Abstract

The development of quantum dot cascade lasers has been proposed as a path to obtain terahertz semiconductor lasers that operate at room temperature. The expected benefit is due to the suppression of nonradiative electron-phonon scattering and reduced dephasing that accompanies discretization of the electronic energy spectrum. We present numerical modeling which predicts that simple scaling of conventional quantum well based designs to the quantum dot regime will likely fail due to electrical instability associated with high-field domain formation. A design strategy adapted for terahertz quantum dot cascade lasers is presented which avoids these problems. Counterintuitively, this involves the resonant depopulation of the laser’s upper state with the LO-phonon energy. The strategy is tested theoretically using a density matrix model of transport and gain, which predicts sufficient gain for lasing at stable operating points. Finally, the effect of quantum dot size inhomogeneity on the optical lineshape is explored, suggesting that the design concept is robust to a moderate amount of statistical variation.

© 2016 Optical Society of America

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References

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2016 (3)

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

B. A. Burnett and B. S. Williams, “Origins of Terahertz Difference Frequency Susceptibility in Midinfrared Quantum Cascade Lasers,” Phys. Rev. Applied 5, 034013 (2016).
[Crossref]

G. Goldozian, F.A. Damtie, G. Kirsankas, and A. Wacker, “Transport in serial spinful multiple-dot systems: The role of electron-electron interactions and coherences,” Sci. Rep. 6, 22761 (2016).
[Crossref] [PubMed]

2015 (2)

A. Albo and Q. Hu, “Investigating temperature degradation in THz quantum cascade lasers by examination of temperature dependence of output power,” Appl. Phys. Lett. 106, 131108 (2015).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “From Photonic Crystal to Subwavelength Micropillar Array Terahertz Lasers,” IEEE J. Sel. Topics Quantum Electron. 21, 870 (2015).
[Crossref]

2014 (4)

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett. 50, 309–311 (2014).
[Crossref]

T. Grange, “Nanowire terahertz quantum cascade lasers,” Appl. Phys. Lett. 105, 141105 (2014).

B.A. Burnett and B.S. Williams, “Density matrix model for polarons in a terahertz quantum dot cascade laser,” Phys. Rev. B 90, 155309 (2014).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Subwavelength micropillar array terahertz lasers,” Opt. Express 22, 274–282 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (3)

S. Fathololoumi, E. Dupont, C. W. I. Chan, Z. R. Wasilewski, S. R. Laframboise, D. Ban, A. Matyas, C. Jirauschek, Q. Hu, and H.C. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express,  20, 3866–3876 (2012).
[Crossref] [PubMed]

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting Factors to the Temperature Performance of THz Quantum Cascade Lasers Based on the Resonant-Phonon Depopulation Scheme,” IEEE Trans. THz Sci. Tech. 2, 83–92 (2012).
[Crossref]

T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonic, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85, 235427 (2012).
[Crossref]

2011 (1)

J. Johansson and K.A. Dick, “Recent advances in semiconductor nanowire heterostructures,” Crys. Eng. Comm. 13, 7175–7184 (2011).
[Crossref]

2010 (2)

J.N. Shapiro, A. Lin, P.S. Wong, A.C. Scofield, C. Tu, P.N. Senanayake, G. Mariani, B.L. Liang, and D.L. Huffaker, “InGaAs heterostructure formation in catalyst-free GaAs nanopillars by selective-area metal-organic vapor phase epitaxy,” Appl. Phys. Lett. 97, 243102 (2010).
[Crossref]

E. Dupont, S. Fathololoumi, and H. C. Liu, “Simplified density-matrix model applied to three-well terahertz quantum cascade lasers,” Phys. Rev. B 81, 205311 (2010).
[Crossref]

2009 (6)

S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
[Crossref]

C. Weber, A. Wacker, and A. Knorr, “Density-matrix theory of the optical dynamics and transport in quantum cascade structure: The role of coherence,” Phys. Rev. B 79, 165322 (2009).
[Crossref]

T. Grange, “Decoherence in quantum dots due to real and virtual transitions: A nonperturbative calculation,” Phys. Rev. B 80, 245310 (2009).
[Crossref]

A. Tredicucci, “Quantum dots: long life in zero dimensions,” Nat. Mater. 8, 775–776 (2009).
[Crossref] [PubMed]

E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
[Crossref] [PubMed]

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B.S. Williams, Q. Hu, and J.L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photon. 3, 41–45 (2009).
[Crossref]

2008 (3)

N. Vukmirovic, D. Indjin, Z. Ikonic, and P. Harrison, “Electron transport and terahertz gain in quantum-dot cascades,” IEEE Photon. Technol. Lett. 20, 129–131 (2008).
[Crossref]

I.A. Dmitriev and R.A. Suris, “Quantum dot cascade laser: Arguments in favor,” Physica E 40, 2007–2009 (2008).
[Crossref]

E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
[Crossref]

2007 (2)

T. Grange, R. Ferreira, and G. Bastard, “Polaron relaxation in self-assembled quantum dots: Breakdown of the semiclassical model,” Phys. Rev. B 76, 241304 (2007).
[Crossref]

B.S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photon. 1, 517–525 (2007).
[Crossref]

2006 (1)

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42, 2 (2006).
[Crossref]

2005 (2)

H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005).
[Crossref]

T. Feil, H.-P. Tranitz, M. Reinwald, and W. Wegscheider, “Electric-field stabilization in a high-density surface superlattice,” Appl. Phys. Lett. 87, 212112 (2005).
[Crossref]

2003 (3)

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003).
[Crossref]

S. Anders, L. Rebohle, F.F. Schrey, W. Schrenk, K. Unterrainer, and G. Strasser, “Electroluminescence of a quantum dot cascade structure,” Appl. Phys. Lett. 82, 3862 (2003).
[Crossref]

C.H. Fischer, P. Bhattacharya, and P.-C. Yu, “Intersublevel electroluminescence from In0.4Ga0.6As/GaAs quantum dots in quantum cascade heterostructure with GaAsN/GaAs superlattice,” Electron. Lett. 39, 1537–1538 (2003).
[Crossref]

2002 (1)

A. Wacker, “Semiconductor superlattices: a model system for nonlinear transport,” Phys. Rep. 357, 1–111 (2002).
[Crossref]

1999 (1)

X.-Q. Li, H. Nakayama, and Y. Arakawa, “Phonon bottleneck in quantum dots: Role of lifetime of the confined optical phonons,” Phys. Rev. B 59, 5069 (1999).
[Crossref]

1998 (1)

X.-Q. Li and Y. Arakawa, “Anharmonic decay of confined optical phonons in quantum dots,” Phys. Rev. B 57, 12285 (1998).
[Crossref]

1997 (1)

N.S. Wingreen and C.A. Stafford, “Quantum-dot cascade laser: Proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33, 1170–1173 (1997).
[Crossref]

1971 (1)

R. F. Kazarinov and R. A. Suris, “Possibility of amplification of electromagnetic waves in a semiconductor with a superlattice,” Sov. Phys. Semicond. 5, 707–709 (1971).

Albo, A.

A. Albo and Q. Hu, “Investigating temperature degradation in THz quantum cascade lasers by examination of temperature dependence of output power,” Appl. Phys. Lett. 106, 131108 (2015).
[Crossref]

Amanti, M.I.

Anders, S.

S. Anders, L. Rebohle, F.F. Schrey, W. Schrenk, K. Unterrainer, and G. Strasser, “Electroluminescence of a quantum dot cascade structure,” Appl. Phys. Lett. 82, 3862 (2003).
[Crossref]

Andrews, A.M.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “From Photonic Crystal to Subwavelength Micropillar Array Terahertz Lasers,” IEEE J. Sel. Topics Quantum Electron. 21, 870 (2015).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Subwavelength micropillar array terahertz lasers,” Opt. Express 22, 274–282 (2014).
[Crossref] [PubMed]

Arakawa, Y.

X.-Q. Li, H. Nakayama, and Y. Arakawa, “Phonon bottleneck in quantum dots: Role of lifetime of the confined optical phonons,” Phys. Rev. B 59, 5069 (1999).
[Crossref]

X.-Q. Li and Y. Arakawa, “Anharmonic decay of confined optical phonons in quantum dots,” Phys. Rev. B 57, 12285 (1998).
[Crossref]

Ban, D.

Bastard, G.

E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
[Crossref] [PubMed]

E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
[Crossref]

T. Grange, R. Ferreira, and G. Bastard, “Polaron relaxation in self-assembled quantum dots: Breakdown of the semiclassical model,” Phys. Rev. B 76, 241304 (2007).
[Crossref]

Beck, M.

Belkin, M. A.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting Factors to the Temperature Performance of THz Quantum Cascade Lasers Based on the Resonant-Phonon Depopulation Scheme,” IEEE Trans. THz Sci. Tech. 2, 83–92 (2012).
[Crossref]

Bhattacharya, P.

C.H. Fischer, P. Bhattacharya, and P.-C. Yu, “Intersublevel electroluminescence from In0.4Ga0.6As/GaAs quantum dots in quantum cascade heterostructure with GaAsN/GaAs superlattice,” Electron. Lett. 39, 1537–1538 (2003).
[Crossref]

Bismuto, A.

