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Research Papers: Micro/Nanoscale Heat Transfer

Influence of Hot Electron Scattering and Electron–Phonon Interactions on Thermal Boundary Conductance at Metal/Nonmetal Interfaces

[+] Author and Article Information
Ashutosh Giri

Department of Mechanical and
Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: ag4ar@virginia.edu

Brian M. Foley

Department of Mechanical and
Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: bmf4su@virginia.edu

Patrick E. Hopkins

Department of Mechanical and
Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: phopkins@virginia.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 4, 2013; final manuscript received May 22, 2014; published online June 12, 2014. Assoc. Editor: Ali Khounsary.

J. Heat Transfer 136(9), 092401 (Jun 12, 2014) (6 pages) Paper No: HT-13-1565; doi: 10.1115/1.4027785 History: Received November 04, 2013; Revised May 22, 2014

It has recently been demonstrated that under certain conditions of electron nonequilibrium, electron to substrate energy coupling could represent a unique mechanism to enhance heat flow across interfaces. In this work, we present a coupled thermodynamic and quantum mechanical derivation of electron–phonon scattering at free electron metal/nonmetal substrate interfaces. A simplified approach to the Fermi's Golden Rule with electron energy transitions between only three energy levels is adopted to derive an electron–phonon diffuse mismatch model, that account for the electron–phonon thermal boundary conductance at metal/insulator interfaces increases with electron temperature. Our approach demonstrates that the metal-electron/nonmetal phonon conductance at interfaces can be an order of magnitude larger than purely phonon driven processes when the electrons are driven out of equilibrium with the phonons, consistent with recent experimental observations.

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Figures

Grahic Jump Location
Fig. 4

hes as a function of effective electron temperature for Au/Si (red solid line), Au/Ge (dashed line), and Au/diamond (dashed-dot line) at T0 = 300 K, substrate temperature. The values of the predicted hes are different for different phonon dispersions of the substrate. (Inset) For comparison, we have also plotted Kapitza conductance for Au/diamond at T0 = 100 K as a function of electron temperature and the model prediction from Ref. [16] for negligible electron–phonon nonequilibrium.

Grahic Jump Location
Fig. 3

hes predicted from the theoretical framework developed in this work compared with the experimentally determined hes from the thermoreflectance data analyzed with the two-temperature model [27]. The hes increases linearly with increasing effective electron temperature.

Grahic Jump Location
Fig. 2

(a) Electronic transition probabilities in a gold film as a function of the phonon angular frequency of Si at 300 K and 3000 K effective electron temperatures. The probability of absorbing a phonon is higher than the probability of emitting a phonon at 300 K but at 3000 K, the probability of emission is higher. There is a sharp drop in the probabilities at ω≈3×1013 rads-1 due to the low group velocities of the transverse acoustic modes near the Brillouin zone edge. (b) Average electronic transition probability, η¯A,E, as a function of temperature. For low temperatures Te,eff≤800 K, the average probability of absorbing phonons is higher than that for emitting phonons. As temperature increases, the phonon emission probability increases while the phonon absorption probability decreases.

Grahic Jump Location
Fig. 1

Schematic diagram showing the transitions in the three energy levels in the metal and phonon frequencies in the nonmetal that we account for in this work. For our calculation of hes of Au/Silicon in this paper, we use the phonon dispersion relation for silicon along the Γ→X direction computed by Weber [37].

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