Quantum Dots
What is a quantum dot?
• In two words, a semiconductor nanocrystal.
• Easily tunable by changing the size and
composition of the nanocrystal
Gallium Arsenide Quantum Dots
• Gallium arsenide is a III-V semiconductor
– Higher saturated electron velocity and higher
electron mobility than silicon
– Gallium arsenide can emit and absorb light, unlike
silicon
• No silicon laser is possible (or has been made yet)
Energy Band Levels
• Electrons exist in discrete
energy levels in bulk
semiconductor material.
– There exists a forbidden
range of energy levels in any
material called the band gap.
• By absorbing some sort of
stimulus (in light or heat
form), an electron can rise to
the conduction band from the
valence band.
– This action leaves behind a
“hole” in the valence band.
The hole and the electron
together are called an exciton.
• The average distance
between an electron and
a hole in a exciton is
called the Excited Bohr
Radius.
• When the size of the
semiconductor falls
below the Bohr Radius,
the semiconductor is
called a quantum dot.
Tuning Quantum Dots
• By changing size, shape,
and composition,
quantum dots can
change their absorptive
and emissive properties
dramatically
Manufacturing methods
• Electron beam lithography
• Molecular beam epitaxy
Electron Beam Lithography
• Electrons are accelerated out
of an electron gun and sent
through condenser lens
optics directly onto a wafer
• λ = (12.3 Å / √V)
• Advantages:
– generation of micron and
submicron resist geometries
– greater depth of focus than
optical lithography
– masks are unnecessary
– Optical diffraction limit is not a
real concern
Electron Beam Lithography
• Disadvantage(s):
– The lithography is serial
(masks aren’t used; instead
the beam itself sweeps across
the wafer) => Comparatively
low throughput ~5 wafers per
hour at less than 1 micrometer
resolution
– The proximity effect:
Electrons scatter because they
are relatively low in mass,
reducing the resolution.
• Heavy ion lithography has
been proposed, but still is in
development stages
Molecular Beam Epitaxy
• Molecular beam epitaxy (MBE) is the deposition of
one or more pure materials onto a single crystal wafer
one layer of atoms at a time in order to form a perfect
crystal
– This is done by evaporating each of the elements to
combine, then condensing them on top of the wafer.
– The word “beam” means that the evaporated atoms only
meet each other on the wafer
Artificial Atom
• Double Barrier
Heterostructure
• Dot: In0.05Ga0.95As
• Source &Drain : GaAs
• 2D Electron Gas
• Confine with gate bias
• D ~ Fermi wavelength →
Discrete energy levels
Adding Electrons, changing Vgate
• 2D-Harmonic Oscillator
• Shell structure as in
atoms
• Magic Numbers: 2, 6,
12...
• To add “even” electron
requires only additional
Coulomb energy
Comparison with Hydrogen
• Artificial Atom:
• Hydrogen:
Energy levels ~
1meV
Energy levels ~ 1eV
Size ~ 10μm
Only strong magnetic
fields can perturb energy
levels
Weak magnetic
fields can affect
energy levels
Size ~ 1Å
Factor 1000...
Tuning the Quantum Dot
• Tune so we have one
valence electron
• Initial state can be set by
applying homogeneous
magnetic field → |0>
• Low temperature:
kT
< ΔE (state gap)
• Now we have defined our
single qubit
Energy
Unoccupied state
Gate bias
Spin up - electron
position
The Physical System: Excitons
Trapped in GaAs Quantum Dots
• Exciton - a Coulomb correlated electronhole pair in a semiconductor, a
quasiparticle of a solid.
• Often formed when photons excite
electrons from the valence band into the
conduction band.
• Wavefunctions are “hydrogen-like” i.e.
an “exotic atom” though the binding
energy is much smaller and the extent
much larger than hydrogen because of
screening effects and the smaller
effective masses
• Decay by radiating photons. Decay time
~50ps-1ns
• Hence can define the computational basis
as absence of an exciton |0>, or existence
of an exciton |1>
Stufler et al.
