• Українська
  • English

< | >

Current issue   Ukr. J. Phys. 2016, Vol. 61, N 9, p.784-794
https://doi.org/10.15407/ujpe61.09.0784    Paper

Seti Ju.O., Tkach M.V., Pan’kiv M.V.

Yu. Fed’kovich National University of Chernivtsi
(2, Kotsyubyns’kyi Str., Chernivtsi 58012, Ukraine; e-mail: ktf@chnu.edu.ua)

Role of Interface Phonons in the Functioning of an Injectorless Quantum Cascade Laser

Section: Optics, Lasers, and Quantum Electronics
Original Author's Text: Ukrainian

Abstract: A Hamiltonian for the electron-phonon system in the double-well resonant tunneling structure in the dc electric field has been obtained, by using the models of rectangular potential profile and effective mass for electrons and the dielectric continuum model for phonons. This structure is a separate cascade of the injectorless quantum cascade laser. The renormalized parameters of the electron spectrum are calculated for an arbitrary temperature, by using the method of thermodynamic Green’s functions. It is shown that, in accordance with the experiment, the laser radiation band broadens out and weakly shifts with the temperature growth.

Key words: resonant tunneling nanostructure, quantum cascade laser, interface phonons, electron-phonon interaction, Green’s function.

References:

  1. S. Kumar, C.W.I. Chan, C. Qing, and J.L. Reno, Two-well terahertz quantum-cascade laser with direct intrawell-phonon depopulation, Appl. Phys. Lett. 95, 141110 (2009).   https://doi.org/10.1063/1.3243459
  2. J. Faist, F. Capasso, D.L. Sivco et al., Quantum cascade laser, Science 264, 553 (1994).   https://doi.org/10.1126/science.264.5158.553
  3. J. Faist, F. Capasso, C. Sirtori et al., Vertical transition quantum cascade laser with Bragg confined excited state, Appl. Phys. Lett. 66, 538 (1995).   https://doi.org/10.1063/1.114005
  4. S. Katz, A. Fridrich, G. Boehm, and M.C. Amann, Continuous wave operation of injectorless quantum cascade lasers at low temperatures, Appl. Phys. Lett. 92, 181103 (2008).   https://doi.org/10.1063/1.2841704
  5. D. Dey, W Wu, O. Memis, and H. Mohseni, Injector-less quantum cascade laser with low voltage defect and improved thermal performance grown by metal-organic chemical-vapor deposition, Appl. Phys. Lett. 94, 081109 (2009).   https://doi.org/10.1063/1.3089362
  6. A. Fridrich, G. Boehm, and M.C. Amann, Short-wave-length intersubband staircase lasers, with and without AlAs-blocking barriers, Semicond. Sci. Technol. 22, 218 (2007).   https://doi.org/10.1088/0268-1242/22/3/008
  7. S. Katz, A. Vizbaras, R. Meyer, and M.-C. Amann, Injectorless quantum cascade lasers, J. Appl. Phys. 109, 081101 (2011).   https://doi.org/10.1063/1.3566072
  8. C. Gmachl, F. Capasso, D.L. Sivco, and A.Y. Cho, Recent progress in quantum cascade lasers andapplications, Rep. Prog. Phys. 64, 1533 (2001).   https://doi.org/10.1088/0034-4885/64/11/204
  9. M. Wanke, F. Capasso, C. Gmachl, A. Tredicucci, D. Sivco, A. Hutchinson, G. Chu, and A. Cho, Injectorless quantum-cascade lasers, Appl. Phys. Lett. 78, 3950 (2001).   https://doi.org/10.1063/1.1378805
  10. J. Faist, Quantum Cascade Lasers (Oxford Univ. Press, Oxford, 2013).   https://doi.org/10.1093/acprof:oso/9780198528241.001.0001
  11. G.G. Zegrya, N.V. Tkach, I.V. Boiko, and Yu.A. Se-ti, Quasi-stationary electron states in a multilayered structure in longitudinal electric and transverse magnetic fields, Phys. Solid State 55, 2182 (2013).   https://doi.org/10.1134/S106378341310034X
