phonon coupling to exciton complexes in single quantum dots d. dufåker a, k. f. karlsson a, v....

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