The Path from Impact Ionization to Quantum Cascade Lasers

1
The Path from Impact Ionization to
QuantumCascade Lasers
FEDERICO CAPASSO Division of Engineering and
Applied Sciences Harvard University capasso_at_deas.
harvard.edu
Work Partially supported by DARPA
Hess Symp., University of Illinois, April 31 -
May 1
2
Impact Ionization in semiconductors before the
eighties

• Ionization rates described by Baraffs theory.
  Quite successful in predicting the correct
  electric field dependence but phenomenological.
• Gives reasonable fit to rates in a variety of
  materials in term of parameters such the high
  field electron phonon mean free path and the
  ionization threshold energy (to be calculated
  from the band structure). Assumes that carriers
  ionize as soon as they reach threshold (not
  applicable to Silicon!). Does not include quantum
  effects ( collision broadening, intracollisional
  field
• effect
• In the low field limit reproduces the lucky
  electron model of Shockley and in the very high
  field regime the diffusive model of Wolff
• Lucky electron model a (F) (Eth/F)
  exp (Eth/eF?) eF? Eph
• Diffusive model a (F) (Eth/F)
  exp -3EthEph/(eF?)2 eF? gt Eph
• Baraffs model bridges these two limits but what
  is the physical interpretation?
• Is there a more satisfactory approach
  which also accounts for the complex bandstructure
  at high energy?
• These questions were addressed and successfully
  solved by Karl Hess and his students
• The solution gave us a deep physical
  insight into the kinetics of impact ionization
  and ultimately helped in the design of novel
  heterostructure devices

3
The Physical Picture of Impact Ionization
GaAs

• Electrons spend most of the time around an
  average
• energy
• Occasionally s few lucky ones gain enough
  energy
• to reach threshold by undergoing at most a few
• collisions with phonons.
• This process which occurs on a time scale longer
  than
• the momentum relaxation time but shorter
• than the energy relaxation time is the lucky
  drift in
• Ridleys theory of impact ionization put
  forth several
• years after the work of Hess and Shichijo.

Schichijo and Hess, Physical Rev. B 1981
4
Impact ionization enhanced by band edge
discontinuities
Electron undergo a ballistic acceleration as they
enter the well large increase of lucky electrons
that can reach threshold (effective reduction of
the ionization energy by ?Ec) with attendant
increase of the ionization rate in the well
Mechanism to enhance ionization ratio of
electrons and holes (Chin, Holonyak, Hess,
1979) Effect observed in Superlattice Avalanche
photodiode (Capasso, Tsang 1981) Band
discontinuities also used to enhance the electron
velocity after the step ( 108 cm/s ) e.g.
ballistic launchers in Heterojunction Bipolar
transistors
5
Solid-state photomultiplier
?Ec gt Eth Difficult to find appropriate high
quality material (possibly AlInAsSb lattice
matched to InP)
If ?Ec lt Eth can light emission occur at the
step?
(Capasso et al. 1983)
6
Quantum Cascade Laser (1994)
Operation only at cryogenic temperatures Wavelengt
h 4.5 microns
1971 Kazarinov Suris proposed an intersubband
laser pumped by Resonant Tunneling
7
Why is it fundamentally different from diode
lasers?

• Diode Laser
• Light from e-h recombination
• wavelength controlled by bandgap
• Gain limited by band-structure (absorption
• coefficient)
• One photon per e-h pair injected above threshold

• Quantum Cascade Laser
• Light from quantum jumps between subbands
• Wavelength controlled by thickness (4 to
  160?m)
• Gain limited by electron density in the excited
  state
• i.e. by maximum current one can inject
• N photons per electron injected above
  threshold
• N is the number of stages

• Quantum design of all laser
• properties through design of
• wavefunctions, matrix elements,
• relaxation times, transport,..

8
Basic Building Blocks of Quantum Cascade Lasers
one quantum-well
coupled quantum-wells more flexible design, all
transitions allowed (asymmetric structures)
superlattice recover transport in growth
direction, Bragg reflection
9
Quantum Design of Optical Transitions
Electron lifetime engineering

• Increase in lifetime due to decrease of
• optical matrix element in diagonal transition
• Often used in Quantum Cascade Laser design

• If we inject electrons in state 3 we can design
  the population inversion ( ?32 gt ?21) by suitable
  state engineering.
• Phonon engineering Energy difference
• between levels made equal to an optical
• phonon to minimize ?21

• Electron lifetime on excited
• subbands increases with
• momentum exchanged through
• emission of optical phonons.

10
Electron lifetime and escape into
continuumsuppression of excited lifetime

• Escape into continuum
• Escape into superlattice electrons cant tunnel
  into minigap

Central in the design of high performance quantum
cascade lasers
11
Band structure Engineering

Electron lifetime engineering Design of
population inversion ?32 gtgt ?2 Bragg reflectors
to suppress electron escape
AlInAs/GaInAs grown by Molecular Beam Epitaxy
(MBE)
12
Quantum Design
Double phonon resonance
Single Phonon Resonance
Superlattice
Superlattice
Bound-to-continuum
13
High Power Room Temperature QCLs by MBE
Prof.Manijeh Razeghi
14
High Power CW Room Temperature QCLs by MOVPE
Mariano Troccoli Laurent Diehl Federico Capasso
David Bour Scott Corzine Gloria Höfler
Importance MOVPE is a technology platform widely
used in optoelectronics because of its high
throuput, high growth rate and low machine down
time
APL in press
15
Fabrication and simulations
Buried heterostructures
Optical mode simulations

