A Model for GRIN-SCH-SQW Diode Lasers

IEEE Journal of Quantum Electronics

Volumn 24, Issue 11, 1988, Pages 2191-2214

  Chinn, Stephen R ^a   Zory, Peter S ^a   Reisinger, Axel R ^a  

^a GENERAL ELECTRIC COMPANY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAND STRUCTURE; RELAXATION PROCESSES; WAVEGUIDES, OPTICAL;

DENSITIES OF STATES; DIODE LASERS; ENERGY LEVELS; QUANTUM WELL LASERS; THRESHOLD TEMPERATURE DEPENDENCE;

LASERS, SEMICONDUCTOR;

EID: 0024104243     PISSN: 00189197     EISSN: 15581713     Source Type: Journal    
DOI: 10.1109/3.8562     Document Type: Article

References (66)

1. H. Qkamoto, “Semiconductor quantum-well structures for optoelectronics—Recent advances and future prospects,” Japan J. Appl. Phys., vol. 26, pp. 315–330, 1987.
2. W.T. Tsang, “A graded-index waveguide separate-confinement laser with very low threshold and a narrow Gaussian beam,” Appl. Phys. Lett., vol. 39, pp. 134-137, 1981; W.T. Tsang, “Extremely low threshold (AlGa)As graded-index waveguide separate confinement heterostructure lasers grown by molecular beam epitaxy,” Appl. Phys. Lett., vol. 40, pp. 217–219, 1982.
3. D. Kasemset, C-S. Hong, N.B. Patel, and P.D. Dapkus, “Graded barrier single quantum well lasers—Theory and experiment,” IEEE J. Quantum Electron., vol. QE-19, pp. 1025–1030, 1983.
4. S.D. Hersee, B. de Cremoux, and J.P. Duchemin, “Some characteristics of the GaAs/GaAlAs graded-index separate-confinement heterostructure quantum well structure,” Appl. Phys. Lett., vol. 44, pp. 476–478, 1984.
5. B. Saint-Cricq, F. Lozes-Dupuy, and G. Vassilieff, “Well width dependence of gain and threshold current in GaAlAs single quantum well lasers,” IEEE J. Quantum Electron., vol. QE-22, pp. 625–630, 1986.
6. S. Colak, R. Eppenga and M.F.H. Schuurmans, “Band mixing effects on quantum well gain,” IEEE J. Quantum Electron., vol. QE-23, pp. 960–968, 1987.
7. M.F. Schuurmans and G.W. ‘t Hooft, “Simple calculations of confinement states in a quantum well,” Phys. Rev. B, vol. 31, pp. 8041–8048, 1985.
8. G. Bastard, “Theoretical investigations of superlattice band structure in the envelope-function approximation,” Phys. Rev. B, vol. 25, pp. 7584–7597, 1982.
9. A.C. Marsh and J.C. Inkson, “The electronic properties of GaAs/AlGaAs heterojunctions,” IEEE J. Quantum Electron., vol. QE-22, pp. 58–66, 1986.
10. T. Hiroshima and R. Lang, “Effect of conduction-band nonparabolicity on quantized energy levels of a quantum well,” Appl. Phys. Lett., vol. 49, pp. 456–457, 1986.
11. J.S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys., vol. 53, pp. R123-R181, 1982.
12. S. Adachi, “GaAs, AlAs, and AlxGa1-x: Material parameters foruse in research and device applications,” J. Appl. Phys., vol. 58, pp. Rl-R29, 1985.
13. T.F. Kuech, D.J. Wolford, R. Potemski, J.A. Bradley, K.H. Kel-leher, D. Yan, J.P. Farrell, P.M.S. Lesser, and F.H. Pollak, “Dependence of the AlxGa1-x As band edge on alloy composition based on the absolute measurement of x,” Appl. Phys. Lett., vol. 51, pp. 505–507, 1987.
14. For a recent review, see G. Duggan, “A critical review of heterojunction band offsets,” J. Vac. Sci. Technol. B, vol. 3, pp. 1224–1230, 1985.
