Controllable synthesis and growth mechanism of dual size distributed PbSe quantum dots

Article abstract of DOI:10.1039/c4ra11012a

To understand the fundamental science of nanocrystal growth, the controllable synthesis and growth mechanism of dual size distributed PbSe quantum dots (QDs) are studied. The characterizations of high-resolution transmission electron microscopy (HR-TEM) and photoluminescence (PL) unambiguously demonstrate the dual size distribution of PbSe QDs. Thermodynamic stability of small QDs is confirmed by a controllable synthesis of temperature variation and kinetic perturbation with successive injection of precursors, suggesting a possible mechanism that a chemical-potential well may lead to the size separation. The control of growth temperature plays an important role in the realization of dual size distributed PbSe QDs. Further study of temporal evolution demonstrates the size refocusing of QDs at a higher temperature. Both kinetic perturbation and thermodynamic perturbation could facilitate QDs to overcome the potential barrier. Understanding this mechanism is of significance for the controllable synthesis and applications of PbSe QDs. This journal is

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Controllable synthesis and growth mechanism of dual
size distributed PbSe quantum dots
a
a
a
*a
b
b
Ruifeng Li , Zhenyu Ye , Weiguang Kong , and Huizhen Wu , Xing Lin and Wei Fang
a) Department of Physics and State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou,
Zhejiang 310027, P.R. China *Email: hzwu@zju.edu.cn
b) Department of Optical engineering, Zhejiang University, Hangzhou, Zhejiang 310027, P.R. China
Abstract: To understand the fundamental science of nanocrystal growth, controllable
synthesis and growth mechanism of dual size distributed PbSe quantum dots (QDs) are
studied. The characterizations of high-resolution transmission electron microscope (HR-TEM)
and photoluminescence (PL) unambiguously demonstrate the dual size distribution of PbSe
QDs. Thermodynamic stability of small QDs is confirmed by a controllable synthesis of
temperature variation and kinetic perturbation with successive injection of precursors,
suggesting a possible mechanism that a chemical-potential well may lead to the size
separation. The control of growth temperature plays an important role in the realization of
dual size distributed PbSe QDs. Further study of temporal evolution demonstrates the size
refocusing of QDs at a higher temperature. Both kinetic perturbation and thermodynamic
perturbation could facilitate QDs to overcome the potential barrier. Understanding this
mechanism is of significance for the controllable synthesis and applications of PbSe QDs.
1
. Introduction
Lead chalcogenide nanocrystal quantum dots (QDs) have attracted continuous scientific
and industrial interests for the extraordinary optical and electrical properties. In particular,

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PbSe QDs, with a large exciton Bohr radius (46nm) and narrow bulk band-gap (0.278eV at
300K), have capability to tune luminescent wavelength from near-infrared to visible, covering
1
an important spectral range that have potential applications in telecommunication ,
2, 3
4
photovoltaic devices and bio-imaging . For instance, PbSe QDs have an effect of multiple
exciton generation (MEG), which can provide an opportunity to increase power conversion
5
, 6
efficiency of solar cells beyond the Shockley-Queisser thermodynamic limit. Particularly,
ultra-small PbSe QDs are getting more attention for its excellent performance derived from
the strong quantum confinement. Recently, ultra-small PbSe QDs fabricated for Schottky
solar cells shows a device efficiency of 4.57% on the size of 2.3nm, where the larger
7
band-gap of the QDs leads to higher open-circuit voltages. Furthermore, high quantum
efficiency of light emitting was also acquired from the study of PbSe magic size clusters,
which allows biological imaging at a window from 700nm to 1000nm, where organic dyes
8
emit poorly. Hence, synthesis and understanding of physical properties of ultra-small PbSe
QDs are well worth studied, while the synthesis of PbSe QDs as small as 2~4 nm will benefit
the photovoltaic and biological applications.
A hot-injection approach to synthesize PbSe QDs was initially introduced by Murray and
9
co-workers in 2001. Typically, lead oleate and n-trioctylphosphine selenide were used as the
precursor of Pb and Se, respectively. The reaction was carried out in the non-coordinating
1
0
solvent (1-octadecene), which was developed by Yu and co-workers. The ultra-small PbSe
magic-sized nano-clusters were also synthesized under a similar approach but at room
8
temperature, which could be carried out even in air for hours. One-pot non-injection method
1
1
with high chemical yields was also utilized to synthesize ultra-small PbSe QDs. In these

