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Nature of the Second Optical Transitionin PbSe Nanocrystals

M. Tuan Trinh, Arjan J. Houtepen,*, Juleon M. Schins,* Jorge Piris,and Laurens D. A. Siebbeles

Optoelectronic Materials, Faculty of Applied Sciences, Delft UniVersity of Technology,

Julianalaan 136, 2628 BL Delft, The Netherlands

Received April 17, 2008; Revised Manuscript Received May 19, 2008

ABSTRACT

The second peak in the optical absorption spectrum of PbSe nanocrystals is arguably the most discussed optical transition in semiconductor

nanocrystals. Ten years of scientific debate have produced many theoretical and experimental claims for the assignment of this feature as the

1Pe1Ph as well as the 1Sh,e1Pe,h transitions. We studied the nature of this absorption feature by pump-probe spectroscopy, exactly controlling

the occupation of the states involved, and present conclusive evidence that the optical transition involves neither 1Se nor 1Sh states. Thissuggests that it is the 1Ph1Pe transition that gives rise to the second peak in the absorption spectrum of PbSe nanocrystals.

Colloidal semiconductor nanocrystals (NCs) are often praised

for their sharp, size-tunable optical transitions. These make

them important candidates for technological applications such

as light-emitting diodes, solid state lasers, and solar cells.13

Consequently, the understanding of the optical transitions

in NCs is of both fundamental and technological interest.

The optical absorption spectrum of the prototypical CdSe

NCs has been explained satisfactorily. Norris et al. studied

the optical transitions in 1995 by size-narrowing excitationspectroscopy and explained their results successfully describ-

ing the energy levels by quantum numbers of the angular

momentum of the envelope wave function and, for hole

states, the total spin-orbit coupled momentum (e.g.,

1S3/21Se).4 In contrast, a similar assignment of the peaks in

the optical absorption spectrum of PbSe NCs, one of the most

studied NC materials in the past five years, has proven

significantly more difficult.513

The exciton Bohr radius in bulk PbSe is particularly large:

46 nm. As a result, quantum confinement is stronger in PbSe

NCs than in most other materials, which results in sharp,

well-separated peaks in the optical absorption spectrum,shown in Figure 1. The first absorption feature (of the lowest

energy) corresponds to an interband transition with both

electrons and holes having a 1S envelope function: 1Sh1Se.

However, the assignment of the second peak has generated

an intense debate. Comparing the energy of this transition

to results from 4-band kp calculations, Du et al. attributed

it to 1Sh1Pe and 1Ph1Se transitions12,14 (in short notation:

1Sh,e1Pe,h). This assignment is controversial since the

1Sh,e1Pe,h transitions are optically forbidden.1517 Despite the

controversy about the 1Sh,e1Pe,h transition strength, this

assignment was also obtained by tight binding calculations,18

and experimental evidence in apparent agreement with this

assignment was presented in refs 6, 7, 10, and 11. These

experiments are discussed in detail below.

However, Liljeroth et al. measured the single particle

energy levels in PbSe NCs using scanning tunneling spec-

troscopy and observed from their measurements that the

energy of the second optical transition matches the energy

difference between the second hole and the second electron

resonances.8 They consequently concluded that this feature

results from the 1Ph1Pe transition. Pseudopotential calcula-

tions by An et al. have supported the assignment of the

* Corresponding author. E-mail: a.j.houtepen@tudelft.nl (A.J.H.) and j.m.schins@tudelft.nl (J.M.S.).

A.J.H. and M.T.T. have contributed equally to this work.

Figure 1. Optical absorption spectrum of 6.8 nm PbSe nanocrystals.

NANO

LETTERS

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second absorption feature as a 1Ph1Pe transition.9 According

to these calculations, the hole levels are more closely spaced

than the electron levels, as a result of coupling between

multiple valence band maxima in the band structure. This is

not the case in the effective mass12,14 and tight-binding

calculations18 mentioned above, which predict symmetric

electron and hole energy levels. The more closely spaced

hole manifold leads to a calculated 1Ph1Pe transition energy

that matches the energy of the second peak in the absorption

spectrum.Thus, there are experimental and theoretical claims for both

the 1Sh,e1Pe,h and the 1Ph1Pe assignments. Deciding this

debate is important to test the validity of the pseudopotential9

and tight-binding18 models and thereby to improve the

understanding of the optical properties of semiconductor

NCs.

