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QDAndrea Fiore
Ecole Polytechnique Fédérale de Lausanne
Quantum Dotsfor optical applications
Tutorial developed with the support of
QD
Andrea Fiorewww.epixnet.org
Integration of research on:•Technologies for photonic VLSI
•Photonic Signal Processing
•Integrated Light Sources
•Advanced M aterials
•Nanophotonics
Access to facilities:42 Research groups12 Affiliate Partners
Through:
European Network of Excellenceon
Photonic Integrated Com ponents and Circuits
•Joint Research Activities
•Joint Education Program s
•Exchange of Researchers
•Dissem ination of Knowledge
QD
Andrea Fiore
Quantum Dots
L
λElectrons in GaAs, T=300K:
*30 nm
2λ⇔ < ≈∆ >
hLm kT
E kT
100 nm
QD devices:Outline:
• QDs: Dreams & reality
• The physics of single QDs
• Laser applications
E
Why care about QDs?
Or: The QD "dream"
QD
Andrea Fiore
Gain calculation:Arakawa, Sakaki 1982Asada et al., 1986
NB:Idealizedpicture !!!
• Lower threshold current• Lower temperature sensitivity• Larger modulation bandwidth
Narrower gain makesbetter lasers
E
Real QDs
Or: The shattered dream?
QD
Andrea Fiore
Nanostructure fabrication:Quantum Dots
• Top-down fabrication Need high-resolution lithography Etching ⇒ Nonradiative defects
Example: InAs on GaAs (but also InAs on InP, Ge on Si, ...)
15 nm
200 nm
High local In content
1300 nm on GaAs
• Bottom-up: Strain-driven self-assembly☺ High crystal quality ⇒ radiative properties
Uncontrolled nucleation ⇒ Size dispersion substrate
QDsWL
QD
Andrea FioreDot density: 300 dots/µm2
0
200
400
600
800
1000
1170 1190 1210 1230 1250
PL
coun
tsWavelength (nm)
50K, 4 µW 300 nm
300 nm diameter:
0
2200
4400
6600
8800
11000
1170 1190 1210 1230 1250
PL
coun
ts
Wavelength (nm)
1 µm40K, 4 µW
1 µm diameter:
300 nm
MacroPL at 5K:
05
101520253035
0.95 1 1.05 1.1PL
inte
nsity
(arb
. un.
)
Energy (eV)
FWHM=31 meV
idealmeas.
E
E Inh. broad.
Gain FWHM:∆EQDs≈∆EQWs
Inhomogeneous broadening
QD
Andrea Fiore
Can we do better?Controlling self-assembly
4 µm
Baier et al., APL 2004
Courtesy: E. Pelucchi, E. Kapon, EPFL
☺ Site control☺ Improved unif.
• SK growth on prepatterned substrates
In adatoms
Kohmoto et al., J. Vac. Sci. Tech. B 2002
• Growth-rate anisotropy driven growth:
GaAs QD
QD
Andrea Fiore
Radiative properties ofself-assembled QDs
QD characteristics:• 1300 nm emission on GaAs• Radiative efficiency ≈20% at RT• Long carrier lifetime ≈ 1ns• Density: ≈3x1010 cm-2
ES1
GS
ES2
WL
A. Zunger, MRS Bulletin 1998
110 A/cm 2
0
5 10-8
1 10-7
1.5 10-7
2 10-7
0.9 1 1.1 1.2 1.3 1.4 1.5
Inte
nsity
(arb
. un.
)
Energy (eV)
W LES1
ES2
GaAs900 A/cm 2
7.2 kA/cm 2
GS
Excited states:
00.20.40.60.8
11.2
0.85 0.95 1.05 1.15
1.11.21.31.4
Inte
nsity
(arb
. un.
)
Energy (eV)
293 K21 A/cm2
Wavelength (µm)
Single QD physics (andapplications):
Like an atom?
?
QD
Andrea Fiore
QDs behave as atoms...
956 960
x2
x2
300nW
760nW
2.5µW
5.3µW
8.3µW
21µW
50µW
PL In
tens
ity (c
ps)
Energy (meV)
x10
x3
X- X+XXX
XXX• Discrete electronic transitions
• Coulomb and exchange effects...
A solid-state toolbox for opticalspectroscopy
• Single QDs generate single photonsN
. pho
tons
1
2
time
Application toQ-cryptography
See invited talk by JM Gérard this afternoon
QD
Andrea Fiore
QDs do not behave asatoms...
( ) ( )2
22 ΓΓ = = + + Γphonolife
n AugerT nT τ
Homogeneous linewidth:
At RT: Γ≈5-15 meV
Interaction with crystal and carriers mustbe considered
Borri et al., PRL 2001Birkedal et al., PRL 2001Bayer et al., PRB 2002
(Bayer et al., PRB 2002)
QD lasers (1):The physics of a different laser
QD
Andrea Fiore
A summary of laserperformance
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
QD
Andrea Fiore
The quantum side of QDlasers
Quantum Dots: Are they really different (better?) than QWs?
Confinement-related aspects:• Discrete n. states
• Low Jtr• Low max gain
• Excited states
• Intraband dynam.• Localization
• Thermal equil.?
... But still it is a different laser!
Inhomog. + homog. broadening makes gain linewidth " QWsFact:
QD
Andrea Fiore
The role of the density ofstates
ρQD E( ) ≈ 2 gS
∆Einh
GaAsGaAs
InAsQDs
QDs:
S
inh
g : areal dot densityE : inhomog. broad.∆
QWs:
ρQW E( ) = m*
π 2
kt
E
InGaAsGaAs
GaAs
QWs:
( )trI
E∝ρτ
Transparency current:
( )2 2
cvmax
0Ee xg
e ncπ ω
ρ=Maximum gain per pass:
2QD S
*QW inh
2g 0.1Em
ρ π≈ ≈
ρ ∆1300 nm QDs on GaAs:
( )10 2S inhg 3x10 cm , E 20meV−= ∆ =
QDs have ≈10 times lowerdensity of states
• Low transparency current• Low max gain
QD
Andrea Fiore
Theoretical estimate for Jtr:(NQD=2, gS=3x1010 cm-2, τ=800 ps)
2A/cm12==τS
QDtregNJ
Huang et al., Electron. Lett. 2000
JRoom-temperature:
Jth=33 A/cm2
Jtr = 9 A/cm2
8.4 µm x 4 mm2 QD layers
Current (mA)
Sing
le fa
cet p
ower
(mW
)
Volta
ge (V
)
Record threshold currentdensity
N quantum dots ⇒ 2N states
The lowes
t J tr of a
ny
semico
nductor la
ser
BUT: Modal gain per QD layer ≈ 3-4 cm-1 • Low-loss cavities• Stack many layers
QD
Andrea Fiore
Gain limitations
Ground state lasing only for low loss:
QD th1 1N g lnL R
= α +
0 1001 10-42 10-43 10-44 10-45 10-46 10-47 10-4
1100 1200 1300In
tens
ity (a
.u.)
Wavelength (nm)
3 QD layers 2 mm
600 µmES1GS
ES2
• Strain compensation (Zhang, APL2003, Lever, JAP 2004)• High-T capping (Ledentsov 2003,Liu APL 2004)
Stacking of >10 layers
Strain issues in QD stacking
50nm
QD
Andrea Fiore
Dual-state lasing
Markus et al., APL 2003
Violates populationclamping theory ???
bias
populationlight
QD
Andrea Fiore
0
1 1GS
stim
fτ τ−
≈
⇒ ESpopulation
τ0
τstim
The role of intrabandrelaxation
Predicted by Grundmann et al., APL 2000
00.05
0.10.15
0.20.25
0.30.35
0 8 16 24 32 40
Pho
ton
num
ber
Carrier injection rate (e/τr)
2 mm
GS
ES
totalModelτ0 ≈ 8 ps
00.02
0.040.06
0.080.1
0.120.14
0 200 400 600 800 1000Inte
gr. i
nt. (
arb.
un.
)Current (mA)
293 K2 mm
GS
ES
total
Exper.
ES
GS
Rate equation model:
0
0.5
1
1.5
2
0 8 16 24 32 40
Popu
latio
n
Carrier injection rate (e/τr)
2 mm
GS
ES
ES thresholdGS threshold
QD
Andrea Fiore
A more general viewCarrier accumulation in non-lasing states:
• Low differential gain • Large gain compression
WL
∆n capture time from WL to QD ⇒ ∆nWL
capture into nonlasing QDs ⇒ ∆nnonlas QDs
relaxation time fromES to GS ⇒ ∆nES
GSGS tot
tot
dgn n g' smalldn
∆ ∆<< ⇒ = • Small frel in lasers• High Psat in SOAs
GS
tot
dgg'dn
=
QD
Andrea Fiore
Modulation characteristics
01234567
0 8 16 24 32 40
Car
rier
s / d
ot
Carrier injection rate (e/τr)
GS
ES
WL
tot 3 QD layers
@10 Gb/s:
10 QD layersExp.: Kuntz, EL 2005
3 QD layers
00.5
11.5
22.5
33.5
0 8 16 24 32 40
Car
rier
s / d
ot
Carrier injection rate (e/τr)
GS
ESWL
tot10 QD layers
QD
Andrea Fiore
Thermal equilibrium?
Inhomogeneous broadening +absence of thermal equilibrium⇒ Broad laser line = many ≈independent lasers!
10-9
10-8
10-7
10-6
10-5
0.0001
0.001
0.01
1150 1250 1350
3 QD layers, 2 mm, pulsed
400 m A200 m A100 m A40 m A
Inte
nsity
(arb
. un.
)
Wavelength (nm)
293 K
increasing current
- -- -
hν3hν2 hν3hν2 hν1hν1
--
QD
Andrea Fiore
Thermal equilibrium
0
0.2
0.4
0.6
0.8
1
0.85 0.9 0.95 1 1.05 1.1
Occ
upat
ion
fact
or
Energy (eV)
Holesk
E
τact
τSHB
real space
QDs: QWs:
τact>100 ps τSHB<1 ps
0
0.2
0.4
0.6
0.8
1
0.85 0.9 0.95 1 1.05 1.1
Occ
upat
ion
fact
or
Energy (eV)
Electrons QDs more prone to non-equilibrium distribution
lasing line
QD lasers (2):Prospects for application?
• Low threshold current• Small linewidth enhancement factor• Temperature performance
Lasers
SOAs, SLEDs• Broad gain, large saturation power
QD
Andrea Fiore
/4 0/
effdn dNdg dN
πα
λ= =
Ideally:
Gai
n
Ref
ract
ive
inde
x
Energy
Linewidth enhancementfactor in QD lasers
Newell et al., PTL 1999Current (mA)
α0
2
4
6
8
10
12
0 10 20 30 40 50
α-f
acto
r
Current (mA)
25 C Experiment
Markus et al., JSTQE 2003
At high bias: Excited states!
0
2
4
6
8
10
12
0 5 10 15
α-f
acto
r
G (el./dot/τrad
)
Model
ESGS
ESGS
QD
Andrea Fiore
Insensitivity to feedback
22
crit 41f + α
∝ Γα
Coherence collapse threshold:
α: linewidth enh. factorΓ: damping rate
f
QDs:• α small• Γ large (gain compression) Reduced feedback sensitivity
Potential for isolator-free modules
feed
back
leve
l (dB
)
I/Ith-1
O'Brien et al, Electron. Lett. 2003
QD
Andrea Fiore
Temperature characteristics
E
No thermal activation if ∆E>>kT
∆E
0.40.50.60.70.80.9
1
0 50 100 150 200 250 300
Occ
upat
ion
fact
or
Temperature (K)
GS electrons
GS holes
-1.5
-1
-0.5
0
0.5
1
0 50 100 150 200 250 300
Gai
n / G
max
Temperature (K)
GS
ES
T0>200 K (Shchekin EL 2002)
Holes spread amongclosely-spaced levels
Shcheckin et al., APL 2002Matthews et al., APL 2002
∆Ec>kT
∆Ev<kT
Use p-dopingT-dependence fixed by
electron distribution
QD
Andrea Fiore
QDs as amplifiersSize dispersion
Broad gainspectrum
Polarisation sensitivity ? Preliminary evidence ofpolarisation control by shape engineering (Jayavel, APL 2004)
Akiyama et al, OFC 2004Carrier reservoir
ES1
GS
ES2
WL
Large saturationpower & fastrecovery time
Psat>19 dBmover 120 nm
QD
Andrea Fiore
GS: 55 nm FWHMES: 45 nm FWHMGS + ES: > 100 nm 120 nm
10-8
10-7
10-6
10-5
10-4
1000 1100 1200 1300 1400
8 µm x 4mm ridge80050030020010050
Inte
nsity
(a.u
.)
Wavelength (nm)
Current (mAmp.)
EPFL & EXALOS AG (Li et al, Electron. Lett. 2005)
GaAsInGaAs
9% In10.5% In12% In13.5% In15% In
Chirped QD multilayers
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 O
utpu
t pow
er (m
W)
Current (A)
20 C pulsed
QD superluminescentdiodes
QD
Andrea Fiore
QD lasers are different, in some cases better
QD lasers: Realapplications coming up?
Low chirp
Feedback insensitivity
Large T0
Low-cost 10 Gb/s transmitters
Broad gain SOAs, tunable lasers, SLDs
QD
Andrea Fiore
Acknowledgements
• 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:
Alexander Markus• Simulations: