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MICRO/NANOSCALE HEAT TRANSFER—PART II

# Examining Interfacial Diffuse Phonon Scattering Through Transient Thermoreflectance Measurements of Thermal Boundary Conductance

[+] Author and Article Information
Pamela M. Norris1

Department of Mechanical and Aerospace Engineering, University of Virginia, P.O. Box 400746, Charlottesville, VA 22904-4746pamela@virginia.edu

Patrick E. Hopkins2

Department of Mechanical and Aerospace Engineering, University of Virginia, P.O. Box 400746, Charlottesville, VA 22904-4746

1

Corresponding author.

2

Present address: Engineering Sciences Center, Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185-0346.

J. Heat Transfer 131(4), 043207 (Feb 20, 2009) (11 pages) doi:10.1115/1.3072928 History: Received June 12, 2008; Revised October 08, 2008; Published February 20, 2009

## Abstract

Today’s electronic and optoelectronic devices are plagued by heat transfer issues. As device dimensions shrink and operating frequencies increase, ever-increasing amounts of thermal energy are being generated in smaller and smaller volumes. As devices shrink to length scales on the order of carrier mean free paths, thermal transport is no longer dictated by the thermal properties of the materials comprising the devices, but rather the transport of energy across the interfaces between adjacent materials in the devices. In this paper, current theories and experiments concerning phonon scattering processes driving thermal boundary conductance $(hBD)$ are reviewed. Experimental studies of thermal boundary conductance conducted with the transient thermoreflectance technique challenging specific assumptions about phonon scattering during thermal boundary conductance are presented. To examine the effects of atomic mixing at the interface on $hBD$, a series of Cr/Si samples was fabricated subject to different deposition conditions. The varying degrees of atomic mixing were measured with Auger electron spectroscopy. Phonon scattering phenomena in the presence of interfacial mixing were observed with the trends in the Cr/Si $hBD$. The experimental results are reviewed and a virtual crystal diffuse mismatch model is presented to add insight into the effect of interatomic mixing at the interface. The assumption that phonons can only transmit energy across the interface by scattering with a phonon of the same frequency—i.e., elastic scattering, can lead to underpredictions of $hBD$ by almost an order of magnitude. To examine the effects of inelastic scattering on $hBD$, a series of metal/dielectric interfaces with a wide range of vibrational similarity is studied at temperatures above and around materials’ Debye temperatures. Inelastic scattering is observed and new models are developed to predict $hBD$ and its relative dependency on elastic and inelastic scattering events.

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## Figures

Figure 1

Schematic of the transient thermoreflectance setup at the University of Virginia’s Microscale Heat Transfer Laboratory

Figure 2

Ratio of measured hBD, hBDmeas, to hBD predicted from the DMM, hBDDMM, versus the ratios of the Debye temperatures of the metal film to the dielectric substrate. The data presented in this figure are selected results from Stevens (6), Lyeo and Cahill (50), Stoner and Maris (41), and Hopkins (31). Some of the diamond substrates were subject to hydrogen termination before metal film deposition represented by the “H/diamond” after the metal film. The general trend shows that the DMM underpredicts measurements on acoustically mismatched samples and overpredicts measurements on acoustically matched samples.

Figure 3

Thermal boundary conductance measurements on various Cr/Si interfaces from Hopkins (32) and corresponding VCDMM calculations from Beechem (34). Where the DMM predicts hBD that is almost eight times larger (0.86 GW m−2 K−1) than that measured on the samples with no dependence on mixing layer thickness or compositions, the VCDMM calculations are within 18% of the measured values and show similar trends with mixing layer thickness when taking into account the change in Si composition in the mixing region.

Figure 4

Ratio of measured hBD, hBDmeas, to hBD predicted from the DMM, hBDDMM, versus temperature for six different acoustically mismatches samples. The data presented in this figure are selected results of Lyeo and Cahill (50), Stoner and Maris (41), and Hopkins (31). Some of the diamond substrates were subject to hydrogen termination before metal film deposition represented by the H/diamond. The general trend shows that the increase in hBD observed with temperature over the temperature range for each sample is much greater than the increase with temperature predicted by the DMM. These data show a linear trend in hBD with temperature, which is evidence of inelastic scattering.

Figure 5

Ratio of measured hBD, hBDmeas, to hBD predicted from the DMM and JFDMM versus temperature for six different acoustically mismatched samples. The data presented in this figure are selected results of Lyeo and Cahill (50), Stoner and Maris (41), and Hopkins (31). The JFDMM captures the temperature trends in the data that exhibit inelastic scattering, and predicts hBD values that are more in line with the experimental measurements.

Figure 6

Relative magnitude of inelastic scattering on hBD. This ratio compares the inelastic contribution to hBD to the elastic contribution. Details of these calculations are found in Ref. 53. The role of inelastic phonon scattering increases as the acoustic mismatch of the film and substrate becomes greater. The range in which hBD should increase linearly with temperature due to inelastic scattering also increases with acoustic mismatch.

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