Large wafer containing InGaAs QD
was placed between a bias voltage
and exposed to ultrafast laser
pulses.
Cos(Θ/2)|0>+Sin(Θ/2)|1>
|1> => electric charge
=>Photocurrent (PC)
PC~Sin2(Θ/2)
π-pulse corresponds to a population
inversion
Saint-Petersburg State University
Quantum Dots. Optical and Photoelectrical
properties of QD of III-V Compounds.
Alexander Senichev
Physics Faculty
Department of Solid State Physics
senichev_spb@mail.ru
8-921-5769793
Introduction
• If the size of semiconductor crystal is reduced to tens or hundreds of
inter-atomic spacing, all major properties of material change because
of size quantization effects.
Introduction
Quantum Well
Quantum Dots
The
extreme case of size quantization is
realized in semiconductor structures with
confinement of carriers in three directions –
they are Quantum Dots.
Introduction
• Generally, electronic spectrum of the ideal quantum dots is
a set of discrete levels.
а)
E
b)
Qualitative behavior of Density of States in:
a) Bulk semiconductor
b) Quantum Wells
c) Quantum Wires
d) Quantum Dots
E
300
с)
250
E
Intensity
200
150
100
d)
50
0
E
1,05
1,10
1,15
1,20
E, eV
1,25
1,30
1,35
Device application of QDs
• Lasers with active area based on QDs
• Light-Emitting Device (LED) based on QDs
• Quantum Dots Solar Cells
Technology of QDs Formation
•
•
1.
2.
3.
The base of technologies of QDs formation is self-organizing phenomenon.
There are three types of initial stage of epitaxial growth:
2D growth of material A on surface of substrate B ; (Frank-van der Merve)
3D growth of material A on surface of substrate B ( Volmer-Weber method);
Intermediate mode of growth – the Stranski-Krastanow mode.
2D growth
3D growth
Stranski-Krastanow
Technology of QDs Formation
• Molecular Beam Epitaxy (MBE)
 MBE may be defined as the deposition of
epitaxial films onto single crystal substrates
using atomic or molecular beams.

MBE involves elementary processes:
1) Adsorption of atoms and molecules;
2) Thermal desorption;
3) Diffusion of adatoms on surface
of substrate;
4) Nucleation;
1
4
Solid substrate
3
2
Technology of QDs Formation
• Molecular Beam Epitaxy (MBE)
MBE system consist of:
• a growth chamber
• a vacuum pump
• a effusion (Knudsen) cells
• a manipulator and substrate heater
• an in-situ characterization tool –
RHEED (reflection high energy
electron diffraction)
The typical rate of MBE growth is about 1 ML/s.
Technology of QDs Formation
• Molecular Beam Epitaxy (MBE)
• The oscillation of the RHEED signal exactly corresponds to the time
needed to grown a monolayer. The diffraction pattern on the RHEED
windows gives direct indication of the state of the surface.
Technology of QDs Formation
• Metal organic chemical vapor deposition (MOCVD)
• Metal organic chemical vapor deposition is a technique used to deposit layers of
materials by vapor deposition process.
MOCVD system contains:
1. the gas handling system to
meter and mix reagents
2. the reactor
3. the pressure control system
4. the exhaust facilities
Technology of QDs Formation
• Metal organic chemical vapor deposition (MOCVD)
• The basic chemistry equation of this reaction is as follows:
(CH3 )3 Ga  AsH 3  GaAs(solid )  3CH 4 (methane gas)
• Group III sources are trimetilgallium (TMGa), TMAl, TMIn.
• Group V sources are typically hydride gases such as arsine,
phosphine.
• Growth rate and composition is controlled by partial pressures of
the species and by substrate temperature
Dependence of QDs morphology on growth
conditions
•
The basic control parameters in the case of MBE growth:
1.
