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Research Papers: Experimental Techniques

# Measuring the Thermal Conductivity of Porous, Transparent $SiO2$ Films With Time Domain Thermoreflectance

[+] Author and Article Information
Patrick E. Hopkins1

Engineering Sciences Center, Sandia National Laboratories, Albuquerque, NM 87185pehopki@sandia.gov

Bryan Kaehr, C. Jeffrey Brinker

Engineering Sciences Center, Sandia National Laboratories, Albuquerque, NM 87185; Department of Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, NM 87106

Leslie M. Phinney, Timothy P. Koehler, Anne M. Grillet

Engineering Sciences Center, Sandia National Laboratories, Albuquerque, NM 87185

Darren Dunphy, Fred Garcia

Department of Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, NM 87106

1

Corresponding author.

J. Heat Transfer 133(6), 061601 (Mar 09, 2011) (8 pages) doi:10.1115/1.4003548 History: Received June 07, 2010; Revised January 25, 2011; Published March 09, 2011; Online March 09, 2011

## Abstract

Nanocomposites offer unique capabilities of controlling thermal transport through the manipulation of various structural aspects of the material. However, measurements of the thermal properties of these composites are often difficult, especially porous nanomaterials. Optical measurements of these properties, although ideal due to the noncontact nature, are challenging due to the large surface variability of nanoporous structures. In this work, we use a vector-based thermal algorithm to solve for the temperature change and heat transfer in which a thin film subjected to a modulated heat source is sandwiched between two thermally conductive pathways. We validate our solution with time domain thermoreflectance measurements on glass slides and extend the thermal conductivity measurements to $SiO2$-based nanostructured films.

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Copyright © 2011 by American Society of Mechanical EngineersThe United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

## Figures

Figure 6

Average thermal conductivity of the CD and EISA samples compared with previous measurements of the thermal conductivity of SiO2-based films (SiO2 sputtered thin film (sputtered), flowable oxide (FOx), and XLK) and bulk amorphous SiO2. The EISA and CD thermal conductivities, along with the previous measurements, all show a substantial reduction in thermal conductivity from bulk, and even thin film sputtered SiO2. The solid line represents the thermal conductivity prediction from the DEM theory.

Figure 5

Representative TDTR data from the samples in this work along with their corresponding best fit thermal models. We probe the Al/cover glass and Al/glass slide samples that have not been coated with EISA or CD silica films from the front (not shown) and back to determine the thermal conductivity of the glass substrate and thermal boundary conductance at the Al/glass interface and verify our thermal model and fitting algorithm.

Figure 4

Thermal sensitivity defined in Eq. 21 to the thermal conductivity of the glass substrate (p=κ0), the thermal boundary conductance between the glass substrate and the Al film (p=h1), the thermal boundary conductance between the Al film and some SiO2 film (p=h2), and the thermal conductivity of some SiO2 film (p=κ2) as a function of time for the measurement geometry shown in Fig. 1. We consider three different cases for the thermal properties of the film on side 2: (a) same properties as the glass slide, (b) same heat capacity as the glass slide with half of the thermal conductivity, and (c) thermal properties of air (C2=1000 J m−3 K−1 and κ2=0.0257 W m−1K−1). Note also that the sensitivity to h1 is nearly as large as that of κ2 for cases (a) and (b), elucidating the importance of determining the thermal boundary conductance between the Al film and the glass slide. We assume bulk thermophysical properties for all other thermophysical parameters (28).

Figure 3

Ratio of rri1D to rriAx for the range of modulation frequencies typical in TDTR experiments assuming that wpr=wpm=17 μm. When rri1D/rriAx=1, the heat transfer is purely one dimensional. For frequencies above 5 MHz, we find that the value of rri1D/rriAx approaches 1, allowing us to safely approximate the heat transport as one dimensional for our sample geometry studied in this work (depicted in Fig. 1).

Figure 2

Frequency domain solution to the axially symmetric heat equation for the sample geometry shown in Fig. 1 as a function of modulation frequency for five different values for the thermal diffusivity of layer 2, D=10−7 m2 s−1, 10−6 m2 s−1, 10−5 m2 s−1, 10−4 m2 s−1, and 10−3 m2 s−1. As discussed in the text, bulk thermophysical properties are assumed for the Al film (layer 1) and the glass slide (layer 0). Both the glass and the nanostructure (layer 2) are assumed to be semi-infinite. The value plotted in this figure is the absolute value of the ratio of the real to imaginary solution of Eq. 19.

Figure 1

Geometry of samples interrogated in this work. A sample is adjacent onto a thin Al film that is evaporated on a glass slide. TDTR is performed on the Al film by probing through the glass slide. Bidirectional heat transfer must be accounted for in this case since many samples that can be measured in this configuration have thermal diffusivities less than glass.

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