Brandstetter, M.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “From Photonic Crystal to Subwavelength Micropillar Array Terahertz Lasers,” IEEE J. Sel. Topics Quantum Electron. 21, 870 (2015).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Subwavelength micropillar array terahertz lasers,” Opt. Express 22, 274–282 (2014).
[Crossref] [PubMed]

Burnett, B. A.

B. A. Burnett and B. S. Williams, “Origins of Terahertz Difference Frequency Susceptibility in Midinfrared Quantum Cascade Lasers,” Phys. Rev. Applied 5, 034013 (2016).
[Crossref]

Burnett, B.A.

B.A. Burnett and B.S. Williams, “Density matrix model for polarons in a terahertz quantum dot cascade laser,” Phys. Rev. B 90, 155309 (2014).
[Crossref]

Callebaut, H.

H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005).
[Crossref]

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003).
[Crossref]

Capasso, F.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting Factors to the Temperature Performance of THz Quantum Cascade Lasers Based on the Resonant-Phonon Depopulation Scheme,” IEEE Trans. THz Sci. Tech. 2, 83–92 (2012).
[Crossref]

Carpenter, B. A.

E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
[Crossref]

Carpenter, B.A.

E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
[Crossref] [PubMed]

Chan, C. W. I.

Chassagneux, Y.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting Factors to the Temperature Performance of THz Quantum Cascade Lasers Based on the Resonant-Phonon Depopulation Scheme,” IEEE Trans. THz Sci. Tech. 2, 83–92 (2012).
[Crossref]

Chen, L.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett. 50, 309–311 (2014).
[Crossref]

Chu, W.

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

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E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
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Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting Factors to the Temperature Performance of THz Quantum Cascade Lasers Based on the Resonant-Phonon Depopulation Scheme,” IEEE Trans. THz Sci. Tech. 2, 83–92 (2012).
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G. Goldozian, F.A. Damtie, G. Kirsankas, and A. Wacker, “Transport in serial spinful multiple-dot systems: The role of electron-electron interactions and coherences,” Sci. Rep. 6, 22761 (2016).
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L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett. 50, 309–311 (2014).
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L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett. 50, 309–311 (2014).
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X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
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M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “From Photonic Crystal to Subwavelength Micropillar Array Terahertz Lasers,” IEEE J. Sel. Topics Quantum Electron. 21, 870 (2015).
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M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Subwavelength micropillar array terahertz lasers,” Opt. Express 22, 274–282 (2014).
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M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “From Photonic Crystal to Subwavelength Micropillar Array Terahertz Lasers,” IEEE J. Sel. Topics Quantum Electron. 21, 870 (2015).
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M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Subwavelength micropillar array terahertz lasers,” Opt. Express 22, 274–282 (2014).
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J. Johansson and K.A. Dick, “Recent advances in semiconductor nanowire heterostructures,” Crys. Eng. Comm. 13, 7175–7184 (2011).
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T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonic, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85, 235427 (2012).
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Faist, J.

Fathololoumi, S.

Fedorov, G.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B.S. Williams, Q. Hu, and J.L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photon. 3, 41–45 (2009).
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E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
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E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
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T. Grange, R. Ferreira, and G. Bastard, “Polaron relaxation in self-assembled quantum dots: Breakdown of the semiclassical model,” Phys. Rev. B 76, 241304 (2007).
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L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett. 50, 309–311 (2014).
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G. Goldozian, F.A. Damtie, G. Kirsankas, and A. Wacker, “Transport in serial spinful multiple-dot systems: The role of electron-electron interactions and coherences,” Sci. Rep. 6, 22761 (2016).
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E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
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T. Grange, R. Ferreira, and G. Bastard, “Polaron relaxation in self-assembled quantum dots: Breakdown of the semiclassical model,” Phys. Rev. B 76, 241304 (2007).
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N. Vukmirovic, D. Indjin, Z. Ikonic, and P. Harrison, “Electron transport and terahertz gain in quantum-dot cascades,” IEEE Photon. Technol. Lett. 20, 129–131 (2008).
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E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
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E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
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S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
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B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42, 2 (2006).
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B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003).
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J.N. Shapiro, A. Lin, P.S. Wong, A.C. Scofield, C. Tu, P.N. Senanayake, G. Mariani, B.L. Liang, and D.L. Huffaker, “InGaAs heterostructure formation in catalyst-free GaAs nanopillars by selective-area metal-organic vapor phase epitaxy,” Appl. Phys. Lett. 97, 243102 (2010).
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T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonic, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85, 235427 (2012).
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N. Vukmirovic, D. Indjin, Z. Ikonic, and P. Harrison, “Electron transport and terahertz gain in quantum-dot cascades,” IEEE Photon. Technol. Lett. 20, 129–131 (2008).
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N. Vukmirovic, D. Indjin, Z. Ikonic, and P. Harrison, “Electron transport and terahertz gain in quantum-dot cascades,” IEEE Photon. Technol. Lett. 20, 129–131 (2008).
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Jiang, T.