In the experiments presented here, we carefully controlled

the occupation of the 1Sh and 1Se levels, which are 8-fold

degenerate, using time- and energy-resolved pump-probe

spectroscopy. The second transition in the absorption spec-

trum is not bleached, even if four electrons and four holes

are introduced into the 1S levels. This shows beyond doubtthat the 1S levels are not involved in the second optical

transition and suggests that it is the 1Ph1Pe transition that is

responsible for the second peak in the absorption spectrum

of PbSe NCs. The experimental results of refs 6, 7, 10, and

11, which are apparently in support of the 1Sh,e1Pe,h assign-

ment, are discussed in light of our new experimental

evidence.

PbSe nanocrystals were prepared following the recipe of

Talapin and Murray.19 Lead(II) oleate was prepared from

2.16 g of lead(II) acetate trihydrate and 7.3 mL of oleic acid

by heating a mixture of these chemicals in 40 mL of squalane

under vacuum. A 14.2 mL sample of the resulting Pb-oleatestock solution was heated to 150 C at which point 5.4 mL

of 1.0 M selenium in trioctyl phosphine was injected

employing 1 bar overpressure in a Schlenk-line. The NCs

were allowed to grow for 5 min resulting in monodisperse,

quasi-spherical NCs with a diameter of 6.8 nm, determined

from the energy of the first exciton absorption (0.65 eV) and

the calibration provided in ref 5. The full width at half-

maximum of the first absorption feature is only 43 meV,

showing that these NCs are very monodisperse. The NCs

were precipitated twice by the addition of a butanol-methanol

mixture (2:1 v/v) and collected by centrifugation. Finally,

the NCs were dispersed in tetrachloroethylene for themeasurements. The sample is carefully kept free from oxygen

and water contamination, both during its preparation and

during the measurement.

The occupation of the 1S electron and hole levels was

controlled and monitored by femtosecond optical pulses from

a chirped-pulse amplified Ti:sapphire laser system (Mira-

Legend USP, Coherent Inc.), which runs at 1 kHz and

delivers pulses of 60 fs, 2.2 mJ, at 795 nm wavelength.

Tunable infrared and visible pulses (

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here, see below) but to a red shift in all optical transitions.23

The absence of trapping, multiexciton recombination, and

carrier cooling shows that the occupation of the levels is

well-defined: only a single 1Sh and 1Se level are occupied.

By varying the probe energy, we obtained the change in

the absorption spectrum resulting from the occupation of

these 1S levels, which is shown in Figure 2B. The first

transition in the absorption spectrum is bleached, as oneexpects from eq 1. The second and third features however

do not show a net bleach. The antisymmetric signature of

these features in the transient absorption spectrum results

from the biexciton effect:24 the Coulomb and exchange

interactions between the exciton created by the probe pulse

and the already present 1Sh1Se exciton produced by the pump

result in a red shift. Since the transient absorption feature

around the second exciton is antisymmetric, that is, the areas

of the positive and negative lobes are equal, it purely results

from a red shift and contains no net bleach. Note that, since

the excited-state absorption is red-shifted, the bleach of the

first peak in Figure 2 is blue-shifted.21

If the red shift of the second transition as a result of the

introduction of the 1Sh1Se exciton is very large (>10 meV),

then the oscillatory behavior in the transient absorption

spectrum is large and may dominate over an eventual bleach.

This would complicate the analysis of the change in oscillator

strength. To circumvent this problem, we have performed a

second experiment, in which on average four 1Sh1Se excitons

were created per NC. In this case, the relative bleach of aneventual 1Sh,e1Pe,h transition would be four times larger than

that for occupation of a single 1Sh1Se state and would easily

be detected.

To obtain these four excitons per NC, we have increased

the fluence of the pump pulse, which was again resonant

with the 1Sh1Se transition in the absorption spectrum. At high

fluence, more than one photon is absorbed per NC, which

results in the characteristic transient signals shown in Figure

3A. Multiple 1Sh1Se excitons are created, which decay on a

picosecond time scale, presumable by Auger recombination,25

although this assignment has recently been challenged.26

The

Figure 2. (A) Selected absorption transients probed at different probe energies (indicated in the figure) around the second absorptionfeature after excitation at the first exciton peak with low laser fluence. (B) The transient absorption spectrum (solid circles) over a largeenergy range taken averaged over the first 100 ps. Since all transients in A are step functions, the transient absorption spectrum does notchange with time within 1 ns. The optical absorption spectrum (solid line) is shown for comparison.

