Ordered Quantum Wire and Quantum Dot Heterostructures
Grown on Patterned Substrates
Eli Kapon
Laboratory 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
Quantum Well Heterostructure
Quantum Well Potential
Potential well
Confined
envelope
functions
AlGaAs
GaAs
AlGaAs
AlGaAs
r
het  :
AlGaAs
 r  u r r
n,k
n,k n,k
Electron envelope functions r:
Schrödinger equation with
V
heterostructure potential
GaAs





2 2

 V r r  E r
2m*
het  n,k
n,k
Low-Dimensional Semiconductors:
Quantum wells, wires and dots
(a)
Density of states
(b)
tx
2D
Quantum Well
QW
bulk
3D
Eg
Eg E1
E2
Energy
Energy
(c)
tx
1D
tx
0D
ty
QD
QWR
ty
(d)
tz
Quantum Dot
Quantum Wire
Eg
E11
E12
Energy
E13
E14
Eg
E111
E112
E113
Energy
E114
E115
Spontaneous Formation of Quantum Nanostructures:
Self-formed quantum dots
« Natural » QDs
400nmX400nm STM scan of MBEgrown GaAs (100) surface
R. Grousson et al., Phys. Rev. B 55, 5253 (1997)
Stranski-Krastanow QDs
TEM cross section of vertically-stacked
SK-grown quantum dots
Zhuang et al., J. Crystal Growth 201/202, 1161 (1999)
Surface fluxes of adatoms are not controlled: random nucleation and broad size distribution
Lateral Patterning during Epitaxial Growth:
Controlling lateral fluxes with the surface chemical potential
ji (x)  
Surface flux:
Chemical potential:  i   0 
0 
 strain

n i Di  i
kT x
 ca pilla rity
 mixing
0
  (x)2  0  ( )   "( ) (x)  kT lnX i (x)
2E
µ
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 Potential
Size and Shape Control
Self-limiting facet width
2

