Abstract

We propose a novel intersubband laser based on transitions between subbands in the k-space region where the light-hole effective mass is inverted. We consider GaAs/AlGaAs quantum well (QW) structures which give rise to several confined subbands including ground state heavy-hole subband (HH1) and light-hole subband (LH1). The inverted-effective-mass feature in subband LH1 emerges only in wide QWs which produce closely spaced subbands in energy that are strongly coupled. Laser wavelength determined by this energy separation is typically in the THz range. The laser structure is designed to facilitate electrical pumping with a quantum cascade scheme consisting of isolated single GaAs/AlGaAs QWs. Our calculation shows that with only a small fraction of the carrier population in the upper subband (LH1), it is still possible to achieve population inversion locally in k-space between the two subbands where the light-hole effective mass is inverted. Our result indicates that optical gain in excess of 150/cm can be achieved with a relatively small pump current density on the order of 100A/cm2.

© 1998 Optical Society of America

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  1. J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994)
    [Crossref] [PubMed]
  2. C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength infrared (λ ≈ 11μm) quantum cascade lasers,” Appl. Phys. Lett. 69, 2810–2812 (1996)
    [Crossref]
  3. S. Slivken, C. Jelen, A. Rybaltowski, J. Diaz, and M. Razeghi, “Gas-source molecular beam epitaxy growth of an 8.5 μm quantum cascade laser,” Appl. Phys. Lett. 71, 2593–2595 (1997)
    [Crossref]
  4. O. Gauthier-Lafaye, P. Boucaud, F. H. Julien, S. Sauvage, S. Cabaret, J.-M. Lourtioz, V. Thierry-Mieg, and R. Planel, “Long-wavelength (≈ 15.5μm) unipolar semiconductor laser in GaAs quantum wells,” Appl. Phys. Lett. 71, 3619–3621 (1997)
    [Crossref]
  5. G. Sun and J. Khurgin, “Optical pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: Feasibility study,” IEEE J. Quantum Electron. 29, 1104–1111(1993)
    [Crossref]
  6. J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertson, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996)
    [Crossref] [PubMed]
  7. E. O. Kane, “Band structure of Indium Antimonide,” J. Phys. Chern. Solids 1, 249–261, (1957)
    [Crossref]
  8. G. Bastard, “Wave mechanics applied to semiconductor heterostructures,” Les Editions de Physique, Les Ulis, (Paris, 1998) Chap. 3

1998 (1)

G. Bastard, “Wave mechanics applied to semiconductor heterostructures,” Les Editions de Physique, Les Ulis, (Paris, 1998) Chap. 3

1997 (2)

S. Slivken, C. Jelen, A. Rybaltowski, J. Diaz, and M. Razeghi, “Gas-source molecular beam epitaxy growth of an 8.5 μm quantum cascade laser,” Appl. Phys. Lett. 71, 2593–2595 (1997)
[Crossref]

O. Gauthier-Lafaye, P. Boucaud, F. H. Julien, S. Sauvage, S. Cabaret, J.-M. Lourtioz, V. Thierry-Mieg, and R. Planel, “Long-wavelength (≈ 15.5μm) unipolar semiconductor laser in GaAs quantum wells,” Appl. Phys. Lett. 71, 3619–3621 (1997)
[Crossref]

1996 (2)

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength infrared (λ ≈ 11μm) quantum cascade lasers,” Appl. Phys. Lett. 69, 2810–2812 (1996)
[Crossref]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertson, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996)
[Crossref] [PubMed]

1994 (1)

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994)
[Crossref] [PubMed]

1993 (1)

G. Sun and J. Khurgin, “Optical pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: Feasibility study,” IEEE J. Quantum Electron. 29, 1104–1111(1993)
[Crossref]

1957 (1)

E. O. Kane, “Band structure of Indium Antimonide,” J. Phys. Chern. Solids 1, 249–261, (1957)
[Crossref]

Bastard, G.

G. Bastard, “Wave mechanics applied to semiconductor heterostructures,” Les Editions de Physique, Les Ulis, (Paris, 1998) Chap. 3

Boucaud, P.

O. Gauthier-Lafaye, P. Boucaud, F. H. Julien, S. Sauvage, S. Cabaret, J.-M. Lourtioz, V. Thierry-Mieg, and R. Planel, “Long-wavelength (≈ 15.5μm) unipolar semiconductor laser in GaAs quantum wells,” Appl. Phys. Lett. 71, 3619–3621 (1997)
[Crossref]

Cabaret, S.

O. Gauthier-Lafaye, P. Boucaud, F. H. Julien, S. Sauvage, S. Cabaret, J.-M. Lourtioz, V. Thierry-Mieg, and R. Planel, “Long-wavelength (≈ 15.5μm) unipolar semiconductor laser in GaAs quantum wells,” Appl. Phys. Lett. 71, 3619–3621 (1997)
[Crossref]

Capasso, F.

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertson, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996)
[Crossref] [PubMed]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength infrared (λ ≈ 11μm) quantum cascade lasers,” Appl. Phys. Lett. 69, 2810–2812 (1996)
[Crossref]

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994)
[Crossref] [PubMed]

Cho, A. Y.

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength infrared (λ ≈ 11μm) quantum cascade lasers,” Appl. Phys. Lett. 69, 2810–2812 (1996)
[Crossref]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertson, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996)
[Crossref] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994)
[Crossref] [PubMed]

Diaz, J.

S. Slivken, C. Jelen, A. Rybaltowski, J. Diaz, and M. Razeghi, “Gas-source molecular beam epitaxy growth of an 8.5 μm quantum cascade laser,” Appl. Phys. Lett. 71, 2593–2595 (1997)
[Crossref]

Faist, J.

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength infrared (λ ≈ 11μm) quantum cascade lasers,” Appl. Phys. Lett. 69, 2810–2812 (1996)
[Crossref]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertson, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996)
[Crossref] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994)
[Crossref] [PubMed]

Gauthier-Lafaye, O.

O. Gauthier-Lafaye, P. Boucaud, F. H. Julien, S. Sauvage, S. Cabaret, J.-M. Lourtioz, V. Thierry-Mieg, and R. Planel, “Long-wavelength (≈ 15.5μm) unipolar semiconductor laser in GaAs quantum wells,” Appl. Phys. Lett. 71, 3619–3621 (1997)
[Crossref]

Hutchinson, A. L.

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength infrared (λ ≈ 11μm) quantum cascade lasers,” Appl. Phys. Lett. 69, 2810–2812 (1996)
[Crossref]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertson, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996)
[Crossref] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994)
[Crossref] [PubMed]

Hybertson, M. S.

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertson, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996)
[Crossref] [PubMed]

Jelen, C.

S. Slivken, C. Jelen, A. Rybaltowski, J. Diaz, and M. Razeghi, “Gas-source molecular beam epitaxy growth of an 8.5 μm quantum cascade laser,” Appl. Phys. Lett. 71, 2593–2595 (1997)
[Crossref]

Julien, F. H.

O. Gauthier-Lafaye, P. Boucaud, F. H. Julien, S. Sauvage, S. Cabaret, J.-M. Lourtioz, V. Thierry-Mieg, and R. Planel, “Long-wavelength (≈ 15.5μm) unipolar semiconductor laser in GaAs quantum wells,” Appl. Phys. Lett. 71, 3619–3621 (1997)
[Crossref]

Kane, E. O.

E. O. Kane, “Band structure of Indium Antimonide,” J. Phys. Chern. Solids 1, 249–261, (1957)
[Crossref]

Khurgin, J.

G. Sun and J. Khurgin, “Optical pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: Feasibility study,” IEEE J. Quantum Electron. 29, 1104–1111(1993)
[Crossref]

Lourtioz, J.-M.

O. Gauthier-Lafaye, P. Boucaud, F. H. Julien, S. Sauvage, S. Cabaret, J.-M. Lourtioz, V. Thierry-Mieg, and R. Planel, “Long-wavelength (≈ 15.5μm) unipolar semiconductor laser in GaAs quantum wells,” Appl. Phys. Lett. 71, 3619–3621 (1997)
[Crossref]

Planel, R.

O. Gauthier-Lafaye, P. Boucaud, F. H. Julien, S. Sauvage, S. Cabaret, J.-M. Lourtioz, V. Thierry-Mieg, and R. Planel, “Long-wavelength (≈ 15.5μm) unipolar semiconductor laser in GaAs quantum wells,” Appl. Phys. Lett. 71, 3619–3621 (1997)
[Crossref]

Razeghi, M.

S. Slivken, C. Jelen, A. Rybaltowski, J. Diaz, and M. Razeghi, “Gas-source molecular beam epitaxy growth of an 8.5 μm quantum cascade laser,” Appl. Phys. Lett. 71, 2593–2595 (1997)
[Crossref]

Rybaltowski, A.

S. Slivken, C. Jelen, A. Rybaltowski, J. Diaz, and M. Razeghi, “Gas-source molecular beam epitaxy growth of an 8.5 μm quantum cascade laser,” Appl. Phys. Lett. 71, 2593–2595 (1997)
[Crossref]

Sauvage, S.

O. Gauthier-Lafaye, P. Boucaud, F. H. Julien, S. Sauvage, S. Cabaret, J.-M. Lourtioz, V. Thierry-Mieg, and R. Planel, “Long-wavelength (≈ 15.5μm) unipolar semiconductor laser in GaAs quantum wells,” Appl. Phys. Lett. 71, 3619–3621 (1997)
[Crossref]

Sirtori, C.

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertson, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996)
[Crossref] [PubMed]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength infrared (λ ≈ 11μm) quantum cascade lasers,” Appl. Phys. Lett. 69, 2810–2812 (1996)
[Crossref]

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994)
[Crossref] [PubMed]

Sivco, D. L.

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength infrared (λ ≈ 11μm) quantum cascade lasers,” Appl. Phys. Lett. 69, 2810–2812 (1996)
[Crossref]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertson, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996)
[Crossref] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994)
[Crossref] [PubMed]

Slivken, S.

S. Slivken, C. Jelen, A. Rybaltowski, J. Diaz, and M. Razeghi, “Gas-source molecular beam epitaxy growth of an 8.5 μm quantum cascade laser,” Appl. Phys. Lett. 71, 2593–2595 (1997)
[Crossref]

Sun, G.

G. Sun and J. Khurgin, “Optical pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: Feasibility study,” IEEE J. Quantum Electron. 29, 1104–1111(1993)
[Crossref]

Thierry-Mieg, V.

O. Gauthier-Lafaye, P. Boucaud, F. H. Julien, S. Sauvage, S. Cabaret, J.-M. Lourtioz, V. Thierry-Mieg, and R. Planel, “Long-wavelength (≈ 15.5μm) unipolar semiconductor laser in GaAs quantum wells,” Appl. Phys. Lett. 71, 3619–3621 (1997)
[Crossref]

Appl. Phys. Lett. (3)

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength infrared (λ ≈ 11μm) quantum cascade lasers,” Appl. Phys. Lett. 69, 2810–2812 (1996)
[Crossref]

S. Slivken, C. Jelen, A. Rybaltowski, J. Diaz, and M. Razeghi, “Gas-source molecular beam epitaxy growth of an 8.5 μm quantum cascade laser,” Appl. Phys. Lett. 71, 2593–2595 (1997)
[Crossref]

O. Gauthier-Lafaye, P. Boucaud, F. H. Julien, S. Sauvage, S. Cabaret, J.-M. Lourtioz, V. Thierry-Mieg, and R. Planel, “Long-wavelength (≈ 15.5μm) unipolar semiconductor laser in GaAs quantum wells,” Appl. Phys. Lett. 71, 3619–3621 (1997)
[Crossref]

IEEE J. Quantum Electron. (1)

G. Sun and J. Khurgin, “Optical pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: Feasibility study,” IEEE J. Quantum Electron. 29, 1104–1111(1993)
[Crossref]

J. Phys. Chern. Solids (1)

E. O. Kane, “Band structure of Indium Antimonide,” J. Phys. Chern. Solids 1, 249–261, (1957)
[Crossref]

Les Editions de Physique, Les Ulis (1)

G. Bastard, “Wave mechanics applied to semiconductor heterostructures,” Les Editions de Physique, Les Ulis, (Paris, 1998) Chap. 3

Phys. Rev. Lett. (1)

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertson, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996)
[Crossref] [PubMed]

Science (1)

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994)
[Crossref] [PubMed]

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Figures (5)

Figure 1.
Figure 1.

Schematic of (a) a band-to-band semiconductor laser, (b) a conventional intersubband laser.

Figure 2.
Figure 2.

In-plane dispersions of subbands HH1, LH1 and HH2 for a single QW with a well width of 70Å. The hole energy is counted downward.

Figure 3.
Figure 3.

A schematic of the active region of the inverted-effective-mass intersubband laser structure with the quantum cascade scheme. The tunneling and phonon scattering processes have been identified as the mechanisms for pumping and current loss in the laser operation, respectively. The hole energy is counted upward.

Figure 4.
Figure 4.

Optical Gain as a function of the photon energy for several hole concentrations in the QW structure of a GaAs well width of 70Åand a AlGaAs barrier width of 50Å.

Figure 5.
Figure 5.

The peak optical gain as a function of the pump current density for a laser structure with a GaAs well width of 70Åand a AlGaAs barrier width of 50Å.

Equations (8)

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Δ N l , h ( k i ) = k i πd f l , h ( k i ) Δ k i
f l , h ( k i ) = 1 1 + exp [ ( E F l , h E l , h ( k i ) ) k B T ]
N = N l + N h
= k i Δ N l ( k i ) + k i Δ N h ( k i )
N l t = N h τ tun k i W ind ( k i ) [ f l ( k i ) f h ( k i ) ] k i πd Δ k i k i W spon ( k i ) f l ( k i ) k i πd Δ k i
W spon ( k i ) = n ˜ e 2 E ( k i ) 3 π 2 o m o 2 c 3 ħ 2 M p ( k i ) 2
γ ( E ) = e 2 ħ η m o 2 E M p 2 Γ [ E ( E l E h ) ] 2 + Γ 2 ρ r ( E l E h ) [ f l ( E l ) f h ( E h ) ] d ( E l E h )
γ ( E ) = πe 2 ħ η m o 2 E M p 2 ρ r ( E ) [ f l ( E l ) f h ( E h ) ] E l E h = E .

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