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
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J. Johansson and K.A. Dick, “Recent advances in semiconductor nanowire heterostructures,” Crys. Eng. Comm. 13, 7175–7184 (2011).
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T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonic, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85, 235427 (2012).
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Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting Factors to the Temperature Performance of THz Quantum Cascade Lasers Based on the Resonant-Phonon Depopulation Scheme,” IEEE Trans. THz Sci. Tech. 2, 83–92 (2012).
[Crossref]

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G. Goldozian, F.A. Damtie, G. Kirsankas, and A. Wacker, “Transport in serial spinful multiple-dot systems: The role of electron-electron interactions and coherences,” Sci. Rep. 6, 22761 (2016).
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O. Jonasson, F. Karimi, and I. Knezevic, “Partially coherent electron transport in terahertz quantum cascade lasers based on a Markovian master equation for the density matrix,” J. Comput. Electron., published online first (2016).
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M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “From Photonic Crystal to Subwavelength Micropillar Array Terahertz Lasers,” IEEE J. Sel. Topics Quantum Electron. 21, 870 (2015).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Subwavelength micropillar array terahertz lasers,” Opt. Express 22, 274–282 (2014).
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Kumar, K.

Kumar, S.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B.S. Williams, Q. Hu, and J.L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photon. 3, 41–45 (2009).
[Crossref]

S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
[Crossref]

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42, 2 (2006).
[Crossref]

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003).
[Crossref]

Laframboise, S. R.

Lever, L. J. M.

T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonic, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85, 235427 (2012).
[Crossref]

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L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett. 50, 309–311 (2014).
[Crossref]

Li, W.

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
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X.-Q. Li, H. Nakayama, and Y. Arakawa, “Phonon bottleneck in quantum dots: Role of lifetime of the confined optical phonons,” Phys. Rev. B 59, 5069 (1999).
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J.N. Shapiro, A. Lin, P.S. Wong, A.C. Scofield, C. Tu, P.N. Senanayake, G. Mariani, B.L. Liang, and D.L. Huffaker, “InGaAs heterostructure formation in catalyst-free GaAs nanopillars by selective-area metal-organic vapor phase epitaxy,” Appl. Phys. Lett. 97, 243102 (2010).
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J.N. Shapiro, A. Lin, P.S. Wong, A.C. Scofield, C. Tu, P.N. Senanayake, G. Mariani, B.L. Liang, and D.L. Huffaker, “InGaAs heterostructure formation in catalyst-free GaAs nanopillars by selective-area metal-organic vapor phase epitaxy,” Appl. Phys. Lett. 97, 243102 (2010).
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Linfield, E. H.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett. 50, 309–311 (2014).
[Crossref]

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting Factors to the Temperature Performance of THz Quantum Cascade Lasers Based on the Resonant-Phonon Depopulation Scheme,” IEEE Trans. THz Sci. Tech. 2, 83–92 (2012).
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Liu, H.Y.

E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
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J.N. Shapiro, A. Lin, P.S. Wong, A.C. Scofield, C. Tu, P.N. Senanayake, G. Mariani, B.L. Liang, and D.L. Huffaker, “InGaAs heterostructure formation in catalyst-free GaAs nanopillars by selective-area metal-organic vapor phase epitaxy,” Appl. Phys. Lett. 97, 243102 (2010).
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Matyas, A.

Nakayama, H.

X.-Q. Li, H. Nakayama, and Y. Arakawa, “Phonon bottleneck in quantum dots: Role of lifetime of the confined optical phonons,” Phys. Rev. B 59, 5069 (1999).
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E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
[Crossref]

Porter, N.E.

E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
[Crossref] [PubMed]

Rebohle, L.

S. Anders, L. Rebohle, F.F. Schrey, W. Schrenk, K. Unterrainer, and G. Strasser, “Electroluminescence of a quantum dot cascade structure,” Appl. Phys. Lett. 82, 3862 (2003).
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Reimhult, E.

Reinwald, M.

T. Feil, H.-P. Tranitz, M. Reinwald, and W. Wegscheider, “Electric-field stabilization in a high-density surface superlattice,” Appl. Phys. Lett. 87, 212112 (2005).
[Crossref]

Reno, J. L.

