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Research Papers: Micro/Nanoscale Heat Transfer

# Influence of Interfacial Mixing on Thermal Boundary Conductance Across a Chromium/Silicon Interface

[+] 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

Thomas E. Beechem, Samuel Graham

GW Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 771 Ferst Drive NE, Atlanta, GA 30332

1

Corresponding author.

J. Heat Transfer 130(6), 062402 (Apr 23, 2008) (10 pages) doi:10.1115/1.2897344 History: Received January 30, 2007; Revised November 21, 2007; Published April 23, 2008

## Abstract

The thermal conductance at solid-solid interfaces is becoming increasingly important in thermal considerations dealing with devices on nanometer length scales. Specifically, interdiffusion or mixing around the interface, which is generally ignored, must be taken into account when the characteristic lengths of the devices are on the order of the thickness of this mixing region. To study the effect of this interfacial mixing on thermal conductance, a series of Cr films is grown on Si substrates subject to various deposition conditions to control the growth around the $Cr∕Si$ boundary. The $Cr∕Si$ interfaces are characterized with Auger electron spectroscopy. The thermal boundary conductance $(hBD)$ is measured with the transient thermoreflectance technique. Values of $hBD$ are found to vary with both the thickness of the mixing region and the rate of compositional change in the mixing region. The effects of the varying mixing regions in each sample on $hBD$ are discussed, and the results are compared to the diffuse mismatch model (DMM) and the virtual crystal DMM (VCDMM), which takes into account the effects of a two-phase region of finite thickness around the interface on $hBD$. An excellent agreement is shown between the measured $hBD$ and that predicted by the VCDMM for a change in thickness of the two-phase region around the interface.

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## Figures

Figure 1

TTR experimental setup used in this study

Figure 2

TEM image of the Cr∕Si interface. The observable mixing from the TEM analysis is based on the Si crystallographic planes, yielding a 8.5nm mixing layer. However, the actual Cr∕Si elemental mixing may not be completely crystalline; therefore, AES is used for interfacial chemical analysis.

Figure 3

Example of a full AES spectrum of one of the Cr∕Si films examined, Cr-1. Note the relatively high concentrations of O2 and C at the sample surface, about 100% more than those in the film. These elements were sputtered away from the surface with the ion gun during the depth profiling procedure. The mixing layer is depicted by the vertical lines at the 10% mark of the Si and Cr.

Figure 4

TTR data of Cr-1 and Cr-2 fits with the model described with Eqs. 5,6,7,8,9,10. A 40% decrease in the best fit hBD from Cr-1 to Cr-2 is observed, with the only change in the experiment occurring in the deposition conditions (see Table 1).

Figure 5

Average of the measured hBD of each sample as a function of mixing layer thickness. The room temperature samples display a linear decrease in hBD with increasing mixing layer thickness. The samples deposited at higher temperatures (Cr-5 and Cr-6) do not follow this trend, which could be due to defects of a change in the microstructure relative to the room temperature deposited samples. The error bars represent the 7% deviation from the mean calculated from the data from each sample, which are the calculated errors associated with the repeatability of the data from the experiment.

Figure 6

Average of the measured hBD of each sample as a function of rate of Si increase at the beginning of the interfacial layer. An increase in hBD is observed as the Si spatial change in the film becomes more gradual. The error bars represent the 7% deviation from the mean calculated from the data from each sample, which are the calculated errors associated with the repeatability of the data from the experiment.

Figure 7

Comparison of the VCDMM to the experimental data on samples Cr-1–Cr-4. Added electron-phonon coupling resistance is taken into account in these calculations since Cr and Si are acoustically matched solids. Where as the DMM predicts hBD that is almost eight times larger 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 8

Auger electron spectroscopy depth profiles

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