The University of Alabama

Department of Chemistry

Graduate Student Seminar Series

Quantum Dots

Literature Seminar

by

Andrei Honciuc

Tuesday, October 7, 2003

1:00 P.M.

Room 231 Lloyd Hall

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1. Introduction

Nanoparticles are objects made out of metallic, semiconductor or insulating materials that are

much smaller than the wavelength of light. In the last two decades there has been much research on

nanoparticles made out of semiconductor materials, especially on II-VI semiconductor types, e.g.

CdSe, CdTe, CdS, ZnS, etc., and III-V, e.g. GaAs.

In 1980’s Louis Brus at Bell Labs, and Alexander Efros in the Soviet Union, were trying to

explore the advantages given by surface to volume ratio in semiconductor nanocrystal particles for

solar energy conversion. It has been observed that different solutions made out of the same

semiconductor nanocrystal exhibit strikingly different colors. That was the first time that scientists

became aware of the quantum confinement effects produced by the change of bulk semiconductor

electronic properties with decreasing size. This transition occurs when the nanostructures themselves

become smaller than a fundamental scale intrinsic to the substance. It was later proven that the exciton

Bohr radius determines this intrinsic scale. Since this intrinsic fundamental scale is determined by

hydrogen atom model of the exciton Bohr radius they were named ‘quantum dots’ or ‘artificial atoms’.

Quantum dots fall into the category of zero dimensional structures. They are composed of few

thousand atoms that keep the structural features of the bulk solid but particularly different electronic

properties as a function of their size.

Currently the research in this field is extremely rich and hundreds of papers are published every year.

Quantum dots are mainly targeted for use in biological applications. Their areas of applicability may

extend soon to where ever semiconductors are used: LEDs, tunable lasers, telecommunications,

quantum computing, etc. Although they are not yet available on the market, a few start-up companies

such as ‘Qdot- Quantum Dot Corporation’ and ‘Evident Technologies’, promise to introduce

quantum dots based products into the diagnosis and research market this year.

2. Synthesis

Quantum dots can be made as colloidal solutions or can be made on solid substrates.

2.1. Colloidal solutions

In this method precursors are reacted in the presence of a stabilizing agent that keeps them from

aggregating. The simplest synthetic route, proven to produce high quality samples (CdE, E= S, Se, Te)

is TOPO/TOP method10 (the name of the method comes from the capping group). Although this

method is presented for CdSe, can be applied for all semiconductor nanocrystallities. All the synthetic

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work has to be done in a inert atmosphere in order to avoid the oxidation of the material. The synthesis

for monodisperse samples of CdSe consist of three steps:

• Nucleation and growth of nanocrystallites. The reaction media n-tri-n-octylphosphine oxide has to

be heated to 300 0C, purged with argon, in order to eliminate any trace of water and oxygen. The

precursors, namely Me2Cd and TOPSe (tri-n-octylphosphine selenide), have to be premixed, in a

1:1 ratio and injected rapidly into the reaction media TOPO:

CdH3C

H3CCH3 (CH2)7 P Se+ CdSe + CH3 (CH2)7 P

3 3

CH3

CH3

TOPO

CdSe nanocrystallites grow under continuous heating conditions ~ 300 0C. Active surface centers

of the nanocrystallite are bonded to TOP/TOPO, called capping groups. These capping groups

prevent nanocrystallites from aggregating. Aliquots of the reaction solution are taken out and the

absorption spectra are recorded to monitor the growth process. Heating is stopped when the desired

features in absorption spectra are observed. In this way CdSe nanoparticles with size distribution

range from 15-115 Å are produced.

• Isolation and purification. The reaction solution obtained is then treated with anhydrous methanol

in order to isolate the quantum dots. After methanol treatment, a flocculate is obtained due to

insolubility in the short chain alcohols and then separated by centrifugation. The flocculate that

contains the nanocrystals of various sizes undergoes a purification process. The flocculate is

soluble in 1-butanol. A further flocculation with anhydrous methanol, followed by centrifugation

and vacuum drying produces a powder of TOPO/TOP capped CdSe nanocrystallites. The powder

obtained is soluble in various solvents: alkanes, aromatics, long-chain alcohols, chlorinated

solvents, amines, pyridine, furan, and phosphine.

• Size-selective precipitation. Size selective precipitation can be carried out in solvent/nonsolvent

pairs, e.g. pyridine/hexane and 1-butanol/methanol, further flocculation and centrifugation will

enrich the flocculate in larger size crystallites.

3. Surface Chemistry

Quantum dots obtained in this way will be surface capped with TOPO and TOP. Surface ligand

is labile and can be transiently displaced by sequential addition of Se2+ and Cd2+, which grow on the

seed to make a larger crystallite. Exposing the quantum dot’s surface to a competing capping agent can

further derivatize the nanocrystallite’s surface.28

3

Ex:

Se

OPOP

OP

OP

OP

OP

OP OP

CdSe

On the surface of the original nanoc

quantum dot is obtained. For practic

increase the emission quantum yield

O P

O P

OP O P

O P

OP

O P OP

C d S e

In order to make them useful in aqu

hydrophilic agents22, e.g. mercaptop

OPO

OO

POP

OP OP

ZnSCdSe

P

OP

PHS

4. Electronic Properties

4.1. Bulk semiconductor electronic p

Semiconductor materials ha

generated by the overlap of the o

conduction band generated the ove

PhSeTMS

Se Se

SeSe

Se

Se Se

CdSeOP

rystallite can be grown another type of semiconductor. A core/shell

al reasons a higher band gap semiconductor material is added e.g.

.29 This process is called surface passivation.

OPOP

OP

OP

OP

OP

OP OP

ZnSCdSeZn(S2CN Me Hex)2/TOP

eous media quantum dot’s surface can be further derivatized with

ropyl-tris-hydroxy-silane:

S SiO H

O HO H

S

S

SiHOO H

O H

S

SiHO OH

O H

S Si

O

OH

S O

S

SiHO

OH

O

S

SiOH

Si

OH

O H

O H

pH~10

SiOHO HHO

S

Si OHOH

HO

roperties

ve their electronic structure orga

ccupied energetic levels of the

rlap of the unoccupied levels. G

4

-H2O

SiOH

O

S

Si

OH

HO

nized in bands: a valence band

individual structural units and a

enerally the conduction and the

valence band in bulk semiconductors are continuous if intraband energetic spacing is smaller than kT

(T is the temperature).

The band gap of a semiconductor is by definition, the energy that is required to create an electron-hole

pair, at rest with respect to each other in the crystal lattice and far enough apart so their Coulomb

interaction is negligible. Once the electron is promoted into the conduction band a hole is left behind in

the valence band; the semiconductor becomes conductive and the electron and hole move freely on the

expense of their kinetic energy. The transition from the ground state to the excited state occurs as a

result of some external perturbation, e.g. a photon. The energy conservation relation in the crystal is

given by:

(1) heg EEE ++=υh

If the charge carriers approach each other around a local defect they may form an electron hole bound

pair that is localized over few lattice constants6 and are held together by the electrostatic attraction.

This electron hole bound pair is called a Mott-Wannier exciton. However this electron hole pair carries

no charge.8

For a localized electron-hole pair, the electron and hole interact via the

Interaction between electron and hole can be described by a hydrogen-like Ham

a)

Kr

Figure 1. a) Free electron and hole moving freely in semiconductor solid- Egap is the energelectron hole pair- Wannier exciton and its energy levels that lie in the band gap of the swave vector of the exciton moving in a periodic lattice Binding energies of the Wanniertens of meV.

|rr|e

2M2H

he

22h

22e

2

−−∇−∇−=

εµhh

where the M is the total mass M= me*+mh* and µ is the reduced mass µ= m

and mh* are the effective masses of the electron and hole. The hydrogen-like H

corrected for the relative dielectric constant 1≠ε .

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electrostatic attraction.

iltonian (cgs units):

b)

y of the band gap; b) Boundemiconductor solid. K is the excitons are on the order of

(2)

e*mh*/ (me*+mh*); me*

amiltonian, Eq.2 is also

The first term in the Eq.3 is the Hamiltonian of a free particle with the mass M that describes

the translation motion energy of the electron-hole pair. The second term and the third term in Eq.2 give

rise to a second Hamiltonian of a free particle with the reduced mass µ. The second Hamiltonian gives

the allowed energy levels between electron and hole in other words the energy of the internal states as

for the hydrogen atom.

In the hydrogen atom the radius of the most probable orbit is called Bohr radius a0 (0.53 Å).

Similarly, Bohr radius of the exciton α equals the Bohr radius of the hydrogen a0, but corrected by the

dielectric constant of the medium ε in which the particle moves and the effective masses me*, mh*:

α = (εr a0 me)/µ (3)

The electron energy states that are given by the second Hamiltonian in the Eq.2 are:

2y

n n*R

E −= (4)

where Ry* is the Rydberg constant corrected for exciton Ry*= e2/2α.

The energy that is necessary to obtain the excited state (the exciton energy given by Eq.3) is:

(5) M2K

n*RyE)K(E

22

2gnh

+−=

where K is the exciton wave vector.

Eq.5 includes the band gap energy Eg, hydrogen-like set of energy levels and the kinetic energy

of the translation motion that is negligible compared to electrostatic interaction energy. We can

conclude that the exciton energy levels lie in the band-gap of the semiconductor and are treated as

shallow traps, as seen in Fig.2.

4.2. Quantum Dot electronic properties

When quantum dot’s size is smaller than the exciton Bohr radius, r < α, the electron hole pair

energy levels in quantum dots cannot be treated further based on hydrogen model. The lowest energy

level of the exciton is now delocalized over the entire quantum dot.11 The Coulomb interaction is

completely neglected and the electrons and holes are taken as free particle in a dot.9 The exciton levels

are given by solving the classical quantum mechanical problem of a particle in a box. For the case

where the electron and the hole are confined in a small space, the Coulomb attraction is negligible

small compared to a potential U(r) that describes a spherically symmetric potential well of length r.

The corresponding Hamiltonian is:

)r(U

|rr|e

m2m2H

her

22h*

h

22e*

e

2

+−

−∇−∇−=ε

hh(6)

6

The energy necessary to obtain this excited state is:

(7) 2

22

r2EgE

⋅⋅

+=µ

πh

where the second term describes the energy levels of a particle of mass µ in a spherically symmetric

potential box.

Eq.7 explains qualitatively very well the quantum size effects in quantum dots: the increase of

interband energy separation with the decrease of quantum dot size.

Quantum Dot Semiconductor type

m*e Electron effective mass

m*h Hole Effective mass

Reduced mass µ

εr Dielectric constant relative to vacuum

α(Å)

CdSe 0.13 0.45 0.108 10.1 61

CdS 0.21 0.68 0.16 9.4 34

ZnS 0.34 1.76 0.29 8.9 18

GaAs 0.067 0.082 0.036 13.2 216

InSb 0.014 0.42 0.013 17.3 785

Table 1. Calculated exciton Bohr radiuses for various semiconductor types quantum dots function of effective

mass and dielectric constant based on Eq. 4.

α is the intrinsic parameter that determines the size condition of a specific semiconductor

material for the transition from bulk characteristics to quantum size effects. If from a bulk

Figure 2. Correlation diagram of the electron energy states that should exist in bulk semiconductors and quantum dots. When nanocrystallities size becomes commensurable with α (Bohr exciton radius), the distinction between shallow traps and broad electronic bands ceases. The deep traps are correlated with the existence of the lattice defects. Exciton lowest energetic state is slightly smaller than the semiconductor band gap Eg. From ref. [5]

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semiconductor apiece smaller than α is cut then the lowest energy of the exciton is delocalized over the

entire quantum dot, as seen in Fig.2.

5. Optical Properties

Optical properties of quantum dots depend on their electronic properties. The exciton is

expected to appear in the absorption spectra as a shoulder right before the band edge absorption

features, as in Figure 3a.

115Å

b)a)

Figure 3. a) Schematic representation of the absorption spectrum of a bulk semiconductor; the energy ranges frommicrowave to X-Ray. From reference [17]; b) Room temperature absorption spectra for different size CdSe nanocrystallitesdispersed in hexane and ranging in size from 12 to 115 Å. Reference [10].

5.1. Absorption

Quantum size effects that are very well predicted by the box model can be also observed in

absorption spectroscopy. The absorption bands shift to higher energies with decreasing quantum dot

radius, “blue shift”. It can be seen that the optical band gap is blue shifting dramatically from the bulk

size value to the quantum sizes, e.g. in Figure 3b, for the CdSe with bulk value of the optical band gap

at the 716 nm10 (~1.68 eV). In Fig.3b the absorption spectrum for a quantum dot of 115Å in size is

broad and featureless, characteristic to the bulk absorption spectrum. Bellow exciton Bohr radius the

absorption spectra exhibits a fine structure. Appearance of a fine structure absorption spectrum is due

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to the presence of discrete energy levels. Since the exciton levels become delocalized over the entire

quantum dot the absorption spectra of this quantum dots will be dominated by the exciton transitions.

5.2. Oscillator strength

The intensity of a UV-Visible absorption band is a function of the energy of the transition and

to the square of the oscillator strength.6 In a bulk semiconductor, the electron and hole are bound

together by the Coulomb attraction with binding energy of a few to tens of milielectronvolts. This

exciton is easily ionized at thermal energies, which accounts for the absence of the ‘strong exciton

bands’ in bulk semiconductors at room temperature.

The oscillator strength for the bound exciton is given by:

222 |)0(U|||Em2f µ∆h

=(10)

where m is the electron mass, ∆E is the transition energy, µ is the transition dipole moment, and |U(0)|2

represents the probability of finding the electron and hole on the same site (the overlap factor) Figure

3b. By confining the electron and hole in a small cluster, the binding energy and the oscillator strength

increase due to the enhanced spatial overlap between the electron and hole wave functions.

5.3. Photoluminescence

The emission characteristic of most of the quantum dots consists of a single-broad emission

band, which is symmetric and comes from states that fall in the quantum dot’s band gap. These states

are not detectable in absorption spectra.11, 12 Photoluminescence excitation spectroscopy may help

distinguish the substructures that are present in the inhomogeneous absorption spectra. However, the

interpretation of the emission spectra is much more difficult to interpret than for the absorption spectra.

The emission in CdSe quantum dots has an unusual long recombination lifetime of ~ 1 µs compared to

that in the bulk of few nanoseconds. Moreover trapping of an exciton by the surface state defects may

lead to nonradiative recombination pathways and thus fluorescence quenching. Coating the quantum

dot with a higher band gap inorganic material has been shown to improve the photoluminescence

quantum yields by passivating the nonradiative recombination sites16, e.g. (CdSe) ZnS core-shell

quantum dots. Quantum yield of the photoluminescence increased from about 5% to 30-50% for this

particular case. In very homogenous high quality QDs samples it has been observed that the

fluorescence band exhibits a blue shift with decreasing size and they can be tuned from 470 to 625 nm,

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spanning most of the visible spectra. This is a very important property for application of the quantum

dots as bio-tracers.

6. Applications

There are many applications that have been proposed for quantum dots: transistors, display

devices, “quantum bits” 19, lasers, LEDs, demultiplexers in optic fibers etc. Below are described few

examples.

6.1. Bioimaging

By far the most important application today is in biological imaging. Fluorescence labeling of

specific compartments in cells is a widely used method in biology to visualize structural units that, due

to lack of contrast or resolution, cannot be distinguished by just recording an image. The idea is to

chemically link a fluorescent dye to a biomolecule that binds specifically and selectively to a certain

compartment in the bio specimen.18, 25, 26, 30 Current biosensors use fluorescent-based dyes; these dyes

emit light over a broad spectral width – which limit their effectiveness to a small number of colors –

and they also degrade over time under the microscope (phenomenon called “bleaching”). Core/shell

CdSe/ZnS semiconductor nanocrystals are more robust fluorescent probes with size tunable emission

properties. A shell of higher band gap semiconductor material can increase dramatically the brightness

of quantum dots and protect them from photo bleaching. The surface of the quantum dots can also be

chemically modified in such a way that the quantum dot can be chemically linked with a biomolecule

that binds specifically to the target.

6.2. LED’s, tunable lasers

Quantum dot materials can provide superior performance in lasing applications compared to

bulk semiconductors. In the zero dimensional (0 D) quantum dots the separation between energy

states is greater than the thermal energy of the charge carriers; this inhibits the thermal

depopulation of the lowest, “emitting” transition, phenomenon that confers high-temperature

stability and a narrow spectral emission width.23 Lasing was initially observed for CdSe quantum

dots, imbedded in a glass matrix, in an optically pumped device. Lasing effect by electrical

pumping (carrier injection) can also be achieved.

In quantum dots more than one electron can be excited; every discrete electron and hole energy

state can be populated either by one or by two particles with different spin orientations. The

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creation of the first electron-hole pair results in absorption saturation; the creation of two pairs with

respectively oriented spin is called population inversion or optical gain. The two electron-hole pair

states are classified as biexciton.24 Lasing effect results from the stimulated decay of a biexciton

into a photon and exciton.

6.3. Quantum Computing

It has been imagined that an arrangement of for quantum dots could be an ideal structure for

building quantum computing cell, as in Figure 4a and 4b. For example if in an arrangement of four

quantum dots placed in the corners of square cell two more electrons are introduced then the

electrons will tend to occupy the opposite corners to minimize their reciprocal interaction; quantum

dots are placed very close to each other so that the electron can tunnel from one quantum dot to

another. In this way a logic state can be represented. Further if the electrons are forced to switch

into opposite quantum dot corners then another logic state can be represented. The idea that a real

possiblity for aligning two or more quantum dots in a pattern that could enable the reprentation of a

logic state seemed imposible only few years ago. Last year researchers from Fujitsu laboratories

were the first to achieve such performance, by electron beam lithography and local induced

oxidation by conductive AFM techniques, Figure 4c.

e-

e-

e-

e-

c)b) a)

01

Figure 4. a) and b) proposed arrangement of four quantum dots that represent a logic state ‘1’ in a) and ‘0’ in b); c)

arrangement of GaAs quantum dots on a solid substrate achieved by e-beam lithography and conductive AFM. Adapted

from Ref. [27]. The electron can travel from one corner to the next corner of the square by tunneling.

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