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42, 2 (2006).
[Crossref]

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003).
[Crossref]

Reno, J.L.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B.S. Williams, Q. Hu, and J.L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photon. 3, 41–45 (2009).
[Crossref]

Schrenk, W.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “From Photonic Crystal to Subwavelength Micropillar Array Terahertz Lasers,” IEEE J. Sel. Topics Quantum Electron. 21, 870 (2015).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Subwavelength micropillar array terahertz lasers,” Opt. Express 22, 274–282 (2014).
[Crossref] [PubMed]

S. Anders, L. Rebohle, F.F. Schrey, W. Schrenk, K. Unterrainer, and G. Strasser, “Electroluminescence of a quantum dot cascade structure,” Appl. Phys. Lett. 82, 3862 (2003).
[Crossref]

Schrey, F.F.

S. Anders, L. Rebohle, F.F. Schrey, W. Schrenk, K. Unterrainer, and G. Strasser, “Electroluminescence of a quantum dot cascade structure,” Appl. Phys. Lett. 82, 3862 (2003).
[Crossref]

Scofield, A.C.

J.N. Shapiro, A. Lin, P.S. Wong, A.C. Scofield, C. Tu, P.N. Senanayake, G. Mariani, B.L. Liang, and D.L. Huffaker, “InGaAs heterostructure formation in catalyst-free GaAs nanopillars by selective-area metal-organic vapor phase epitaxy,” Appl. Phys. Lett. 97, 243102 (2010).
[Crossref]

Senanayake, P.N.

J.N. Shapiro, A. Lin, P.S. Wong, A.C. Scofield, C. Tu, P.N. Senanayake, G. Mariani, B.L. Liang, and D.L. Huffaker, “InGaAs heterostructure formation in catalyst-free GaAs nanopillars by selective-area metal-organic vapor phase epitaxy,” Appl. Phys. Lett. 97, 243102 (2010).
[Crossref]

Shapiro, J.N.

J.N. Shapiro, A. Lin, P.S. Wong, A.C. Scofield, C. Tu, P.N. Senanayake, G. Mariani, B.L. Liang, and D.L. Huffaker, “InGaAs heterostructure formation in catalyst-free GaAs nanopillars by selective-area metal-organic vapor phase epitaxy,” Appl. Phys. Lett. 97, 243102 (2010).
[Crossref]

Shen, C.

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

Skolnick, M. S.

E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
[Crossref]

Skolnick, M.S.

E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
[Crossref] [PubMed]

Smirnov, D.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B.S. Williams, Q. Hu, and J.L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photon. 3, 41–45 (2009).
[Crossref]

Stafford, C.A.

N.S. Wingreen and C.A. Stafford, “Quantum-dot cascade laser: Proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33, 1170–1173 (1997).
[Crossref]

Steer, M. J.

E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
[Crossref]

Stehr, D.

E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
[Crossref] [PubMed]

Strasser, G.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “From Photonic Crystal to Subwavelength Micropillar Array Terahertz Lasers,” IEEE J. Sel. Topics Quantum Electron. 21, 870 (2015).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Subwavelength micropillar array terahertz lasers,” Opt. Express 22, 274–282 (2014).
[Crossref] [PubMed]

S. Anders, L. Rebohle, F.F. Schrey, W. Schrenk, K. Unterrainer, and G. Strasser, “Electroluminescence of a quantum dot cascade structure,” Appl. Phys. Lett. 82, 3862 (2003).
[Crossref]

Strupiechonski, E.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting Factors to the Temperature Performance of THz Quantum Cascade Lasers Based on the Resonant-Phonon Depopulation Scheme,” IEEE Trans. THz Sci. Tech. 2, 83–92 (2012).
[Crossref]

Suris, R. A.

R. F. Kazarinov and R. A. Suris, “Possibility of amplification of electromagnetic waves in a semiconductor with a superlattice,” Sov. Phys. Semicond. 5, 707–709 (1971).

Suris, R.A.

I.A. Dmitriev and R.A. Suris, “Quantum dot cascade laser: Arguments in favor,” Physica E 40, 2007–2009 (2008).
[Crossref]

Tranitz, H.-P.

T. Feil, H.-P. Tranitz, M. Reinwald, and W. Wegscheider, “Electric-field stabilization in a high-density surface superlattice,” Appl. Phys. Lett. 87, 212112 (2005).
[Crossref]

Tredicucci, A.

A. Tredicucci, “Quantum dots: long life in zero dimensions,” Nat. Mater. 8, 775–776 (2009).
[Crossref] [PubMed]

Tu, C.

