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.

© 2005 Optical Society of Korea

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 [CrossRef]
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 [CrossRef]
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 [CrossRef]
4. B. F. Levine, G. Hasnain, C. G. Bethea and N. Chand, "Broadband 8-12 <TEX>${\mu}$</TEX>m high-sensitivity GaAs quantum well infrared photodetector," Appl. Phys. Lett., vol. 54, no. 26, pp. 2704-2706, 1989 [CrossRef]
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 [CrossRef]
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 [CrossRef]
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 [CrossRef]
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 [CrossRef]
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 [CrossRef]
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 [CrossRef]
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 [CrossRef]
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 [CrossRef]

Applied Physics Letters

• B. F. Levine, G. Hasnain, C. G. Bethea and N. Chand, "Broadband 8-12 <TEX>${\mu}$</TEX>m high-sensitivity GaAs quantum well infrared photodetector," Appl. Phys. Lett., vol. 54, no. 26, pp. 2704-2706, 1989 [CrossRef]

Japanese Journal of Applied Physics

• 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 [CrossRef]

Journal of Applied Physics

• 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 [CrossRef]
• 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 [CrossRef]

Phys. Rev. B

• 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 [CrossRef]
• 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 [CrossRef]
• W. Trzeciakowski and M. Gurioli, "Electric-field effects in semiconductor quantum wells," Phys. Rev. B, vol. 44, no. 8, pp. 3880-3890, 1991 [CrossRef]
• 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 [CrossRef]
• 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 [CrossRef]

Quantum Electronics, IEEE Journal of

• 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 [CrossRef]
• 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 [CrossRef]

Superlattices and Microstructures

• 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 [CrossRef]

Other

• L. I. Shiff, Quantum Mechanics (McGraw-Hill, New York, USA, 1949), pp. 41-103
• R. Shankar, Principles of Quantum Mechanics, 2nd ed. (Plenum, New York, USA, 1994), pp. 167-175
• G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures (Les Editions de Physique, Les Ulis, France, 1988), pp. 63-113 and pp. 237-257

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