2
r

L

sl
lb   0 s s 
 rkB T 
1 /3
 Nano-template width adjusted by surface diffusion length
 Wires/dots produced by switching surface diffusion length
G. Biasiol et al., PRL 81, 2962 (1998);
Phys. Rev. B 65, 205306 (2002)
Excitons in Quantum Wires:
Signatures of a 1D system
e 1-h 1
e 2 -h 2
e 3-h 3
e 4-h 4
e 2-h 6
PLE, Excit. pol. ||
e 1-h 6
+ "2s"
1.56
PLE, Excit. pol. 
1.60
1.64
Theory: excitonic absorption
X optical absorption (arb. units)
PLE optical spectra (arb. units)
Experiment: PL-excitation spectra
A1 exc.
B1 exc. (pol. ||)
A2 exc. (pol.  
1.56
1.60
Photon energy (eV)
1.64
Photon energy (eV)
 Excitonic transitions dominate (reduced Sommerfeld factor in 1D)
 Polarization anisotropy due to valence band mixing
 Enhanced exciton binding energy (14.5 meV) deduced
M.-A. Dupertuis et al., to be published
Contacting a Single Quantum Wire:
1D Electron Gas in V-Groove QWRs
-
+
-
QWs
+
-
-
+
+
-
-
+
+
-
+
+
+
+
wire
- --- --
-
+
Etched
Areas
Current
flow
+
+
+
+
+
+
-
-
-
-
1 µm
-
+
QWR
QWR
8
QWR Conductance
7
0.3 um
6
0.45 um
1.5 um
2
 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
G [e /h]
1.0 um
5
4
1.9 um
3
2
1
D. Kaufmann et al., Phys. Rev. B 59, R10433.(1999)
0
-3,2
-3
-2,8
-2,6
-2,4
-2,2
-2
-1,8
Structural Disorder Along a V-Groove QWR:
Monolayer steps at the central (100) wire facet
(100) top
(311) facets
Sidewalls
12nm- thick
GaAs cap
layer
(100) bottom with ML steps
Height profile (nm)
0
4
2000nm
Bottom (100) facet
MLs steps
2
•Long range (~1µm) variations
induced by lithography imperfection
0
-2
-4
•Short range (~100nm) variations
induced by monolayer steps
Sidewalls
-6
0
200
400
600
800
1000
Groove axis (nm)
1200
1400
Charged Excitons in V-Groove QWR:
Binding energies and localization
Localization Effects
• Micro-PL spectra through sub-m apertures
• Modulation doped QWRs for charging control
• Sharp lines represent localized excitons
Self-Ordering of Pyramidal Quantum Dots:
OMCVD growth on pyramidal patterns
pump
(111)B
PL
{111}A
GaAs
QD
GaAs substrate
(111B) substrates patterning
GaAs-support
Self-limited OMCVD growth
Substrate removal
SEM
QD
AlGaAs
{111}A
gold
(111)B
1µm
1 m
QDs self-formed at a dip in the surface chemical potential
1 µm
Dense Site-Controlled Pyramidal QD Arrays:
CL Intensity (arb. units)
Cathodoluminescene spectroscopy
T = 7K
CL spectrum
Ground state CL image (7 meV window)
950 QDs
7 meV
1.5
1.6
1.7
1.8
Photon Energy (eV)
 >99% of QDs emit light
 Highly uniform dot arrays
1 m
Single Quantum Dot Spectroscopy:
Origin of optical transitions
QWR
~ 3-4 nm
Back-Etched Pyramids
10 K, 1W on
single pyramid
QD
~ 6 nm
Micro-PL of
Single Pyramids
QW
~ 1-1.5 nm
VQW
Monochromatic
CL Imaging
1.60 eV
1.94eV
QD
1.70eV
A. Hartmann et al., J. Phys.: Condens. Matter 11 5901 (1999)
QWR
QW
Multi-Particle States in Quantum Dots:
Excitonic states and charging mechanism
l = -1
0
+1
p
s
QD
AlGaAs
s
p
l = -1
0
X-
X- -
2X
Emission
X
+1
n ~ 1017 cm-3 background
doping
Energy
2D harmonic oscillator model
Chrage control by
photoexcitation
Quantum Dots in an N-type Environment:
Charged excitonic complexes
A. Hartmann et al., PRL 84, 5648 (2000)
10 K laser =
2.42 eV
Experiment
Theory
Full CI model
3e-2h
3X
2X
x10
2e-h
X
3e-h
2.5 nW
3e-h
4e-h
5e-h
6e-h 5e-h
4e-h
6e-h
1.56
1.565
1.57
30 pW
1.575
photon energy [eV]
1.58
1.585
calculated PL intenisty [a.u.]
PL intensity [a.u.]
4X
Single exciton regime
Multi exciton regime
600 nW
2X
2e-h
3e-h
3e-h
4e-h
4e-h
5e-h
5e-h
6e-h
6e-h
-20
-15
X
-10
-5
Photon energy [meV]
0
5
Pyramidal QDs as Single-Photon Emitters:
i
time
delay
1.4
monochromator B
1.2
1.0
mes
g
(2)
(t)
c unter
photon counter
l
Hanbury Brown and Twiss correlation measurements
monochromator A
0.8
0.6
0.4
0.2 g(2) (t) = 1-(1-g(2) (0))e-|t|/
mes
mes
 ~ 770 ps
0.0
-15
-10
-5
0
QD
sample
5
t (ns)
Pulse.
Laser
Analyz.
Diode
Laser
Laser
 Single QDs are readily observed and probed
 Photon antibunching observed at X line
TiSa
Laser
M. Baier et al., Appl. Phys. Lett. 84, 648-650 (2004)
Controlled Photon Emission from 0D Excitons:
Exciton dynamics probed by photon correlations
QD PL spectra
X-X correl.
X--X-
2X-X
X--X
2X-X-
Carrier Transport into Quantum Wires:
Preferential Injection via connected quantum wells
p+ doped side
E v
VQW
+
Al x
QWR
0.3
–
 Low-energy QWs form next to wires
 Carriers injected via QWs into quantum wires
0.2
E c
20 nm
n+ doped side
H. Weman et al., Appl. Phys. Lett. 73, 2959 (1998);79, 1402 (2001)
Electronic States in Pyramidal QDs:
Finite element k.p modeling
lateral
quantum
wells
tqw
Z [111
]
a
t
w
ground state
h
first excited state
X [112]
quantum dot
F. Michelini et al.
Y [110]
Electronic States in Pyramidal QDs:
Impact of vertical quantum wire
E12 (meV)
Electronic confinement energy (eV)
0.3
Without Wire
80
ground state
40
with VQWR
without VQWR
0
0
4
8
Dot height (nm)
0.2
e3
e2
0.1
second excited state
e1
without VQWR
with VQWR
first and second VQWR subbands
0.0
2
4
6
Dot height (nm)
F. Michelini et al.
8
10
With Wire
Single Quantum Dot Light Emitting Diode:
PL
EL
QD
VQWR
GaAs
Preferential carrier injection into a single dot
M. Baier et al., APL, 2004 (in print)
QWRs VQW QWs
+
QD
Vertical
Quantum wire
quantum
dot
VQWR
 Quantum dot light emitting diode structure
 Emission from vertical QWR and QD only (at low current)
VQWR
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
Ordered Quantum Wire and Quantum Dot Heterostructures
Grown on Patterned Substrates
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