Abstract

Low density charge mobility from below bandgap, two-photon photoexcitation of bulk silicon (Si) is interrogated using time-resolved terahertz spectroscopy (TRTS). Total charge mobility is measured as a function of excitation frequency and fluence (charge carrier density), cut angle, and innate doping levels. Frequency dependent complex photoconductivities are extracted using the Drude model to obtain average and DC-limit mobility and carrier scattering times. These dynamic parameters are compared to values from contact-based Hall, above bandgap photoexcitation, and comparable gallium arsenide (GaAs) measurements. Mobilities are shown to increase beyond Hall values at low carrier densities and are modestly higher with increasing dopant density. The former occurs in part from below bandgap photoexcitation exhibiting abnormally small (faster) scattering times, while both reflect unique conduction characteristics at lowest (> 2x1012 cm−3) carrier densities achieved through photodoping.

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2018 (1)

2017 (1)

2015 (1)

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

2013 (1)

K. J. Willis, S. C. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013).
[Crossref]

2011 (3)

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

F. Schindler, J. Geilker, W. Kwapil, W. Warta, and M. C. Schubert, “Hall mobility in multicrystalline silicon,” J. Appl. Phys. 110(4), 043722 (2011).
[Crossref]

C. M. Cirloganu, L. A. Padilha, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. V. Stryland, “Extremely nondegenerate two-photon absorption in direct-gap semiconductors [Invited],” Opt. Express 19(23), 22951–22960 (2011).
[Crossref]

2008 (1)

O. Esenturk, J. S. Melinger, and E. J. Heilweil, “Terahertz mobility measurements on poly-3-hexylthiophene films: Device comparison, molecular weight, and film processing effects,” J. Appl. Phys. 103(2), 023102 (2008).
[Crossref]

2007 (2)

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

T. Bronger and R. Carius, “Carrier mobilities in microcrystalline silicon films,” Thin Solid Films 515(19), 7486–7489 (2007).
[Crossref]

2003 (1)

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

2002 (1)

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002).
[Crossref]

2000 (1)

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy,” Phys. Rev. B 62(23), 15764–15777 (2000).
[Crossref]

1992 (1)

1989 (1)

A. Penzkofer and A. A. Bugayev, “Two-photon absorption and emission dynamics of bulk GaAs,” Opt. Quantum Electron. 21(4), 283–306 (1989).
[Crossref]

1986 (2)

D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−x As,” J. Appl. Phys. 60(2), 754–767 (1986).
[Crossref]

F. Szmulowicz, “Calculation of the mobility and the Hall factor for doped p-type silicon,” Phys. Rev. B 34(6), 4031–4047 (1986).
[Crossref]

1980 (2)

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Boron-Doped Silicon,” J. Electrochem. Soc. 127(10), 2291–2294 (1980).
[Crossref]

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127(8), 1807–1812 (1980).
[Crossref]

1976 (1)

J. R. Chelikowsky and M. L. Cohen, “Nonlocal pseudopotential calculations for the electronic structure of eleven diamond and zinc-blende semiconductors,” Phys. Rev. B 14(2), 556–582 (1976).
[Crossref]

1974 (1)

R. Chwang, B. J. Smith, and C. R. Crowell, “Contact size effects on the van der Pauw method for resistivity and Hall coefficient measurement,” Solid-State Electron. 17(12), 1217–1227 (1974).
[Crossref]

1967 (1)

D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE 55(12), 2192–2193 (1967).
[Crossref]

Alberding, B. G.

Aspnes, D. E.

D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−x As,” J. Appl. Phys. 60(2), 754–767 (1986).
[Crossref]

Beard, M. C.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002).
[Crossref]

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy,” Phys. Rev. B 62(23), 15764–15777 (2000).
[Crossref]

Becouarn, L.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

Bhat, R.

