Knowledge of the mean-free-path distribution of heat-carrying phonons is key to understanding phononmediated thermal transport. We demonstrate that thermal conductivity measurements of thin membranes spanning a wide thickness range can be used to characterize how bulk thermal conductivity is distributed over phonon mean free paths. A noncontact transient thermal grating technique was used to measure the thermal conductivity of suspended Si membranes ranging from 15-1500 nm in thickness. A decrease in the thermal conductivity from 74-13% of the bulk value is observed over this thickness range, which is attributed to diffuse phonon boundary scattering. Due to the well-defined relation between the membrane thickness and phonon mean-free-path suppression, combined with the range and accuracy of the measurements, we can reconstruct the bulk thermal conductivity accumulation vs. phonon mean free path, and compare with theoretical models.

The thermal boundary conductances between c-axis oriented highly ordered pyrolytic graphite and several metals have been measured in the temperature range 87–300 K and are found to be similar to those of metal–diamond interfaces. The values obtained are indicative of the thermal interface conductance between metals and the sidewalls of multiwall carbon nanotubes (CNTs) and, therefore, have relevance for the accurate characterization of the thermal properties of CNTs, graphene, and the design and performance of composite materials and electronic devices based on these structures. A modified diffuse mismatch model is used to interpret the data and extract the phonon transmissivity at the interface. The results indicate that metal–graphite adhesion forces and interfacial mixing effects play important roles in determining the boundary conductance.

Heat conduction in semiconductors and dielectrics depends upon their phonon mean free paths that describe the average travelling distance between two consecutive phonon scattering events. Nondiffusive phonon transport is being exploited to extract phonon mean free path distributions. Here, we describe an implementation of a nanoscale thermal conductivity spectroscopy technique that allows for the study of mean free path distributions in optically absorbing materials with relatively simple fabrication and a straightforward analysis scheme. We pattern 1D metallic grating of various line widths but fixed gap size on sample surfaces. The metal lines serve as both heaters and thermometers in time-domain thermoreflectance measurements and simultaneously act as wire-grid polarizers that protect the underlying substrate from direct optical excitation and heating. We demonstrate the viability of this technique by studying length-dependent thermal conductivities of silicon at various temperatures. The thermal conductivities measured with different metal line widths are analyzed using suppression functions calculated from the Boltzmann transport equation to extract the phonon mean free path distributions with no calibration required. This table-top ultrafast thermal transport spectroscopy technique enables the study of mean free path spectra in a wide range of technologically important materials.

The relaxation of an one-dimensional transient thermal grating (TTG) in a medium with phonon-mediated thermal transport is analyzed within the framework of the Boltzmann transport equation (BTE), with the goal of extracting phonon mean free path (MFP) information from TTG measurements of non-diffusive phonon transport. Both gray-medium (constant MFP) and spectrally dependent MFP models are considered. In the gray-medium approximation, an analytical solution is derived. For large TTG periods compared to the MFP, the model yields an exponential decay of grating amplitude with time in agreement with Fourier's heat diffusion equation, and at shorter periods, phonon transport transitions to the ballistic regime, with the decay becoming strongly non-exponential. Spectral solutions are obtained for Si and PbSe at 300 K using phonon dispersion and lifetime data from density functional theory calculations. The spectral decay behaviors are compared to several approximate models: a single MFP solution, a frequency-integrated gray-medium model, and a “two-fluid” BTE solution. We investigate the utility of using the approximate models for the reconstruction of phonon MFP distributions from non-diffusive TTG measurements.

Articles you may be interested inEffect of van der Waals forces on thermal conductance at the interface of a single-wall carbon nanotube array and silicon AIP Advances 4, 127118 (2014); 10.1063/1.4904099 Influence of diamond surface termination on thermal boundary conductance between Al and diamondSynthetic diamond has potential as a heat spreading material in small-scale devices. Here, we report thermal conductance values at interfaces between aluminum and diamond with various surface terminations over a range of temperatures from 88 to 300 K. We find that conductance at oxygenated diamond interfaces is roughly four times higher than at hydrogen-treated diamond interfaces. Furthermore, we find that Al grain structure formation is not strongly dependent on diamond surface chemistry, which suggests that interfacial bonding influences thermal conductance. The results reported here will be useful for device design and for advancing models of interfacial heat flow.