Abstract

Femtosecond thermoreflectance data for thin films and bulk quantities of Au, Cr, and Al are compared with the parabolic two-step thermal diffusion model for the purpose of determining the electron-phonon coupling factor. The thin films were evaporated and sputtered onto different substrates to produce films that vary structurally. The measurement of the electron-phonon coupling factor is shown to be sensitive to grain size and film thickness. The thin-film thermoreflectance data are compared with that of the corresponding bulk material and to a theoretical model relating the coupling rate to the grain-boundary scattering and size effects on the mean free path of the relevant energy carrier.

© 1999 Optical Society of America

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References

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  1. P. Das, Lasers and Optical Engineering, 1st ed. (Springer-Verlag, New York, 1991).
    [CrossRef]
  2. K. S. Yngvesson, Microwave Semiconductor Devices, 1st ed. (Kluwer Academic, Norwell, Mass., 1991).
    [CrossRef]
  3. S. I. Anisimov, B. L. Kapeliovich, T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).
  4. T. Q. Qiu, C. L. Tien, “Femtosecond laser heating of multi-layer metals. I. Analysis,” Int. J. Heat Mass Transfer 37, 2789–2797 (1994).
    [CrossRef]
  5. S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
    [CrossRef] [PubMed]
  6. H. E. Elsayed-Ali, T. Juhasz, G. O. Smith, W. E. Bron, “Femtosecond thermoreflectivity of polycrystalline and single-crystalline gold films,” Phys. Rev. B 43, 4488–4491 (1991).
    [CrossRef]
  7. T. Q. Qiu, C. L. Tien, “Size effects on nonequilibrium laser heating of metal films,” J. Heat Transfer 115, 842–847 (1993).
    [CrossRef]
  8. C. A. Paddock, G. L. Eesley, “Transient thermoreflectance from thin metal films,” J. Appl. Phys. 60, 285–290 (1986).
    [CrossRef]
  9. J. L. Hostetler, A. N. Smith, P. M. Norris, “Thin-film thermal conductivity and thickness measurements using picosecond ultrasonics,” Micro. Thermophys. Eng. 1, 237–244 (1997).
    [CrossRef]
  10. C. Kittel, Introduction to Solid State Physics, 7th ed. (Wiley, New York, 1996).
  11. B. R. Cooper, H. Ehrenreich, “Optical properties of noble metals II,” Phys. Rev. 138, A494–A507 (1965).
    [CrossRef]
  12. H. Ehrenreich, H. R. Philip, “Optical properties of Ag and Cu,” Phys. Rev. 28, 1622–1629 (1962).
    [CrossRef]
  13. J. L. Hostetler, D. Stewart, C. E. Daitch, C. S. Ashley, P. M. Norris, “Optical polarized reflectance characterization of thin aerogel and xerogel films,” J. Non-Cryst. Solids 225, 19–23 (1998).
    [CrossRef]
  14. D. Y. Tzou, Macro- to Microscale Heat Transfer (Taylor & Francis, Bristol, Pa., 1997).
  15. H. R. B. Orlande, M. N. Ozisik, D. Y. Tzou, “Inverse analysis for estimating the electron-phonon coupling factor in thin metal films,” J. Appl. Phys. 78, 1843–1849 (1995).
    [CrossRef]
  16. S. S. Fouad, A. H. Ammar, M. H. El-Fazary, “A new approach to the correlation of the electrical properties with interband and intraband transitions of thin Cr films,” Phys. Status Solidi 187, 99–108 (1995).
    [CrossRef]
  17. S. Kumar, G. C. Vradis, “Thermal conductivity of thin metallic films,” J. Heat Transfer 116, 28–34 (1994).
    [CrossRef]
  18. H. Ehrenreich, “The optical properties of metals,” IEEE Spectrum 2, 162–170 (1965).
    [CrossRef]
  19. J. W. C. De Vries, “Temperature and thickness dependence of the resistivity of thin polycrystalline aluminum, cobalt, nickel, palladium, silver and gold films,” Thin Solid Films 167, 25–32 (1988).
    [CrossRef]
  20. T. Q. Qiu, C. L. Tien, “Heat transfer mechanisms during short-pulse laser heating of metals,” J. Heat Transfer 115, 835–841 (1993).
    [CrossRef]

1998 (1)

