Abstract

We present a theoretical analysis of the change in refractive index and absorption of Wurtzite GaN due to free carriers for a wavelength range of 1 to 5 μm using the Drude model. The separate role of holes and electrons as well as their combined effect are discussed and the results are compared to those of Si and GaAs. The results show that promising modulators based on electrorefraction and electroabsorption can be implemented in a GaN integrated photonic platform. We also discuss the validity of the Drude model as well as the interaction of longitudinal optical (LO) phonons in GaN with the electron-hole plasmons, especially the impact on the absorption of GaN at high carrier concentrations. While LO phonon-plasmon (LOPP) interaction is shown to be stronger for electrons than for holes, the overall effect is negligible at the wavelength range of discussion (1-5 µm) for the moderate injection levels examined here for carrier-induced electro-optic modulation.

© 2015 Optical Society of America

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  1. B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs, andInGaAsP,” J. Quantum Electron. 26(1), 113–122 (1990).
    [Crossref]
  2. R. A. Soref and B. R. Bennett, “Electro-optical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
    [Crossref]
  3. Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
    [Crossref]
  4. C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10462–10470 (2011).
    [Crossref] [PubMed]
  5. C. Xiong, W. Pernice, C. Schuck, and H. X. Tang, “Integrated photonics circuits in gallium nitride and aluminum nitride,” Int. J. High Speed Electron. Syst. 23(01n02), 1450001 (2014).
    [Crossref]
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    [Crossref]
  13. A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
    [Crossref]
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    [Crossref]
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    [Crossref]
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  17. N. Dupuis, B. G. Lee, A. V. Rylyakov, D. M. Kuchta, C. W. Baks, J. S. Orcutt, D. M. Gill, W. M. J. Green, and C. L. Schow, “Design and fabrication of low-insertion-loss and low-crosstalk broadband 2×2 Mach-Zehnder silicon photonic switches,” J. Lightwave Technol. 33, 3597–3606 (2014).
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    [Crossref]
  19. U. Haboeck, H. Siegle, A. Hoffmann, and C. Thomsen, “Lattice dynamics in GaN and AlN probed with first- and second- order Raman spectroscopy,” Phys. Status Solidi 0(6), 1710–1731 (2003).
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    [Crossref]

2014 (4)

2012 (3)

M. Welna, R. Kudrawiec, M. Motyka, R. Kucharski, M. Zajac, M. Rudzinski, J. Misiewicz, R. Doradzinski, and R. Dwilinski, “Transparency of GaN substrate in the mid-infrared spectral range,” Cryst. Res. Technol. 47(3), 347–350 (2012).
[Crossref]

G. Shkerdin, S. Rabbaa, J. Stiens, and R. Vounckx, “Free-electron absorption in n-doped GaN semiconductors at mid-IR wavelengths in the strong photon-plasmon coupling regime,” J. Phys. D Appl. Phys. 45(49), 495103 (2012).
[Crossref]

U. Dharanipathy, N. Vico Triviño, C. Yan, Z. Diao, J. F. Carlin, N. Grandjean, and R. Houdré, “Near-infrared characterization of gallium nitride photonic-crystal waveguides and cavities,” Opt. Lett. 37(22), 4588–4590 (2012).
[Crossref] [PubMed]

2011 (2)

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10462–10470 (2011).
[Crossref] [PubMed]

2010 (1)

C. Bulutay, C. M. Turgut, and N. A. Zakhleniuk, “Carrier-induced refractive index change and optical absorption in wurtzite InN and GaN: Full-band approach,” Phys. Rev. B 81(15), 155206 (2010).
[Crossref]

2003 (2)

U. Haboeck, H. Siegle, A. Hoffmann, and C. Thomsen, “Lattice dynamics in GaN and AlN probed with first- and second- order Raman spectroscopy,” Phys. Status Solidi 0(6), 1710–1731 (2003).
[Crossref]

T. T. Mnatsakanov, M. E. Levinshtein, L. I. Pomortseva, S. N. Yurkov, G. S. Simin, and M. A. Khan, “Carrier mobility model for GaN,” Solid-State Electron. 47(1), 111–115 (2003).
[Crossref]

2002 (1)

H. Harima, “Properties of GaN and related compounds studied by means of Raman scattering,” J. Phys. Condens. Matter 14(38), R967–R993 (2002).
[Crossref]

2001 (1)

A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
[Crossref]

2000 (1)

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, and T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62(11), 7365–7377 (2000).
[Crossref]

1997 (1)

G. Popovici, G. Y. Xu, A. Botchkarev, W. Kim, H. Tang, A. Salvador, H. Morkoc, R. Strange, and J. O. White, “Raman scattering and photoluminescence of Mg-doped GaN films grown by molecular beam epitaxy,” Appl. Phys. Lett. 82, 4020–4023 (1997).

