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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:

Energy levels ~ 1meV

Size ~ 10μm

Weak magnetic fields can affect energy levels

• Hydrogen:

Energy levels ~ 1eV

Size ~ 1Å

Only strong magnetic fields can perturb energy levels

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

position

Gate bias

Spin up - electron

Unoccupied state

The Physical System: Excitons Trapped in GaAs Quantum Dots

• Exciton - a Coulomb correlated electron-hole 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

Quantum Dots. Optical and Photoelectrical properties of QD of III-V Compounds.

Alexander Senichev Physics Faculty

Department of Solid State [email protected]

8-921-5769793

Saint-Petersburg State University

mailto:[email protected]

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

The extreme case of size quantization is realized in semiconductor structures with confinement of carriers in three directions – they are Quantum Dots.

Quantum Dots

Introduction

• Generally, electronic spectrum of the ideal quantum dots is a set of discrete levels.

E

E

E

E

а)

b)

с)

d)

Qualitative behavior of Density of States in:a) Bulk semiconductorb) Quantum Wellsc) Quantum Wiresd) Quantum Dots

1,05 1,10 1,15 1,20 1,25 1,30 1,35

0

50

100

150

200

250

300

Inte

nsity

E, eV

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

• The base of technologies of QDs formation is self-organizing phenomenon.

• There are three types of initial stage of epitaxial growth:

1. 2D growth of material A on surface of substrate B ; (Frank-van der Merve)

2. 3D growth of material A on surface of substrate B ( Volmer-Weber method);

3. Intermediate mode of growth – the Stranski-Krastanow mode.

2D growth 3D growth Stranski-Krastanow


• 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;

Solid substrate

1 2

34


• 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.


• 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.


• 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 reagents2. the reactor3. the pressure control system4. the exhaust facilities


• Metal organic chemical vapor deposition (MOCVD)• The basic chemistry equation of this reaction is as follows:

• 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

3 3 3 4( ) ( ) 3 ( )CH Ga AsH GaAs solid CH methane gas

Dependence of QDs morphology on growth conditions

• The basic control parameters in the case of MBE growth:

1. the substrate temperature;2. the growth rate;3. the quantity InAs, ratios of III/V materials;4. 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:

1,05 1,10 1,15 1,20 1,25 1,30 1,35

0

50

100

150

200

250

300

Inte

nsity

E, eV

1,00 1,05 1,10 1,15 1,20 1,25 1,30 1,35

0

500

1000

1500

2000

Inte

nsi

ty

E, eV


• The major processes which explain the temperature behavior of QDs PL-spectra:

1. Thermal quenching of photoluminescenceThermal 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.


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 processesTunneling 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 DotsSemiconductor Quantum Dots

Justin Galloway2-26-07

Department of Materials Science & Engineering

I. Introduction

II. Effective Mass Model

III. Reaction Techniques

IV. Applications

V. Conclusion

OutlineOutline

HowHow 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

PropertiesProperties 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

http://www.sussex.ac.uk/Users/kaf18/QDSpectra.jpg

CdSe

CdTe

J. Am. Chem. Soc. 2001, 123, 183-184

ExcitationExcitation Excitation in a Semiconductor

The excitation of an electron from the valance band to the

conduction band creates an electron hole pair

h e (CB)h(VB)

E=h

optical detector

semiconductor

E

EVB

CBE h=Eg

Creation of an electron hole pair where h is the photon energy

exciton: bound electron and hole pairusually associated with an electron trapped in a localized state in the band gap

Band Gap (energy barrier)

E

EVB

CBE

band-to-band recombination

recombination atinterband trap states (e.g. dopants, impurities)

E

EVB

CBEE=h

radiative recombination

non-radiative recombination

recombination processes

radiative recombination photonnon-radiative recombination phonon (lattice vibrations)

e (CB)h(VB) h

ReleaseRelease Recombination of Electron Hole Pairs

Recombination can happen two ways:

radiative and non-radiative

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:

Egbulk - bulk band gap (eV), h - Plank’s constant (h=6.626x10-34 J·s)

r - particle radius e - charge on the electron (1.602x10-19 C)me - electron effective mass - relative permittivitymh - hole effective mass 0 - permittivity of free space (8.854 x10-14 F cm-1) m0 - free electron mass (9.110x10-31 kg) Brus, L. E. J. Phys. Chem. 1986, 90, 2555

