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3. 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)

4. 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

5. 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

6. MWIR Auger coefficient=  3 R=  1 +  2 n+  3 n 2 W.W. Bewley et al., APL 93, 041118 (2008) Superlattice Band Structure Engineering  Responsible for order of magnitude or greater reductions of Auger rates LWIR Good agreement between theory and expt. for n>10 17 cm -3 Shockley-Read-Hall dominates for n<10 17 cm -3 Youngdale et al., APL 64, 3160 (1994)

7. Observed Strained Layer Superlattice and Bulk Auger Coefficients R=  1 +  2 n+  3 n 2 SystemT (K)  3 (cm 6 /s) Ref. InAs/GaInSb c =8.8  m vs. HgCdTe c =9  m 771.3x10 -27 2x10 -25 Youngdale et al. (1994) InAs/InAsSb c =9  m vs. InSb c =7  m 3001.4x10 -28 1.0x10 -26 Ciesla et al. (1996) InAs/InGaSb/InAs/AlG aInAsSb c =4.1  m vs. InAsSb c =4.5  m 3002.9x10 -27 2.0x10 -26 Flatte et al. (1999) InAs/GaInSb c =3.6  m vs. InAs c =3.5  m 3004.0x10 −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

8. K.p Electronic Band Structure Model Expansion in zone-center basis (emphasizing zone-center accuracy)  k typically less than 0.2 Å -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

9. InAs/GaSb: A Type II Broken Gap Superlattice With Controllable Interface Bonds

10. 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

11. Auger Recombination Formalism Rate for band-to-band transitions (Fermi’s Golden Rule): Matrix element is 49.7Å InAs/57Å Ga 0.9 In 0.1 Sb Auger-1 most probable carriers at 40 K (electrons-solid circles; holes and empty states-hollow circles) 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

12. Experiment vs. Theory: Auger Recombination Rates

13. Case Study: 15 Micron Cutoff SLs and In % 49.7Å InAs/57Å Ga 0.9 In 0.1 Sb (10% In) 47Å InAs/21.5Å Ga 0.75 In 0.25 Sb (25% In) Vary In % but keep band gap fixed Test effects of band structure on Auger recombination Importance of Strain

14. Hole-Hole Auger Transitions: =15  m, T=40 K 49.7Å InAs/57Å Ga 0.9 In 0.1 Sb (10% In)  A7 =5.2x10 -9 s 47Å InAs/21.5Å Ga 0.75 In 0.25 Sb (25% In)  A7 > 1 s

15. 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 In 0.25 Ga 0.75 Sb-optimization ceases above 150 K; T o good figure of merit –12.5Å InAs/39Å In 0.25 Ga 0.75 Sb- optimized from 250 K to 350 K; T o figure of merit inapplicable

16. Temperature Sensitivity of Electronic Band Structure

17. Valence Intersubband Absorption 12.5Å InAs/39Å In 0.25 Ga 0.75 Sb

18. Intersubband Absorption, Threshold Carrier and Threshold Current Densities

19. Layer Thickness Sensitivity of Optimization Band structures for superlattices with same energy gap but different In 0.25 Ga 0.75 Sb layer thicknesses (300 K)

20. Intersubband Absorption, Threshold Carrier and Current Densities Require growth accuracy ±3.5 Å for InGaSb, ±0.25 Å for InAs

21. MWIR Four-Layer Superlattice Incorporate strain-compensating quintarnary layer: InAs/In 0.25 Ga 0.75 Sb/InAs/Al 0.30 Ga 0.42 In 0.28 A 0.50 Sb 0.50 –strain compensation occurs over ~100 Å SL period –provides Auger recombination and intersubband absorption optimization –3.7 µm wavelength at 300 K

22. Importance of Umklapp and Saturation

23. Temperature Sensitivity of Auger Final State Optimization Blue: valence subbands 4, 5, 6

24. 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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