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synthesis approaches, the formation of QDs undergoes the nucleation and growth process,
where the thermodynamic and kinetic factors exert significant influence on the reaction.
However, how these factors affect the reaction has not been thoroughly understood.
Moreover, few studies have reported the bimodal or multi-model size distribution of
IV-VI QDs, where the mechanism of this phenomenon probably provides an opportunity to
understand the role of thermodynamic and kinetic factors on nanocrystal growth. In general,
synthesis of QDs for high quality and monodispersity undergoes a temporally discrete
nucleation event followed by relatively rapid growth from monomers and finally slower and
1
2
long-time growth by Ostwald ripening. This standard model simply demonstrates a
continuous growth process. Recent study of magic size CdSe QDs has reported individual
1
3
emission peaks which stem from a non-continuous growth process. Thus by varying and
control of the synthetic conditions, non-continue growth may occur. It offers a possible
approach to achieve desired size distribution.
Herein, it is the first time that dual size distributed PbSe QDs are directly observed. A
10, 14, 15
typical hot-injection method
was applied in our synthesis of dual-size distributed PbSe
QDs. In the general approach of synthesis, the reaction is always under a single temperature
control. Differently, dual-size distributed PbSe QDs were realized by varying the growth
temperature when the nanocystals just started to grow at the early stage right after a
nucleation event. High-resolution transmission electron microscope (HR-TEM) and
photoluminescence (PL) provide a strong evidence of dual-size distribution of the PbSe QDs.
In order to gain insight into the nature of the dual-size distribution, we then performed a
kinetic perturbation experiment to identify the thermodynamic stability of our QDs. Moreover,

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the temporal evolution from dual size distribution to uniform size distribution is probed via
thermodynamic perturbation. Thereby, both kinetic perturbation and thermodynamic
perturbation are found to facilitate QDs overcoming the chemical-potential barrier. We
conclude these findings with a schematic theoretical description. The study of the dual size
distribution phenomena offers a good opportunity to get insight into the fundamental science
of nanocrystal growth. Thus, understanding the growth mechanism may benefit both synthesis
and application of PbSe QDs.
2
. Experiments
.1 Chemicals
Chemicals used are commercially available from Alfa Aesar (or otherwise specified) and
2
were used as received: Lead oxide (PbO; 99.95%), selenium powder (Se; 99.999%), Oleic
acid (OA; 90%), 1-octadecane (ODE; 90%) and trioctylphosphine (TOP; 90%). Toluene
(
99.5%), methanol (99.5%), hexane (97%) and acetone (99.5%) were purchased from
Sinopharm.
2.2 Synthesis of dual size distributed PbSe QDs
A 1.0 M solution of trioctylphosphine-selenide (TOP-Se) was prepared by dissolving
selenium powders in TOP in a flask under an N atmosphere. The flask was then put in an
2
ultrasonic device to make the selenium powder fully dissolved. Lead oxide (0.892 g, 4 mmol),
oleic acid (2 mL, 6 mmol), and ODE (10 mL) were loaded into a three-neck flask and heated
to 100 ºC to remove air and water under N flow for an hour. Clear solution was achieved
2
after the flask was heated to 150 ℃. 4mL of 1.0 M TOP-Se was quickly injected into the
reaction flask at different temperatures to synthesize specific QDs. The colour of the mixture

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changed from nearly transparent to dark brown in 30 seconds after Se-precursor injection,
indicating the nucleation and growth of PbSe QDs. To achieve dual-size distributed PbSe QDs,
the heater was quickly removed after 30 seconds. To study the effect of different injection
temperatures, the solution was naturally cooled down to room temperature in a rate of ~15℃
/
min. To perform the study of thermodynamic stability, solution was firstly cooled down to 70℃
as fast as ~40℃/min by an ice-water bath and was kept 70℃ for different reaction time.
Successive 1mL of Se-precursors was then injected to initiate the growth again. Another
temporal evolution experiments were carried out by a reaction started with a TOP-Se injection
at 130 ℃. These samples were extracted twice (3min and 5min) with a cooling rate of ~15℃
/
min to achieve dual size distributed PbSe QDs. Then the rest of the solution was set to 110℃
for the further growth and ripening. Unreacted precursors and excess ligands were extracted
by adding methanol and toluene in a ratio of 3:1. The extraction procedure was repeated by 3
times. The QDs were then centrifuged by acetone and hexane in 4000 r/min. Finally, the QDs
were re-dispersed in hexane for characterizations.
2.3 Characterizations
All samples were immediately purified after they were taken out from the reaction flask.
Sample preparations were quickly completed by spin-coating PbSe QDs on a silicon substrate
to form a solid state film. Samples prepared for XRD were performed via a thick coating of
PbSe QDs on a silicon substrate to acquire high intensity and signal to noise ratio. Some of
the PL measurements were performed by two systems on account of experimental limitations
from gratings and detectors. The near-infrared signals (>1100nm) were collected by an InAs
detector on an Edinburgh FLS920 system equipped with an EPL405 laser diode. Spectra

