Journal of Crystal Growth 378 (2013) 537–541

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Journal of Crystal Growthjournal homepage: www.elsevier.com/locate/jcrysgro

Infrared emitting property and spherical symmetry of colloidal PbS
quantum dots
Seisuke Nakashima a,b,n, Kosuke Kikushima a, Kohki Mukai aaDepartment of Solid State Materials and Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama-shi, Kanagawa 240-8501,
Japanb
RIKEN—Advanced Research Institute, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japana r t i c l e i n f oabstract

Available online 29 January 2013

Infrared emitting properties and spherical symmetry of colloidal PbS quantum dots (QDs) chemicallysynthesized in organic solvent oleylamin as a ligand were investigated in terms of synthesis
temperature, time, and precursor concentrations. The progress of the nucleation process and crystal
growth of PbS nanocrystals can be interpreted using the LaMer mechanism. By decreasing thetemperature or increasing the concentration of precursors, the degree of supersaturation becomes
higher, resulting in precipitation of small nuclei. Meanwhile, in the case of the lower supersaturation,
the particle size and the size distribution of nanocrystals become larger and narrower. Direct
evaluations of the spherical symmetry of the synthesized QDs were carried out using symmetryindexes derived from the transmission electron microscopy images. These results clearly indicated thatlower reaction temperature, higher supersaturation, and longer growing time are favorable for thesynthesis of spherical QDs emitting at the wavelength of the 1.3 mm region.
& 2013 Elsevier B.V. All rights reserved.

Keywords:
A1. Nanostructures
A1. Quantum dots
B1. Nanomaterials
B1. SulﬁdesB2. Semiconducting lead compounds
B3. Infrared devices

1. Introduction
The semiconductor quantum dot (QD) is actively studied foradvanced applications in a variety of ﬁelds, such as biomedical
engineering, solar cells, optical communication, [1–6] due to thewide-range spectral tunability. For the purpose of developing
quantum communication and quantum information technologies,
in particular, perfectly symmetrical (spherical) QDs emitting in
the infrared range are required as a source of entangled photon
pairs. However, the epitaxial QDs grown on substrates possess
shape anisotropy, which is caused by the lattice mismatch and theanisotropy in the atomic arrangement of crystalline surface [7]. In
contrast, colloidal synthesis methods in liquid solvent are freefrom the substrate restriction, and therefore, the highly spherical
QDs are expected to be created easily compared with the epitaxial
growth methods.
The spherical symmetry of colloidal QDs is strongly inﬂuenced
by several synthesis conditions, such as precursor concentrations,
synthesis temperature, and so on. Hence, further detailed understanding of the mechanism of crystal growth is quite important
for the control of shape symmetry of QDs. It is well known thatnCorresponding author at: Department of Solid State Materials and Engineering,
Yokohama National University, 79-5 Tokiwadai, Hodogaya-Ku, Yokohama-shi,
Kanagawa 240-8501, Japan.
E-mail address: nakashima@ynu.ac.jp (S. Nakashima).

0022-0248/$ - see front matter & 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jcrysgro.2012.12.132

the synthesis of QDs in organic solvent conforms to the LaMer
mechanism [8]. The LaMer diagram schematically illustrates how
the rapid nucleation and the subsequent crystal growth progressunder the continuous supply of monomers. In the initial nucleation stage, the critical nuclear radius and the shape symmetry are
determined by the degree of supersaturation, which depends on
the temperature and the concentration of precursors. In thesubsequent growth stage, the nucleation stops, since the concentration of precursors falls below the critical supersaturation. Then,the size and the spherical symmetry of QDs will be graduallychanged until the precursor concentrations settle down to thesaturation solubility.
From the viewpoint of application for information–communication technology in the NIR spectral region, lead sulﬁde (PbS)
nanocrystals is one of the most promising materials. Hines andScholes for the ﬁrst time reported the organometallic synthesis of
PbS QDs with size-tunable emission in the NIR region using oleic
acid as a ligand, and lead oxide and bis(trimethilsilyl) sulﬁde((TMS)2S) as precursors [9]. Ozin’s group successfully synthesized
PbS QDs with narrow size distribution by applying the hot
injection method to the viscous reaction system due to highconcentration of PbCl2 [10]. Recently, the ligand and precursor
effects on the crystal growth and optical properties of PbS QDs
have been systematically studied [11,12]. In this paper, thecorrelation between the emission properties and the sphericalsymmetry of PbS QDs has been investigated in terms of synthesis

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temperature, time, and precursor concentrations. We have also
explored synthetic conditions suited for the emission at the
wavelength of the 1.3 mm region, which is potentially advantageous for the utilization of the existing ﬁber communication
systems. Then, the spherical symmetry of synthesized QDs was
directly evaluated using symmetry indexes which were statisticallycalculated using transmission electron microscopy (TEM) images.
At present, the control of the spherical symmetry for colloidal
nanocrystals is a difﬁcult and challenging trial although a variety ofshapes of PbS micro- or submicro-crystals have been alreadyexamined [13,14].

