# Impact of limiting dimension on thermal conductivity of one-dimensional silicon phononic crystals

Ryoto Yanagisawa, Jeremie Maire, Aymeric Ramiere, Roman Anufriev, Masahiro Nomura

March 2017
## Abstract

We present experimental and theoretical investigations on the roles of the limiting dimensions, such as the smallest dimension, surface roughness, and density of holes in the reduction of thermal conductivity of one-dimensional phononic nanostructures at temperatures of 4 and 295 K. We discover that the thermal conductivity does not strongly depend on the period of the phononic crystal nanostructures whereas the surface roughness and the smallest dimension of the structure—the neck—play the most important roles in thermal conductivity reduction. Surface roughness is a very important structural parameter in nanostructures with a characteristic length less than 100 nm in silicon. The importance of the roughness increases as the neck size decreases, and the thermal conductivity of the structure can differ by a factor of four, reaching the thermal conductivity of a small nanowire. The experimental data are analyzed using the Callaway–Holland model of Boltzmann equation and Monte Carlo simulation providing deeper insight into the thermal phonon transport in phononic nanostructures.

*Applied Physics Letters* 110, 133108 (2017)