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ranging from 600nm to 1100nm were measured by an EMCCD from Princeton Instrument.
Absorption spectra were performed on a Shimadzu UV-3600 UV–VIS System. HR-TEM
measurements were performed by a Tecnai G2 F20 system.
3
. Results and discussion
3.1 Morphology and crystalline structure
Fig.1. (a,b,c) The HR-TEM images of dual size distributed PbSe QDs with 20\10\5 nm
scale, the inset of Fig.1.(c) displays an FFT transformed pattern of PbSe QDs. (d) The
XRD pattern of PbSe QDs.
Fig.1 (a)(b)(c) present the HR-TEM images of the dual size distributed PbSe QDs, which
are direct evidences that both the large and small QDs coexist. The inset of Fig.1(c) is the FFT
transformed pattern of the HR-TEM image. The atoms and lattice structure are well
observable. A d-spacing of 0.62nm is determined, which is in accordance with previous data
of bulk PbSe powder. The image of HR-TEM shows that only single crystallized QDs with

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regular spherical shapes are observed, indicating that the oriented attachment could be
excluded as it always results in a formation of irregular shapes like nano rods or nano sheets.
Fig.1 (d) shows the XRD pattern of the PbSe QDs which were spin-coated on a silicon
substrate. The peaks are well matched with the rock-salt structure of PbSe crystal (JCPDS No.
01-078-1903). A narrow and sharp peak at 28 degree originates from (111) plane of Si while
the nearby 29 degree is determined to be (200) plane of PbSe QDs. The XRD pattern shows a
highly crystallized structure, which coincides with the HR-TEM result.
3.2 Optical evidences of dual size distributed PbSe QDs
Fig.2. (a) PL spectra of dual emissions with different injection temperatures. (b)
Corresponding absorption spectra of the PbSe QDs. (c) Emission peak positions as well as
energy gaps (black dot) between the small QDs (blue square) and large QDs (red square) of
the four samples versus injection temperatures.
Herein, the dual emissions of PL spectra correspond to the samples of different injection
temperatures (100℃, 120℃, 130℃, and 150℃). The solutions were naturally cooled down to
room temperature in a rate of ~15℃/min. The dual emissions of PbSe QDs are shown in Fig.2
(
a), which demonstrates the existence of dual-size distributed PbSe QDs. The PL peaks were
extracted from two systems and fitted by a Gaussian function for the limitations. The solid
lines represent the large PbSe QDs while the dash lines represent the small QDs. We assumed

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that QDs may have suffered some stable status during the growth of the decreasing
temperature, where the growth of smaller QDs are more tempted to suspend while the larger
QDs keep growing. Then the size distributions of PbSe QDs were separated. Optical
absorption spectra of the samples are shown in Fig.2 (b). However, compared with the PL
spectra, the absorption peaks overlap each other, thus being difficult to estimate QDs sizes
and size distribution directly from the absorption spectra. (See S1 in supporting
information)
Table 1. Peaks of dual emissions of PbSe QDs
100℃ 120℃ 130℃ 150℃
Small QDs (nm) 805
Large QDs (nm) 981
856
879
1009
1249
0.23
1151
0.37
1172
0.35
훥퐸 (푒푉)
0.27
To verify the existence of dual size distribution, the analysis of peak positions and
energy gaps are given in Table 1 and Fig.1 (c). Smaller QDs are attributed to the shorter
wavelength with larger band-gaps, while the larger QDs are attributed to the longer
wavelength with smaller band-gaps, which are derived from the size-dependent quantum
confinement in nanostructures. Apart from the size-dependent quantum confinement effect
that determine the PL properties in our systems, other important features for small-size
16
nanocrystals such as surface-related effects were described in the literature. Here, the peaks
of both small and large QDs shift to longer wavelength with increasing injection temperature.
In general, after a rapid nucleation event at a moderate to high temperature (100℃-150℃ for

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IV-VI QDs), higher reaction temperature always yields larger average sizes of QDs. However,
the energy gaps (훥퐸) between the two emission peaks do not increase with temperature in
monotone. Moreover, our tight-binding calculation (see S2 in supporting information)
reveal that the energy gaps between 1P -1P and 1S -1S transitions of PbSe QDs are larger
h
e
h
e
than the energy gaps between two emission peaks on corresponding sizes, suggesting that the
two emission peaks originate from the dual size distributed QDs, other than the two energy
17, 18
transitions of one-size QDs (1S -1S and 1P -1P ).
Evidently, distinct and independent
h
e
h
e
luminescent emissions of both large and small QDs are observed in each group of QDs, which
means the dual-size distribution of QDs were obtained in each reaction.
3.3 Thermodynamic stability and kinetic perturbation of QDs
Fig.3. (a) PL spectra of PbSe QDs taken from 130℃/70℃ when temperature was decreasing
and QDs taken after 7 injections of precursors at 70℃. (b) PL spectra of small PbSe QDs
when temperature was decreasing from 130℃ to 70℃ as well as temperature was kept for
st rd
th
3
0 minutes at 70℃.(c) PL spectra of QDs taken from the 1 ,3 and 5 injection of precursors
at 70℃.
In general, the growth of PbSe QDs is performed at a certain high temperature. When the
growth temperature decreases to 70℃ rapidly, the thermodynamic stability of small QDs may
be a key factor for the size separation. To verify the stability of small QDs, we firstly take

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aliquots from the reaction with a fast cooling rate (~40℃/min). Peaks located around 850nm
represent the PL emissions of small QDs while the longer wavelengths represent the larger
QDs in Fig 3(a). In this case, the peak positions of small QDs are hardly shift，while lager
QDs shifts more obviously (>100nm). When sufficient precursors were added, after 7
injections, the QDs even developed into a multi-model distribution.
For a better comprehension of the thermodynamic stability of small QDs, further
studies of both temperature variation and kinetic perturbation were carried out. Aliquots were
taken from the reaction to monitor the process. PL emissions in Fig.3(b) show that the
emissions of small QDs hardly shift both when temperature was decreasing to 70℃ as well
as temperature was kept at 70℃ for 30 minutes, which indicates that the growth are
temporarily suspended. However, when kinetic perturbation is performed with injecting
precursors (TOP-Se) to the reaction, the monomer concentration increases, which activates
the growth again (shown in Fig.3(c)).
It is of great interest to understand the mechanism of suspension and restart of the
growth. In a classic growth mechanism, nanocrystals grow continuously after the particles
reach a certain radius (the critical size). However, the thermodynamic stability of QDs
probably stems from the chemical-potential well during growth. When QDs fall into the
chemical-potential well, as the temperature being dropped to 70℃, the growth will be
suspended to retain the QDs in a certain size. In scope of the kinetic process on particle
surface, monomers dynamically bind and unbind to the particle. However, when particle falls
into the chemical-potential well, the binding and unbinding rates of monomers are temporally
balanced, which means the growth is suspended. On the other hand, monomers tend to unbind

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when the size is slightly larger than this certain size. Only when sufficient energy is supplied,
like the injection of successive monomers, can the particle overcome the potential barrier and
continue to grow.
3.4 Thermodynamic perturbation and size refocusing of QDs
Fig.4. (a) PL spectra of the PbSe QDs with different reaction time. (b) Corresponding
absorption spectra. (c) (d): HR-TEM images of the PbSe QDs. (e) (f): Histogram of size
distributions and fittings.
The temporal evolutions demonstrate the size separation during the reaction with a
naturally decreasing temperature and size refocusing under thermodynamic perturbation with
higher temperature. PL and absorption spectra are illustrated in Fig.4 (a) and (b), respectively.

