorption. The
scattering needs to be taken into consideration in comparing
cluster spectra to that of bulk Si. Figure 4 shows the extinc-
tion spectrum of relatively large (dϭ10 nm) Si clusters
calculated from Mie theory and compares it to the absorp-
tion spectrum of bulk Si. The two spectra are normalized
around the absorption shoulder corresponding to the ⌫25
15
2
5
2
Ј
͑a͒
8
absorbance in Kanemitsu’s data at ϳ350 nm. We have seen
this feature in the absorbance data on several of our samples.
A particularly interesting example for dϭ8–10 nm nanoc-
rystals is shown in Fig. 5 where the feature appears as a
shoulder at ϳ370 nm followed by a relatively sharp increase
in absorbance and double peaks at ϳ270 nm and 220 nm.
The resemblance of these features and closeness in ␭ to those
in the spectrum of bulk Si ͑see Fig. 3͒ is striking indicating
that clusters of this size (dϭ8–10 nm), which is comparable
to the size of the excitonic diameter in the bulk, retain much
of the character of bulk Si with very little evidence for quan-
tum confinement effects.
Some of our smaller size nanocrystal samples exhibited
highly structured absorption spectra. An example is shown in
Fig. 6 for a sample with dϭ2.0 nm. The figure also shows
the bulk Si spectrum for comparison. The two spectra are
remarkably similar with that of the nanoclusters shifted to
shorter ͑higher͒ wavelength ͑energy͒. The long absorption
tail associated with the indirect band gap and the two direct
2
,10
˜
⌫15 direct transition. One of the obvious differences in the
two spectra is the significantly enhanced extinction of the
clusters which is due to scattering. Shown also in Fig. 4 are
three cluster spectra ͑also normalized at about the shoulder
of the ⌫ ˜⌫ transition͒, two (dϭ10 and 1.8 nm͒ from
2
5
15
the present work and the third (dϭ3.7 nm) from Kanemit-
8
su’s work. Our dϭ10 nm spectrum is from one of our ear-
liest samples that was not purified and size-separated by
HPLC, and thus we suspect that it had a relatively broad size
distribution. Because of uncertainties in the absolute values
of the measured extinction coefficients, the normalization of
the nanocrystal spectra in Fig. 4 is only approximate and is

PRB 60
OPTICAL AND ELECTRONIC PROPERTIES OF Si . . .
2707
FIG. 5. The extinction and PL ͑excitation at 490 nm͒ spectra for
a dϭ8–10 nm Si nanocrystal sample.
transitions (⌫ ˜⌫ and ⌫ ˜⌫ or possibly that at X͒
2
5
15
25
2
Ј
are very well defined in the nanocrystal spectrum. Because
Ϫ4
our samples are very dilute (ϳ10 molar) the signal-to-
noise ratio for this sample is low for the low absorbance
associated with the indirect transitions, hence the noise in
this region of the spectrum.
FIG. 7. The photodissociation spectrum of Si30 clusters from
Ref. 25 is coplotted with the absorption ͑or extinction͒ spectra for
bulk Si and one of our (dϭ2 nm) nanocrystal samples.
Figure 7 provides a linear absorbance vs. wavelength plot
for the same two samples as in Fig. 6 with emphasis on the
region of the direct transitions. The absorbances have been
normalized as before to the value at the shoulder associated
with the ⌫ ˜⌫ transition. The close resemblance of the
cally, both direct transitions of the nanocrystals are blue-
shifted by about 0.4 eV compared to the bulk. As we shall
see below, this is a smaller quantum confinement effect than
is found for the indirect gap, but it is larger than is predicted
by model calculations.
2
5
15
two spectra shows that the bulk-like character of the band
structure of Si is preserved down to the dϷ2 nm size ͑i.e.,
down to nanocrystals with ϳ200 atoms or less͒. The data in
Fig. 7 show clear evidence for quantum confinement; specifi-
There is another aspect of the results in Fig. 7 that de-
serves attention. Reference to Fig. 3 reminds us that the Si
conduction band at ⌫ involves two overlapping bands of p␴
*
states, one with positive and the other with negative disper-
sion. Quantum size confinement can be expected to influence
these two bands differently resulting in their splitting which
in turn might be reflected in the shape of the ⌫ ˜⌫ ab-
2
5
15
sorption. While model calculations18 do indeed predict such
splitting, our cluster results in Fig. 7 and for other samples
do not reveal it. However, our result19 and those of others
on Ge nanocrystals do show evidence for such splitting.
The absorption data in Figs. 4–7 suggest a blueshift of the
indirect absorption tail with decreasing nanocrystal size, and
the gap appears to remain indirect. The small absorbance
values in the tail region along with some uncertainty due to
correcting the data for the scattering contribution make de-
tailed analysis of the data in this wavelength region uncer-
tain. However, the quality of the data on some of our
samples was sufficiently good to allow meaningful analysis.
For an indirect transition the absorption data in the region of
the band edge can be described by21 ␣hϭC(h␯ϪEg)2
where ␣ is the absorption coefficient, h␯ is the photon en-
20
FIG. 6. The absorption spectrum of a dϭ2 nm Si nanocrystal
sample. The spectrum of bulk Si is shown for comparison. The inset
shows absorption results for dϭ1.8 nm Si nanocrystals. The inter-
cept of the straight line with the x axis defines the indirect band-gap
energy.
ergy, C is a constant and E is the band-gap energy. Analysis
g

2
708
J. P. WILCOXON, G. A. SAMARA, AND P. N. PROVENCIO
PRB 60
loosely-bound, liquidlike state. We shall return below to a
discussion of the spectra of small Si nanocrystals and to a
comparison of our results to theory.
of data for dϭ1.8 nm clusters using this relationship ͑inset in
Fig. 6͒ yielded E ϭ2.2 eV. While the uncertainty in this
g
value may be as large as Ϯ͑0.2-0.3͒ eV because of the afore-
mentioned weak absorption of the cluster solutions in the tail
region as well as some inaccuracies introduced in correcting
for scattering, the result clearly demonstrates a significant
quantum confinement effect for the indirect gap of Si. Our
result is in close agreement with a study by Brus et al.2 on
B. Photoluminesence
1. Present results
͑b͒
The fate of photogenerated electron-hole pairs in a semi-
conductor is determined by traps and intrinsic recombination
processes. Weak photoluminescence ͑PL͒ from phonon-
assisted, indirect band-gap e-h recombination in bulk Si has
been observed.27 At room temperature, this PL peaks in the
near IR at 1130 nm ͑ϭ1.1 eV͒, and at low temperatures ͑e.g.,
77 K͒ there is also emission from, or to, shallow impurity
levels. In the present work on Si nanocrystals we have ob-
served room temperature emission at various wavelengths in
the range 700–350 nm ͑ϳ1.8–3.5 eV͒, i.e., across the visible
range. All our data were obtained at room temperature ͑295
K͒ and the solvent was in almost all cases acetonitrile.
In nanocrystals, a large number of the atoms are at or near
the surface leading to a preponderance of dangling bonds and
defects which result in surface states. Adsorbed impurities
can produce additional surface states, and all of these states
can act as traps or recombination sites. Consequently, light
emission from nanostructures, be they nanocrystals or porous
Si, can be quite complex with considerable uncertainties
about the origin of the observed PL. In solution-grown
nanocrystals such as our own, there is the added concern that
excess precursors and reaction products can lead to some
luminescence which can interfere with that due to the Si
clusters. In this regard, HPLC separation/purification has led
to significant improvement in the quality of the observed PL
spectra. Even so, it is difficult to definitively rule out the role
of contaminants in the measured PL spectra of nanoclusters
in colloidal solutions.
SiO -capped Si nanocrystals. From photoluminescence exci-
2
tation ͑PLE͒ and photoluminescence ͑PL͒ measurements on
nanoclusters estimated to have a Si core diameter in the
range 1–2 nm, these authors deduced a bandgap of 2.06 eV.
As we shall discuss later, these measured quantum confine-
ment effects are smaller than those predicted by effective
mass theory but are comparable to results of some model
calculations.
Our smallest Si nanocrystals (dϭ1.8 nm) have ϳ150 at-
oms and still retain bulklike optical properties. There has
been considerable theoretical interest in the structure, shape
and properties of Si clusters containing up to few tens atoms
and in answering the question of how small can Si clusters
be and still retain bulklike properties.2
2–24
The results have
revealed major changes in shape as a function of size with a
qualitative change from prolate to more spherical structures
2
2
in the narrow range between 24 and 30 atoms. .
Rinnen and Mandich25 determined the absorption spectra
of gas-phase neutral Si clusters in the size range Si18 to Si41
using resonant one-and two-color photodissociation spectros-
copy. A surprising aspect of their results is that the spectra
are essentially identical over the whole size range studied,
despite the theoretical findings that there is a wide variation
in the structure of the clusters over this range. The spectrum
of Si30 is shown and compared to bulk and dϭ2 nm cluster
spectra in Fig. 7. The authors observed that the Si18–41 spec-
tra have much in common with the spectrum of bulk crystal-
line Si, however, the similarity in the spectra is not so obvi-
ous.
In considering optical absorption and PL spectra it is nec-
essary to take into account the exciton binding energy, EB .
For nanocrystals EB is expected to be significantly enhanced
over its bulk value due to quantum confinement and the ex-
pected smaller ෈ of the nanocrystals. For example, Zunger
and Wang28 find ෈Ϸ8 for dϭ2 nm Si nanocrystals com-
pared with a bulk value of 11.4. The smaller ෈ also strength-
ens the Coulombic e-h attraction which is given by U(r)
On the basis of their results Rinnen and Mandich25 con-
cluded that these small Si clusters must share one or more
common structural entities which are strong chromophores.
One possibility is that these small clusters share a common
bonding network which persists and extends as the cluster
grows in size, and that this network may be related to that of
bulk Si. Another possibility is that all of these clusters con-
tain at least one loosely bound smaller cluster such as the
abundant Si10 which may be responsible for the sharp spec-
tral structure in Fig. 7. We believe that the latter explanation
is the correct one and offer the following explanation.
In the photodissociation experiments25 the temperature of
the clusters was estimated to be in the range 700–900 K. In
work on metallic and semiconducting clusters, it is generally
found that the melting point is substantially depressed with
decreasing cluster size. Thus, for example, the melting point
of CdSe decreases sharply with decreasing cluster size, its
value for dϭ3 nm being about one half of its bulk value and
is expected to be much less for smaller clusters.1 Thus, we
suggest that for the conditions of Rinnen and Mandich’s ex-
periments, their Si clusters are essentially in a ‘‘molten
state’’ and that small entities like Si10 are indeed the domi-
nant species. These entities have closed shape
2
ϭϪe /෈r, where r is the distance between the electron and
hole. Tight binding calculations by Leung and Whalley29
yield a large increase in EB of Si with decreasing cluster
size. Similarly, Takagahara and Takeda30 calculated a large
increase in EB with decreasing cluster size for indirect-gap
semiconductors in the framework of effective mass theory.
Their results for Si show that EB increases from 14.3 meV
for the bulk to ϳ250 meV for dϭ2 nm clusters.
Figure 8 shows a room temperature PL spectrum of one of
our earliest nanocrystal samples (dр5 nm) obtained before
developing our HPLC capability. For excitation at 256 nm,
the PL spectrum exhibits intense, structured emission cen-
tered at ϳ365 nm ͑3.4 eV͒ and a weaker, also structured,
emission centered at 600 nm ͑2.06 eV͒. It may well be that
the structure in both emissions is associated with the pres-
ence of impurities or even different size populations. The
365 nm emission appears to be largely due to direct e-h
recombination at ⌫(⌫ Ϫ⌫ ), and its high intensity and
1
2
6
configurations which can quite conceivably exist in a
2
5
15

PRB 60
OPTICAL AND ELECTRONIC PROPERTIES OF Si . . .
