Transcript University of Notre Dame Center for Nano Science and Technology

Optical Properties at the
Nanoscale
J es L
am
.M
er z
Dep ar tm en t o f E
le c tr ica l E
n gin eer in g
Dep ar tm en t o fP hysic s
Univ er sity o fN otr e D am e
E98D
6 –A
dvan cedS
em icon ducto r P hysic s
Notr e D am e
23N ovem ber 204
University of Notre Dame
Center for Nano Science and Technology
References
► Primary reference for this talk:
Quantum Semiconductor Structures, Fundamentals and Applications,
C. Weisbuch and B. Vinter, Academic Press, Inc., San Diego, 1991.
(referred to throughout the talk as W & V.)
► The Quantum Dot, R. Turton, Oxford Univ. Press, NY, 1995.
► Quantum Dot Heterostructures, D. Bimberg, M. Grundmann, and
N.N. Ledentsov, John Wiley and Sons, Chichester, England, 1999
► Electronic and Optoelectronic Properties of Semiconductor Structures,
J. Singh, Cambridge Univ. Press, Cambridge, 2003.
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References (continued)
► Many of the slides were taken from a Plenary talk by Maurice
Skolnick at the International Conference on the Physics of
Semiconductors (ICPS),
Flagstaff, AZ (July 2004). Used with his permission.
► "Near-field Magneto-photoluminescence Spectroscopy of
Composition Fluctuations in InGaAsN", A.M. Mintairov, J.L.
Merz, et al, Phys. Rev. Letters 87, 277401 (31 December 2001);
“Exciton Localization in InGaAsN and GaAsSbN Observed by
Near-field Magnetoluminescence”, James L. Merz, A.M. Mintairov
et al, Proceedings of the Spring meeting of the European
Marterials Research Society, Symposium M, to be published in
IEE Proceedings Optoelectronics. (referred to in the talk as M &
M)
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Howdo we make Quantum Wells (QWs)?
► Typically by MBE or MOCVD.
► Grow thin films (a few monolayers to tens of
monolayers) of a narrow-bandgap semiconductor
bounded by a wider-bandgap semiconductor.
► The process can be repeated several times or many
times, to make multiple (non-interacting) QWs, or a
superlattice of interacting QWs.
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Fundamentals of Quantum-ConfinedStructures
Quantum Wells (1-D structures)
W & V, pg.3, Fig.1
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“Classical” Quantum Mechanical Problem:
Particle in a Box
►
These structures are best grown by Molecular Beam Epitaxy (MBE) or Metal-Organic
Chemical Vapor Deposition (MOCVD)
►
Let the potential barriers be infinitely high
►
Solve the Schrödinger Equation for this one-dimensional case
►
Solutions are sinusoidal functions:
Ψ(z) = sin(kz) or cos(kz), where z is growth direction.
► Solutions must vanish at the well/barrier interfaces (i.e., Ψ(z) = 0 at z = 0 and z = b,
where b is the thickness of the film)
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E
igenfunctions andEigenvalues
W & V, pg.12, Fig.5
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Finitebar r ier (Vo) allows exponential
penetr ation into thebar r ier
W & V, pg.13, Fig.6
Note that this problem is mathematically equivalent to
the dielectric waveguide. Energy eigenstates then become
guided optical modes.
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CoupledQuantum Wells
W&V, pg.29, Fig.14
► As two wells approach each other, their wave functions overlap
► This leads to a pair of eigenstates which split into two levels
► For many coupled wells, get multiple states → energy band
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S
uper latticeEnergy Bands
►At a given well or barrier
width a, the higher energy
states become broader bands.
This results from the fact that
the wave function overlap
increases for the higher-lying
energy eigenstates.
►Thus, for a = 50 Å, E1 is a
discrete state, while E2, E3,E4,
etc. form successively
broader bands.
W & V, pg.38, Fig.18c
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A
lxGa1-xAs:
an ideal mater ial to
form Quantum Wells
andSuper lattices
nEer gy G
a p
gE(e V)
► For 0 < x < 0.4 AlxGa1-xAs
has a direct bandgap that is
larger than GaAs.
► GaAs and AlGaAs are very
nearly lattice matched.
► Thus, AlGaAs is an excellent
potential barrier for GaAs
quantum wells.