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number of excitons per NC that can be created this way is

four, since at this value (which equals half the degeneracy

of the 1S electron and hole levels) the rate of stimulated

emission is equal to the rate of absorption.

The initial average number of excitons per excited NC

(the exciton multiplicity, Nx) can be obtained from the ratio

A/B of the transient absorption at short time (A, cf. Figure

3A) to the transient absorption at long time (B, where the

number of excitons per photoexcited NC equals 1),25

provided one spectrally integrates the first absorption feature

to correct for shifts in the energy of the transition.21

This isillustrated in Figure 3A. The ratio A/B at the maximum of

the first peak in the absorption spectrum (0.646 eV) reaches

a value of6. However, when integrated from 0.57 to 0.71

eV, the value of the multiplicity obtained at the highest

fluence is 3.9, in full agreement with the expected exciton

multiplicity of four at saturation. This confirms the 8-fold

degeneracy of the 1S levels in PbSe and shows that, to obtain

the correct multiplicity, the transient absorption has to be

integrated over the entire transition.

Since the optical transition is close to saturation, the

average number of excitons per NC is four throughout the

sample. The integrated A/B ratio of4 suggests that the

bleach of the first optical transition is indeed linear with the

number of excitons, as stated by eq 1. This is in contrast to

recent calculations by Franceschetti and Zhang20 who predict

a more complex dependence (at least for CdSe NCs) that

results from changes in the matrix elements of the optical

transitions upon photoexcitation.

The transient absorption spectrum is shown in Figure 3B,C

at short and long delay times, respectively. It is immediately

clear from these figures that there is no significant bleach of

the second transition, since the signature produced by the

red shift of this transition is antisymmetric. If the secondpeak is due to the 1Sh,e1Pe,h transitions, the relative bleach

(-R/R0) should be 0.5 upon the addition of four electrons

or holes to the 1S levels. For comparison, the 1Sh1Se should

be fully bleached (-R/R0 ) 1). In the linear absorption

spectrum (Figure 1), the area of the second peak is 56% of

that of the first peak.27 In case the nature of the second

peak is 1Sh,e1Pe,h, we can deduce that Rsecond peak )

0.28Rfirst peak. In case the nature of that peak is 1P h1Pe, one

should of course find Rsecond peak) 0. We have integrated

the transient absorption over the first transition as well as

over the second transition and found that the bleach of the

second transition is (0.02 ( 0.03)Rfirst peak. This shows thatthe bleach of the second absorption is zero within the noise

of the measurement. We conclude that the oscillator strength

of the second transition in the optical absorption spectrum

is not affected by the presence of as many as four 1S excitons

per NC.

A quantitative description of the transient absorption

spectrum can be obtained by a simple model that assumes a

bleach of optical transitions according to eq 1, and a shift

in the energy of those transitions as a result of the presence

of excitons in the NCs. Both bleach and shift are a function

of the exciton multiplicity Nx:

Figure 3. (A) Relaxation dynamics for exciting and probing at thefirst exciton maximum at increasing laser fluence. At the lowestfluences, a step function is observed (cf. Figure 2A). At higherfluences, multiphoton absorption creates multiple excitons, whichdecay in tens of picoseconds. Also shown are transient absorptionspectra at 0.5 ps (B) and 1.0 ns (C) delay time. The solid circlesare experimental data points. The solids lines are fits of a modelthat assumes the second exciton is a 1P h1Pe transition; the dashedlines are fits of a 1Sh,e1Pe,h model (see text). The insets show theregion around the second optical transition in more detail.

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R(E,Nx))i)1

Npeak

Ri(Nx)e-(E-E0,i+i[Nx])

2/2wi2

-

i)1

Npeak

Ri(0)e-(E-E0,i)

2/2wi2

(2)

The peak energies (Ei,0), amplitudes (Ri,0), and widths (wi)of the optical transitions in the ground-state are obtained byfitting the low energy part of the absorption spectrum (below1.0 eV, cf. Figure 1) to three Gaussian functions, after

subtraction of an increasing background.5 The amplitudesRi(Nx) are obtained from eq 1 using the known excitonmultiplicities of 4 (0.5 ps delay time) and 1 (1 ns delay time),while the biexciton shifts i(Nx) of the transitions in excitednanocrystals are free fitting parameters. Two models can beformulated: one that assumes the second feature to be dueto the 1Sh,e1Pe,h transitions, and one that assumes it is due tothe 1Ph1Pe transition. The models differ only in the value ofthe bleach of the second transition.

