Ordered Quantum Wire and Quantum Dot Heterostructures Grown on Patterned Substrates
Ordered Quantum Wire and Quantum Dot Heterostructures Grown on Patterned Substrates
Eli KaponLaboratory of Physics of Nanostructures
Swiss Federal Institute of Technology Lausanne (EPFL)
Introduction Self-ordering on nonplanar substartes Neutral and charged low-D excitons Contacting single QWRs and QDs Summary and outlook
ADMOL, Dresden, Germany, February 23-27, 2004
Quantum Confinement:Compound semiconductor heterostructures
Electron envelope functions :
Schrödinger equation with heterostructure potential :
Ψn,kr( )=un,kr( )φn,kr( )
− h22m*∇2+Vhetr( )
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥ φn,kr( )=Eφn,kr( )
φr( )
Vhetr( )
AlGaAs GaAs AlGaAs
Quantum Well Heterostructure
AlGaAs
Confinedenvelopefunctions
AlGaAs GaAs
Potential well
Quantum Well Potential
Low-Dimensional Semiconductors:Quantum wells, wires and dots
Den
sit
y o
f st
ates
Quantum Well
Quantum DotQuantum Wire
Spontaneous Formation of Quantum Nanostructures:Self-formed quantum dots
400nmX400nm STM scan of MBE-grown GaAs (100) surface
R. Grousson et al., Phys. Rev. B 55, 5253 (1997)
« Natural » QDs
Zhuang et al., J. Crystal Growth 201/202, 1161 (1999)
TEM cross section of vertically-stackedSK-grown quantum dots
Stranski-Krastanow QDs
Surface fluxes of adatoms are not controlled: random nucleation and broad size distribution
€
μ i =μ0+ Δμstrain + Δμcapillarity + Δμmixing
=μ0+Ω 0
2Eστ (x)[ ]
2 +Ω0 γ(θ)+γ"(θ)[ ]κ(x)+kT lnXi (x)
Chemical potential:
€
ji (x) =−niDi
kT∂μi
∂xSurface flux:
Lateral Patterning during Epitaxial Growth:Controlling lateral fluxes with the surface chemical potential
Strain Capilarity Entropy of mixing
G. Biasiol and E. Kapon, Phys. Rev. Lett. 81, 2962 (1998); G. Biasiol et al., Phys. Rev. B 65, 205306 (2002)
V-Groove Quantum Wires:Size and shape control by growth adjustments
Surface Chemical Potentialrbrslbslµinitial, etched
profilefaceted profile
s
G. Biasiol et al., PRL 81, 2962 (1998);Phys. Rev. B 65, 205306 (2002)
Size and Shape Control
Nano-template width adjusted by surface diffusion length Wires/dots produced by switching surface diffusion length
lbsl =
2Ω0rsγLs2
ΔrkBT
⎛
⎝ ⎜ ⎞
⎠ ⎟
1/3
Self-limiting facet width
Excitons in Quantum Wires:Signatures of a 1D system
PLE, Excit. pol. ||
PLE, Excit. pol. ⊥
1.56 1.60 1.64
e1-h
1e2-h
2e3-h
3e4-h
4
e1-h
6+ "2 "s
( . )PLE optical spectra arb units
( )Photon energy eV
e2-h
6
Experiment: PL-excitation spectra
Excitonic transitions dominate (reduced Sommerfeld factor in 1D) Polarization anisotropy due to valence band mixing Enhanced exciton binding energy (14.5 meV) deduced
1.56 1.60 1.64
A1 exc.
B1 exc. (pol. ||)
A2 exc. (pol. ⊥)
( . )X optical absorption arb units
( )Photon energy eV
Theory: excitonic absorption
M.-A. Dupertuis et al., to be published
Contacting a Single Quantum Wire:1D Electron Gas in V-Groove QWRs
EtchedAreas
1 µm
Currentflow
QWR
wire
---- - -
--
--
---
--
+
++
+
++
+ +
+
+
+
+
++
+
++
++
+
-+
+
++
-- +
--QWs
QWR
D. Kaufmann et al., Phys. Rev. B 59, R10433.(1999)
Moduation-doped V-groove QWR structure Wire contacted via 2D electron gas on sidewalls Conductance quantized close to 2e2/h Discrepancy due to quantum contact resistance
012345678
-3,2-3 -2,8-2,6-2,4-2,2-2 -1,8
QWR Conductance0.3 um0.45 um1.0 um1.5 um1.9 um
Gate Voltage [V]
Groove axis (nm)
-6
-4
-2
0
2
4
0 200 400 600 800 1000 1200 1400
Hei
ght p
rofi
le (
nm)
Sidewalls
Bottom (100) facetMLs steps
•Long range (~1µm) variations induced by lithography imperfection
•Short range (~100nm) variations induced by monolayer steps
Structural Disorder Along a V-Groove QWR:Monolayer steps at the central (100) wire facet
2000nm0
Sidewalls
(100) bottom with ML steps
(311) facets(100) top
12nm-thickGaAs cap
layer
Charged Excitons in V-Groove QWR:Binding energies and localization
• Micro-PL spectra through sub-m apertures• Modulation doped QWRs for charging control• Sharp lines represent localized excitons
Localization Effects
Self-Ordering of Pyramidal Quantum Dots:OMCVD growth on pyramidal patterns
1µm
(111)B
{111}A
GaAs substrate
{111}A
