UniversitUniversitàà di Baridi Bari CNRCNR--INFM INFM RegionalRegional LabLab

Miriam S. Vitiello, Gaetano Scamarcio, Regional Laboratory LIT 3, CNR – INFM and Physics Dept.,University of Bari, Italy

Giacomo Scalari, Christoph Walther, Jerome FaistETH Zürich Switzerland

Harvey Beere, David RitchieCavendish Laboratory, University of Cambridge, Cambridge, UK

Hot electrons in THz quantum cascade Hot electrons in THz quantum cascade lasers lasers

OutlineOutline

Experimental evidence of hot-electron cooling associated with photon emission

Energy balance equation model in QCLs→ correlation of laser induced hot electron cooling with quantum efficiency

Assessment of:

• Internal quantum efficiency

• External differential efficiency

• Wall-plug efficiency

• Slope efficiency

• Electron-lattice energy relaxation times

• In Electronic and Photonic devices electrons release the excess energy gained from the applied electric field by:

• exciting other electrons • emitting phonons or photons

• Equilibrium condition between PP and the energy loss rate: average electron energies > crystal lattice one → hothot--electron populationselectron populations

• Electronic distributions: Fermi-Dirac functions characterized by temperatures Te >> TL

• Relevance of including hot-electron distributions in semiconductor laser modellingsemiconductor laser modelling →hot electron effects are directly correlated with physical parameters central in the laser theory

MotivationMotivation

Lattice TL

Heat sink TH

Input Power(P)

ττeLeL

ElectronsElectrons

Non equilibrium distributionThermalized by

e-e (∼ 0.1 ps above ∼ 1010 cm-2)e- LO phon scattering (∼ 0.1 ps)

• Energy relaxation channels in QCL:

-Inter and intra-subband e-e scattering

ττeeee ∝∝ ΔΔE/E/nnjj → scattering time is proportional to the energy separation between the initial and final states

-e - phonon scattering ττeLeL energy loss lifetime between each electronic subsystem and the lattice

- e-impurity-interface roughness

Interplay between above processes → different electron temperatures among subbands

-QCL ideal to study hot electron populations: Large P High thermal resistancesLimited e-lattice relaxation efficiency

Energy balance in Energy balance in QCLsQCLs

Lattice TL

Heat sink TH

ττeLeL

ττeeee 8

1,2

Input Power(P)

ττeLeL

6

InjectorInjector Active regionActive region

MM11

Quantum design:Quantum design:

• Bound-to-continuum scheme • Two-level injection/depletion module•• EE8686 = 7.4 = 7.4 meVmeV ; ; zz8686 = = 10.1 nm10.1 nm•• EE11--2,8 2,8 ~ 0.6 ~ 0.6 meVmeV

Two electronic subsystems can be identified:

• Active regionActive region: includes the upper laser level and the depletion miniband.

• The injectorThe injector: doublet of closely spaced lowest energy levels.

Low frequency THz Low frequency THz QCLsQCLs

Walther et al. APL 89, 231121

Distance (nm)

100 0

Ene

rgy

(eV

)

86

12

Injector Active

0.10

0.05

0

Experimental approachExperimental approach

8→k

1,21,2→ k

(1) (2)(3)(4)

ΔE = (E-EP) (eV)

PL

Inte

nsity

(arb

. un

its)

0.02 0.040

100

10-1

10-2

(1) 70A/cm2

(2) 93 A/cm2

(3) 118 A/cm2

(4) 140 A/cm2

• Photoluminescence spectroscopy on the laser front facets

• Extract local lattice and electronic temperaturesfrom PL analysis

Si CCD

Monochromator

Objective

Kr+ Laser

He-flow micro-cryostat

X-Y control (100nm)

(1) (1) →→ Low V; Below the threshold for carrier injection into the upper state → most of the electrons are sitting in the injector doubletinjector doublet

((22--33--44) →→ Higher V; the energy difference between the injector and the upper state is reduced → additional peaks on the high energy tail of the main PL bands shows that electrons are injected into level 8electrons are injected into level 8..

Electronic and Lattice temperaturesElectronic and Lattice temperatures

Measurement of the electron temperatures:

- Below threshold of alignment- After injection into the upper state- Above lasing threshold

50

100

150

0 0.2 0.4 0.6 0.8 1.0

50 100 150

50

100

150

0

4

8

0 0.2 0.4 0.6 0.8 1.00

40

80

a

b

Power (W)

Vol

tage

(V)

dV/d

I (Ω

)

Te

j(K

)

TL

(K)

I

IIIII

IV

Current density (A/cm2)

Four regionsFour regions, clearly correlated with features in the transport transport measurementsmeasurements can be identified.

0

4

8

0 0.2 0.4 0.6 0.8 1.00

40

80

50

100

150

0 0.2 0.4 0.6 0.8 1.0

50 100 150

50

100

150

Electronic and Lattice temperaturesElectronic and Lattice temperatures

Efficient electron-lattice scattering Rate equation:Rate equation:

[ ] ps..)RR(NkN LeBeeL 250220 −=−=τ

I I Below injection into level 8Below injection into level 8

M1

8

61,2

• Efficient (τee≈100 fs) energy redistribution process between the injector and M1 → Te

inj ≈ Teactive

• )( Lej

eL

jj TTkn

Ρdt

dE−−=

τ

L

einj

e RP

TR ≈=ExperimentalExperimental

a

b

Power (W)

Vol

tage

(V)

dV/d

I (Ω

)

Te

j(K

)

TL

(K)

I

IIIII

IV

Current density (A/cm2)

Electronic and Lattice temperaturesElectronic and Lattice temperatures

II II AboveAbove alignmentalignment

• The measured electronic temperature corresponds to Te

active

– Injection in level 8 → confirmed by new PL peaks

– Subband populations in the same quantum wells equilibrate quickly (100-200 fs) to a common Te

– Experiments in BTC THz QCLs demonstrate that the miniband and the upper subbandshare a common Te

Vitiello et al. APL APL 89, 021111, (2006).89, 021111, (2006).

50

100

150

0 0.2 0.4 0.6 0.8 1.0

50 100 150

50

100

150

0

4

8

0 0.2 0.4 0.6 0.8 1.00

40

80

a

b

Power (W)

Vol

tage

(V)

dV/d

I (Ω

)

Te

j(K

)

TL

(K)

I

IIIII

IV

Current density (A/cm2)

Electronic and Lattice temperaturesElectronic and Lattice temperatures

• Cold electrons progressively populate level 8

• electrons are scattered elastically or quasi-elastically with a large excess energy to a lower state

• electrons thermalize within their respective subbands at a temperature Te

active > Teinj

M1

861,2

II II AboveAbove alignmentalignment

HeatingHeating of the upper laser of the upper laser levellevel::• A comparable amount of injected electrical power is distributed between the two subsystems• But nactive << ninj

50

100

150

0 0.2 0.4 0.6 0.8 1.0

50 100 150

50

100

150

0

4

8

0 0.2 0.4 0.6 0.8 1.00

40

80

a

b

Power (W)

Vol

tage

(V)

dV/d

I (Ω

)

Te

j(K

)

TL

(K)

I

IIIII

IV

Current density (A/cm2)

Electronic and Lattice temperaturesElectronic and Lattice temperatures

LasingLasing regionregion

50

100

150

0 0.2 0.4 0.6 0.8 1.0

50 100 150

50

100

150

0

4

8

0 0.2 0.4 0.6 0.8 1.00

40

80

a

b

Power (W)

Vol

tage

(V)

dV/d

I (Ω

)

Te

j(K

)

TL

(K)

I

IIIII

IV

Current density (A/cm2)

Efficient hot electron cooling hot electron cooling by photon emission →Photon emission extracts part of the input power

Further proof: Lasers vs mesas

0

50

100

150

80 100 120 140 160 180

(Te ac

tive-

TL)

(K)

Current density (A/cm2)

laser

mesa

• Mesa device → No evidence of change in the slope

• Change in the slope at the onset of lasing

( )dJ

TTd Le

active −

( )dJ

TTd Le

active −

Electronic and Lattice temperaturesElectronic and Lattice temperatures

Sample A (50 Sample A (50 µµmm ×× 1mm)1mm) Sample B (140 Sample B (140 µµmm ×× 1mm)1mm)

50

100

150

0 0.2 0.4 0.6 0.8 1.050

100

1500

4

8

1250 100 150

0

40

80

120

Tej

(K)

TL

(K)

Power (W)

V (

Vol

t)

dV/d

I (Ω

)

J (A/cm2)

(a)

(b)

50

100

150

0 1 2 350

100

1500

4

8

12

50 100 150

0

20

40(a)

(b)

Tej

(K)

TL

(K)

Power (W)

V (

Vol

t)

dV/d

I (Ω

)

J (A/cm2)

Energy balance in Energy balance in QCLsQCLs

thotot PPP

dt

dE −−=

Electrical ThermalOptical

)TT(kn

)kTkT(q

J

dt

dEL

einj

eL

injeinj

eactive

inj −−+−=τ

Δ1

ντ

nShgTTkn

EkTkTq

J

dt

dEL

eactive

eL

activemb

eactive

einj

active Δ−−−Δ+Δ+−= )()( 86

86EkTkT mbe

inje

active Δ+Δ<<−Present case

Lattice TL

Heat sink TH

ττeLeL

ττeeee 8

1,2

Input Power(P)

ττeLeL

6

Injector Active region

MM11

Hot electron cooling Hot electron cooling →→ probe of the laser probe of the laser efficiencyefficiency

• Cooling of hot electrons in the active region is correlated with the internal quantum efficiency of a laser

S=S= 00

SS≠≠ 00

qdJ

dStotint ⋅⋅=

+⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

= ατ

τττ

τττ

η

686

68

86

68

1

1

InternalInternal quantum quantum efficiencyefficiency

( )mbactive

eLLe

active EkqndJ

TTd Δ+Δ≈−68

)( τ

( )intmbactive

eLLe

active hhkqndJ

)TT(dνηΔν

τ−+=

−

020406080

100

80 100 120 140 160

020406080

100

80 100 120 140 1600

20406080

100

80 100 120 140 160

020406080

100

80 100 120 140 160

J (A/cm2) J (A/cm2)

J (A/cm2) J (A/cm2)

40K 60K

50K 70K

(Tac

tivee-

TL)(

K)

(Tac

tive

e-T

L)(

K)

(Tac

tive

e-T

L)(

K)

(Tac

tivee-

TL)(

K)

Temperature dependence of Temperature dependence of TTeeactiveactive

At increasing TH, the slope the slope d(Td(Tactiveactiveee--TTLL)/dJ)/dJ above lasing threshold above lasing threshold increases → laser cooling

less effective

Internal quantum efficiency ηint

0

1

2

3

4

5

0 20 40 60 80 100

TH (K)η d

(%

)

Differential external Differential external quantum efficiency quantum efficiency

per stageper stage

0

20

40

60

80

100

0 20 40 60 80 100

TH (K)

η in

t(%

)

tot

mintd α

αη=η

( )( )

υΔυ

Δυτη

h

h

h

kqn

dJ

)TT(d mb

mbeL

activeLactive

eint

+⎟⎟⎠

⎞⎜⎜⎝

⎛

+−−= 1

Internal quantum efficiencyInternal quantum efficiency

Comparison with alternative experimental approachesComparison with alternative experimental approaches

• The measured efficiency values are a factor ≈ 4.5 larger than those obtained by conventional optical measurements

• Optical testing → inherently limited by:– the small collection efficiencies of the optical set-ups – the high optical beam divergence of metal-metal waveguides

•• Alternative approachesAlternative approaches → relative change in the differential resistance above and below threshold

⎟⎠

⎞⎜⎝

⎛ −=R

Rint

Δη 1

- Due to residual resistances in the device understimation of ≈40% in the internal quantum efficiency have been obtained

WallWall--plug efficiencyplug efficiency

0

0.1

0.2

0.3

0 20 40 60 80 100

TH (K)

η wM

AX

(%)

⎟⎠

⎞⎜⎝

⎛ −=J

J

Ve

Nh th

tot

mw 1

1int

νααηη

η w (%

)

64

2

0

(TL

-T

H –

RL

×P

) (K

)

Power (W)

(d)

(e)

01

-1-2

0 2 4 6

Our thermal selfOur thermal self--calibrated approach in calibrated approach in surface surface plasmonplasmon THz THz QCLsQCLs

• Deviations from the thermal resistance trend in the lasing range Pthermal ηW

ηηw w = 1= 1-- ΔΔT/(PT/(Pinin ×× RRLL))

Sensitivity:Sensitivity: ηW > 1%

Hot electron probe → Higher sensitivityHigher sensitivity, particularly useful in the characterization of terahertz sources with highly diverging beams like doubledouble--metal metal QCLsQCLs.

M.S.Vitiello, et al.APL 90, 191115 (2007)

Alternative gain mediaAlternative gain media

• The processes observed in the terahertz QCLs are quite general and can be conveniently extended also to other gain media

•• DoubleDouble--heterostructureheterostructure interbandinterband laserslasers → carrier heating by Auger recombination plays a very fundamental role

– The hot carrier cooling rate may be much slower than the energy loss rate by phonon emission

– The excited level temperature increase well above the one of the lattice or the carrier reservoir

– Less abrupt change of the heating rate at threshold is expected → a significant amount of power is extracted from the laser via spontaneous emission processes even below threshold.

SummarySummary

• Experimental evidence of a new physical phenomenon characteristic of semiconductor lasers: the cooling of the electrons above the laser threshold for stimulated emission

• Correlation between the hot electron cooling and the internal quantum efficiency of a laser

• Self-calibrated approach to extract the internal quantum efficiency and the wall-plug efficiency in a QCL

•• ImplicationsImplications →→

–– Inclusion of the electronic temperature in the general theory ofInclusion of the electronic temperature in the general theory of semiconductor semiconductor laserslasers

–– HotHot--electron effects must be fully understood in THz QCL to explore electron effects must be fully understood in THz QCL to explore the device the device physical limits in terms of maximum temperature, wavelength and physical limits in terms of maximum temperature, wavelength and quantum quantum efficiencies.efficiencies.