Unifying first-principles theoretical predictions and experimental measurements of size effects in thermal transport in SiGe alloys

Abstract

In this work, we demonstrate the correspondence between first principle calculations and experimental measurements of size effects on thermal transport in SiGe alloys. Transient thermal grating (TTG) is used to measure the effective thermal conductivity. The virtual crystal approximation under the density functional theory (DFT) framework combined with impurity scattering is used to determine the phonon properties for the exact alloy composition of the measured samples. With these properties, classical size effects are calculated for the experimental geometry of reflection mode TTG using the recently-developed variational solution to the phonon Boltzmann transport equation (BTE), which is verified against established Monte Carlo simulations. We find agreement between theoretical predictions and experimental measurements in the reduction of thermal conductivity (as much as ∼ 25% of the bulk value) across grating periods spanning one order of magnitude. This work provides a framework for the tabletop study of size effects on thermal transport. * gchen2@mit.edu 1 arXiv:1704.01386v2 [cond-mat.mes-hall]

Thermal diffusivity determination using heterodyne phase insensitive transient grating spectroscopy

“…These directions are indicated by the manufacturer and confirmed by comparing the measured surface acoustic wave velocity to values computed for these surface directions using elastic theory [20,21]. In materials with phonon-dominated thermal transport, several authors have shown that thermal diffusivities measured using short-wavelength excitations, like those used in TGS, will be smaller than bulk diffusivities [4,11]. In brief, this reduction occurs due to the exclusion of long-wavelength ballistic phonons from the heat transport process.…”

“…In brief, this reduction occurs due to the exclusion of long-wavelength ballistic phonons from the heat transport process. For SiGe alloys, Huberman et al have implemented a variational approach to solving the Boltzmann transport equation (BTE) for shortwavelength, 1D periodic excitations [11]. That method allows for the calculation of the expected value of the effective thermal diffusivity in pure Ge comfortably including the normal operating range of TGS test wavelengths of Λ = 1−10 µm.…”

“…where A and B are constants, to uniquely determine the thermal diffusivity of the sample in question. This method has been used to study thermal transport in a variety of systems including thick PbTe films [1], bulk SiGe alloys [11], and bulk GaAs [26]. However, as mentioned above, measurements of this type do not retain any information related to acoustic properties as those properties are uniquely contained in u(t).…”

“…Optically heterodyne amplified transient grating spectroscopy (TGS) measurements are a powerful tool used in the study of surface thermal transport [1], elastic mechanical performance [2], film properties [3][4][5][6], and a variety of other dynamic processes [7][8][9]. TGS has proven a particularly useful tool for studying the properties of heterostructures [10] as well as short-wavelength, nonballistic heat transport in semiconductors [11]. Recently, TGS has become of particular interest in the study of the effects of ion irradiation on material properties, as the micron-scale excitations imposed can be tuned to match the length scale of imposed damage profiles [12][13][14][15].…”

“…Given the ability to isolate the reflectivity dynamics in the amplitude grating response, most authors choose this signal character when measuring thermal performance using TGS [1,11]. However, amplitude grating measurements require absolute heterodyne phase calibration and only contain information regarding thermal transport characteristics.…”