1990 (1)

B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs, andInGaAsP,” J. Quantum Electron. 26(1), 113–122 (1990).
[Crossref]

1987 (1)

R. A. Soref and B. R. Bennett, “Electro-optical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Avrutsky, I.

Baks, C. W.

Beadie, G.

Bennett, B. R.

B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs, andInGaAsP,” J. Quantum Electron. 26(1), 113–122 (1990).
[Crossref]

R. A. Soref and B. R. Bennett, “Electro-optical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Botchkarev, A.

G. Popovici, G. Y. Xu, A. Botchkarev, W. Kim, H. Tang, A. Salvador, H. Morkoc, R. Strange, and J. O. White, “Raman scattering and photoluminescence of Mg-doped GaN films grown by molecular beam epitaxy,” Appl. Phys. Lett. 82, 4020–4023 (1997).

Bowman, S.

Brindza, M.

Brown, C. G.

Bulutay, C.

C. Bulutay, C. M. Turgut, and N. A. Zakhleniuk, “Carrier-induced refractive index change and optical absorption in wurtzite InN and GaN: Full-band approach,” Phys. Rev. B 81(15), 155206 (2010).
[Crossref]

Calvez, S.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

Carlin, J. F.

Cleary, J. W.

Cryan, M. J.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

Dawson, M.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

Del Alamo, J. A.

B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs, andInGaAsP,” J. Quantum Electron. 26(1), 113–122 (1990).
[Crossref]

Dharanipathy, U.

Diao, Z.

Doradzinski, R.

M. Welna, R. Kudrawiec, M. Motyka, R. Kucharski, M. Zajac, M. Rudzinski, J. Misiewicz, R. Doradzinski, and R. Dwilinski, “Transparency of GaN substrate in the mid-infrared spectral range,” Cryst. Res. Technol. 47(3), 347–350 (2012).
[Crossref]

Dupuis, N.

Dwilinski, R.

M. Welna, R. Kudrawiec, M. Motyka, R. Kucharski, M. Zajac, M. Rudzinski, J. Misiewicz, R. Doradzinski, and R. Dwilinski, “Transparency of GaN substrate in the mid-infrared spectral range,” Cryst. Res. Technol. 47(3), 347–350 (2012).
[Crossref]

Eddy, C. R.

Einfeldt, S.

A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
[Crossref]

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, and T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62(11), 7365–7377 (2000).
[Crossref]

Engin, E.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

Fong, K. Y.

Freitas, J. A.

Gill, D. M.

Grandjean, N.

Green, W. M. J.

Gu, E.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

Haboeck, U.

U. Haboeck, H. Siegle, A. Hoffmann, and C. Thomsen, “Lattice dynamics in GaN and AlN probed with first- and second- order Raman spectroscopy,” Phys. Status Solidi 0(6), 1710–1731 (2003).
[Crossref]

Harima, H.

H. Harima, “Properties of GaN and related compounds studied by means of Raman scattering,” J. Phys. Condens. Matter 14(38), R967–R993 (2002).
[Crossref]

Hendrickson, J. R.

Hite, J. K.

Hoffmann, A.

U. Haboeck, H. Siegle, A. Hoffmann, and C. Thomsen, “Lattice dynamics in GaN and AlN probed with first- and second- order Raman spectroscopy,” Phys. Status Solidi 0(6), 1710–1731 (2003).
[Crossref]

Hommel, D.

A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
[Crossref]

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, and T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62(11), 7365–7377 (2000).
[Crossref]

Houdré, R.

Kasic, A.

A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
[Crossref]

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, and T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62(11), 7365–7377 (2000).
[Crossref]

Keiffer, P.

Khan, M. A.

T. T. Mnatsakanov, M. E. Levinshtein, L. I. Pomortseva, S. N. Yurkov, G. S. Simin, and M. A. Khan, “Carrier mobility model for GaN,” Solid-State Electron. 47(1), 111–115 (2003).
[Crossref]

Kim, W.

G. Popovici, G. Y. Xu, A. Botchkarev, W. Kim, H. Tang, A. Salvador, H. Morkoc, R. Strange, and J. O. White, “Raman scattering and photoluminescence of Mg-doped GaN films grown by molecular beam epitaxy,” Appl. Phys. Lett. 82, 4020–4023 (1997).

Kucharski, R.

M. Welna, R. Kudrawiec, M. Motyka, R. Kucharski, M. Zajac, M. Rudzinski, J. Misiewicz, R. Doradzinski, and R. Dwilinski, “Transparency of GaN substrate in the mid-infrared spectral range,” Cryst. Res. Technol. 47(3), 347–350 (2012).
[Crossref]

Kuchta, D. M.

Kudrawiec, R.

M. Welna, R. Kudrawiec, M. Motyka, R. Kucharski, M. Zajac, M. Rudzinski, J. Misiewicz, R. Doradzinski, and R. Dwilinski, “Transparency of GaN substrate in the mid-infrared spectral range,” Cryst. Res. Technol. 47(3), 347–350 (2012).
[Crossref]

Kuhn, B.

A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
[Crossref]

Lee, B. G.

Levinshtein, M. E.

T. T. Mnatsakanov, M. E. Levinshtein, L. I. Pomortseva, S. N. Yurkov, G. S. Simin, and M. A. Khan, “Carrier mobility model for GaN,” Solid-State Electron. 47(1), 111–115 (2003).
[Crossref]

McKnight, L.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

Meyer, J. R.

Misiewicz, J.

M. Welna, R. Kudrawiec, M. Motyka, R. Kucharski, M. Zajac, M. Rudzinski, J. Misiewicz, R. Doradzinski, and R. Dwilinski, “Transparency of GaN substrate in the mid-infrared spectral range,” Cryst. Res. Technol. 47(3), 347–350 (2012).
[Crossref]

Mnatsakanov, T. T.

T. T. Mnatsakanov, M. E. Levinshtein, L. I. Pomortseva, S. N. Yurkov, G. S. Simin, and M. A. Khan, “Carrier mobility model for GaN,” Solid-State Electron. 47(1), 111–115 (2003).
[Crossref]

Morkoc, H.

G. Popovici, G. Y. Xu, A. Botchkarev, W. Kim, H. Tang, A. Salvador, H. Morkoc, R. Strange, and J. O. White, “Raman scattering and photoluminescence of Mg-doped GaN films grown by molecular beam epitaxy,” Appl. Phys. Lett. 82, 4020–4023 (1997).

Motyka, M.

M. Welna, R. Kudrawiec, M. Motyka, R. Kucharski, M. Zajac, M. Rudzinski, J. Misiewicz, R. Doradzinski, and R. Dwilinski, “Transparency of GaN substrate in the mid-infrared spectral range,” Cryst. Res. Technol. 47(3), 347–350 (2012).
[Crossref]

Nader, N.

O’brien, J. L.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

Off, J.

A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
[Crossref]

Orcutt, J. S.

Palacios, T.

Pernice, W.

C. Xiong, W. Pernice, C. Schuck, and H. X. Tang, “Integrated photonics circuits in gallium nitride and aluminum nitride,” Int. J. High Speed Electron. Syst. 23(01n02), 1450001 (2014).
[Crossref]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10462–10470 (2011).
[Crossref] [PubMed]

Pomortseva, L. I.

T. T. Mnatsakanov, M. E. Levinshtein, L. I. Pomortseva, S. N. Yurkov, G. S. Simin, and M. A. Khan, “Carrier mobility model for GaN,” Solid-State Electron. 47(1), 111–115 (2003).
[Crossref]

Popovici, G.

G. Popovici, G. Y. Xu, A. Botchkarev, W. Kim, H. Tang, A. Salvador, H. Morkoc, R. Strange, and J. O. White, “Raman scattering and photoluminescence of Mg-doped GaN films grown by molecular beam epitaxy,” Appl. Phys. Lett. 82, 4020–4023 (1997).

Rabbaa, S.

G. Shkerdin, S. Rabbaa, J. Stiens, and R. Vounckx, “Free-electron absorption in n-doped GaN semiconductors at mid-IR wavelengths in the strong photon-plasmon coupling regime,” J. Phys. D Appl. Phys. 45(49), 495103 (2012).
[Crossref]

Rheinlander, B.

A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
[Crossref]

Riede, V.

A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
[Crossref]

Rudzinski, M.

M. Welna, R. Kudrawiec, M. Motyka, R. Kucharski, M. Zajac, M. Rudzinski, J. Misiewicz, R. Doradzinski, and R. Dwilinski, “Transparency of GaN substrate in the mid-infrared spectral range,” Cryst. Res. Technol. 47(3), 347–350 (2012).
[Crossref]

Rylyakov, A. V.

Ryu, K. K.

Salvador, A.

G. Popovici, G. Y. Xu, A. Botchkarev, W. Kim, H. Tang, A. Salvador, H. Morkoc, R. Strange, and J. O. White, “Raman scattering and photoluminescence of Mg-doped GaN films grown by molecular beam epitaxy,” Appl. Phys. Lett. 82, 4020–4023 (1997).

Scholz, F.

A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
[Crossref]

Schow, C. L.

Schubert, M.

A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
[Crossref]

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, and T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62(11), 7365–7377 (2000).
[Crossref]

Schuck, C.

C. Xiong, W. Pernice, C. Schuck, and H. X. Tang, “Integrated photonics circuits in gallium nitride and aluminum nitride,” Int. J. High Speed Electron. Syst. 23(01n02), 1450001 (2014).
[Crossref]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10462–10470 (2011).
[Crossref] [PubMed]

Shkerdin, G.

G. Shkerdin, S. Rabbaa, J. Stiens, and R. Vounckx, “Free-electron absorption in n-doped GaN semiconductors at mid-IR wavelengths in the strong photon-plasmon coupling regime,” J. Phys. D Appl. Phys. 45(49), 495103 (2012).
[Crossref]

Siegle, H.

U. Haboeck, H. Siegle, A. Hoffmann, and C. Thomsen, “Lattice dynamics in GaN and AlN probed with first- and second- order Raman spectroscopy,” Phys. Status Solidi 0(6), 1710–1731 (2003).
[Crossref]

Simin, G. S.

T. T. Mnatsakanov, M. E. Levinshtein, L. I. Pomortseva, S. N. Yurkov, G. S. Simin, and M. A. Khan, “Carrier mobility model for GaN,” Solid-State Electron. 47(1), 111–115 (2003).
[Crossref]

Soref, R. A.

B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs, andInGaAsP,” J. Quantum Electron. 26(1), 113–122 (1990).
[Crossref]

R. A. Soref and B. R. Bennett, “Electro-optical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Stiens, J.

G. Shkerdin, S. Rabbaa, J. Stiens, and R. Vounckx, “Free-electron absorption in n-doped GaN semiconductors at mid-IR wavelengths in the strong photon-plasmon coupling regime,” J. Phys. D Appl. Phys. 45(49), 495103 (2012).
[Crossref]

Strange, R.

G. Popovici, G. Y. Xu, A. Botchkarev, W. Kim, H. Tang, A. Salvador, H. Morkoc, R. Strange, and J. O. White, “Raman scattering and photoluminescence of Mg-doped GaN films grown by molecular beam epitaxy,” Appl. Phys. Lett. 82, 4020–4023 (1997).

Tang, H.

G. Popovici, G. Y. Xu, A. Botchkarev, W. Kim, H. Tang, A. Salvador, H. Morkoc, R. Strange, and J. O. White, “Raman scattering and photoluminescence of Mg-doped GaN films grown by molecular beam epitaxy,” Appl. Phys. Lett. 82, 4020–4023 (1997).

Tang, H. X.

C. Xiong, W. Pernice, C. Schuck, and H. X. Tang, “Integrated photonics circuits in gallium nitride and aluminum nitride,” Int. J. High Speed Electron. Syst. 23(01n02), 1450001 (2014).
[Crossref]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10462–10470 (2011).
[Crossref] [PubMed]

Thompson, M. G.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

Thomsen, C.

U. Haboeck, H. Siegle, A. Hoffmann, and C. Thomsen, “Lattice dynamics in GaN and AlN probed with first- and second- order Raman spectroscopy,” Phys. Status Solidi 0(6), 1710–1731 (2003).
[Crossref]

Tiwald, T. E.

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, and T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62(11), 7365–7377 (2000).
[Crossref]

Turgut, C. M.

C. Bulutay, C. M. Turgut, and N. A. Zakhleniuk, “Carrier-induced refractive index change and optical absorption in wurtzite InN and GaN: Full-band approach,” Phys. Rev. B 81(15), 155206 (2010).
[Crossref]

Vangala, S. R.

Vico Triviño, N.

Vounckx, R.