2. Experimental
PbS QDs were synthesized by the hot injection method [15]using oleylamine (OLA) as the ligand. PbCl2 (0.56 g) and 10 ml of
OLA were loaded into a three-neck ﬂask at room temperature. The
mixture was magnetically stirred and heated to the synthesis
temperature to form the homogeneous PbCl2–OLA suspension
while the ﬂask was purged by N2. The synthesis temperature wasset at 70 and 80 1C. At the same time, 0.16 g of sulfur was
dissolved in 15 ml of OLA and the solution was kept at 120 1C
for 30 min. The sulfur–OLA solution was then quickly injected
into the ﬂask under vigorous stirring, and the reaction wasallowed to continue at the same temperature for 1–25 min to
obtain PbS QDs of different sizes. For each synthesis time, aliquotsof the solution were taken from the ﬂask and quenched by cold
hexane. The solution with the addition of methanol was centrifuged to remove excess OLA. Then, the precipitate was redispersed in hexane. Photoluminescence (PL) spectra for the solution
dispersed with PbS QDs were measured at room temperature byusing a 635 nm laser diode as a pump. The particle size and shapesymmetry were directly examined by TEM measurement using a
JEOL JEM2100F at 200 kV.

3. Results and discussions
In a LaMer diagram [9], the particle formation process consistsof two stages: a nucleation stage (Stage I), and a growth stage(Stage II). In the ﬁrst stage where the solution concentration
reaches the critical supersaturation, the nucleation process starts.
The nuclear size is determined by the synthesis temperatureand the degree of supersaturation. The critical radius of nuclei isgiven byr c ¼ 2gv=RTln s

ð1Þ

where g is the interface energy, n is the molar volume of thecrystalline phase, R is the gas constant, T is the absolute temperature, and s is the degree of supersaturation. The equation
represents that the critical nuclear radius is inversely proportional to a logarithm of the degree of supersaturation, which
depends on the saturating concentration and the concentrationsof precursors. After nucleation, the solution concentration begins
to decrease and falls below the critical supersaturation again,
then the growth stage starts. In Stage II, the nuclei grow and the
QD size increases. Then the solution concentration settles down
to the saturation solubility and the growth of QDs almost
completely stops.
Fig. 1 shows the evolution of PL spectra with respect to time
during the growth of the PbS QDs synthesized at (a) 70 and (b) 80 1C,
when the molar ratio of precursors, PbCl2:S:OLA¼10:1:24. The full
width at half maximum (FWHM) and the wavelength of theluminescence peak are also plotted as a function of synthesis timein Fig. 1(c) and (d). With the synthesis time increasing from 1 toFig. 1. Time evolution of PL spectra of the PbS QDs synthesized at (a) 70 and(b) 80 1C, when the molar ratio of precursors is PbCl2:S:OLA¼ 10:1:24. (c) Fullwidth at half maximum (FWHM) and (d) the peak wavelength of the luminescencepeak plotted as a function of synthesis time.

25 min, the luminescence wavelength of the QDs exhibits red shifts of1221–1288 nm for 70 1C and of 1282–1370 nm for 80 1C. These peakshifts correspond to the increases in the size of QDs. In both cases,
the nucleation of PbS nanocrystals in the initial stage immediately
ﬁnishes, and then the crystal growth starts and the growth rate
gradually slows down. This means that the growth rate depends on
the amount of available precursors. A notable difference in the
wavelength after 1 min between these two temperatures can beobserved, which suggests that the critical radius, rc, of the PbS nuclei
synthesized at 80 1C is larger than that of the nuclei synthesized at
70 1C. Generally, the saturating solubility of precursors increases athigher temperatures. Therefore, in the synthesis condition at 80 1C,
the supersaturation, s, is lower than that for 70 1C. According to Eq.
(1), the lower s at 80 1C gives rise to a larger rc compared with thecase of 70 1C, even though T becomes higher. In this case, the criticalsupersaturation also increases, which makes the duration time of thenucleation stage shorter. As a result, the size distribution of PbS nuclei
becomes narrower, which is consistent with the fact that the FWHM
of the luminescence peak for 80 1C is totally smaller than for 70 1C.
After 10 min, however, the FWHM of the luminescence peak for 70 1C
rapidly decreased, while that for 80 1C slightly but clearly increases.
This increase is presumably due to the effects of Ostwald ripening or
agglomeration.
Fig. 2 displays the bright-ﬁeld TEM images of PbS QDs
synthesized for 1 and 15 min at 70 and 80 1C, respectively. The
insets show the size frequency histograms for the QDs. The
estimated values of the QD sizes and the standard deviations
were summarized in Table 1. With increase in the temperatureand the synthesis time, the average size increases and thestandard deviation decreases. The tendencies are mostly

