intersubband transitions: their physics and their future

ITQW ITQW AmblesideAmbleside Sept 2007.Sept 2007.

Intersubband Transitions: Their Physics and Their future.

Prof. Chris Phillips, Experimental Solid State Group, Physics Dept., Imperial College London.


Outline

*What are ISBT’s?

*What’s good (and bad) about them?

BIG JUMP!

*New wrinkles to try for improved devices.

*New bits of science to try, just for the sake of it.


Confinement Energies

* d~ few nm

*∆Ec ~ few 100 meV.1

2

3

*Much wider range of material possibilities than interband-based devices.

∆Ec

2*2

123

dmhE ≈


C2H5(OH)

CO2

Gas SensingGas Sensing

CH4

N N JaminJamin et al PNAS et al PNAS USA 951, 4837USA 951, 4837--4840 4840

(1998)(1998)


Transition strengths

*∆n-odd selection rule (in principle).

* z12 ~2-3 nm. i.e. big!

* Highly anisotropic absorption (dichroism) and dispersion (birefringence).

-5 0 5 10 15 20

-500

01500

2000

2500

ωSideband

ωQCL

ωNIR|hh1>

|e3>

|e2>

|e1>

Ener

gy (m

eV)

Distance (nm)

EInterband~ 1-3 eV

EISBT ~10-300meV

ћωprobe

* Optical response has unusual quasi-cylindrical point group symmetry.


Tunable ISBT oscillator strengths.

*ISBT transition energy (almost) independent of kll

* ISBT absorption is peaked

* Absorption ∝ electron density

EISBT ~ 10-300meV

ћω KII

EII

E?

Energy

E12 ~ 10-300meV

Photon energy (ћω)

E23

Interband Absorption,

~1 -3 eV

Doping None Low High Too High

E⊥ Absorption coefficient

Drude free carrier absorption ∝ λ2


Interband Absorption, ~1 -3 eV

Doping None Low High Too High

Ell Absorption coefficient


Dipole selection rules.

*ISBT oscillator is z-polarised

* Normally no absorption at normal incidence.

* No vertical laser cavitiesEISBT ~ 10-300meV

ћω KII

EII

E?

Energy

* Can be dodged with e.g VB and non-Γ CB material. In principle.ћωprobe

ћωc

E-vector “p”

“s”

10°

* Makes for easy absorption spectroscopy though!


Designable dispersion.

*ISBT peak is surrounded by transparent regions.

* Can add oscillators to waveguide to design-in desired dispersion characteristics.

* Electro-optical control possible through QCSE.

E12 ~ 10-300meV


E⊥ Absorption coefficient

Refractive index

* Useful for coherent optical experiments.


Broadening mechanisms (1).

*m* increases with energy (non-parabolicity), broadens transition.

* Exchange correlation effects counteract this broadening effect.

* Often a good fit to Lorentzian lineshape.

E12 ~


E⊥

With just the non-parabolicity effects

Low doping

High doping

Including many-body interactions

EISBT ~ 10-300meV

ћω KII

EII

E?

Energy

1⟩

2⟩ 3⟩

170 175 180 185 190

0.0

0.3

0.6

0.9

1.2

Photon Energy (meV)

Abs

orpt

ion

Γ ~ 5 meV


Broadening mechanisms (2).

*300k Linewidth ~10 meV , <<kT!

* Interface roughness and phonon scattering W~ 1/q2

* Scattering respects dipole selection rules.

EISBT ~10-300meV

ћω KII

EII

E?

Energy

1⟩

2⟩ 3⟩

170 175 180 185 190

0.0

0.3

0.6

0.9

1.2

Photon Energy (meV)

Abs

orpt

ion

* Low-q acoustic Phonons do the damage it seems.

Γ ~ 5 meV

* Temperature insensitivity VERY good for laser J0’s

Lasing wavelength


Intersubband laser Low Temp

High Temp

Interband laser

GAIN


Cascaded Electron Transport Idea .

* Majority carriers, insensitive to Temp and Materials quality.

* Very versatile cf pn junctions.

* Suited to wide cavities needed for IR.

* Resonant tunnelling can help keep everything aligned.

* Important “transformer”side effect.

C Sirtori et al. APL 69 (19) , 2810 (1996).


Thermal Transport .

* It’s rubbish. Frankly.

* GaAs Phonon mfp’s 1000 nm (50K) to ~40nm (375K)

* Heterostructures scatter phonons on nm length scales

* QCL conductivities ~ 10 x worse than bulk

* Comparatively few systematic studies.

C Sirtori et al. APL 69 (19) , 2810 (1996).

20 40 60 80 1000.0

0.5

1.0

1.5

2.0

2.5

3.0

0.040.060.080.100.120.140.160.180.200.220.24

Ther

mal

con

duct

ivity

, kAr

(W c

m-1K-1

)

Temperature (K)

Specific heat, σAR , (Jg

-1 K-1)

A J Borak et al. APL 82 (23) , 4020 (2003).

* CRITICAL for 300K CW devices.


Intersubband dynamics .

* Faster than a very fast thing.

* GaAs LO phonon scattering in ~100fsec.

* Poor spontaneous radiative efficiency.

* High Jth in lasers

* High saturation intensities in switches.

K L Vodopyanov et al. Semicond. Sci. Tech !2 , 08 (1994).

Kll

Energy

~10 nsec

hω

Kll

Energy

~10 nsec

hω

hωLO

~100 fsec

* “Phonon bottleneck” failed to appear.

400 fsec600 fsec

1 psec 1.2 psec


Half time summary .

Tunable in energy and strength throughout IR and FIR

* Intersubband transitions are…..

Fast, (due to intrinsic non-radiative recombination channel)

Quite sharply peaked (∆λ/λ ~ 10% @ 300K).

Insensitive to temperature and materials.

Tunable in energy and strength throughout IR and FIR.

Fast, (due to intrinsic non-radiative recombination channel)

Quite sharply peaked (∆λ/λ ~ 10% @ 300K).

Insensitive to temperature and materials.


What next then?

* New Materials possibilities.

* Plasmonics

* Non-linear optics for new wavelengths.

* Strongly coupled light-matter systems.

* Coherent Quantum Optical effects.

* Phonon Engineering.

* Subbands for Science:-Artificial Atoms.


New Materials.

* Shorter λ’s need larger ∆Ec materials

1

2

3

* Feeling Brave?

∆Ec

2*2

123

dmhE ≈

* Larger ∆Ec goes with larger bandgapand m*, and higher bond strengths.

* This means higher temp growth and doping problems.

R Akimoto et al. APL 81(16), 2998 (2002). [Tsukuba]


PlasmonicsPlasmonics

+ + +

+ + +

+

z

x

y

+

+

λ/2 = π/ kx

ε1<0

ε2>0

Conductor

Dielectric

++

Ex

+ + +

+ +

+ +

+

z

x

y

+

+

Hx Sx

λ/2 = π/ kx

ε1

ε1

Conductor

Dielectric

Dielectric

*Field Concentration*Field Concentration--sensorssensors

*Shrinking *Shrinking OptoOpto--ElectronicsElectronics

* Metallic Optics* Metallic Optics

* Opportunities for * Opportunities for semiconductors!semiconductors!

rp mne

εεω0

*22 ≈

**εε< 0 for < 0 for ωω<<ωωpp


PlasmonicsPlasmonicsr

p mne

εεω0

*22 ≈

+ + +

+ +

+ +

+

z

x

y

+

+

Hx Sx

λ/2 = π/ kx

ε1

ε1

Artificial atoms

MQW

Dielectric

Dielectric

*Already being used for QCL *Already being used for QCL cavities.cavities.

*Compresses mode volumes.*Compresses mode volumes.

••Way of guiding FIR in Way of guiding FIR in sensors?sensors?

* Quantum anisotropy means * Quantum anisotropy means new opportunities for new opportunities for semiconductors!semiconductors!

Sirtori et al. APL 66 (24), 3242 (1995).Sirtori et al. APL 66 (24), 3242 (1995).

* Negative refraction exotica * Negative refraction exotica possible.possible.

Jonathan Plumridge and Jonathan Plumridge and CCP.Phys.RevCCP.Phys.Rev. . B 76, 075326 (Aug 2007) .B 76, 075326 (Aug 2007) .

V A V A PodolskiyPodolskiy and EE and EE NarimanovNarimanov , PRB , PRB 71, 201101,(2005) .71, 201101,(2005) .


NonNon--linear optics for new linear optics for new wavelengthswavelengths

*QCL cavities have high *QCL cavities have high radiation density and the radiation density and the intrinsic intrinsic χχ(2) of (2) of llllll--VV’’s.s.

*Artificial resonances can be *Artificial resonances can be designeddesigned--in.in.

*Designable dispersion for *Designable dispersion for phase matching.phase matching.

N N OwschinikowOwschinikow et al. PRL, et al. PRL, 90 (4), 04390290 (4), 043902--1 (2003).1 (2003).

S S S S DhillonDhillon et al. APL 87, et al. APL 87, 071101 (2005).071101 (2005).

K L K L VodopyanovVodopyanov et al. APL et al. APL 72(21), 2654 (1998).72(21), 2654 (1998).

Polarisation

E

E Input at ω

P response at ω + 2ω


Strongly coupled cavitiesStrongly coupled cavities

1⟩

2⟩

hω Photon energy.

Absorption

*Einstein*Einstein’’s rules assume s rules assume matter and light only matter and light only perturbativelyperturbatively coupled.coupled.

*Small mode volume, high Q, *Small mode volume, high Q, coupling energy dominates all coupling energy dominates all other terms.other terms.

*Non*Non--EinsteinianEinsteinian lasers?lasers?

D D DiniDini et al. PRL, 90, 116401 (2003)et al. PRL, 90, 116401 (2003)

*Good for weakly absorbing *Good for weakly absorbing detectors.detectors.

ET ET JeynesJeynes and FW Cummings Proc, and FW Cummings Proc, IEEE , 51, (1), 89IEEE , 51, (1), 89--109 (1963).109 (1963).

**QCLQCL’’ss uniquely suitable for this.uniquely suitable for this.


Quantum Optics: Rabi Splitting and EITQuantum Optics: Rabi Splitting and EITħΩRabi

1

2

3

ħωCouple

ħωprobe

Generalised Rabi Frequency

ħΩ2Rabi = (µ.E)2 + (ħ∆Couple)2

Just the dressingJust the dressing Dressing Dressing andandQuantum InterferenceQuantum Interference

EE1212EE1212


MatterMatter--wave interferencewave interference

1

2

3

ħωCouple

ħωprobe


EIT was first seen in atomic vapoursEIT was first seen in atomic vapours……

K J Boller, A Imamoglu and S E Harris, PRL 66,2593 (1991), using Rubidium vapour.


0.0

0.2

0.4

0.6

0.8

1.0

155 160 165 170 175 180 185 190-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

170 175 180 185 190

0.00

0.02

0.04

0.06

-Ln(

Tran

smis

sion

)

Photon Energy (meV)

ħωCouple = 155meV

GWI with subband transitions!

Rabi sideband expected at 155meV (= Ecouple)

Intensity ofCoupling Field

1.3MW/cm2

1.5MW/cm2

M D Frogley et al, Nature Materials, Vol. 5 M D Frogley et al, Nature Materials, Vol. 5 , 175, 175--178, March 2006.178, March 2006.


Slow Light.

Vgroup = c/40 in the region where the sample is transparent/amplifying.

Vgroup = c/ngroup = c/(n0 + ωdn/dω)

165 170 175 180 185 190 195-0.7-0.5-0.20.00.20.50.70.9

-0.6-0.4-0.20.00.20.40.6

Abs.

Coe

ff. (1

04 cm-1)

Photon Energy (meV)

Refractive Index


Phonon Engineering?Phonon Engineering?*We already structure *We already structure electronics an optical aspects, electronics an optical aspects, why not acoustic as well?why not acoustic as well?

*Dephasing Acoustic and *Dephasing Acoustic and depopulating phonons both depopulating phonons both have have λλ~ 15 nm.~ 15 nm.

**PhononicPhononic SLSL’’s for improved s for improved thermal conductivity? thermal conductivity?

**PhononicPhononic antianti--nodal cavities nodal cavities for decoupling electrons from for decoupling electrons from crystal? crystal?

Kll

Energy

~10 nsec

hω

hωLO

~100 fsec

1

2

3


Artificial atoms for Science!Artificial atoms for Science!

+ + + +

+ +

+

z

x

y

+

+

λ/2 = π/ kx

ε1

ε1

Artificial atoms

MQW

Dielectric

Dielectric

++

Ex 850 1350 1850 2350

wavenumber / cm-1

p/s

refle

ctiv

ity ra

tio

**ISBTISBT’’ss behave like behave like designable atomsdesignable atoms

*New symmetries and energy *New symmetries and energy level juxtapositions possible.level juxtapositions possible.

*Cavities are easy*Cavities are easy

*They stay put!*They stay put!

*Cavity QED?*Cavity QED?

*Flying *Flying qubitsqubits??


AcknowledgementsMark Frogley (exMark Frogley (ex--Imperial, now RAL)Imperial, now RAL) Spectroscopy Jon PlumridgeJon Plumridge (Imperial)(Imperial) and modellingJames Dynes (exJames Dynes (ex--Imperial, now Imperial, now UCL))Mary Matthews (Imperial)(Imperial)Rob Steed (Imperial)(Imperial)

Ed Clarke (Imperial)(Imperial) MBE growth MBE growth Ray Murray

H C Liu Strongly coupledEmmanuel Dupont Cavity samples

Ben Williams (ex-MIT, now UCLA) THz frequency mixingMaurice Skolnick (Sheffield) QCL’sLuke Wilson (Sheffield)

Jerome Faist and Jerome Faist and Mattias Beck (Neuchatel) Mattias Beck (Neuchatel) Artificial atom Artificial atom multilayersmultilayers

Elodie Roussard (Imperial) DMT/Gaussian beam

Justin Rodger (Masters ICL) AQW Design/DMT software

Danny Segal, Almut Beige (ICL) Discussion – Dressed states

EPSRC (UK) – Funding

intersubband transitions: their physics and their future

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