2709
FIG. 8. The PL spectrum of an as-prepared dр5 nm Si nano-
crystal sample. The dashed curve is for dϽ5 nm Si nanoclusters
FIG. 9. Coplot of the extinction and PL spectra ͑for two excita-
tion wavelengths͒ for dϭ2 nm Si nanocrystal samples.
capped by SiO excited at 350 nm, taken from Ref. 2. The inset
2
shows a coplot of the extinction and PL spectra for a dϭ4.0 nm Si
nanocrystal sample.
culations for Si and attributed to quantum confinement and
reduced electronic screening. As we have already noted,
Takagahara and Takeda30 find E Ͼ0.25 eV for the indirect
B
3
short PL decay lifetime (␶ϭ1.5 ns, as will be discussed
later͒ are consistent with this assignment. The origin of the
gap of Si clusters with dр2 nm. Tagaki et al. deduced a
value of E ϭ0.32 eV for dϷ3.3 nm Si clusters. Similarly,
B
Read et al.3 find E ϭ0.32 eV for the indirect gap of Si
1
600 nm PL is more uncertain. If both emissions were intrin-
B
sic properties of Si nanocrystals, then the 600 nm emission
would be due to bandgap recombination. In this scenario,
reference to the absorption data discussed above, would sug-
gest that the 365 and 600 nm emission peaks are associated
with a small nanocrystal population with dХ2 nm.
quantum wires of ϳ3 nm diameter. More recent first prin-
¨
32͑a͒
ciples calculations by Og u¨ t et al.
show EB increasing
from 0.3 eV for dϭ3 nm to ϳ1.0 eV for dϭ1 nm. However,
before concluding that the shift between absorption and
emission peaks is equal to E , caution is in order. For small
B
The dashed curve in Fig. 8 is the PL spectrum of
nanocrystals the electron and hole will be in very close prox-
imity and the exciton state should be strong in both absorp-
tion and emission suggesting that the shift should be
small.3 Thus, some uncertainty remains as to the origin of
the observed 0.4 eV shift. Possible contributors are size poly-
dispensity, electronic fine structure and/or phonon effects.
It can be seen that the major PL peak in Fig. 9 is asym-
metric. Analysis of the spectrum reveals a secondary peak at
ϳ420 nm ͑ϳ3.0 eV͒. As appears to be typical for Si nano-
structures, the 365 nm peak ͑with the 420 nm peak sub-
tracted͒ is fairly broad, its width at half max being ϳ1 eV.
This sample also exhibits weaker and quite broad emission at
wavelengths longer than 500 nm, as shown. This lumines-
cence is less well defined than that for the sample in Fig. 8.
In addition to being purer, the sample in Fig. 9 is also more
monodisperse as suggested by its sharper absorption fea-
tures. Consistent with this observation, the extra structure in
the PL spectrum in Fig. 8, attributed to different size popu-
lations of nanocrystals, is absent in Fig. 9.
2
͑a͒
SiO -capped Si nanoclusters reported by Littau et al.
for
2
their ‘‘1.0 colloid’’ sample (dϽ5 nm) excited at 350 nm.
We believe that this luminescence has the same origin as that
peaked at ϳ600 nm in our spectrum, but is red shifted be-
cause of larger crystallite size. As will be discussed later, we
believe this luminescence is due to band gap indirect recom-
bination.
For excitation at 320 nm the PL spectrum for our sample
in Fig. 8 retains its structured two-peak character, but the
peaks are red shifted compared to excitation at 256 nm. Spe-
cifically, the more intense emission is centered at ϳ380 nm
2͑b͒
͑
͑
3.3 eV͒ and the less intense emission is peaked at ϳ680 nm
1.82 eV͒. The redshift of the emission may come from ex-
citing a population of larger clusters with the longer wave-
length excitation. The ϳ680 nm peak in our PL spectrum
2
excited at 320 nm is redshifted from Littau et al.’s PL spec-
trum in Fig. 8, consistent with a larger cluster population.
Results on a dϭ2 nm size-selected, purified sample are
shown in Fig. 9. The absorption spectrum was discussed ear-
lier ͑Figs. 6 and 7͒. The first absorption peak at 325 nm ͑3.81
eV͒ is attributed to the ⌫ Ϫ⌫ direct gap, but blueshifted
Figure 9 also shows the PL spectrum for a similar sample
excited at 490 nm ͑2.53 eV͒ i.e., just above the indirect gap
for this nanocrystal size. This PL peak is centered at 580 nm
͑2.14 eV͒, and it is tempting to attribute it to indirect band-
gap recombination. However, we note that this luminescence
is identical to that observed on much larger (dХ8–10 nm)
nanocrystals as shown in Fig. 5. We are thus led to conjec-
ture that this PL is due to surface or defect recombination.
The independence of this luminescence of nanocrystal size
may be relevant to semiempirical tight-binding and ab initio
local density calculations by Allan et al.33 which demon-
2
5
15
by ϳ0.4 eV due to quantum confinement. Excitation at 245
nm yields the PL spectrum shown. The major peak is cen-
tered at 365 nm ͑ϭ3.40 eV͒ i.e., essentially at the same
wavelength as for the sample in Fig. 8. Again, we attribute
this peak to direct e-h recombination at ⌫. It is redshifted
from the absorption peak by 0.4 eV. It is tempting to view
this shift as a measure the exciton binding energy. Indeed, its
magnitude is comparable to values deduced from model cal-

2710
J. P. WILCOXON, G. A. SAMARA, AND P. N. PROVENCIO
PRB 60
x-ray absorption fine structure ͑NEXAFS͒ and extended
x-ray absorption fine structure ͑EXAFS͒ measurements.