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539

Fig. 2. Bright-ﬁeld TEM images of PbS QDs synthesized at 70 1C for (a) 1 min and (b) 15 min and at 80 1C for (c) 1 min and (d) 15 min. Insets: histograms of QD size.

Table 1
QD average sizes, standard deviations, and symmetry indexes analyzed using the
TEM images.
Temperature (1C)70

Synthesis time (min)Average size (nm)Standard deviation
Symmetry index

1
4.47
0.920
0.60

80
15
5.30
0.572
0.72

1
4.53
0.527
0.58

15
6.27
0.468
0.63

consistent with the increase in the wavelength of PL emission
peak and the decrease in the FWHM, as shown in Fig. 1.
We also changed the amount and the ratio of precursors toinvestigate the effect of these conditions on the crystal growth
and the size uniformity of QDs. The time evolution of PL spectra
for PbS QDs synthesized at 70 1C at the PbCl2:S:OLA ratio of
7.5:0.75:24 is shown in Fig. 3(a). The FWHM and the wavelengthof the PL peak are plotted in Fig. 3(b) and (c), respectively.
Compared with the QDs synthesized at the PbCl2:S:OLA ratio of
10:1:24, a wider wavelength shift from 1239 to 1327 nm andrelatively narrower FWHMs were observed. In the lower concentration of precursors, the degree of the supersaturation, s, wasdecreased, resulting in a short nucleation stage. The number of
PbS nuclei that grew within the short period of time is so smallthat the size distribution would become narrower. In addition, thelow s provides a situation in which larger-critical-radius nuclei
are energetically stable (Eq. (1)). Therefore, the crystal growth ofFig. 3. (a) Time evolution of PL spectra of the PbS QDs synthesized at 70 1C whenthe molar ratio of precursors is PbCl2:S:OLA¼ 7.5:0.75:24. (b) Full width at half
maximum (FWHM) and (c) the peak wavelength of the luminescence peak plotted
as a function of synthesis time.

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S. Nakashima et al. / Journal of Crystal Growth 378 (2013) 537–541

the nuclei progresses further into a size larger than that in thecase of the higher s.
In Fig. 4(a), the time evolution of PL spectra for PbS QDs
synthesized at 80 1C at the PbCl2:S:OLA ratio of 10:2:24 is shown.
The variations of FWHM and the position of luminescence peaks as afunction of synthesis time are also plotted in Fig. 4(b) and (c),respectively. The amount of available sulfur was doubled in thiscondition compared with the ratio of 10:1:24 (Fig. 1(b)). Hence, theFig. 4. (a) Time evolution of PL spectra of the PbS QDs synthesized at 80 1C whenthe molar ratio of precursors is PbCl2:S:OLA¼ 10:2:24. (b) Full width at half
maximum (FWHM) and (c) the peak wavelength of the luminescence peak plotted
as a function of synthesis time.