2.
3.
4.
the substrate temperature;
the growth rate;
the quantity InAs, ratios of III/V materials;
Exposure time in As stream;
•
As research shows, morphology of QDs ensembles strongly
depends on temperature of substrate and growth rate.
Dependence of QDs morphology on growth
conditions
Optical properties of QDs
• Photoluminescence spectra of various ensembles of QDs:
300
2000
250
1500
Intensity
Intensity
200
150
100
1000
500
50
0
0
1,05
1,10
1,15
1,20
E, eV
1,25
1,30
1,35
1,00
1,05
1,10
1,15
E, eV
1,20
1,25
1,30
1,35
Optical properties of QDs
•
1.
The major processes which explain the temperature behavior
of QDs PL-spectra:
Thermal quenching of photoluminescence
Thermal quenching is explained by thermal escape of carriers from QD into the
barrier (or wetting layer)
2.
“Red shifting”
As experiment shows, at the temperature, when thermal quenching begins, we
can see a following change: the maximum of PL line is shifting in the “red
region”. Such behavior of PL spectrum is explained by thermal quenching
of carriers and their redistribution between small and large QDs.
Optical properties of QDs
3.
Thermal broadening of PL-spectrum.
The one of the major factors which defines PL-line width is size dispersion of QDs,
i.e. statistic disregistry in ensembles of QDs. Other process which affects on
PL-line width is the electron-phonon interaction.
4.
Tunnel processes
Tunneling of carriers between QDs competes with escape of carriers from QDs in all
temperature range. Probability of tunneling increases with temperature growth.
Tunneling processes can affect on high-temperature component of
photoluminescence spectrum.
Photoelectrical properties of
QDs
Photoluminescence spectra at 10 K as a function of bias excited at
(a) 1.959 eV above the GaAs band gap, (b) 1.445 eV resonant with
the wetting layer, and (c) 1.303 eV resonant with the second dot
excited state. Schematic excitation, carrier loss, and recombination
processes are indicated for the three cases.
Photocurrent spectra as a function of bias at 10 K. Quantum-dot features are
observed for biases between -3 and -6 V. The inset shows photocurrent from
two-dimensional wetting-layer transition, observed to its full intensity at
biases of only ~ -0.5 V.
Semiconductor Quantum Dots
Justin Galloway
2-26-07
Department of Materials Science & Engineering
Outline
I.
Introduction
II.
Effective Mass Model
III.
Reaction Techniques
IV.
Applications
V.
Conclusion
How
Quantum Dots
Semiconductor nanoparticles that exhibit quantum
confinement (typically less than 10 nm in diameter)
Nanoparticle: a microscopic particle of an inorganic material
(e.g. CdSe) or organic material (e.g. polymer, virus) with a
diameter less than 100 nm
More generally, a particle with diameter less than 1000 nm
1. Gaponenko. Optical properties of
semiconductor nanocrystals
2. www.dictionary.com
Properties
Properties of Quantum Dots Compared to
Organic Fluorphores?
