Abstract

The understanding of free-carrier dynamics in silicon photonic nano-waveguides and micro-cavities is fundamental to several nonlinear optical phenomena. Through time-resolved pump and probe experiments, a complex and nonlinear carrier recombination dynamics is revealed. Our results show that the carrier lifetime varies as the recombination evolves, with faster decay rates at the initial stages (with lifetime of ∼800  ps) and much slower lifetimes at later stages (up to ∼300  ns). The large surface-to-volume ratio in nano-waveguides enables clear observation of the effect of carrier trapping, manifesting as a decay curve that is highly dependent on the initial carrier density. Further, we demonstrate faster recombination rates by operating at high carrier density. Our results, along with a theoretical framework based on trap-assisted recombination statistics applied to nano-waveguides, can impact the dynamics of several nonlinear nanophotonic devices in which free carriers play a critical role, and open further opportunities to enhance the performance of all-optical silicon-based devices.

© 2017 Optical Society of America

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  3. L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32, 2031–2033 (2007).
    [Crossref]
  4. A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. Krauss, and B. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat. Commun. 5, 3160 (2014).
    [Crossref]
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    [Crossref]
  7. T. Baba, S. Akiyama, M. Imai, N. Hirayama, H. Takahashi, Y. Noguchi, T. Horikawa, and T. Usuki, “50-Gb/s ring-resonator-based silicon modulator,” Opt. Express 21, 11869–11876 (2013).
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    [Crossref]
  10. A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
    [Crossref]
  11. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
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  12. L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32, 391–393 (2007).
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  13. F. Leo, S.-P. Gorza, S. Coen, B. Kuyken, and G. Roelkens, “Coherent supercontinuum generation in a silicon photonic wire in the telecommunication wavelength range,” Opt. Lett. 40, 123–126 (2015).
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  15. T. J. Johnson, M. Borselli, and O. Painter, “Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator,” Opt. Express 14, 817–831 (2006).
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  16. W. H. Pernice, M. Li, and H. X. Tang, “Time-domain measurement of optical transport in silicon micro-ring resonators,” Opt. Express 18, 18438–18452 (2010).
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  21. Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90, 211105 (2007).
    [Crossref]
  22. J. S. Blakemore, Semiconductor Statistics (Courier Corporation, 2002).
  23. S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).
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    [Crossref]
  25. D. K. Schroder, “Carrier lifetimes in silicon,” IEEE Trans. Electron Devices 44, 160–170 (1997).
    [Crossref]
  26. D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
    [Crossref]
  27. Y. Zhang, C. Husko, S. Lefrancois, I. H. Rey, T. F. Krauss, J. Schröder, and B. J. Eggleton, “Non-degenerate two-photon absorption in silicon waveguides: analytical and experimental study,” Opt. Express 23, 17101–17110 (2015).
    [Crossref]
  28. J. Meitzner, F. G. Moore, B. M. Tillotson, S. D. Kevan, and G. L. Richmond, “Time-resolved measurement of free carrier absorption, diffusivity, and internal quantum efficiency in silicon,” Appl. Phys. Lett. 103, 092101 (2013).
    [Crossref]
  29. A. Singh, “Influence of carrier transport on Raman amplification in silicon waveguides,” Opt. Express 418, 12569–12580 (2010).
  30. H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
    [Crossref]
  31. A. G. Aberle, S. Glunz, and W. Warta, “Impact of illumination level and oxide parameters on Shockley–Read–Hall recombination at the Si-SiO2 interface,” J. Appl. Phys. 71, 4422–4431 (1992).
    [Crossref]
  32. K. C. Nomura and J. S. Blakemore, “Decay of excess carriers in semiconductors,” Phys. Rev. 112, 1607–1615 (1958).
    [Crossref]
  33. K. C. Nomura and J. S. Blakemore, “Decay of excess carriers in semiconductors. II,” Phys. Rev. 121, 734–740 (1961).
    [Crossref]
  34. R. Ahrenkiel, B. Keyes, and D. Dunlavy, “Intensity-dependent minority-carrier lifetime in III-V semiconductors due to saturation of recombination centers,” J. Appl. Phys. 70, 225–231 (1991).
    [Crossref]
  35. L. Alloatti, C. Koos, and J. Leuthold, “Optical loss by surface transfer doping in silicon waveguides,” Appl. Phys. Lett. 107, 031107 (2015).
    [Crossref]
  36. P. J. Caplan, E. H. Poindexter, B. E. Deal, and R. R. Razouk, “ESR centers, interface states, and oxide fixed charge in thermally oxidized silicon wafers,” J. Appl. Phys. 50, 5847–5854 (1979).
    [Crossref]