University of Notre Dame
H.C. Casey andM
.B. Panish, J.A
ppl. Phys.40,4910(1969).
Center for Nano Science and Technology
Optical absorption of multipleuncoupledquantum
wells–compar ison with bulk
GaAs:
Eg = 1.43 eV
Al.3Ga.7As: Eg = 1.79 eV
50 periods of 100 Å GaAs = .5 mm
Comparison with 1 mm bulk GaAs
W & V, pg.64, Fig.30e
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What are thedifferences??
► For quantum wells, the absorption edge is at higher energy than
the bulk absorption edge, due to increased energy of the confined
state in the GaAs quantum well.
► Bulk GaAs shows √E energy dependence due to direct gap of GaAs
(3-D bulk density of states).
► GaAs quantum well absorption shows “stair case” dependence on
energy (2-D density of states).
► Sharp peaks are due to exciton absorption.
► Some corrections must be made for e-h correlation effects.
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What is the Density ofStates?
► The density of states is the number of states per unit volume per unit
energy interval that are available for occupation by electrons (or holes).
► Optical absorption must be proportional to the density of states,
because a photon cannot be absorbed if there is no final state
available for the electronic transition.
► For 3-D parabolic bands (bulk), ICBST N(E)= (1/2p2)(2m*/ħ2)3/2√E,
where m* is the effective mass of the electron.
► For a 2-D quantum well, ICBST N(E)= m*/pħ2, independent of E.
For each quantum state in the quantum well, there will be a step
in the density of states.
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A
sorption of BulkSemiconductor s:
b
Direct andIndirect Bandgap
► Direct Bandgap: a ~ (hn – Eg)1/2
► Indirect Bandgap: Must have momentum conservation
Absorb a phonon: aa ~ (hn – Eg + ħw)2
Emit a phonon:
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ae ~ (hn – Eg – ħw)2
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2-D and3-D Density ofStates
W & V, pg. 21, Fig.10
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E
xcitons
► Exciton: photon produces
electron-hole pair.
► Electron-hole pair is
bound by Coulomb
attraction, losing energy
and creating sharp
energy states (analogous
to H2 atom)
► The 2-D Rydberg is 4x
greater than the 3-D
Rydberg.
► Sommerfeld factor is due
to electron-hole correlation
in unbound states.
W & V, pg.26,Fig.13
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E
xcitons andShallow Impurities
► Hydrogen atom: e2/err term gives series of energy states:
En = ERydb/n2,
where ERydb = e4mo/2ħ2 = 13.6 eV,
and the Bohr radius aB = ħ2/moe2 = 0.529 Å.
► For a donor, must correct for the electron mass and the dielectric
constant:
En = (me*/er2)ERydb → 10-20 meV
► For an exciton, must use reduced mass: 1/m = 1/me* + 1/mh*
En = (mr*/er2)ERydb → 5-20 meV
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The2-D Rydberg
► Can solve the problem for an infinite potential model
ERydb2-D = ERydb3-D * 1/(n – ½)2 = ERydb3-D * 4/(2n-1)2
Ground state: n = 1 → ERydb2-D = 4 * ERydb3-D
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Optical absorption of multipleuncoupledquantum
wells–compar ison with bulk
GaAs:
Eg = 1.43 eV
Al.3Ga.7As: Eg = 1.79 eV
50 periods of 100 Å GaAs = .5 mm
Comparison with 1 mm bulk GaAs
W & V, pg.64, Fig.30e
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Dependence of exciton bindingenergy (EBX)
on quantum well thickness
-----Light-hole exciton
_____ Heavy-hole exciton
► For an infinite well,EBX increases as
the well gets thinner, just as does the
single-electron state.
► For a finite well, EBX reaches a max.
and then decreases because e and h
wave functions spread out into the
barrier.
► As d becomes very large, the light
hole binding energy > heavy hole
because EBX ~ 1/mass.
W & V, pg.25, Fig.12
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OpticalAsborption of CoupledWells
► (a) Single well: one state,
split into heavy & light hole.
► (b) Double well: two states
(bonding and antibonding),
each of which is split into
heavy & light hole.
► (c) Triple well: three states,
each split into heavy &
light hole.