J.N. Shapiro, A. Lin, P.S. Wong, A.C. Scofield, C. Tu, P.N. Senanayake, G. Mariani, B.L. Liang, and D.L. Huffaker, “InGaAs heterostructure formation in catalyst-free GaAs nanopillars by selective-area metal-organic vapor phase epitaxy,” Appl. Phys. Lett. 97, 243102 (2010).
[Crossref]

Unterrainer, K.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “From Photonic Crystal to Subwavelength Micropillar Array Terahertz Lasers,” IEEE J. Sel. Topics Quantum Electron. 21, 870 (2015).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Subwavelength micropillar array terahertz lasers,” Opt. Express 22, 274–282 (2014).
[Crossref] [PubMed]

S. Anders, L. Rebohle, F.F. Schrey, W. Schrenk, K. Unterrainer, and G. Strasser, “Electroluminescence of a quantum dot cascade structure,” Appl. Phys. Lett. 82, 3862 (2003).
[Crossref]

Valavanis, A.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett. 50, 309–311 (2014).
[Crossref]

T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonic, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85, 235427 (2012).
[Crossref]

Vinh, N. G.

E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
[Crossref]

Vukmirovic, N.

N. Vukmirovic, D. Indjin, Z. Ikonic, and P. Harrison, “Electron transport and terahertz gain in quantum-dot cascades,” IEEE Photon. Technol. Lett. 20, 129–131 (2008).
[Crossref]

Wacker, A.

G. Goldozian, F.A. Damtie, G. Kirsankas, and A. Wacker, “Transport in serial spinful multiple-dot systems: The role of electron-electron interactions and coherences,” Sci. Rep. 6, 22761 (2016).
[Crossref] [PubMed]

C. Weber, A. Wacker, and A. Knorr, “Density-matrix theory of the optical dynamics and transport in quantum cascade structure: The role of coherence,” Phys. Rev. B 79, 165322 (2009).
[Crossref]

A. Wacker, “Semiconductor superlattices: a model system for nonlinear transport,” Phys. Rep. 357, 1–111 (2002).
[Crossref]

Wade, A.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B.S. Williams, Q. Hu, and J.L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photon. 3, 41–45 (2009).
[Crossref]

Wang, Q. J.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting Factors to the Temperature Performance of THz Quantum Cascade Lasers Based on the Resonant-Phonon Depopulation Scheme,” IEEE Trans. THz Sci. Tech. 2, 83–92 (2012).
[Crossref]

Wang, X.

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

Wasilewski, Z. R.

Weber, C.

C. Weber, A. Wacker, and A. Knorr, “Density-matrix theory of the optical dynamics and transport in quantum cascade structure: The role of coherence,” Phys. Rev. B 79, 165322 (2009).
[Crossref]

Wegscheider, W.

T. Feil, H.-P. Tranitz, M. Reinwald, and W. Wegscheider, “Electric-field stabilization in a high-density surface superlattice,” Appl. Phys. Lett. 87, 212112 (2005).
[Crossref]

Williams, B. S.

B. A. Burnett and B. S. Williams, “Origins of Terahertz Difference Frequency Susceptibility in Midinfrared Quantum Cascade Lasers,” Phys. Rev. Applied 5, 034013 (2016).
[Crossref]

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42, 2 (2006).
[Crossref]

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003).
[Crossref]

Williams, B.S.

B.A. Burnett and B.S. Williams, “Density matrix model for polarons in a terahertz quantum dot cascade laser,” Phys. Rev. B 90, 155309 (2014).
[Crossref]

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B.S. Williams, Q. Hu, and J.L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photon. 3, 41–45 (2009).
[Crossref]

B.S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photon. 1, 517–525 (2007).
[Crossref]

B.S. Williams, (2003) , “Terahertz quantum cascade lasers” (PhD Thesis)

Wilson, L. R.

E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
[Crossref]

Wilson, L.R.

E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
[Crossref] [PubMed]

Wingreen, N.S.

N.S. Wingreen and C.A. Stafford, “Quantum-dot cascade laser: Proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33, 1170–1173 (1997).
[Crossref]

Winnerl, S.

E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
[Crossref] [PubMed]

Wong, P.S.

J.N. Shapiro, A. Lin, P.S. Wong, A.C. Scofield, C. Tu, P.N. Senanayake, G. Mariani, B.L. Liang, and D.L. Huffaker, “InGaAs heterostructure formation in catalyst-free GaAs nanopillars by selective-area metal-organic vapor phase epitaxy,” Appl. Phys. Lett. 97, 243102 (2010).
[Crossref]

Wu, W.

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

Yang, N.

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

Yu, P.-C.

C.H. Fischer, P. Bhattacharya, and P.-C. Yu, “Intersublevel electroluminescence from In0.4Ga0.6As/GaAs quantum dots in quantum cascade heterostructure with GaAsN/GaAs superlattice,” Electron. Lett. 39, 1537–1538 (2003).
[Crossref]

Zhan, Z.

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

Zhu, J.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett. 50, 309–311 (2014).
[Crossref]

Zibik, E. A.