The experimental transient absorption spectra in Figure

3B,C were fitted with both models; the fits are included as

the solid (1Ph1Pe) and dashed (1Sh,e1Pe,h) lines. The biexciton

shift of the first exciton that we obtained from these fits is 6

meV at Nx ) 4 and 3 meV at Nx ) 1, while the biexciton

shift of the second exciton is 15 and 6 meV at Nx ) 4 and

Nx ) 1, respectively (see Tables S1 and S2 in the Supporting

Information for all parameters). While the 1Ph1Pe model

gives an excellent description of the data, the 1Sh,e1Pe,h model

deviates strongly in the spectral region around the second

optical transition; the bleach of this feature, which is

predicted by the 1Sh,e1Pe,h model is clearly not present in

the experimental data.

The data presented here represent a single size of nanoc-

rystals dispersed in tetrachloroethylene that were excited at

the first exciton. However, we have also investigated different

NC sizes, different solvents, and different excitation energies(i.e., exciting the NCs at higher pump photon energy after

which the hot carriers quickly relax to the 1S electron and

hole levels) with the same result: the second transition is

not bleached. The evidence is conclusive: neither the initial

nor the final state of the second transition in the absorption

spectrum of PbSe NCs involves a 1S electron or hole state.

A natural conclusion is that the second absorption feature

corresponds to the optically allowed 1Ph1Pe transition.

Apparent experimental support for the 1Sh,e1Pe,h assign-

ment has been presented in several papers. We will now

discuss the experimental findings of those papers in light of

the current conclusive evidence against the 1Sh,e1Pe,h natureof the second optical transition. Wehrenberg et al.6 measured

an infrared absorption feature that appeared upon optical

excitation of the PbSe NCs and assigned this feature to the

1Se1Pe and 1Sh1Ph intraband transitions, which they assumed

to be degenerate. They further noted a strong similarity

between the energy of this absorption feature and the energy

difference between the first and the second interband

absorption peaks. Since they expected that the difference

between the 1Ph1Pe and the 1Sh1Se interband transitions

should correspond to two times the 1S-1P single particle

level splitting and should be twice the energy of the 1Se1Pe

and 1Sh1Ph intraband transitions, they assigned the second

absorption peak to the 1Sh,e1Pe,h transitions. This assignment

is tacitly based on several assumptions: (i) electron-hole

symmetry (i.e., the hole level splittings and the electron level

splittings are the same) and (ii) the electron and hole

polarization energies and (iii) their Coulomb and exchange

interactions28,29 depend weakly on the specific level that is

excited (i.e., a 1S or a 1P level). Assumption (i) is not valid,

since it has been shown by Liljeroth et al.8 that the hole SP

splitting is smaller than the electron SP splitting. This

asymmetry is supported by pseudopotential calculations andmay be as large as ESP(electron):ESP(hole) ) 2.9,28 However, this

electron-hole asymmetry is not large enough to explain the

energy spacing between the 1Sh1Se and the 1Ph1Pe transitions.

Thus, the results of Wehrenberg et al. do not agree with our

experimental results. We wish to stress, however, that our

results leave no room for interpretation: the second interband

transition does not contain 1S states. Therefore, we speculate

that the assumptions (ii) and (iii) mentioned above may not

be valid. Little is known about the polarization energies and

electron-hole interactions of the 1P levels.

The simultaneous bleaching of the first and second peaks

was reported upon electrochemical charging of films of PbSeNCs with either electrons or holes.7 On the basis of this, it

was concluded that the second peak must involve 1S states

and must be due to the 1Sh,e1Pe,h transitions. However, in

Figure 3 of ref 7, there is an induced absorption of similar

intensity to the low energy side of the bleach of the second

transition. This resembles the antisymmetric signatures

shown in Figures 2 and 3. We, therefore, conclude that the

change in absorption that was reported is in fact not a bleach

but a red shift of the second peak as a result of the

introduction of spectator charges. It is apparent from Figure

3 in ref 7 that this antisymmetric signature only evolves into

a net bleach at high oxidation or reduction potentials, wherecarriers are also injected into states other than the 1Sh and

1Se levels, namely, 1Ph and 1Pe levels. Consequently, the

experimental data presented in ref 7 are in line with the

1Ph1Pe assignment of the second optical transition.