G. Shkerdin, S. Rabbaa, J. Stiens, and R. Vounckx, “Free-electron absorption in n-doped GaN semiconductors at mid-IR wavelengths in the strong photon-plasmon coupling regime,” J. Phys. D Appl. Phys. 45(49), 495103 (2012).
[Crossref]

Vurgaftman, I.

Walker, D.

Watson, I. M.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

Welna, M.

M. Welna, R. Kudrawiec, M. Motyka, R. Kucharski, M. Zajac, M. Rudzinski, J. Misiewicz, R. Doradzinski, and R. Dwilinski, “Transparency of GaN substrate in the mid-infrared spectral range,” Cryst. Res. Technol. 47(3), 347–350 (2012).
[Crossref]

White, J. O.

G. Popovici, G. Y. Xu, A. Botchkarev, W. Kim, H. Tang, A. Salvador, H. Morkoc, R. Strange, and J. O. White, “Raman scattering and photoluminescence of Mg-doped GaN films grown by molecular beam epitaxy,” Appl. Phys. Lett. 82, 4020–4023 (1997).

Xiong, C.

C. Xiong, W. Pernice, C. Schuck, and H. X. Tang, “Integrated photonics circuits in gallium nitride and aluminum nitride,” Int. J. High Speed Electron. Syst. 23(01n02), 1450001 (2014).
[Crossref]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10462–10470 (2011).
[Crossref] [PubMed]

Xu, G. Y.

G. Popovici, G. Y. Xu, A. Botchkarev, W. Kim, H. Tang, A. Salvador, H. Morkoc, R. Strange, and J. O. White, “Raman scattering and photoluminescence of Mg-doped GaN films grown by molecular beam epitaxy,” Appl. Phys. Lett. 82, 4020–4023 (1997).

Yan, C.

Yurkov, S. N.

T. T. Mnatsakanov, M. E. Levinshtein, L. I. Pomortseva, S. N. Yurkov, G. S. Simin, and M. A. Khan, “Carrier mobility model for GaN,” Solid-State Electron. 47(1), 111–115 (2003).
[Crossref]

Zajac, M.

M. Welna, R. Kudrawiec, M. Motyka, R. Kucharski, M. Zajac, M. Rudzinski, J. Misiewicz, R. Doradzinski, and R. Dwilinski, “Transparency of GaN substrate in the mid-infrared spectral range,” Cryst. Res. Technol. 47(3), 347–350 (2012).
[Crossref]

Zakhleniuk, N. A.

C. Bulutay, C. M. Turgut, and N. A. Zakhleniuk, “Carrier-induced refractive index change and optical absorption in wurtzite InN and GaN: Full-band approach,” Phys. Rev. B 81(15), 155206 (2010).
[Crossref]

Zhang, Y.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

Appl. Phys. Lett. (2)

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’brien, and M. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. 99(16), 161119 (2011).
[Crossref]

G. Popovici, G. Y. Xu, A. Botchkarev, W. Kim, H. Tang, A. Salvador, H. Morkoc, R. Strange, and J. O. White, “Raman scattering and photoluminescence of Mg-doped GaN films grown by molecular beam epitaxy,” Appl. Phys. Lett. 82, 4020–4023 (1997).

Cryst. Res. Technol. (1)

M. Welna, R. Kudrawiec, M. Motyka, R. Kucharski, M. Zajac, M. Rudzinski, J. Misiewicz, R. Doradzinski, and R. Dwilinski, “Transparency of GaN substrate in the mid-infrared spectral range,” Cryst. Res. Technol. 47(3), 347–350 (2012).
[Crossref]

IEEE J. Quantum Electron. (1)

R. A. Soref and B. R. Bennett, “Electro-optical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Int. J. High Speed Electron. Syst. (1)

C. Xiong, W. Pernice, C. Schuck, and H. X. Tang, “Integrated photonics circuits in gallium nitride and aluminum nitride,” Int. J. High Speed Electron. Syst. 23(01n02), 1450001 (2014).
[Crossref]

J. Lightwave Technol. (1)

J. Phys. Condens. Matter (1)

H. Harima, “Properties of GaN and related compounds studied by means of Raman scattering,” J. Phys. Condens. Matter 14(38), R967–R993 (2002).
[Crossref]

J. Phys. D Appl. Phys. (1)

G. Shkerdin, S. Rabbaa, J. Stiens, and R. Vounckx, “Free-electron absorption in n-doped GaN semiconductors at mid-IR wavelengths in the strong photon-plasmon coupling regime,” J. Phys. D Appl. Phys. 45(49), 495103 (2012).
[Crossref]

