Generic picture of the emission properties of III-nitride polariton laser diodes: Steady state and current modulation response

Physical Review B - Condensed Matter and Materials Physics

Volumn 86, Issue 12, 2012, Pages

  Iorsh, Ivan ^a   Glauser, Marlene ^b   Rossbach, Georg ^b   Levrat, Jacques ^b   Cobet, Munise ^b   Butté, Raphaël ^a,b   Grandjean, Nicolas ^b   Kaliteevski, Mikhail A ^c,e   Abram, Richard A ^a   Kavokin, Alexey V ^d,f  

^a DURHAM UNIVERSITY   (United Kingdom)

^b EPFL   (Switzerland)

^c ST PETERSBURG ACADEMIC UNIVERSITY   (Russian Federation)

^d UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^e IOFFE INSTITUTE   (Russian Federation)

^f CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84866363535     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.86.125308     Document Type: Article

References (63)

1. C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.3314 69, 3314 (1992).
2. M. S. Skolnick, T. A. Fisher, and D. M. Whittaker, Semicond. Sci. Technol. SSTEET 0268-1242 10.1088/0268-1242/13/7/003 13, 645 (1998).
3. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, Nature (London) NATUAS 0028-0836 10.1038/nature05131 443, 409 (2006). (Pubitemid 44477272)
4. S. Christopoulos, G. Baldassarri Höger von Högersthal, A. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.126405 98, 126405 (2007). (Pubitemid 46474052)
5. G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2966369 93, 051102 (2008).
6. S. Kéna-Cohen and S. R. Forrest, Nat. Phot. 1749-4885 10.1038/nphoton.2010.86 4, 371 (2010).
7. K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, Nat. Phys. 1745-2473 10.1038/nphys1051 4, 706 (2008).
8. K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, Science SCIEAS 0036-8075 10.1126/science.1177980 326, 974 (2009).
9. A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, Nature (London) NATUAS 0028-0836 10.1038/nature07640 457, 291 (2009).
10. A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, Nat. Phys. 1745-2473 10.1038/nphys1364 5, 805 (2009).
11. K. G. Lagoudakis, B. Pietka, M. Wouters, R. André, and B. Deveaud-Plédran, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 105.120403 105, 120403 (2010).
12. A. A. Khalifa, A. P. D. Love, D. N. Krizhanovskii, M. S. Skolnick, and J. S. Roberts, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2844860 92, 061107 (2008); (Pubitemid 351263778)
13. D. Bajoni, E. Semenova, A. Lemaître, S. Bouchoule, E. Wertz, P. Senellart, and J. Bloch, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77. 113303 77, 113303 (2008);
14. S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, Nature (London) NATUAS 0028-0836 10.1038/nature06979 453, 372 (2008); (Pubitemid 351693134)
15. S. I. Tsintzos, P. G. Savvidis, G. Deligeorgis, Z. Hatzopoulos, and N. T. Pelekanos, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.3082093 94, 071109 (2009).
16. H. Mathieu, P. Lefebvre, and P. Christol, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.46.4092 46, 4092 (1992).
17. M. Saba, C. Ciuti, J. Bloch, V. Thierry-Mieg, R. André, L. Si Dang, S. Kundermann, A. Mura, G. Bongiovanni, J. L. Staehli, and B. Deveaud, Nature (London) NATUAS 0028-0836 10.1038/414731a 414, 731 (2001). (Pubitemid 34000766)
18. R. Butté and N. Grandjean, Semicond. Sci. Technol. SSTEET 0268-1242 10.1088/0268-1242/26/1/014030 26, 014030 (2011).
19. 2 D, crit derived in
20. J. Levrat, Phys. Rev. B 1098-0121 10.1103/PhysRevB.81.125305 81, 125305 (2010) (the present Ref.) was overestimated by a factor of 10 leading to the same error for the estimate of the threshold current density quoted in Ref.
21. A. Imamoǧlu, R. J. Ram, S. Pau, and Y. Yamamoto, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.53.4250 53, 4250 (1996).
22. See, e.g., L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits, Chap. 2 (Wiley, New York, 1995).
23. For a review, see I. A. Shelykh, A. V. Kavokin, Y. G. Rubo, T. C. H. Liew, and G. Malpuech, Semicond. Sci. Technol. SSTEET 0268-1242 10.1088/0268-1242/25/1/013001 25, 013001 (2010), and references therein.
24. D. Solnyshkov, E. Petrolati, A. Di Carlo, and G. Malpuech, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.3067859 94, 011110 (2009).
25. G. Christmann, R. Butté, E. Feltin, A. Mouti, P. A. Stadelmann, A. Castiglia, J.-F. Carlin, and N. Grandjean, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.085310 77, 085310 (2008).
26. G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73.153305 73, 153305 (2006). (Pubitemid 43563411)
27. R. Butté, J. Levrat, G. Christmann, E. Feltin, J.-F. Carlin, and N. Grandjean, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.233301 80, 233301 (2009).
28. M. Suzuki, J. Nishio, M. Onomura, and C. Hongo, J. Cryst. Growth JCRGAE 0022-0248 10.1016/S0022-0248(98)00341-8 189/190, 511 (1998).
29. G. Cosendey, J.-F. Carlin, N. A. K. Kaufmann, R. Butté, and N. Grandjean, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.3586767 98, 181111 (2011).
30. G. Christmann, D. Simeonov, R. Butté, E. Feltin, J.-F. Carlin, M. Mosca, and N. Grandjean, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2420788 89, 261101 (2006). (Pubitemid 46057974)
31. A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2839305 92, 053502 (2008). (Pubitemid 351230052)