supersaturation was relatively increased, leading to a longer time of
nucleation stage. As a result, a wider size distribution of nuclei was
obtained, as shown in Fig. 4(b). Meanwhile, the critical radius of QDs
was expected to be smaller for a higher supersaturation condition. In
Fig. 4(c), however, the luminescence peaks appeared at the longer
wavelength compared to the ratio of 10:1:24, suggesting that larger
particles were formed. This can be explained as follows. However, thecritical radius at the PbCl2:S:OLA ratio of 10:2:24 is relatively smallerin the nucleation stage. On the other hand, the doubled amount ofsulfur presumably induces the signiﬁcant increase in the number of
PbS clusters. Unstable clusters, the size of which does not reach thecritical radius, can contribute to the crystal growth, resulting in muchhigher growth rate. Therefore, after the nucleation stage, the size of
PbS QDs rapidly increases, and then exceeds to that in the case of theratio of 10:1:24. Zhao et al. also reported the peak shift as a functionof synthesis time in a variety of ratios of precursors, which shows thesame tendency as our results [11].
For the purpose of evaluating the suitability of the synthesized
PbS NCs for the source of entangled photon pairs, quantitative
measurement of spherical symmetry is particularly indispensable.
Generally, the in-plane symmetry of the SK-type QDs can be
examined using grazing-incidence X-ray diffraction (XRD). Sincesuch QDs are epitaxially grown on single-crystal substrates, longaxes of elongated NCs align along the speciﬁc crystalline orientationof substrates. By contrast, the shape of chemically synthesized
colloidal NCs is not necessarily elongated or uniaxially anisotropic.
In addition, since the NCs are dispersed with no orientation inaqueous solutions or organic solvents, the particles do not align along
one direction. Thus, the measurements give spatially- and timeaveraged information about the shape symmetry of NCs usinggrazing-incidence XRD. Therefore, direct evaluation of the sphericalsymmetry of QDs using the TEM results is the only available method
at present. We selected about 200 particles at random in TEM
images, and maximum inscribed circles and minimum circumscribedones were systematically determined for each particle. A symmetryindex is calculated as an average of the ratio of diameters (Dmin/Dmax)

Fig. 5. (a) Schematic illustrations of the determination of symmetry indexes for distorted nanocrystals. High resolution TEM images of QDs synthesized (b) at 70 1C for
15 min at PbCl2:S:OLA¼ 10:1:24 (c) at 80 1C for 1 min at PbCl2:S:OLA¼ 10:1:24, and (d) at 80 1C for 5 min at PbCl2:S:OLA¼ 2:1:24. The scale bars represent 5 nm.

S. Nakashima et al. / Journal of Crystal Growth 378 (2013) 537–541

for all of the particles, as illustrated in Fig. 5(a). High-resolution TEM
images of these PbS QDs synthesized at three different conditions areshown in Fig. 5(b)–(d). The calculated index values are summarized inTable 1 for the PbS QDs synthesized for 1 and 15 min at 70 and 80 1C,
respectively. For lower synthesis temperature and longer synthesis
time, the symmetry index tended to be higher. Since higher temperature is advantageous for the homogeneity of the particle size, it is
difﬁcult to obtain QDs with both highly spherical symmetry andnarrow size distribution. According to Fig. 1(d), the PbS QDs synthesized under the two different conditions (at 70 1C for 15 min and at
80 1C for 1 min) provided the luminescence peaks at the same
wavelength of 1282 nm. The estimated symmetry indexes were0.72 for the former and 0.58 for the latter. For the lower synthesis
temperature, that is, the higher supersaturation, a relatively larger
number of small nuclei will be precipitated at the ﬁrst nucleation
stage, leading to the slower-rate growth of the particle, which isconsistent with the fact that the PL-peak shift at the condition of
70 1C is smaller than that of 80 1C. If the particle growth progressed
rapidly, the spherical symmetry of QDs would be expected to belower because of an anisotropic crystal growth in directions preferable for a stable crystal structure. Thus, it is speculated that the highly
symmetrical PbS QDs were achieved due to the slower-rate condition
induced by the higher supersaturation.

4. Conclusions
Colloidal PbS QDs were chemically synthesized in organic
solvent, OLA, as a ligand under a variety of conditions. At lower
synthetic temperature or higher concentration of precursors, thedegree of supersaturation becomes higher, leading to the precipitation of larger amount of nuclei with a smaller critical radius.
In this case, the PL peaks had a relatively wide FWHM, suggesting
the wide distribution of particle size of the nuclei. In contrast, at
higher temperature or lower precursor concentrations giving rise
to lower supersaturation, the larger particle size and the narrower
distribution of PbS nanocrystals can be obtained. Symmetry541

indexes for PbS QDs with diameters of about 1.3 mm were
evaluated using TEM images. This comparison clariﬁed that lower
reaction temperature, higher supersaturation, and longer growing
time are suited for the synthesis of spherical PbS QDs which canbe a promising candidate as the source of entangled photon pairs
in the infrared region.

Acknowledgments
This study was ﬁnancially supported by Grants-in-Aids for
Scientiﬁc Research (B) and Young Scientists (B) from the Ministryof Education, Culture, Sports, Science, and Technology (MEXT),
Japan, and by the Nippon Sheet Glass Foundation for Materials
Science and Engineering.
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