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Research Papers: Experimental Techniques

# Optical Measurement of Thermal Conductivity Using Fiber Aligned Frequency Domain Thermoreflectance

[+] Author and Article Information
Jonathan A. Malen1

Department of Mechanical Engineering, UC Berkeley, Berkeley, CA 94720jonmalen@andrew.cmu.edu

Kanhayalal Baheti

Department of Chemistry, UC Berkeley, Berkeley, CA 94720

Tao Tong, Yang Zhao

Department of Mechanical Engineering, UC Berkeley, Berkeley, CA 94720

Janice A. Hudgings

Department of Physics, Mount Holyoke College, South Hadley, MA 01075

Arun Majumdar2

Department of Mechanical Engineering, UC Berkeley, Berkeley, CA 94720

1

Corresponding author. Present address: Department of Mechanical Engineering, Carnegie Mellon, Department of Mechanical Engineering, Pittsburgh, PA 15213.

2

Present address: U.S. Department of Energy, 1000 Independence Avenue SW, Washington, DC 20585.

J. Heat Transfer 133(8), 081601 (May 02, 2011) (7 pages) doi:10.1115/1.4003545 History: Received June 01, 2010; Revised January 10, 2011; Published May 02, 2011; Online May 02, 2011

## Abstract

Fiber aligned frequency domain thermoreflectance (FAFDTR) is a simple noncontact optical technique for accurately measuring the thermal conductivity of thin films and bulk samples for a wide range of materials, including electrically conducting samples. FAFDTR is a single-sided measurement that requires minimal sample preparation and no microfabrication. Like existing thermoreflectance techniques, a modulated pump laser heats the sample surface, and a probe laser monitors the resultant thermal wave via the temperature dependent reflectance of the surface. Via the use of inexpensive fiber coupled diode lasers and common mode rejection, FAFDTR addresses three challenges of existing optical methods: complexity in setup, uncertainty in pump-probe alignment, and noise in the probe laser. FAFDTR was validated for thermal conductivities spanning three orders of magnitude $(0.1–100 W/m K)$, and thin film thermal conductances greater than $10 W/m2 K$. Uncertainties of 10–15% were typical, and were dominated by uncertainties in the laser spot size. A parametric study of sensitivity for thin film samples shows that high thermal conductivity contrast between film and substrate is essential for making accurate measurements.

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## Figures

Figure 1

Experimental setup and spot radius calibration. (a) FAFDTR uses fiber coupled diode lasers to produce pump (shown in red) and probe (shown in blue) beams of that are subsequently merged into a single fiber, leading to perfect pump-probe alignment at the sample surface. The pump power is periodically modulated (dashed line), resulting in a periodic temperature change of the sample surface. Due to the temperature dependant reflectivity of the sample, when the probe beam is reflected, it too becomes modulated. The phase lag between the periodic signals of the pump beam and reflected probe beam varies with modulation frequency and is used to evaluate the sample’s thermal conductivity. Details of the setup are explained in the text. (b) CCD images of the pump beam reflected from patterned samples were used to determine the spot radius of our beam at the sample surface for 10×, 20×, and 50× lenses. Arrays of dots, with known dot-dot pitch (10 μm), were used for calibration. (Color online only.)

Figure 2

FAFDTR data, fits, and comparison to reference samples. (a) Measured phase lag between the surface temperature and the applied heat flux for bulk samples; solid lines show the best fit of the model to the experimental data. (b) Phase lag data and best fit for thin film samples. (c) Comparison between thermal conductivity measured by FAFDTR (kFAFDTR) and the reference thermal conductivity of our samples (kref). A linear fit to these points has a slope of 1.02, indicating that FAFDTR is accurate for measurement of k∼0.1–100 W/m K. (d) FAFDTR’s ability to measure high thermal conductance thin film samples is demonstrated by comparing the reference thermal conductance (href=kref/Lfilm) to the FAFDTR prediction of thermal conductance (hFAFDTR=kFAFDTR/Lfilm). A linear fit to these points has a slope of 1.02, indicating that FAFDTR is accurate for measurement of hfilm∼0.1–35 W/m K.

Figure 3

Sensitivity of FAFDTR to uncertainty in heating spot radius for thin film samples. Subplots (a)–(c) correspond to the percent uncertainty in kfilm due to a 1% uncertainty in rspot for cases (a)–(c) discussed in the text. Contours of percent uncertainty are labeled. Using case (a) as an example, the contours can be interpreted as follows: For rspot of 10 μm and kfilm of 10 W/m2-K, there will be an ∼3% uncertainty in kfilm, given a 1% uncertainty in rspot. High uncertainty results when the thermal conductivities of the film and substrate are similar.

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