Electroplated Au
n InGaAs layer
InP cladding
re-grown FeInP
re-grown FeInP
Active
InP cladding
InP substrate
Combination of dry and wet etching 3 to 12.5 µm
wide ridges Mounted epi-side up In-soldered on
Au-plated Cu heatsink
3 µm wide device G 38
InP cladding
16
High power CW room temperature QCLs at ? 8.38
mm
CW operation, 7.5 mm wide, 3mm long, with HR
coating
Optical spectra above threshold without coating

• Max. CW output power of 291 mW at 300K
• CW operation above 400K 21 mW at 400 K)
• Max. power efficiency 3.8 at 300K

17
High Power RoomTemperature CW QCLs by MOVPE at ?
5.3 mm
CW operation, 7.5 mm wide, 3mm long, with HR
coating

• Max. CW output power
• 312 mW at 300K
• Lases up at 375 K
• Max. power efficiency
• 4.5 at 300K

18
Exciting research opportunities in high power QCLs

• High Power QC lasers are a unique system to study
  quantum transport in the presence of high static
  electric fields 104 105 V/cm) and high
  radiation fields ( gt104 V/cm). Photon driven
  transport.
• Quantum kinetic equation Keldysh-Kadanoff-Ba
  ym formalism
• AC Stark effect and its effect on transport and
  resonant tunneling.
• Coherent regime Rabi frequency greater than
  dephasing frequency inversion is modulated at
  the Rabi frequency.
• Leads to parametric laser gain at sidebands
  of Rabi frequency
• (Risken, Nummedal, Graham, Haken instability)
  
• Interplay of transport and optical nonlinearities

19
New phenomena in high Power QC lasers
Reminiscent of RNGH instability
20
QC-laser ISB resonant nonlinearity nonlinear
QC laser
QC- Laser
ISB- NL
21
Magic solution active nonlinear medium
Active laser medium and resonant nonlinear
cascade can coincide
3
Laser field serves as a coherent optical pump for
the specific nonlinear process
N2
2
Ip
N2 gt N1
N1
1
Cross-section of resonant absorption on the
transition 2-3 is smaller than that of stimulated
emission on the laser transition 2-1
Nonlinear signal is not absorbed since N1 N3
0.
PRA 63, 053803 PRA 64, 013814 (2001) PRL 90,
043902 (2003)
22
Single-mode and tunable SH emission
Fabry-Perot Laser
Single-mode Laser
Intensity (a.u.)
Intensity (a.u.)
0
0
7.2
7.3
7.0
6.8
Intensity (a.u.)
Intensity (a.u.)
0
0
3.65
3.6
3.4
3.5
Wavelength (mm)
Wavelength (mm)
23
Optimized Second Harmonic Power
? 3.5?m
Phase matching wase used using the modal
dispersion of the waveguide
Maximum power and efficiency 2mW and 35mW/W2
Maximum Theoretical efficiency 2W/W2
24
QC Laser Highlights

• Wavelength agility
• layer thickness determines emission wavelength
  3.5 to 24 ?m (AlInAs/GaInAs) and 60 to 160 ?m
  (AlGaAs/GaAs)
• - Multi-wavelength and ultrabroadband operation
• High optical power at RT gt 1 W pulsed, 0.6 W cw
• cascading re-uses electrons
• Narrow linewidth lt 100 kHz stabilized lt 10 kHz
• Ultra-fast operation gain switching (50 ps),
• modelocking (3-5 ps),
• Applications trace gas analysis, combustion
  medical diagnostics,
• environmental monitoring, military and law
  enforcement
• Reliability, reproducibility, long-term stability
• Industrial Research and Commercialization
  Hamamatsu, Thales, Pranalytica, Alpes Lasers,
  Maxion, Laser Components, Nanoplus, Cascade
  Technologies, Q-MACS Fraunhofer Institute, PSI,
  Aerodyne,

25
References
F. Capasso, C.Gmachl, D.L. Sivco, A.Y.Cho Physics
Today May, 2002 Reviews in Special Issue of IEEE
J. Quantum Electronics, June 2002 on Quantum
Cascade Lasers
26
Collaborators
Crystal growers A.Y. Cho, D.L. Sivco and A.L.
Hutchinson Bell Labs, Lucent Technologies,
Murray Hill, NJ David Bour, Agilent
Technologies Postdocs Jerome Faist, Univ. of
Neuchatel Carlo Sirtori, Univ. of Paris and
Thales, Inc. from Univ. of Pavia Alessandro
Tredicucci, Scuola Normale Superiore, Pisa Fabio
Beltram, Scuola Normale Superiore, Direttore
Centro NEST Raffaele Colombelli, CNRS, Paris,
from Scuola Normale Superiore Claire Gmachl,
Princeton University, from Technical University
of Vienna Mariano Troccoli, Harvard University
from University of Bari Laurent Diehl, Harvard
University from University of Neuchatel Plus
over 40 collaborators (USA and Europe) who have
been using our devices for a broad range of
science and technology applications
27
Karl this is a pseudo-retirement!

• Keep stirring the pot (Bell Theorem, etc.)!!