Hot Hot electronselectrons and Hot and Hot phononsphonons in in Quantum Quantum CascadeCascade LasersLasers

Vincenzo Spagnolo, Miriam S. Vitiello, Gaetano ScamarcioCNRCNR--INFM INFM –– University and Politecnico of Bari, ItalyUniversity and Politecnico of Bari, Italy

• Motivation: all important device characteristics are strongly dependent from the electron energy relaxation processes and the mean energy of electron, phonon and lattice subsystems

• Technique:• Photoluminescence and Raman Stokes-AntiStokes spectra with high spatial

resolution (~ 1 µm)– PL: local lattice temperature; electronic temperature– Raman: optical phonon population;

ResultsResults: : •• Hot Hot electronselectrons in in SbSb--basedbased QCLsQCLs•• NonNon--equilibriumequilibrium phononphonon generation via generation via electricalelectrical methodmethod ((midmid--irir QCLsQCLs))•• SuperlinearSuperlinear increaseincrease of hot of hot phononphonon populationpopulation vsvs electricalelectrical power (power (THzTHz QCLsQCLs))

kz

0

π/dk//

EN

ER

GY EnergyEnergy RelaxationRelaxation

ProcessesProcesses in in QCLsQCLs

Electrical PowerElectrical PowerElectronsElectrons Laser Emission

Optical Phonons

Lattice Temperature

Hot-PhononsSpagnolo, Scamarcio et al

APL 80, 4303 (2002)

Hot-Electrons

Sub-systems characterized by different temperatures

Acoustic Phonons

Hot electrons in Hot electrons in SbSb--based based midmid--IR IR QCLsQCLs

Electronic spatial distribution vsvsvoltagevoltage in InGaAs/AlAsSb mid-IR QCLs:

• Correlate the quantum design of devices with their thermal performance

• Thermal backfilling of the lower laser level

Electron-lattice energy relaxation in InGaAs/AlGaAsSb quaternary barrier mid-IR QCLs

• First electronic temperature measurements in Sb-based QCLs

•• Good electronGood electron--lattice couplinglattice coupling � τe ~ 5,1ps50

70

90

110

0 1 2 3 4Power (W)

Tem

pera

ture

(K)

InGaAs/AlGaAsSbInGaAs/AlGaAsSb--based based QCLsQCLs

8.5V

Vitiello, Spagnolo, Scamarcio, Vitiello, Spagnolo, Scamarcio, RevinRevin, Cockburn, Cockburn etet al., al., JAPJAP, 98, , 98, 086107 (2005)086107 (2005)Vitiello, Spagnolo, Scamarcio, Vitiello, Spagnolo, Scamarcio, Yang, Wagner Yang, Wagner etet al., al., (2006)(2006)

9.6V

0.9 1.0 1.1 1.2

off

6V

PL I

nten

sity

(ar

b.un

its)

Energy (eV)

GaInAsGaInAs//AlAsSbAlAsSb-- basedbased QCLsQCLsactive region lower

emission level

7V

ground injector

ElectronElectron--optical phonon interactionoptical phonon interaction

1 injected electron � 4- 6 optical phonons/stage in Mid- IR QCLs� 1 optical phonons/stage in RP THZ QCLs

(larger number of stages)phonon emission rates >> phonon lifetime � hot phonons

QC Laser structures “optical phonon factory”

DetermineDetermine the PHONONS OCCUPATION the PHONONS OCCUPATION NUMBERNUMBER

RP-THz QCLs

OpticalOpticalphononphonon

kz k//k//

SL-based QCLs

OpticalOpticalphononphonon

0

0.1

0.2

0.3

50 100 150 200 250 300

DETERMINATION OF PHONONS OCCUPATION NUMBERDETERMINATION OF PHONONS OCCUPATION NUMBER

NN

StokesAStokes 1+∝−

Raman Scattering � Probe of phonon population

ConstantConstant far fromResonant condition

( )( )

14

0

0 1)()(

−

−

−+−=

ωωωωωωωωωωωωωωωω

ωωωωσσσσωωωωσσσσ

L

L

LAS

LS

SISAIN

KK

Anti-Stokes/Stokes Intensity ratio vsLattice temperature (device off)

Anti-Stokes/Stokes Intensity ratio vsLattice temperature (device off)

0

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3IAS / IS

Occ

upat

ion

Num

ber

Calibration curve

Temperature (K)

I AS

/ IS

IAS/IS=K·e-hω/(kTL )

nearResonance

0

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3IAS / IS

HotHot--OpticalOptical PhononPhonon populationpopulation

Anti-Stokes/StokesRatio vs Temp

Occupation NumberCalibration curve

PL Spectra@ device on Lattice temperature

Occ

upat

ion

Num

ber

Calibration curve

Raman Spectra@ device off

Phonon (Thermal) Occupation number

Raman Spectra@ device on

Phonon total occupation number

HOTHOT-- phononphononpopulationpopulation

500 mA

Antistokes

Stokes

-350 -300 -250 -200 150 200 250 300 350

Raman Shift (cm-1)

Inte

nsity

(a.u

.)

* *

**

*0 mA

Hot phonon generation in Hot phonon generation in InGaAsInGaAs--AlInAsAlInAs MidMid--IR IR QCLsQCLs(V. Spagnolo et al. APL 2002)

( )I

nVr

NkkdAk hotpp ⋅

∆⋅⋅−⋅⋅⋅⋅= ωωωω

ππππττττ {

minmax2

2

2

0

0.1

0.2

0.3

0.4

50 100 150 200 250 300

Occ

upat

ion

num

ber

Occ

upat

ion

num

ber

Temperature (K)Temperature (K)

nntottotnneqeq

nnhothot

P=3P=3.2.2 WW ••GaAsGaAs--like interface phonon (like interface phonon (IFIFGaAsGaAs))

•Monte Carlo Simulationrelative IFIFGaAsGaAs relaxation rate r=25%

••FixedFixed electricalelectrical PowerPower••Interface Phonon LifetimeInterface Phonon Lifetime

Temperature (K)Ph

onon

lifet

ime

ττ ττ(p

s)

1

2

3

4

5

6

100 150 200 250 300

∆∆∆∆∆∆∆∆V V ·· II

Electron injection rate Phonon generation rate

Rate equation ( ) ( )τ

nknkG tot 0−=

Frohlich interaction ( ) 2kαkG =

Investigated THz Investigated THz QCLsQCLs based on based on LOLO--phonon depopulation emitting @ 2.8 THzphonon depopulation emitting @ 2.8 THz

45

321

• Laser transition 5→ 4 (vertical)• 3-4 anticrossing → fast optical phonon scattering• 1-2 anticrossing → selective injection; parasitic channel reduction

Metal-Metal (Cu-Cu) waveguide

•10-µm thick active region

• 176 periods of a GaAs/Al0.15Ga0.85As

•Tmax = 105 K (CW)

What kind of phonons can be investigated What kind of phonons can be investigated in a (001) GaAsin a (001) GaAs--AlGaAsAlGaAs QCL structure ?QCL structure ?

Raman Raman SelectionSelection RulesRulesin in backscatteringbackscattering fromfrom devicedevice facetfacet

LO

TO

GaAs

AlGaAs

LO GaAs-like

LO AlAs-like

TO GaAs-like

TO AlAs-like

IF

LOGaAsIF

TOGaAsIF

LOAlAsIF

TOAlAsIF

Z(001)

X’

Y’

Y’(ZX’)Y’

DeformationDeformationPotentialPotential

The symmetry selection rules are broken close the resonances The symmetry selection rules are broken close the resonances

µµ-- Raman investigation of GaAsRaman investigation of GaAs-- AlGaAsAlGaAs RP THz RP THz QCLsQCLs

2nd Order

Inte

nsity

(a.u

) GaAs-IFTO

Stokes shift (cm-1)

0

10

20

250 300 350

*

VerifyVerify the ABSENCEthe ABSENCEof of ResonanceResonance ConditionsConditions

%71

2 <st

nd

II

Anti-Stokes/Stokes Intensity ratio vs Lattice temperature (device off)Anti-Stokes/Stokes Intensity ratio vs Lattice temperature (device off)

Temperature (K)I A

S / I

S

0

0.1

0.2

0.3

0.4

100 150 200 250 300

Calibration curve

IAS/IS=K·e-hω/(kT)

Exciting Laser

Light Scattering in Solids, Plenum, pg.249 (1979)

Raman Raman spectraspectra followfollow selectionselection rulerule

0

0.1

0.2

0.3

1.0 1.2 1.4 1.6 1.8 2.01.6 1.8 2.0

Hot phonon generation in GaAsHot phonon generation in GaAs--AlGaAsAlGaAs RP THz RP THz QCLsQCLs

Electron injection rate

dAeIGe ⋅⋅

=I=injected currentA=active layer aread=active layer width

Occ

upat

ion

num

ber

Occ

upat

ion

num

ber

Power (W)Power (W)

••FixedFixed QC QC devicedevice HeatHeat sinksink temperaturetemperature@ 80 K@ 80 K••GaAsGaAs--like interface phonon (like interface phonon (IFIFGaAsGaAs))nnTotTot

nneqeq

nnhothot

[ ]3326 Min

hotp kkAd

VInr

Max−⋅⋅

∆=⋅

ππππωωωωττττ �

Phonongeneration rate ep Gr

ωVeG ⋅⋅∆=

{

∆∆∆∆V=voltage across active layerr =relative phonon relaxation rate�ω = phonon energy

Laser Laser ThresholdThreshold

Rate equation ( ) ( )τ

nknkG tot 0−= Deformation Potential ( ) 0kkG ⋅= β

240 260 300280

1.85W

1W

0W

AntiStokes shift (cm-1)

0.5 counts/sec

5 counts/sec

Stokes shift (cm-1)

1.85W1W0W

240 260 300280

GaAs-IFTO

PHONONS PHONONS lifetimelifetime and and relaxationrelaxation raterate

••PhononPhonon LifetimeLifetime τP decreasesdecreases withwith TTLL

••Increases of the Relative Phonon Increases of the Relative Phonon Relaxation Rate “Relaxation Rate “r”r”

CHARACTERISTIC OF PHONON CHARACTERISTIC OF PHONON STIMULATED STIMULATED EMISSIONEMISSION

Triggered by electronic population Triggered by electronic population inversioninversion

NO NO LinewidthLinewidth narrowingnarrowing

AcknowledgmentsAcknowledgmentsBenjamin S. Williams

Sushil Kumar

Qing Hu

John L. Reno

Mariano Troccoli

Federico Capasso

Claire Gmachl

Quankui Yang

Joackin Wagner

Dmitry Revin

John Cockburn