Keeping in mind the above precautions, we can now offer
some observations on the data in Fig. 10. Looking first at the
results of earlier work, we note that there are differences in
the dependence on size reported by different authors. Some
of the differences, but not all, are almost certainly due to
uncertainties in size. Secondly, we note that essentially all of
the PL peaks energies on Si nanocrystals capped with SiO2
or embedded in glass matrices fall within the shaded region
in Fig. 10, albeit this region embodies a wide band of ener-
gies or wavelengths at each value of d. An issue for these
samples2
,3,7,8,35͑a͒
is the role of the SiO or glass and suboxide
2
layer that almost certainly exists at the interface. There are
undoubtedly defects and surface states at this interface, and
they could play a significant role in determining the lumines-
cence from such samples.33 The authors of most of these
works imply generally that the observed PL is intrinsic to the
Si nanocrystal cores, but doubts remain. The shaded region
also embodies much of the published PL peak energies on
porous Si samples, an observation that has been used by
some authors to suggest that the PL of porous Si is intrinsic
to Si nanostructures. Strong doubts and many puzzles remain
in this area as well.2
FIG. 10. Summary of data ͑literature and present work͒ on peak
PL energy versus Si nanocrystal size.
strated the stability of self-trapped excitons at the surface of
Si nanocrystals. The excitons are obtained for dimer bonds
passivated by, e.g., hydrogen ͑relevant to our clusters͒ or
silicon oxide. Light emission from these trapped excitons is
essentially independent of size.
The inset in Fig. 8 shows the absorption and PL spectra of
a nanocrystal sample (dϭ4 nm) with structured absorption
peaks at 355 nm ͑3.48 eV͒ and 280 nm ͑4.40 eV͒ which we
believe are associated with the quantum confinement-shifted
two direct transitions at ⌫͔ exhibited a PL peak centered at
40 nm ͑2.30 eV͒ for excitation at 470 nm ͑2.64 eV͒, i.e.,
well below the first direct transition at ⌫. This emission is at
slightly shorter wavelength than the peaks in Figs. 5 and 9
suggesting extrinsic origin. The PL spectrum in the inset in
Fig. 8 also has a secondary peak at ϳ700 nm ͑ϳ1.8 eV͒
which is most likely due to recombination at the indirect
band gap.
͑a͒,35͑b͒
Whereas some of our data points fall in the shaded region
in Fig. 10, the rest fall well above this region. As noted
earlier, our PL spectra generally exhibited a higher energy
major peak and a lower energy minor peak. It is the energies
of these minor peaks that fall in the shaded region. Our high-
est energy points in the figure are, we believe, associated
with direct (⌫ Ϫ⌫ ) recombination. As far as we know,
͓
2
5
15
5
this is the first observation of such direct recombination from
Si and is made possible by quantum confinement. Consistent
with this conclusion, the decay lifetime of the luminescence
is on the order of a nanosecond ͑as discussed below͒. Kim’s
highest energy point in Fig. 10 may also be due to this direct
recombination.
The heavy dashed curve in Fig. 10 depicts the intermedi-
8
ate part of our data, and the data of Kanemitsu and Iwasaki
2. Comparison with earlier luminescence results
6
et al. Here two scenarios can be examined. The first pre-
As seen above, Si nanocrystals in solvents produced by
our inverse micellar synthesis photoluminesce at various
wavelengths in the range ϳ700–350 nm ͑ϳ1.8–3.6 eV͒.
Figure 10 summarizes the results for our samples and com-
pares the PL peak energies with those from other authors. In
doing this comparison it is necessary to caution that a major
uncertainty in the figure is knowledge of the size of the
nanocrystals. We have presented the data using the nominal
diameters deduced from our work and reported by the vari-
ous authors. It is very difficult to be certain that TEM images
will give truly representative dimensions and shapes in the
absence of large statistical samples. In the few cases where
statistical analyses were performed, it was found that nano-
crystal samples embody a broad distribution of sizes. These
broad distributions are evident to some extent in the very
broad PL peaks of nanocrystal Si samples. Even for our
HPLC-separated and purified cluster populations, we find
relatively broad PL peaks, suggesting, at least in part, size
dispersion. Undoubtedly, the most accurate size information
in Fig. 10 is that due to Schuppler et al.34 who deduced the
sumes that the low energy emissions ͑and thereby all emis-
sions in the lower shaded region͒ are due to Si bandgap
emission, i.e., indirect recombination. The intermediate en-
ergy emissions would then be associated with some chro-
mophore that may be related to the synthesis. The measured
PL decay lifetimes for these emissions are on the order of a
few to tens of nanoseconds, as we shall see later. Alterna-
tively, the intermediate energy emissions are due to bandgap
emissions and the low energy emissions due to surface-state
recombination as also suggested by Kanemitsu.8 The
electron-hole pairs are generated in the interior of the Si
nanocrystals. Some of the electrons rapidly decay into the
lower-energy surface states while some ͑a larger fraction in
our case͒ recombine with the holes across the gap. One dif-
ficulty with this scenario is that some of the emission ener-
gies for sizes dϾ4 nm fall above effective mass ͑EMA͒ pre-
diction ͑discussed below͒ which overestimates the quantum
confinement effect—an observation that argues in favor of
the first scenario.
Some observations on porous Si are relevant to the inter-
mediate energy regime in Fig. 10. Blue light emission is
sizes of their SiO -capped nanocrystals from SiK near-edge
2

PRB 60
OPTICAL AND ELECTRONIC PROPERTIES OF Si . . .
2711
commonly observed from aged and or oxidized porous Si.
This emission is observed in the range 410–490 nm ͑ϳ3.0–
2.5 eV͒ depending on the aging/oxidation conditions, and the
radiative lifetime is in the ns range for some samples and in
the ␮s range for other samples. The energy range of this PL
overlaps most of the data in the intermediate regime in Fig.
10. The origin of this PL is a subject of continuing debate
between two competing mechanisms. In one, as in the recent
3
5͑c͒
work of Li et al.,
the PL with ␮s lifetime is believed to
come from the crystalline cores of oxidized nanometer-size
Si particles, whereas the PL with ns lifetime is attributed to
the oxidized layer. In the second mechanism, the PL is at-
tributed to e-h recombination at centers located at the inter-
face between the Si nanocrystals and the Si oxide as well as
on the inside of the oxide layers.3 In this mechanism, the
photoexcitation most likely occurs in the crystalline Si cores
and the carriers transfer to the luminescent centers at the
interface or in the oxide. This second mechanism comes
closer to our present case where we believe that the PL in the
intermediate regime is due to surface state recombination.
5͑d͒
FIG. 11. Decay of the PL intensity at 460 nm for a dϭ3 nm Si
nanocrystal sample. The inset shows the decay of the PL of a simi-
lar sample at lower time resolution.
3. Radiative recombination rate and quantum efficiency
The radiative e-h recombination rate ͑1/␶͒, where ␶ is the
radiative lifetime, is an important measure of the effective-
ness of a luminescing material. For direct band gap semicon-
ductors like GaAs the recombination is fast, ␶ being on the
order of 1–10 nanoseconds or less. For indirect gap materials
like Si, on the other hand, the recombination is slow, ␶ being
on the order of tens of microseconds to milliseconds. In
nanocrystals all vibronic as well as recombination rates are
expected to increase as the electron and hole wave functions
become more compact and more overlapping with decreas-
ing size.
We have obtained ␶ for a couple of our Si nanocrystal
samples from PL decay measurements at 295 K. The first
experiment was performed on dϭ3 nm nanocrystals in sol-
vent using an apparatus with picosecond resolution in the
laboratory of our collaborator Professor David Kelley of
Colorado State University. The results expressed as PL am-
plitude vs time at 460 nm for excitation at 300 nm are shown
in Fig. 11. The decay is multiexponential but can be satis-
factorily fitted by two lifetimes, a fast initial component with
To estimate the quantum efficiency ͑Q.E.͒ of various so-
lutions of Si nanoclusters, we measured the total area under
the PL curve and normalized this by the absorbance of the
sample at the excitation wavelength. We performed identical
measurements on a laser dye, Coumarin 500, known to be
close to 100% efficient at light emission. We took the ratio
of the cluster solution PL area to the dye emission PL area
under identical excitation conditions, lamp energy, and spec-
trometer bandpass as a measure of the efficiency of light
emission of the nanoclusters. The largest room temperature
Q.E. achieved was 3.9% for 2.0 nm Si nanocrystals in aceto-
nitrile with no special treatment of the cluster surface, or
annealing.
In a similar study on Ge nanocrystals19 we examined the
influence of the polarity of the solvent on the Q.E. Extensive
data on dϭ2 nm Ge nanocrystals revealed a gradual de-
crease in PL efficiency with decreasing solvent polarity ͑eth-
ylene glycolϾacetonitrileϾtolueneϾorthoxylene). The same
trend is expected for Si.
␶ϭ46 ps and a slow component with ␶ϭ1.6 ns. It is not clear
what the origin of the fast component is, but the slower is
comparable to that for direct-like e-h recombination as in
bulk GaAs. The inset in Fig. 11 shows the PL decay kinetics
for another sample with dϭ3 nm measured at lower time
resolution. The decay ͑for PL at 440 nm͒ can be adequately
fit by two exponentials. The fast component with ␶ϭ17 ns is
convolved by the instrument response so that the decay of
the sample may be actually faster. The slow component with
C. Comparison with theory
There has been an evolution of theoretical treatments of
the electronic structure of semiconducting nanocrystals. The
earliest treatment is the effective mass approximation ͑EMA͒
due to Efros and Efros36 which assumed spherical nanocrys-
tals, parabolic energy bands and infinite potential barriers at
the crystal boundary. In the EMA one replaces the micro-
scopic quasi-periodic potential of the bulk material by a con-
stant potential, and the kinetic energy operator is replaced by
an effective-mass operator derived from the parabolic expan-
sion of the bulk band structure. Experience on a large num-
ber of materials has shown that EMA generally treats large
(dϾ5–6 nm) nanocrystals fairly accurately but fails seri-
ously for smaller nanocrystals.37 Consequently, there have
been a number of attempts at improving it. For example,
Brus38 included the electron-hole (e-h) interaction energy,
i.e., the Coulomb term, dealt with finite-potential walls to
␶
ϭ48 ns is due to the sample. The scatter at long times is
due to digitization noise. As discussed above, the origin of
this PL is not known, but we believe it is due to surface state
recombination. This ␶ϭ48 ns is also much shorter than ␶’s
2
observed for SiO -capped Si nanoclusters; e.g., Littau et al.
2
fit their time-resolved PL results on their colloid 1.0 sample
(
dϽ5 nm) with two exponentials yielding ␶ ϭ17 ␮s and
1
␶2
decay is measured over a very narrow range of times and the
’s should be considered tentative.͒
ϭ76 ␮s. ͑A note of caution is in order: in Fig. 11 the
␶

2712
J. P. WILCOXON, G. A. SAMARA, AND P. N. PROVENCIO
PRB 60
data consist of PL peak energies vs. size as was presented in
Fig. 10. Thus, we superimpose on the theoretical results in
Fig. 12 the experimental data of Fig. 10 in an attempt to look
for trends. We caution, however, that many of the experi-
mental data shown are not necessarily attributed to recombi-
nation associated with the ͑indirect͒ band gap, rather, they
may be due to surface or impurity recombination or, in the
case of some of our results, to direct recombination at ⌫.
Additionally, in comparing the experimental and theoretical
results, one needs to keep in mind the relatively large and
size-dependent exciton binding energy as well as the large
uncertainty in determining size.
Zunger and Wang28 compared their calculated exciton en-
ergy vs. size both with band-gaps estimated from absorption
measurements and with experimental PL peak energies and
found some systematic trends. Specifically, all the experi-
mental bandgap data fell above the calculated Energy vs d
curve, whereas all the PL data fell below this curve leading
to the conjecture that the observed PL originates from some
persistent ͑approximately size-independent͒ surface states
rather than from intrinsic nanocrystal states. However, it
should be noted that in this comparison the absorption and
PL data came from different sources, and, furthermore, the
absorption data are from porous Si samples, making defini-
tive conclusions difficult. Although many of our findings ap-
pear to be in qualitative agreement with Zunger and Wang’s
observations, it is premature to come to any definitive con-
clusions about mechanisms. The experimental situation has
to greatly improve before we reach that stage.
FIG. 12. Comparison of theoretical band-gap energies and ex-
perimental PL peak energies ͑same data as in Fig. 10͒ for Si nano-
crystals.
calculate excited state energies, and considered the influence
of the dielectric constant of the surrounding medium.
3
9
Kayanuma went on to consider the influence of nanocrystal
shape, specifically, spheres vs cylinders. Despite these im-
provements, EMA results generally overestimate the con-
finement effect, especially for small clusters.
In an attempt to overcome this shortcoming, tight
4
0–42
18,28,43,44
binding
and pseudopotential
methods have been
employed with various degrees of success. Rama Krishna
1
8
29
and Friesner used empirical pseudopotentials to calculate
the influence of size confinement on the indirect gap as well
as on the ⌫ Ϫ⌫ and ⌫ ϪL transitions. An interesting
Leung and Whalley investigated e-h interactions in
truncated small spherical Si nanocrystals by incorporating
Coulomb, exchange and spin-orbit couplings into tight-
binding models. They reported the optical absorption spectra
for nanocrystals with 41, 83, and 147 atoms in size, corre-
sponding to dϭ1.16, 1.47, and 1.78 nm, respectively, the
latter being equal in size to our smallest nanocrystals. The
nanocrystals were constructed by sequentially adding shells
about a central atom, and therefore have tetrahedral symme-
try. Figure 13 compares their calculated ෈2 vs energy spec-
trum for the 147-atom cluster with the extinction data for our
1.8 nm nanocrystals which are of comparable size. (෈2 is
the imaginary part of the dielectric constant.͒ The absorption
spectrum, ␴abs(␻), is directly related to ෈2(␻) by ␴absϳ␻
2
5
15
25
aspect of their work is the finding that the direct ⌫ Ϫ⌫
2
5
15
transition energy first increases slightly with decreasing crys-
tal size and then decreases. The decrease is attributed to the
inverted parabolic shape of the conduction band at ⌫. Our
results do not agree with this finding. Rather, we find a sig-
nificant increase in this energy for our smallest nanocrystals.
Another feature of their results is the finding that size con-
finement splits the two overlapping (p␴ ) conduction bands
*
at ⌫ (⌫ ) as well as the two overlapping bands at the top of
1
5
the valence band also at ⌫. ͑Actually, these two latter bands
are slightly split in bulk Si by spin-orbit interaction as shown
in Fig. 3.͒ These splittings should, in principle, be reflected
in that part of the absorption spectrum due to direct transi-
tions at ⌫. However, as we have already noted, there is no
discernible evidence for it in our Si nanocrystal spectra. The
reason for the absence of such evidence is embodied in the
results in Fig. 3, namely the curvature of the two split-off
conduction bands at ⌫. Specifically, the first split-off band is
concave and the second is convex providing a potential well
for electrons. Thus, the first direct optical transition at ⌫ in Si
nanocrystals is to this second band.
Figure 12 shows various theoretical results on the varia-
tion of the indirect bandgap energy with size for Si nanoc-
rystals. Clearly, there are very substantial quantitative differ-
ences among these results, especially at small sizes making it
difficult to draw any meaningful conclusions. In attempting
to compare these results with experimental data, we note that
very few authors have reported the experimental magnitude
of the bandgap for Si clusters. Almost all of the available
෈ (␻). The agreement between the two spectra in Fig. 13 is
2
fairly good, especially with respect to the bandgap and the
first direct (⌫ Ϫ⌫ ) transition.
2
5
15
Several groups have calculated the intrinsic recombina-
tion rate, 1/␶, as a function of size using different models for
band gap recombination in Si nanocrystals. Some of these
results are summarized in Fig. 14 which also shows our ex-
perimental results as well as those of other authors. Because
of aforementioned uncertainties in the experimental data,
particularly in size determination, it had been hoped that
model calculations will provide guidance as to the depen-
dence of ␶ on size. Unfortunately, the very large disparities
among the various model results in Fig. 14 do not allow us to
draw any definitive conclusion. The only certainty in these
results is that ␶ decreases with decreasing cluster size, as is
expected. Leung and Whaley29 provided two bounds for ␶ vs
d as shown by the dot-dash curves. The bounds account for
variations in model parameters for both surface-truncated

PRB 60
OPTICAL AND ELECTRONIC PROPERTIES OF Si . . .
2713
FIG. 13. Comparison of the extinction spectrum for a d
ϭ1.8 nm Si nanocrystal sample with the calculated ␧ (w), spec-
2
FIG. 14. Summary of the available ͑present work and literature͒
data on the dependence of the PL decay lifetime on Si nanocrystal
size. Theoretical results are also shown.
trum for 147-atom Si nanocrystals ͑from Ref. 29͒. The two nano-
crystal samples are of about the same size. The arrow indicates the
location of the calculated indirect band gap which is in good agree-
ment with our experimental value.
oms͒. HPLC techniques with on-line optical and electrical
diagnostics were developed to purify and size separate the
clusters and to ensure obtaining background-free absorbance
and PL spectra.
In addition to the long wavelength absorption tail associ-
ated with the indirect-bandgap, several direct transitions
were evident in the data. It was found that the smallest gap in
nanosize Si remains indirect to the smallest sizes studied, d
ϭ1.8 nm. The different electronic transitions exhibited vari-
ous quantum confinement effects. The indirect band-gap
shifts from 1.1 eV in the bulk to ϳ2.1 eV for nanocrystals
ϳ2 nm in diameter ͑in qualitative agreement with theoretical
and hydrogen-terminated nanocrystals. Most all of the other
calculated results fall between these two bounds.
As for the experimentally determined ␶’s, we can make
the following observations. First we note that the model re-
sults in Fig. 14 are for band gap recombination. Three data
points on SiO -capped Si nanocrystals ͑one from Wilson
2
1
0
et al. and two, presumably on the same sample, from Littau
et al. ͒ fall in the middle of the band of model results. The
2
associated ␶’s are on the order of a few tens of microseconds.
1
We also show a band of experimental results on porous Si.
These data also fall within the broad band of model results.
Our two data points (␶’sϭ1.5 and ϳ50 ns͒ and Kanemitsu’s
datum point (␶ϭ0.8 ns) fall well outside the range of the
model results as they should, consistent with our interpreta-
tion of the associated PL as being due to direct e-h recom-
bination and surface/defect recombination and not due to
bandgap recombination. There are no model calculations ap-
propriate for these data.
preductions͒, and the direct transition at ⌫ (⌫ Ϫ⌫ ) blue
25
15
shifts by 0.4 eV from its 3.4 eV bulk value over the same
size range. Some transitions were relatively insensitive to
cluster size, a feature that can be qualitatively understood in
terms of the shape of the associated dispersion curves in the
band structure.
We have observed room-temperature photoluminescence
from Si nanocrystals at various wavelengths in the range
7
00–350 nm ͑1.8–3.5 eV͒, i.e., across the visible range. The
IV. SUMMARY AND CONCLUSIONS
largest quantum efficiencies were ϳ4% for dϭ2 nm Si. No
post synthesis surface treatment was employed to achieve
these results. Solvent polarity was shown to influence quan-
tum efficiency.
The most intense PL was in the blue region of the spec-
trum ͑ϳ365 nm͒ and is attributed it to direct electron-hole
recombination at ⌫ (⌫ Ϫ⌫ transition͒. The short radiative
We have successfully grown size-selected Si nanocrystals
in the size range 1.8 to 10 nm. HRTEM fringe images show
that the nanocrystals are of high crystalline quality, and elec-
tron diffraction results show that they retain their bulk dia-
mond structure down to about 4–5 nm diameter. Optical ab-
sorption data suggest that these nanocrystals retain their
bulklike properties and structure down to the smallest sizes
produced ͑ϳ1.8 nm diameter containing about 150 Si at-
2
5
15
lifetime for this PL (tϭ1.5 ns with a faster initial compo-
nent͒ is comparable to that for GaAs and is consistent with

2714
J. P. WILCOXON, G. A. SAMARA, AND P. N. PROVENCIO
PRB 60
our assignment. This observation of direct recombination in
Si is a consequence of quantum confinement. A relatively
strong PL centered around 580 nm is fairly insensitive to
cluster size, and is attributed to surface ͑or defect͒ recombi-
nation. Other PL peaks were tentatively assigned, but more
work is needed to confirm the assignments.
which is very sensitive to small changes in surface charac-
teristics, may play a significant role in elucidating the influ-
ence of surface structure on the optical properties of nano-
clusters.
ACKNOWLEDGMENTS
The work presented here represents an exploratory at-
tempt to understand the relationship between Si nanocluster
size, structure, surface chemistry and the resulting optical
properties. We have identified features in the optical proper-
ties that deserve much more detailed study in order to under-
stand the influence of size and of surface bonding and termi-
nation on the electronic properties. In this regard, HPLC,
This work was supported by the Division of Materials
Sciences, Office of Basic Energy Sciences, U.S. Department
of Energy, and by a Laboratory Directed R&D project under
Contract No. DE-AC04-AL8500. Sandia is a multiprogram
laboratory operated by Sandia Corporation, a Lockheed Mar-
tin Company, for the Department of Energy.
1
21
See, e.g., S. S. Iyer and Y. H. Xie, Science 260, 40 ͑1993͒, and
See, e.g., J. I. Pankove, Optical Processes in Semiconductors
references therein.
͑Dover, New York, 1975͒, Chap. 2.
2
2
2
M. F. Jarrold and V. A. Constant, Phys. Rev. Lett. 67, 2994
1991͒.
͑
a͒ K. A. Littau, P. J. Szajowski, A. J. Muller, A. R. Kortan, and
L. E. Brus, J. Phys. Chem. 97, 1224 ͑1993͒; ͑b͒ L. E. Brus, P. F.
Szajowski, W. L. Wilson, T. D. Harris, S. Schuppler, and P. H.
Citrin, J. Am. Chem. Soc. 117, 2915 ͑1995͒, and references
therein.
H. Takagi, H. Ogawa, Y. Yamazaki, A. Ishizaki, and T. Nakagiri,
Appl. Phys. Lett. 56, 2379 ͑1990͒.
M. Yamamoto, K. Hayashi, K. Tsunetomo, K. Khono, and Y.
Saka, Jpn. J. Appl. Phys., Part 1 30, 136 ͑1991͒; Y. Osaka, K.
Tsunetomo, F. Toyomura, H. Myoren, and K. Kohno, Jpn. J.
Appl. Phys., Part 2 31, L565 ͑1992͒.
W. A. Saunders, P. C. Sercel, R. B. Lee, H. Atwater, K. J. Va-
hala, R. C. Flanagan, and E. J. Escorsi-Aparcio, Appl. Phys.
Lett. 63, 1549 ͑1993͒.
S. Iwasaki, T. Ida, and K. Kimura, Jpn. J. Appl. Phys., Part 2 35,
L551 ͑1996͒.
