Effect of interface adhesion and impurity mass on phonon transport at atomic junctions

Abstract

With the characteristic lengths of electronic and thermal devices approaching the mean free paths of the pertinent energy carriers, thermal transport across these devices must be characterized and understood, especially across interfaces. Thermal interface conductance can be strongly affected by the strength of the bond between the solids comprising the interface and the presence of an impurity mass between them. In this work, we investigate the effects of impurity masses and mechanical adhesion at molecular junctions on phonon transmission via non-equilibrium Green's functions (NEGF) formalisms. Using NEGF, we derived closed form solutions to the phonon transmission across an interface with an impurity mass and variable bonding. We find that the interface spring constant that yields the maximum transmission for all frequencies is the harmonic mean of the spring constants on either side of the interface, while for a mass impurity, the arithmetic average of the masses on either side of the interface yields the maximum transmission. However, the maximum transmission for each case is not equal. For the interface mass case, the maximum transmission is the transmission predicted by a frequency dependent form of the acoustic mismatch model, which we will refer to as the phonon mismatch model (PMM), which is valid for specular phonon scattering outside the continuum limit. However, in the interface spring case, the maximum transmission can be higher or lower than the transmission predicted by the PMM. V

Qualitative link between work of adhesion and thermal conductance of metal/diamond interfaces

“…We attribute the very high conductances measured to the presence of interfacial states due to the strong bonding which has been suggested to impact the transmissivity of an interface 70,73 . This is due to the existence of modes that are intermediate between those of the substrate and metallic layer, which is thought to be beneficial to TBC 71,72,74 .…”

Role of crystal structure and junction morphology on interface thermal conductance

“…2 shows a conductance maximum when the junction mass is the arithmetic mean (AM) of the contact masses. This follows from a generalization of the same result in 1D interfaces with a single atomic junction [27,28]. By Fourier transforming the transverse coordinates, our 3D problem decouples into a sum of 1D chains with IFCs that depend on the transverse wavevector.…”

“…This quantity is related to the escape rate of a phonon into the contacts and is given by Γ k ⊥ = 2ωρv k ⊥ , with ρ the mass density A similar generalization from its 1D counterpart [27,28] leads us to conclude that in an abrupt interface where interfacial bonding is the only variable, conductance is maximized when the force constant is the harmonic mean of the contact force constants. In the same fashion, we can generalize other 1D results to 3D interfaces [29].…”

Thermal conductance of strongly bonded metal-oxide interfaces

“…Alternatively, several theoretical studies have predicted that the transmission probability can be reduced by a small amount if the stiffness of interfacial bonds is made larger than the stiffness of the bonds of the two constituent materials. 35,36 To our knowledge, a reduction in G due to overly stiff interfacial bonds has not been experimentally observed.…”

“…9,10,21,[35][36][37] In other words, weak interfacial bonding significantly lowers the probability that phonons that impinge on an interface will transmit to the other side, thereby resulting in a value for G that is determined by the microscopic details of the interface and not the two constituent materials. Alternatively, several theoretical studies have predicted that the transmission probability can be reduced by a small amount if the stiffness of interfacial bonds is made larger than the stiffness of the bonds of the two constituent materials.…”