2015 (3)

2014 (1)

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. Krauss, and B. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat. Commun. 5, 3160 (2014).
[Crossref]

2013 (3)

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

J. Meitzner, F. G. Moore, B. M. Tillotson, S. D. Kevan, and G. L. Richmond, “Time-resolved measurement of free carrier absorption, diffusivity, and internal quantum efficiency in silicon,” Appl. Phys. Lett. 103, 092101 (2013).
[Crossref]

T. Baba, S. Akiyama, M. Imai, N. Hirayama, H. Takahashi, Y. Noguchi, T. Horikawa, and T. Usuki, “50-Gb/s ring-resonator-based silicon modulator,” Opt. Express 21, 11869–11876 (2013).
[Crossref]

2012 (1)

2011 (1)

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

2010 (5)

S. Park, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, H. Nishi, R. Kou, and S. Ichi Itabashi, “Influence of carrier lifetime on performance of silicon p-i-n variable optical attenuators fabricated on submicrometer rib waveguides,” Opt. Express 18, 11282–11291 (2010).
[Crossref]

W. H. Pernice, M. Li, and H. X. Tang, “Time-domain measurement of optical transport in silicon micro-ring resonators,” Opt. Express 18, 18438–18452 (2010).
[Crossref]

A. Singh, “Influence of carrier transport on Raman amplification in silicon waveguides,” Opt. Express 418, 12569–12580 (2010).

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[Crossref]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

2008 (1)

2007 (5)

Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90, 211105 (2007).
[Crossref]

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32, 391–393 (2007).
[Crossref]

L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32, 2031–2033 (2007).
[Crossref]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
[Crossref]

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

2006 (1)

2005 (1)

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

2004 (3)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref]

T. Liang and H. Tsang, “Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 84, 2745–2747 (2004).
[Crossref]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12, 4742–4750 (2004).
[Crossref]

1997 (1)

D. K. Schroder, “Carrier lifetimes in silicon,” IEEE Trans. Electron Devices 44, 160–170 (1997).
[Crossref]

1993 (1)

H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
[Crossref]

1992 (1)

A. G. Aberle, S. Glunz, and W. Warta, “Impact of illumination level and oxide parameters on Shockley–Read–Hall recombination at the Si-SiO2 interface,” J. Appl. Phys. 71, 4422–4431 (1992).
[Crossref]

1991 (1)

R. Ahrenkiel, B. Keyes, and D. Dunlavy, “Intensity-dependent minority-carrier lifetime in III-V semiconductors due to saturation of recombination centers,” J. Appl. Phys. 70, 225–231 (1991).
[Crossref]

1987 (1)

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

1979 (1)

P. J. Caplan, E. H. Poindexter, B. E. Deal, and R. R. Razouk, “ESR centers, interface states, and oxide fixed charge in thermally oxidized silicon wafers,” J. Appl. Phys. 50, 5847–5854 (1979).
[Crossref]

1961 (1)

K. C. Nomura and J. S. Blakemore, “Decay of excess carriers in semiconductors. II,” Phys. Rev. 121, 734–740 (1961).
[Crossref]

1958 (1)

K. C. Nomura and J. S. Blakemore, “Decay of excess carriers in semiconductors,” Phys. Rev. 112, 1607–1615 (1958).
[Crossref]

1952 (1)

W. Shockley and W. Read, “Statistics of the recombinations of holes and electrons,” Phys. Rev. 87, 835–842 (1952).
[Crossref]

Aberle, A. G.

A. G. Aberle, S. Glunz, and W. Warta, “Impact of illumination level and oxide parameters on Shockley–Read–Hall recombination at the Si-SiO2 interface,” J. Appl. Phys. 71, 4422–4431 (1992).
[Crossref]

Agrawal, G. P.

Ahrenkiel, R.

R. Ahrenkiel, B. Keyes, and D. Dunlavy, “Intensity-dependent minority-carrier lifetime in III-V semiconductors due to saturation of recombination centers,” J. Appl. Phys. 70, 225–231 (1991).
[Crossref]

Akiyama, S.

Alloatti, L.

L. Alloatti, C. Koos, and J. Leuthold, “Optical loss by surface transfer doping in silicon waveguides,” Appl. Phys. Lett. 107, 031107 (2015).
[Crossref]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref]

Baba, T.

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref]

Bennett, B.

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

Blakemore, J. S.

K. C. Nomura and J. S. Blakemore, “Decay of excess carriers in semiconductors. II,” Phys. Rev. 121, 734–740 (1961).
[Crossref]

K. C. Nomura and J. S. Blakemore, “Decay of excess carriers in semiconductors,” Phys. Rev. 112, 1607–1615 (1958).
[Crossref]

J. S. Blakemore, Semiconductor Statistics (Courier Corporation, 2002).

Blanco-Redondo, A.

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. Krauss, and B. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat. Commun. 5, 3160 (2014).
[Crossref]

Borselli, M.

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

Caplan, P. J.

P. J. Caplan, E. H. Poindexter, B. E. Deal, and R. R. Razouk, “ESR centers, interface states, and oxide fixed charge in thermally oxidized silicon wafers,” J. Appl. Phys. 50, 5847–5854 (1979).
[Crossref]

Carmon, T.

Chu, T.

Cirloganu, C. M.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Claps, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

Coen, S.

Cox, J. A.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Day, I. E.

H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
[Crossref]

Deal, B. E.

P. J. Caplan, E. H. Poindexter, B. E. Deal, and R. R. Razouk, “ESR centers, interface states, and oxide fixed charge in thermally oxidized silicon wafers,” J. Appl. Phys. 50, 5847–5854 (1979).
[Crossref]

Dimitropoulos, D.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

Dunlavy, D.

R. Ahrenkiel, B. Keyes, and D. Dunlavy, “Intensity-dependent minority-carrier lifetime in III-V semiconductors due to saturation of recombination centers,” J. Appl. Phys. 70, 225–231 (1991).
[Crossref]

Eades, D.

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. Krauss, and B. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat. Commun. 5, 3160 (2014).
[Crossref]

Eggleton, B.

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. Krauss, and B. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat. Commun. 5, 3160 (2014).
[Crossref]

Eggleton, B. J.

Fishman, D. A.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[Crossref]

Glunz, S.

A. G. Aberle, S. Glunz, and W. Warta, “Impact of illumination level and oxide parameters on Shockley–Read–Hall recombination at the Si-SiO2 interface,” J. Appl. Phys. 71, 4422–4431 (1992).
[Crossref]

Gorza, S.-P.

Grant, R. S.

H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
[Crossref]

Hagan, D. J.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Hirayama, N.

Horikawa, T.

Hu, Y.

Husko, C.

Y. Zhang, C. Husko, S. Lefrancois, I. H. Rey, T. F. Krauss, J. Schröder, and B. J. Eggleton, “Non-degenerate two-photon absorption in silicon waveguides: analytical and experimental study,” Opt. Express 23, 17101–17110 (2015).
[Crossref]

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. Krauss, and B. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat. Commun. 5, 3160 (2014).
[Crossref]

Ichi Itabashi, S.

Imai, M.

Jalali, B.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

Jarecki, R.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Jhaveri, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

Johnson, T. J.

Kennedy, G. T.

H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
[Crossref]

Kevan, S. D.

J. Meitzner, F. G. Moore, B. M. Tillotson, S. D. Kevan, and G. L. Richmond, “Time-resolved measurement of free carrier absorption, diffusivity, and internal quantum efficiency in silicon,” Appl. Phys. Lett. 103, 092101 (2013).
[Crossref]

Keyes, B.

R. Ahrenkiel, B. Keyes, and D. Dunlavy, “Intensity-dependent minority-carrier lifetime in III-V semiconductors due to saturation of recombination centers,” J. Appl. Phys. 70, 225–231 (1991).
[Crossref]

Koos, C.

L. Alloatti, C. Koos, and J. Leuthold, “Optical loss by surface transfer doping in silicon waveguides,” Appl. Phys. Lett. 107, 031107 (2015).
[Crossref]

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[Crossref]

Kou, R.

Krauss, T.