E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
[Crossref]

Zibik, E.A.

E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
[Crossref] [PubMed]

AIP Adv. (1)

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

Appl. Phys. Lett. (6)

A. Albo and Q. Hu, “Investigating temperature degradation in THz quantum cascade lasers by examination of temperature dependence of output power,” Appl. Phys. Lett. 106, 131108 (2015).
[Crossref]

S. Anders, L. Rebohle, F.F. Schrey, W. Schrenk, K. Unterrainer, and G. Strasser, “Electroluminescence of a quantum dot cascade structure,” Appl. Phys. Lett. 82, 3862 (2003).
[Crossref]

J.N. Shapiro, A. Lin, P.S. Wong, A.C. Scofield, C. Tu, P.N. Senanayake, G. Mariani, B.L. Liang, and D.L. Huffaker, “InGaAs heterostructure formation in catalyst-free GaAs nanopillars by selective-area metal-organic vapor phase epitaxy,” Appl. Phys. Lett. 97, 243102 (2010).
[Crossref]

T. Grange, “Nanowire terahertz quantum cascade lasers,” Appl. Phys. Lett. 105, 141105 (2014).

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003).
[Crossref]

T. Feil, H.-P. Tranitz, M. Reinwald, and W. Wegscheider, “Electric-field stabilization in a high-density surface superlattice,” Appl. Phys. Lett. 87, 212112 (2005).
[Crossref]

Crys. Eng. Comm. (1)

J. Johansson and K.A. Dick, “Recent advances in semiconductor nanowire heterostructures,” Crys. Eng. Comm. 13, 7175–7184 (2011).
[Crossref]

Electron. Lett. (3)

C.H. Fischer, P. Bhattacharya, and P.-C. Yu, “Intersublevel electroluminescence from In0.4Ga0.6As/GaAs quantum dots in quantum cascade heterostructure with GaAsN/GaAs superlattice,” Electron. Lett. 39, 1537–1538 (2003).
[Crossref]

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett. 50, 309–311 (2014).
[Crossref]

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42, 2 (2006).
[Crossref]

IEEE J. Quantum Electron. (1)

N.S. Wingreen and C.A. Stafford, “Quantum-dot cascade laser: Proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33, 1170–1173 (1997).
[Crossref]

IEEE J. Sel. Topics Quantum Electron. (1)

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, A.M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “From Photonic Crystal to Subwavelength Micropillar Array Terahertz Lasers,” IEEE J. Sel. Topics Quantum Electron. 21, 870 (2015).
[Crossref]

IEEE Photon. Technol. Lett. (1)

N. Vukmirovic, D. Indjin, Z. Ikonic, and P. Harrison, “Electron transport and terahertz gain in quantum-dot cascades,” IEEE Photon. Technol. Lett. 20, 129–131 (2008).
[Crossref]

IEEE Trans. THz Sci. Tech. (1)

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting Factors to the Temperature Performance of THz Quantum Cascade Lasers Based on the Resonant-Phonon Depopulation Scheme,” IEEE Trans. THz Sci. Tech. 2, 83–92 (2012).
[Crossref]

J. Appl. Phys. (1)

H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005).
[Crossref]

Nat. Mater. (2)

A. Tredicucci, “Quantum dots: long life in zero dimensions,” Nat. Mater. 8, 775–776 (2009).
[Crossref] [PubMed]

E.A. Zibik, T. Grange, B.A. Carpenter, N.E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H.Y. Liu, M.S. Skolnick, and L.R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8, 803–807 (2009).
[Crossref] [PubMed]

Nat. Photon. (2)

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B.S. Williams, Q. Hu, and J.L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photon. 3, 41–45 (2009).
[Crossref]

B.S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photon. 1, 517–525 (2007).
[Crossref]

Opt. Express (3)

Phys. Rep. (1)

A. Wacker, “Semiconductor superlattices: a model system for nonlinear transport,” Phys. Rep. 357, 1–111 (2002).
[Crossref]

Phys. Rev. Applied (1)

B. A. Burnett and B. S. Williams, “Origins of Terahertz Difference Frequency Susceptibility in Midinfrared Quantum Cascade Lasers,” Phys. Rev. Applied 5, 034013 (2016).
[Crossref]

Phys. Rev. B (10)

S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
[Crossref]

E. Dupont, S. Fathololoumi, and H. C. Liu, “Simplified density-matrix model applied to three-well terahertz quantum cascade lasers,” Phys. Rev. B 81, 205311 (2010).
[Crossref]

T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonic, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85, 235427 (2012).
[Crossref]