32. G. Malpuech, D. Solnyshkov, A. Di Carlo, and E. Petrolati, Bull. Officiel Propriété Industrielle 10/19, 132 (2010), published by Institut National de la Propriété Industrielle, France.
33. See R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J.-F. Carlin, and N. Grandjean, Proc. SPIE PSISDG 0277-786X 10.1117/12.803718 7216, 721619 (2009), and references therein.
34. A. Castiglia, D. Simeonov, H.-J. Buehlmann, J.-F. Carlin, E. Feltin, J. Dorsaz, R. Butté, and N. Grandjean, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2431484 90, 033514 (2007). (Pubitemid 46146410)
35. T.-C. Lu, C.-C. Kao, H.-C. Kuo, G.-S. Huang, and S.-C. Wang, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2908034 92, 141102 (2008); (Pubitemid 351535567)
36. Y. Higuchi, K. Omae, H. Matsumura, and T. Mukai, Appl. Phys. Express 1882-0778 10.1143/APEX.1.121102 1, 121102 (2008).
37. S. Nakamura, G. Fasol, and S. J. Pearton, The Blue Laser Diode: The Complete Story, 2nd ed. (Springer, Berlin, 2000).
38. V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, Solid State Commun. SSCOA4 0038-1098 10.1016/0038-1098(94)00865-5 93, 733 (1995).
39. H. A. McLeod, Thin-Film Optical Filters, 2nd ed. (Adam Hilger, Bristol, UK, 1986).
40. H. Benisty, H. De Neve, and C. Weisbuch, IEEE J. Quantum Electron. IEJQA7 0018-9197 10.1109/3.709578 34, 1612 (1998).
41. 4 layers were determined by spectroscopic ellipsometry using thick layers grown on sapphire substrates.
42. D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, R. Dimitrov, O. Ambacher, and M. Stutzmann, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.366309 82, 5090 (1997).
43. J.-F. Carlin and M. Ilegems, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.1596733 83, 668 (2003).
44. J.-F. Carlin, C. Zellweger, J. Dorsaz, S. Nicolay, G. Christmann, E. Feltin, R. Butté, and N. Grandjean, Phys. Status Solidi B PSSBBD 0370-1972 10.1002/pssb.200560968 242, 2326 (2005). (Pubitemid 41335602)
45. M. J. Bergmann and H. C. Casey Jr., J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.368185 84, 1196 (1998).
46. R. Schmidt, B. Rheinländer, M. Schubert, D. Spemann, T. Butz, J. Lenzner, E. M. Kaidashev, M. Lorenz, A. Rahm, H. C. Semmelhack, and M. Grundmann, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.1565185 82, 2260 (2003).
47. J. Levrat, R. Butté, G. Christmann, E. Feltin, J.-F. Carlin, and N. Grandjean, Phys. Status Solidi C 1610-1634 10.1002/pssc.200982563 6, 2820 (2009).
48. J. Levrat, R. Butté, E. Feltin, J.-F. Carlin, N. Grandjean, D. Solnyshkov, and G. Malpuech, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81. 125305 81, 125305 (2010).
49. R. P. Leavitt and J. W. Little, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.42.11774 42, 11774 (1990).
50. For this pumping geometry, taking into account the large number of quantum wells in QWs-2 and the high reflectivity of the bottom III-nitride DBR, it is a reasonable assumption to consider that all photons emitted downward from the pumping LED will be absorbed by QWs-2. For the sake of simplicity, a similar assumption has been made for photons emitted upward that would be perfectly reflected by the highly reflective top dielectric DBR and subsequently recycled by QWs-1 or more likely directly absorbed by QWs-2 (i.e., losses due, e.g., to the sidewall roughness and leaky modes have not been accounted for since their accurate estimate lies beyond the scope of this work).
51. A. Castiglia (private communication). Such a linewidth is typical of optimized UV-violet LEDs emitting in the 390-420 nm range.
52. A. V. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University Press, Oxford, 2007), Appendix B.
53. F. Tassone and Y. Yamamoto, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.59.10830 59, 10830 (1999).
54. x is taken from the work of Narukawa and co-workers: Y. Narukawa, Y. Kawakami, S. Fujita, and S. Nakamura, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.59.10283 59, 10283 (1999), where it was shown that for state of the art InGaN QWs, localized and delocalized excitonic states exhibit nearly the same lifetime.
55. W. G. Scheibenzuber, U. T. Schwarz, L. Sulmoni, J. Dorsaz, J.-F. Carlin, and N. Grandjean, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.3585872 109, 093106 (2011);
56. e - h value of 5 ns has therefore been chosen as a typical value.
57. M. Suzuki, T. Uenoyama, and A. Yanase, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.52.8132 52, 8132 (1995).
58. See, e.g., X. B. Zhang and B. Gil, in Low-Dimensional Nitride Semiconductors, edited by, B. Gil, (Oxford University Press, Oxford, 2002).
59. R. Truell, C. Elbaum, and B. B. Chick, Ultrasonic Methods in Solid State Physics (Academic, New York, 1969).
60. J. Kasprzak, D. D. Solnyshkov, R. André, Le Si Dang, and G. Malpuech, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.146404 101, 146404 (2008).
61. G. Malpuech, A. Kavokin, A. Di Carlo, and J. J. Baumberg, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.153310 65, 153310 (2002);
62. A. Kavokin, G. Malpuech, A. Di Carlo, and J. J. Baumberg, Phys. Status Solidi A PSSABA 0031-8965 10.1002/1521-396X(200204)190:3<725::AID- PSSA725>3.0.CO;2-F 190, 725 (2002). (Pubitemid 34613289)
63. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).