Quantum Dots

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Quantum Dots
Sofie Ye
December 10, 2014
Course:
Supervisor:

Colloidal and surface chemistry
Erik Johansson
Abstract

The concepts and importance of nanotechnology are briefly discussed.
Basic theory facilitating the understanding of the quantum confinement effects in a certain class of nanomaterials called quantum dots follows and
thereafter, the most common way to synthesise these semiconductor nanocrystals (colloidal synthesis) is described. Furthermore, some general information about the many application fields for quantum dots is included.

Figure 1: “Quantum Dots with gradually stepping emission from violet to deep
red are being produced in a kg scale at PlasmaChem GmbH” From: Wikimedia Commons.
(2012) Quantum Dots. Retrieved 9 December, 2014.

Contents
1 Introduction
2 Theory
2.1 Surface effects . . . . . . . . .
2.2 Quantum confinement effects .
2.2.1 The density of states .
2.2.2 The band gap . . . . .
2.3 Quantum dots . . . . . . . . .

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3 Production
3.1 Colloidal synthesis . . . . . . . . . . .
3.1.1 General outline . . . . . . . . .
3.1.2 The organic-inorganic interface
3.1.3 Kinetic size control . . . . . . .
3.1.4 Kinetic shape control . . . . . .
3.2 Passivation . . . . . . . . . . . . . . .

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4 Applications
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4.1 Biological imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2 Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
References

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1

Introduction

In a review published in the journal Chemical Society Reviews, March 2006, Professor Roduner pointed out that “We might still want to think, though, that gold
is gold, platinum is platinum and CdS is CdS, but we slowly have to get used to
the fact that this is also not true...” (Roduner, [1]). By these words he wanted to
emphasize the fact that many materials exhibit new properties when going from
bulk sizes, down to sizes of the nanoscale. There are no distinct boundaries for the
so called “nanoscopic scale” but in most cases it is considered to include materials
with a size of 1-100 nm [2] (in this review, the “size” is assumed to be the length
or the diameter of the material or particle).
The study of matter at the nanoscale is referred to as nanotechnology. This
term was first introduced in 1986 by Drexler [3] but the concept had been brought
up already in the late ’50s by the physicist Richard Feynman, who in a famous
lecture with the title There’s Plenty of Room at the Bottom, asked “What would
happen if we could arrange the atoms one by one the way we want them?” (Feynman, [4]). This phrase provides us with a definition of nanotechnology as the manipulation of individual atoms, molecules etc. at the nanoscopic scale. However,
this branch of science also includes the applications of so called nanomaterials.
As mentioned earlier in this section, nanomaterials are usually built up by units
of sizes between 1 and 100 nm and in accordance with this, a crystal with at least
one dimension confined to these limits is said to be a nanocrystal.
More specifically, structures confined to the mentioned nanoscale in only one
dimension are called quantum wells, while those confined in two directions are
thought of as quantum wires. In this review, the case where a nanocrystal is
confined in all three spatial dimensions will be studied. Materials of this type have
been given a bunch of names (colloidal particle, pseudo/artificial atom, quantum
sphere, nanoparticle, nanocluster etc. [6]), however the most used one is no-doubt
quantum dots. Figure 2 depicts the density of states (see section 2.2.1) as function
of the dimensionally confined structures named above.

Figure 2: The density of states as a function of the dimensional confinement degree.
From: “Semiconductor Clusters, Nanocrystals, and Quantum Dots” by A. P. Alivisatos, 1996, Science. .

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Due to the highly tunable optical and electrical properties of quantum dots,
they are of great interest to many researchers of today. The application fields
are many and for example, they have been or are used in the development of
solar cells [7], biological imaging [8] and light emitting diodes (LEDs) [9]. In
this review, the basics of quantum dots and how they can be synthesized, will be
covered. Furthermore, some of their interesting applications are brought up.

2

Theory

As stated in the introduction, a nanomaterial is considered to have a size in the
range of 1 to 100 nm. However, this definition is a bit poor since the limit of 100
nm actually is not valid for all materials to be considered as “nano”. A better way
of defining a nanomaterial, would be to look for the region where the material
exhibits properties different from those of both the bulk material (a big piece of
material that is not considered to be confined in any spatial dimension) as well
as the distinct molecules/atoms. During the past two decades, it has been shown
that fundamental properties like melting point, color (i.e. band gap), ionisation
potential, catalytic actvity, magnetism and so on, can be tuned by changing the
size of the material [2]. This is particularly true for semiconductor nanocrystals
(also called quantum dots) [10]. The reason why all those properties vary with
size is usually said to be a combination of two major effects: surface effects and
quantum confinement effects [1]. Since the main topic of this particular study is
quantum dots, the focus will be on the latter.

2.1

Surface effects

Consider the atoms in the bulk and those at the surface of a cluster, it is quite
obvious that they will posess different properties since they are situated in rather
different environments. A surface atom has a lower coordination number (fewer
neigbours) than an atom in the bulk and thus, it is less stabilised and has a higher
affinity to create bonds to e.g. adsorbate molecules.

Figure 3: The increase of the surface-to-volume ratio with smaller volume. The
numbers at the corners of the cubes represents the side length in length units and
the first row of numbers below the cubes shows the surface area in area units. The
second row gives the volume of each cube in volume units and in the last row, the
resulting surface-to-volume ratios are given (in length units). From: The McGraw-Hill
Companies, inc. (2001) Biology Retrieved 8 December, 2014. New York City: Author.

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As can be seen in Figure 3, a small cluster (or particle) will have a larger fraction
of surface atoms than a large one and since surface atoms are less stabilised than
those of the bulk, small clusters have lower melting points than large ones. A
striking example of this is in the case of gold where it has been observed that the
melting point for particles of the size 2.5 nm is about 400 K lower than that of
the bulk [11]. Another property dependening on the so called “surface-to-volume
ratio” is the catalytic activity. In this case, it has been proved that a small gold
cluster, having a higher number of low coordinated surface atoms comparing to a
large cluster, is more reactive and has a higher catalytic activity [12].

2.2

Quantum confinement effects

A bulk material is considered to extend in all three directions. In contrast, a
quantum dot is said to be confined in all three spatial dimensions. Thus, when
going from a bulk material to a quantum dot, there is a dimensional change from 3
to 0. Due to this “gain in confinement”, a quantum dot will exhibit some properties
similar to a “particle in a box” [13].
An essential model in quantum mechanics is the “particle in a box” model,
where a particle is thought of as being trapped in a potential well. The well has
infinitly high walls which can not be crossed by the particle but otherwise, the
particle is free to move. By solving the Schrödinger equation for a particle in a
box, the allowed quantised energy levels for the particle can be determined.
The crucial part of the section above is the fact that a particle in a box has
quantised energy levels, because that is the property which is “inherited” by quantum dots due to spatial confinement. Following subsections will go a bit further
in the discussion of this phenomena.
2.2.1

The density of states

Discrete atoms have well-defined atomic orbitals of certain energies. Each orbital
has a characteristic wave function and can be combined to, as a first step, form
molecular orbitals (MOs). Also these, are rather well-defined concerning energy
and thus, have individual wave functions. At this point the energy difference between successive energy levels is still distinguishable. Nonetheless, as more atoms
are added, the difference between adjacent energy states decreases and eventually,
this leads to the formation of so called bands. In other words, a band is just a
way of describing a huge amount of energy states so tightly packed that there is
no reason to even try disjuncting them.
The number of energy states divided by the energy interval covered by a band,
is called the denisty of states (DOS). And so, it is also possible to to describe the
progress of the electronic structure when going from a discrete atom to a large
crystal as an increase of the DOS.
A nanocrystal can be thought of as being the “transfer structure” when going
from an unlimited crystal to individual molecules or atoms. Consequently, its
electronic structure lies somewhere in between the continuous band of a typical
crystal and the discrete DOS for separated molecules/atoms [14], see Figure 4.
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(a) Metal

(b) Semiconductor

Figure 4: The DOS in a metal (a) and a semiconductor (b), respectively. The
variation of the electronic structures in their corresponding bulk, nanocrystal and
atomic/molecular form are shown. From: Alivisatos, A. P. (1996) Perspectives on the Physical
Chemistry of Semiconductor Nanocrystals. Retrieved 9 December, 2014.

2.2.2

The band gap

Not all of the energy states are filled with electrons and a special name, the band
gap, has been assigned to the energy difference between that of the highest occupied
MO (HOMO) and that of the lowest unoccupied MO (LUMO). In band theory, the
energy states lower than the HOMO are considered to be part of the valence band,
while those of energies higher than the LUMO are said to constitute the conduction
band. The band gap is usually given in eV and depending on its magnitude, a solid
is considered to be a metal, semiconductor or insulator, see Figure 5.

Figure 5: General band structures for different solids.

From: Wikimedia Commons. (2006)
“A comparison of the band gaps of metals, semiconductors and insulators.” Retrieved 9 December, 2014.

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2.3

Quantum dots

In the process where a material goes from a smaller to a larger size, i.e. when
becoming more bulk-like, the center of a band will appear before the edges. That
is to say, the energy states in the middle of a “soon-to-be” band adopt to the new
band structure before the edges does. This is illutrated for a metal in Figure 4a
and for a semiconductor in Figure 4b.
Both Figure 4b and 5, shows that the Fermi level of a metal lies in the center of
a band while that of a semiconductor is located in the middle of a band gap (this
is true for an undoped semiconductor). Therefore, the Fermi level of a metal is
almost not affected at all when going from bulk to nanocrystal (since the changes
are most significant at the edges and not in the middle). The Fermi level of a
semiconductor though, will be highly influenced by the changes at the band edges.
This explains why the optical and electrical properties of nanocrystals made from
semiconductors (quantum dots) are affected to a much greater extent than those
made from metals, when tuning their size and thus, band gap.
The inversely proportional relationship between the size of a quantum dot
and the size of its band gap, can be proved by performing several spectroscopic
experiments [1]. By considering the fact that a smaller particle will be have a larger
portion of “atom-like” behaviour comparing to a larger particle, it is reasonable to
assume that a smaller particle will also have a larger band gap (more separated
energy levels). The same reasoning holds for the opposite case – a larger particle
behaving more like bulk material, will have a smaller band gap, see Figure 6a.

(a) Band gap sizes
(b) Quantum dot colors

Figure 6: (a) The particle size effect on the band gap. (b) Fluorescence of CdSeCdS core-shell nanoparticles with a diameter of 1.7 nm to about 6 nm. From: Roduner,
E. (2006) Size matters: why nanomaterials are different. Retrieved 9 December, 2014.

For electrons of the discrete energies in the vicinity of the HOMO in a quantum
dot to overcome the band gap and reach one of the discrete energy levels above
the LUMO, quantised amounts of energy are required. The larger the band gap,
the higher the energy needed to overcome it.
High-energy, or high-frequency, wavelengths are short and thus appear as being
“blueish” and low-energy, or low-frequency, wavelengths are long and “reddish”.
Thence, by changing the particle size from smaller to larger, it is possible to tune
the fluorescence of the quantum dots between blue and red [1], see Figure 6b.
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3

Production

Quantum dots can be made through several methods such as epitaxial growth,
optical litography and colloidal synthesis. In epitaxial growth, a crystalline layer
is deposited on a crystalline substrate [15] and in litography, which has some
similarities to common photography, light is used to forward a pattern from a
photomask onto a light-sensitive so called “resist” [16]. “Colloidal synthesis” is the
method which is most related to this course (Colloidal and Surface Chemistry),
which is why it is going to be studied in more detail.

3.1

Colloidal synthesis

The products of this particular synthesis are called colloidal nanocrystals, or in the
case of nanocrystals made from semiconductors, colloidal quantum dots. These are
grown from solution and are typically inorganic particles coated by a stabilising
layer of organic surfactants. The synthesis is based on the introduction of inorganic
precursors to a hot solution containing organic surfactants.
Colloidal synthesis is a great tool for chemists today. By offering the possibility
to regulate parameters like composition; size; shape; surface properties; and crystal
structure (through changing, for example, temperature and/or monomer concentration [17]), it indirectly enables design of the electronic and optical properties of
quantum dots.
3.1.1

