Phonon coupling to exciton complexes in
single 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, Sweden
National Institute, University College Cork, Ireland
b Tyndall
The 11th edition of the international conference PLMCN:
Physics of Light-Matter Coupling in Nanostructures
Cuernavaca (Mexico), 12-16 April, 2010
Outline
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•
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•
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Introduction to Pyramidal QDs
Introduction to LO-phonon coupling
Experimental results
Interpretation/Computational results
Conclusions
Pyramidal QDs
• InGaAs QDs in AlGaAs barriers
Patterned GaAs substrate (111)B
MOCVD
InGaAs
QD
GaAs
AlGaAs
Barrier
A. Hartmann PRL 84 5648(2000)
•self-limiting profile
•growth anisotropy
•capilarity effects
•alloy segregation
G. Biasiol et al., PRL 81, 2962 (1998);
Phys. Rev. B 65, 205306 (2002)
Pyramidal QDs
Simplified model
AlGaAs VQWR1
4%
InGaAs QD
15 %
AlGaAs layer 30 % Al
InGaAs layer 15 % In
Surrounding
AlGaAs Barrier
20-30 %
Pyramidal QDs
C3v
•Efficient light extraction >120 kcnts/sec
•Site-controlled, isolated QDs
•C3v-symmetry – emitters of entangled photons1
•Designed with excited electron levels
(x4) p
(x2) s
(x2) s
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)
2X
X
Vac
Pyramidal QDs
•Control of charge population by excitation conditions1
Normalized PL Intensity
QD2
1A.
Hartmann PRL 84 5648(2000)
LO-phonon coupling
Coupling of LO-phonons with excitons is electric (Fröhlich)
The total coupling is given by the difference between the couplings of
electrons 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
Charge density
Side view
Top view
Side view
 (r )
[111]B
[112]
Charge distribution
Gray:Quantum dot profile
Red: Hole probability density (10% of max)
Blue:Electron probablity density (10% of max)
[1 1 0]
[1 1 0]
LO-phonon coupling
0-phonon
Excitation spectrum
T=0K
No spectral linewidth
Dispersion less phonon branch
Huang-Rhys parameter
e S S n
    
   SLO  nLO 
n!
n 0

S
1-phonon
2-phonon
ħLO
0-phonon
Emission spectrum
S
ħLO
Energy
S
I1
I0
1-phonon
1
2 3
4e 2
2 LO
 1
1   q 
   
dq
2
  0  q
2
 q     q   F  r 
2-phonon
ħLO
ħLO
Energy
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)
Single InAs/GaAs QDs, PL-excitation
spectroscopy
P. Hawrylak et al., PRL 85 389 (2000)
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)
PL-excitation spectroscopy InAs/GaAs QDs
PRL 85 389 (2000)
Experimental results
X
Direct emission
X
X2
X
QD1
T=4K
Phonon replicas
(1st order)
X2
1000
X
2X
X+
Experimental results
QD1
•Replica of X+ significantly weaker than X and X•Replica of X- similar strength as replica of X
•LO-phonon energy 36.40.1 meV
•Larger spectral linewidth of replicas
Measured Huang-Rhys Parameter
Experimental results
17 QDs
Computations
Excitonic ground states computed self-consistently by 88 band kp
theory in Hartree approximation
Strain induced deformation potentials simulated by continuum
elastic theory
 r    initialr    final r 
S
4e
2 LO
2
1
2 
3
 1
1   q 
   
dq
2
q
  0 
2
Computations
X+
X
2X
X
[1 1 0]
Huang-Rhys parameters S1000
Charge density
(e/nm3)
[111]
Real space maps
   initial   final
Interpretation
Coulomb interactions induces changes in the charge distribution;
different exciton complexes have different charge distributions
X+
X
Side
Top
Repulsion  Delocalization
Attraction  Localization
J. J. Finley et al., PRB 70 201308R (2004)
Computations
X
2X
X
 initial
Charge density (e/nm3)

X+
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: 36.40.1 meV (GaAs bulk: ~36.6 meV)
GaAs-like LO-phonon energy in AlGaAs
VQWR (4% Al)
ħLO= 36.4 meV
04%: E -0.2 meV
Surrounding barrier (20-30% Al)
ħLO= 35.0-35.5 meV
Interpretation
Spectral linewidth
Bulk-like LO-phonon dispersion  broadening < 50 eV
GaAs LO-phonon lifetime  broadening ~ 70 eV1
•Composition variations and alloys disorder2
1M.
Canonico PRL 88 215502 (2002)
2B.
Jusserand PRB 24 7194 (1981)
Conclusions
Comparison of phonon replicas of charged and neutral
exciton complexes. S = 0.001 – 0.004
Extra positive charge may result in strongly reduced
phonon replicas due to the heavier mass of the hole
X+
X
Coulomb induced charge cancellation of an electronhole pair
X+: Strongest LO-phonon scattering matrix element and
simultaneously the weakest phonon replicas
S
1
2 3
4e 2
2 LO
 1 1   q 
   
dq
2


q
0 
 
2
Adiabatic independent-phonon model yield values
of the Huang-Rhys parameter in agreement with
experiments