Modeling optical absorption for thermoreflectance measurements
Abstract
Optical pump-probe techniques based on thermoreflectance, such as time domain thermoreflectance and frequency domain thermoreflectance (FDTR), have been widely used to characterize the thermal conductivity of thin films and the thermal conductance across interfaces. These techniques typically use a transducer layer to absorb the pump light and improve the thermoreflectance signal. The transducer, however, complicates the interpretation of the measured signal because the approximation that all the energy from the pump beam is deposited at the transducer surface is not always accurate. In this paper, we consider the effect of laser absorption in the top layer of a multilayer sample, and derive an analytical solution for the thermoreflectance signal in the diffusion regime based on volumetric heating. We analyze the measurement sensitivity to the pump absorption depth for transducers with different thermal conductivities, and investigate the additional effect of probe laser penetration depth on the measured signal. We validate our model using FDTR measurements on 490 nm thick amorphous silicon films deposited on fused silica and silicon substrates.
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Many attempts have been made on direct TDTR measurements of semiconductors without metal transducers.
“While many attempts have been made on direct TDTR measurements of semiconductors without metal transducers, 223-227”
From Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials (2018) · cites this paper as [227]
Cites
CRC Handbook of Chemistry and Physics
(2014) · doi:10.1201/b17118 · Cited by 57,706 · see citing works
Introduction to Solid State Physics
KITTEL, C., & Fan, H. (1957) · American Journal of Physics · doi:10.1119/1.1934457 · Cited by 22,539 · see citing works
Swartz, E. T., & Pohl, R. O. (1989) · Reviews of Modern Physics · doi:10.1103/revmodphys.61.605 · Cited by 2,937 · see citing works
Nanoscale thermal transport. II. 2003–2012
Cahill, D. G., Braun, P. V., Chen, G., Clarke, D. R., Fan, S., Goodson, K. E., Keblinski, P., King, W. P., Mahan, G. D., Majumdar, A., et al. (2014) · Applied Physics Reviews · doi:10.1063/1.4832615 · Cited by 1,763 · see citing works
Surface generation and detection of phonons by picosecond light pulses
Thomsen, C., Grahn, H. T., Maris, H. J., & Tauc, J. (1986) · Physical review. B, Condensed matter · doi:10.1103/physrevb.34.4129 · Cited by 1,636 · see citing works
Analysis of heat flow in layered structures for time-domain thermoreflectance
Cahill, D. G. (2004) · Review of Scientific Instruments · doi:10.1063/1.1819431 · Cited by 1,543 · see citing works
Femtosecond spectroscopy of electron-electron and electron-phonon energy relaxation in Ag and Au
Groeneveld, R. H. M., Sprik, R., & Lagendijk, A. (1995) · Physical review. B, Condensed matter · doi:10.1103/physrevb.51.11433 · Cited by 674 · see citing works
Schmidt, A. J., Chen, X., & Chen, G. (2008) · Review of Scientific Instruments · doi:10.1063/1.3006335 · Cited by 655 · see citing works
Self-citationRegner, K. T., Sellan, D. P., Su, Z., Amon, C. H., McGaughey, A. J. H., & Malen, J. A. (2013) · Nature Communications · doi:10.1038/ncomms2630 · Cited by 646 · see citing works
Coherent Phonon Heat Conduction in Superlattices
Luckyanova, M. N., Garg, J., Esfarjani, K., Jandl, A., Bulsara, M. T., Schmidt, A. J., Minnich, A. J., Chen, S., Dresselhaus, M. S., Ren, Z., et al. (2012) · Science · doi:10.1126/science.1225549 · Cited by 630 · see citing works
Self-citationThermal conductance of interfaces between highly dissimilar materials
Lyeo, H.-K., & Cahill, D. G. (2006) · Physical Review B · doi:10.1103/physrevb.73.144301 · Cited by 576 · see citing works
Thermal Conductivity Spectroscopy Technique to Measure Phonon Mean Free Paths
Minnich, A. J., Johnson, J. A., Schmidt, A. J., Esfarjani, K., Dresselhaus, M. S., Nelson, K. A., & Chen, G. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.095901 · Cited by 556 · see citing works
Self-citationA frequency-domain thermoreflectance method for the characterization of thermal properties
Schmidt, A. J., Cheaito, R., & Chiesa, M. (2009) · Review of Scientific Instruments · doi:10.1063/1.3212673 · Cited by 543 · see citing works
Self-citationTransient thermoreflectance from thin metal films
Paddock, C. A., & Eesley, G. L. (1986) · Journal of Applied Physics · doi:10.1063/1.337642 · Cited by 530 · see citing works
Role of electron–phonon coupling in thermal conductance of metal–nonmetal interfaces
Majumdar, A., & Reddy, P. (2004) · Applied Physics Letters · doi:10.1063/1.1758301 · Cited by 511 · see citing works
Thermal conductance of metal-metal interfaces
Gundrum, B. C., Cahill, D. G., & Averback, R. S. (2005) · Physical Review B · doi:10.1103/physrevb.72.245426 · Cited by 417 · see citing works
Spectral mapping of thermal conductivity through nanoscale ballistic transport
Hu, Y., Zeng, L., Minnich, A. J., Dresselhaus, M. S., & Chen, G. (2015) · Nature Nanotechnology · doi:10.1038/nnano.2015.109 · Cited by 349 · see citing works
Thermal conductivity accumulation in amorphous silica and amorphous silicon
Larkin, J. M., & McGaughey, A. J. H. (2014) · Physical Review B · doi:10.1103/physrevb.89.144303 · Cited by 308 · see citing works
Stevens, R. J., Smith, A. N., & Norris, P. M. (2005) · Journal of Heat Transfer · doi:10.1115/1.1857944 · Cited by 293 · see citing works
Custer, J. S., Thompson, M. O., Jacobson, D. C., Poate, J. M., Roorda, S., Sinke, W. C., & Spaepen, F. A. (1994) · Applied Physics Letters · doi:10.1063/1.111121 · Cited by 281 · see citing works
Liu, J., Choi, G.-M., & Cahill, D. G. (2014) · Journal of Applied Physics · doi:10.1063/1.4904513 · Cited by 262 · see citing works
Thermal Conductivity of Glasses: Theory and Application to Amorphous Si
Allen, P. B., & Feldman, J. L. (1989) · Physical Review Letters · doi:10.1103/physrevlett.62.645 · Cited by 259 · see citing works
Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments
Wilson, R. B., & Cahill, D. G. (2014) · Nature Communications · doi:10.1038/ncomms6075 · Cited by 244 · see citing works
Thermal property microscopy with frequency domain thermoreflectance
Yang, J., Maragliano, C., & Schmidt, A. J. (2013) · Review of Scientific Instruments · doi:10.1063/1.4824143 · Cited by 176 · see citing works
Self-citationImproved apparatus for picosecond pump-and-probe optical measurements
Capinski, W. S., & Maris, H. J. (1996) · Review of Scientific Instruments · doi:10.1063/1.1147100 · Cited by 170 · see citing works
Thermal Conductivity and Specific Heat of Thin-Film Amorphous Silicon
Zink, B. L., Pietri, R., & Hellman, F. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.055902 · Cited by 162 · see citing works
Thermoreflectance of metal transducers for optical pump-probe studies of thermal properties
Wilson, R. B., Apgar, B. A., Martin, L. W., & Cahill, D. G. (2012) · Optics Express · doi:10.1364/oe.20.028829 · Cited by 160 · see citing works
Characterization of thin metal films via frequency-domain thermoreflectance
Schmidt, A. J., Cheaito, R., & Chiesa, M. (2010) · Journal of Applied Physics · doi:10.1063/1.3289907 · Cited by 159 · see citing works
Self-citationExtraction of optical constants of zinc oxide thin films by ellipsometry with various models
Liu, Y. C., Hsieh, J. H., & Tung, S. K. (2006) · Thin Solid Films · doi:10.1016/j.tsf.2005.10.089 · Cited by 130 · see citing works
Two-channel model for nonequilibrium thermal transport in pump-probe experiments
Wilson, R. B., Feser, J. P., Hohensee, G. T., & Cahill, D. G. (2013) · Physical Review B · doi:10.1103/physrevb.88.144305 · Cited by 112 · see citing works
Thermoreflectance of metal transducers for time-domain thermoreflectance
Wang, Y., Park, J. Y., Koh, Y. K., & Cahill, D. G. (2010) · Journal of Applied Physics · doi:10.1063/1.3457151 · Cited by 112 · see citing works
Computation of Interfacial Thermal Resistance by Phonon Diffuse Mismatch Model
Wang, H., Xu, Y., Shimono, M., Tanaka, Y., & Yamazaki, M. (2007) · MATERIALS TRANSACTIONS · doi:10.2320/matertrans.maw200717 · Cited by 105 · see citing works
Thermal transport through GaN–SiC interfaces from 300 to 600 K
Ziade, E., Yang, J., Brummer, G., Nothern, D. M., Moustakas, T. D., & Schmidt, A. J. (2015) · Applied Physics Letters · doi:10.1063/1.4930104 · Cited by 100 · see citing works
Self-citationThermal conductance imaging of graphene contacts
Yang, J., Ziade, E., Maragliano, C., Crowder, R., Wang, X., Stefancich, M., Chiesa, M., Swan, A. K., & Schmidt, A. J. (2014) · Journal of Applied Physics · doi:10.1063/1.4889928 · Cited by 91 · see citing works
Self-citationThermal conductivity of epitaxial layers of dilute SiGe alloys
Cahill, D. G., Watanabe, F., Rockett, A., & Vining, C. B. (2005) · Physical Review B · doi:10.1103/physrevb.71.235202 · Cited by 67 · see citing works
Sub-picosecond electron and phonon dynamics in nickel
van Kampen, M., Kohlhepp, J. T., de Jonge, W. J. M., Koopmans, B., & Coehoorn, R. (2005) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/17/43/004 · Cited by 42 · see citing works
Collins, K. C., Maznev, A. A., Cuffe, J., Nelson, K. A., & Chen, G. (2014) · Review of Scientific Instruments · doi:10.1063/1.4903463 · Cited by 39 · see citing works
Regner, K. T., Wei, L. C., & Malen, J. A. (2015) · Journal of Applied Physics · doi:10.1063/1.4937995 · Cited by 26 · see citing works
Ta and Au(Pd) alloy metal film transducers for time-domain thermoreflectance at high pressures
Hsieh, W., & Cahill, D. G. (2011) · Journal of Applied Physics · doi:10.1063/1.3592882 · Cited by 23 · see citing works
Girardeau-Montaut, J. P., Afif, M., Girardeau-Montaut, C., Moustaizis, S. D., & Papadogiannis, N. A. (1996) · Applied Physics A · doi:10.1007/bf01568079 · Cited by 21 · see citing works
Anisotropy of heat conduction in Mo/Si multilayers
Medvedev, V. V., Yang, J., Schmidt, A. J., Yakshin, A., van de Kruijs, R. W. E., Zoethout, E., & Bijkerk, F. (2015) · Journal of Applied Physics · doi:10.1063/1.4928958 · Cited by 17 · see citing works
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- Authors
- Yang, J., Ziade, E., & Schmidt, A. J.
- Affiliations
- Boston University (US)
- Venue
- Journal of Applied Physics
- Publisher
- AIP Publishing
- Published
- 2016-03-07
- Volume
- 119
- Issue
- 9
- ISSN
- 0021-8979 (ISSN-L)
- 1089-7550
- OpenAlex
- W2295254326
- Cited by
- 37
- References
- 41
- Citations by year
- 2026: 5 · 2025: 4 · 2024: 5 · 2023: 1 · 2022: 4 · 2020: 5 · 2019: 6 · 2018: 2 · 2017: 4 · 2016: 1
- FWCI
- 1.93
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Applied Physics (publishedVersion)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Thermal properties of materials
- Physical Sciences › Engineering › Mechanics of Materials › Thermography and Photoacoustic Techniques
- Physical Sciences › Engineering › Mechanics of Materials › Thermoelastic and Magnetoelastic Phenomena
- Keywords
- thermoreflectance, optical absorption, frequency-domain thermoreflectance, time-domain thermoreflectance, thermal conductivity, thin films, thermal conductance, diffusion regime, volumetric heating, analytical model, amorphous silicon thin films
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