E* Egbulk

22

2er2

1me m0

1

mhm0

1.8e40r

0.124e3

2 40 2

1me m0

1

mhm0

1

ModelModel Effective Mass Model

Developed in 1985 By Louis Brus

Relates the band gap to particle size of a spherical quantum dot

Brus, L. E. J. Phys. Chem. 1986, 90, 2555

ModelModel 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

of an electron compared to a bulk material

Consider a particle of mass m confined in a potential well of length L. n = 1, 2, …

En n222

2mL2 n2h2

8mL2

For a 3D box: n2 = nx2 + ny

2 + nz2

0 Lx

Pot

entia

l Ene

rgy

E* Egbulk h2

8r21

mem0 1

mhm0

1.8e2

40r 0.124e4

h2 20 21

mem0 1

mhm0

1

Brus, L. E. J. Phys. Chem. 1986, 90, 2555

ModelModel 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 me-

E* Egbulk h2

8r21

mem0 1

mhm0

1.8e2

40r 0.124e4

h2 20 21

mem0 1

mhm0

1

Electrostatic force (N) between two charges (Coulomb’s Law):

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:

E e2

40r2dr e2

40r

r

F q1q2

40r2 Work, w = F·dr

ModelModel Term Influences

The last term is negligibly small

Term one, as expected, dominates as the radius is decreased

0

1E

nerg

y (e

V)

0 5 10

d (nm)

term 3

term 2

term 1

Conclusion: Control over the particle’s fluorescence is possible by adjusting the radius of the particle

Mod

ulus

ModelModel 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

3

4

Eg

(eV

)

250

300

350

400

ons

et (

nm

)

0 5 10

d (nm)

ZnO

3

4

Eg

(eV

)

250

300

350

400

on

set (

nm

)

0 5 10

d (nm)

TiO2

TheThe

MakingMaking

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

•Aqueous Solution•Nonaqueous Solution

Semiconductor NanoparticlesII-VI: CdS, CdSe, PbS, ZnSIII-V: InP, InAsMO: 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/)

TheThe

MakingMaking

Nucleation and Growth

C. B. Murray, C. R. Kagan, and M. G. Bawendi, Annu. Rev. Mater. Sci. 30, 545, 2000.

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

TheThe

MakingMaking

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 increasedfrom ~5% to 55%

Shinae, J. Nanotechnology. 2006, 17, 3892

Synthesis typically consisted of lower concentrated of precursors injected at lower temperatures at slow speeds

TheThe

MakingMaking

Quantum Dot Images

Quantum dot images prepared in the Searson Lab using CdO and

TOPSe with a rapid injection

455000x560000x

770000x

Quantum Dot Ligands Provide new Insight into erbB/HER receptor – Mediated Signal TransductionUsed biotinylated EGF bound to commercial quantum dots

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

Nat. Biotechnol. 2004, 22; 198-203

A431 cell expressing erbB3-mCitrine

Dynamics of endosomal fusion

ApplicationApplication

QD’s


Cartoon of

assay

Fluoresence data for all 4 toxin assays at high concentrations

Anal. Chem. 2004, 76; 684-688

QD’s

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

At high concentrations all four toxins can be deciphered and at low concentrations 3 of the 4

Gao et al., “In vivo cancer targeting and imaging with semiconductor quantum dots,” Nat. Biotechnol. 22, 969 (2004).

Quantum Dot ImagingQDs with antibodies to human prostate-specific membrane antigen indicate murine tumors developed from human prostate cells15 nm CdSe/ZnS TOPO/Polymer/PEG/target


QD’s

Biological Biological ParticlesParticles

Magnetic Nanoparticles

Nano-sized magnetic particles can be superparamagnetic

Widely Studied – Suggested as early as the 1970’s

Offers control/manipulation in magnetic field

J. Phys. D: Appl. Phys. 36, 2003; 167-181.

Science 291, 2001; 2115-2117.

An Attractive Biological Tool

Co has higher magnetization compared to magnetite and maghemite

Magnetic Nanoparticles: Inner Ear Targeted

Molecule Delivery and Middle Ear Implant

SNP controlled by magnets while transporting a payload

Studies included in vitro and in vivo on rats, guinea pigs and human cadavers

Demonstrated magnetic gradients can enhance drug delivery

Perilymphatic fluid samplesfrom animals exposed to magnetic forces

Perilymphatic fluid from the cochleaof magnet-exposed temporal bone

Audiol Neurotol 2006; 11: 123-133


Magnetic

Particles

Magnetic

Particles

WhatWhat

isis

MQD ?MQD ?

