Abstract

We present a theoretical model for metal-cavity submonolayer quantum-dot surface-emitting microlasers, which operate at room temperature under electrical injection. Size-dependent lasing characteristics are investigated experimentally and theoretically with device radius ranging from 5 μm to 0.5 μm. The quantum dot emission and cavity optical properties are used in a rate-equation model to study the laser light output power vs. current behavior. Our theory explains the observed size-dependent physics and provides a guide for future device size reduction.

© 2013 Optical Society of America

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    [CrossRef]
  2. K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express18, 8790–8799 (2010).
    [CrossRef] [PubMed]
  3. M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
    [CrossRef]
  4. C.-Y. Lu, C.-Y. Ni, M. Zhang, S. L. Chuang, and D. Bimberg, “Metal-cavity surface-emitting microlasers with size reduction: theory and experiment,” IEEE J. Sel. Top. Quantum Electron.19, 1701809 (2013).
  5. K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Ntzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108 (2011).
    [CrossRef]
  6. D. Bimberg, “Quantum dot based nanophotonics and nanoelectronics,” Electron. Lett.44, 168–171 (2008).
    [CrossRef]
  7. S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
    [CrossRef]
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    [CrossRef]
  9. J. Kim and S. L. Chuang, “Theoretical and experimental study of optical gain, refractive index change, and linewidth enhancement factor of p-doped quantum-dot lasers,” IEEE J. Quantum Electron.42, 942–952 (2006).
    [CrossRef]
  10. T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of a microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron.27, 1347–1358 (1991).
    [CrossRef]
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    [CrossRef]
  12. A. Schliwa, M. Winkelnkemper, and D. Bimberg, “Impact of size, shape, and composition on piezoelectric effects and electronic properties of In(Ga)As/GaAs quantum dots,” Phys. Rev. B76, 205324 (2007).
    [CrossRef]
  13. G. Bester, X. Wu, D. Vanderbilt, and A. Zunger, “Importance of second-order piezoelectric effects in zinc-blende semiconductors,” Phys. Rev. Lett.96, 187602 (2006).
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  14. S. L. Chuang, Physics of Photonic Devices, 2nd ed. (Wiley, 2009), Chap. 4, 9, and 11.
  15. C. Pryor, “Eight-band calculations of strained InAs/GaAs quantum dots compared with one-, four-, and six-band approximations,” Phys. Rev. B57, 7190–7195 (1998).
    [CrossRef]
  16. G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, 1974).
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    [CrossRef]
  18. Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica34, 149–154 (1967).
    [CrossRef]
  19. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev.69, 681 (1946).
  20. L. Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).
  21. J. M. Gérard and B. Gayral, “InAs quantum dots: artificial atoms for solid-state cavity-quantum electrodynamics,” Physica E9, 131–139 (2001).
    [CrossRef]
  22. Y. Yamamoto, “Microcavity semiconductor laser with enhanced spontaneous emission,” Phys. Rev. A44, 657–668 (1991).
    [CrossRef] [PubMed]
  23. S.-W. Chang, C.-Y. A. Ni, and S. L. Chuang, “Theory for bowtie plasmonic nanolasers,” Opt. Express16, 10580–10595 (2008).
    [CrossRef] [PubMed]
  24. C.-Y. Lu, S. L. Chuang, and D. Bimberg, “Metal-cavity surface-emitting nanolasers,” IEEE J. Quantum Electron.49, 114–121 (2013).
    [CrossRef]
  25. S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron.17, 1681–1692 (2011).
    [CrossRef]
  26. P. V. Mena, J. J. Morikuni, S.-M. Kang, A. V. Harton, and K. W. Wyatt, “A comprehensive circuit-level model of vertical-cavity surface-emitting lasers,” J. Lightwave Technol.17, 2612–2632 (1999).
    [CrossRef]
  27. S.-W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron.8, 1014–1023 (2009).
    [CrossRef]

2013

C.-Y. Lu, C.-Y. Ni, M. Zhang, S. L. Chuang, and D. Bimberg, “Metal-cavity surface-emitting microlasers with size reduction: theory and experiment,” IEEE J. Sel. Top. Quantum Electron.19, 1701809 (2013).

