Multi-scale Simulations of Nonequilibrium and Non-local Thermal Transport

2019-01-03T15:58:17Z (GMT) by Zexi Lu
Metallic components and metal-dielectric interfaces appear widely in modern electronics and the thermal management is an important issue. A very important feature that has been overlooked in the conventional Fourier's equations analyses is the nonequilibrium thermal transport induced by selective electron-phonon (e-p) coupling and phonon-phonon (p-p) coupling. It signi cantly affects many processes such as laser heating and ignoring this phenomenon can lead to wrong or misleading predictions. On the other hand, as devices shrink into nano-scale, heat generation and dissipation at the interfaces between different components start to dominate the thermal process and present a challenge for thermal mitigations. Many unresolved issues also arise from interfaces, such as the unexpected high interfacial thermal conductance (ITC) at metal-diamond interfaces. Both of these require a deep understanding of the physics at interfaces.

Therefore in this work, I present multi-scale simulations in metals/dielectrics and interfaces based on two-temperature model (TTM) and establish the new multitemperature model (MTM). The methods are combined with Fourier's Law, molecular dynamics (MD), Boltzmann transport equations (BTE) and implemented to predict the thermal transport in several materials and interfaces where e-p coupling and p-p coupling are important. First-principles studies based on density functional theory (DFT) are also presented as predictive approaches to acquire the properties, as well as investigating the new physical phenomenon of non-local e-p coupling in metals. This research seeks to provide general, sophisticated but also simple simulation approaches which can help people accurately predict the thermal transport process. It also seeks to explore new physics which cannot be captured and predicted by conventional analyses based on Fourier's Law and can advance our understanding as well as providing new insights in the current thermal analysis paradigm.

The rst part of this thesis focuses on the non-equilibrium thermal transport in metals and across metal-dielectric interfaces based on TTM. First of all, nonequilibrium thermal transport in metal matrix composites (MMC) is investigated. Metal particle is usually added to polymer matrix for enhanced thermal performance. Here we apply TTM calculations and manifest a \critical particle size" above which the thermal conductivity of the composite material can be enhanced. MD simulations are performed to predict the thermal properties. TTM-Fourier and TTM-BTE calculations are conducted as comparisons. The widely used Au-SAM (self-assemblymonolayers) material pair is chosen to demonstrate our models. For a 1-D SAMAu-SAM sandwich system, the two calculation approaches present almost identical results, and the critical particle size is 10.7 nm. A general interpretation of thermal transport in sandwiched metal thin lms between two dielectric materials is also presented. It is found that when the lm thickness is on the order of several nanometers, due to strong e-p non-equilibrium the thermal transport is dominated by phonons
and electrons hardly contribute.

Then the e-p non-equilibrium thermal transport across metal-dielectric interfaces is investigated using TTM-MD. One possible explanation to the unexpected ITC at metal-diamond interfaces is the cross-interface e-p coupling mechanism, which is based on the hypothesis that electrons can couple to phonons within a certain distance rather than just those at the same location. Therefore we extend TTM-MD by modifying its governing equation to a non-local integral form. Two models are proposed to describe the coupling distance: the \joint-phonon-modes" model and the \phonon-wavelength" model. A case study of thermal transport across Cu-Si interfaces is presented, and both models predict similar coupling distances of 0.5 nm in Cu and 1.4 nm in Si near the interfaces. The cross-interface e-p coupling can increase the ITC by 20% based on our models. Based on the results, we construct a new mixed series-parallel thermal circuit. It is shown that such a thermal circuit is essential for understanding metal-nonmetal interfacial transport, while calculating a single resistance without solving temperature pro les as done in most previous studies is generally incomplete.

Inspired by the previous work, we investigate further into the physics of nonlocal e-p coupling. First-principles calculations based on DFT is used due to their predictive feature without assumptions or adjustable parameters. By calculating the e-p coupling in metal lms of different sizes, we nd that e-p coupling has size effect which can only be explained by a non-local coupling picture. Results show that in Al, electrons and phonons can couple to each other in a range of up to 2 lattice-constants, or 0.8 nm. The coupling strength between electrons and phonons in adjacent atomic layers still has 75% of that in the same layer. Comparative studies are also performed on Cu and Ag. Results show that their non-local e-p coupling is not as signi cant as in Al, with coupling distances of 0.37 nm for Cu and 0.49 nm for Ag. Similar results in Cu and Ag also indicate that materials with similar electronic structures have similar non-local e-p coupling properties.

In TTM, it is assumed that phonons are in thermal equilibrium and have a common temperature. In the second part of this thesis we go beyond TTM to investigate the non-equilibrium between phonons as well. TTM is extended to a general MTM with e-p coupling strength for each phonon branch. An averaged scattering lattice reservoir is de ned to represent p-p scattering. The thermal transport process in single-layer graphene under constant and pulse laser irradiation is investigated. Results show that the phonon branches are in strong non-equilibrium. A comparison with TTM reveals that MTM can increase the thermal conductivity prediction by 50% and the hot electron relaxation time by 60 times. We also perform MTM simulations on Si-Ge interfaces to investigate the effect of non-equilibrium thermal transport on ITC. Results show that thermal non-equilibrium between phonons will introduce additional resistance at the interfaces, which is similar with e-p non-equilibrium's impact on ITC at metal-dielectric interfaces.