High quantum yield; often 20 times brighter
 Narrower and more symmetric emission spectra
 100-1000 times more stable to photobleaching
 High resistance to photo-/chemical degradation
Tunable wave length range 400-4000 nm
CdSe
CdTe
http://www.sussex.ac.uk/Users/kaf18/QDSpectra.jpg
J. Am. Chem. Soc. 2001, 123, 183-184
Excitation
Excitation in a Semiconductor
The excitation of an electron from the valance band to the
conduction band creates an electron hole pair
E
ECB
h=E g
h  e (CB)  h (VB)
Creation of an electron hole pair where h
is the photon energy
EVB

optical
detector
semiconductor
Band Gap
(energy barrier)
E=h
exciton: bound electron and hole pair
usually associated with an electron trapped in a
localized state in the band gap
Recombination of Electron Hole Pairs
Release
Recombination can happen two ways:
radiative and non-radiative
E
ECB
recombination processes
EVB
E
ECB
E=h
EVB
radiative
recombination
non-radiative
recombination
band-to-band
recombination
recombination
atinterband trap states
(e.g. dopants, impurities)
radiative recombination  photon
non-radiative recombination  phonon (lattice
vibrations)
e (CB)  h (VB)  h
Model
Effective Mass Model
Developed in 1985 By Louis Brus
Relates the band gap to particle size of a spherical quantum dot
Band gap of spherical particles
The average particle size in suspension can be obtained from the
absorption onset using the effective mass model where the band gap E* (in
eV) can be approximated by:
 2  1
1  1.8e
*
bulk


E  Eg 
2 m m  m m  4 r 
2er  e 0
h 0 
0
2
Egbulk - bulk band gap (eV),
r - particle radius
me - electron effective mass
mh - hole effective mass
cm-1)
m0 - free electron mass (9.110x10-31
1
 1
1 


2 m m  m m 
2
4 0   e 0
h 0 
0.124e 3
h - Plank’s constant (h=6.626x10-34 J·s)
e - charge on the electron (1.602x10-19 C)
 - relative permittivity
0 - permittivity of free space (8.854 x10-14 F
kg)
Brus, L. E. J. Phys. Chem. 1986, 90, 2555
Model
Term 2
The second term on the rhs is consistent with the particle in a box
quantum confinement model
Adds the quantum localization energy of effective mass me
High Electron confinement due to small size alters the effective mass
Consider a particle of mass m confined
in a potential well of length L. n = 1, 2, …
For a 3D box: n2 = nx2 + ny2 + nz2
n2 2 2 n2h2
En 

2
2mL
8mL2
Pote ntia l Ene rgy
of an electron compared to a bulk material
•
0
L
x
1
2 
2
4 


h
1
1
1.8e
0.124e
1
1
E*  E gbulk  2 





2 m m
2
m
m
m
m
4
r
8r  e 0
h 20   e 0 mh m0 
h 0 
0
Brus, L. E. J. Phys. Chem. 1986, 90, 2555
Model
Term 3
 The Coulombic attraction between electrons and holes lowers the
energy
Accounts for the interaction of a positive hole me+ and a negative
electron meElectrostatic force (N) between two charges (Coulomb’s Law):
qq
F 1 2 2
Work, w = F·dr
40r
Consider an electron (q=e-) and a hole (q=e+)
The decrease in energy on bringing a positive
charge to distance
 r from a negative charge is:
r
e2
e2
E  
dr  
2
40r
40r
1
2 
2
4 


h
1
1
1.8e
0.124e
1
1
E*  E gbulk  2 





2 m m
2
m
m
m
m
4
r
8r  e 0
h 20   e 0 mh m0 
h 0 
0
Brus, L. E. J. Phys. Chem. 1986, 90, 2555
The last term is negligibly small
Term one, as expected, dominates as the radius is decreased
Energy
(eV)
Modulus
Model
Term Influences
1
term 1
term 2
term 3
0
0
5
10
d (nm)
Conclusion: Control over the
particle’s fluorescence is possible
by adjusting the radius of the
particle
Model
Quantum Confinement of ZnO & TiO2
ZnO has small effective masses  quantum effects can be observed for
relatively large particle sizes
Confinement effects are observed for particle sizes <~8 nm
TiO2 has large effective masses  quantum effects are nearly
unobservable
4
TiO2
Eg (eV)
Eg (eV)
ZnO
4
3
400
 onset (nm)
 onset (nm)
3
400
350
300
350
300
250
250
0
5
d (nm)
10
0
5
d (nm)
10
The
Making
Formation of Nanoparticles
Varying methods for the synthesis of
nanoparticles
Synthesis technique is a function of the
material, desired size, quantity and quality of
dispersion
Synthesis Techniques
• Vapor phase (molecular beams, flame synthesis etc…
• Solution phase synthesis
Semiconductor Nanoparticles
•Aqueous Solution
II-VI: CdS, CdSe, PbS, ZnS
•Nonaqueous Solution
III-V: InP, InAs
MO: TiO2, ZnO, Fe2O3, PbO, Y2O3
Semiconductor Nanoparticles Synthesis:
Typically occurs by the rapid reduction
of organmetallic precusors in hot
organics with surfactants
some examples of in vitro imaging with QDs
(http://www.evidenttech.com/)
The
Nucleation and Growth
Making
Figure 1. (A) Cartoon depicting the stages of nucleation and growth for the preparation of monodisperse NCs
in the framework of the La Mer model. As NCs grow with time, a size series of NCs may be isolated by
periodically removing aliquots from the reaction vessel. (B) Representation of the simple synthetic apparatus
employed in the preparation of monodisperse NC samples.