General outline

Three main ingredients are needed in order to perform a plain colloidal synthesis:
precursors, organic surfactants and solvents. To start the crystal formation, an
initial thermolysis is required. This is easily done by simply combining the three
components in some kind of container and add heat. When the temperature is
high enough (n.b. low-temperature synthesis is also feasible [18]) for the precursor
to chemically transform into reactive monomers, the nucleation takes place. The
nucleation is, according to IUPAC [19], defined as the inital step of a process in
which a new phase is to be formed.
After the thermal decomposition of precursors in the formation of new nuclei,
the latter will start to grow by including additional free monomers in the solution
to their assembly. Only if the formed nanoparticles are able to simultaneously
rearrange and anneal during the formation, crystalline solids will be formed. Thus,
the outcome of the process is highly dependent on choosing a proper temperature
which allows rearrangement of atoms but at the same time, permits annealing
within the growing crystal.
3.1.2

The organic-inorganic interface

The interface between the inorganic nanocrystal and the organic shell of surfactants
is, according to Yin and Alivisatos [17], of great interest to many researchers. But
why? Well, consider the adhesive energy between the organic surfactants and the
inorganic nanocrystal. This energy has to be in a range where the exhange of
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surfactants, for a given temperature, at the interface is kept at a dynamic level.
Anything else would prevent the growth of the crystal. Probably this is why
this interface is thought to be so “attractive” – the interactions taking place at it
actually determines the possibility of crystal growth.
Organic surfactants at the interface often have electron donating headgroups
(EDGs) such as metal coordination groups and so, they are polar and hydrophilic.
This allows coordination with metals that are electron deficient and thus, prevents
aggregation [17]. The hydrophobic tails of the surfactants construct the outer
surface of the nanocrystal providing it with a hydrophobic coating.
3.1.3

Kinetic size control

Figure 7 illustrates the relation between the growth rate of a nanocrystal and its
size. The dashed line divides the graph in two parts; a “left side” describing what
happens to small clusters; and a “right side” showing the “destiny” of large clusters.
By studying these curves, it is possible to see a small nanocrystal which posess a
high surface-to-volume ratio making it quite unstable, has a negativ growth rate
in a low monomer concentration (blue curve). Another observation is that larger
crystals, which are more stable (having a smaller surface-to-volume ratio) have
positive growth rates in both low and high monomer concentration.

Figure 7: “Size-distribution focusing”

From: Yin, Y.; Alivisatos, A. P. (2005) Colloidal nanocrystal
synthesis and the organic–inorganic interface. Retrieved 10 December, 2014.

The critical size is the particle size when the growth rate is zero. At this point,
the nanocrystal can be thought of as being quite pleased with itself and hence,
does not grow nor shrink.
The rather vague but still existing peak of the blue curve arises from the fact
that larger crystals need a lot more monomers than smaller crystals, in order to
be able to grow even larger. Thus, the growth rate eventually slows down and
reaches a maximum value.
A slow growth rate is favoured by low monomer concentrations. In this case, the
critical size is a bit larger than that in a solution of high monomer concentration
and thus, there is a higher probability that it will be in the same range as the
nanocrystals present in the solution. Due to the effect of “Ostwald ripening”,
when small particles shrink and deposit themselves on larger ones, a broad size
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distribution is obtained. If a less broad distribution is desired. One can perform
so called “size-selective precipitation”, a method where a poor solvent relative to
the nanocrystals, is added a little at the time. Since larger crystals brings with
them stronger electrostatical forces, they will fall out leaving the smaller crystals
dissolved in the solution.
Another way of getting a more narrow size distribution is to apply a method
called “size-distribution focusing”. Here, a solution of high monomer concentration
is used. In such a solution, small clusters are said to have a higher growth rate than
large ones. As monomers are used to build up the crystals, the concentration will
eventually go down and the critical size (where the crystals stop growing) increases.
Continuous injections of monomers can prevent this from happen, keeping the high
concentration and thus, the critical size rather constant. If this is achieved and the
critical size is small enough, all different crystal sizes will find themselves having
a growth rate in the “negative” direction, that is to say all of them will shrink to
smaller sizes and thus, the distribution will be more narrow and focused.
The optimal size focusing is obtained for a monomer concentration with an
average crystal size that is slightly larger than the critical size. Because then, if
the monomer concentration decreases, the critical size will increase to an extent
where it is larger than the average crystal size and then small crystals will deposit
on larger ones due to Ostwals ripening and so on. It is possible to produce large
quantities of narrow size distributed colloidal nanocrystals using “focusing”.
3.1.4