C.-Y. Lu, S. L. Chuang, and D. Bimberg, “Metal-cavity surface-emitting nanolasers,” IEEE J. Quantum Electron.49, 114–121 (2013).
[CrossRef]

2011

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron.17, 1681–1692 (2011).
[CrossRef]

K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Ntzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108 (2011).
[CrossRef]

2010

K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express18, 8790–8799 (2010).
[CrossRef] [PubMed]

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
[CrossRef]

2009

S.-W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron.8, 1014–1023 (2009).
[CrossRef]

2008

S.-W. Chang, C.-Y. A. Ni, and S. L. Chuang, “Theory for bowtie plasmonic nanolasers,” Opt. Express16, 10580–10595 (2008).
[CrossRef] [PubMed]

D. Bimberg, “Quantum dot based nanophotonics and nanoelectronics,” Electron. Lett.44, 168–171 (2008).
[CrossRef]

2007

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

A. Schliwa, M. Winkelnkemper, and D. Bimberg, “Impact of size, shape, and composition on piezoelectric effects and electronic properties of In(Ga)As/GaAs quantum dots,” Phys. Rev. B76, 205324 (2007).
[CrossRef]

2006

G. Bester, X. Wu, D. Vanderbilt, and A. Zunger, “Importance of second-order piezoelectric effects in zinc-blende semiconductors,” Phys. Rev. Lett.96, 187602 (2006).
[CrossRef] [PubMed]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
[CrossRef]

J. Kim and S. L. Chuang, “Theoretical and experimental study of optical gain, refractive index change, and linewidth enhancement factor of p-doped quantum-dot lasers,” IEEE J. Quantum Electron.42, 942–952 (2006).
[CrossRef]

2001

I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parameters for IIIV compound semiconductors and their alloys,” J. Appl. Phys.89, 5815–5875 (2001).
[CrossRef]

J. M. Gérard and B. Gayral, “InAs quantum dots: artificial atoms for solid-state cavity-quantum electrodynamics,” Physica E9, 131–139 (2001).
[CrossRef]

2000

S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

1999

1998

C. Pryor, “Eight-band calculations of strained InAs/GaAs quantum dots compared with one-, four-, and six-band approximations,” Phys. Rev. B57, 7190–7195 (1998).
[CrossRef]

1991

Y. Yamamoto, “Microcavity semiconductor laser with enhanced spontaneous emission,” Phys. Rev. A44, 657–668 (1991).
[CrossRef] [PubMed]

T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of a microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron.27, 1347–1358 (1991).
[CrossRef]

1979

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection lasers,” Jpn. J. Appl. Phys.18, 2329–2330 (1979).
[CrossRef]

1967

Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica34, 149–154 (1967).
[CrossRef]

1946

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev.69, 681 (1946).

Alferov, Z. I.

S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

Baba, T.

T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of a microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron.27, 1347–1358 (1991).
[CrossRef]

Bedarev, D. A.

S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

Bester, G.

G. Bester, X. Wu, D. Vanderbilt, and A. Zunger, “Importance of second-order piezoelectric effects in zinc-blende semiconductors,” Phys. Rev. Lett.96, 187602 (2006).
[CrossRef] [PubMed]

Bimberg, D.

C.-Y. Lu, S. L. Chuang, and D. Bimberg, “Metal-cavity surface-emitting nanolasers,” IEEE J. Quantum Electron.49, 114–121 (2013).
[CrossRef]

C.-Y. Lu, C.-Y. Ni, M. Zhang, S. L. Chuang, and D. Bimberg, “Metal-cavity surface-emitting microlasers with size reduction: theory and experiment,” IEEE J. Sel. Top. Quantum Electron.19, 1701809 (2013).

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron.17, 1681–1692 (2011).
[CrossRef]

D. Bimberg, “Quantum dot based nanophotonics and nanoelectronics,” Electron. Lett.44, 168–171 (2008).
[CrossRef]

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

A. Schliwa, M. Winkelnkemper, and D. Bimberg, “Impact of size, shape, and composition on piezoelectric effects and electronic properties of In(Ga)As/GaAs quantum dots,” Phys. Rev. B76, 205324 (2007).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
[CrossRef]

S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

Bir, G. L.

G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, 1974).

Bondarenko, O.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
[CrossRef]

Bornholdt, C.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

Chang, S.-W.

