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