Thermal boundary resistance predictions with non-equilibrium Green's function and molecular dynamics simulations

Abstract

The non-equilibrium Green's function (NEGF) method with Büttiker probe scattering self-energies is assessed by comparing its predictions for the thermal boundary resistance with molecular dynamics (MD) simulations. For simplicity, the interface of Si/heavy-Si is considered, where heavy-Si differs from Si only in the mass value. With Büttiker probe scattering parameters tuned against MD in homogeneous Si, the NEGF-predicted thermal boundary resistance quantitatively agrees with MD for wide mass ratios. Artificial resistances that plagued NEGF calculations in homogeneous systems so far are absent in the present NEGF approach. Spectral transport information result from NEGF without transformations in its natural representation. The spectral results show that the scattering between different phonon modes plays a crucial role in thermal transport across interfaces.Semiconductor nanodevices such as quantum cascade lasers, LEDs and thermoelectric devices are typically composed of several semiconductor materials 1-4 . Scattering of thermal energy carriers at the interface between two materials results in thermal boundary resistance 5 . The size of the thermal boundary resistance was previously reported 6 to be comparable to that of pure materials with lengths of a few to tens of nanometers. Predicting the thermal boundary resistance gives important insight into the device physics and enables design improvements. Often, molecular dynamics (MD) is used to model the thermal boundary resistance and reproduce experimental data 7 . Inelastic phonon scattering is included in MD simulations through the anharmonicity of the interatomic potential 8 . The non-equilibrium Green's function (NEGF) method 9 is widely accepted as one of the most consistent methods for electronic quantum transport in nanodevices 10,11 . In particular for predicting stationary device physics, NEGF is potentially more attractive than MD given that it is a spectral approach when setup in energy space. When electrons and phonons are both solved in the NEGF framework, interparticle interactions and energy and momentum transfer in e.g. self-heating or thermoelectric situations can be described on equal footing with the predictions of the respective particles' propagation 12 . For phonon transport, however, the NEGF method has been used predominantly in the coherent (harmonic) regime due to the fact that the inclusion of incoherent scattering such as phonon-phonon decay usually requires solving polarization graphs in the self-consistent Born approximation which entails a large numerical load 13 . Coherent NEGF based on the Landauer approach has been plagued by artificial interface resistances in homogeneous systems 6 .In this work, a numerically efficient method to solve phonon transport in the NEGF framework including phe- * ) These authors contributed equally to this work, email: chu72@purdue.edu nomenological phonon scattering with Büttiker probes is presented and benchmarked against MD. When solved for homogeneous systems, this NEGF method yields vanishing ...

Applications and Impacts of Nanoscale Thermal Transport in Electronics Packaging

“…Copyright 2020 American Chemical Society. transmission functions from AMM, DMM, AGF, or phonon wave-packet method [71,257,[267][268][269][270][271][272][273]. Within the framework of MD methods, nonequilibrium MD (NEMD) [274][275][276] and interface conductance modal analysis [115,143,[277][278][279][280][281][282][283] are usually applied to predict h BD .…”

“…However, it is very difficult to include anharmonicity in Landauer approach, and the consideration of detailed interface structure or interface bonding strength in AMM or DMM is very hard to implement. Recently, there are several studies of considering anharmonicity in AGF [270,279], but there are still some limitations like high computational costs and inaccuracy from estimated scattering rate at interfaces. At interfaces between two crystalline materials, because of the growth limitation, the crystalline quality of one or both of the materials near the interface is usually not very good or the interfacial bonding is not very strong from different growing methods, like evaporation [262], CVD [115,280], and atomic layer deposition [281,284].…”

Quantum mechanical modeling of anharmonic phonon-phonon scattering in nanostructures

“…(27). Here we keep the convention of using local energy density to characterize the local temperature in nonequilibrium transport as currently done in the heat transport community [21,[67][68][69].…”

“…Very few works [43,44,[62][63][64][65][66] directly take into account the anharmonic phonon-phonon scattering, yet often consider few-atom systems like the atomic chain or junction [43,44,62,63], and single-unit-cell interface [66]. An indirect treatment of incoherent phonon scattering was also proposed by the Büttiker probe approach [67][68][69] inspired by its counterpart in electron NEGF, yet it relies on fitting the anharmonic scattering rates with empirical expressions. The challenge in NEGF modeling of anharmonic heat transport comes from not only the difficulty in numerical implementation, but also the less established theoretical formalism.…”

High thermal conductive copper/diamond composites: state of the art

“…Classical lattice dynamical theory is quite powerful to make prediction; we mainly adopt this perspective to elucidate this problem. The relatively rigorous approaches such as Molecule dynamics simulation and non-equilibrium Green's function method require accurate atomic-level interface boundary information plus huge computational expenses, which are not included in this review but can be found in other works [27,[82][83][84][85].…”