Thermal transport at nanoscale interfaces is a critical area of study in nanoscience, particularly for applications in electronics, thermoelectrics, and photonics. The thermal boundary conductance (TBC) between dissimilar materials, such as metal-dielectric heterostructures, governs heat dissipation and thermal management in nanodevices. Computational methods provide insights into the fundamental mechanisms of interfacial thermal transport, bridging the gap between theoretical models and experimental observations.
One of the earliest theoretical frameworks for understanding TBC is the acoustic mismatch model (AMM). This model treats phonons as plane waves and assumes that thermal resistance arises from the impedance mismatch between two materials. The AMM predicts TBC based on the acoustic properties of the materials, including their densities and sound velocities. The transmission probability of phonons across the interface is derived from the acoustic impedance ratio, given by:
TBC_AMM = (1/4) * ∑ v_i * ρ_i * C_i * α_i
where v_i is the phonon group velocity, ρ_i is the material density, C_i is the specific heat, and α_i is the transmission coefficient for each phonon polarization (longitudinal and transverse). While AMM provides a simplified analytical approach, it often underestimates TBC in real systems due to its neglect of interfacial roughness, anharmonic effects, and inelastic scattering.
To address these limitations, atomistic simulations have become indispensable for studying TBC. Molecular dynamics (MD) simulations, particularly non-equilibrium molecular dynamics (NEMD) and equilibrium molecular dynamics (EMD) with the Green-Kubo method, allow direct computation of heat flux across interfaces. In NEMD, a temperature gradient is imposed across the interface, and the resulting heat flux is measured to compute TBC. For example, simulations of Au-SiO2 interfaces have shown TBC values ranging from 100 to 300 MW/m²K, depending on interfacial bonding and roughness.
The choice of interatomic potentials is crucial in MD simulations. For metal-dielectric systems, embedded atom method (EAM) potentials are often used for metals, while Buckingham or Stillinger-Weber potentials describe dielectrics like SiO2. Cross-interaction parameters must be carefully parameterized to reproduce interfacial bonding. Poorly fitted potentials can lead to unrealistic phonon scattering or overestimated adhesion energies, skewing TBC predictions.
Phonon wave-packet simulations offer another approach, tracking the reflection and transmission of individual phonon modes. These simulations reveal that high-frequency phonons contribute minimally to TBC due to strong scattering, while mid-frequency modes dominate heat transfer. For instance, in Al-Al2O3 interfaces, nearly 70% of heat is carried by phonons below 10 THz, despite the broader phonon spectrum of aluminum.
Recent advances in machine learning potentials (MLPs) have improved the accuracy of TBC predictions. MLPs trained on ab initio data can capture anharmonicity and defect effects more reliably than classical potentials. For example, neural network potentials applied to Cu-diamond interfaces have reproduced experimental TBC values within 10% error, outperforming traditional potentials.
Interfacial defects and mixing play a significant role in TBC. MD studies of rough or alloyed interfaces show that atomic-scale disorder can enhance phonon scattering, reducing TBC by up to 50%. Conversely, chemically bonded interfaces, such as TiN-MgO, exhibit higher TBC due to stronger phonon coupling. The formation of interfacial layers, such as silicides in metal-Si systems, can further modify thermal transport by introducing intermediate phonon modes.
Temperature dependence is another critical factor. At low temperatures (<100 K), TBC follows the AMM trend, scaling with the material-specific heat. Above room temperature, anharmonic effects and umklapp scattering become dominant, leading to a saturation or slight decrease in TBC. For Au-Si interfaces, TBC peaks near 200 K and plateaus at higher temperatures, consistent with experimental observations.
Comparative studies of different metal-dielectric pairs reveal material-specific trends. Noble metals (Au, Ag) generally exhibit lower TBC with oxides than transition metals (Ti, Cr) due to weaker bonding. Covalent interfaces, such as SiC-GaN, show exceptionally high TBC (>500 MW/m²K) owing to phonon spectrum overlap and strong adhesion.
Despite progress, challenges remain in bridging simulations with experiments. Finite-size effects in MD simulations can artificially constrain phonon modes, while experimental measurements are sensitive to interfacial contamination and strain. Multiscale methods combining ab initio phonon calculations with continuum models are emerging as a solution to reconcile these discrepancies.
Future directions include investigating the role of 2D materials in heterostructures, where anisotropic phonon transport and van der Waals interactions introduce new complexities. Additionally, the integration of machine learning for high-throughput screening of interfacial materials could accelerate the discovery of optimal pairs for thermal management applications.
In summary, computational studies of TBC in nanoscale heterostructures have advanced significantly, combining theoretical models like AMM with sophisticated atomistic simulations. These tools provide a deeper understanding of phonon-mediated heat transfer, guiding the design of materials for next-generation thermal management systems.