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron.17, 1681–1692 (2011).
[CrossRef]

S.-W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron.8, 1014–1023 (2009).
[CrossRef]

S.-W. Chang, C.-Y. A. Ni, and S. L. Chuang, “Theory for bowtie plasmonic nanolasers,” Opt. Express16, 10580–10595 (2008).
[CrossRef] [PubMed]

Chuang, S. L.

C.-Y. Lu, S. L. Chuang, and D. Bimberg, “Metal-cavity surface-emitting nanolasers,” IEEE J. Quantum Electron.49, 114–121 (2013).
[CrossRef]

C.-Y. Lu, C.-Y. Ni, M. Zhang, S. L. Chuang, and D. Bimberg, “Metal-cavity surface-emitting microlasers with size reduction: theory and experiment,” IEEE J. Sel. Top. Quantum Electron.19, 1701809 (2013).

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron.17, 1681–1692 (2011).
[CrossRef]

S.-W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron.8, 1014–1023 (2009).
[CrossRef]

S.-W. Chang, C.-Y. A. Ni, and S. L. Chuang, “Theory for bowtie plasmonic nanolasers,” Opt. Express16, 10580–10595 (2008).
[CrossRef] [PubMed]

J. Kim and S. L. Chuang, “Theoretical and experimental study of optical gain, refractive index change, and linewidth enhancement factor of p-doped quantum-dot lasers,” IEEE J. Quantum Electron.42, 942–952 (2006).
[CrossRef]

S. L. Chuang, Physics of Photonic Devices, 2nd ed. (Wiley, 2009), Chap. 4, 9, and 11.

Coldren, L.

L. Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

Corzine, S.

L. Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

Dahne, M.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

Ding, K.

K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Ntzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108 (2011).
[CrossRef]

Eisele, H.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

Fainman, Y.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
[CrossRef]

Feng, L.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
[CrossRef]

Fiol, G.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
[CrossRef]

Gayral, B.

J. M. Gérard and B. Gayral, “InAs quantum dots: artificial atoms for solid-state cavity-quantum electrodynamics,” Physica E9, 131–139 (2001).
[CrossRef]

Gérard, J. M.

J. M. Gérard and B. Gayral, “InAs quantum dots: artificial atoms for solid-state cavity-quantum electrodynamics,” Physica E9, 131–139 (2001).
[CrossRef]

Germann, T. D.

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron.17, 1681–1692 (2011).
[CrossRef]

Haisler, V. A.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

Hamano, T.

T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of a microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron.27, 1347–1358 (1991).
[CrossRef]

Harton, A. V.

Hill, M. T.

K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Ntzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108 (2011).
[CrossRef]

Hopfer, F.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
[CrossRef]

Iga, K.

T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of a microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron.27, 1347–1358 (1991).
[CrossRef]

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection lasers,” Jpn. J. Appl. Phys.18, 2329–2330 (1979).
[CrossRef]

Kang, S.-M.

Kim, J.

J. Kim and S. L. Chuang, “Theoretical and experimental study of optical gain, refractive index change, and linewidth enhancement factor of p-doped quantum-dot lasers,” IEEE J. Quantum Electron.42, 942–952 (2006).
[CrossRef]

Kitahara, C.

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection lasers,” Jpn. J. Appl. Phys.18, 2329–2330 (1979).
[CrossRef]

Kopev, P. S.

S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

Kovsh, A. R.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
[CrossRef]

S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

Koyama, F.

T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of a microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron.27, 1347–1358 (1991).
[CrossRef]

Krestnikov, I. L.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
[CrossRef]

Kuntz, M.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
[CrossRef]

Lakhani, A.

Ledentsov, N. N.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
[CrossRef]

S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

Lenz, A.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

Liu, R.

K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Ntzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108 (2011).
[CrossRef]

Liu, Z.

K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Ntzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108 (2011).
[CrossRef]

Livshits, D. A.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

Livshits, D. L.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
[CrossRef]

Lomakin, V.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
[CrossRef]

Lu, C.-Y.

C.-Y. Lu, C.-Y. Ni, M. Zhang, S. L. Chuang, and D. Bimberg, “Metal-cavity surface-emitting microlasers with size reduction: theory and experiment,” IEEE J. Sel. Top. Quantum Electron.19, 1701809 (2013).

