Phonon coupling to exciton complexes insingle quantum dots

D. Dufåkera, K. F. Karlssona, V. Dimastrodonatob, L. Merenib, P. O. Holtza, B. E. Serneliusa , and E. Pelucchib

a IFM Semiconductor materials, Linköping University, Swedenb Tyndall National Institute, University College Cork, Ireland

The 11th edition of the international conference PLMCN:Physics of Light-Matter Coupling in Nanostructures

Cuernavaca (Mexico), 12-16 April, 2010

Outline

• Introduction to Pyramidal QDs

• Introduction to LO-phonon coupling

• Experimental results

• Interpretation/Computational results

• Conclusions

Pyramidal QDs

• InGaAs QDs in AlGaAs barriersPatterned GaAs substrate (111)B

G. Biasiol et al., PRL 81, 2962 (1998);Phys. Rev. B 65, 205306 (2002)

•self-limiting profile•growth anisotropy•capilarity effects•alloy segregation

A. Hartmann PRL 84 5648(2000)

GaAs

AlGaAsBarrier

InGaAsQD

MOCVD

Pyramidal QDs

Simplified model

AlGaAs layer 30 % AlInGaAs layer 15 % In

InGaAs QD15 %

SurroundingAlGaAs Barrier

20-30 %

AlGaAs VQWR1

4 %

Pyramidal QDs

•Efficient light extraction >120 kcnts/sec•Site-controlled, isolated QDs•C3v-symmetry – emitters of entangled photons1

1R. Singh et al., PRL 103 063601 (2009);K. F. Karlsson el al., PRB Accepted (R) (2010);A. Schliwa et al., PRB 80 161307R (2009);A. Mohan et al., Nature Phot. 2 (2010)

•Designed with excited electron levels

(x2) s

(x4) p

(x2) s

2X

X

Vac

C3v

Pyramidal QDs

•Control of charge population by excitation conditions1

1A. Hartmann PRL 84 5648(2000)

Nor

mal

ized

PL

Inte

nsity

QD2

LO-phonon coupling

Coupling of LO-phonons with excitons is electric (Fröhlich)

The total coupling is given by the difference between the couplings ofelectrons and holes

An exciton formed by an electron-hole pair is a neutral entitiy

Equal probability density function of electrons and holes vanishing coupling

In real systems: electrons and holes have different charge distribution

B]111[

]011[

]211[

]011[

Side viewTop view

Gray:Quantum dot profileRed: Hole probability density (10% of max)Blue:Electron probablity density (10% of max)

Side view

)(r

Charge distributionCha

rge

dens

ity

LO-phonon couplingExcitation spectrumT = 0 KNo spectral linewidthDispersion less phonon branch

Huang-Rhys parameter S

LOLOn

nS

nSn

Se

0 !

0

1

I

IS

qq

dq

eS

LO2

2

0

2

3

11

2

4

2

1

rqq F

0-phonon

1-phonon

2-phononEnergy

ħLO ħLO

0-phonon

1-phonon

2-phononEnergy

Emission spectrum

ħLOħLO

LO-phonon coupling

Ensemble measurements InAs/GaAs QDs S ~ 0.015

R. Heitz et al., PRL 83 4654 (1999)

Single CdSe/ZnCdSe QD (X, 2X) S ~0.035, 0.032

F. Gindele et al., PRB 60 2157R (1999)

P. Hawrylak et al., PRL 85 389 (2000)

Single InAs/GaAs QDs, PL-excitationspectroscopy

LO-phonon coupling

• Extra charge?

Spherical GaAs microcrystallities (r>11 nm)

S enhanced from 0.001 to 0.01 by an extra charge Nomura & Kobayashi PRB 45 1305 (1992)

PRL 85 389 (2000)

PL-excitation spectroscopy InAs/GaAs QDs

Experimental results

XX+

X

2X1000

X

X

X2X2

Direct emission

Phonon replicas(1st order)

T=4K

QD1

Experimental resultsQD1

•Replica of X+ significantly weaker than X and X-

•Replica of X- similar strength as replica of X•LO-phonon energy 36.40.1 meV•Larger spectral linewidth of replicas

Experimental results

Mea

sure

d H

uang

-Rhy

s P

aram

eter

17 QDs

Computations

rrr finalinitial

qq

dq

eS

LO2

2

0

2

3

11

2

4

2

1

Excitonic ground states computed self-consistently by 88 band kptheory in Hartree approximation

Strain induced deformation potentials simulated by continuumelastic theory

Computations

finalinitial

XX+ X2X

Cha

rge

de

nsity

(e/n

m3)

]111[

]011[

Rea

l s

pac

e m

aps

Huang-Rhys parameters S1000

Interpretation

XX+

Side

Top

Repulsion DelocalizationAttraction Localization

Coulomb interactions induces changes in the charge distribution; different exciton complexes have different charge distributions

J. J. Finley et al., PRB 70 201308R (2004)

Computations

in

itia

l

Cha

rge

de

nsity

(e/

nm

3)

XX+ X2X

Integrated diagonal phonon scattering matrix elements relative X

•Strong phonon coupling for an exciton comples does not imply strong phonon replicas.

Interpretation

Measured LO-phonon energy: 36.40.1 meV (GaAs bulk: ~36.6 meV)

VQWR (4% Al)ħLO= 36.4 meV

Surrounding barrier (20-30% Al)ħLO= 35.0-35.5 meV

GaAs-like LO-phonon energy in AlGaAs

04%: E -0.2 meV

InterpretationSpectral linewidth

Bulk-like LO-phonon dispersion broadening < 50 eVGaAs LO-phonon lifetime broadening ~ 70 eV1

•Composition variations and alloys disorder2

1M. Canonico PRL 88 215502 (2002) 2B. Jusserand PRB 24 7194 (1981)

Comparison of phonon replicas of charged and neutral

exciton complexes. S = 0.001 – 0.004

X+ X Coulomb induced charge cancellation of an electron-hole pair

Extra positive charge may result in strongly reducedphonon replicas due to the heavier mass of the hole

X+: Strongest LO-phonon scattering matrix element andsimultaneously the weakest phonon replicas

Adiabatic independent-phonon model yield valuesof the Huang-Rhys parameter in agreement withexperiments

qq

dq

eS

LO2

2

0

2

3

11

2

4

2

1

Conclusions