Harbold et al. performed pump-probe studies on PbSe

NCs.11 They excited them at the second absorption feature

with a pump pulse and monitored the time-resolved bleach

of the first (1Sh1Se) feature. The transient absorption showed

a fast component and a slower component, which they

assigned to a bleach resulting from a 1S electron/hole directly

excited by the pump and a 1P electron/hole that cooled to a

1S state in several picoseconds, respectively. Thus, theyconcluded that this composite signal is evidence for the

1Sh,e1Pe,h character of the second transition. However, it

follows from the present work that the fast component is

actually due to a red shift induced instantaneously by the

exciton created by the pump pulse. We have observed

identical transient signals when exciting the second exciton

and probing at the maximum or at the blue side of the

maximum of the first peak. Similar signals were reported

by Schaller et al.30 and were correctly assigned to the

biexciton effect. Probing at the red side of the maximum,

we find that the transient is composed of an instantaneous

induced absorption (caused by the biexciton effect) and a2116 Nano Lett., Vol. 8, No. 7, 2008

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slower bleach that results from cooling of 1P carriers to the

1S levels. This will be elaborately discussed in a forthcoming

publication. When it is spectrally integrated over the first

absorption feature, we find that the net bleach goes to zero

at short times, which again illustrates that 1S levels are not

involved in the second optical transition.

Finally, Peterson et al. recently presented two-photon

photoluminescence excitation spectra of PbSe NCs and

showed that there is a two-photon absorption close to the

second peak in the single-photon absorption spectrum.10

According to tight-binding calculations by these authors, the

selection rules for two-photon transitions are complementary

to those for one-photon transitions; that is, the 1Sh,e1Pe,h two-

photon transitions should theoretically be dipole-allowed.

Therefore, Peterson et al. concluded that their measurement

confirmed the 1Sh,e1Pe,h nature of the second peak in the

absorption spectrum. However, the two-photon spectrum is

only shown in a very limited energy range, and it is not clear

what the strength of the observed two-photon absorption is

relative to other two-photon transitions. Moreover, the

conclusion by Peterson et al. is based on two-photon selection

rules but violates single-photon selection rules. They couldequivalently have concluded that their observed absorption

is a two-photon 1Ph1Pe transition, violating the two-photon

but obeying the one-photon selection rules. In any case, either

the one- or the two-photon selection rules are violated.

In conclusion, we have shown that the strength of the

second optical transition in the absorption spectrum of PbSe

NCs is not affected by the presence of 1Sh1Se excitons, even

if four of those excitons are introduced. The second optical

transition exhibits a red shift due to the presence of other

excitons, which results in an antisymmetric signature in the

transient absorption spectrum. However, integration of this

oscillation shows that the transition is not bleached. Thisclearly shows that the 1S levels are not involved in the second

optical transition, in contrast to previous assignments of this

feature as a arising from the 1Sh,e1Pe,h transitions. We

conclude that it is very likely the 1P h1Pe transition that gives

rise to the second optical transition in PbSe NCs. This

confirms pseudopotential calculations by An et al.,9 but it

disagrees with calculations using the effective mass14 or tight-

binding18 approximations.

Acknowledgment. This work is part of the Joint Solar

Programme (JSP) of the Stichting voor Fundamenteel

Onderzoek der Materie (FOM), which is supported finan-

cially by Nederlandse Organisatie voor Wetenschappelijk

Onderzoek (NWO). JSP is cofinanced by Gebied Chemische

Wetenschappen of NWO and by Stichting Shell Research.

In The Netherlands, the three Universities of Technology

have formed the 3TU.Federation. This article is the result

of joint research in the 3TU.Centre for Sustainable Energy

Technologies. This work was financially supported by The

Netherlands Organisation for Scientific Research (NWO),

Division of Chemical Sciences (VICI Award No.

700.53.443).

Supporting Information Available: Mathematical deri-

vation of eq 1 and parameters used to model the transient

absorption spectra in Figure 3B,C. This material is available

free of charge via the Internet at http://pubs.acs.org.

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