From resonant tunneling diodes to quantum cascade lasers...

Tera-Mir, Cortona 2013

G. Scalari, D. Turcinkova, K. Ohtani, M. Geiser, V. Liverini, P. Liu, M. Beck

Jérôme Faist

From resonant tunneling diodes to quantum

cascade lasers: quantum confinement between

optics and electronics

Quantum well

AlAs AlAsGaAs

Growth direction

Conduction band

Valence band

= 0.3nm

3eV 1.5eV

MBEGrowth

Electronic potential

Control of semiconductor layers at the atomic level (<0.3nm)

Devices (A.Y. Cho, R. Arthur) Physics (A. Gossart, Weinmann)

Heterojunction transistors

Semiconductor lasers

Integer Quantum Hall

Fractional Quantum Hall

MBE: a key technology for nanoscience

Bricks of the quantum world

2D: Quantum Well

THz light from quantum confined structures

Intersubband energy scale well fitted to the THz Very short lifetimes

Radiative efficiency very poor Einstein’s factor

Need for Lasers/gain

Optical sources based on quantum confinement

Quantum cascade lasers THz quantum cascade lasers

Resonant tunneling diodes Could we try to improve on QCLs learning from RTDs?

Why a laser, after all? Purcell enhancement

Strong coupling

Do we need a QW? Q-dot TE luminescence

Do we even need III-V materials? Graphene THz emission

Superlattice – Bloch oscillator

Original proposal

Esaki and Tsu, IBM JRD 14, 61 (1970)

Gain predicted in the semiclassical model

Ktitorov et al., Fiz.tverd.Tela., 13, 2230, (1971), Ignatov and Romanov, Phys. Stat. Sol. B73, 327,

(1976)

1971: the superlattice under high field

Key idea: use intersubband transitions in quantum wells

R. Kazarinov R. Suris

R. F. Kazarinov, R.A. Suris, Sov. Phys. Semicond. 5, 707 (1971)

Interband versus intersubband laser

Photon energy is fixed by chemistry Photon energy is fixed by size

Cascade Laser

Cascade: N repetition of a period -> 1 electron may generate N photons

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A.L. Hutchinson, A. Y. Cho, Science 264, 553 (1994)

First quantum cascade laser

1994: First intersubband laser (quantum cascade laser) is

demonstrated in Bell Labs

Tmax = 125K (pulsed), Pmax = 10mW, = 4.26 m

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A.L. Hutchinson, A. Y. Cho, Science 264, 553 (1994)

Commercial device (c.w., single mode, = 4.6 m)

www.alpeslasers.ch

QCLs were first thought for the THz

Emission of optical phonons is quenched for T = 0 -> “Long” upper state lifetime!

Tmax ~ 65K

The probability of injecting the electronin the upper state of the lower miniband isvery small. However, once there, the electronhas a large phase space to scatter out of thisstate.

Phase space in superlattice:

MINIBAND

MINIGAP

Population inversion by phase space engineering

Covering a wide spectrum

Same device covers from the optics to the electronics

Terahertz QCL: 12 years after

Frequency

coverage

1.2 – 4.9THz

Maximum power 100mW-200mW

Linewidth

Gain bandwidth 1THz

The Good

Terahertz QCL

Frequency

coverage

1.2 – 4.9THz

Maximum power ~100mW

Linewidth

Gain bandwidth 1THz

Freq tunability 30GHz – 330GHz ETH/MIT

External cavity Very difficult SNS

The Good

The Bad

Terahertz QCL

Frequency

coverage

1.2 – 4.9THz

Maximum power ~100mW

Linewidth

Gain bandwidth 1THz

Freq tunability 30GHz – 300GHz ETH/MIT

External cavity Very difficult SNS

Max pulsed

temperature

199.5K MIT

CW max op

temperature

120K MIT/ETH

The Good

The Bad

The Ugly

Why so bad?

It is not directly h /kT

From mid-IR to THz: lifetimes

Mid-IR: - Optical phonon dominated - Weak temperature dependence

THz: - Optical phonon dominated at high T - Strong temperature dependence

Lifetime measurement

- persists T>77K- Linewidth: 0.7meV @ 10K, 2.2meV @ 120k

10 15 20 25

I = 68mA

Photon Energy [meV]

optical phonon activation (22meV)

- as expected, optical phonons are dominant above T~ 60K

- fit using computed optical phonon lifetime gives ee = 11ps@ low T- L-I curve is perturbed by blackbody radiation

0 0.04 0.08 0.12

10050 20 10

L-I curve (68 mA)Spectra (68mA)Fit (

ee= 11ps @ 0K)

1/T [K-1

d life

Temperature (K)

Emission measured up to 120K

- Fits the computed optical phonon lifetime - Extrapolate lifetime < 1ps for T > 170K

Temperature limitation: kT/h

kT = h

These ones are interesting!

Strong coupling

Room temperature THz QCL?

Operates at room temperature at = 1THz

Limited to low temperature

Comparison

J. Faist and G. Scalari, Elec. Lett. 46 (26) pp. S46 (2011)

Resonant tunneling diode characteristics

T = 300K

J > 100kA/cm2

P ~ 10uW

Comparison

Gain: negative resistance intersubband transition

Non-cascaded Cascaded

Cavity: Resonant antenna optical resonator

Comparison

A circuit-based resonator with QC active material

Active

The ideal device …

Electrical field is confined in the

dielectric of the capacitor

Gain medium as dielectric is a

QCL at 1.5 THz

Electric field of the capacitor

couples to the ISB transition

2 capacitors are required for

electrical pumping scheme

… and the real device

Planar inductor for

fabrication reasons

Half circular shaped

capacitor plates

Length is 30 m

Target frequency is

1.5 THz ( =200 m)

Circuit-based microcavity

Small size

Purcell effect (enhancement of spontaneous emission)

Microfabricated LC circuits

Circuit diagram: two LC

C. Walther et al., Science 327, p 1495 (2010)

Electromagnetic simulations:

Electric field E normal to the capacitor plates for the antisymmetric mode

Magnetic field B wraps around the inductance

Could easily be further downscaled

Same resonant frequency (1.5THz), about ½ length (15 m)

Is it a “lumped circuit”?

Compare to “oversimplified” formula Planar capacitor (1/2 disk)

“Unrolled” coaxial inductance (very rough approximation)

we get:

Passive resonator at 1.5THz

Voigt fit: Gaussian component Q = 26 Lorenzian Q = 40

Reflexion measurements

LC with active region

C. Walther et al, unpublished

Strong narrowing observed

Superexponential increase of measured power

Tuning with the inductance L

The LC laser is clearly lasing!

C. Walther et al., Science 327, p 1495 (2010)

B = 2.3T With the help of a small magnetic field

A QCL with an circuit resonant cavity

Conceptual differences

Compared to other cavities, mode volume and Q are

tunable separately.

Possible to minimize C at constant (increase L) Concentrate the E-field in a small region of space

Tunable outcoupling through current j (E confined)

Comparison

Resonant tunnel diode

Negative resistance comes

from the misalignement

between two subbands

Intersubband device?

Density matrix model

Goal: describe both current flow and gain using the same

formalism

Hamiltonian

Equation of motion

Write in terms of a Liouville equation

Liouville equation

With the terms

And compute the current

Resonant tunneling

Kasarinov-Suris result

Dephasing Upper state lifetime

Coupling

Detuning

Can be improved by a more refined model

Takes into account a better model of k-space

For degenerate subbands

Oscillation condition of a RTD

Gain = losses (in electronic terms..)

Maximum negative conductance:

Written as a function of cavity Q

Maximum current needed

Experimental parameters: = 800GHz, = 50meV (from IV curves), Q = 10

Extrapolation to mid-IR: j0-> 1MA/cm2

Second-order gain formula

Back to QCL: Use the same formalism, but with the light

interaction

Get finally a long formula for the gain

Derive the Bloch gain

Gain is achieved even w/o population inversion

but…

H. Willenberg et al., Phys Rev. B 67, 085315

(2003)

Mid-IR experiment

Good agreement with theory

R. Terazzi, T. Gresch et al., Nature Phys. 3, 329 (2007)

Structure is unstable…

Negative conductivity extends to

Cannot be cascaded

-> add an injector (make it a QCL)

Model of the injector …

Is a RTD biased before resonance.. (i.e. to stabilize

structure). Need ng>n2> n1 Further decrease the gain

Gain: strong requirement on /h

RTD vs QCLs

At high frequencies, RTDs are limited by cavity losses and their

impossibility of cascading

At low frequencies, the QCL is limited by the need for an injector

and the loss that it generates

Need for a “narrow” “injector” stabilizer, characterized by a small

Design evolution: progressively reduce the number of wells

7 QW 6 QW 4 QW

3 QW 3 QW

Kohler et al. Walther et al.

Williams et al.

Luo et al. Kumar et al.

bound-to continuum

Electrical stability is more of an issue

Two QW active

G. Scalari, Opt. Express (2010)

Injection by scattering?

For example, we separate the “stabilization” and the

“injection” functions Usually decreases the selectivity

However, enables ng>n3, n2>n1

Better results at a specific n (c.f. S. Kumar’s talk)

Reduce the injector absorption

Scattering – assisted

Extraction – assisted (lower state controls transport)

Separate “stabilizer” – but keep resonant tunneling

injection (past stable point)

Optimization of active region design

Density matrix model

Takes into account the injection reabsorption + parasitic

resonances

Conclusion: stability, leakage and waveguide losses are

limits Fathololoumi et al.,

Strong coupling

Enhance THz emission: Purcell effect

Enhance spontaneous emission “concentrate” vacuum modes to the electronic transition to enhance

emission

As Q limited by ISB broadening, need very small V Use LC resonator

Extraction efficiency remains reasonable

Y. Todorov et al., PRL 99, 223603 (2007)

Rate equations with Purcell effect

Define photon number p and electron density N

Write rate equations

Purcell

Purcell enhancement in our structure (x17)

Data are well represented

by Fp = 17

Rate equation model

C. Walther et al., Optics Letters 36, 2623 (2011)

Could easily be further downscaled

Same resonant frequency (1.5THz)

Vr = 0.12,

Q = 41

Vr = 0.02,

Q = 26

Vr = 0.002,

Q = 63

Radiative Q

frequency Cavity photon mode material excitation (cavity size)-1

Strong light-matter coupling

Cavity and a material excitation interact like coupled oscillators.

Strong light-matter coupling: Interaction strength

Figure of merit: B

ele tR

-Fast energy transfer from electronic to photonic excitation -Photonic fraction of polariton can radiate photons

Strong coupling in intersubband

First observed in the mid-infrared

Ultra-strong coupling regime Dynamical Casimir effect

Superfluidity

Enhanced emission efficiency >103

Observation of emission in mid-IR

C. Ciuti et. al., Phys. Rev. B 72 115303 (2005) S. de Liberato et al., Phys. Rev. B 77, 155321 (2008)

L. Sapienza et al., PRL 100, 136806 (2008) P. Jouy et al. Phys. Rev. B 82, 045322 (2010)

Dini et al, PRL 90, 116401 (2003)

Electroluminescence from strong coupling: theory

PPrediction: enhanced luminescence efficiency.. But..

Strong light-matter coupling: the implementation

C. Walther et al., Science, 327, 1495 (2010)

Parabolic quantum wells

- Effective parabolic potential - Digital Alloy of GaAs/AlGaAs -Designed transition E=15meV=3.9THz -Doped to 3.2x1011cm-2

-Temperature independent -No depolarization shift (Kohn‘s theorem)

Sample: Parabolic QWs & Nonresonant excitation

Reflection spectra

-Spectra taken at T=10K -ΩR=0.8THz

M. Geiser et al., Phys. Rev. Lett. 108, 106402 (2012)

Electroluminescence: Spectra

- Power: up to 60pW (100mW pump power / Conversion efficiency 6x10-10 )

M. Geiser et al. APL 101, 141118 (2012)

Anticrossing curve

Model: Y. Todorov et al., PRL 102, 186402 (2009)

M. Geiser et al. APL 101, 141118 (2012)

Electroluminescence: Temperature Performance

J. Ulrich et al., APL, 74, 3158 (1999)

60pW at T=10K, ~2pW at T=300K

M. Geiser et al. APL 101, 141118 (2012)

Efficiency

Geometric pumping efficiency: 0.03

Cavity outcoupling 0.0014

Excitation decay paths 0.24

Bright/dark Excitations

Measured efficiency: 106 10

104.7 10

M. Geiser et al. APL 101, 141118 (2012)

Strong coupling

Brick of the quantum world

Quantum dots: the electron is confined in three directions

Intersubband lasers based on dots?

Reduce the intersubband scattering rate Potential avenue for 300K THz QCL

Cascade Structure Design

Liverini, V. et al., Appl. Phys. Lett. 101 261113 (2012)

EL dependence on crystallographic orientation

y • 30µm x 1.5 mm ridges

• pulsed operation 3% duty cycle

EL dependence on crystallographic orientation

• 30µm x 1.5 mm ridges

• pulsed operation 3% duty cycle

Strong coupling

Conclusion

QCL THz Limited in high-T

Compatible with LC resonators

High power possible (0.8W)

More cavity (antenna,

Injector and ways to maintain electrical stability with the

lowest possible losses is crucial

Emission using Purcell enhancement and strong coupling

Quantum dots and graphene are still challenging – but

interessant!

Reference:

From resonant tunneling diodes to quantum cascade lasers...

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