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Thermal Conductivity Measurements in Challenging Regimes

  • Author(s): Lubner, Sean
  • Advisor(s): Dames, Chris
  • et al.

Creating technologies to address increasingly diverse challenges ranging from biomedical devices to carbon-free energy solutions requires measuring material properties and system behaviors in increasingly challenging regimes. In the biomedical field, accurate determination of the thermal conductivity (k) of biological tissues is important for cryopreservation, thermal ablation, and cryosurgery, but is hampered by the delicate nature and often-small sizes of tissues. In the electronics and clean energy fields, it is increasingly necessary to reliably model the dissipation of heat from micro and nanoelectronics for thermal management, and the transport of heat through nanostructured materials for energy control and conversion technologies such as batteries and thermoelectrics. However, the classical equations of heat transfer break down at these short length scales, calling into question the validity of various formulations of heat transfer theory and the very concept of thermal conductivity itself. Here, too, is a need for challenging thermal conductivity measurements at micron and nanometer scales. In this thesis, we describe and demonstrate two techniques that combined are capable of measuring the key thermal transport properties in all of these regimes.

We adapt the 3ω method—widely used for rigid, inorganic solids—as a reusable sensor to measure k of soft biological samples, two orders of magnitude thinner than conventional tissue characterization methods. Analytical and numerical studies quantify the error of the commonly used “boundary mismatch approximation” of the bi-directional 3ω geometry, confirm that the generalized slope method is exact in the low-frequency limit, and bound its error for finite frequencies. The bi-directional 3ω measurement device is validated using control experiments to within ± 2% (liquid water, std. dev.) and ± 5% (ice). Measurements of mouse liver cover a temperature range from -69 oC to + 33 oC. The liver results are independent of sample thicknesses from 3 mm down to 100 μm, and agree with available literature for non-mouse liver to within the measurement scatter.

Next, we focus the laser spot 1/e^2 radius in TDTR measurements down to single micron length scales to measure quasi-ballistic thermal transport at length scales where Fourier’s law breaks down. We present an in-depth discussion of the instrumentation and provide comprehensive analyses of system sensitivities to all experimental parameters. The system is first validated on sapphire and single crystal silicon control samples. We then measure two nano-grained Si samples (550 nm and 76 nm average grain size) and two SiGe alloys (1% and 9.9% Ge concentration), representing two classes of silicon-based materials with qualitatively different phonon scattering physics. All samples are 5 mm x 5 mm x 0.5 mm or larger. Sub-diffusion measurements are performed on all samples using 1/e^2 laser spot radii down to 1.6 μm. Apparent thermal conductivity suppressions ranging from 18% to 76% are observed at room temperature, indicating that while most of the heat in sapphire, Si, and nano-grained Si is carried by phonons with mean free paths of a couple microns or less, much of the heat in SiGe alloys is still carried by phonons with mean free paths up to a few tens of microns at room temperature. We present a discussion of the microscale origins of this suppressed thermal conductivity and its physical interpretation, addressing some common misconceptions. Our results show that alloying and nanostructuring shift the spectral phonon mean free path distributions in opposite directions. Alloying skews the phonon distribution toward long mean free paths, increasing k suppression at small length scales, while nanostructuring skews the distribution toward short mean free paths, reducing k suppression.

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