15. J. Menendez, A. Pinczuk, D.J. Werder, A.C. Gossard, J.H. English, T.H. Chi, and W.T. Tsang, “Light scattering determination of band offsets in GaAs/(AlGa) As and GaSb/(AlGa)Sb quantum wells: A comparative study.” Superlattices, Microstruct., vol. 3, pp. 163–166. 1987.
16. N. Holonyak, Jr., R.B. Kolbas, R.D. Dupuis, and P.D. Dapkus, “Quantum-well heterostructure lasers,” IEEE J. Quantum Electron., vol. QE-16, pp. 170–186, 1980.
17. A. Sugimura, “Threshold currents for AlGaAs quantum well lasers,” IEEE J. Quantum Electron., vol. QE-20, pp. 336–343, 1984.
18. Y. Arakawa, H. Sakaki, M. Nishioka, J. Yoshino, and T. Kamiya. “Recombination lifetime of carriers in GaAs-GaAlAs quantum wells near room temperature,” Appl. Phys. Lett., vol. 46, pp. 519–521, 1985.
19. E.H. Böttcher, K. Ketterer, D. Bimberg, G. Weimann, and W. Schlapp. “Excitonic and electron-hole contributions to the spontaneous recombination rate of injected charge carriers in GaAs-GaAlAs multiple quantum well lasers at room temperature,” Appl. Phys. Lett., vol. 50, pp. 1074–1076, 1987.
20. G. Bastard, E.E. Mendez, L.L. Chang, and L. Esaki, “Exciton binding energy in quantum wells,” Phys. Rev. B, vol. 26, pp. 1974–1979, 1982.
21. M. Asada, A. Kameyama, and Y. Suematsu, “Gain and intervalence band absorption in quantum-well lasers,” IEEE J. Quantum Electron., vol. QE-20, pp. 745–753, 1984.
22. M. Yamada, S. Ogita, M. Yamagishi, K. Tabata, N. Nakaya, M. Asada, and Y. Suematsu, “Polarization-dependent gain in GaAs/AIGaAs multiquantum-well lasers: Theory and experiment,” Appl. Phys. Lett., vol. 45, pp. 324–325, 1984.
23. M. Yamada, S. Ogita, M. Yamagishi, and K. Tabata, “Anisotropy and broadening of optical gain in a GaAs/AIGaAs multiquantum well laser.” IEEE J. Quantum Electron., vol. QE-21, pp. 640–645, 1985.
24. E.O. Kane, “Band structure of indium antimonide,” J. Phys. Chem. Solids, vol. 1, pp. 249–261, 1957.
25. G.P. Agrawal and N.K. Dutta, Long-Wavelength Semiconductor Lasers. New York: Van Nostrand, 1986, ch. 9, p. 384.
26. M. Yamanishi and Y. Lee, “Phase dampings of optical dipole moments and gain spectra in semiconductor lasers,” IEEE J. Quantum Electron., vol. QE-23, pp. 367–370, 1987.
27. E. Zielinski, H. Schweizer, S. Hausser, R. Stuber, M.H. Pilkuhn, and G. Weimann, “Systematics of laser operation in GaAs/AIGaAs multiquantum well heterostructures,” IEEE J. Quantum Electron., vol. QE-23, pp. 969–976, 1987.
28. S.R. Chinn, “Modal analysis of GRIN-SCH and triangular-well waveguides,” Appl. Opt., vol. 23, pp. 3508–3509, 1984.
29. W. Streifer, R.D. Burnham, and D.R. Scifres, “Modal analysis of separate-confinement heterojunction lasers with inhomogeneous cladding layers,” Opt. Lett., vol. 8, pp. 283–285, 1983.
30. G.A. Evans and J.K. Butler, unpublished.
31. H.C. Casey and M.B. Panish, Heterostructure Lasers. New York: Academic, 1978, part A, ch. 4, pp. 248–253.
32. N.K. Dutta. “Calculated temperature dependence of threshold current of GaAs-AlxGa1-x As double heterostructure lasers,” J. Appl. Phys., vol. 52, pp. 70–73, 1981.
33. A.R. Reisinger, P.S. Zory, and R.G. Waters, “Cavity length dependence of the threshold behavior in thin quantum well semiconductor lasers.” IEEE J. Quantum Electron., vol. QE-23, pp. 993–999, 1987.
34. N.K. Dutta and R.J. Nelson, “The case for Auger recombination in In1-xGaxAsyP1-x” J. Appl. Phys., vol. 53. pp. 74–92, 1982.
35. N.K. Dutta, “Calculation of Auger rates in a quantum well structure and its application to InGaAsP quantum well lasers,” J. Appl. Phys., vol. 54, pp. 1236–1245, 1983.
36. A. Sugimura, “Comparison of band-to-band Auger processes in InGaAsP,” IEEE J. Quantum Electron., vol. QE-19. pp. 930–932, 1983.
37. A. Sugimura, “Auger recombination effect on threshold current of InGaAsP quantum well lasers,” IEEE J. Quantum Electron., vol. QE-19, pp. 932–941, 1982.
38. M. Takeshima, “Effect of Auger recombination on laser operation in Ga1-xAlxAs,” J. Appl. Phys., vol. 58, pp. 3846–3850, 1985.
39. R.I. Taylor, R.A. Abram, M.G. Burt, and C. Smith, “Auger recombination in a quantum-well-heterostructure laser,” Proc. Inst. Elec. Eng., vol. 132, pt. J, pp. 364–370, 1985.
40. P. Blood, E.D. Fletcher, P.J. Hulyer, and P.M. Smowton. “Emission wavelength of AlGaAs-GaAs multiple quantum well lasers,” Appl. Phys. Lett., vol. 48, pp. 1111–1113, 1986.
41. J. Camassel, D. Auvergne, and H. Mathieu, “Temperature dependence of the band gap and comparison with the threshold frequency of pure GaAs lasers,” J. Appl. Phys., vol. 46, pp. 2683–2689, 1975.
42. H. Kressel and J.K. Butler, Semiconductor Lasers and Heterojunction LEDs. New York: Academic, 1977, ch. 3, p. 91.
43. D.A. Kleinman and R.C. Miller, “bandgap renormalization in semiconductor quantum wells containing carriers,” Phys. Rev. B, vol. 32, pp. 2266–2272, 1985.
44. S. Tarucha, H. Kobayashi, Y. Horikoshi, and H. Okamoto, “Carrier-induced energy-gap shrinkage in current-injection GaAs/AIGaAs MQW heterostructures,” Japan. J. Appl. Phys., vol. 23, pp. 874–878, 1984.
45. A. Tornita and A. Suzuki, “Carrier-induced lasing wavelength shift for quantum well laser diodes,” IEEE J. Quantum Election., vol. QE-23, pp. 1155–1159, 1987.
46. D.K. Wagner, R.G. Waters, P.L. Tihanyi, D.S. Hill, A.J. Roza, Jr., H.J. Vollmer, and M.M. Leopold. “Operating characteristics of single quantum well AlGaAs/GaAs high-power lasers,” IEEE J. Quantum Electron., vol. QE-24, pp. 1258–1264, July 1988.
47. P.S. Zory, A.R. Reisinger, L.J. Mawst, G. Costrini, C.A. Zmudzinski, M.A. Emanuel, M.E. Givens, and J.J. Coleman. “Anomalous length dependence of threshold for thin quantum well AlGaAs diode lasers,” Electron. Lett., vol. 22, pp. 475–476, 1986.
48. N.K. Dutta, “Temperature dependence of threshold current of GaAs quantum well lasers,” Electron. Lett., vol. 18, pp. 451–453, 1982.
49. P. Blood, S. Colak, and A.I. Kucharska, “Temperature dependence of threshold current in GaAs/AIGaAs quantum well lasers.” Appl. Phys. Lett., vol. 52, pp. 599–601, 1988.
50. P.S. Zory, A.R. Reisinger, R.G. Waters. L.J. Mawst, C.A. Zmudzinski, M.A. Emanuel, M.E. Givens, and J.J. Coleman, “Anomalous temperature dependence of threshold for thin quantum well AlGaAs diode lasers,” Appl. Phys. Lett., vol. 49, pp. 16–18, 1986.