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. Krauss, and B. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat. Commun. 5, 3160 (2014).
[Crossref]

Krauss, T. F.

Kuyken, B.

Lefrancois, S.

Leo, F.

Leuthold, J.

L. Alloatti, C. Koos, and J. Leuthold, “Optical loss by surface transfer doping in silicon waveguides,” Appl. Phys. Lett. 107, 031107 (2015).
[Crossref]

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[Crossref]

Li, J.

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. Krauss, and B. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat. Commun. 5, 3160 (2014).
[Crossref]

Li, M.

Li, X.

Li, Z.

Liang, T.

T. Liang and H. Tsang, “Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 84, 2745–2747 (2004).
[Crossref]

Lin, Q.

Lipson, M.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref]

Liu, Y.

Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90, 211105 (2007).
[Crossref]

Matsuo, S.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

Meitzner, J.

J. Meitzner, F. G. Moore, B. M. Tillotson, S. D. Kevan, and G. L. Richmond, “Time-resolved measurement of free carrier absorption, diffusivity, and internal quantum efficiency in silicon,” Appl. Phys. Lett. 103, 092101 (2013).
[Crossref]

Monroe, M.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Moore, F. G.

J. Meitzner, F. G. Moore, B. M. Tillotson, S. D. Kevan, and G. L. Richmond, “Time-resolved measurement of free carrier absorption, diffusivity, and internal quantum efficiency in silicon,” Appl. Phys. Lett. 103, 092101 (2013).
[Crossref]

Ng, K. K.

S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).

Nishi, H.

Noguchi, Y.

Nomura, K. C.

K. C. Nomura and J. S. Blakemore, “Decay of excess carriers in semiconductors. II,” Phys. Rev. 121, 734–740 (1961).
[Crossref]

K. C. Nomura and J. S. Blakemore, “Decay of excess carriers in semiconductors,” Phys. Rev. 112, 1607–1615 (1958).
[Crossref]

Notomi, M.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

T. Tanabe, H. Taniyama, and M. Notomi, “Carrier diffusion and recombination in photonic crystal nanocavity optical switches,” J. Lightwave Technol. 26, 1396–1403 (2008).
[Crossref]

Nozaki, K.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

Olsson, R. H.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Padilha, L. A.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Painter, O.

Painter, O. J.

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref]

Park, S.

Penty, R. V.

H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
[Crossref]

Pernice, W. H.

Poindexter, E. H.

P. J. Caplan, E. H. Poindexter, B. E. Deal, and R. R. Razouk, “ESR centers, interface states, and oxide fixed charge in thermally oxidized silicon wafers,” J. Appl. Phys. 50, 5847–5854 (1979).
[Crossref]

Qiu, W.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Rakich, P. T.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Razouk, R. R.

P. J. Caplan, E. H. Poindexter, B. E. Deal, and R. R. Razouk, “ESR centers, interface states, and oxide fixed charge in thermally oxidized silicon wafers,” J. Appl. Phys. 50, 5847–5854 (1979).
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Read, W.

W. Shockley and W. Read, “Statistics of the recombinations of holes and electrons,” Phys. Rev. 87, 835–842 (1952).
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Rey, I. H.

Richmond, G. L.

J. Meitzner, F. G. Moore, B. M. Tillotson, S. D. Kevan, and G. L. Richmond, “Time-resolved measurement of free carrier absorption, diffusivity, and internal quantum efficiency in silicon,” Appl. Phys. Lett. 103, 092101 (2013).
[Crossref]

Roelkens, G.

Rotenberg, N.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

Sato, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
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D. K. Schroder, “Carrier lifetimes in silicon,” IEEE Trans. Electron Devices 44, 160–170 (1997).
[Crossref]

Schröder, J.

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H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Shinojima, H.

Shinya, A.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

Shockley, W.

W. Shockley and W. Read, “Statistics of the recombinations of holes and electrons,” Phys. Rev. 87, 835–842 (1952).
[Crossref]

Sibbett, W.

H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
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Singh, A.

A. Singh, “Influence of carrier transport on Raman amplification in silicon waveguides,” Opt. Express 418, 12569–12580 (2010).

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H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
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Soref, R.

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
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Starbuck, A.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Su, Z.

H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
[Crossref]

Sze, S. M.

S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).

Takahashi, H.

Tanabe, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

T. Tanabe, H. Taniyama, and M. Notomi, “Carrier diffusion and recombination in photonic crystal nanocavity optical switches,” J. Lightwave Technol. 26, 1396–1403 (2008).
[Crossref]

Tang, H. X.

Taniyama, H.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

T. Tanabe, H. Taniyama, and M. Notomi, “Carrier diffusion and recombination in photonic crystal nanocavity optical switches,” J. Lightwave Technol. 26, 1396–1403 (2008).
[Crossref]

Tillotson, B. M.

J. Meitzner, F. G. Moore, B. M. Tillotson, S. D. Kevan, and G. L. Richmond, “Time-resolved measurement of free carrier absorption, diffusivity, and internal quantum efficiency in silicon,” Appl. Phys. Lett. 103, 092101 (2013).
[Crossref]

Tsang, H.

T. Liang and H. Tsang, “Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 84, 2745–2747 (2004).
[Crossref]

Tsang, H. K.

Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90, 211105 (2007).
[Crossref]

H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
[Crossref]

Tsuchizawa, T.

Usuki, T.

Vahala, K. J.

Van Driel, H. M.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

Van Stryland, E. W.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Wang, Z.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
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A. G. Aberle, S. Glunz, and W. Warta, “Impact of illumination level and oxide parameters on Shockley–Read–Hall recombination at the Si-SiO2 interface,” J. Appl. Phys. 71, 4422–4431 (1992).
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Watanabe, T.

Webster, S.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

White, I. H.

H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
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Woo, J.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
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Xiao, X.

Xu, H.

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Y. Zhang, C. Husko, S. Lefrancois, I. H. Rey, T. F. Krauss, J. Schröder, and B. J. Eggleton, “Non-degenerate two-photon absorption in silicon waveguides: analytical and experimental study,” Opt. Express 23, 17101–17110 (2015).
[Crossref]

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. Krauss, and B. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat. Commun. 5, 3160 (2014).
[Crossref]

Appl. Phys. Lett. (7)

T. Liang and H. Tsang, “Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 84, 2745–2747 (2004).
[Crossref]

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90, 211105 (2007).
[Crossref]

J. Meitzner, F. G. Moore, B. M. Tillotson, S. D. Kevan, and G. L. Richmond, “Time-resolved measurement of free carrier absorption, diffusivity, and internal quantum efficiency in silicon,” Appl. Phys. Lett. 103, 092101 (2013).
[Crossref]

H. K. Tsang, P. A. Snow, I. E. Day, I. H. White, R. V. Penty, R. S. Grant, Z. Su, G. T. Kennedy, and W. Sibbett, “All-optical modulation with ultrafast recovery at low pump energies in passive InGaAs/InGaAsP multiquantum well waveguides,” Appl. Phys. Lett. 62, 1451–1453 (1993).
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L. Alloatti, C. Koos, and J. Leuthold, “Optical loss by surface transfer doping in silicon waveguides,” Appl. Phys. Lett. 107, 031107 (2015).
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IEEE J. Quantum Electron. (1)

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D. K. Schroder, “Carrier lifetimes in silicon,” IEEE Trans. Electron Devices 44, 160–170 (1997).
[Crossref]

J. Appl. Phys. (3)

P. J. Caplan, E. H. Poindexter, B. E. Deal, and R. R. Razouk, “ESR centers, interface states, and oxide fixed charge in thermally oxidized silicon wafers,” J. Appl. Phys. 50, 5847–5854 (1979).
[Crossref]

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J. Lightwave Technol. (1)

Nat. Commun. (2)

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. Krauss, and B. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat. Commun. 5, 3160 (2014).
[Crossref]

Nat. Photonics (3)

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
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J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[Crossref]

Nature (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref]

Opt. Express (9)

A. Singh, “Influence of carrier transport on Raman amplification in silicon waveguides,” Opt. Express 418, 12569–12580 (2010).