D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−x As,” J. Appl. Phys. 60(2), 754–767 (1986).
[Crossref]

Bonn, M.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

Bothe, K.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Brendel, R.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

Bronger, T.

T. Bronger and R. Carius, “Carrier mobilities in microcrystalline silicon films,” Thin Solid Films 515(19), 7486–7489 (2007).
[Crossref]

Bugayev, A. A.

A. Penzkofer and A. A. Bugayev, “Two-photon absorption and emission dynamics of bulk GaAs,” Opt. Quantum Electron. 21(4), 283–306 (1989).
[Crossref]

Carius, R.

T. Bronger and R. Carius, “Carrier mobilities in microcrystalline silicon films,” Thin Solid Films 515(19), 7486–7489 (2007).
[Crossref]

Caughey, D. M.

D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE 55(12), 2192–2193 (1967).
[Crossref]

Chelikowsky, J. R.

J. R. Chelikowsky and M. L. Cohen, “Nonlocal pseudopotential calculations for the electronic structure of eleven diamond and zinc-blende semiconductors,” Phys. Rev. B 14(2), 556–582 (1976).
[Crossref]

Christian Peest, P.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Chwang, R.

R. Chwang, B. J. Smith, and C. R. Crowell, “Contact size effects on the van der Pauw method for resistivity and Hall coefficient measurement,” Solid-State Electron. 17(12), 1217–1227 (1974).
[Crossref]

Cirloganu, C. M.

Cohen, M. L.

J. R. Chelikowsky and M. L. Cohen, “Nonlocal pseudopotential calculations for the electronic structure of eleven diamond and zinc-blende semiconductors,” Phys. Rev. B 14(2), 556–582 (1976).
[Crossref]

Cooke, D. G.

F. A. Hegmann, O. Ostroverkhova, and D. G. Cooke, “Probing Organic Semiconductors with Terahertz Pulses," in Photophysics of Molecular Materials (John Wiley & Sons, Ltd, 2006), pp. 367–428.

Crowell, C. R.

R. Chwang, B. J. Smith, and C. R. Crowell, “Contact size effects on the van der Pauw method for resistivity and Hall coefficient measurement,” Solid-State Electron. 17(12), 1217–1227 (1974).
[Crossref]

Ellmer, K.

K. Ellmer, “Hall Effect and Conductivity Measurements in Semiconductor Crystals and Thin Films," in Characterization of Materials (American Cancer Society, 2012), pp. 1–16.

Esenturk, O.

O. Esenturk, J. S. Melinger, and E. J. Heilweil, “Terahertz mobility measurements on poly-3-hexylthiophene films: Device comparison, molecular weight, and film processing effects,” J. Appl. Phys. 103(2), 023102 (2008).
[Crossref]

Eyres, L. A.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

Fejer, M. M.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

Filliben, J. J.

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Boron-Doped Silicon,” J. Electrochem. Soc. 127(10), 2291–2294 (1980).
[Crossref]

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127(8), 1807–1812 (1980).
[Crossref]

Fishman, D. A.

Geilker, J.

F. Schindler, J. Geilker, W. Kwapil, W. Warta, and M. C. Schubert, “Hall mobility in multicrystalline silicon,” J. Appl. Phys. 110(4), 043722 (2011).
[Crossref]

Gerard, B.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

Hagan, D. J.

Hagness, S. C.

K. J. Willis, S. C. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013).
[Crossref]

Harris, J. S.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

Hegmann, F. A.

F. A. Hegmann, O. Ostroverkhova, and D. G. Cooke, “Probing Organic Semiconductors with Terahertz Pulses," in Photophysics of Molecular Materials (John Wiley & Sons, Ltd, 2006), pp. 367–428.

Heilweil, E. J.

Heinz, T. F.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

Hendry, E.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

Jeon, T.-I.

J. Lloyd-Hughes and T.-I. Jeon, “A Review of the Terahertz Conductivity of Bulk and Nano-Materials | SpringerLink," https://link.springer.com/article/10.1007%2Fs10762-012-9905-y .

Kelso, S. M.

D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−x As,” J. Appl. Phys. 60(2), 754–767 (1986).
[Crossref]

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 8th Edition (John Wiley & Sons Inc., 2005).

Knezevic, I.

K. J. Willis, S. C. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013).
[Crossref]

Kröger, I.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Kuo, P. S.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

Kwapil, W.

F. Schindler, J. Geilker, W. Kwapil, W. Warta, and M. C. Schubert, “Hall mobility in multicrystalline silicon,” J. Appl. Phys. 110(4), 043722 (2011).
[Crossref]

Lallier, E.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

Levi, O.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

Lim, S.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Liu, Y. M.

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Boron-Doped Silicon,” J. Electrochem. Soc. 127(10), 2291–2294 (1980).
[Crossref]

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127(8), 1807–1812 (1980).
[Crossref]

Lloyd-Hughes, J.

J. Lloyd-Hughes and T.-I. Jeon, “A Review of the Terahertz Conductivity of Bulk and Nano-Materials | SpringerLink," https://link.springer.com/article/10.1007%2Fs10762-012-9905-y .

Logan, R. A.

D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−x As,” J. Appl. Phys. 60(2), 754–767 (1986).
[Crossref]

MacDonald, D.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Mattis, R. L.

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Boron-Doped Silicon,” J. Electrochem. Soc. 127(10), 2291–2294 (1980).
[Crossref]

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127(8), 1807–1812 (1980).
[Crossref]

Melinger, J. S.

O. Esenturk, J. S. Melinger, and E. J. Heilweil, “Terahertz mobility measurements on poly-3-hexylthiophene films: Device comparison, molecular weight, and film processing effects,” J. Appl. Phys. 103(2), 023102 (2008).
[Crossref]

Nguyen, H. T.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Ostroverkhova, O.

F. A. Hegmann, O. Ostroverkhova, and D. G. Cooke, “Probing Organic Semiconductors with Terahertz Pulses," in Photophysics of Molecular Materials (John Wiley & Sons, Ltd, 2006), pp. 367–428.

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A. Penzkofer and A. A. Bugayev, “Two-photon absorption and emission dynamics of bulk GaAs,” Opt. Quantum Electron. 21(4), 283–306 (1989).
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Pinguet, T. J.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
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D. L. Rode, “Chapter 1 Low-Field Electron Transport," in Semiconductors and Semimetals (Academic Press, N.Y., 1975), Vol. 10, pp. 1–86.

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A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

Said, A. A.

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F. Schindler, J. Geilker, W. Kwapil, W. Warta, and M. C. Schubert, “Hall mobility in multicrystalline silicon,” J. Appl. Phys. 110(4), 043722 (2011).
[Crossref]

Schinke, C.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Schirmacher, A.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Schmidt, J.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

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M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002).
[Crossref]

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy,” Phys. Rev. B 62(23), 15764–15777 (2000).
[Crossref]

Schubert, M. C.

F. Schindler, J. Geilker, W. Kwapil, W. Warta, and M. C. Schubert, “Hall mobility in multicrystalline silicon,” J. Appl. Phys. 110(4), 043722 (2011).
[Crossref]

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R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

Sheik-Bahae, M.

Skauli, T.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

Smith, B. J.

R. Chwang, B. J. Smith, and C. R. Crowell, “Contact size effects on the van der Pauw method for resistivity and Hall coefficient measurement,” Solid-State Electron. 17(12), 1217–1227 (1974).
[Crossref]

Stryland, E. W. V.

Sze, S. M.

S. M. Sze, Physics of Semiconductor Devices, Second (John Wiley & Sons, Inc., 1981).

Szmulowicz, F.

F. Szmulowicz, “Calculation of the mobility and the Hall factor for doped p-type silicon,” Phys. Rev. B 34(6), 4031–4047 (1986).
[Crossref]

Thomas, R. E.