C.-Y. Lu, S. L. Chuang, and D. Bimberg, “Metal-cavity surface-emitting nanolasers,” IEEE J. Quantum Electron.49, 114–121 (2013).
[CrossRef]

S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron.17, 1681–1692 (2011).
[CrossRef]

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S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

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K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Ntzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108 (2011).
[CrossRef]

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S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

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Meyer, J. R.

I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parameters for IIIV compound semiconductors and their alloys,” J. Appl. Phys.89, 5815–5875 (2001).
[CrossRef]

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F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
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S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
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M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
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F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
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F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
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M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
[CrossRef]

Ni, C.-Y.

C.-Y. Lu, C.-Y. Ni, M. Zhang, S. L. Chuang, and D. Bimberg, “Metal-cavity surface-emitting microlasers with size reduction: theory and experiment,” IEEE J. Sel. Top. Quantum Electron.19, 1701809 (2013).

Ni, C.-Y. A.

Ning, C. Z.

K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Ntzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108 (2011).
[CrossRef]

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K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Ntzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108 (2011).
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G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, 1974).

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S.-W. Chang, C.-Y. Lu, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Theory of metal-cavity surface-emitting microlasers and comparison with experiment,” IEEE J. Sel. Top. Quantum Electron.17, 1681–1692 (2011).
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F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett.89, 141106 (2006).
[CrossRef]

Shernyakov, Y. M.

S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

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M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
[CrossRef]

Slutsky, B.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
[CrossRef]

Soda, H.

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection lasers,” Jpn. J. Appl. Phys.18, 2329–2330 (1979).
[CrossRef]

Soshnikov, I. P.

S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

Stock, E.

F. Hopfer, A. Mutig, G. Fiol, M. Kuntz, V. A. Shchukin, V. A. Haisler, T. Warming, E. Stock, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, C. Bornholdt, A. Lenz, H. Eisele, M. Dahne, N. N. Ledentsov, and D. Bimberg, “20 Gb/s 85 °C error-free operation of vcsels based on submonolayer deposition of quantum dots,” IEEE J. Sel. Top. Quantum Electron.13, 1302–1308 (2007).
[CrossRef]

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H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection lasers,” Jpn. J. Appl. Phys.18, 2329–2330 (1979).
[CrossRef]

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S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

Tsatsulnikov, A. F.

S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
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S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

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K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Ntzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108 (2011).
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S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, N. A. Maleev, V. M. Ustinov, Y. M. Shernyakov, I. P. Soshnikov, D. A. Livshits, I. S. Tarasov, D. A. Bedarev, B. V. Volovik, M. V. Maximov, A. F. Tsatsulnikov, N. N. Ledentsov, P. S. Kopev, D. Bimberg, and Z. I. Alferov, “0.94 μm diode lasers based on Stranski-Krastanow and sub-monolayer quantum dots,” Semicond. Sci. Technol.15, 1061 (2000).
[CrossRef]

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I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parameters for IIIV compound semiconductors and their alloys,” J. Appl. Phys.89, 5815–5875 (2001).
[CrossRef]

Wang, H.

K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldhoven, R. Ntzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108 (2011).
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Figures (7)

Fig. 1
Fig. 1

(a) Schematic of a submonolayer (SML) quantum-dot (QD) metal-cavity surface-emitting laser. The active region contains 3 groups of SML QDs. (b) Schematic of each group of SML QDs, consisting of 10 stacks of 0.5 ML InAs QDs separated by 2.2 ML thick GaAs spacers. [8] (c) A scanning electron micrograph of a 0.5-μm-radius microlaser before SiNx passivation and metal coating.

Fig. 2
Fig. 2

(a) Wavefunctions of the first two conduction band states (CB1 and CB2) and the first two heavy-hole states (HH1 and HH2). The wavefunctions are shown at the isosurface of | Ψ | 2 = 0.5 | Ψ | max 2. The blue disks are the 10-fold vertically-correlated submonolayer quantum dots, assuming no lateral coupling. (b) Wavefunction of the conduction band ground state (CB1), considering lateral coupling. The wavefunction is shown at the isosurface of | Ψ | 2 = 0.16 | Ψ | max 2. In this example, the quantum-dot 2D fill factor is 62.8% and the 2D dot density is 2 × 1011 cm−2.

Fig. 3
Fig. 3

(a) Ground state transition energy as a function of the temperature for different effective dot sizes. The measured photoluminescence peak is shown as the star. [8] (b) The quasi-Fermi level Fc for conduction band (blue circles) as a function of injected carrier density. Horizontal lines show 50 conduction band states with bound states circled. (c) The quasi-Fermi level Fv for valence band (red circles) as a function of injected carrier density. Horizontal lines show 50 heavy-hole and 20 light-hole states.

Fig. 4
Fig. 4

(a) TE-polarized material gain and (b) TE-polarized spontaneous emission rate calculated for the submonolayer quantum dots at T = 300 K, with carrier densities from n = 6 × 1017 cm−3 to n = 5.4 × 1018 cm−3.

Fig. 5
Fig. 5

(a) Calculated lasing wavelength and the photon lifetime as a function of the cavity diameter for the fundamental HE11 transverse mode. (b) Calculated cavity quality factor and effective mode volume as a function of the cavity diameter for the HE11 transverse mode.

Fig. 6
Fig. 6

Theoretical and measured light output power vs. current (L-I) curves for submono-layer quantum-dot metal-cavity surface-emitting microlasers with different device diameters at T = 300 K. The turn-on behavior below lasing threshold is explained by the increasing βsp factor with carrier injection, i.e., increasing amount of spontaneous emission coupled into the cavity mode.

Fig. 7
Fig. 7

(a) Calculated Purcell factor for the fundamental mode in the metal-cavity micro-lasers with different cavity diameters. (b) Extracted spontaneous emission coupling factor βsp from the fitting of device light output power vs. current (L-I) curves with the rate-equation model.

Tables (2)

Tables Icon

Table 1 Size-dependent laser characteristics extracted from the rate-equation model.

Tables Icon

Table 2 Parameters used in our theoretical model.

Equations (23)

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n = 2 N dot 2 D L z i d E [ 1 2 π σ c e ( E E c i ) 2 / 2 σ c 2 ] f c ( E , F c ) , p = 2 N dot 2 D L z j d E [ 1 2 π σ v e ( E E v j ) 2 / 2 σ v 2 ] f v ( E , F v )
g ( h ¯ ω ) = 2 N dot 2 D L z C 0 i , j d E | M env i j | 2 | e ^ p c v | 2 D ( E , E c v i j ) L ( E , h ¯ ω ) ( f c , i f v , j ) , r spon ( h ¯ ω ) = 2 N dot 2 D L z B 0 C 0 i , j d E | M env i j | 2 | e ^ p c v | 2 D ( E , E c v i j ) L ( E , h ¯ ω ) f c , i ( 1 f v , j )
D ( E , E c v i j ) = 1 2 π ( σ c 2 + σ v 2 ) exp [ ( E E c v i j ) 2 / 2 ( σ c 2 + σ v 2 ) ] , L ( E , h ¯ ω ) = Γ c v π 1 Γ c v 2 + ( E h ¯ ω ) 2 , B 0 = n a 2 ω 2 π 2 h ¯ c 2 , C 0 = π e 2 n a c ε 0 m 0 2 ω
F p = 3 Q 4 π 2 V eff ( λ n r ) 3
β = F p / 3 g F p / 3 + 1
β = λ 4 4 π 2 V Δ λ ε 3 / 2
R sp , m = d ( h ¯ ω ) { [ 2 N dot 2 D L z c V eff n a C 0 i j | M env i j | 2 | e ^ p c v | 2 f c , i ( 1 f v , j ) Γ c v / π Γ c v 2 + ( E c v i j h ¯ ω ) 2 ] × Γ m / π Γ m 2 + ( h ¯ ω m h ¯ ω ) 2 }
R sp , m = d ( h ¯ ω ) c / ( V eff n a ) B 0 r spon ( h ¯ ω ) Γ m / π Γ m 2 + ( h ¯ ω h ¯ ω m ) 2 D cav ( h ¯ ω m ) d ( h ¯ ω ) r spon ( h ¯ ω ) Γ m / π Γ m 2 + ( h ¯ ω h ¯ ω m ) 2
D cav ( h ¯ ω m ) = c / ( V eff n a ) B 0 = π 2 h ¯ c 3 V eff n a 3 ω m 2 = h ¯ ω m 8 π V eff ( λ m n a ) 3 = 2 Γ m Q 8 π V eff ( λ m n a ) 3 = π Γ m [ Q 4 π 2 V eff ( λ m n a ) 3 ] = π Γ m F p 3
β sp , m = R sp , m R sp = R sp , m g R sp , m + R sp , cont = D cav ( h ¯ ω m ) d ( h ¯ ω ) r spon ( h ¯ ω ) Γ m / π Γ m 2 + ( h ¯ ω h ¯ ω m ) 2 g D c a v ( h ¯ ω m ) d ( h ¯ ω ) r spon ( h ¯ ω ) Γ m / π Γ m 2 + ( h ¯ ω h ¯ ω m ) 2 + R spon , cont
β sp , m = γ F p / 3 γ g F p / 3 + 1
γ = 1 R sp , cont d ( h ¯ ω ) r spon ( h ¯ ω ) Γ m 2 Γ m 2 + ( h ¯ ω h ¯ ω m ) 2 = τ sp , cont V a d ( h ¯ ω ) r spon ( h ¯ ω ) Γ m 2 Γ m 2 + ( h ¯ ω h ¯ ω m ) 2
[ t 2 + n 2 ( ρ ) k 0 2 ] [ E z H z ] = k z 2 [ E z H z ] = n eff 2 k 0 2 [ E z H z ]
d n d t = η i I I l ( n ) q V a ( A n + C n 3 ) R sp ( n ) v g g ( n ) S , d S d t = Γ E v g g ( n ) S S τ p + Γ E β sp , m ( n ) R sp ( n )
A = A a V a v s = 4 D v s ( cylindrical )
I l ( n ) = I l 0 exp ( E g , barrier [ F c ( n ) F v ( n ) ] k T )
P = β c 1 h ¯ ω V a Γ E v g α m S + β c 2 h ¯ ω R sp V a
R sp , m = 2 N dot 2 D L z 2 π h ¯ i , j | ψ i c | μ E m 2 | ψ v j | 2 Γ c v + Γ m π f c , i ( 1 f v , j ) ( E c v i j h ¯ ω m ) 2 + ( Γ c v + Γ m ) 2 2 N dot 2 D L z 2 π h ¯ [ V a d 3 r V a | E m ( r ) | 2 4 ] i , j | ψ c i | μ e ^ | ψ v j | 2 Γ c v + Γ m π f c , i ( 1 f v , j ) ( E c v i j h ¯ ω m ) 2 + ( Γ c v + Γ m ) 2
V a V eff = Γ E = V a d 3 r ε 0 n a 2 | E m ( r ) | 2 / 2 V d 3 r ε 0 n 2 ( r ) | E m ( r ) | 2 / 2 = V a d 3 r ε 0 n a 2 | E m ( r ) | 2 / 2 h ¯ ω m
n 2 1 2 [ [ ω n 2 ( ω ) ] ω | ω = ω + n 2 ( ω ) ]
| ψ c i | μ e ^ | ψ v j | 2 = | M env i j | 2 | μ c v e ^ | 2 = | M env i j | 2 e 2 m 0 2 ω i j 2 | e ^ p c v i j | 2
R sp , m = 2 N dot 2 D L z 2 π h ¯ ( Γ E h ¯ ω m 2 ε 0 n a 2 V a ) i , j e 2 m 0 2 ω i j 2 | M env i j | 2 | e ^ p c v | 2 Γ c v + Γ m π f c , i ( 1 f v , j ) ( E c v i j h ¯ ω m ) 2 + ( Γ c v + Γ m ) 2
R sp , m = 2 N dot 2 D L z 2 π h ¯ i , j { h ¯ e 2 2 ε 0 n a 2 V eff m 0 2 ω m | M env i j | 2 | e ^ p c v | 2 f c , i ( 1 f v , j ) d ( h ¯ ω ) Γ c v / π ( E c v i j h ¯ ω ) 2 + Γ c v 2 Γ m / π ( h ¯ ω h ¯ ω m ) 2 + Γ m 2 } = d ( h ¯ ω ) [ 2 N dot 2 D L z c C 0 V eff n a i , j | M env i j | 2 | e ^ p c v | 2 f c , i ( 1 f v , j ) Γ c v / π ( E c v i j h ¯ ω ) 2 + Γ c v 2 ] Γ m / π ( h ¯ ω h ¯ ω m ) 2 + Γ m 2

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