W & V, pg.73,Fig.35
Dingle et al, Phys.Rev.Lett.34, 1327 (1975)
Dingle et al, Phys.Rev.Lett.33,827 (1974)
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E
ffect of Quantum Well Thickness
► In layer-to-layer growth mode, one expects
thickness variations of ~0.5 monolayer from
average monolayer thickness.
► Intralayer thickness fluctuations cause
variations of confining energies.
► For thin wells (51Å), these variations cause
a larger relative effect, hence lines broaden.
► Note increase in photon energy of absorption
edge as well gets thinner, as expected.
W & V, pg.76, Fig.38
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Franz-KeldyshEffect for BulkM
ater ial
► Bulk material
Applied field E ≠ 0
Franz-Keldysh Effect:
bands are tilted.
► Absorption below Eg because
of exponential wave-function
tails.
► Oscillations above Eg due to
wave-function interference.
W & V, pg.89,Fig.46
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Quantum-ConfinedStar kEffect (QCSE)
► Quantum Well, E = 0
Usual case seen before.
► Quantum Well, E ≠ 0
Bands tilt and
energy of quantum states
decreases → “red” shift
of luminescence energy.
Wave function overlap
decreases → reduction
of luminescence intensity.
W & V, pg.89,Fig.46
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OpticalAbsorption due to QCSE
► Values of applied electric field:
(i)
E=0
(ii)
E = 60 kV/cm
(iii) E = 110 kV/cm
(iv) E = 150 kV/cm
(v)
E = 200 kV/cm
► The predicted red shift and
intensity decrease are both
observed with increasing
electric field.
W & V, pg.90,Fig.47
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Wannier-Star kLocalization (WSL)
► QCSE is observed for a single QW.
► WSL is observed for a QW superlattice.
► At E = 0 the discrete QW states form
bands in a superlattice, and the electron
can be anywhere in the superlattice.
► As E increases, the superlattice bands
tilt, and the energy eigenstates no longer
overlap. Bands get narrower and then
coalesce into sharp states.
► At high electric fields, the electron is
completely localized.
Mendez et al, Phys.Rev.Lett.
60, 2426 (1988)
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Formation of “Star kLadders” in WSL
QCS
r e dsh ift
E
At low E-field, e is delocalized.
With increasing E, up to 5 states
are seen, which reduce to one
at high field.
M
endezet al, Phys.Rev.Lett.
Plot of photocurrent peak energies
vs. E. Stark ladders from outlying
states are clearly seen, which quickly
disappear at high field.
60,2426(198)
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n-i-p-iStructures
► These are n-i-p-i homojunctions.
► Electrons from n region fall into
holes in p regions, leaving ionized
impurities.
► Resulting space charge distribution
modulates the bands, forming
energy eigenstates.
► The result is a homojunction
superlattice.
W & V, pg.52, Fig.27
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n-i-p-iLight M
odulation Phenomena
Turton, pg.134, Fig.8
In the dark, the n-i-p-i structure has reduced the effective bandgap of the
structure, as shown by the energy arrow in (a). If above-bandgap monochromatic
light is incident on the structure, electrons and holes are produced which reduce
the space charge, flattening the bands and increasing the radiative recombination
energy, as shown by the energy arrow in (b). Thus, changes in the intensity of
monochromatic light shining on the sample changes the wavelength of the emission.
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S
emiconductor Laser s
► electrons and holes
are injected into GaAs
active region by p-n
junction.
► Carriers are confined
to active region by
potential barriers.
W & V, pg.166, Fig.8
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► Photons are confined
to active region by
refractive index
difference.
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Confinement of Optical GuidedWave
► Double Heterostructure –
Optical mode well confined.
Too many electron states available.
G~1
► Single Quantum Well
Optical mode poorly confined.
Electrons well confined to single state.
G ~ Dn d2
W& V, pg.168, Fig.89
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► Separate Confinement Heterostructure
Optical mode moderately confined
to the quantum well.
Electrons well confined.
G ~ Dn d
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Confinement Factor (G)
d/2
G =
∞
∫│E(z)│2dz/ ∫│E(z)│2dz
-d/2
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ThresholdCurrent Density (Ith )
W & V, pg.171, Fig.92
►Want to minimize Ith.
