Evaluation of the Phonon Mean Free Path in Thin Films by Using Classical Molecular Dynamics

Abstract

A non-equilibrium molecular dynamic (NEMD) study has been performed to evaluate the phonon mean free path (MFP) of a solid material. Solid argon with a Lennard-Jones (L-J) potential is selected as a simulation material. The thermal conductivity of a thin film plays an important role in the design of nano-electro-mechanical systems (NEMS) or micro-electro-mechanical systems (MEMS) since heat removal from these devices is a crucial factor for their intended proper operations. The values calculated by using molecular dynamics (MD) simulations are compared with the available bulk experimental data when possible. It is confirmed that there is apparently a size effect on the thermal conductivity, which indicates that the microscale system has a lower thermal conductivity than that of the bulk material in the heat transfer direction. The dependence of the thermal conductivity on the system size is the result of a reduction in the phonon mean free path (MFP) as the system size becomes microscaled, and the MD simulations can be used to predict the phonon MFP of such a system.

Thermal boundary resistance at an epitaxially perfect interface of thin films

“…Time interval for an iteration was selected as Δt=1.0x10 -15 s (=1 fs) and, for the cut-off length of an intermolecular interaction, 3.5 σ AR was used. We confirmed from our previous studies that those parameters produced the calculation data with small fluctuations [16,25,30]. The properties of argon used in a simulation are σ AR =3.4 Å, m AR =6.634x10 -26 kg, and ε AR =1.67x10 -21 J [28,29].…”

“…An intermolecular distance was determined to maintain a system to be under a freestanding state, which means a system to be in the zero stress state during a simulation. When the average temperature of a system is 40 K, the intermolecular length of 1.1115 σ AR provides a freestanding state [3,15,16,24,25].…”

“…Although the fixed BC at both ends seems not to be realistic, we confirmed that this BC did not affect the thermal conductivity of a thin film compared with other BCs in our previous study [30] and, within our experience, it was the simplest BC in the NEMD simulation for the calculation of a thermal conductivity. The x-y plane perpendicular to the heat flow direction was set as a periodic boundary condition (PBC), which behaviors just as an actual thin film [15,16,24,25,30]. The velocity scaling method was used for the temperature control of both TCLs and the equation of a motion was integrated by the Velocity Verlet method [26][27][28][29].…”

“…The reduced thermal conductivity resulting from an extremely thin thickness was reported in many other studies [11][12][13][14][15], which mentioned that the MEMS/NEMS devices may fail their intended performances if the thermal characteristics related with a highly reduced size are not properly considered in the design or the fabrication of them. Recently, Choi et al proved that the thermal conductivity with a film thickness could be accurately calculated from the phonon mean free path (MFP) in a bulk state, l BULK , determined by the molecular dynamics (MD) simulation [16]; furthermore, their approach to evaluate a thermal conductivity with the film thickness can be directly applicable to experiment.…”

“…the completion of the C-M model. As same as our earlier studies [3,15,16,24,25], solid argon is selected as a target material because it is the typical Lennard-Jones (L-J) potential material; it is the simplest type of a potential; moreover, there is no need to consider the contribution by free electrons to the thermal conductivity since argon is a non-conductor, which means that the energy transportation is occurred only by a lattice vibration. It has been found from this study that the TBR is explicitly dependent on the potential ratio as well as the mass ratio between two different materials.…”