S. Park, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, H. Nishi, R. Kou, and S. Ichi Itabashi, “Influence of carrier lifetime on performance of silicon p-i-n variable optical attenuators fabricated on submicrometer rib waveguides,” Opt. Express 18, 11282–11291 (2010).
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W. H. Pernice, M. Li, and H. X. Tang, “Time-domain measurement of optical transport in silicon micro-ring resonators,” Opt. Express 18, 18438–18452 (2010).
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H. Xu, X. Xiao, X. Li, Y. Hu, Z. Li, T. Chu, Y. Yu, and J. Yu, “High speed silicon Mach-Zehnder modulator based on interleaved PN junctions,” Opt. Express 20, 15093–15099 (2012).
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T. Baba, S. Akiyama, M. Imai, N. Hirayama, H. Takahashi, Y. Noguchi, T. Horikawa, and T. Usuki, “50-Gb/s ring-resonator-based silicon modulator,” Opt. Express 21, 11869–11876 (2013).
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Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
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Y. Zhang, C. Husko, S. Lefrancois, I. H. Rey, T. F. Krauss, J. Schröder, and B. J. Eggleton, “Non-degenerate two-photon absorption in silicon waveguides: analytical and experimental study,” Opt. Express 23, 17101–17110 (2015).
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T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12, 4742–4750 (2004).
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T. J. Johnson, M. Borselli, and O. Painter, “Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator,” Opt. Express 14, 817–831 (2006).
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Opt. Lett. (3)

Phys. Rev. (3)

K. C. Nomura and J. S. Blakemore, “Decay of excess carriers in semiconductors,” Phys. Rev. 112, 1607–1615 (1958).
[Crossref]

K. C. Nomura and J. S. Blakemore, “Decay of excess carriers in semiconductors. II,” Phys. Rev. 121, 734–740 (1961).
[Crossref]

W. Shockley and W. Read, “Statistics of the recombinations of holes and electrons,” Phys. Rev. 87, 835–842 (1952).
[Crossref]

Other (2)

J. S. Blakemore, Semiconductor Statistics (Courier Corporation, 2002).

S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).

Supplementary Material (1)

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» Supplement 1       Supplemental document

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Figures (6)

Fig. 1.
Fig. 1. Scanning electron microscope images for an unclad silicon strip waveguide of 450  nm×220  nm, similar to the one used in our experiments: (a) perspective and (b) cross-section views.

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Fig. 2.
Fig. 2. (a) Experimental setup employed to characterize the free-carrier lifetime in SOI strip waveguides. WG, waveguide under test. Other acronyms are defined within the text. (b) Power spectrum at the input of WG. (c) Power spectra before and after BPF4.

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Fig. 3.
Fig. 3. Analysis of carrier density dynamics using 130 ps pump pulses. (a) Nonlinear loss as a function of time for 0.28 W pump power. The inset shows a zoom of the normalized nonlinear loss around the pump pulse in linear time scale. (b) Carrier density as a function of time for different pump peak powers. (c) Recombination lifetime as a function of carrier density for different pump peak powers. (d) Detail of the carrier density as a function of time for different pump peak powers in the first few nanoseconds.

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Fig. 4.
Fig. 4. Analysis of the carrier recombination dynamics using 20 ns pulses. (a) Normalized nonlinear loss for pump power levels of 2, 19, 75, and 170 mW. (b) Rise and fall times for different pump peak powers. (c) Nonlinear loss for a pseudo-random sequence of 10 ns pulses for three power levels of 2, 19, and 38 mW.

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Fig. 5.
Fig. 5. Normalized carrier density transient decay for (a) small and (b) large trap density. (c) Total normalized carrier density n shown for both normalized trap densities D=0.1 and D=10. In all figures, we plotted n/2 for better visualization.

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Fig. 6.
Fig. 6. (a) Transient decay and (b) instantaneous lifetime for different initial carrier densities. Each curve was calculated using the simulation parameters in Table 1 and large trap density (D=10).

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Tables (1)

Tables Icon

Table 1. Definition of Variables and Parameters Used in the Simulation of Carrier Decay Dynamics (Expressions for the Rest of Parameters are Given in Supplement 1)

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Equations (5)

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

LFCA(t)=exp[αrη∫0LN(z,t)dz]=exp[αrηN¯(t)L],
dnedt=G−1τn[(n0+n1+ne)(ne−pe)Dt+nen1n0+n1],
dpedt=G−1τp[(p0+p1+pe)(pe−ne)Dt+pep1p0+p1],
dxdt′=g−[(x–y)[x+a(1+b)]D+x1+b],
dydt′=g−[γ(y–x)(y+1+b)D+γby1+b],

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