51. J.R. Shealy, “Optimizing the performance of AlGaAs graded index separate confining heterostructure quantum well lasers,” Appl. Phys. Lett., vol. 50, pp. 1634–1636, 1987.
52. M.M. Leopold, A.P. Specht, C.A. Zmudzinski, M.E. Givens, and J.J. Coleman, “Temperature-dependent factors contributing to T0 in graded-index separate-confinement-heterostructure single quantum well lasers,” Appl. Phys. Lett., vol. 50, pp. 1403–1405, 1987.
53. N.B. Patel, T.J.S. Mattos, F.C. Prince, and A.S. Nunes, Jr., “Narrow stripe graded barrier single quantum well lasers—Threshold current considerations,” IEEE J. Quantum Electron., vol. QE-23, pp. 988–992, 1987.
54. J. Nagle, S. Hersee, M. Krakowski, T. Weil, and C. Weisbuch. “Threshold current of single quantum well lasers: The role of the confining layers,” Appl. Phys. Lett., vol. 49, pp. 1325–1327, 1986.
55. M. Mittelstein, Y. Arakawa, A. Larsson, and A. Yariv, “Second quantized state lasing of a current pumped single quantum well laser.” Appl. Phys. Lett., vol. 49, pp. 1689–1691, 1986.
56. Y. Tokuda, T. Matsui, F. Fujiwara, N. Tsukuda, and T. Nakayama, “Lasing wavelength of an asymmetric double quantum well laser diode,” Appl. Phys. Lett., vol. 51, pp. 209–211, 1987.
57. T. Hayakawa, T. Suyama, K. Takahashi, M. Kondo, S. Yamamoto. and T. Hijikata, “Near-ideal low threshold behavior in (11) oriented GaAs/AIGaAs quantum well lasers,” Appl. Phys. Lett., vol. 52, pp. 339–341, 1988.
58. H.Z. Chen, A. GhafTari, H. Morkoc, and A. Yariv, “Effect of substrate tilting on molecular beam epitaxial grown AlGaAs/GaAs lasers having very low threshold current densities,” Appl. Phys. Lett., vol. 51, pp. 2094–2096, 1987.
59. T. Hayakawa, M. Kondo, T. Suyama, K. Takahashi, S. Yamamoto, and T. Hijikata, “Reduction in threshold current density in quantum well lasers grown by molecular beam epitaxy on 0.5° misoriented (111) B substrates,” Japan. J. Appl. Phys., vol. 26, pp. L302-L305, 1987.
60. M. Asada and Y. Suematsu, “Density-matrix theory of semiconductor lasers with relaxation broadening model—Gain and gain-suppression in semiconductor lasers,” IEEE J. Quantum Electron., vol. QE-21, pp. 434–442, 1985.
61. M. Abramowitz and I.A. Stegun, Eds., Handbook of Mathematical Functions, Washington, DC: U.S. Gov. Printing Off., 1972, p. 449.
62. W.B. Joyce and R.W. Dixon, “Analytic approximations for the Fermi energy of an ideal Fermi gas,” Appl. Phys. Lett., vol. 31, pp. 354–356, 1977.
63. J.A. Brum, T. Weil, J. Nagle, and B. Vinter, “Calculation of carrier capture time of a quantum well in graded-index separate-confinement heterostructures,” Phys. Rev. B, vol. 34, pp. 2381–2384, 1986.
64. J. Feldmann, G. Peter, E.O. Göbel, K. Leo, H.-J. Polland, K. Ploog, K. Fujiwara, and T. Nakayama, “Carrier trapping in single quantum wells with different confinement structures,” Appl. Phys. Lett., vol. 51, pp. 226–228, 1987.
65. L.I. Schiff, Quantum Mechanics, 3rd ed. New York: McGraw-Hill, 1968, pp. 268–279.
66. R.C. Weast, Ed., CRC Handbook of Chemistry and Physics. Boca Raton, FL: CRC, 1983, ch. A, p. A-69, eq. 609.