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: