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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
Tera-Mir, Cortona 2013
Quantum well
AlAs AlAsGaAs
Growth direction
Al
As
GaUHV
Conduction band
Valence band
Po
ten
tia
l
= 0.3nm
3eV 1.5eV
MBEGrowth
Electronic potential
Control of semiconductor layers at the atomic level (<0.3nm)
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
Bricks of the quantum world
2D: Quantum Well
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
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)
Tera-Mir, Cortona 2013
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)
Tera-Mir, Cortona 2013
Interband versus intersubband laser
Photon energy is fixed by chemistry Photon energy is fixed by size
Tera-Mir, Cortona 2013
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)
Tera-Mir, Cortona 2013
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)
Tera-Mir, Cortona 2013
Commercial device (c.w., single mode, = 4.6 m)
www.alpeslasers.ch
Tera-Mir, Cortona 2013
QCLs were first thought for the THz
Emission of optical phonons is quenched for T = 0 -> “Long” upper state lifetime!
Tera-Mir, Cortona 2013
Tmax ~ 65K
E2
E1
E3
k
32 2
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
32
Population inversion by phase space engineering
Tera-Mir, Cortona 2013
Covering a wide spectrum
Same device covers from the optics to the electronics
Tera-Mir, Cortona 2013
Terahertz QCL: 12 years after
Frequency
coverage
1.2 – 4.9THz
Maximum power 100mW-200mW
Linewidth
60Hz
Gain bandwidth 1THz
The Good
Tera-Mir, Cortona 2013
Terahertz QCL
Frequency
coverage
1.2 – 4.9THz
Maximum power ~100mW
Linewidth
60Hz
Gain bandwidth 1THz
Freq tunability 30GHz – 330GHz ETH/MIT
External cavity Very difficult SNS
The Good
The Bad
Tera-Mir, Cortona 2013
Terahertz QCL
Frequency
coverage
1.2 – 4.9THz
Maximum power ~100mW
Linewidth
60Hz
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
Tera-Mir, Cortona 2013
Why so bad?
It is not directly h /kT
Tera-Mir, Cortona 2013
From mid-IR to THz: lifetimes
Mid-IR: - Optical phonon dominated - Weak temperature dependence
THz: - Optical phonon dominated at high T - Strong temperature dependence
Tera-Mir, Cortona 2013
Lifetime measurement
- persists T>77K- Linewidth: 0.7meV @ 10K, 2.2meV @ 120k
10 15 20 25
(x 3)
I = 68mA
10 K
40 K
60 K
80 K
100 K
120 K
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
2
5
10
20
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
]
Fitte
d life
tim
e (
ps)
Temperature (K)
Emission measured up to 120K
- Fits the computed optical phonon lifetime - Extrapolate lifetime < 1ps for T > 170K
2
1
Tera-Mir, Cortona 2013
Temperature limitation: kT/h
kT = h
MIT
These ones are interesting!
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
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)
Tera-Mir, Cortona 2013
Resonant tunneling diode characteristics
T = 300K
J > 100kA/cm2
P ~ 10uW
Tera-Mir, Cortona 2013
Comparison
Gain: negative resistance intersubband transition
Non-cascaded Cascaded
Cavity: Resonant antenna optical resonator
Tera-Mir, Cortona 2013
Comparison
Gain: negative resistance intersubband transition
Cavity: Resonant antenna optical resonator
Non-cascaded Cascaded
Tera-Mir, Cortona 2013
A circuit-based resonator with QC active material
Active
<< l
+
-
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
… 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)
Tera-Mir, Cortona 2013
Circuit-based microcavity
Small size
Purcell effect (enhancement of spontaneous emission)
Tera-Mir, Cortona 2013
Microfabricated LC circuits
Circuit diagram: two LC
C. Walther et al., Science 327, p 1495 (2010)
L
C
/2
Tera-Mir, Cortona 2013
Electromagnetic simulations:
Electric field E normal to the capacitor plates for the antisymmetric mode
E
Magnetic field B wraps around the inductance
Tera-Mir, Cortona 2013
Could easily be further downscaled
Same resonant frequency (1.5THz), about ½ length (15 m)
Tera-Mir, Cortona 2013
Is it a “lumped circuit”?
Compare to “oversimplified” formula Planar capacitor (1/2 disk)
“Unrolled” coaxial inductance (very rough approximation)
we get:
A
d
r1
r2
Tera-Mir, Cortona 2013
Passive resonator at 1.5THz
10K
Voigt fit: Gaussian component Q = 26 Lorenzian Q = 40
Reflexion measurements
Tera-Mir, Cortona 2013
LC with active region
C. Walther et al, unpublished
Strong narrowing observed
Superexponential increase of measured power
Tera-Mir, Cortona 2013
Tuning with the inductance L
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
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)
Tera-Mir, Cortona 2013
Comparison
Gain: negative resistance intersubband transition
Cavity: Resonant antenna optical resonator
Non-cascaded Cascaded
Tera-Mir, Cortona 2013
Resonant tunnel diode
Negative resistance comes
from the misalignement
between two subbands
Intersubband device?
Tera-Mir, Cortona 2013
Density matrix model
Goal: describe both current flow and gain using the same
formalism
Hamiltonian
Equation of motion
Tera-Mir, Cortona 2013
Write in terms of a Liouville equation
Liouville equation
With the terms
And compute the current
Tera-Mir, Cortona 2013
Resonant tunneling
Kasarinov-Suris result
Dephasing Upper state lifetime
Coupling
Detuning
Tera-Mir, Cortona 2013
Can be improved by a more refined model
Takes into account a better model of k-space
For degenerate subbands
Tera-Mir, Cortona 2013
Oscillation condition of a RTD
Gain = losses (in electronic terms..)
Maximum negative conductance:
RTD
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
Second-order gain formula
Back to QCL: Use the same formalism, but with the light
interaction
Get finally a long formula for the gain
Tera-Mir, Cortona 2013
Derive the Bloch gain
Gain is achieved even w/o population inversion
but…
H. Willenberg et al., Phys Rev. B 67, 085315
(2003)
Tera-Mir, Cortona 2013
Mid-IR experiment
Good agreement with theory
R. Terazzi, T. Gresch et al., Nature Phys. 3, 329 (2007)
Tera-Mir, Cortona 2013
Structure is unstable…
Negative conductivity extends to
= 0.
Cannot be cascaded
-> add an injector (make it a QCL)
2
1
g
3
21
g
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
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.
Tera-Mir, Cortona 2013
bound-to continuum
Electrical stability is more of an issue
Two QW active
G. Scalari, Opt. Express (2010)
Tera-Mir, Cortona 2013
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)
g 3
2 1
Tera-Mir, Cortona 2013
Reduce the injector absorption
Scattering – assisted
Extraction – assisted (lower state controls transport)
Separate “stabilizer” – but keep resonant tunneling
injection (past stable point)
Tera-Mir, Cortona 2013
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.,
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
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)
Tera-Mir, Cortona 2013
Rate equations with Purcell effect
Define photon number p and electron density N
Write rate equations
Purcell
Tera-Mir, Cortona 2013
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)
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
frequency Cavity photon mode material excitation (cavity size)-1
Strong light-matter coupling
66
Cavity and a material excitation interact like coupled oscillators.
Tera-Mir, Cortona 2013
Strong light-matter coupling: Interaction strength
67
Figure of merit: B
R
IS
2
2 *
04
ele tR
cfNne
n m L
-Fast energy transfer from electronic to photonic excitation -Photonic fraction of polariton can radiate photons
Tera-Mir, Cortona 2013
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)
Tera-Mir, Cortona 2013
Electroluminescence from strong coupling: theory
PPrediction: enhanced luminescence efficiency.. But..
Tera-Mir, Cortona 2013
Strong light-matter coupling: the implementation
70
C. Walther et al., Science, 327, 1495 (2010)
Tera-Mir, Cortona 2013
Parabolic quantum wells
71
- 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)
Tera-Mir, Cortona 2013
Sample: Parabolic QWs & Nonresonant excitation
72
Tera-Mir, Cortona 2013
Reflection spectra
73
-Spectra taken at T=10K -ΩR=0.8THz
M. Geiser et al., Phys. Rev. Lett. 108, 106402 (2012)
Tera-Mir, Cortona 2013
Electroluminescence: Spectra
74
- Power: up to 60pW (100mW pump power / Conversion efficiency 6x10-10 )
M. Geiser et al. APL 101, 141118 (2012)
Tera-Mir, Cortona 2013
Anticrossing curve
75
Model: Y. Todorov et al., PRL 102, 186402 (2009)
M. Geiser et al. APL 101, 141118 (2012)
Tera-Mir, Cortona 2013
Electroluminescence: Temperature Performance
76
J. Ulrich et al., APL, 74, 3158 (1999)
60pW at T=10K, ~2pW at T=300K
M. Geiser et al. APL 101, 141118 (2012)
Tera-Mir, Cortona 2013
Efficiency
77
Geometric pumping efficiency: 0.03
Cavity outcoupling 0.0014
Excitation decay paths 0.24
Bright/dark Excitations
Measured efficiency: 106 10
65 10
104.7 10
M. Geiser et al. APL 101, 141118 (2012)
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
Brick of the quantum world
Quantum dots: the electron is confined in three directions
Tera-Mir, Cortona 2013
Intersubband lasers based on dots?
Reduce the intersubband scattering rate Potential avenue for 300K THz QCL
Tera-Mir, Cortona 2013
Cascade Structure Design
81
Liverini, V. et al., Appl. Phys. Lett. 101 261113 (2012)
Tera-Mir, Cortona 2013
EL dependence on crystallographic orientation
82
Liverini, V. et al., Appl. Phys. Lett. 101 261113 (2012)
x
y • 30µm x 1.5 mm ridges
• pulsed operation 3% duty cycle
Tera-Mir, Cortona 2013
EL dependence on crystallographic orientation
83
x
y
Liverini, V. et al., Appl. Phys. Lett. 101 261113 (2012)
• 30µm x 1.5 mm ridges
• pulsed operation 3% duty cycle
Tera-Mir, Cortona 2013
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
Tera-Mir, Cortona 2013
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!
Tera-Mir, Cortona 2013
Reference: