Interfacial thermal resistance in van der Waals (vdW) stacks, such as MoS2/graphene heterostructures, is a critical factor influencing thermal management in nanoscale devices. The weak vdW interactions between layers lead to unique thermal transport phenomena, necessitating multiscale modeling approaches to bridge atomic-scale interactions with macroscopic thermal properties. Understanding the role of interlayer vibrational modes and twist-angle effects is essential for optimizing thermal conductance in these systems. Experimental validation, particularly through Raman thermometry, provides crucial insights into the accuracy of these models.

At the atomic scale, ab initio methods like density functional theory (DFT) are employed to calculate phonon dispersion relations and interatomic force constants. These calculations reveal the vibrational modes contributing to heat transfer across the interface. For instance, in MoS2/graphene stacks, low-frequency shear and layer-breathing modes dominate interfacial thermal transport due to their coupling across the vdW gap. DFT-based simulations have shown that the thermal conductance of such interfaces can range from 10 to 30 MW/m²K, depending on the overlap of phonon density of states between the layers. However, ab initio methods are computationally expensive and limited to small system sizes, necessitating coarser-grained approaches for larger scales.

Molecular dynamics (MD) simulations extend these insights by modeling larger systems with empirical potentials. Classical MD, using potentials like the Lennard-Jones or Tersoff forms, captures the anharmonicity and temperature-dependent effects absent in DFT. Non-equilibrium MD (NEMD) simulations, where a temperature gradient is imposed, directly compute the interfacial thermal resistance. Studies on twisted MoS2/graphene interfaces reveal that misalignment angles significantly alter thermal transport. At twist angles below 5°, the thermal conductance can drop by up to 40% compared to aligned stacks due to phonon scattering from moiré superlattices. The interlayer conductance in these systems typically falls between 15 and 50 MW/m²K, consistent with experimental observations.

To bridge the gap between atomistic and continuum scales, Boltzmann transport equation (BTE) approaches are employed. The BTE, solved numerically or via relaxation-time approximations, quantifies the contribution of different phonon modes to heat transfer. Diffuse mismatch models (DMM) and atomistic Green's function (AGF) methods are often used to predict interfacial resistance. The AGF method, for example, has demonstrated that high-frequency optical phonons in MoS2 contribute minimally to cross-plane heat transfer, while acoustic modes in graphene play a dominant role. These findings align with experimental measurements showing that interfacial conductance is largely insensitive to temperature above 100 K, indicating a saturation of phonon scattering channels.

Continuum models, such as finite element analysis (FEA), incorporate the effective thermal conductivity extracted from lower-scale simulations into device-level predictions. These models are particularly useful for designing thermal management solutions in multilayer devices. However, they rely heavily on accurate inputs from atomistic simulations to account for interfacial resistance. For instance, FEA simulations of MoS2/graphene heterostructures have shown that interfacial resistance can lead to a 20-30% reduction in effective thermal conductivity compared to ideal, resistance-free interfaces.

Experimental validation of these models is primarily achieved through Raman thermometry, a non-contact optical technique. By measuring the temperature-dependent shift of Raman peaks, the local heating and thermal resistance at the interface can be quantified. For MoS2/graphene stacks, experiments report interfacial thermal conductance values of 20-35 MW/m²K, in good agreement with theoretical predictions. Twist-angle-dependent measurements further confirm the reduction in thermal transport at small misalignment angles, with a 30% decrease observed at 3° twist compared to aligned interfaces. These results underscore the importance of interlayer coupling and phonon mode matching in vdW heterostructures.

The interplay between interlayer modes and twist angles is a key determinant of thermal resistance. Phonon transmission spectra reveal that low-frequency modes are highly sensitive to interfacial alignment, while high-frequency modes are more robust to twist angles. This frequency-dependent behavior explains why thermal conductance plateaus at higher temperatures, where anharmonic scattering reduces the relative contribution of low-frequency modes. Additionally, the presence of defects or adsorbates at the interface can further suppress thermal transport, as evidenced by MD simulations showing a 15-20% reduction in conductance with oxygen functionalization.

Future directions in modeling interfacial thermal resistance include integrating machine learning potentials to accelerate ab initio-level accuracy in large-scale MD simulations. Furthermore, advanced experimental techniques like ultrafast pump-probe spectroscopy could provide deeper insights into phonon dynamics at interfaces. The combination of multiscale modeling and precise experimental validation will continue to refine our understanding of thermal transport in vdW stacks, enabling the design of efficient thermal management solutions for next-generation nanodevices.

In summary, multiscale modeling approaches—from ab initio to continuum methods—provide a comprehensive framework for predicting interfacial thermal resistance in vdW heterostructures. The role of interlayer phonon modes and twist-angle effects is critical, with experimental data from Raman thermometry serving as a vital benchmark. These insights are instrumental for optimizing thermal performance in emerging electronic and optoelectronic applications.