►GSCH is Graded-index Separate Confinement Heterostructure
(also called GRINSCH)
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Vertical CavitySurfaceEmittingLaser (VCSE
L
)
► Active layer: GaInAs/GaAs QWs
► Mirrors: GaAs/AlGaAs multiple layers
with thickness ~ optical wavelengths
→ Distributed Bragg Reflectors (DBRs)
► Advantages:
• Low Ith due to QW active layer
(Ith≤400 A/cm2)
• Very low I (<70 mA) due to small
cross-sectional area (8 mm)
• Low output diffraction → can couple
efficiently into optical fibers
• Can make large arrays
W & V, pg.183, Fig.102a
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Huffaker & Deppe, Appl. Phys. Letters 70, 1781 (1997).
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VCSE
L
A
rr ays
J.Jewell et al,A
ppl. Phys.Letter s 55,2724(1989)
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Thus far:
►
We solved the Schrödinger Equation for the one-dimensional “particle in a box”
►
These results were appropriate for a two-dimensional semiconductor structure
i.e., a quantum well
►
Now we are interested in confinement in two and three directions, leading to
structures that are one-dimensional and zero-dimensional, respectively
i.e., quantum wires and quantum dots or boxes.
►
We also said that we could derive the so-called “density of states”, and that this
concept is very important to understand electrical and optical phenomena of these
quantum-confined structures.
► Now the concept of density of states becomes increasingly important, and
for quantum wires and dots the experimental techniques of single-electron transport
(Snider) and near-field optics (Merz) become increasingly important.
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2-D and3-D Density ofStates
W & V, pg. 21, Fig.10
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Quantum Wires (QWires)
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Early Prediction about
Quantum Wires
► Hiroyuki Sakaki1 predicted, more than two decades ago,
that ideal 1-D electrons moving at the Fermi level in quantum wires would
require very large momentum changes (Dk = 2kF, where kF is the Fermi
wave-vector) to undergo any scattering,
► The result would be that electron scattering would be strongly forbidden.
► This is a consequence of the fact that in one dimension, electrons
can scatter only in one of two directions: forward and 180o backwards.
► With this large reduction in scattering, electrons would achieve excellent
transport properties (e.g., very high mobility).
1
H. Sakaki, J. Vac. Sci. Technol. 19(2), 148 (1981)
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Quantum Dots (QDs)
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Early Prediction about
Quantum Dots
► A year later, Arakawa and Sakaki1 predicted significant increases in the
gain, and decreases in the threshold current, of semiconductor lasers
utilizing quantum dots or boxes in the active layer of the laser.
► Highly efficient, low power lasers could be the consequence of these
predictions.
► These predictions set off an intense effort worldwide to fabricate such
structures.
1 Arakawa
and Sakaki, Appl. Phys. Letters 40, 939 (1982)
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L
ow-dimensionalSemiconductor Laser
Per for mance Calculations
A
sada,M
iyamoto, &Suematsu,
IEEJ.QuantumElectronics QE-22, 1915 (1986)
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Why are Quantum Dots Impor tant
• SAQDs important for both physics and
applications
• Strong confinement and high radiative efficiency
• Quasi-0D systems in the solid state. ‘Atom-like’
• Embedded in semiconductor matrix. Wide variety
of semiconductor devices, processing technology
from Skolnick
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Modification of Density of States by
Reduction of Dimensionality
Density of States
(a)
(b)
well
bulk
3D
2D
0
(c)
(d)
1D
0D
dot
0
wire
Energy
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Gener al approaches to QD synthesis
Colloidal growth of CdSe dots
Artificial patterning
Self-assembled quantum dots
(SAQDs) by MBE
Bimberget al, pg.5, Fig.1.3
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Colloidal CdSe QDs
Colloids of CdSe QDs are fluorescent at various frequencies within the
visible range. The highly tunable nature of the QD size yields a broad
range of colors in the visible spectrum.
E
.Kar reich, Nature 413,450(201)
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Self-Assembled Crystal Growth of QDs
in Strained Systems by MBE
Stranski-Krastanow
growth
InAs-GaAs 7% lattice
mismatch
Note wetting
layer
ost im por tan t sy stem :
M
InAs
GaAs
Embedded in crystal matrix – like any other
semiconductor laser or light emitting diode
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from Skolnick
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Quantum Dots and the Wetting layer
QDs
WL
20nm
UHV-STM
cross sections
PM Koenraad,
TU
Eindhoven
from Skolnick
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Quantum Dots andA
nti-dotsusingGates
► Fabricate a square grid of
electrodes on the surface of a
sample having a 2DEG.
►Apply a positive voltage to the grid.
► With increasing positive voltage to
the periodic gate, electrons are
attracted to it, causing EF to rise,
forming QDs.
► With increasing bias, the QDs
merge into a sea of electrons, with
periodic islands which electrons
cannot occupy (antidots).
W & V, pg.194, Fig.104
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•Energy Level
Structure
z
x,y
QW like potential
• Electron energy level splitting
20-70meV, hole levels spaced
by ~10meV.
• Favourable for room
temperature operation
d-shell
n=2.
l=0,±1,±2
2D
state
p-shell
n=1. l=±1
0D states
s-shell
n=0, l=0
~20nm
• Discrete energy levels – atomlike
~ HO like potential
~10n
m
Photon
emitted
from Skolnick
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Optical Spectra
Photocurrent (pA)
10
EL2
EL Intensity (a.u.)
emission
Sample M1638
T = 300 K
E3
E2
EL1
5
E1
E0
0
0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30
Studies of large numbers
~107 dots.
Energy (eV)
Absorption
from Skolnick
Linewidth ~30meV due to
shape and
sizeof Notre
fluctuations
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Dame
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Three ways to measure Absorption Properties
1. Directly:M
easure tr ansmission.Simple conceptually,but sometimesdifficult in
pr acticedue to weak absorption. One step process.
2.Photocurrent: exciton createdby resonant absorption, electron and hole
tunnel out ofdot andgive current. Two step process.
3.Photoluminescence excitation spectroscopy: absorption, relaxation and
then recombination.Excitedstates. Coupling to environment. Three step
process.
PC
Electron tunnelling
ttun
PLE
Resonant
excitation
ttun
Recombination
trec~1ns
excite
detect
Hole tunnelling
from Skolnick
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Asymmetric Stark shifts (QCSE)
•
1.08
T=200K
Transition Energy (eV)
1.07
n-i-p
1.06
DE = aF + bF2
p-i-n
• Linear term implies
existence of
permanent dipole
moment.
1.05
F
1.04
-300
-200
-100
F
0
100
Electric Field (kV/cm)
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Quadratic Stark
shifts, DE,
asymmetric about
zero field.
200
300
PRL 84, 733, 2000
from Skolnick
Center for Nano Science and Technology
From the sign of the dipole
deduce that In composition
increases from base to apex
QDs are intermixed
Interdiffusion
Polarisability - height
5.5nm
InAs
In0.5Ga0.5As
15.5nm
Increasing indium along
growth direction
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Theory, JA Barker
and EP O’Reilly
PR B61, 13840,
2000
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Emission: Spatially resolved PL
PL Intensity (arb. units)
T = 10 K
► Emission spectrum breaks up into very
sharp lines with homogeneous linewidth
~ 1µeV
Single Dot
200nm
Spatially
Resolved PL
>1 QD
500nm
Far Field PL
7
~10 QDs
200µm
1250
1300
1350
Energy (meV)
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► Ground (s-shell) and excited state (p
shell) emission observed
► Single dots may be optically isolated
using apertures or mesas with ~2 or 3
within a size of 500nm.
1400
from Skolnick
Center for Nano Science and Technology
Howdo we measure single QDs?
► Etch mesas whose size is ~ 1 mm and see discrete lines
from individual dots.
► Cover sample with mask and open holes of order 1 mm.
► Use NEAR-FIELD OPTICS: Near-field Scanning
Optical Microscopy (NSOM).
