Universality of phonon transport in nanowires dominated by surface roughness

Abstract

We analyze, both theoretically and numerically, the temperature dependent thermal conductivity κ of two-dimensional nanowires with surface roughness. Although each sample is characterized by three independent parameters -the diameter (width) of the wire, the correlation length and strength of the surface corrugation -our theory predicts that there exists a universal regime where κ is a function of a single combination of all three model parameters. Numerical simulations of propagation of acoustic phonons across thin wires confirm this universality and predict a d 1/2 dependence of κ on the diameter d. arXiv:1802.03281v1 [cond-mat.dis-nn]

Non-equilibrium phonon transport in surface-roughness dominated nanowires

“…where N imp is the number of impurities over which the averaging is done, u u q q -is related to the roughness power spectrum of the surface corrugation, and d q n ( ) and D p q w n --( ) are Green's functions corresponding to the localized and propagating phonons, respectively. From experiments, the following model for u u q q emerges [17,35,36]:…”

“…For simplicity, we assume the phonon-phonon coupling parameter to be given by W 0 =1. Because of the universality of the disorder parameter as observed in [36], the surface roughness can be characterized by a single dimensionless parameter…”

“…In our model, the width of the localized phonon Γ is an independent phenomenological parameter. However since it arises from the mapping of the surface roughness, it also reflects the universality in terms of disorder, as shown in [36], where it was argued that…”

“…For definiteness, in this plot we choose ζ=11.3 as a fixed disorder. As noted in [36], experiments on silicon nanowires with ELE surface disorder [15,17] have one sample with h=2.3, l c =8.9 and d=77.5 in units of nm, corresponding to ζ=11.3. We therefore choose this value as a representative number that can be achieved in real experiments.…”

“…This, in turn, would allow more detailed theoretical predictions for phonon transport in these systems. Following [36], we take advantage of the fact that the effects of surface disorder, characterized by the mean surface corrugation height h, a roughness correlation length l c as well as the diameter d of the wire, can be described by a single combination of the parameters. We show how the temperature difference ΔT between the leads affects the frequency-dependent current J(ω) as well as the net current J net for a given value of this universal disorder parameter.…”