Ong, Z.-Y. (2024). Effect of boundary roughness on the attenuation of specular phonon reflection in graphene. Physical Review B, 109(18). https://doi.org/10.1103/physrevb.109.184207
Abstract:
The reduced phonon specularity p from boundary roughness scattering plays a major role in
the lower thermal conductivity in semiconducting and insulating nanowires and films. Although
the well-known Ziman formula p = exp(−4σ2q2x), where σ and qx denote the root-mean-square
boundary roughness and the normal component of the incident phonon wave vector, respectively,
and its variants are commonly used in the literature to estimate how roughness attenuates p, their
validity and accuracy remain poorly understood, especially when the effects of mode conversion
cannot be ignored. In this paper, we investigate the accuracy and validity of the more general
Ogilvy formula, from which the Ziman formula is derived, by comparing its predictions to the p
values computed from Atomistic Green’s Function (AGF) simulations for an ensemble of rough
boundaries in single-layer graphene. The effects of phonon dispersion, incident angle, polarization,
mode conversion, and correlation length are analyzed. Our results suggest that the Ogilvy formula
is remarkably accurate for 0 < qx <π 4σ when the lateral correlation length L is large or the phonon
is at normal incidence. At large qx in the short-wavelength limit, the qx-dependence of p becomes
significantly weaker. In the large-L limit, the numerical results suggest the existence of a minimum
p for short-wavelength phonons, given by p ∼ p0 exp(−π2/4), where p0 is the baseline specularity
for the ideal boundary.
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Funding Info:
This research / project is supported by the Agency for Science, Technology and Research - MTC Programmatic Grant - Advanced Models for Additive Manufacturing (AM2)
Grant Reference no. : M22L2b0111
This research / project is supported by the Agency for Science, Technology and Research - Science and Engineering Research Council (SERC) - Polymer Matrix Composites Program
Grant Reference no. : A19C9a004