C. Weber, A. Wacker, and A. Knorr, “Density-matrix theory of the optical dynamics and transport in quantum cascade structure: The role of coherence,” Phys. Rev. B 79, 165322 (2009).
[Crossref]

B.A. Burnett and B.S. Williams, “Density matrix model for polarons in a terahertz quantum dot cascade laser,” Phys. Rev. B 90, 155309 (2014).
[Crossref]

X.-Q. Li, H. Nakayama, and Y. Arakawa, “Phonon bottleneck in quantum dots: Role of lifetime of the confined optical phonons,” Phys. Rev. B 59, 5069 (1999).
[Crossref]

T. Grange, R. Ferreira, and G. Bastard, “Polaron relaxation in self-assembled quantum dots: Breakdown of the semiclassical model,” Phys. Rev. B 76, 241304 (2007).
[Crossref]

X.-Q. Li and Y. Arakawa, “Anharmonic decay of confined optical phonons in quantum dots,” Phys. Rev. B 57, 12285 (1998).
[Crossref]

E. A. Zibik, T. Grange, B. A. Carpenter, R. Ferreira, G. Bastard, N. G. Vinh, P. J. Philips, M. J. Steer, M. Hopkinson, J. W. Cockburn, M. S. Skolnick, and L. R. Wilson, “Intersublevel polaron dephasing in self-assembled quantum dots,” Phys. Rev. B 77, 041307 (2008).
[Crossref]

T. Grange, “Decoherence in quantum dots due to real and virtual transitions: A nonperturbative calculation,” Phys. Rev. B 80, 245310 (2009).
[Crossref]

Physica E (1)

I.A. Dmitriev and R.A. Suris, “Quantum dot cascade laser: Arguments in favor,” Physica E 40, 2007–2009 (2008).
[Crossref]

Sci. Rep. (1)

G. Goldozian, F.A. Damtie, G. Kirsankas, and A. Wacker, “Transport in serial spinful multiple-dot systems: The role of electron-electron interactions and coherences,” Sci. Rep. 6, 22761 (2016).
[Crossref] [PubMed]

Sov. Phys. Semicond. (1)

R. F. Kazarinov and R. A. Suris, “Possibility of amplification of electromagnetic waves in a semiconductor with a superlattice,” Sov. Phys. Semicond. 5, 707–709 (1971).

Other (2)

B.S. Williams, (2003) , “Terahertz quantum cascade lasers” (PhD Thesis)

O. Jonasson, F. Karimi, and I. Knezevic, “Partially coherent electron transport in terahertz quantum cascade lasers based on a Markovian master equation for the density matrix,” J. Comput. Electron., published online first (2016).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) Energy eigenstates obtained with (solid) and without (dashed) the polaron coupling in an InAs QD with varying sublevel separations E2E1. Ωpol is given a typical value of 3 meV. Downward arrows depict start/end states of electron relaxation. (b,c) Relaxation dynamics for different sublevel energy separations assuming the LO-phonon decay time of 2.5 ps and for pure dephasing times of T 2 * = , 3 ps. Colors correspond to downward arrows in (c).
Fig. 2
Fig. 2 Electronic bandstructures and level schematics at parasitic/design biases for (a) a conventional QCL design and (b) a modified design for a QDCL. The chosen material system is InAs/InAs0.8P0.2 and the layer thickness in nm starting with the tunnel barrier are 5.5/14/3/30 for (a) and 5.5/18/3/35 for (b), so that the only difference is a widening of the wells. Effective masses used are m*/m0 = 0.026, 0.0367 for the wells and barriers, respectively. The level schematics illustrate the design strategy which is to engineer resonant LO-phonon depopulation of the upper state ΨU, rather than the lower state ΨL, to the injector state ΨI.
Fig. 3
Fig. 3 Simulated transport characteristics and bias-dependent small-signal optical gain at 300 K for the conventional and modified designs, showing regions of electrical stability/instability. The designed and predicted gain in the modified design is circled by the dashed oval.
Fig. 4
Fig. 4 Simulated effects of saturation on the conventional and modified designs at their respective design biases. Saturated gain profiles in (a) and (b) are cross-saturation by intensity at ωpeak (marked by dashed line), and (c) is the peak of these profiles in relation to the small-signal gain at ωpeak.
Fig. 5
Fig. 5 Simulated gain spectra of 50 different variations of each design, where all length dimensions vary by a Gaussian distribution of 5% standard deviation. The solid black lines are the gain in the intended designs, and the solid red lines are the average of all variations.

Equations (3)

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

J para N s q 2 τ L J 0 N s q 2 τ U ,
Δ N = J q τ U ( 1 τ L τ U L ) ,
I sat ( ν ) = h ν σ ( ν ) [ τ L + τ U ( 1 τ L τ U L ) ] ,

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