D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE 55(12), 2192–2193 (1967).
[Crossref]

Thurber, W. R.

B. G. Alberding, W. R. Thurber, and E. J. Heilweil, “Direct comparison of time-resolved terahertz spectroscopy and Hall Van der Pauw methods for measurement of carrier conductivity and mobility in bulk semiconductors,” J. Opt. Soc. Am. B 34(7), 1392–1406 (2017).
[Crossref]

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Boron-Doped Silicon,” J. Electrochem. Soc. 127(10), 2291–2294 (1980).
[Crossref]

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127(8), 1807–1812 (1980).
[Crossref]

Turner, G. M.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002).
[Crossref]

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy,” Phys. Rev. B 62(23), 15764–15777 (2000).
[Crossref]

Ulbricht, R.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

van Driel, H. M.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

Vodopyanov, K. L.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

Vogt, M. R.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Wahlstrand, J. K.

Wang, J.

Warta, W.

F. Schindler, J. Geilker, W. Kwapil, W. Warta, and M. C. Schubert, “Hall mobility in multicrystalline silicon,” J. Appl. Phys. 110(4), 043722 (2011).
[Crossref]

Webster, S.

Wei, T. H.

Wild, C. J.

G. A. F. Seber and C. J. Wild, Nonlinear Regression (John Wiley & Sons, 2003).

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K. J. Willis, S. C. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013).
[Crossref]

Winter, S.

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Young, J.

AIP Adv. (1)

C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, and D. MacDonald, “Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon,” AIP Adv. 5(6), 067168 (2015).
[Crossref]

Appl. Phys. Lett. (2)

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

K. J. Willis, S. C. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013).
[Crossref]

J. Appl. Phys. (4)

O. Esenturk, J. S. Melinger, and E. J. Heilweil, “Terahertz mobility measurements on poly-3-hexylthiophene films: Device comparison, molecular weight, and film processing effects,” J. Appl. Phys. 103(2), 023102 (2008).
[Crossref]

D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−x As,” J. Appl. Phys. 60(2), 754–767 (1986).
[Crossref]

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003).
[Crossref]

F. Schindler, J. Geilker, W. Kwapil, W. Warta, and M. C. Schubert, “Hall mobility in multicrystalline silicon,” J. Appl. Phys. 110(4), 043722 (2011).
[Crossref]

J. Electrochem. Soc. (2)

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Boron-Doped Silicon,” J. Electrochem. Soc. 127(10), 2291–2294 (1980).
[Crossref]

W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127(8), 1807–1812 (1980).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. Chem. B (1)

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002).
[Crossref]

Opt. Express (2)

Opt. Quantum Electron. (1)

A. Penzkofer and A. A. Bugayev, “Two-photon absorption and emission dynamics of bulk GaAs,” Opt. Quantum Electron. 21(4), 283–306 (1989).
[Crossref]

Phys. Rev. B (3)

J. R. Chelikowsky and M. L. Cohen, “Nonlocal pseudopotential calculations for the electronic structure of eleven diamond and zinc-blende semiconductors,” Phys. Rev. B 14(2), 556–582 (1976).
[Crossref]

F. Szmulowicz, “Calculation of the mobility and the Hall factor for doped p-type silicon,” Phys. Rev. B 34(6), 4031–4047 (1986).
[Crossref]

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy,” Phys. Rev. B 62(23), 15764–15777 (2000).
[Crossref]

Proc. IEEE (1)

D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE 55(12), 2192–2193 (1967).
[Crossref]

Rev. Mod. Phys. (1)

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

Solid-State Electron. (1)

R. Chwang, B. J. Smith, and C. R. Crowell, “Contact size effects on the van der Pauw method for resistivity and Hall coefficient measurement,” Solid-State Electron. 17(12), 1217–1227 (1974).
[Crossref]

Thin Solid Films (1)

T. Bronger and R. Carius, “Carrier mobilities in microcrystalline silicon films,” Thin Solid Films 515(19), 7486–7489 (2007).
[Crossref]

Other (9)

K. Ellmer, “Hall Effect and Conductivity Measurements in Semiconductor Crystals and Thin Films," in Characterization of Materials (American Cancer Society, 2012), pp. 1–16.

