Post on 31-Mar-2015
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
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
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
dq
eS
LO2
2
0
2
3
11
2
4
2
1
Conclusions