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The purple lines represent a sample that was extracted from the reaction at 3 min during
cooling, while the blue lines represent the reaction at 5 min. The emission with single peak
(
red line) corresponds to a further growth and ripening for 30 minutes, which shows a size
refocusing effect. Narrower and more distinct absorption peak of QDs after size refocusing is
observed in Fig. 4 (b). The TEM image and corresponding statistics (shown in Fig.4 (c) and
(
e)) of the QDs synthesized with 5 minutes show a clear dual-size distribution of QDs. The
TEM image also gives the clear evidence that both large and small QDs coexist, which is
consistent with the dual peaks of luminescent emissions in Fig.4 (a) and calculations via a
tight-binding method. (See S2 in supporting information) The TEM image and
corresponding statistics (shown in Fig.4 (d) and (f)) of QDs with 30 minutes at 110℃ show
the more uniform shapes and narrower size distribution, suggesting that the thermodynamic
perturbation with higher temperature and long reaction time facilitate the QDs to overcome
chemical-potential well and ripen to uniform size distribution.
3.5 Mechanism of QDs growth
So far, it is confirmed that a dual size distribution of PbSe QDs is obtained during the
early stage of growth. Then the size distribution refocuses in the further growth and ripening.
19-21
The growth mechanism of dual-size distributed PbSe QDs is illustrated in Fig.5. Classic
size chemical-potential curve is shown in the black curve (dash line in Fig.5). Normally, after
quick injection of precursor in hot solvent, precursor reagents decompose and form the
supersaturated monomers that lead to nucleation. Monomers then add to existing particles,
rather than form new nuclei when the particles reach the critical size (r ) for nucleation. Once
c
monomer concentrations are sufficiently depleted, growth would be dominated by Ostwald

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ripening.
Fig.5. Schematic diagram for the growth mechanism of dual-size QDs
Situation can be different at the early stage of QDs growth, where the small QDs are
supposed to stay in a relative low energy state, namely in an energy well (red curve) in the
classic size chemical-potential curve from thermodynamic aspect. Inset of Fig.5 illustrates
that the growth is suspended (Stage I) when monomers could not provide sufficient energy to
overcome the chemical-potential well (훥퐸). If extra precursors are injected (Stage II), higher
concentration of monomers would initiate the growth again. The details have also been
demonstrated in Section 3.3.
It should be noticed that the most important difference between the typical synthesis
and the synthesis of dual size distributed PbSe QDs is the lower growth temperature. In
general, the growth of IV-VI quantum dots are performed at higher temperatures above
1
0, 22
120℃.
Only at a relatively low growth temperature, the QDs would be easily trapped in
8
,13
the chemical-potential well at the early stage of growth. In this case, we assume that the
dual size distribution results from the existence of ultra-small QDs which we attribute to the
injection rates or incidental fluctuation in temperature during nucleation or early stage of

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growth. Our experiments revealed that ultra-small QDs are more stable during
relatively-low-temperature growth because of them being easily trapped in the
chemical-potential well, while the larger QDs grow faster. This leads to the remarkable size
separation.
Despite the successive injection of precursors (kinetic perturbation), higher growth
temperature (thermodynamic perturbation) could also facilitate QDs to overcome the
chemical-potential well. When the growth temperature is maintained high, system can provide
enough energy that helps small QDs overcome the potential well and keep growing. Size
distribution will refocus at the following stage where the small QDs grow faster than the large
QDs for the monomer addition rate being scaled as the inverse of the QD radius R
19, 23
(
rate∼1/R).
As monomers are consumed, the average size slowly increase while the size
distribution slightly broaden because of the Ostwald ripening. But this broadening is limited
and won’t cause a remarkable variation of size distribution.
4
. Conclusion
In summary, controllable synthesis and growth mechanism of dual size distributed PbSe
QDs are systematically studied. Both HR-TEM images and photoluminescence emissions
observed in PL spectra clearly demonstrate the co-existence of dual-size QDs. The studies of
temperature variation and kinetic perturbation with successive injection of precursors verify
the thermodynamic stability of QDs, suggesting a possible growth mechanism that leads to
the dual size distribution. A chemical-potential well prevents the small QDs from growing
while the large QDs are still growing, which causes a remarkable size separation. Further
study of temporal evolution reveals the size refocusing of QDs. Both successive injections of

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precursors (kinetic perturbation) and higher growth temperature (thermodynamic perturbation)
can provide enough energy that facilitates small QDs to overcome the chemical-potential well.
Understanding of this process is essential for the controllable synthesis and various
applications of PbSe QDs.
Acknowledgements
This work was supported by National Key Basic Research Program of China (No.
2
6
011CB925603) and Natural Science Foundation of China (No. 61290305, 11374259, and
1275108).
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