J. Quantum Electron. (1)

B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs, andInGaAsP,” J. Quantum Electron. 26(1), 113–122 (1990).
[Crossref]

Mater. Sci. Eng. B (1)

A. Kasic, M. Schubert, B. Rheinlander, V. Riede, S. Einfeldt, D. Hommel, B. Kuhn, J. Off, and F. Scholz, “Effective carrier mass and mobility versus carrier concentration in p- and n-type α-GaN determined by infrared ellipsometry and Hall resistivity measurements,” Mater. Sci. Eng. B 82(1-3), 74–76 (2001).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Opt. Mater. Express (1)

Phys. Rev. B (2)

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, and T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62(11), 7365–7377 (2000).
[Crossref]

C. Bulutay, C. M. Turgut, and N. A. Zakhleniuk, “Carrier-induced refractive index change and optical absorption in wurtzite InN and GaN: Full-band approach,” Phys. Rev. B 81(15), 155206 (2010).
[Crossref]

Phys. Status Solidi (1)

U. Haboeck, H. Siegle, A. Hoffmann, and C. Thomsen, “Lattice dynamics in GaN and AlN probed with first- and second- order Raman spectroscopy,” Phys. Status Solidi 0(6), 1710–1731 (2003).
[Crossref]

Solid-State Electron. (1)

T. T. Mnatsakanov, M. E. Levinshtein, L. I. Pomortseva, S. N. Yurkov, G. S. Simin, and M. A. Khan, “Carrier mobility model for GaN,” Solid-State Electron. 47(1), 111–115 (2003).
[Crossref]

Other (4)

H. Morkoc, Handbook of Nitride Semiconductors and Devices (Wiely-VCH Verlag GMBH & Co., 2008).

S. Adachi, Properties of Group-IV, III–V and II–VI Semiconductors (Wiely, 2009).

D. K. Gaskill, L. B. Rowland, and K. Doverspike, “Electrical transport properties of AlN, GaN, and AlGaN” in Properties of Group III Nitrides, J. Edgar, eds. (Wiley, 1995), pp. 101–116.

K. Takahashi, A. Yoshikawa, and A. Sandhu, Wide Bandgap Semiconductors, Fundamental Properties and Modern Photonic and Electronic Devices (Springer, 2007).

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Figures (2)

Fig. 1
Fig. 1 Comparison of free-carrier electro-refraction and electro-absorption effects in GaN (green), Si (red), and GaAs (blue) with parameters given in Table 1 for a carrier injection of 5 × 1017 cm−3. The plots show the variation of (Δn), (Δn/ Δk), and loss Δα versus wavelength when the free carriers are electrons only ((a), (b), (c)), holes only ((d), (e), (f)), and both electrons and holes ((g), (h), (i)). The plots for Si and GaAs start from wavelength of 1.5 microns.
Fig. 2
Fig. 2 The carrier-density dependence of coupled LOPP resonance wavelengths for (a) electrons and (b) holes in w-GaN. Upper and lower coupled resonances have been designated by LOPP + and LOPP-, respectively. The variation of plasmon wavelength in the absence of LOPP coupling is shown in each figure. (c) a zoomed-in view and comparison of the upper resonances (LOPP + ) of holes and electrons at different carrier densities.

Tables (1)

Tables Icon

Table 1 Conductivity effective mass and mobility of electrons and holes (in cm2V−1s−1 unit) at the carrier concentration of 5 × 1017 cm−3. m0 is the free-electron mass. For each data, the reference is shown in its front.

Equations (5)

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

Δ n = e 2 λ 2 8 π 2 c 2 ε 0 n ( Δ N m c e + Δ P m c h )
Δ k = e 3 λ 3 16 π 3 c 3 ε 0 n ( Δ N μ e m c e 2 + Δ P μ e m c h 2 )
ε ( ω ) = ε ( 1 + ω L O 2 ω T O 2 ω T O 2 ω 2 i Γ ω + ω p 2 ω ( 1 + i γ ω ) )
ω p = ( Δ N e 2 m c e * ε 0 ε ) 1 / 2 , γ = e m c e * μ e ( e l e c t r o n ) ω p = ( Δ P e 2 m c h * ε 0 ε ) 1 / 2 , γ = e m c h * μ h ( h o l e )
ω L O P P ± = 1 2 [ ω L O 2 + ω p 2 ± ( ω L O 2 + ω p 2 ) 2 4 ω p 2 ω T O 2 ] 1 / 2

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