J. L. Hostetler, D. Stewart, C. E. Daitch, C. S. Ashley, P. M. Norris, “Optical polarized reflectance characterization of thin aerogel and xerogel films,” J. Non-Cryst. Solids 225, 19–23 (1998).
[CrossRef]

1997 (1)

J. L. Hostetler, A. N. Smith, P. M. Norris, “Thin-film thermal conductivity and thickness measurements using picosecond ultrasonics,” Micro. Thermophys. Eng. 1, 237–244 (1997).
[CrossRef]

1995 (2)

H. R. B. Orlande, M. N. Ozisik, D. Y. Tzou, “Inverse analysis for estimating the electron-phonon coupling factor in thin metal films,” J. Appl. Phys. 78, 1843–1849 (1995).
[CrossRef]

S. S. Fouad, A. H. Ammar, M. H. El-Fazary, “A new approach to the correlation of the electrical properties with interband and intraband transitions of thin Cr films,” Phys. Status Solidi 187, 99–108 (1995).
[CrossRef]

1994 (2)

S. Kumar, G. C. Vradis, “Thermal conductivity of thin metallic films,” J. Heat Transfer 116, 28–34 (1994).
[CrossRef]

T. Q. Qiu, C. L. Tien, “Femtosecond laser heating of multi-layer metals. I. Analysis,” Int. J. Heat Mass Transfer 37, 2789–2797 (1994).
[CrossRef]

1993 (2)

T. Q. Qiu, C. L. Tien, “Size effects on nonequilibrium laser heating of metal films,” J. Heat Transfer 115, 842–847 (1993).
[CrossRef]

T. Q. Qiu, C. L. Tien, “Heat transfer mechanisms during short-pulse laser heating of metals,” J. Heat Transfer 115, 835–841 (1993).
[CrossRef]

1991 (1)

H. E. Elsayed-Ali, T. Juhasz, G. O. Smith, W. E. Bron, “Femtosecond thermoreflectivity of polycrystalline and single-crystalline gold films,” Phys. Rev. B 43, 4488–4491 (1991).
[CrossRef]

1990 (1)

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef] [PubMed]

1988 (1)

J. W. C. De Vries, “Temperature and thickness dependence of the resistivity of thin polycrystalline aluminum, cobalt, nickel, palladium, silver and gold films,” Thin Solid Films 167, 25–32 (1988).
[CrossRef]

1986 (1)

C. A. Paddock, G. L. Eesley, “Transient thermoreflectance from thin metal films,” J. Appl. Phys. 60, 285–290 (1986).
[CrossRef]

1974 (1)

S. I. Anisimov, B. L. Kapeliovich, T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).

1965 (2)

B. R. Cooper, H. Ehrenreich, “Optical properties of noble metals II,” Phys. Rev. 138, A494–A507 (1965).
[CrossRef]

H. Ehrenreich, “The optical properties of metals,” IEEE Spectrum 2, 162–170 (1965).
[CrossRef]

1962 (1)

H. Ehrenreich, H. R. Philip, “Optical properties of Ag and Cu,” Phys. Rev. 28, 1622–1629 (1962).
[CrossRef]

Ammar, A. H.

S. S. Fouad, A. H. Ammar, M. H. El-Fazary, “A new approach to the correlation of the electrical properties with interband and intraband transitions of thin Cr films,” Phys. Status Solidi 187, 99–108 (1995).
[CrossRef]

Anisimov, S. I.

S. I. Anisimov, B. L. Kapeliovich, T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).

Ashley, C. S.

J. L. Hostetler, D. Stewart, C. E. Daitch, C. S. Ashley, P. M. Norris, “Optical polarized reflectance characterization of thin aerogel and xerogel films,” J. Non-Cryst. Solids 225, 19–23 (1998).
[CrossRef]

Bron, W. E.

H. E. Elsayed-Ali, T. Juhasz, G. O. Smith, W. E. Bron, “Femtosecond thermoreflectivity of polycrystalline and single-crystalline gold films,” Phys. Rev. B 43, 4488–4491 (1991).
[CrossRef]

Brorson, S. D.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef] [PubMed]

Cheng, T. K.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef] [PubMed]

Cooper, B. R.

B. R. Cooper, H. Ehrenreich, “Optical properties of noble metals II,” Phys. Rev. 138, A494–A507 (1965).
[CrossRef]

Daitch, C. E.