Kinetic shape control

Nanocrystals at equilibrium are generally quite round (minimized surface area).
Although, there are also nanocrystals which have highly anisotropic shapes (a ray
of light would behave differently depending on the propagation direction on its
way through the crystal) and thus, have large surface areas. Once again, talking
about growth rate – low rates give approximately round crystals while rates slightly
higher than where focusing occurs, result in highly anisotropic shapes including
rods, arrows, tetrapods and so on.

3.2

Passivation

One of many ideas of the ideal semiconductor nanocrystal, is “A compositionally
pure collection of atoms, mass-selected, isolated in the gas phase, and thermally
annealed...” (Alivisatos, [14]). In the same review as the one just cited, Alivisatos
states that the observation of such an arrangement would result in the most convincing evidence of the existence of size-tunable properties.
However, compositions of this type are hard to prepare in larger quantities and
evenmore, the surfaces of pure clusters have been shown to be highly defective [10].
This is a consequence of the high surface-to-volume ratio of a nanosized cluster.
As mentioned in section 2.1, surface atoms have lower coordination numbers than
those at the inside of the cluster. In other words, they may have unsaturated
bonds (or orbitals) “dangling” around. Unfortunately, the energy levels of these
dangling bonds often lie somewhere within the band gap of the quantum dot [20],
resulting in a much higher risk of nonradiative “recombination”, i.e. trapping of
10

excitons. Since excitons are the charge carriers of quantum dots, the trapping of
them will degrade both electrical and optical properties.
To prevent this negative effect of surface recombination, passivation is applied.
This is done by covering the quantum dot with a material that has a higher band
gap. Thereby, the orbitals of the surface atoms are saturated and the energy levels
within the “forbidden” gap will be eliminated [1], see Figure 8 for a schematic picture. Encapsulated quantum dots are often referred to as core/shell quantum dots.
In general, they are composed by semiconductors of type II–VI, IV–VI and II–V, where the
roman numbers indicate in which groups (n.b.
old group numbers, thus III is actually 13) of
the periodic table the combined materials are
found. Combinations that have been widely
studied are CdSe/ZnS, CdS/HgS, InAs/CdSe
and CdS/CdSe [21].
At the moment, there seems to be a worldwide agreement among researchers about inorganic coatings being much more beneficial than
organic ones. Almost two decades ago, Hines Figure 8: Illustration describing
and Guyot-Sionnest [22], managed to show that the concept of passivation.
by coating a CdSe colloidal quantum dot with
a shell of ZnS, they could measure a photoluminiscence quantum yield of 50%
comparing to ⇠5-15% for organic shells. The quantum yield improvement has
later been proved to be a persistent trend for inorganic passivation. This is very
promising since the shell also acts like a shield, protecting the core from being
damaged through interactions with the surrounding medium [20]. Figure 9 shows
a simple illustration of a core/shell colloidal quantum dot. Note that even though
the inorganic shell is applied after the synthesis of the colloidal quantum dot (having a layer of surfactants surrounding it), the inorganic coating will be in between
the core and the surfactants.

Figure 9: A core/shell colloidal quantum dot.

From: RUSNANO (2011) High-Tech Synthesis
of Colloidal Quantum Dots Begins in Dubna. Retrieved 10 December, 2014.

11

4

Applications

Due to their size-tunable electric and optical properties, quantum dots are today
used in a wide range of applications from biological imaging [8], light emitting
diodes (LEDs) [9] and solution processed lasers [20], to photovoltaics [20] like solar
cells [7]. Short descriptions of how quantum dots are used in biological imaging
and solar cells are given below.