͑
2
2
3
4
E. Kaxiras and K. Jackson, Phys. Rev. Lett. 71, 727 ͑1993͒.
U. Rothlisberger, W. Andreoni, and M. Parrinello, Phys. Rev.
Lett. 72, 665 ͑1994͒.
25
26
27
K. D. Rinnen and M. L. Mandich, Phys. Rev. Lett. 69, 1823
3
4
͑
1992͒.
N. Binggeli and J. R. Chelikowsky, Phys. Rev. Lett. 75, 493
1995͒.
͑
J. R. Haynes and W. C. Westphal, Phys. Rev. 101, 1676 ͑1956͒.
A. Zunger and L. W. Wang, Appl. Surf. Sci. 102, 350 ͑1996͒.
K. Leung and K. B. Whaley, Phys. Rev. B 56, 7455 ͑1997͒.
T. Takagahara and K. Takeda, Phys. Rev. B 46, 15 578 ͑1992͒.
See, A. J. Read, R. J. Needs, K. J. Nash, L. T. Canham, P. D. J.
Calcott, and A. Qteish, Phys. Rev. Lett. 69, 1232 ͑1992͒; T.
Ohno, K. Shiraishi, and T. Ogawa, ibid. 69, 2400 ͑1992͒.
2
2
8
9
5
30
3
1
6
7
3
2
¨
͑a͒ S. Og u¨ t, J. R. Chelikowsky, and S. G. Louie, Phys. Rev. Lett.
S. H. Risbud, L. C. Liu, and J. F. Shackelford, Appl. Phys. Lett.
79, 1770 ͑1997͒; ͑b͒ We are thankful to Professor L. E. Brus for
emphasizing this point.
G. Allan, C. Delerue, and M. Lannoo, Phys. Rev. Lett. 76, 2961
͑1996͒.
63, 1648 ͑1993͒.
8
9
33
Y. Kanemitsu, Phys. Rev. B 49, 16 845 ͑1994͒.
C. W. White, S. P. Withrow, A. Meldrum, J. D. Budai, D. M.
Hembree, J. G. Zhu, D. O. Henderson, and S. Prawer ͑unpub-
lished͒; see also J. Appl. Phys. 78, 4386 ͑1995͒.
3
3
4
5
S. Schuppler, S. L. Friedman, M. A. Marcus, D. L. Adler, Y. H.
Xie, F. M. Ross, T. D. Harris, W. L. Brown, Y. J. Chabal, L. E.
Brus, and P. H. Citrin, Phys. Rev. Lett. 72, 2648 ͑1994͒.
͑a͒ K. Kim, Phys. Rev. B 57, 13 072 ͑1998͒; ͑b͒ Y. Kanemitsu, H.
Uto, and Y. Masumoto, ibid. 48, 2827 ͑1993͒; ͑c͒ P. Li, G.
Wang, Y. Ma, and R. Fang, ibid. 58, 4057 ͑1998͒; ͑d͒ G. G. Qin,
X. S. Liu, S. Y. Ma, J. Lin, G. Q. Yao, X. Y. Lin, and K. X. Lin,
ibid. 55, 12 876 ͑1997͒.
Al. L. Efros and A. L. Efros, Fiz. Tekh. Poluprovodn. 16, 6209
͑1982͒ ͓Sov. Phys. Semicond. 16, 772 ͑1982͔͒.
See, e.g., A. D. Yoffee, Adv. Phys. 42, 173 ͑1993͒ for a review.
L. E. Brus, J. Chem. Phys. 79, 5566 ͑1983͒; 80, 4403 ͑1984͒.
Y. Kayanuma, Phys. Rev. B 38, 9797 ͑1988͒; 44, 13 085 ͑1991͒.
Y. Wang and N. Herron, J. Phys. Chem. 91, 257 ͑1987͒; 92, 4988
͑1988͒.
1
1
0
1
W. L. Wilson, P. F. Szajowski, and L. E. Brus, Science 262, 1242
͑
1993͒.
A. P. Alvisatos, Mater. Res. Bull. 19, 23 ͑1995͒ and references
therein.
J. P. Wilcoxon, U.S. Patent No. 5147841 ͑15 September 1992͒.
J. P. Wilcoxon, R. L. Williamson, and R. J. Baughman, J. Chem.
Phys. 98, 9933 ͑1993͒.
J. P. Wilcoxon and G. A. Samara, Phys. Rev. B 51, 7299 ͑1995͒;
see also J. P. Wilcoxon, P. P. Newcomer, and G. A. Samara,
Solid State Commun. 98, 581 ͑1996͒.
1
1
2
3
3
6
1
4
3
3
7
8
1
1
5
6
39
J. P. Wilcoxon and S. A. Craft, NanoStructured Materials
4
0
͑
Elsevier Science Ltd., Amsterdam, 1997͒, Vol. 9, pp. 85–88.
See, e.g., S. M. Sze, Physics of Semiconductor Devices ͑Wiley-
Interscience, New York, 1969͒, Chap. 2, and references therein.
M. L. Cohen and T. K. Bergstresser, Phys. Rev. 141, 789 ͑1966͒.
M. V. Rama Krishna and R. A. Friesner, J. Chem. Phys. 96, 873
4
1
P. E. Lippens and M. Lannoo, Phys. Rev. B 39, 10 935 ͑1989͒;
41, 6079 ͑1990͒.
N. A. Hill and K. B. Whaley, Phys. Rev. Lett. 75, 1130 ͑1995͒.
L. W. Weng and A. Zunger, J. Phys. Chem. 100, 2394 ͑1994͒,
and references therein.
1
1
7
8
42
4
3
͑
1992͒.
1
2
9
0
J. P. Wilcoxon and G. A. Samara ͑unpublished͒.
J. R. Heath, J. J. Shiang, and A. P. Alivisatos, J. Chem. Phys. 101,
44
M. S. Hybertsen, Phys. Rev. Lett. 72, 1514 ͑1994͒, and references
therein.
1607 ͑1994͒.