  12. M.V. Tkach, Ju.O. Seti, I.V. Boyko, and O.M. Voitsekhivska, Dynamic conductivity of resonance tunnel structures in the model of open cascade in nanolasers, Rom. Rep. Phys. 65, 1443 (2013).
  13. M.V. Tkach, Ju.O. Seti, I.V. Boyko, and O.M. Voitsekhivska, Optimization of quantum cascade laser operation by geometric design of cascade active band in open and closed models, Condens. Matter Phys. 16, 33701 (2013).   https://doi.org/10.5488/CMP.16.33701
  14. A. Gaji, J. Radovanovi, V. Milanovi, D. Indjin, and Z. Ikoni, Optimizing optical nonlinearities in GaInAs/AlInAs quantum cascade lasers, J. Appl. Phys. 115, 05712 (2014).
  15. M. Lindskog, J. M. Wolf, V. Trinite et al., Comparative analysis of quantum cascade laser modeling based on density matrices and non-equilibrium Green's functions, Appl. Phys. Lett. 105, 103106 (2014).   https://doi.org/10.1063/1.4895123
  16. C. Jirauschek and T. Kubis, Modeling techniques for quantum cascade lasers, Appl. Phys. Rev. 1, 011307 (2014).   https://doi.org/10.1063/1.4863665
  17. A. Jiang, A. Matyas, K. Vijayraghavan, C. Jirauschek, Z.R. Wasilewski, and M.A. Belkin, Experimental investigation of terahertz quantum cascade laser with variable barrier heights, J. Appl. Phys. 115, 163103 (2014).   https://doi.org/10.1063/1.4873461
  18. Z.W. Yan, S.L. Ban, and X.X. Liang, Pressure dependence of electron–IO-phonon interaction in multi-interface heterostructure systems, Int. J. Mod. Phys. B 17, 6085 (2003).   https://doi.org/10.1142/S0217979203023653
  19. B.H. Wu, J.C. Cao, G.Q. Xio, and H.C. Lio, Interface pho-non assisted transition in double quantum well, Eur. Phys. J. B 33, 9 (2003).   https://doi.org/10.1140/epjb/e2003-00135-2
  20. X. Gao, D. Botez, and I. Knezevic, Phonon confine-ment and electron transport in GaAs-based quantum cascade structures, J. Appl. Phys. 103, 073101 (2008).   https://doi.org/10.1063/1.2899963
  21. J.G. Zhu and S.L. Ban, Effect of electron-optical phonon interaction on resonant tunneling in coupled quantum wells, Eur. Phys. J. B 85, 140 (2012).   https://doi.org/10.1140/epjb/e2012-20981-9
  22. R. Aggarwal, A.A. Ingale, S. Pal, V.K. Dixit, T.K. Sharma, and S.M. Oak, Intersubband plasmon-phonon coupling in GaAsP/AlGaAs near surface quantum well, Appl. Phys. Lett. 102, 181120 (2013).   https://doi.org/10.1063/1.4804360
  23. Y.B. Shi and I. Knezevic, Nonequilibrium phonon effects in midinfrared quantum cascade lasers, J. Appl. Phys. 116, 123105 (2014).   https://doi.org/10.1063/1.4896400f
  24. N. Mori and T. Ando, Electron–optical-phonon interaction in single and double heterostructures, Phys. Rev. B 40, 6175 (1989).   https://doi.org/10.1103/PhysRevB.40.6175
  25. X. Gao, D. Botez, and J.I. Knezevic, X-valley leakage in GaAs-based mid-infrared quantum cascade lasers: a Monte Carlo study, Appl. Phys. 101, 063101 (2007).   https://doi.org/10.1063/1.2711153
  26. M.A. Stroscio and M. Dutta, Phonons in Nanostructures (Cambridge Univ. Press, Cambridge, UK, 2001) [ISBN: 0521792797].   https://doi.org/10.1017/CBO9780511534898
  27. M.V. Tkach, Ju.O. Seti, and O.M. Voitsekhivska, Quantum Dots, Wires, and Films (Knygy-XXI, Chernivtsi, 2015) (in Ukrainian).
  28. Y.Z. Wei and X.X. Liang, Transfer matrix method for electron-IO-phonon interaction in asymmetric double-barrier structures, Int. J. Mod. Phys. B 15, 3539 (2001).   https://doi.org/10.1142/S0217979201007804
  29. A.A. Abrikosov, L.P. Gorkov, and I.E. Dzyaloshinsky, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 2012) [ISBN-13: 978-0486632285].