4.1

Biological imaging

An application that is already commercially used is so called fluorescent tags for
biological imaging. In section 3.2, the improved stability of photoluminiscence by
passivation was mentioned and as a matter of fact, the photostability of quantum
dots has been found to be higher than that of existing molecular dyes [5]. Furthermore, the absorption coefficients of quantum dots are in general very large, while
the emission spectra is rather narrow and therefore, a single excitation source can
produce a wide range of different colours [8].
In biological imaging, quantum dots are covalently bonded to biomolecules like
antibodies, peptides, nucleic acids and so on. These are also called “biorecognition
molecules” and can be used to track other biomolecules like cancer cells etc. Due to
the long luminiscence lifetime, quantum dots are widely used in the development
of in vivo targeting and imaging. Figure 10 shows the in vivo tracking and imaging
of cancer cells in a mice by using quantum dots of different sizes.

Figure 10: “In vivo imaging of multicolor QD-encoded microbeads ”
Ciu, Y.; Levenson, R. M.; Chung, L. W. K.; Nie, S. (2004). Retrieved 10 December, 2014.

12

From: Gao, X.;

4.2

Solar Cells

Quantum dots are used in the production of so called quantum-dot-sensitized solar cells (QDSC, where the organic molecular dye in a typical dye-sensitized solar
cell (DSSC) has simply been exhanged to semiconductor nanocrystals. The quantum dots are the light harvester and these solar cells have already shown nice
results with efficiencies of about 10% for all solid “nano-devices” using lead halide
perovskite [7].

References
[1] Roduner, E. Chem. Soc. Rev. 2006, 35 (7), 583-592.
[2] Roduner, E. Nanoscopic Materials: Size-Dependent Phenomena ; Royal Society of Chemistry: Cambridge, 2006.
[3] Wikipedia. Nanotechnology. [Online] December 8, 2014. Available on internet:
http://en.wikipedia.org/wiki/Nanotechnology (accessed Dec 9, 2014)
[4] Feynman, R. P. Eng. Sci. 1960, 23 (5), 22-36.
[5] Guyot-Sionnest, P. C. R. Physique 2008, 9, 777-787.
[6] Eychmüller, A. J. Phys. Chem. B 2000, 104 (28), 6514-6528.
[7] Fuente, M. S.; Sánchez, R. S.; González-Pedro, V.; Boix, S. G. M.; Rincón,
M. E.; Bisquert, J.; Mora-Seró, I. J. Phys. Chem. Lett. 2013, 4, 1519-1525.
[8] Gao, X.; Ciu, Y.; Levenson, R. M.; Chung, L. W. K.; Nie, S. Nature Biotechnology 2004, 22 (8), 969-076.
[9] Colvin, V. L.; Schlamp, M. C.; Alivisatos, A. P. Nature 1994, 370, 354-357.
[10] Alivisatos, A. P. Science 1996, 271 (5251), 933-937.
[11] Koga, K.; Ikeshoji, T.; Sugawara, K. Phys. Rev. Lett. 2004, 92 (11), 115507.
[12] Hvolbæk, B.; Janssens, T. V. W.; Clausen, B.; Falsig, H.; Christensen, C. H.;
Nørskov, J. K. Nano Today 2007, 2 (4), 14-18.
[13] Buhro, W. E.; Colvin, V. K. Nature Materials 2003, 2, 138-139.
[14] Alivisatos, A. P. J. Phys. Chem. 1996, 100 (31), 13226-13239.
[15] Wikipedia. Epitaxy. [Online] November 23, 2014. Available on internet: http:
//en.wikipedia.org/wiki/Epitaxy (accessed Dec 9, 2014)
[16] Wikipedia. Photolitography. [Online] November 29, 2014. Available on internet: http://en.wikipedia.org/wiki/Photolitography (accessed Dec 9,
2014)
[17] Yin, Y.; Alivisatos, A. P. Nature 2005, 437 (7059), 664-670.
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[18] Siy, J. T.; Brauser, E. M.; Bartl, M. H. Chem. Commun. 2011, 47, 364-366.
[19] IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book").
Compiled by McNaught, A. D.; Wilkinson, A. Blackwell Scientific Publications, Oxford (1997).
[20] Kim, J. Y.; Voznyy, O.; Zhitomirsky, D.; Sargent, E. H. Adv. Mater. 2013,
25, 4986-5010.
[21] Reiss, P.; Protière, M.; Li, L. Small 2009, 5 (2), 154-168.
[22] Hines, M. A.; Guyot-Sionnest, P. J. Phys. Chem. 1996, 100, 469-471.

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