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Near-Field Spectroscopy of Quantum Structures
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Low-temperature near-field optical scanning
microscope
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Temperature dependence of near-field
spectra of InGaAsN
C5
C4
1.12
Energy, eV
=514.5 nm
P=20 mW
1.10
In content = 8%
N content = 3%
A
A
1.08
Near-field PL intensity
C3
C2
C1
1.06
C2
C1
0
50 100 150 200 250 300
Temperature
10K
20K
Band A  Weak localization
Localization energy = ~ 40 meV
30K
35K
40K
45K
50K
C2
55K
C1
60K
A
C Lines  Strong localization
(Quantum Dots)
Localization energy ~ 50-60 meV
65K
1.06
1.08
1.10
1.12
Energy, eV
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1.14
1.16
M
&M
Center for Nano Science and Technology
Magnetic Field Effects
Zeeman Splitting and Diamagnetic Shift
C7
1.0840
Energy, eV
PL intensity
C6
T=5K
1.06
C7h
1.0830
C7l
1.0825
1.08
1.10
E nergy, eV
C6l C6 C7l
h
b
1.0835
0
2
C7h
4
6
8
10
12
Magnetic field, T
10T
C6
C7
4T
, m eV/T
6T
10
c
15
r, nm
8T
2
N ear-field PL intensity
a
5
0T
5
1.06
1.080
1.085
Energy, eV
1.07
1.08
1.09
1.10
Energy, eV
M
&M
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Center for Nano Science and Technology
y, m m
NSOM Images of Individual QDs
NPL intensity, cps
50
Density ~100 mm
-3
2
c
b
a
1
0
0
1
2
x, m m
40
e
d
30
c
(x=0.2, y=1.4)
20
e
b
(x=0.8, y=0.4)
d
10
a
(x=1.8, y=1.8)
0
1120
1140
1160
W avelength, nm
1180
M
&M
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Digital Information Storage
J. J. Finley et al, APL, 73, (1998) M. Kroutvar et al, APL 83 (2003)
AlGaAs
Barrier
STORAGE
QDs
Metal
AlGaAs Barrier
-Vapp
F
p+
Contact
i-GaAs Buffer
p-substrate
-eVstore
READ / RESET
AlGaAs Barrier
+Vapp
F
i-GaAs Buffer
+eVreset
p-substrate
from Skolnick
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Center for Nano Science and Technology
Applications (much physics as well!)
1. QD lasers
2. Mid infra-red detectors
Ensembles
3. Memory devices
4. Quantum information
Single dots
5. Single photon sources
University of Notre Dame
Center for Nano Science and Technology
Quantum Dot Lasers
QD lasers first discussed Arakawa and Sakaki, APL 40, 939 (1982)
First report Kirstaedter, Bimberg et al, El Lett 30, 1416, 1994
Low threshold, temperature insensitive threshold current etc
Breakthrough application, 1.3mm lasers for local area networks
Distinct potential advantages over installed InP-based lasers (GaAs-based technology,
large area substrates, good thermal conductivity, Bragg mirrors, low temperature
dependence of threshold current)
Major contributors: Berlin, Ioffe, New Mexico etc
from Skolnick
University of Notre Dame
Center for Nano Science and Technology
Semiconductor Laser Performance Versus Year
Ledentsov et al, IEEE J. Select.
Topics Quant. Electron. 6, 439 2000
17A/cm2,
cw, 300K,
1.31mm,
from Skolnick
University of Notre Dame
Liu, Sellers,
Mowbray et
al
Center for Nano Science and Technology
QD laser T=300K
Ground state lasing
1100
1200
1300
o
26 C
o
85 C
o
100 C
EL Intensity
EL Intensity (arb)
Emission spectra from 1.3mm quantum dot lasers
1400
1100
1200
1300
1400
Wavelength (nm)
Wavelength (nm)
Record threshold currents, continuous wave 17A/cm2 at 300K at true 1.3mm.
Very encouraging temperature performance
University of Notre Dame
from Skolnick
Center for Nano Science and Technology
1500
1-D Structures -- Conclusions
1. Self assembled quantum dots have led to a huge
variety of new physics and applications
2. Key points, high radiative efficiency 0D states in a
solid state matrix
3. Good approximation to atoms in the solid state, but
there are exceptions
4. Challenges include higher uniformity, predetermined
positions, larger binding energy materials, longer
coherence times, incorporation in very high finesse,
small volume cavities for e.g. cavity QED
from Skolnick
University of Notre Dame
Center for Nano Science and Technology
Goodbye–It hasbeen fun!
Octopus Optics Lab
University of Notre Dame
Center for Nano Science and Technology