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Measuring Thermal Conductivity with Magnitude-Dependent Frequency–Domain Thermoreflectance Using Modulated CW Lasers

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Abstract

We demonstrate a minimally invasive optical pump–probe technique for measuring thermal conductivity. Like time-domain thermoreflectance, the version of frequency–domain thermoreflectance demonstrated here relies on a non-zero thermo-optic coefficient in the sample, but uses moderate cost continuous wave lasers modulated at kHz or MHz frequencies rather than a more expensive ultrafast laser system. The longer timescales of these frequency ranges enable this technique to take measurements of films with thicknesses ranging from 100 nm to \(10\, \upmu \hbox {m}\), complimentary to time-domain thermoreflectance. This method differentiates itself from other frequency–domain methods in that it is also capable of simultaneous independent measurements of both the in-plane and out-of-plane values of the thermal conductivity in anisotropic samples through measurements of relative reflective magnitude rather than of phase. We validated this alternate technique by measuring the thermal conductivity of \(\hbox {Al}_2\hbox {O}_3\) and soda-lime and found agreement both with literature values and with separate measurements obtained with a conventional time-domain thermoreflectance setup.

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References

  1. R. Venkatasubramanian, E. Siivola, T. Colpitts, B. O’Quinn, Thin-film thermoelectric devices with high room-temperature figures of merit. Nature 413, 597 (2001)

    Article  ADS  Google Scholar 

  2. G.J. Snyder, E.S. Toberer, Complex thermoelectric materials. Nat. Mater. 7, 105 (2008)

    Article  ADS  Google Scholar 

  3. M. Morgen, E.T. Ryan, J.H. Zhao, C. Hu, T. Cho, P.S. Ho, Low dielectric constant materials for ulsi interconnects. Annu. Rev. Mater. Sci. 30, 645 (2000)

    Article  ADS  Google Scholar 

  4. D. Langley, G. Giusti, C. Mayousse, C. Celle, D. Bellet, J. Simonato, Flexible transparent conductive materials based on silver nanowire networks: a review. Nanotechnology 24, 452001 (2013)

    Article  ADS  Google Scholar 

  5. S. Stankovich, D. Dikin, G. Dommett, K. Kohlhaas, E. Zimmney, E. Stach, R. Piner, S. Nguyen, R. Ruoff, Graphene-based composite materials. Nature 442, 282 (2006)

    Article  ADS  Google Scholar 

  6. E.K. Kim, S.I. Kwun, S.M. Lee, H. Seo, J.G. Yoon, Thermal boundary resistance at \(\text{ Ge }_2\text{ Sb }_2\text{ Te }_5/\text{ ZnS:SiO }_2\) interface. Appl. Phys. Lett. 76, 3864 (2000)

    Article  ADS  Google Scholar 

  7. M. Bäumer, H.J. Freund, Metal deposits on well-ordered oxide films. Prog. Surf. Sci. 61, 127 (1999)

    Article  ADS  Google Scholar 

  8. Z. Ge, D. Cahill, P. Braun, Thermal conductance of hydrophilic and hydrophobic interfaces. Phys. Rev. Lett. 96, 186101 (2006)

    Article  ADS  Google Scholar 

  9. H.K. Lyeo, D. Cahill, Thermal conductance of interfaces between highly dissimilar materials. Phys. Rev. B 73, 144301 (2006)

    Article  ADS  Google Scholar 

  10. R. Costescu, M. Wall, D. Cahill, Thermal conductance of epitaxial interfaces. Phys. Rev. B 67, 054302 (2003)

    Article  ADS  Google Scholar 

  11. J. Opsal, A. Rosencwaig, D. Willenborg, Thermal-wave detection and thin-film thickness measurements with laser beam deflection. J. Appl. Opt. 22, 3169 (1983)

    Article  ADS  Google Scholar 

  12. M. Olmstead, N. Amer, A new probe of optical properties of surfaces. J. Vac. Sci. Technol. B 1, 751 (1983)

    Article  Google Scholar 

  13. A. Rosencwaig, J. Opsal, D.L. Willenborg, Detection of thermal waves through optical reflectance. Appl. Phys. Lett. 46, 1013 (1985)

    Article  ADS  Google Scholar 

  14. C. Paddock, G. Eesley, Transient thermoreflectance from thin metal films. J. Appl. Phys. 60, 285 (1986)

    Article  ADS  Google Scholar 

  15. D.A. Young, C. Thomsen, H.T. Grahn, H.J. Maris, J. Tauc, Heat Flow in Glasses on a Picosecond Timescale (Springer, Berlin, 1986), pp. 49–51. https://doi.org/10.1007/978-3-642-82912-3

    Book  Google Scholar 

  16. D. Cahill, W. Ford, K. Goodson, G. Mahan, A. Majumdar, H. Maris, R. Merlin, S. Phillpot, Nanoscale thermal transport. J. Appl. Phys. 93, 793 (2003)

    Article  ADS  Google Scholar 

  17. D. Cahill, P. Braun, G. Chen, D. Clarke, S. Fan, K. Goodson, P. Keblinski, W. King, G. Mahan, A. Majumdar, H. Maris, S. Phillpot, E. Pop, L. Shi, Nanoscale thermal transport. II. 2003–2012. Appl. Phys. Rev. 1, 011305 (2014)

    Article  ADS  Google Scholar 

  18. D. Cahill, K. Goodson, A. Majumdar, Thermometry and thermal transport in micro/nanoscale solid-state devices and structures. J. Heat Transf. 124, 223 (2001)

    Article  Google Scholar 

  19. A.J. Schmidt, R. Cheaito, M. Chiesa, Characterization of thin metal films via frequency-domain thermoreflectance. J. Appl. Phys. 107, 024908 (2010)

    Article  ADS  Google Scholar 

  20. J. Zhu, D. Tang, W. Wang, J. Liu, K. Holub, R. Yang, Ultrafast thermoreflectance techniques for measuring thermal conductivity and interface thermal conductance of thin films. J. Appl. Phys. 108, 094315 (2010)

    Article  ADS  Google Scholar 

  21. A.J. Schmidt, R. Cheaito, M. Chiesa, A frequency-domain thermoreflectance method for the characterization of thermal properties. Rev. Sci. Instrum. 80, 094901 (2009)

    Article  ADS  Google Scholar 

  22. F. Lepoutre, D. Balageas, P. Forge, S. Hirschi, J.L. Jouland, D. Rochais, F.C. Chen, Micronscale thermal characterizations of interfaces parallel or perpendicular to the surface. J. Appl. Phys. 78, 2208 (1995)

    Article  ADS  Google Scholar 

  23. J.H. Kim, D. Seong, G.H. Ihm, C. Rhee, Measurement of thermal conductivity of Si and GaAs wafers using the photothermal displacement technique. Int. J. Thermophys. 19, 281 (1998)

    Article  Google Scholar 

  24. B. Li, J.P. Roger, L. Pottier, D. Fournier, Complete thermal characterization of film-on-substrate system by modulated thermoreflectance microscopy and multiparameter fitting. J. Appl. Phys. 86, 5314 (1999)

    Article  ADS  Google Scholar 

  25. D. Cahill, Thermal conductivity measurement from 30 to 750 k: the \(3\omega \) method. Rev. Sci. Instrum. 61, 802 (1990)

    Article  ADS  Google Scholar 

  26. L. Lu, W. Yi, D.L. Zhang, A 3 omega method for specific heat and thermal conductivity measurements. Rev. Sci. Instrum. 72, 2996 (2001)

    Article  ADS  Google Scholar 

  27. Y.K. Koh, S. Singer, W. Kim, J. Zide, H. Lu, D. Cahill, A. Majumdar, A. Gossard, Comparison of the \(3 \omega \) method and time-domain thermoreflectance for measurements of the cross-plane thermal conductivity of epitaxial semiconductors. J. Appl. Phys. 105, 05303 (2009)

    Article  Google Scholar 

  28. D. Cahill, Analysis of heat flow in layered structures for time-domain thermoreflectance. Rev. Sci. Instrum. 75, 5119 (2004)

    Article  ADS  Google Scholar 

  29. R.J. Wells, Rapid approximation to the voigt/faddeeva function and its derivatives. J. Quant. Spectrosc. Radiat. Transf. 62, 29 (1999)

    Article  ADS  Google Scholar 

  30. D. Sands, Pulsed Laser Heating and Melting (INTECH Open Access Publisher, Rijeka, 2011)

    Book  Google Scholar 

  31. K. Ujihara, Reflectivities of metals at high temperatures. J. Appl. Phys. 43, 2376 (1972)

    Article  ADS  Google Scholar 

  32. M. Rashidi-Huyeh, B. Palpant, Counterintuitive thermo-optical response of metal-dielectric nanocomposite materials as a result of local electromagnetic field enhancement. Phys. Rev. B 74, 075405 (2006)

    Article  ADS  Google Scholar 

  33. R.R. Mammei, Thin films for the transport of polarized ultracold neutrons for fundamental symmetry study. Ph.D. thesis, Virginia Polytechnic Institute and State University (2010)

  34. M. Shamsa, W.L. Liu, A.A. Balandin, C. Casiraghi, W.I. Milne, A.C. Ferrari, Thermal conductivity of diamond-like carbon films. Appl. Phys. Lett. 89, 161921 (2006)

    Article  ADS  Google Scholar 

  35. M. Rubin, Optical properties of soda lime silica glasses. Sol. Energy Mater. 12, 275 (1985)

    Article  Google Scholar 

  36. J.A. Harrington, D.A. Gregory, W.F. Otto, Infrared absorption in chemical laser window materials. Appl. Opt. 15, 1953 (1976)

    Article  ADS  Google Scholar 

  37. L.A.L.V. Pishchik, E.R. Dobrovinskaya, Sapphire Materials, Manufacturing, Applications (Springer, Berlin, 2009), p. 170

    Google Scholar 

  38. T.P.S. Iii, High Temperature Glass Melt Property Database for Process Modeling (The American Ceramic Society, Westerville, 2005)

    Google Scholar 

  39. W. Haynes, CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, 2016)

    Book  Google Scholar 

  40. L. Janssen, M. Warmoeskerken, Transport Phenomena Data Companion (Leeghwaterstraat, Delft, 2006)

    Google Scholar 

  41. P. Yoder Jr., Optomechanical Systems Design, 2nd edn. (Marcel Dekker, New York, 1993)

    Google Scholar 

  42. L.A.L.V. Pishchik, E.R. Dobrovinskaya, Sapphire Materials, Manufacturing, Applications (Springer, Berlin, 2009), pp. 110–111

    Google Scholar 

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Acknowledgements

This research was performed under a contract with the Air Force Office of Scientific Research with Contract No. FA9550-12-C-0076.

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Correspondence to Hans D. Robinson.

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Myers, K.B., Gaddam, P.R., Ding, X. et al. Measuring Thermal Conductivity with Magnitude-Dependent Frequency–Domain Thermoreflectance Using Modulated CW Lasers. Int J Thermophys 39, 139 (2018). https://doi.org/10.1007/s10765-018-2458-0

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