Quantum Dots
for optical applications
Andrea Fiore
Ecole Polytechnique Fédérale de Lausanne
Tutorial developed with the support of
QD
QD
European N etw ork ofExcellence
on
Photonic Integrated C om ponents and C ircuits
Integration ofresearch on:
•Technologies forphotonic VLSI
•Photonic SignalProcessing
•Integrated LightSources
•Advanced M aterials
•N anophotonics
Through:
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Access to facilities:
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•D issem ination ofKnow ledge
12 Affiliate Partners
Andrea
Fiore
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g
Quantum Dots
QD
E
Electrons in GaAs, T=300K:
h
30 nm
∆E > kT ⇔ L < λ ≈
*
2m kT
λ
L
QD devices:
Outline:
• QDs: Dreams & reality
100 nm
• The physics of single QDs
• Laser applications
Andrea Fiore
Why care about QDs?
Or: The QD "dream"
Narrower gain makes
better lasers
QD
Gain calculation:
Arakawa, Sakaki 1982
Asada et al., 1986
E
• Lower threshold current
• Lower temperature sensitivity
• Larger modulation bandwidth
NB:
Idealized
picture !!!
Andrea Fiore
Real QDs
Or: The shattered dream?
QD
•
Nanostructure fabrication:
Quantum Dots
Top-down fabrication
Need high-resolution lithography
Etching ⇒ Nonradiative defects
•
Bottom-up: Strain-driven self-assembly
☺ High crystal quality ⇒ radiative properties
Uncontrolled nucleation ⇒ Size dispersion
QDs
WL
substrate
Example: InAs on GaAs (but also InAs on InP, Ge on Si, ...)
15 nm
High local In content
200 nm
1300 nm on GaAs
Andrea Fiore
QD
Inhomogeneous broadening
1 µm diameter:
11000
40K , 4 µ W
PL counts
8800
300 nm
6600
4400
2200
0
1170
25
20
15
10
Inh. broad.
E
FW H M =
31 m eV
5
0
0.95
1
1250
1.05
E nergy (eV )
1.1
1000
50K , 4 µ W
Gain FWHM:
∆EQDs≈∆EQWs
300 n m
800
P L counts
PL intensity (arb. un.)
ideal
meas.
E
30
1190
1210
1230
Wavelength (nm )
300 nm diameter:
MacroPL at 5K:
35
1 µm
600
400
200
0
1170
1190
1210
1230
Wavelength (nm )
1250
2
Andrea Fiore
Dot density: 300 dots/µm
QD
Can we do better?
Controlling self-assembly
• SK growth on prepatterned substrates
In adatoms
Kohmoto et al., J. Vac. Sci. Tech. B 2002
• Growth-rate anisotropy driven growth:
☺ Site control
☺ Improved unif.
Baier et al., APL 2004
GaAs
QD
4 µm
Courtesy: E. Pelucchi, E. Kapon, EPFL
Andrea Fiore
Radiative properties of
self-assembled QDs
QD
Intensity (arb. un.)
1.2
1.4
Wavelength (µm)
1.3
1.2
1.1
QD characteristics:
293 K
1
2
21 A/cm
0.8
0.6
• 1300 nm emission on GaAs
• Radiative efficiency ≈20% at RT
0.4
• Long carrier lifetime ≈ 1ns
0.2
0
0.85
0.95
1.05
Energy (eV)
1.15
• Density: ≈3x1010 cm-2
A. Zunger, MRS Bulletin 1998
Intensity (arb. un.)
Excited states:
2 10
1.5 10
1 10
-7
ES2
ES1
-7
-7
7.2 kA/cm
GS
90 0 A/cm
5 10
11 0 A/cm
0.9
1
2
ES2
ES1
2
-8
0
WL
WL
GaAs
2
GS
1.1 1.2 1.3 1.4 1.5
E nergy (eV)
Andrea Fiore
Single QD physics (and
applications):
Like an atom?
?
QDs behave as atoms...
• Discrete electronic transitions
• Coulomb and exchange effects...
A solid-state toolbox for optical
spectroscopy
XXX
PL Intensity (cps)
QD
XX
X
+
X
X
50µW
21µW
8.3µW
x2
5.3µW
x2
2.5µW
x3
760nW
x10
300nW
956
Energy (meV)
960
N. photons
• Single QDs generate single photons
2
1
Application to
Qcryptography
time
See invited talk by JM Gérard this afternoon
Andrea Fiore
QD
QDs do not behave as
atoms...
