Research Papers: Micro/Nanoscale Heat Transfer

Hotspot Size-Dependent Thermal Boundary Conductance in Nondiffusive Heat Conduction

[+] Author and Article Information
Yanbao Ma

School of Engineering,
University of California at Merced,
Merced, CA 95343
e-mail: yma5@ucmerced.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 5, 2014; final manuscript received March 18, 2015; published online April 16, 2015. Assoc. Editor: Robert D. Tzou.

J. Heat Transfer 137(8), 082401 (Aug 01, 2015) (7 pages) Paper No: HT-14-1517; doi: 10.1115/1.4030170 History: Received August 05, 2014; Revised March 18, 2015; Online April 16, 2015

Thermal transport across interfaces can play a critical role in nanosystems for thermal management and thermal energy conversion. Here, we show the dependence of the thermal boundary conductance (G) of the interface between a 70-nm Al transducer and a Si substrate on the size of a laser pump diameter (D) in the time-domain thermoreflectance (TDTR) experiments at room temperature. For D ≥ 30 μm, G approaches to a constant where diffusion dominates the heat transfer processes. When D decreases from 30 μm to 3.65 μm, G decreases from 240 to 170 MW/m2K due to the increasing nonlocal effects from nondiffusive heat transport. This finding is vital to our understanding of the thermal boundary conductance: it depends not only on inherent interfacial conditions but also on external heating conditions, which makes the accurate measurements and theoretical predictions of thermal transport across interfaces in micro/nanosystems more challenging.

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Cahill, D. G., Ford, W. K., Goodson, K. E., Mahan, G. D., Majumdar, A., Maris, H. J., Merlin, R., and Phillpot, S. R., 2003, “Nanoscale Thermal Transport,” J. Appl. Phys., 93(1), p. 011305. [CrossRef]
Cahill, D. G., Braun, P. V., Chen, G., Clarke, D. R., Fan, S. H., Goodson, K. E., Keblinski, P., King, W. P., Mahan, G. D., Majumdar, A., Maris, H. J., Phillpot, S. R., Pop, E., and Shi, L., 2014, “Nanoscale Thermal Transport. II. 2003-2012,” Appl. Phys. Rev., 93(2), pp. 794–817.
Ziman, J. M., 1960, Electrons and Phonons: The Theory of Transport Phenomena in Solids, Oxford University Press, New York.
Hopkins, P. E., 2013, “Thermal Transport Across Solid Interfaces With Nanoscale Imperfections: Effects of Roughness, Disorder, Dislocations, and Bonding on Thermal Boundary Conductance,” ISRN Mech. Eng., 2013, p. 682586. [CrossRef]
Swartz, E. T., and Pohl, R. O., 1989, “Thermal-Boundary Resistance,” Rev. Mod. Phys., 61(3), pp. 605–668. [CrossRef]
Chen, G., and Zeng, T. F., 2001, “Nonequilibrium Phonon and Electron Transport in Heterostructures and Superlattices,” Microscale Thermophys. Eng., 5(2), pp. 71–88. [CrossRef]
Khalatnikov, I. M., 1952, “Teploobmen Mezhdu Tverdym Telom I Geliem-Ii,”Sov. Phys. JETP (Zh. Eksperimentalnoi I Teor. Fiz.), 22(6), pp. 687–704.
Prasher, R. S., and Phelan, P. E., 2001, “A Scattering-Mediated Acoustic Mismatch Model for the Prediction of Thermal Boundary Resistance,” ASME J. Heat Transfer, 123(6), pp. 105–112. [CrossRef]
Loh, G. C., Tay, B. K., and Teo, E. H. T., 2010, “Flux-Mediated Diffuse Mismatch Model,” Appl. Phys. Lett., 97(12), p. 121917. [CrossRef]
Hopkins, P. E., and Norris, P. M., 2007, “Effects of Joint Vibrational States on Thermal Boundary Conductance,” Nanoscale Microscale Thermophys. Eng., 11(3–4), pp. 247–257. [CrossRef]
Beechem, T., and Hopkins, P. E., 2009, “Predictions of Thermal Boundary Conductance for Systems of Disordered Solids and Interfaces,” J. Appl. Phys., 106(12), p. 124301. [CrossRef]
Le, N. Q., Duda, J. C., English, T. S., Hopkins, P. E., Beechem, T. E., and Norris, P. M., 2012, “Strategies for Tuning Phonon Transport in Multilayered Structures Using a Mismatch-Based Particle Model,” J. Appl. Phys., 111(8), p. 084310. [CrossRef]
Singh, D., Murthy, J. Y., and Fisher, T. S., 2011, “Effect of Phonon Dispersion on Thermal Conduction Across Si/Ge Interfaces,” ASME J. Heat Transfer, 133(12), p. 122401. [CrossRef]
Huang, Z., Fisher, T., and Murthy, J., 2011, “An Atomistic Study of Thermal Conductance Across a Metal-Graphene Nanoribbon Interface,” J. Appl. Phys., 109(7), p. 074305. [CrossRef]
Tian, Z. T., Esfarjani, K., and Chen, G., 2012, “Enhancing Phonon Transmission Across a Si/Ge Interface by Atomic Roughness: First-Principles Study With the Green's Function Method,” Phys. Rev. B, 86(23), p. 235304. [CrossRef]
Landry, E. S., and Mcgaughey, A. J. H., 2009, “Thermal Boundary Resistance Predictions From Molecular Dynamics Simulations and Theoretical Calculations,” Phys. Rev. B, 80(16), p. 165304. [CrossRef]
Swartz, E. T., and Pohl, R. O., 1987, “Thermal-Resistance at Interfaces,” Appl. Phys. Lett., 51(26), pp. 2200–2202. [CrossRef]
Li, B. C., Roger, J. P., Pottier, L., and Fournier, D., 1999, “Complete Thermal Characterization of Film-on-Substrate System by Modulated Thermoreflectance Microscopy and Multiparameter Fitting,” J. Appl. Phys., 86(9), pp. 5314–5316. [CrossRef]
Lee, S. M., and Cahill, D. G., 1997, “Heat Transport in Thin Dielectric Films,” J. Appl. Phys., 81(6), pp. 2590–2595. [CrossRef]
Stevens, R. J., Smith, A. N., and Norris, P. M., 2005, “Measurement of Thermal Boundary Conductance of a Series of Metal-Dielectric Interfaces by the Transient Thermoreflectance Technique,” ASME J. Heat Transfer, 127(3), pp. 315–322. [CrossRef]
Chen, G., 2005, Nanoscale Energy Transport and Conversion, Oxford University Press, New York.
Mcconnell, A. D., Uma, S., and Goodson, K. E., 2005, “Thermal Conduction in Silicon Micro and Nanostructures,” Annu. Rev. Heat Transfer, 14, pp. 129–168. [CrossRef]
Minnich, A. J., Dresselhaus, M. S., Ren, Z. F., and Chen, G., 2009, “Bulk Nanostructured Thermoelectric Materials: Current Research and Future Prospects,” Energy Environ. Sci., 2(5), pp. 466–479. [CrossRef]
Cahill, D. G., Goodson, K. E., and Majumdar, A., 2002, “Thermometry and Thermal Transport in Micro/Nanoscale Solid-State Devices and Structures,” ASME J. Heat Transfer, 124(2), pp. 223–241. [CrossRef]
Brites, C. D. S., Lima, P. P., Silva, N. J. O., Millan, A., Amaral, V. S., Palacio, F., and Carlos, L. D., 2012, “Thermometry at the Nanoscale,” Nanoscale, 4(16), pp. 4799–4829. [CrossRef] [PubMed]
Cattaneo, C., 1958, “Sur Une Forme De Lequation De La Chaleur Eliminant Le Paradoxe Dune Propagation Instantanee,” C. R. Hebd. Seances Acad. Sci., 247(4), pp. 431–433.
Vernotte, P., 1958, “Les Paradoxes De La Theorie Continue De Lequation De La Chaleur,” C. R. Hebd. Seances Acad. Sci., 246(22), pp. 3154–3155.
Guyer, R. A., and Krumhansl, J. A., 1966, “Solution of Linearized Phonon Boltzmann Equation,” Phys. Rev., 148(2), pp. 766–778. [CrossRef]
Cimmelli, V. A., Sellitto, A., and Jou, D., 2010, “Nonlinear Evolution and Stability of the Heat Flow in Nanosystems: Beyond Linear Phonon Hydrodynamics,” Phys. Rev. B, 82(18), p. 184302. [CrossRef]
Majumdar, A., 1993, “Microscale Heat-Conduction in Dielectric Thin-Films,” ASME J. Heat Transfer, 115(1), pp. 7–16. [CrossRef]
Tamma, K. K., and Zhou, X. M., 1998, “Macroscale and Microscale Thermal Transport and Thermo-Mechanical Interactions: Some Noteworthy Perspectives,” J. Therm. Stresses, 21(3–4), pp. 405–449. [CrossRef]
Chen, G., 2001, “Ballistic-Diffusive Heat-Conduction Equations,” Phys. Rev. Lett., 86(11), pp. 2297–2300. [CrossRef] [PubMed]
Tzou, D. Y., 2011, “Nonlocal Behavior in Phonon Transport,” Int. J. Heat Mass Transfer, 54(1–3), pp. 475–481. [CrossRef]
Wang, H. D., Cao, B. Y., and Guo, Z. Y., 2012, “Non-Fourier Heat Conduction in Carbon Nanotubes,” ASME J. Heat Transfer, 134(5), p. 051004. [CrossRef]
Wang, M., and Guo, Z. Y., 2010, “Understanding of Temperature and Size Dependences of Effective Thermal Conductivity of Nanotubes,” Phys. Lett. A, 374(42), pp. 4312–4315. [CrossRef]
Wang, M. R., Yang, N., and Guo, Z. Y., 2011, “Non-Fourier Heat Conductions in Nanomaterials,” J. Appl. Phys., 110(6), p. 064310. [CrossRef]
Wilson, R. B., Feser, J. P., Hohensee, G. T., and Cahill, D. G., 2013, “Two-Channel Model for Nonequilibrium Thermal Transport in Pump-Probe Experiments,” Phys. Rev. B, 88(14), p. 144305. [CrossRef]
Liang, L. H., Wei, Y. G., and Li, B. W., 2008, “Size-Dependent Interface Phonon Transmission and Thermal Conductivity of Nanolaminates,” J. Appl. Phys., 103(8), p. 084314. [CrossRef]
Regner, K. T., Mcgaughey, A. J. H., and Malen, J. A., 2014, “Analytical Interpretation of Nondiffusive Phonon Transport in Thermoreflectance Thermal Conductivity Measurements,” Phys. Rev. B, 90(6), p. 064302. [CrossRef]
Wilson, R. B., and Cahill, D. G., 2014, “Anisotropic Failure of Fourier Theory in Time-Domain Thermoreflectance Experiments,” Nat. Commun., 5, p. 6075. [CrossRef]
Gorham, C. S., Hattar, K., Cheaito, R., Duda, J. C., Gaskins, J. T., Beechem, T. E., Ihlefeld, J. F., Biedermann, L. B., Piekos, E. S., Medlin, D. L., and Hopkins, P. E., 2014, “Ion Irradiation of the Native Oxide/Silicon Surface Increases the Thermal Boundary Conductance Across Aluminum/Silicon Interfaces,” Phys. Rev. B, 90(2), p. 024301. [CrossRef]
Ding, D., Chen, X., and Minnich, A. J., 2014, “Radial Quasiballistic Transport in Time-Domain Thermoreflectance Studied Using Monte Carlo Simulations,” Appl. Phys. Lett., 104(14), p. 143104. [CrossRef]
Ma, Y., 2014, “A Two-Parameter Nondiffusive Heat Conduction Model for Data Analysis in Pump-Probe Experiments,” J. Appl. Phys., 116(24), p. 243505. [CrossRef]
Cahill, D. G., 2004, “Analysis of Heat Flow in Layered Structures for Time-Domain Thermoreflectance,” Rev. Sci. Instrum., 75(12), pp. 5119–5122. [CrossRef]
Schmidt, A. J., Chen, X. Y., and Chen, G., 2008, “Pulse Accumulation, Radial Heat Conduction, and Anisotropic Thermal Conductivity in Pump-Probe Transient Thermoreflectance,” Rev. Sci. Instrum., 79(11), p. 114902. [CrossRef] [PubMed]
Guo, L., Hodson, S. L., Fisher, T. S., and Xu, X. F., 2012, “Heat Transfer Across Metal-Dielectric Interfaces During Ultrafast-Laser Heating,” ASME J. Heat Transfer, 134(4), p. 042402. [CrossRef]


Grahic Jump Location
Fig. 1

Comparison of data fitting results of the TPHC model with TDTR data [26]. (a) Amplitude versus time delay and (b) phase angle versus time delay. Pump laser 1/e2 diameter D = 3.65 μm and modulation frequency f = 2.01 MHz.

Grahic Jump Location
Fig. 2

Comparison of data fitting results of the TPHC model and Fourier's law in the TDTR data analyses. A-fitting stands for amplitude fitting, and P-fitting means phase angle fitting. (a) and (b) Amplitude and phase angle versus time delay for pump laser diameter D = 3.65 μm and modulation frequency f = 2.01 MHz. (c) and (d) Amplitude and phase angle versus time delay for pump laser diameter D = 5.44 μm and modulation frequency f = 2.01 MHz.

Grahic Jump Location
Fig. 3

Comparison of data fitting results of the TPHC model and Fourier's law in the TDTR data analyses. A-fitting stands for amplitude fitting, and P-fitting means phase angle fitting. (a) and (b) Amplitude and phase angle versus time delay for pump laser diameter D = 8.9 μm and modulation frequency f = 4.77 MHz. (c) and (d) Amplitude and phase angle versus time delay for pump laser diameter D = 60 μm and modulation frequency f = 6.85 MHz.

Grahic Jump Location
Fig. 4

Thermal boundary conductance G versus the pump laser 1/e2 diameter D



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