Horizontal dashed lines represent the critical concentration for nucleation and the saturation concentration
C. B. Murray, C. R. Kagan, and M. G. Bawendi, Annu. Rev. Mater. Sci. 30, 545, 2000.
The
Making
Capping Quantum Dots
Due to the extremely high surface area of a nanoparticle there is a
high quantity of “dangling bonds”
Adding a capping agent consisting of a higher band gap energy
semiconductor (or smaller) can eliminate dangling bonds and
drastically increase Quantum Yield
With the addition of
CdS/ZnS the Quantum
Yield can be increased
from ~5% to 55%
Synthesis typically consisted of
lower concentrated of
precursors injected at lower
temperatures at slow speeds
Shinae, J. Nanotechnology. 2006, 17, 3892
The
Making
Quantum Dot Images
Quantum dot images prepared in the Searson Lab using CdO and
TOPSe with a rapid injection
770000x
560000x
455000x
Application
Quantum Dot Ligands Provide new Insight into
erbB/HER receptor – Mediated Signal Transduction
Used biotinylated EGF bound to commercial quantum dots
QD’s
Studied in vitro microscopy the binding of EGF to erbB1 and erbB1
interacts with erbB2 and erbB3
Conclude that QD-ligands are a vital reagent for in vivo studies of
signaling pathways – Discovered a novel retrograde transport
mechanism
Dynamics of endosomal fusion
A431 cell
expressing erbB3mCitrine
Nat. Biotechnol. 2004, 22; 198-203
Application
Multiplexed Toxin Analysis Using Four Colors of
Quantum Dot Fluororeagents
Demonstrated multiplexed assays for toxins in the same well
Four analyte detection was shown at 1000 and 30 ng/mL for each toxin
QD’s
At high concentrations all four toxins can be deciphered and at low
concentrations 3 of the 4
Fluoresence data for all 4 toxin assays at
high concentrations
Cartoon of
assay
Anal. Chem. 2004, 76; 684-688
Application
QD’s
Quantum Dot Imaging
QDs with antibodies to human prostate-specific
membrane antigen indicate murine tumors developed
from human prostate cells
15 nm CdSe/ZnS TOPO/Polymer/PEG/target
Gao et al., “In vivo cancer targeting and imaging with semiconductor quantum dots,” Nat. Biotechnol. 22, 969 (2004).
Biological
Particles
Magnetic Nanoparticles
Nano-sized magnetic particles can be superparamagnetic
 Widely Studied – Suggested as early as the 1970’s
 Offers control/manipulation in magnetic field
 Co has higher magnetization compared
to magnetite and maghemite
Science 291, 2001; 2115-2117.
J. Phys. D: Appl. Phys. 36, 2003; 167-181.
 An Attractive Biological Tool
Application
Magnetic Nanoparticles: Inner Ear Targeted
Molecule Delivery and Middle Ear Implant
SNP controlled by magnets while transporting a payload
Magnetic
Particles
Studies included in vitro and in vivo on rats, guinea pigs and
human cadavers
Demonstrated magnetic gradients can enhance drug delivery
Perilymphatic fluid from the cochlea
of magnet-exposed temporal bone
Perilymphatic fluid samples
from animals exposed to magnetic forces
Audiol Neurotol 2006; 11: 123-133
Magnetic
Quantum
Dot
Composite with A Novel Structure for Active Sensing in Living cells
① Cobalt core : active manipulation
diameter : ~10 nm
What
is
MQD ?
superparamagnetic NPs
Co
CdSe
ZnS
Silica
→ manipulated or positioned by an external field
without aggregation in the absence of an
external field
② CdSe shell : imaging with fluorescence
thickness : 3-5 nm
visible fluorescence (~450 – 700 nm)
④ Silica shell : bio-compatibility &
functionalization with specific
targeting group
thickness : ~10 nm
bio-compatible,
& non-toxic to live cell functions
ability to tune the band gap
→ by controlling the thickness, able to tune the
emission wavelength, i.e., emission color
③ ZnS shell : electrical passivation
thickness : 1-2 nm
stable in aqueous environment
having wider band gap (3.83 eV) than CdSe
(1.91 eV)
ability to functionalize its surface
enhancement of QY
with specific targeting group
→ CdSe (5-10%)  CdSe/ZnS (~50%)
Rap-Up
Conclusions
The effective mass model give an excellent
approximation of the size dependence of electronic
properties of a quantum dot
Recent synthesis advances have shown many quantum
dot reactions to be robust, cheap, and safe then previously
thought
Quantum dots offer wide range electronic properties
that make them an attractive tool for biological and
medical work
MQD’s improve afford in vivo manipulation expanded
the applicability of quantum dots
Nanotechnology for the lazy:
self-assembled semiconductor quantum
dots
Gavin Bell
University of Warwick
Outline
• Semiconductor quantum dots – what, why?
– Artificial versus self-assembled (SAQD)
• InAs/GaAs SAQDs
– Strained heteroepitaxy in MBE
• Analysing and controlling SAQD growth
– STM-MBE versus “STMBE”
– SEM, TEM, CAFM
Direct Gap Semiconductors
• Direct gap
semiconductors:
lighting, optical
communication,
sensors, etc…
• For bulk material, the
band gap controls the
emission wavelength.
•
Technology sets various ‘target’ wavelengths:
– CD player laser 780 nm, DVD 640 nm, Blu-ray and HD-DVD 405 nm.
– optical fibre transmission 1300 and 1550 nm.
Low Dimensional Semiconductors
• Carriers in electrons
can be confined by
potential barriers (e.g.
in a low gap material
surrounded by higher
gap material).
• Confinement can be in
one dimension only –
a 2D quantum well.
• Confinement in all
three directions gives a
zero-dimensional
quantum dot (QD).
• Quantum dot density of states g(E) just
discrete levels (no continuum of states –
just ‘particle-in-a-box’ energy levels).
• Confinement sizes are a few nanometres.
Semiconductor Lasers and LEDs
• Various flavours of
quantum well lasers –
well established
technology.
• Arakawa and Sakaki
(1982) predicted that
quantum dot lasers
should be more
efficient
Real Quantum Dot Lasers
• Innolume GmbH
– QD lasers 1064 – 1320 nm
•
QD Laser Inc., Japan
– QD lasers 1.3 and 1.55 micro
Artificial Quantum Dots
• Nano-fabricated QDs
– Position and size control.
– Electrical contacting.
– Poor quality for optical
applications (surfaces and
defects cause strong nonradiative recombination).
– Hard work!
• How about self-assembled
QDs?
Molecular Beam Epitaxy
• Fire beams of material at
substrate crystal in vacuum.
• Perfect for growing layerby-layer (2D) structures.
•
Can we grow 3D / 1D / 0D structures
by MBE?
