Abstract

A Strong temperature dependence of microdisk lasers and photonic crystal nanocavity lasers with InAs quantum dot active regions is reported. These lasers operate at 1.3 μm at room temperature under optical pumping conditions. T0, microdisk = 31 K. T0, photonic crystal nanocavity = 14 K. The lasing threshold dependence on the lasing wavelength is also reported. We observe a minimum absorbed threshold pump power of 9 μW. This temperature and wavelength dependent lasing behavior is explained qualitatively by a simple model which attributes the experimental observations predominantly to surface recombination at threshold and the high quality factors of these cavities.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Sugawara, "Self-assembled InGaAs/GaAs quantum dots," in Semiconductors and Semimetals, vol. 60. (Academic, 1999).
  2. Y. Masumoto, T. Takagahara, Semiconductor quantum dots : physics, spectroscopy, and applications (Springer, 2002).
  3. Yoshihiro Akahane, Takashi Asano, Bong-Shik Song, and Susumu Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
    [CrossRef] [PubMed]
  4. Tian Yang, Samuel Lipson, J. D. O'Brien, and D.G. Deppe, "InAs Quantum Dot Photonic Crystal Lasers and Their Temperature Dependence," IEEE Photon. Technol. Lett. 17, 2244-2246 (2005).
    [CrossRef]
  5. T. Yang, J. Cao, P. Lee, M. Shih, R. Shafiiha, S. Farrell, J. O'Brien, O. Shchekin, and D. Deppe, "Microdisks with quantum dot active regions lasing near 1300 nm at room temperature," in Tech. Digest Conf. On Lasers and Electro-Optics, (Baltimore, MD, 2003), CWK3.
  6. R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
    [CrossRef]
  7. H. Chen, Z. Zou, O. B. Shchekin, D. G. Deppe, "InAs quantum-dot lasers operating near 1.3 μm with high characteristic temperature for continuous-wave operation," Electron. Lett. 36, 1703-1704 (2000).
    [CrossRef]
  8. Private communication with Hua Huang, a former student in Dennis Deppe’s group in University of Texas at Austin.
  9. E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, "Nearly ideal InP/ln0.53Ga0.47As heterojunction regrowth on chemically prepared ln0.53Ga0.47As surfaces," Appl. Phys. Lett. 60, 371-373 (1992).
    [CrossRef]
  10. Han-Youl Ryu, Jeong-Ki Hwang, Dae-Sung Song, Il-Young Han, and Yong-Hee Lee, "Effect of nonradiative recombination on light emitting properties of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).
    [CrossRef]
  11. T. F. Boggessa, L. Zhang, D. G. Deppe, D. L. Huffaker, and C. Cao, "Spectral engineering of carrier dynamics in In(Ga)As self-assembled quantum dots," Appl. Phys. Lett. 78, 276-278 (2001).
    [CrossRef]
  12. Shun Lien Chuang, Physics of Optoelectronic Devices (John Wiley & Sons, 1995).
  13. V. I. Zubkov, M. A. Melnik, A. V. Solomonov, and E. O. Tsvelev, "Determination of band offsets in strained InxGa1−xAs/GaAs quantum wells by capacitance-voltage profiling and Schrödinger-Poisson self-consistent simulation," Phys. Rev. B 70, 075312 (2004).
    [CrossRef]
  14. J.-P. Reithmaier, R. Hoger, H. Riechert, A. Heberle, G. Abstreiter, and G. Weimann, "Band offset in elastically strained InGaAs/GaAs multiple quantum wells determined by optical absorption and electronic Raman scattering," Appl. Phys. Lett. 56, 536-538 (1990).
    [CrossRef]
  15. Kyu-Seok Lee, and El-Hang Lee, "Optical Determination of the Heavy-hole Effective Mass of (In, Ga)As/GaAs Quantum Wells," ETRI Journal 17, 13-24 (1996).
    [CrossRef]
  16. mhhz of In0.15Ga0.85As QWs has not been found in the literature and is obtained by fitting to the experimentally measured QW band gap of 1.297eV.
  17. O. B. Shchekin, and D. G. Deppe, "Low-Threshold High-T0 1.3-μm InAs Quantum-Dot Lasers Due to P-type Modulation Doping of the Active Region," IEEE Photon. Technol. Lett. 14, 1231-1233 (2002).
    [CrossRef]

2005

Tian Yang, Samuel Lipson, J. D. O'Brien, and D.G. Deppe, "InAs Quantum Dot Photonic Crystal Lasers and Their Temperature Dependence," IEEE Photon. Technol. Lett. 17, 2244-2246 (2005).
[CrossRef]

2004

V. I. Zubkov, M. A. Melnik, A. V. Solomonov, and E. O. Tsvelev, "Determination of band offsets in strained InxGa1−xAs/GaAs quantum wells by capacitance-voltage profiling and Schrödinger-Poisson self-consistent simulation," Phys. Rev. B 70, 075312 (2004).
[CrossRef]

2003

Yoshihiro Akahane, Takashi Asano, Bong-Shik Song, and Susumu Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

2002

O. B. Shchekin, and D. G. Deppe, "Low-Threshold High-T0 1.3-μm InAs Quantum-Dot Lasers Due to P-type Modulation Doping of the Active Region," IEEE Photon. Technol. Lett. 14, 1231-1233 (2002).
[CrossRef]

2001

Han-Youl Ryu, Jeong-Ki Hwang, Dae-Sung Song, Il-Young Han, and Yong-Hee Lee, "Effect of nonradiative recombination on light emitting properties of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).
[CrossRef]

T. F. Boggessa, L. Zhang, D. G. Deppe, D. L. Huffaker, and C. Cao, "Spectral engineering of carrier dynamics in In(Ga)As self-assembled quantum dots," Appl. Phys. Lett. 78, 276-278 (2001).
[CrossRef]

2000

H. Chen, Z. Zou, O. B. Shchekin, D. G. Deppe, "InAs quantum-dot lasers operating near 1.3 μm with high characteristic temperature for continuous-wave operation," Electron. Lett. 36, 1703-1704 (2000).
[CrossRef]

1996

Kyu-Seok Lee, and El-Hang Lee, "Optical Determination of the Heavy-hole Effective Mass of (In, Ga)As/GaAs Quantum Wells," ETRI Journal 17, 13-24 (1996).
[CrossRef]

1993

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

1992

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, "Nearly ideal InP/ln0.53Ga0.47As heterojunction regrowth on chemically prepared ln0.53Ga0.47As surfaces," Appl. Phys. Lett. 60, 371-373 (1992).
[CrossRef]

1990

J.-P. Reithmaier, R. Hoger, H. Riechert, A. Heberle, G. Abstreiter, and G. Weimann, "Band offset in elastically strained InGaAs/GaAs multiple quantum wells determined by optical absorption and electronic Raman scattering," Appl. Phys. Lett. 56, 536-538 (1990).
[CrossRef]

Abstreiter, G.

J.-P. Reithmaier, R. Hoger, H. Riechert, A. Heberle, G. Abstreiter, and G. Weimann, "Band offset in elastically strained InGaAs/GaAs multiple quantum wells determined by optical absorption and electronic Raman scattering," Appl. Phys. Lett. 56, 536-538 (1990).
[CrossRef]

Akahane, Yoshihiro

Yoshihiro Akahane, Takashi Asano, Bong-Shik Song, and Susumu Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Bhat, R.

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, "Nearly ideal InP/ln0.53Ga0.47As heterojunction regrowth on chemically prepared ln0.53Ga0.47As surfaces," Appl. Phys. Lett. 60, 371-373 (1992).
[CrossRef]

Boggessa, T. F.

T. F. Boggessa, L. Zhang, D. G. Deppe, D. L. Huffaker, and C. Cao, "Spectral engineering of carrier dynamics in In(Ga)As self-assembled quantum dots," Appl. Phys. Lett. 78, 276-278 (2001).
[CrossRef]

Cao, C.

T. F. Boggessa, L. Zhang, D. G. Deppe, D. L. Huffaker, and C. Cao, "Spectral engineering of carrier dynamics in In(Ga)As self-assembled quantum dots," Appl. Phys. Lett. 78, 276-278 (2001).
[CrossRef]

Chen, H.

H. Chen, Z. Zou, O. B. Shchekin, D. G. Deppe, "InAs quantum-dot lasers operating near 1.3 μm with high characteristic temperature for continuous-wave operation," Electron. Lett. 36, 1703-1704 (2000).
[CrossRef]

Deppe, D. G.

O. B. Shchekin, and D. G. Deppe, "Low-Threshold High-T0 1.3-μm InAs Quantum-Dot Lasers Due to P-type Modulation Doping of the Active Region," IEEE Photon. Technol. Lett. 14, 1231-1233 (2002).
[CrossRef]

T. F. Boggessa, L. Zhang, D. G. Deppe, D. L. Huffaker, and C. Cao, "Spectral engineering of carrier dynamics in In(Ga)As self-assembled quantum dots," Appl. Phys. Lett. 78, 276-278 (2001).
[CrossRef]

H. Chen, Z. Zou, O. B. Shchekin, D. G. Deppe, "InAs quantum-dot lasers operating near 1.3 μm with high characteristic temperature for continuous-wave operation," Electron. Lett. 36, 1703-1704 (2000).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, "Nearly ideal InP/ln0.53Ga0.47As heterojunction regrowth on chemically prepared ln0.53Ga0.47As surfaces," Appl. Phys. Lett. 60, 371-373 (1992).
[CrossRef]

Heberle, A.

J.-P. Reithmaier, R. Hoger, H. Riechert, A. Heberle, G. Abstreiter, and G. Weimann, "Band offset in elastically strained InGaAs/GaAs multiple quantum wells determined by optical absorption and electronic Raman scattering," Appl. Phys. Lett. 56, 536-538 (1990).
[CrossRef]

Hoger, R.

J.-P. Reithmaier, R. Hoger, H. Riechert, A. Heberle, G. Abstreiter, and G. Weimann, "Band offset in elastically strained InGaAs/GaAs multiple quantum wells determined by optical absorption and electronic Raman scattering," Appl. Phys. Lett. 56, 536-538 (1990).
[CrossRef]

Huffaker, D. L.

T. F. Boggessa, L. Zhang, D. G. Deppe, D. L. Huffaker, and C. Cao, "Spectral engineering of carrier dynamics in In(Ga)As self-assembled quantum dots," Appl. Phys. Lett. 78, 276-278 (2001).
[CrossRef]

Koza, M. A.

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, "Nearly ideal InP/ln0.53Ga0.47As heterojunction regrowth on chemically prepared ln0.53Ga0.47As surfaces," Appl. Phys. Lett. 60, 371-373 (1992).
[CrossRef]

Lee, El-Hang

Kyu-Seok Lee, and El-Hang Lee, "Optical Determination of the Heavy-hole Effective Mass of (In, Ga)As/GaAs Quantum Wells," ETRI Journal 17, 13-24 (1996).
[CrossRef]

Lee, Kyu-Seok

Kyu-Seok Lee, and El-Hang Lee, "Optical Determination of the Heavy-hole Effective Mass of (In, Ga)As/GaAs Quantum Wells," ETRI Journal 17, 13-24 (1996).
[CrossRef]

Levi, A. F. J.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

Logan, R. A.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

McCall, S. L.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

Melnik, M. A.

V. I. Zubkov, M. A. Melnik, A. V. Solomonov, and E. O. Tsvelev, "Determination of band offsets in strained InxGa1−xAs/GaAs quantum wells by capacitance-voltage profiling and Schrödinger-Poisson self-consistent simulation," Phys. Rev. B 70, 075312 (2004).
[CrossRef]

Mohideen, U.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

Pearton, S. J.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

Reithmaier, J.-P.

J.-P. Reithmaier, R. Hoger, H. Riechert, A. Heberle, G. Abstreiter, and G. Weimann, "Band offset in elastically strained InGaAs/GaAs multiple quantum wells determined by optical absorption and electronic Raman scattering," Appl. Phys. Lett. 56, 536-538 (1990).
[CrossRef]

Riechert, H.

J.-P. Reithmaier, R. Hoger, H. Riechert, A. Heberle, G. Abstreiter, and G. Weimann, "Band offset in elastically strained InGaAs/GaAs multiple quantum wells determined by optical absorption and electronic Raman scattering," Appl. Phys. Lett. 56, 536-538 (1990).
[CrossRef]

Shchekin, O. B.

O. B. Shchekin, and D. G. Deppe, "Low-Threshold High-T0 1.3-μm InAs Quantum-Dot Lasers Due to P-type Modulation Doping of the Active Region," IEEE Photon. Technol. Lett. 14, 1231-1233 (2002).
[CrossRef]

H. Chen, Z. Zou, O. B. Shchekin, D. G. Deppe, "InAs quantum-dot lasers operating near 1.3 μm with high characteristic temperature for continuous-wave operation," Electron. Lett. 36, 1703-1704 (2000).
[CrossRef]

Slusher, R. E.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

Solomonov, A. V.

V. I. Zubkov, M. A. Melnik, A. V. Solomonov, and E. O. Tsvelev, "Determination of band offsets in strained InxGa1−xAs/GaAs quantum wells by capacitance-voltage profiling and Schrödinger-Poisson self-consistent simulation," Phys. Rev. B 70, 075312 (2004).
[CrossRef]

Tsvelev, E. O.

V. I. Zubkov, M. A. Melnik, A. V. Solomonov, and E. O. Tsvelev, "Determination of band offsets in strained InxGa1−xAs/GaAs quantum wells by capacitance-voltage profiling and Schrödinger-Poisson self-consistent simulation," Phys. Rev. B 70, 075312 (2004).
[CrossRef]

Weimann, G.

J.-P. Reithmaier, R. Hoger, H. Riechert, A. Heberle, G. Abstreiter, and G. Weimann, "Band offset in elastically strained InGaAs/GaAs multiple quantum wells determined by optical absorption and electronic Raman scattering," Appl. Phys. Lett. 56, 536-538 (1990).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, "Nearly ideal InP/ln0.53Ga0.47As heterojunction regrowth on chemically prepared ln0.53Ga0.47As surfaces," Appl. Phys. Lett. 60, 371-373 (1992).
[CrossRef]

Yang, Tian

Tian Yang, Samuel Lipson, J. D. O'Brien, and D.G. Deppe, "InAs Quantum Dot Photonic Crystal Lasers and Their Temperature Dependence," IEEE Photon. Technol. Lett. 17, 2244-2246 (2005).
[CrossRef]

Zah, C. E.

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, "Nearly ideal InP/ln0.53Ga0.47As heterojunction regrowth on chemically prepared ln0.53Ga0.47As surfaces," Appl. Phys. Lett. 60, 371-373 (1992).
[CrossRef]

Zhang, L.

T. F. Boggessa, L. Zhang, D. G. Deppe, D. L. Huffaker, and C. Cao, "Spectral engineering of carrier dynamics in In(Ga)As self-assembled quantum dots," Appl. Phys. Lett. 78, 276-278 (2001).
[CrossRef]

Zou, Z.

H. Chen, Z. Zou, O. B. Shchekin, D. G. Deppe, "InAs quantum-dot lasers operating near 1.3 μm with high characteristic temperature for continuous-wave operation," Electron. Lett. 36, 1703-1704 (2000).
[CrossRef]

Zubkov, V. I.

V. I. Zubkov, M. A. Melnik, A. V. Solomonov, and E. O. Tsvelev, "Determination of band offsets in strained InxGa1−xAs/GaAs quantum wells by capacitance-voltage profiling and Schrödinger-Poisson self-consistent simulation," Phys. Rev. B 70, 075312 (2004).
[CrossRef]

Appl. Phys. Lett.

E. Yablonovitch, R. Bhat, C. E. Zah, T. J. Gmitter, and M. A. Koza, "Nearly ideal InP/ln0.53Ga0.47As heterojunction regrowth on chemically prepared ln0.53Ga0.47As surfaces," Appl. Phys. Lett. 60, 371-373 (1992).
[CrossRef]

Han-Youl Ryu, Jeong-Ki Hwang, Dae-Sung Song, Il-Young Han, and Yong-Hee Lee, "Effect of nonradiative recombination on light emitting properties of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).
[CrossRef]

T. F. Boggessa, L. Zhang, D. G. Deppe, D. L. Huffaker, and C. Cao, "Spectral engineering of carrier dynamics in In(Ga)As self-assembled quantum dots," Appl. Phys. Lett. 78, 276-278 (2001).
[CrossRef]

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

J.-P. Reithmaier, R. Hoger, H. Riechert, A. Heberle, G. Abstreiter, and G. Weimann, "Band offset in elastically strained InGaAs/GaAs multiple quantum wells determined by optical absorption and electronic Raman scattering," Appl. Phys. Lett. 56, 536-538 (1990).
[CrossRef]

Electron. Lett.

H. Chen, Z. Zou, O. B. Shchekin, D. G. Deppe, "InAs quantum-dot lasers operating near 1.3 μm with high characteristic temperature for continuous-wave operation," Electron. Lett. 36, 1703-1704 (2000).
[CrossRef]

ETRI Journal

Kyu-Seok Lee, and El-Hang Lee, "Optical Determination of the Heavy-hole Effective Mass of (In, Ga)As/GaAs Quantum Wells," ETRI Journal 17, 13-24 (1996).
[CrossRef]

IEEE Photon. Technol. Lett.

O. B. Shchekin, and D. G. Deppe, "Low-Threshold High-T0 1.3-μm InAs Quantum-Dot Lasers Due to P-type Modulation Doping of the Active Region," IEEE Photon. Technol. Lett. 14, 1231-1233 (2002).
[CrossRef]

Tian Yang, Samuel Lipson, J. D. O'Brien, and D.G. Deppe, "InAs Quantum Dot Photonic Crystal Lasers and Their Temperature Dependence," IEEE Photon. Technol. Lett. 17, 2244-2246 (2005).
[CrossRef]

Nature

Yoshihiro Akahane, Takashi Asano, Bong-Shik Song, and Susumu Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Phys. Rev. B

V. I. Zubkov, M. A. Melnik, A. V. Solomonov, and E. O. Tsvelev, "Determination of band offsets in strained InxGa1−xAs/GaAs quantum wells by capacitance-voltage profiling and Schrödinger-Poisson self-consistent simulation," Phys. Rev. B 70, 075312 (2004).
[CrossRef]

Other

Private communication with Hua Huang, a former student in Dennis Deppe’s group in University of Texas at Austin.

mhhz of In0.15Ga0.85As QWs has not been found in the literature and is obtained by fitting to the experimentally measured QW band gap of 1.297eV.

T. Yang, J. Cao, P. Lee, M. Shih, R. Shafiiha, S. Farrell, J. O'Brien, O. Shchekin, and D. Deppe, "Microdisks with quantum dot active regions lasing near 1300 nm at room temperature," in Tech. Digest Conf. On Lasers and Electro-Optics, (Baltimore, MD, 2003), CWK3.

M. Sugawara, "Self-assembled InGaAs/GaAs quantum dots," in Semiconductors and Semimetals, vol. 60. (Academic, 1999).

Y. Masumoto, T. Takagahara, Semiconductor quantum dots : physics, spectroscopy, and applications (Springer, 2002).

Shun Lien Chuang, Physics of Optoelectronic Devices (John Wiley & Sons, 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Scanning electron micrographs of a microdisk cavity and a photonic crystal nanocavity.

Fig. 2.
Fig. 2.

(a) Lasing spectrum of a 3.1 μm diameter microdisk at room temperature under pumping conditions of a 1.6 mW peak pump power, 104 ns pulse widths, and a 9.4% duty cycle. (b) Output power versus pump power characteristic of a lasing mode at 1.30 μm in a 3.2 μm diameter microdisk under varied substrate temperatures. Pumping conditions are 24 ns pulse widths and a 1% duty cycle.

Fig. 3.
Fig. 3.

(a) Lasing spectrum of a photonic crystal nanocavity at room temperature under 2.5 mW peak incident pump power. (b) The data points are output power versus incident pump power characteristic of a lasing mode at 1.33 μm in another photonic crystal nanocavity at varied substrate temperatures. The curves are fitting results with T0 = 14 K and Tη = 18 K, the pump heating rate of 0.19 K / pJ included.

Fig. 4.
Fig. 4.

Data points: Experimental results of threshold incident pump power versus lasing wavelength for photonic crystal nanocavities. Dashed curves: Calculation results of threshold versus lasing wavelength for photonic crystal nanocavities. Solid curve: photoluminescence spectrum from an unpatterned area on the same sample.

Fig. 5.
Fig. 5.

The band diagram and the effective mass values used for the InAs QD material. E: energy level, m: effective mass, c: conduction band, v: valence band, e: electron, hh: heavy hole, lh: light hole, ρ: orthogonal to growth direction, z: along growth direction, m0: mass of electron. There are one electron state and two heavy hole states confined in the QW. [12-16]

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

N bulk = 2 [ m * k B T 2 π ħ 2 ] 3 2 e E F E 0 k B T , N QW = m * k B T π ħ 2 e E F E 0 k B T / 180 nm
[ N ( k B T , E Fe E Fh ) ] 2
= ( N e , bulk + N e , QWc ) ( N hh , bulk + N lh , bulk + N hh , QWv 1 + N hh , QWv 2 )
= 2 [ m e k B T 2 π ħ 2 ] 3 2 2 [ ( m hh 3 2 + m lh 3 2 ) 2 3 k B T 2 π ħ 2 ] 3 2 e ( E Fe E Fh ) ( E c , GaAs E v , GaAs ) k B T
+ 2 [ m e k B T 2 π ħ 2 ] 3 2 [ m hhρ k B T π ħ 2 × 180 nm ] e ( E Fe E Fh ) k B T ( e E c , GaAs E QWv 1 k B T + e E c , GaAs E QWv 2 k B T )
+ [ m k B T π ħ 2 × 180 nm ] 2 [ ( m hh 3 2 + m lh 3 2 ) 2 3 k B T 2 π ħ 2 ] 3 2 e ( E Fe E Fh ) ( E QWc E v , GaAs ) k B T
+ [ m k B T π ħ 2 × 180 nm ] [ m hhρ k B T π ħ 2 × 180 nm ] e ( E Fe E Fh ) k B T ( e E QWc E QWv 1 k B T + e E QWc E QWv 2 k B T )
1 1 + e ( E QDc E Fe ) k B T = 1 1 + e ( E Fh E QDv ) k B T
ρ QD ( λ ) [ 1 1 + e ( E QDc E Fe ) k B T + 1 1 + e ( E Fh E QDv ) k B T 1 ] = ρ QD ( λ 0 ) [ G th / G 0 ]
E Fe E Fh = 2 k B T ln ( 2 ρ QD ( λ 0 ) ρ QD ( λ ) G th G 0 + 1 1 ) + hc / λ
1 1 + e ( E E F ) k B T

Metrics