S. M. Sze, Physics of Semiconductor Devices, Second (John Wiley & Sons, Inc., 1981).

“Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.," (n.d.).

G. A. F. Seber and C. J. Wild, Nonlinear Regression (John Wiley & Sons, 2003).

C. Kittel, Introduction to Solid State Physics, 8th Edition (John Wiley & Sons Inc., 2005).

S. L. Dexheimer, ed., Terahertz Spectroscopy: Principles and Applications, 1 edition (CRC Press, 2007).

J. Lloyd-Hughes and T.-I. Jeon, “A Review of the Terahertz Conductivity of Bulk and Nano-Materials | SpringerLink," https://link.springer.com/article/10.1007%2Fs10762-012-9905-y .

D. L. Rode, “Chapter 1 Low-Field Electron Transport," in Semiconductors and Semimetals (Academic Press, N.Y., 1975), Vol. 10, pp. 1–86.

F. A. Hegmann, O. Ostroverkhova, and D. G. Cooke, “Probing Organic Semiconductors with Terahertz Pulses," in Photophysics of Molecular Materials (John Wiley & Sons, Ltd, 2006), pp. 367–428.

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Figures (8)

Fig. 1.
Fig. 1. (a) Penetration depths of various pump energies into a typical Si wafer shown to scale. 3.10 eV excitation penetrates ca. 100 nm (omitted). (b) Band structure diagrams for Si and GaAs shown to scale energetically. Colored arrows represent the energy above the valence band for each excitation energy considered in this work (1.03 eV, 1.55 eV, 2.07 eV, and 3.10 eV as green, red, yellow, and blue respectively). Each lobe represents a different type of electron (conduction band) or hole (valence band) and dashed lines indicate the energetic minima of each band or energies reached via 1.55 eV and 2.07 eV (equivalently the two-photon absorption of 1.03 eV) photoexcitation pulses.
Fig. 2.
Fig. 2. Total charge mobility of Si_2018 determined by (a) averaging across all THz frequencies (µTHz) and (b) extrapolating to the DC limit (µDC) using the Drude model from Eq. (2) and fit with a Caughey-Thomas curve from Eq. (4). The results are plotted as a function of pump energy (color) and photoinduced carrier density. Data points for 3.10 eV and 1.55 eV excitation in (a) are taken from previous work. [8] Error bars represent 95% CIs of the associated mobility.
Fig. 3.
Fig. 3. Normalized frequency dependence of the real photoinduced conductivity of sample Si_2018 when excited at (a) different 1.03 eV photoexcitation fluences (i.e., carrier densities) and (b) the highest and lowest fluences of each excitation frequency. In (a), the progression flattens as ΔN (carrier density) increases from 1.5 x1013 cm−3 (red) to 1.2 x1015 cm−3 (purple). In (b) 1.03 eV, 1.55 eV, and 2.07 eV excitation (green, red, and yellow, respectively) at high (circle/solid line) and low (square/dashed line) fluences.
Fig. 4.
Fig. 4. (a) Scattering times (τ) for samples Si_2018 (<100>, circles) and Si_3094 (<111>, squares) as for different pump energies and (b) The DC-limit conduction for Si_2018 at each pump energy, both as functions of carrier density. Green, red, yellow, and blue represent 1.03 eV two-photon, and 1.55 eV, 2.07 eV, and 3.10 eV one-photon, excitation energies, respectively. The dashed line in (b) represents a power law fit through all four sets, indicating a common trend in ΔσDC despite the discontinuity in τ. Error bars represent 95% CIs and are not visible in (b).
Fig. 5.
Fig. 5. Extracted (a) DC-limit mobility (µDC) and (b) carrier scattering times (τ) for GaAs_4234 photoexcited above bandgap (3.10 eV/blue, 2.07 eV/yellow, and 1.55 eV/red) and below bandgap (1.03 eV/green). These values can be compared to the Si_2018 results in Figs. 2(b) and 4(a), respectively. A fit to a Caughey-Thomas curve, Eq. (4) is applied to the combined data in (a) as the dashed line. Error bars (95% CIs) are included with smaller ones obscured by the points shown.
Fig. 6.
Fig. 6. (a) Real total charge mobility, from Eq. (3), for n- and p-doped Si as a function of THz probe frequency. The inset key describes the dopant type and resistivity (Ω•cm) for each sample. (b) Average (µTHz) and DC (µDC) mobility determined for each sample plotted as a function of innate (doped) conductivity (S/m) for p-(red, squares) and n-type (blue, circles) Si samples. The two-photon excitation fluence was set to generate a carrier density of ≈ 1.2x1015 cm−3. Red and blue dashed vertical lines represent the conductivity at which the doped charge carrier density is approximately equivalent to the photoexcited carrier density for p- and n-type samples, respectively. Total charge mobility is found to nominally increase with increasing dopant level visualized through fits with models for µTHz and µDC (green and black dashed lines, respectively). Error bars indicate 95% CIs.
Fig. 7.
Fig. 7. (a) Example TDS and TRTS two-photon (1.03 eV) photoexcited time-dependent sweeps for sample Si 3094 and (b) the corresponding frequency-dependent (real) FFT of the time-domain signals in (a). Ei, E0, and ΔE represent the THz electric field signal passing though air, unexcited silicon, and the difference between excited and unexcited silicon, respectively.
Fig. 8.
Fig. 8. (a) Charge density distribution from 1.03 eV excitation (white → blue colormap) relative to data collection iris (red outline). (b) Fluence dependence of TRTS measured photoconductivity for three silicon samples collected using 1.03 eV two-photon photoexcitation. All Si samples (blue, orange, and green) exhibit >90% two-photon generated carrier population with the GaAs sample (yellow) exhibiting ≈ 78% overall two-photon absorption character.