3D structure
(or ‘0D’ if small)
2D structure
Strained Heteroepitaxy
•
• 6.7% strain is huge!
• Epitaxial stress 5.3 GPa
for the (001) surface.
• Strain energy in growing
layer must be relieved.
• Normally: dislocations.
InAs on GaAs leads to 6.7% compressive strain.
STM-MBE
Asx
~10-4 Pa
STM-MBE
Interrupt MBE growth.
Transfer pristine surface to STM for
atomic-resolution imaging.
UHV
~10-8 Pa
0.5 ML
InAs on
GaAs(110)
0.5 ML
2 ML
2 ML
STM-MBE
(vacuum transfer)
200 nm images.
2D islands then
dislocations in 2D layerby-layer growth.
5 ML
InAs on GaAs(001)
1 ML
2 ML
Regular layer-bylayer growth
3D islands
Height ~ 3 – 8 nm
Width ~ 10 – 20 nm
 ~ 10nm, so 0D?
Strain Relief
Wetting layer (WL)
WL + QDs
ε
σ
-6.7 %
5.3 GPa
< 1.7 ML
•
•
•
•
> 1.7 ML (very rapid transition)
In-plane strain (epitaxial stress) relieved by 3D islands.
Lattice planes ‘bulge out’.
No dislocations – QDs are coherent.
Balance surface energy against elastic energy.
Control of self-assembly?
•
Average size & size distribution.
– Affects emission wavelength and sharpness.
•
Density.
– Affects gain of QD laser.
•
Position?
– Lateral ordering after many layers.
– Don’t need for independent
QDs in lasers.
•
Need to understand growth process.
QD Nucleation
InAs-GaAs heteroepitaxy
adatoms
islands
GaAs homoepitaxy
3D island density jumps suddenly
at the critical thickness.
In vacuo STM-MBE: Quenching
GaAs(001)-(2x4)
homoepitaxy
100nm images.
‘Rapid’ quench
vs. 10s anneal at
the growth
temperature:
island density
drops by 2/3.
1. Surface rearrangement during quench process?
2. Cannot return tip to a particular feature to observe its development.
3. Cannot capture surface dynamics.
4. QD nucleation extremely rapid – problems?
STMBE versus STM-MBE
Asx
~10-6
mbar
UHV
~10-10
mbar
STMBE
Anan NCT, Japan:
Prof. Shiro Tsukamoto.
STM-MBE
The rest of the world!
Relatively easy to operate compared
to STMBE.
QD Nucleation – STMBE
1.70 ML
A
B
1.75 ML
c
b
a
Images obtained during growth: 200s
per image, corresponds to 0.05 ML
coverage interval (0.00025 ML / s).
Tip raster
direction
Quantum Dot Nucleation – Up Close
A
Blue arrows: 1 ML height
Red arrows: 3-fold lattice space (1.2 nm)
B
C
• 3D islands develop over a coverage
interval of 0.01 ML.
• Total volume in 3D islands jumps
from zero to 0.49 ML over a coverage
interval of 0.05 ML.
• 0.44 ML ‘extra’ In quickly available
for QDs.
Wetting Layer Growth
• STMBE ‘movie’ of WL growth.
• Observe normal step-flow growth.
– Fill in pits.
– Terrace advances.
– Island grows and joins up with terrace.
• Each frame 200 s, 0.05 ML.
• Measure area of ‘new’ terrace developed in each frame.
– Can’t do this with STM-MBE.
• Amount of new terrace always less than amount of deposited InAs.
• About 0.5 ML In available for rapid QD nucleation as mobile, weakly
bound adatoms.
STMBE: Does the ‘ST’
Interfere With the ‘MBE’?
Incommensurate RHEED patterns
(2x4)
1.4
1.2
(2xa3)
(1x3)
1.0
DIFFUSE
InAs coverage / ML
1.6
0.8
0.6
0.4
COEXISTING
0.2 c(4x4) + (1x3)
0
c(4x4)
350
400
(4x2)
(1xa3)
(2xa3)
2
(2x4)
450
500
550
Substrate Temperature / °C
600
Direct Fourier transform of
STMBE images follow
RHEED intensity maxima
quite nicely.