Composite with A Novel Structure forComposite with A Novel Structure for ActiveActive Sensing in Sensing in LivingLiving cellscells

SilicaZnS

CdSe

Co

① Cobalt coreCobalt core : active manipulation

diameter : ~10 nm

superparamagnetic NPs

→ manipulated or positioned by an external field without aggregation in the absence of an external field

② CdSe shellCdSe shell : imaging with fluorescence

thickness : 3-5 nm

visible fluorescence (~450 – 700 nm)

ability to tune the band gap

→ by controlling the thickness, able to tune the emission wavelength, i.e., emission color

④ Silica shellSilica shell : bio-compatibility &

functionalization with specific

targeting group

thickness : ~10 nm

bio-compatible,

& non-toxic to live cell functions

stable in aqueous environment

ability to functionalize its surface

with specific targeting group

MMagneticagnetic

QQuantumuantum

DDotot

③ ZnS shellZnS shell : electrical passivation

thickness : 1-2 nm

having wider band gap (3.83 eV) than CdSe (1.91 eV)

enhancement of QY

→ CdSe (5-10%) CdSe/ZnS (~50%)

Rap-UpRap-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 non-radiative recombination).

– Hard work!

• How about self-assembled QDs?

Molecular Beam Epitaxy• Fire beams of material at

substrate crystal in vacuum.

• Perfect for growing layer-by-layer (2D) structures.

• Can we grow 3D / 1D / 0D structures by MBE?

2D structure3D structure

(or ‘0D’ if small)

Strained Heteroepitaxy

• InAs on GaAs leads to 6.7% compressive strain.

• 6.7% strain is huge!• Epitaxial stress 5.3 GPa

for the (001) surface.• Strain energy in growing

layer must be relieved.• Normally: dislocations.

STM-MBE

STM-MBEInterrupt MBE growth.

Transfer pristine surface to STM for atomic-resolution imaging.

Asx

~10-4 Pa

UHV~10-8 Pa

InAs on GaAs(110)

0.5 ML

2 ML0.5 ML 2 ML

5 ML

STM-MBE

(vacuum transfer)

200 nm images.

2D islands then dislocations in 2D layer-by-layer growth.

InAs on GaAs(001)

1 ML

Regular layer-by-layer growth

2 ML

3D islands

Height ~ 3 – 8 nmWidth ~ 10 – 20 nm

~ 10nm, so 0D?

Strain Relief

σ 5.3 GPa

< 1.7 ML

Wetting layer (WL)

> 1.7 ML (very rapid transition)

WL + QDs

ε -6.7 %

• 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 NucleationGaAs homoepitaxy InAs-GaAs heteroepitaxy

3D island density jumps suddenly at the critical thickness.

isla

nd

sad

atom

s

In vacuo STM-MBE: QuenchingGaAs(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

STMBEAnan NCT, Japan:

Prof. Shiro Tsukamoto.

STM-MBEThe rest of the world!

Relatively easy to operate compared to STMBE.

Asx

~10-6 mbar

UHV~10-10 mbar

QD Nucleation – STMBE1.75 MLBA 1.70 ML

a

b

c

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 CloseA

B

C

Blue arrows: 1 ML height

Red arrows: 3-fold lattice space (1.2 nm)

• 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’?

Direct Fourier transform of STMBE images follow RHEED intensity maxima quite nicely.

(1x3)

(1xa3)

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

350 400 450 500 550 600

COEXISTINGc(4x4) + (1x3)

(2x4)

(2xa3)

DIF

FU

SE (4x2)

(2xa3)increasing

asymmetry

c(4x4) (2x4) 2

Substrate Temperature / °C

InA

s co

vera

ge /

ML

Incommensurate RHEED patterns

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

Channelling (lots of low-anglecollisions 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.

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.

surface

Sample MEIS DataSample 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 near-atomic 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.

• 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.

Ion entry point

Shallower scattering

Deeper scattering

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%, 40-100%, 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 Ga-rich.

• 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).