Phonon relaxation time reconstruction from transient thermal grating experiments and comparison with density functional theory predictions

Abstract

Phonon relaxation time and free path distributions are reconstructed from experimental measurements on a two-dimensional transient thermal grating and compared with density functional theory (DFT) results for silicon. The reconstruction is performed using the inverse problem formulation of Forghani et al. [Phys. Rev. B 94, 155439 (2016)]. The discrepancies observed between reconstructed and DFT results are analyzed in terms of the ability of each set of data to reproduce the experimental temperature relaxation profiles; the reconstructed data are found to predict temperature profiles in closer agreement with the experimental data than the DFT results, possibly due to discrepancies between the actual material and the idealized model studied in the DFT calculations. The reconstructed phonon properties accurately predict temperature relaxation profiles at grating length scales smaller than those spanned by the experimental data. This is a very important feature since in a variety of experimental setups, including the one providing the data in the present study, measurements are not available at all scales spanned by the material free paths.

Comparison on two ways of phonon spectral property reconstruction from thermal spectroscopy experiment

“…The discussions provided previously in [7,9,11], and more importantly, in the previous section, show that F (Λ), regardless of the method being used to reconstruct it and its accuracy, is not able to predict the material thermal behavior in all regimes, and the submicron regime in particular, which is of interest presently. This is in sharp contrast with the relaxation-times function which is related to the system thermal response through a direct, one-to-one relationship.…”

“…Here, without loss of generality, we have assumed U to be a set of parameters that allows different branches of the relaxation-times function to take the form of a piece-wise linear function with three segments as a function of the phonon frequency; this is the same parameterization that has been used previously in [7,9,11]. This objective function attempts to find free path-dependent thermal conductivity distribution functions f(Λ) that match the true thermal conductivity distribution function by searching in the parameter space U.…”

“…The study of phonon dynamics in the context of nanoscale solid-state heat transport has received considerable attention [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. One area of significant interest is the study of phonon relaxation-time and free path distributions [12][13][14][15][16][17][18][19].…”

“…However, such approaches have yet to rise to a stature level where they can replace experimental results, in part due to their failure to consistently reproduce experimental observations [4]. Another popular (alternative) class of approaches relies on extracting material constitutive information from thermal spectroscopy experiments [7][8][9][10][11][12][13]. However, the analysis of thermal spectroscopy data remains a challenging task.…”

“…As noted above, in response to the failure of κ eff -based methods to provide accurate reconstructions at all scales, in [7,9,11] we developed and extensively validated an optimization-based methodology for directly reconstructing phonon relaxation-times from thermal spectroscopy data. In this work, we attempt to address some more fundamental questions, such as the uniqueness of reconstructed quantities (e.g., F (Λ)), as well as their ability to reproduce the experimental results.…”