Tables (4)

Tables Icon

Table 1. Average and DC-limit total mobility determined from conductivity values in Fig. 6(a) for fixed ≈1.2x1015 cm−3 two-photon photo-density (error limits with 95% CIs).

Tables Icon

Table 2. Properties of the investigated silicon (Si) and gallium arsenide (GaAs) wafers; ß measured at 1.03 eV.

Tables Icon

Table 3. Assumed Si and GaAs penetration depths (1/α, µm) and pump wavelength refractive indices (n1).

Tables Icon

Table 4. Parameters for Caughey-Taylor curve fits applied to Si_2018 and GaAs_4234 µDC values.

Equations (9)

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η ^ ( ω ) = ε ^ ( ω ) + i Δ σ ^ ( ω ) ε 0 ω
Δ σ ^ ( ω ) = Δ N q 2 m τ ( 1 ( i ω τ ) )
Δ σ D C = e Δ N ( µ e + µ h + ) = e Δ N µ D C
µ = µ m a x µ m i n 1 + ( N N r e f ) α + µ m i n
σ D C ( S / m ) = 9.72 10 12 Δ N 0.83 ( c m 3 )
I = I 0 10 α ( 1 1 1 + ² d I 0 )
n ( ω ) = 1 + c ω d l n ( ϕ ϕ 0 ) , n ( ω ) = c ω d l n ( 1 + Δ E E 0 )
ε ^ ( ω ) = ε + ε : ε = n 2 n 2 , ε = 2 n n
σ ^ ( ω ) = σ + σ : σ = ε 0 ω ( η ε ) , σ = ε 0 ω ( ε η )

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