Homogeneous linewidth:
2
2
Γ=
=
+ Γ phonon (T ) + Γ Auger ( n )
T2 τ life
At RT: Γ≈5-15 meV
Borri et al., PRL 2001
Birkedal et al., PRL 2001
Bayer et al., PRB 2002
(Bayer et al., PRB 2002)
Interaction with crystal and carriers must
be considered
Andrea Fiore
QD lasers (1):
The physics of a different laser
QD
A summary of laser
performance
TTBOMK (To The Best Of My Knowledge)
On GaAs, at ≈1300 nm:
•
Jth<30 A/cm2 at RT (Huang et al. EL 2000, Park et al. PTL 2000)
•
Linewidth enhancement factor <1 (several groups)
•
10 Gb/s modulation (Hatori et al. ECOC 2004, Kuntz et al., EL 2005)
•
T0>200 K and Jth<200 A/cm2 (Shchekin EL 2002)
On GaAs (metamorphic), at ≈1500 nm:
•
Jth≈1.5 kA/cm2 at RT (Ledentsov et al., EL 2003)
On InP at ≈1550 nm:
•
Jth<400 A/cm2 at RT (Saito APL 2001, Wang PTL 2001)
•
Linewidth enhancement factor <3 (Ukhanov et al., APL 2002)
•
10 Gb/s: •
T0=84 K (Schwertberger PTL 2002)
see also A. Kovsh's talk Fr A1-1
Andrea Fiore
QD
The quantum side of QD
lasers
Quantum Dots: Are they really different (better?) than QWs?
Fact:
Inhomog. + homog. broadening makes gain linewidth " QWs
... But still it is a different laser!
Confinement-related aspects:
• Discrete n. states
• Low Jtr
• Low max gain
• Excited states
• Intraband dynam.
• Localization
• Thermal equil.?
Andrea Fiore
QD
The role of the density of
states
Transparency current:
Maximum gain per pass:
I tr ∝
g max
ρ ( E)
τ
2
πe 2 xcv
ω
=
ρ ( E)
e0nc
E
QWs:
QDs: 2
QWs:
1300 nm QDs on GaAs:InAs ρQD GaAsπ
2g S
GaAs
≈ *
≈ 0.1
QDs
10
−2
InGaAs
GaAs
S = 3x10 cm , ∆Einh = 20meV ) ρ QW
( gGaAs
m ∆Einh
kt
*
gS
QDs have ≈10mtimes
lower ρ E• Low
g S : areal dot
density
transparency
current
2
≈
(
)
ρ QW (E ) = 2
QD
∆Einh : inhom og. broad.
density of
states
• Low∆E
max
π
inh gain
Andrea Fiore
Record threshold current
density
Room-temperature:
Jth=33 A/cm2
Jtr = 9 A/cm2
Theoretical estimate for Jtr:
(NQD=2, gS=3x1010 cm-2, τ=800 ps)
8.4 µm x 4 mm
2 QD layers
y
n
a er
f
o las
tr r
J
t to
s
e uc
w nd
o
l o
e
J
ic
h
T em
s
Voltage (V)
N quantum dots ⇒ 2N states
Single facet power (mW)
QD
Current (mA)
Huang et al., Electron. Lett. 2000
eg S
J tr = N QD
= 12 A/cm 2
τ
BUT: Modal gain per QD layer ≈ 3-4 cm-1
• Low-loss cavities
• Stack many layers
Andrea Fiore
QD
Gain limitations
Strain issues in QD stacking
• Strain compensation (Zhang, APL
2003, Lever, JAP 2004)
• High-T capping (Ledentsov 2003,
Liu APL 2004)
Stacking of >10 layers
50nm
Ground state lasing only for low loss:
1 1
ln
L R
ES2
ES1
GS
Intensity (a.u.)
N QD g th = α +
-4
7 10
-4 3 QD layers
2 mm
6 10
-4
5 10
-4
4 10
-4
600 µm
3 10
-4
2 10
-4
1 10
0
0 10
1100
1200
1300
Andrea
Wavelength
(nm)Fiore
QD
Dual-state lasing
Markus et al., APL 2003
Violates population
clamping theory ???
light
population
bias
Andrea Fiore
The role of intraband
relaxation
ES
1 − fGS
1
≈
τ0
τ stim
τ0
0.35
Model
τ0 ≈ 8 ps
⇒ ES
population
GS
τstim
Photon num ber
QD
0.25
0.2
0.1
0.05
0
Population
ES threshold
GS threshold
0
8
16
24
32
40
Carrier injection rate (e/τ )
r
Integr. int. (arb. un.)
0
Exper.
GS
0.5
0
8
16
24
32
40
r
ES
1
ES
C arrier injection rate (e/ τ )
2 mm
1.5
GS
0.15
Rate equation model:
2
total
2 mm
0.3
0.14
2 mm
0.12
total
293 K
0.1
0.08
0.06
GS
0.04
0.02
0
ES
0
200
400
600
800
C urrent (m A)
1000
Fiore
Predicted by Grundmann et al.,Andrea
APL 2000
QD
A more general view
Carrier accumulation in non-lasing states:
• Low differential gain
• Large gain compression
∆n
dg GS
g' =
dn tot
capture time from WL to QD ⇒ ∆nWL
WL
relaxation time from
ES to GS ⇒ ∆nES
capture into nonlasing QDs ⇒ ∆nnonlas QDs
∆nGS << ∆n tot
dg GS
⇒ g' =
small
dn tot
• Small frel in lasers
• High Psat in SOAs
Andrea Fiore
Carriers / dot
QD
7
6
5
4
3
2
1
0
Modulation characteristics
3 QD layers
3 QD layers
tot
@10 Gb/s:
ES
GS
WL
0
8
16
24
32
40
Carrier injection rate (e/τ )
Carriers / dot
r
3.5
3
2.5
2
1.5
1
0.5
0
10 QD layers
Exp.: Kuntz, EL 2005
10 QD layers
tot
GS
ES
0
WL
8
16
24
32
40
Carrier injection rate (e/τ )
r
Andrea Fiore
Thermal equilibrium?
QD
3 Q D layers, 2 mm, pulsed
Intensity (arb. un.)
0.01
4 00 m A
0.001
293 K
2 00 m A
1 00 m A
0.0001
40 m A
10
-5
10
-6
in creasing
current
10
-7
10
-8
10
-9
1150
-
--
-
--
hν2 hν3 hν1 hν2 hν3 hν1
1250
W avelength (nm )
1350
Inhomogeneous broadening +
absence of thermal equilibrium
⇒ Broad laser line = many ≈independent lasers!
Andrea Fiore
Thermal equilibrium
QD
Occupation factor
Occupation factor
1
QDs:
lasing line
0.8
E
0.6
τact
0.4
0.2
QWs:
τSHB
k
Holes
0
10.85
0.9
0.8
0.95 1 1.05
Energy (eV)
1.1
real space
τact>100 ps
τSHB<1 ps
0.6
0.4
0.2
Electrons
0
0.85
0.9
0.95 1 1.05
Energy (eV)
1.1
QDs more prone to nonequilibrium distribution
Andrea Fiore
QD lasers (2):
Prospects for application?
• Low threshold current
• Small linewidth enhancement factor
• Temperature performance
Lasers
• Broad gain, large saturation power
SOAs, SLEDs
4π dneff / dN
=0
α =
λ
dg / dN
Gain
Ideally:
α
Refractive index
Linewidth enhancement
factor in QD lasers
QD
Current (mA)
Newell et al., PTL 1999
Energy
At high bias: Excited states!
12
10
ES
GS
8
6
4
ES
GS
2
0
5
10
G (el./dot/ τ
rad
)
Experiment
8
6
4
2
0
0
25 C
10
α -factor
α -factor
12
Model
15
0
10
20
30
Current (m A)
40
50
Markus et al., JSTQE 2003Andrea Fiore
f
Coherence collapse threshold:
fcrit
2
+
α
1
∝ Γ2
α4
α: linewidth enh. factor
Γ: damping rate
feedback level (dB)
Insensitivity to feedback
QD
I/Ith-1
O'Brien et al, Electron. Lett. 2003
QDs:
• α small
Reduced feedback sensitivity
• Γ large (gain compression)
Potential for isolator-free modules
Andrea Fiore
Temperature characteristics
∆Ec>kT
∆E <kT
∆E v
Holes spread among
closely-spaced levels
Shcheckin
et activation
al., APL 2002
No thermal
Matthews
et al., APL 2002
if ∆E>>kT
Use p-doping
T-dependence fixed by
electron distribution
T0>200 K
(Shchekin EL 2002)
Occupation factor
1
E
0.9
GS electrons
0.8
0.7
0.6
GS holes
0.5
0.4
10
Gain / Gmax
QD
0.5
50 100 150 200 250 300
Temperature (K)
GS
0
ES
-0.5
-1
-1.5
0
50 100 150 200 250 300
Temperature (K)
Andrea Fiore
QD
QDs as amplifiers
Size dispersion
Broad gain
spectrum
Carrier reservoir
WL
Akiyama et al, OFC 2004
ES2
Large saturation
power & fast
recovery time
ES1
GS
Psat>19 dBm
over 120 nm
Polarisation sensitivity ? Preliminary evidence of
2004)
polarisation control by shape engineering (Jayavel, APLAndrea
Fiore
QD superluminescent
diodes
QD
Chirped QD multilayers
Current (mAmp.)
-4
-5
10
-6
10
800
500
300
200
100
50
GaAs
InGaAs
15% In
8 µm x 4mm ridge
13.5% In
12% In
10.5% In
9% In
-7
10
-8
10
1000 1100 1200 1300 1400
Wavelength (nm)
GS: 55 nm FWHM
ES: 45 nm FWHM
GS + ES: > 100 nm
120 nm
Output power (mW)
Intensity (a.u.)
10
1.5
20 C pulsed
1
0.5
0
EPFL & EXALOS AG (Li et al, Electron. Lett. 2005)
0
0.2
0.4 0.6 0.8
1
Current (A)
Andrea Fiore
QD
QD lasers: Real
applications coming up?
QD lasers are different, in some cases better
Low chirp
Feedback insensitivity
Low-cost 10 Gb/s transmitters
Large T0
Broad gain
SOAs, tunable lasers, SLDs
Andrea Fiore
QD
Acknowledgements
• Simulations: Alexander Markus
• QD lasers: M. Rossetti, L.H. Li
• Single QDs: B. Alloing, C. Monat, C. Zinoni
• Collaborations with Alcatel CIT and EXALOS AG
Funding:
• For this tutorial: ePIXnet NoE
• For QD research at EPFL:
Andrea Fiore