Thermal conductivity calculation in Si membranes : a homogeneous non-equilibrium molecular dynamics approach

Abstract

In this work, we calculated the thermal conductivity in the 110 direction of Si membranes with a thickness of a single unit cell (5.431 Angstrom), using the homogeneous non-equilibrium molecular dynamics method. The calculated conductivity using this method for these mem- branes exhibits a size dependence with respect to to the x, y plane dimensions, but shows convergence for sizes larger than L × L with L = 30.72 nm. The conductivity is found to be 61.73 W/m/K. We also employed the spectral decomposition method of heat flux to separate the average contribution of vibrational modes (phonons) to thermal conductivity. This analysis revealed that the major contribution comes from low-frequency modes (f ≤ 4.5 THz). Addi- tionally, decomposing the conductivity into in-plane and out-of-plane components allows us to show that the in-plane components (longitudinal and transverse acoustic modes) are the pre- dominant ones. It was observed that the introduction of periodic defects in these membranes reduces the conductivity value by around 90% . This reduction also depends on the defect’s geometrical shape. We tested circular, square, and equilateral triangle shapes for the same removed material density (different shapes with same area). The reduction is approximately 90% for squares (κ = 6.037 W/m/K) and circles (κ = 6.116 W/m/K), while it is 95% for tri- angles (κ = 3.290 W/m/K). This suggests that the phonon scattering at the defect interface depends not only on the removed material density, as already known in literature, but also on the geometric shape of the inserted defects.