About Omics Group

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About Omics Group

• OMICS Group International through its Open Access
  Initiative is committed to make genuine and
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  community. OMICS Group hosts over 400
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About Omics Group conferences

• OMICS Group signed an agreement with more than
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Growth and Operation Tolerances for Sb-based
Mid-Infrared Lasers C.H. Grein University of
Illinois at Chicago Collaborators M.E. Flatté
and T.F. Boggess (University of Iowa)
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Outline

• Background on Sb-based superlattice mid-infrared
  lasers
• Sensitivity of optimization of mid-infrared
  InAs/GaInSb superlattice laser active regions to
• Temperature
• Superlattice layer thicknesses
• Structure of intersubband absorption spectrum
• Initial/final state optimization in four-layer
  superlattices

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Optimization Strategies

• Band edge optimization
• reduce valence band density of states
• strained layer superlattices heavy hole becomes
  lighter in in-plane direction
• Intersubband absorption reduction
• engineering bands which would otherwise provide
  initial or final states for intervalence or
  interconduction transitions at the lasing energy
• Auger final state optimization
• band structure engineering to reduce the number
  of final states in Auger transitions

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• Superlattice Band Structure Engineering
• Responsible for order of magnitude or greater
  reductions of Auger rates

• LWIR
• Good agreement between theory and expt. for
  ngt1017 cm-3
• Shockley-Read-Hall dominates for nlt1017 cm-3
• Youngdale et al., APL 64, 3160 (1994)

• MWIR
• Auger coefficient?3
• R?1 ?2n ?3n2
• W.W. Bewley et al., APL 93, 041118 (2008)

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Observed Strained Layer Superlattice and Bulk
Auger Coefficients R?1 ?2n ?3n2
System T (K) ?3 (cm6/s) Ref.
InAs/GaInSb?c8.8 ?m vs. HgCdTe ?c9 ?m 77 1.3x10-27 2x10-25 Youngdale et al. (1994)
InAs/InAsSb ?c9 ?m vs. InSb ?c7 ?m 300 1.4x10-28 1.0x10-26 Ciesla et al. (1996)
InAs/InGaSb/InAs/AlGaInAsSb ?c4.1 ?m vs. InAsSb ?c4.5 ?m 300 2.9x10-27 2.0x10-26 Flatte et al. (1999)
InAs/GaInSb ?c3.6 ?m vs. InAs ?c3.5 ?m 300 4.0x10-27 1.1x10-26 Kost et al. (2005) Vodopyanov et al. (1992)

• Roughly two orders of magnitude slower Auger
  recombination in LWIR SLs than in bulk
• Roughly one order of magnitude slower in MWIR

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K.p Electronic Band Structure Model

• Expansion in zone-center basis (emphasizing
  zone-center accuracy)
• k typically less than 0.2Å-1
• Spherical (8-band) or cubic (14-band) symmetry
• Relevant region of bulk band structure for
  optical and recombination properties

SUCCESSES Simplicity Parameters connected 1-1
with experiments Energy levels and masses 5-10
meV Absorption/gain spectra 10 fundamental
absorption (inc. excitons) 20 differential
transmission in SLMQW Auger/radiative
rates Within factor of 2 for several material
systems
CHALLENGES Indirect constituents e.g.
AlSb Defects Sometimes require full Brillouin
zone Interface roughness For islands of diameter
less than 15Å
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InAs/GaSb A Type II Broken Gap Superlattice With
Controllable Interface Bonds
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Carrier Recombination Calculations

• Auger recombination
• three dimensional formalism
• non-parabolic bands splined from K?p
• dispersion in matrix elements, splined from K?p
• possible degenerate carrier statistics
• modified version of well-tested superlattice code
• typical factor of 2 agreement with experiment
• Radiative recombination
• excludes photon recycling
• based on van Roosbroeck- Shockley
• Impurity and defect mediated recombination
• Neglected ?theoretical upper bounds to carrier
  lifetimes

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Auger Recombination Formalism
Rate for band-to-band transitions (Fermis Golden
Rule)
Matrix element is
Common approximations (not employed
here) -parabolic and isotropic bands -constant
matrix elements -Boltzmann statistics -limitations
to i, f -neglect Umklapp-neglect T-dependence
of bands -neglect dopant/phonon/defect-assisted
Auger
49.7Å InAs/57Å Ga0.9In0.1Sb Auger-1 most probable
carriers at 40 K (electrons-solid circles holes
and empty states-hollow circles)
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Experiment vs. Theory Auger Recombination Rates
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Case Study 15 Micron Cutoff SLs and In
Importance of Strain

• 49.7Å InAs/57Å Ga0.9In0.1Sb (10 In)
• 47Å InAs/21.5Å Ga0.75In0.25Sb (25 In)
• Vary In but keep band gap fixed
• Test effects of band structure on Auger
  recombination

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Hole-Hole Auger Transitions ?15 ?m, T40 K
49.7Å InAs/57Å Ga0.9In0.1Sb (10 In) ?A75.2x10-9
s
47Å InAs/21.5Å Ga0.75In0.25Sb (25 In) ?A7 gt 1 s
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Temperature Sensitivity of Optimization

• Valence bands approximately one energy gap below
  top of valence band provide
• initial states for intersubband absorption
• final states for dominant Auger processes at room
  temperature (AM-7)
• Temperature changes move valence bands through
  resonance region
• Two-layer MWIR superlattices
• 16.7Å InAs/35Å In0.25Ga0.75Sb-optimization
  ceases above 150 K To good figure of merit
• 12.5Å InAs/39Å In0.25Ga0.75Sb- optimized from 250
  K to 350 K To figure of merit inapplicable

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Temperature Sensitivity of Electronic Band
Structure
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Valence Intersubband Absorption
12.5Å InAs/39Å In0.25Ga0.75Sb
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Intersubband Absorption, Threshold Carrier and
Threshold Current Densities
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Layer Thickness Sensitivity of Optimization

• Band structures for superlattices with same
  energy gap but different In0.25Ga0.75Sb layer
  thicknesses (300 K)

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Intersubband Absorption, Threshold Carrier and
Current Densities
Require growth accuracy 3.5 Å for InGaSb, 0.25
Å for InAs
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MWIR Four-Layer Superlattice

• Incorporate strain-compensating quintarnary
  layer InAs/In0.25Ga0.75Sb/InAs/Al0.30Ga0.42In0.28
  A0.50Sb0.50
• strain compensation occurs over 100 Å SL period
• provides Auger recombination and intersubband
  absorption optimization
• 3.7 µm wavelength at 300 K

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Importance of Umklapp and Saturation
23
Temperature Sensitivity of Auger Final State
Optimization
Blue valence subbands 4, 5, 6
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Artificially Shift Valence Subbands 4, 5, 6

• Increasing temperature has a profound impact on
  final-state optimization for Auger suppression
• At 77 K the final-state optimization is very
  important
• At 300 K the final-state optimization has just
  ceased to be of any importance
• -this structure it may still be important at
  temperatures just slightly lower

25
SUMMARY

• Details of temperature dependent valence band
  structure particularly important for optimizing
  design of Sb-based MWIR active regions
• Strong intersubband absorption structure can make
  To parameterization inapplicable
• Observe saturation of Auger recombination at high
  carrier densities
• Occurs when holes become degenerate?hh Auger
  dominant
• Superlattice Umklapp processes provide about half
  of total Auger rate

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