0
Research Papers: Micro/Nanoscale Heat Transfer

# Influence of Inelastic Scattering at Metal-Dielectric Interfaces

[+] Author and Article Information
Patrick E. Hopkins

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

Pamela M. Norris1

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

Robert J. Stevens

Department of Mechanical Engineering, Rochester Institute of Technology, 76 Lomb Memorial Drive, Rochester, NY 14623-5604

1

Corresponding author.

J. Heat Transfer 130(2), 022401 (Feb 04, 2008) (9 pages) doi:10.1115/1.2787025 History: Received July 24, 2006; Revised June 14, 2007; Published February 04, 2008

## Abstract

Thermal boundary conductance is becoming increasingly important in microelectronic device design and thermal management. Although there has been much success in predicting and modeling thermal boundary conductance at low temperatures, the current models applied at temperatures more common in device operation are not adequate due to our current limited understanding of phonon transport channels. In this study, the scattering processes across $Cr∕Si$, $Al∕Al2O3$, $Pt∕Al2O3$, and $Pt∕AlN$ interfaces were examined by transient thermoreflectance testing at high temperatures. At high temperatures, traditional models predict the thermal boundary conductance to be relatively constant in these systems due to assumptions about phonon elastic scattering. Experiments, however, show an increase in the conductance indicating inelastic phonon processes. Previous molecular dynamic simulations of simple interfaces indicate the presence of inelastic scattering, which increases interfacial transport linearly with temperature. The trends predicted computationally are similar to those found during experimental testing, exposing the role of multiple-phonon processes in thermal boundary conductance at high temperatures.

<>

## Figures

Figure 8

The slopes of the linear trends (η) as a function of film∕substrate Debye temperature ratio (ξ) are shown for the Pt data from this study, the Pb∕diamond and Bi∕diamond data from Lyeo and Cahill (24), and the Au∕diamond data from Stoner and Maris (15). The linear trends were determined from hBD data measured above the various samples’ Debye temperatures to make sure that these slopes represented regimes where inelastic scattering was contributing to hBD. The linear fit to these points is depicted by the solid line. It is apparent that the two materials become acoustically similar (increasing ξ), and inelastic scattering becomes increasingly temperature dependent.

Figure 1

Thermal boundary conductance calculations of the Al∕Al2O3 and Pt∕Al2O3 interfaces using DMM and PRL. The models level off at higher temperatures due to the assumption of elastic scattering used in the calculations. The inset graphs show the DMM and PRL for the materials systems over only the temperature range used in this work.

Figure 2

TTR setup

Figure 3

Thermal model (Eqs. (8)–(14)) fit to TTR data taken on (a) Pt∕Al2O3 at 293K and 495K and (b) Al∕Al2O3 at 293K and 473K. The thermal model is scaled to the TTR data at 200ps for reasons that will be discussed later in this paper. The TTR data were phase fixed (29) and normalized at the peak reflectance to make clear the differences in the exponential cooling profiles at the different temperatures.

Figure 4

Thermal boundary conductance data across the Cr∕Si interface over a range of temperatures. The data show a linear increase with temperature at a much greater rate than the DMM and PRL.

Figure 5

Thermal boundary conductance data across the Al∕Al2O3 interface over a range of temperatures. This figure also includes data taken by Stoner and Maris (1993) at low temperatures (15). The linear trend continues at temperatures higher than the Debye temperature of Al, indicating that inelastic phonon processes could be contributing to hBD at these elevated temperatures.

Figure 6

Thermal boundary conductance data across the Pt∕Al2O3 interface over a range of temperatures. These temperatures are above the Debye temperature of Pt. According to theory, hBD should not change at temperatures above the Debye temperature of one of the materials assuming only elastic scattering. However, the continued linear increase in measured hBD indicates a contribution from inelastic processes.

Figure 7

Thermal boundary conductance data across the Pt∕AlN interface over a range of temperatures. A similar linear increase of hBD to the data in Fig. 7 is observed, presenting further evidence toward nonelastic phonon transport channels.

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections