DOI QR코드

DOI QR Code

Dependence of Optical Matrix Elements on the Boundary Conditions of the Continuum States in Quantum Wells

  • Jang Y. R. (Department of Physics and Research Institute for Basic Sciences, Kyung Hee University) ;
  • Yoo K. H. (Department of Physics and Research Institute for Basic Sciences, Kyung Hee University) ;
  • Ram-Mohan L. R. (Departments of Physics, Electrical and Computer Engineering, Worcester Polytechnic Institute)
  • 투고 : 2005.02.14
  • 발행 : 2005.06.01

초록

Unlike for the bound states, several different boundary conditions are used for the continuum states above the barrier in semiconductor quantum wells. We employed three boundary conditions, infinite potential barrier boundary condition, periodic boundary condition and scattering boundary condition, and calculated the local number of states, wavefunctions and optical matrix elements for the symmetric and asymmetric quantum wells. We discussed how these quantities are related in the three boundary conditions. We argue that the scattering boundary condition has several advantages over the other two cases. These results would be useful in understanding quantum well lasers and detectors involving continuum states.

키워드

참고문헌

  1. S. T. Yen and C.-P. Lee, 'Theoretical analysis of 630 nm band GalnP-AIGalnP strained quantum-well lasers considering continuum states,' IEEE J. Qunatum Electron., vol. 33, no. 3, pp. 443-456, 1997 https://doi.org/10.1109/3.556014
  2. H. Hirayama, Y. Miyaki and M. Asada, 'Analysis of current injection efficiency of separate-confinement-heterostructure quantum-film lasers,' IEEE J. Qunatum Electron., vol. 38, no. 1, pp. 68-74, 1992 https://doi.org/10.1109/3.119499
  3. B. F. Levine, C. G. Bethea, K. K. Choi, J. Walker and R. J. Malik, 'Bound-to-extended state absorption GaAs superlattice transport infrared detectors,' J. Appl. Phys., vol. 64, no. 3, pp. 1591-1593, 1988 https://doi.org/10.1063/1.341794
  4. B. F. Levine, G. Hasnain, C. G. Bethea and N. Chand, 'Broadband 8-12 ${\mu}$m high-sensitivity GaAs quantum well infrared photodetector,' Appl. Phys. Lett., vol. 54, no. 26, pp. 2704-2706, 1989 https://doi.org/10.1063/1.101002
  5. Y. Fu, 'Boundary conditions of continuum states in characterizing photocurrent of GaAs/AIGaAs quantum well infrared photodetector,' Superlattices and Microstructures, vol. 30, no. 2, pp. 69-74, 2001 https://doi.org/10.1006/spmi.2001.0996
  6. J. D. Bruno and T. B. Bahder, 'Local density of states in double-barrier resonant-tunneling structures, II. Finite-width barriers,' Phy. Rev. B, vol. 39, no. 6, pp. 3659-3663, 1989 https://doi.org/10.1103/PhysRevB.39.3659
  7. S. Fafard, 'Energy levels in qunatum wells with capping barrier layer of finite size: bound states and oscillatory behavior of the continuum states,' Phys. Rev. B, vol. 46, no. 8, pp. 4659-4666, 1992 https://doi.org/10.1103/PhysRevB.46.4659
  8. Rusli, T. C. Chong and S. J. Chua, 'Theoretical analysis of bound-to-continuum state infrared absorption in Ga As/ AlxGalxAs quantum well structures,' Jpn. J. Appl. Phys., vol. 32, part 1, no. 5A, pp. 1998-2004, 1993 https://doi.org/10.1143/JJAP.32.1998
  9. T. B. Bahder, J. D. Bruno, R. G. Hay and C. A. Morrison, 'Local density of states in double-barrier resonant-tunneling structures,' Phys. Rev. B, vol. 37, no. 11, pp. 6256-6261, 1988 https://doi.org/10.1103/PhysRevB.37.6256
  10. G. Iannaccone, 'General relation between density of states and dwell times in mesoscopic systems,' Phys. Rev. B, vol. 51, no. 7, pp. 4727-4729, 1995 https://doi.org/10.1103/PhysRevB.51.4727
  11. L. I. Shiff, Quantum Mechanics (McGraw-Hill, New York, USA, 1949), pp. 41-103
  12. R. Shankar, Principles of Quantum Mechanics, 2nd ed. (Plenum, New York, USA, 1994), pp. 167-175
  13. W. Trzeciakowski and M. Gurioli, 'Electric-field effects in semiconductor quantum wells,' Phys. Rev. B, vol. 44, no. 8, pp. 3880-3890, 1991 https://doi.org/10.1103/PhysRevB.44.3880
  14. G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures (Les Editions de Physique, Les Ulis, France, 1988), pp. 63-113 and pp. 237-257
  15. I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, 'Band parameters for III-V compound semiconductors and their alloys,' J. Appl. Phys., vol. 89, no. 11, pp. 5815-5875, 2001 https://doi.org/10.1063/1.1368156