Disparate quasiballistic heat conduction regimes from periodic heat sources on a substrate

Abstract

ABSTRACT:We report disparate quasiballistic heat conduction trends for periodic nanoscale line heaters deposited on a substrate, depending upon whether measurements are based on the peak temperature of the heaters or the temperature difference between the peak and the valley of two neighboring heaters. The degree of quasiballistic transport is characterized by the effective thermal conductivities of the substrate which are obtained by matching the diffusion solutions to the phonon Boltzmann transport equation (BTE) results. We find that while the ballistic heat conduction effect based on the peak temperature diminishes as the two heaters become closer, it becomes stronger based on the peak-valley temperature difference. Our results also show that the collective behavior of closely spaced heaters can counteract the nonlocal effects caused by an isolated nanoscale hot spot. These results are relevant to thermal conductivity spectroscopy techniques under a) To whom correspondence should be addressed. Electronic mail: gchen2@mit.edu 2 development and also have important implications for understanding nonlocal heat conduction in integrated circuits and carbon nanotube array thermal interface materials.

Spectral mapping of thermal conductivity through nanoscale ballistic transport

“…We have performed such detailed simulations and discussions in Ref. 11. As the distance between adjacent heaters becomes shorter than the phonon mean free path, additional size effects are introduced [11]. This effect is properly accounted for by the suppression function S(/D, D/L), which is extracted by comparing experimental data and firstprinciples simulation results on Si, as explained in the manuscript.…”

Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation

“…This integral equation is easily solved with a Laplace transform, and the temperature profile can be solved for with an inverse transform as obtained by Hua and Minnich [25]. Other methods to solving the BTE is to either obtain a numerical solution by solving the integral equation by finite differences [8,24] or by utilizing Monte Carlo techniques [23,33,34]. We depart from these established approaches by treating the unknown temperature distribution as a variational function and rewrite Eq.…”

“…The thermal conductivity accumulation function has been utilized as an elegant metric for understanding which MFP phonons contribute predominantly to thermal transport in a material [13][14][15]. Various experimental tools such as time-domain thermoreflectance (TDTR) [4,6,8,12,16,17], frequency-domain thermoreflectance (FDTR) [18,19], and transient thermal grating (TTG) [3,5,7,20] techniques have been extensively utilized recently in order to probe and observe nondiffusive transport by using ultrafast time scales or ultrashort length scales and gain key insight into the material's MFP spectrum.When the length scales in a system become comparable to the MFPs in a material, the effective thermal conductivity is reduced compared to its bulk, diffusive limit value [21,22]. A suppression function S ω is used to quantify this reduction or suppression of thermal conductivity, defined as…”

“…In particular, there has been a growing interest recently in developing numerical and analytical solutions to the BTE to model thermal transport in phonon spectroscopy experiments [1][2][3][4][5][6][7][8][9][10][11][12] to extract phonon mean free path (MFP) distribution. The thermal conductivity accumulation function has been utilized as an elegant metric for understanding which MFP phonons contribute predominantly to thermal transport in a material [13][14][15].…”

Heating-frequency-dependent thermal conductivity: An analytical solution from diffusive to ballistic regime and its relevance to phonon scattering measurements

“…30,47 This is trivial for the gray MFT solution since there is only one ω to consider. However, in the general non-gray case the corresponding BTE can only be solved numerically, using techniques such as Monte Carlo 47 , discrete ordinates 34,48 , finite volumes 49 , or the LBTE method 18 . On the other hand, analytical solutions have great advantages for understanding the essential physics and reducing computational time.…”