QD Composition
• Very important in defining potential well (hence optical properties).
• STM can’t easily measure composition.
– Can infer from cross-sectional STM.
– Total QD volume too large for pure InAs QDs.
– Must be an InGaAs alloy.
• Which technique?
– Scanning Transmission Electron Microscopy (Super-STEM).
– Grazing incidence X-ray diffraction (synchrotron radiation source).
• Medium energy ion scattering (MEIS).
Scanning electron microscopy
• SEM
• Z-contrast: brighter
means more In-rich
• QD tops In-rich.
• QD bases Ga-rich.
• Aligned along
steps.
• QDs 20-25 nm
across.
100 nm
Medium Energy Ion Scattering
• UK MEIS facility at Daresbury Laboratories.
• Beamline: typically He+ or H+ at 100 keV primary energy.
• Toroidal electrostatic analyser records scattered ion energy and angular
distributions simultaneously (energy resolution ~ 400 eV).
• Able to probe typical samples to a depth of several nm.
Introduction to MEIS
surface
Align incident beam
either along a crystal
direction or ‘random’
angle (little channelling
hence high counts).
Measure the angular
and energy spectra of
scattered ions.
Channelling (lots of low-angle
collisions along a crystal direction)
Electronic stopping – ion loses energy at a calculable rate (‘stopping
power’); these energy losses can be converted to a depth scale.
Elastic collision – ion recoils at energy dependent only on scattering
angle and mass of target nucleus.
Sample MEIS Data
Sample data from two Sb delta-layers in Si.
Angular data – crystallographic information
(e.g. depth of channelling dip depends on
crystalline perfection; e.g. surface structure)
Energy spectra – energy resolution best for
high mass species in a low mass matrix (e.g.
In in GaAs): highest recoil energy.
Convert energy scale to depth scale by:
energy loss = path length x stopping power
Hence produce depth profiles, with nearatomic layer depth resolution.
QD Energy Spectra
Channelled spectra, [110] in and
normal out, very similar for uncapped
(red) and 1 nm GaAs cap (partially
capped QDs).
Thicker GaAs cap (5 nm): In signal
merges into GaAs.
Concentrate on uncapped QDs.
Modelling Discrete Structures
• MEIS normally applied to 2D layered
structures
– Every ion recoiling from a particular
depth has travelled the same path
length.
– This is no longer true for discrete
structures.
Ion entry point
Shallower scattering
Deeper scattering
• Need to model every possible path
through the QD.
• Place an average QD on a grid of
points and allow ions to enter at each
point on the grid.
• Energy spectrum is sum over all
possible paths.
Sample Results for Simulations
Simulations for constant In
concentration through the QDs
(size and density fixed by
AFM). Composition is 100% In
for the top curve, then 80%,
60%, 40% and 20%.
Simulations of linear
composition gradient QDs
(curves are 0-100% In from
bottom to top, 20-100%, 40100%, 60-100% and 80-100%
on each graph).
Best Fit for QDs
• Include contributions from
QDs, WL and large 3D islands.
• Best fit is a linear In gradient
from 20% at the QD base to
100% at the QD tops.
• The QD bases are rather Garich.
• Complex growth kinetics: the
WL plays a very important role.
Conclusions
• Semiconductor quantum dots.
– Self-assembled versus fabricated.
• InAs-GaAs QDs easy to grow by MBE.
– Possible to tailor to important wavelengths (e.g. 1300 nm).
• Study growth in detail with STM.
– STMBE ‘movies’ versus STM-MBE ‘snapshots’.
– Growth kinetics not fully understood.
• Study composition of discrete nanostructures with
medium energy ion scattering (MEIS).