Optical injection and control in germanium: Thirty-band kp theory

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 15, 2010, Pages

  Rioux, J ^a   Sipe, J E ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955350052     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.155215     Document Type: Article

References (56)

1. D. J. Hilton and C. L. Tang, Phys. Rev. Lett. 89, 146601 (2002). 10.1103/PhysRevLett.89.146601
2. Z. G. Yu, S. Krishnamurthy, M. van Schilfgaarde, and N. Newman, Phys. Rev. B 71, 245312 (2005). 10.1103/PhysRevB.71.245312 (Pubitemid 41702956)
3. E. J. Loren, B. A. Ruzicka, L. K. Werake, H. Zhao, H. M. van Driel, and A. L. Smirl, Appl. Phys. Lett. 95, 092107 (2009). 10.1063/1.3222869
4. A. L. Smirl, E. J. Loren, B. A. Ruzicka, L. K. Werake, H. Zhao, and H. M. van Driel, OSA Technical Digest, Conference on Lasers and Electro-Optics/ International Quantum Electronics Conference (Optical Society of America, Baltimore, 2009), paper IWA6.
5. E. Yablonovitch, H. W. Jiang, H. Kosaka, H. D. Robinson, D. S. Rao, and T. Szkopek, Proc. IEEE 91, 761 (2003). 10.1109/JPROC.2003.811799
6. I. Žutić, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004). 10.1103/RevModPhys.76.323 (Pubitemid 39063520)
7. Modern Problems in Condensed Matter Sciences, edited by, F. Meier, and, B. P. Zakharchenya, (North-Holland, Amsterdam, 1984), Vol. 8, Chap., pp. 15-71.
8. M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, IEEE J. Quantum Electron. 30, 256 (1994). 10.1109/3.283768
9. D. C. Hutchings and B. S. Wherrett, Phys. Rev. B 49, 2418 (1994). 10.1103/PhysRevB.49.2418
10. D. C. Hutchings and B. S. Wherrett, Opt. Mater. 3, 53 (1994). 10.1016/0925-3467(94)90029-9
11. M. Murayama and T. Nakayama, Phys. Rev. B 52, 4986 (1995). 10.1103/PhysRevB.52.4986
12. S. B. Arifzhanov and E. L. Ivchenko, Fiz. Tverd. Tela (Leningrad) 17, 81 (1975)
13. S. B. Arifzhanov and E. L. Ivchenko, [Sov. Phys. Solid State 17, 46 (1975)].
14. G. W. Bryant, Phys. Rev. B 22, 1992 (1980). 10.1103/PhysRevB.22.1992
15. A. F. Gibson, C. B. Hatch, P. N. D. Maggs, D. R. Tilley, and A. C. Walker, J. Phys. C 9, 3259 (1976). 10.1088/0022-3719/9/17/019
16. E. Tuncel, J. L. Staehli, C. Coluzza, G. Margaritondo, J. T. McKinley, R. G. Albridge, A. V. Barnes, A. Ueda, X. Yang, and N. H. Tolk, Phys. Rev. Lett. 70, 4146 (1993). 10.1103/PhysRevLett.70.4146
17. C. Rauscher and R. Laenen, J. Appl. Phys. 81, 2818 (1997). 10.1063/1.364308
18. R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, Phys. Rev. Lett. 76, 1703 (1996). 10.1103/PhysRevLett.76.1703
19. A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997). 10.1103/PhysRevLett.78.306
20. A. Haché, J. E. Sipe, and H. M. van Driel, IEEE J. Quantum Electron. 34, 1144 (1998). 10.1109/3.687857
21. D. Côté, J. M. Fraser, M. DeCamp, P. H. Bucksbaum, and H. M. van Driel, Appl. Phys. Lett. 75, 3959 (1999). 10.1063/1.125531
22. M. Spasenović, M. Betz, L. Costa, and H. M. van Driel, Phys. Rev. B 77, 085201 (2008). 10.1103/PhysRevB.77.085201
23. R. D. R. Bhat and J. E. Sipe, Phys. Rev. Lett. 85, 5432 (2000). 10.1103/PhysRevLett.85.5432 (Pubitemid 32089649)
24. M. J. Stevens, A. L. Smirl, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, J. Appl. Phys. 91, 4382 (2002). 10.1063/1.1456943 (Pubitemid 34435586)
25. M. J. Stevens, A. L. Smirl, R. D. R. Bhat, A. Najmaie, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 90, 136603 (2003). 10.1103/PhysRevLett.90.136603
26. J. Hübner, W. W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 90, 216601 (2003). 10.1103/PhysRevLett.90.216601
27. S. Richard, F. Aniel, and G. Fishman, Phys. Rev. B 70, 235204 (2004) 10.1103/PhysRevB.70.235204
28. S. Richard, F. Aniel, and G. Fishman, Phys. Rev. B 71, 169901 (E) (2005). 10.1103/PhysRevB.71.169901 (Pubitemid 41749429)
29. R. D. R. Bhat, P. Nemec, Y. Kerachian, H. M. van Driel, J. E. Sipe, and A. L. Smirl, Phys. Rev. B 71, 035209 (2005). 10.1103/PhysRevB.71.035209 (Pubitemid 40396406)