J. L. Hostetler, D. Stewart, C. E. Daitch, C. S. Ashley, P. M. Norris, “Optical polarized reflectance characterization of thin aerogel and xerogel films,” J. Non-Cryst. Solids 225, 19–23 (1998).
[CrossRef]

Das, P.

P. Das, Lasers and Optical Engineering, 1st ed. (Springer-Verlag, New York, 1991).
[CrossRef]

De Vries, J. W. C.

J. W. C. De Vries, “Temperature and thickness dependence of the resistivity of thin polycrystalline aluminum, cobalt, nickel, palladium, silver and gold films,” Thin Solid Films 167, 25–32 (1988).
[CrossRef]

Dresselhaus, G.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef] [PubMed]

Dresselhaus, M. S.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef] [PubMed]

Eesley, G. L.

C. A. Paddock, G. L. Eesley, “Transient thermoreflectance from thin metal films,” J. Appl. Phys. 60, 285–290 (1986).
[CrossRef]

Ehrenreich, H.

B. R. Cooper, H. Ehrenreich, “Optical properties of noble metals II,” Phys. Rev. 138, A494–A507 (1965).
[CrossRef]

H. Ehrenreich, “The optical properties of metals,” IEEE Spectrum 2, 162–170 (1965).
[CrossRef]

H. Ehrenreich, H. R. Philip, “Optical properties of Ag and Cu,” Phys. Rev. 28, 1622–1629 (1962).
[CrossRef]

El-Fazary, M. H.

S. S. Fouad, A. H. Ammar, M. H. El-Fazary, “A new approach to the correlation of the electrical properties with interband and intraband transitions of thin Cr films,” Phys. Status Solidi 187, 99–108 (1995).
[CrossRef]

Elsayed-Ali, H. E.

H. E. Elsayed-Ali, T. Juhasz, G. O. Smith, W. E. Bron, “Femtosecond thermoreflectivity of polycrystalline and single-crystalline gold films,” Phys. Rev. B 43, 4488–4491 (1991).
[CrossRef]

Face, D. W.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef] [PubMed]

Fouad, S. S.

S. S. Fouad, A. H. Ammar, M. H. El-Fazary, “A new approach to the correlation of the electrical properties with interband and intraband transitions of thin Cr films,” Phys. Status Solidi 187, 99–108 (1995).
[CrossRef]

Hostetler, J. L.

J. L. Hostetler, D. Stewart, C. E. Daitch, C. S. Ashley, P. M. Norris, “Optical polarized reflectance characterization of thin aerogel and xerogel films,” J. Non-Cryst. Solids 225, 19–23 (1998).
[CrossRef]

J. L. Hostetler, A. N. Smith, P. M. Norris, “Thin-film thermal conductivity and thickness measurements using picosecond ultrasonics,” Micro. Thermophys. Eng. 1, 237–244 (1997).
[CrossRef]

Ippen, E. P.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef] [PubMed]

Juhasz, T.

H. E. Elsayed-Ali, T. Juhasz, G. O. Smith, W. E. Bron, “Femtosecond thermoreflectivity of polycrystalline and single-crystalline gold films,” Phys. Rev. B 43, 4488–4491 (1991).
[CrossRef]

Kapeliovich, B. L.

S. I. Anisimov, B. L. Kapeliovich, T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).

Kazeroonian, A.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef] [PubMed]

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 7th ed. (Wiley, New York, 1996).

Kumar, S.

S. Kumar, G. C. Vradis, “Thermal conductivity of thin metallic films,” J. Heat Transfer 116, 28–34 (1994).
[CrossRef]

Moodera, J. S.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef] [PubMed]

Norris, P. M.

J. L. Hostetler, D. Stewart, C. E. Daitch, C. S. Ashley, P. M. Norris, “Optical polarized reflectance characterization of thin aerogel and xerogel films,” J. Non-Cryst. Solids 225, 19–23 (1998).
[CrossRef]

J. L. Hostetler, A. N. Smith, P. M. Norris, “Thin-film thermal conductivity and thickness measurements using picosecond ultrasonics,” Micro. Thermophys. Eng. 1, 237–244 (1997).
[CrossRef]

Orlande, H. R. B.

H. R. B. Orlande, M. N. Ozisik, D. Y. Tzou, “Inverse analysis for estimating the electron-phonon coupling factor in thin metal films,” J. Appl. Phys. 78, 1843–1849 (1995).
[CrossRef]

Ozisik, M. N.