(111)B
(111B) substrates patterning
GaAs-support
Substrate removal
pump PL
1 m
AlGaAs
GaAsQD
Self-limited OMCVD growth
QDs self-formed at a dip in the surface chemical potential
>99% of QDs emit light Highly uniform dot arrays
Ground state CL image (7 meV window)
1 m
950 QDs7 meV
CL
Inte
nsity
(ar
b. u
nits
)
Photon Energy (eV)1.5 1.6 1.7 1.8
T = 7K CL spectrum
Dense Site-Controlled Pyramidal QD Arrays:Cathodoluminescene spectroscopy
Single Quantum Dot Spectroscopy:Origin of optical transitions
Back-Etched PyramidsMicro-PL of
Single Pyramids
Monochromatic CL Imaging
QD1.60 eVQWR1.70eV
QW1.94eV
10 K, 1W on single pyramid
QD~ 6 nm
QWR~ 3-4 nm
QW~ 1-1.5 nm
VQW
A. Hartmann et al., J. Phys.: Condens. Matter 11 5901 (1999)
Multi-Particle States in Quantum Dots:Excitonic states and charging mechanism
l = -1 0 +1
s
p
s
p
l = -1 0 +1
Energy
Em
iss
ion
X X- X- - 2X
2D harmonic oscillator model
QD
AlGaAs
n ~ 1017 cm-3 background doping
Chrage control by photoexcitation
Quantum Dots in an N-type Environment:Charged excitonic complexes
Sin
gle
exc
ito
n r
eg
ime
Mu
lti
exc
ito
n r
egim
e
X
2X
3e-2h
2e-h
3e-h
4e-h
5e-h
6e-h6e-h
5e-h
4e-h
3e-h
Theory
Full CI model
X
4e-h
5e-h5e-h
3e-h
4e-h
6e-h
6e-h
3e-h
2e-h
2X
3X
4X
laser = 2.42 eV
Experiment
30 pW
2.5 nW
600 nW
A. Hartmann et al., PRL 84, 5648 (2000)
TiSaLaser
DiodeLaser
c
unte
r
Laser
LaserPulse.Analyz.
i
l
QDsample
monochromator A
monochromator B
timedelay
ph
oto
n c
ou
nte
r
Single QDs are readily observed and probed Photon antibunching observed at X line
M. Baier et al., Appl. Phys. Lett. 84, 648-650 (2004)
Pyramidal QDs as Single-Photon Emitters:Hanbury Brown and Twiss correlation measurements
Controlled Photon Emission from 0D Excitons:Exciton dynamics probed by photon correlations
QD PL spectra
X-X correl.
X--X- X--X
2X-X 2X-X-
Carrier Transport into Quantum Wires:Preferential Injection via connected quantum wells
Vext0.5 µmn+ GaAsn+ AlGaAsp+ AlGaAs
Low-energy QWs form next to wires Carriers injected via QWs into quantum wires
600 650 700 750 800
Wavelength (nm)
AlGaAs VQW
QWR
(100) QW
(111)A QW
13 2
4EL:
PL:FB (0 mA)
051015202530
0 0.51 1.52 2.5Voltage (V)
T = 10 K•
•••
H. Weman et al., Appl. Phys. Lett. 73, 2959 (1998);79, 1402 (2001)
Electronic States in Pyramidal QDs:Finite element k.p modeling
ground stateground state
first excifirst excited stateted state
t
tqw
h
w
quantum dotquantum dot
lateral quantum wells
Z
Y
[112]
[111]
[110]
X
F. Michelini et al.
Electronic States in Pyramidal QDs:Impact of vertical quantum wire
ground state
second excited state
Without Wire With Wire80
40
0
840 ( )Dot height nm
with VQWR without VQWR
0.3
0.2
0.1
0.0108642
( )Dot height nm
first and second VQWR subbands
e3
e1
e2
without VQWR
with VQWR
F. Michelini et al.
Single Quantum Dot Light Emitting Diode:Preferential carrier injection into a single dot
quantumdot
Vertical Quantum wire
+
-
QWRsV
QW
R
Ga
As VQW QWs
QDPLEL
VQWR
Quantum dot light emitting diode structure Emission from vertical QWR and QD only (at low current)
QD
VQWR
M. Baier et al., APL, 2004 (in print)
QDs Embedded in Photonic Crystals:Energy tuning of ground and excited state transitions
QD in Hexagonal PhC « Defect »
S. Watanabe et al.
Wavelength-Dispersive CL images
QD positioned in a photonic crystal microcavity Emission energy tuned by epitaxial growth effect
Ordered Quantum Wire and Quantum Dot Heterostructures Grown on Patterned Substrates
Summary:
-Self-ordering during epitaxial growth on non-planar substrates is useful for producing high quality QWRs and QDs
-New excitonic states are made stable by lateral quantum confinement in QWRs and QDs
-Low-dimensional quantum nanostructures should be useful in novel optoelectronic devices such as single photon emitters and optically active photonic crystals
Collaborators:
Crystal growth:A. Rudra, E. Pelucchi
Nanofabrication and nanocharacterization:B. Dwir , K. Leifer, S. Watanabe, C. Constantin
Optical spectroscopy:D. Oberli, H. Weman, A. Malko, T. Otterburg, M. Baier
Theory:M.-A. Dupertuis, F. Michelini
Ordered Quantum Wire and Quantum Dot Heterostructures Grown on Patterned Substrates