Thermal boundary resistance predictions from molecular dynamics simulations and theoretical calculations

Abstract

The accuracies of two theoretical expressions for thermal boundary resistance are assessed by comparing their predictions to independent predictions from molecular dynamics ͑MD͒ simulations. In one expression ͑R E ͒, the phonon distributions are assumed to follow the equilibrium, Bose-Einstein distribution, while in the other expression ͑R NE ͒, the phonons are assumed to have nonequilibrium, but bulk-like distributions. The phonon properties are obtained using lattice dynamics-based methods, which assume that the phonon interface scattering is specular and elastic. We consider ͑i͒ a symmetrically strained Si/Ge interface, and ͑ii͒ a series of interfaces between Si and "heavy-Si," which differs from Si only in mass. All of the interfaces are perfect, justifying the assumption of specular scattering. The MD-predicted Si/Ge thermal boundary resistance is temperature independent and equal to 3.1ϫ 10 −9 m 2-K/ W below a temperature of ϳ500 K, indicating that the phonon scattering is elastic, as required for the validity of the theoretical calculations. At higher-temperatures, the MD-predicted Si/Ge thermal boundary resistance decreases with increasing temperature, a trend we attribute to inelastic scattering. For the Si/Ge interface and the Si/heavy-Si interfaces with mass ratios greater than two, R E is in good agreement with the corresponding MD-predicted values at temperatures where the interface scattering is elastic. When applied to a system containing no interface, R E is erroneously nonzero due to the assumption of equilibrium phonon distributions on either side of the interface. While R NE is zero for a system containing no interface, it is 40%-60% less than the corresponding MD-predicted values for the Si/Ge interface and the Si/heavy-Si interfaces at temperatures where the interface scattering is elastic. This inaccuracy is attributed to the assumption of bulk-like phonon distributions on either side of the interface.

Effect of lattice mismatch on phonon transmission and interface thermal conductance across dissimilar material interfaces

“…The interface thermal conductance across a strained lattice-matched Si/Ge interface is calculated using nonequilibrium MD (NEMD) simulation following the direct method for the calculation of interface thermal conductance in Ref. 10. The average lattice constant of Si and Ge along the interface direction is used to form the interface and the average stress perpendicular to the interface direction is relaxed to zero.…”

“…In the past two decades, molecular dynamics (MD) simulations have been employed extensively to study the interface thermal conductance across various material interfaces, [5][6][7][8][9][10][11][12][13] such as Kr/Ar, 7 Si/In, 11 carbon nanotube/Si, 12 Si/polymer 9 and PbTe/GeTe. 13 A relatively good understanding of the reduced lattice thermal conductivity in nanostructured materials due to the thermal boundary resistance has been obtained.…”

Relationship of thermal boundary conductance to structure from an analytical model plus molecular dynamics simulations

“…Care has been taken to distinguish our work from previous studies. For instance, we will significantly expand the time scale used in the previous MD simulations (up to only several ns) [21][22][23][24][25][26][27] to more than 100 ns so that highly-converged MD data can be generated for verifying the analytical relationships between Kapitza conductance and structural features. In addition, we will ensure the generality of the results by using three different interatomic potentials.…”

“…On the other hand, MD simulations have been successfully used to directly calculate thermal boundary resistance [21][22][23][24][25][26][27] . These studies established the effects of sizes [28][29][30][31] , temperature 21,26,32 , mass differential of the two layers 21,26,27 , lattice mismatch between layers 26,27 , interfacial defects 26,27 , stiffness of the materials, and bond strength at the interface 22,24,32,33 . While the MD data provided knowledge significantly beyond that achieved from analytical models (e.g., the acoustic mismatch model and the diffuse mismatch model 2,9 ), our current understanding of the thermal boundary conduc-tance is far from the material/structure design requirement.…”

Phonon transport across a vacuum gap

“…14,20 We evaluate β L (κ κ κ, ν, T ) and β R (κ κ κ, ν, T ) at a temperature of 300 K using a model based on the Boltzmann transport equation under the relaxation-time approximation and the Fourier law. 14 Because bulk extents of silicon are considered on either side of the vacuum-gap, the bulk phonon properties that we previously predicted using harmonic and anharmonic lattice dynamics calculations 21,22 are used to evaluate Eqs.…”