H. R. B. Orlande, M. N. Ozisik, D. Y. Tzou, “Inverse analysis for estimating the electron-phonon coupling factor in thin metal films,” J. Appl. Phys. 78, 1843–1849 (1995).
[CrossRef]

Paddock, C. A.

C. A. Paddock, G. L. Eesley, “Transient thermoreflectance from thin metal films,” J. Appl. Phys. 60, 285–290 (1986).
[CrossRef]

Perelman, T. L.

S. I. Anisimov, B. L. Kapeliovich, T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).

Philip, H. R.

H. Ehrenreich, H. R. Philip, “Optical properties of Ag and Cu,” Phys. Rev. 28, 1622–1629 (1962).
[CrossRef]

Qiu, T. Q.

T. Q. Qiu, C. L. Tien, “Femtosecond laser heating of multi-layer metals. I. Analysis,” Int. J. Heat Mass Transfer 37, 2789–2797 (1994).
[CrossRef]

T. Q. Qiu, C. L. Tien, “Heat transfer mechanisms during short-pulse laser heating of metals,” J. Heat Transfer 115, 835–841 (1993).
[CrossRef]

T. Q. Qiu, C. L. Tien, “Size effects on nonequilibrium laser heating of metal films,” J. Heat Transfer 115, 842–847 (1993).
[CrossRef]

Smith, A. N.

J. L. Hostetler, A. N. Smith, P. M. Norris, “Thin-film thermal conductivity and thickness measurements using picosecond ultrasonics,” Micro. Thermophys. Eng. 1, 237–244 (1997).
[CrossRef]

Smith, G. O.

H. E. Elsayed-Ali, T. Juhasz, G. O. Smith, W. E. Bron, “Femtosecond thermoreflectivity of polycrystalline and single-crystalline gold films,” Phys. Rev. B 43, 4488–4491 (1991).
[CrossRef]

Stewart, D.

J. L. Hostetler, D. Stewart, C. E. Daitch, C. S. Ashley, P. M. Norris, “Optical polarized reflectance characterization of thin aerogel and xerogel films,” J. Non-Cryst. Solids 225, 19–23 (1998).
[CrossRef]

Tien, C. L.

T. Q. Qiu, C. L. Tien, “Femtosecond laser heating of multi-layer metals. I. Analysis,” Int. J. Heat Mass Transfer 37, 2789–2797 (1994).
[CrossRef]

T. Q. Qiu, C. L. Tien, “Size effects on nonequilibrium laser heating of metal films,” J. Heat Transfer 115, 842–847 (1993).
[CrossRef]

T. Q. Qiu, C. L. Tien, “Heat transfer mechanisms during short-pulse laser heating of metals,” J. Heat Transfer 115, 835–841 (1993).
[CrossRef]

Tzou, D. Y.

H. R. B. Orlande, M. N. Ozisik, D. Y. Tzou, “Inverse analysis for estimating the electron-phonon coupling factor in thin metal films,” J. Appl. Phys. 78, 1843–1849 (1995).
[CrossRef]

D. Y. Tzou, Macro- to Microscale Heat Transfer (Taylor & Francis, Bristol, Pa., 1997).

Vradis, G. C.

S. Kumar, G. C. Vradis, “Thermal conductivity of thin metallic films,” J. Heat Transfer 116, 28–34 (1994).
[CrossRef]

Yngvesson, K. S.

K. S. Yngvesson, Microwave Semiconductor Devices, 1st ed. (Kluwer Academic, Norwell, Mass., 1991).
[CrossRef]

IEEE Spectrum (1)

H. Ehrenreich, “The optical properties of metals,” IEEE Spectrum 2, 162–170 (1965).
[CrossRef]

Int. J. Heat Mass Transfer (1)

T. Q. Qiu, C. L. Tien, “Femtosecond laser heating of multi-layer metals. I. Analysis,” Int. J. Heat Mass Transfer 37, 2789–2797 (1994).
[CrossRef]

J. Appl. Phys. (2)

C. A. Paddock, G. L. Eesley, “Transient thermoreflectance from thin metal films,” J. Appl. Phys. 60, 285–290 (1986).
[CrossRef]

H. R. B. Orlande, M. N. Ozisik, D. Y. Tzou, “Inverse analysis for estimating the electron-phonon coupling factor in thin metal films,” J. Appl. Phys. 78, 1843–1849 (1995).
[CrossRef]

J. Heat Transfer (3)

T. Q. Qiu, C. L. Tien, “Size effects on nonequilibrium laser heating of metal films,” J. Heat Transfer 115, 842–847 (1993).
[CrossRef]

S. Kumar, G. C. Vradis, “Thermal conductivity of thin metallic films,” J. Heat Transfer 116, 28–34 (1994).
[CrossRef]

T. Q. Qiu, C. L. Tien, “Heat transfer mechanisms during short-pulse laser heating of metals,” J. Heat Transfer 115, 835–841 (1993).
[CrossRef]

J. Non-Cryst. Solids (1)

J. L. Hostetler, D. Stewart, C. E. Daitch, C. S. Ashley, P. M. Norris, “Optical polarized reflectance characterization of thin aerogel and xerogel films,” J. Non-Cryst. Solids 225, 19–23 (1998).
[CrossRef]

Micro. Thermophys. Eng. (1)

J. L. Hostetler, A. N. Smith, P. M. Norris, “Thin-film thermal conductivity and thickness measurements using picosecond ultrasonics,” Micro. Thermophys. Eng. 1, 237–244 (1997).
[CrossRef]

Phys. Rev. (2)

B. R. Cooper, H. Ehrenreich, “Optical properties of noble metals II,” Phys. Rev. 138, A494–A507 (1965).
[CrossRef]

H. Ehrenreich, H. R. Philip, “Optical properties of Ag and Cu,” Phys. Rev. 28, 1622–1629 (1962).
[CrossRef]

Phys. Rev. B (1)

H. E. Elsayed-Ali, T. Juhasz, G. O. Smith, W. E. Bron, “Femtosecond thermoreflectivity of polycrystalline and single-crystalline gold films,” Phys. Rev. B 43, 4488–4491 (1991).
[CrossRef]

Phys. Rev. Lett. (1)

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef] [PubMed]

Phys. Status Solidi (1)

S. S. Fouad, A. H. Ammar, M. H. El-Fazary, “A new approach to the correlation of the electrical properties with interband and intraband transitions of thin Cr films,” Phys. Status Solidi 187, 99–108 (1995).
[CrossRef]

Sov. Phys. JETP (1)

S. I. Anisimov, B. L. Kapeliovich, T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).

Thin Solid Films (1)

J. W. C. De Vries, “Temperature and thickness dependence of the resistivity of thin polycrystalline aluminum, cobalt, nickel, palladium, silver and gold films,” Thin Solid Films 167, 25–32 (1988).
[CrossRef]

Other (4)

C. Kittel, Introduction to Solid State Physics, 7th ed. (Wiley, New York, 1996).

P. Das, Lasers and Optical Engineering, 1st ed. (Springer-Verlag, New York, 1991).
[CrossRef]

K. S. Yngvesson, Microwave Semiconductor Devices, 1st ed. (Kluwer Academic, Norwell, Mass., 1991).
[CrossRef]

D. Y. Tzou, Macro- to Microscale Heat Transfer (Taylor & Francis, Bristol, Pa., 1997).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup. AOM, acousto-optic modulator.

Fig. 2
Fig. 2

AFM contrast maps of (a) evaporated Au on Si and (b) sputtered Au on glass.

Fig. 3
Fig. 3

AFM contrast map of evaporated Al on SiO2.

Fig. 4
Fig. 4

Thermoreflectance traces of evaporated thin film and bulk Au where G is given in units of 1016 W/m3 K.

Fig. 5
Fig. 5

Thermoreflectance traces and corresponding curve fits for evaporated thin film and bulk Cr where values of G are given in units of 1016 W/m3 K.

Fig. 6
Fig. 6

Thermoreflectance traces and corresponding curve fits for evaporated thin film and bulk Al where values of G are given in units of 1016 W/m3 K.

Fig. 7
Fig. 7

Electron-phonon coupling factor for Au versus average grain diameter.

Tables (1)

Tables Icon

Table 1 Measured Value of Thickness, Grain Size, and Electron-Phonon Coupling Factor

Equations (8)

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

CeTeTet=KTeTe-GTe-Tl+S,
ClTlt=GTe-Tl,
CeTe=γTe,
KTe=KeqTeTl,
ΔR=aΔTe+bΔTl,
Gf=916nk2TD2νFΛfTlEF,
Λf=Λe,b1+3Λe,b8d1-P+75Rg1-RgΛe,bD,
tc=CeG,

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