30. R. D. R. Bhat, F. Nastos, A. Najmaie, and J. E. Sipe, Phys. Rev. Lett. 94, 096603 (2005). 10.1103/PhysRevLett.94.096603 (Pubitemid 40620622)
31. R. D. R. Bhat and J. E. Sipe, arXiv:cond-mat/0601277 (unpublished).
32. F. Nastos, R. W. Newson, J. Hübner, H. M. van Driel, and J. E. Sipe, Phys. Rev. B 77, 195202 (2008) 10.1103/PhysRevB.77.195202
33. M. Cardona and F. H. Pollak, Phys. Rev. 142, 530 (1966). 10.1103/PhysRev.142.530
34. G. F. Koster, J. O. Dimmock, R. G. Wheeler, and H. Statz, Properties of the Thirty-Two Point Groups (MIT Press, Cambridge, MA, 1963).
35. By symmetry of the diamond structure, the nonzero momentum matrix elements are given by: S | p x | X = S | p y | Y = S | p z | Z, X | p y | z = Y | p z | x = Z | p x | y = X | p z | y = Y | p x | z = Z | p y | x, D z | p x | X = D z | p y | Y = - 1 2 D z | p z | Z = - 1 √ 3 D x | p x | X = 1 √ 3 D x | p y | Y, and complex conjugates of these relations.
36. ) y | y.
37. - factor (Refs.) but not critical for the calculations of this paper. It is included in many 14-band models (Refs.); its earliest introduction seems to date back to M. Cardona, F. H. Pollak, and J. G. Broerman, Phys. Lett. 19, 276 (1965). 10.1016/0031-9163(65)90983-2
38. M. Cardona, N. E. Christensen, M. Dobrowolska, J. K. Furdyna, and S. Rodriguez, Solid State Commun. 60, 17 (1986). 10.1016/0038-1098(86)90006-2
39. P. Pfeffer and W. Zawadzki, Phys. Rev. B 41, 1561 (1990). 10.1103/PhysRevB.41.1561
40. N. Fraj, S. Ben Radhia, and K. Boujdaria, Solid State Commun. 142, 342 (2007). 10.1016/j.ssc.2007.02.037 (Pubitemid 46560785)
41. F. Nastos, J. Rioux, M. Strimas-Mackey, B. S. Mendoza, and J. E. Sipe, Phys. Rev. B 76, 205113 (2007). 10.1103/PhysRevB.76.205113
42. Z. H. Levine and D. C. Allan, Phys. Rev. Lett. 63, 1719 (1989). 10.1103/PhysRevLett.63.1719
43. Z. H. Levine and D. C. Allan, Phys. Rev. B 43, 4187 (1991). 10.1103/PhysRevB.43.4187
44. Semiconductors: Group IV Elements and III-V Compounds, edited by, O. Madelung, (Springer-Verlag, New York, 1991).
45. P. E. Blöchl, O. Jepsen, and O. K. Andersen, Phys. Rev. B 49, 16223 (1994). 10.1103/PhysRevB.49.16223
46. For details of the germanium band structure, see Fig. 4 of Ref..
47. H. M. van Driel and J. E. Sipe, in Ultrafast Phenomena in Semiconductors, edited by, K.-T. Tsen, (Springer-Verlag, Berlin, 2000), Chap., pp. 261-306.
48. C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, and A. Miller, Phys. Rev. Lett. 42, 1785 (1979) 10.1103/PhysRevLett.42.1785
49. C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, and A. Miller, Phys. Rev. Lett. 43, 1843 (E) (1979). 10.1103/PhysRevLett.43.1843.2
50. G. Jalbert, H. S. Brandi, B. Koiller, and N. Zagury, Opt. Commun. 65, 213 (1988). 10.1016/0030-4018(88)90352-5 (Pubitemid 18565652)
51. I. M. Catalano, A. Cingolani, R. Cingolani, and M. Lepore, Phys. Scr. 37, 579 (1988). 10.1088/0031-8949/37/4/014
52. J. M. Fraser, A. I. Shkrebtii, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 83, 4192 (1999). 10.1103/PhysRevLett.83.4192
53. This is the simplest orientation. For the same crystal cut, one can get a slightly larger current injection with beams polarized along 110 ; the largest current injection is achieved with beams polarized along 111 (Ref.). We choose to present 100 polarization results to keep the expressions simple.
54. J. E. Sipe, A. I. Shkrebtii, and O. Pulci, Phys. Status Solidi A 170, 431 (1998). 10.1002/(SICI)1521-396X(199812)170:2<431::AID-PSSA431>3.0.CO;2-6
55. M. J. Stevens, R. D. R. Bhat, J. E. Sipe, H. M. van Driel, and A. L. Smirl, Phys. Status Solidi B 238, 568 (2003). 10.1002/pssb.200303173 (Pubitemid 37035471)
56. V. M. Asnin, A. A. Bakun, A. M. Danishevskii, E. L. Ivchenko, G. E. Pikus, and A. A. Rogachev, Solid State Commun. 30, 565 (1979). 10.1016/0038-1098(79)91137-2 (Pubitemid 10409477)