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Studies of possible localization of phonons in nanomaterials have gained importance in recent years in the context of thermoelectricity where phonon-localization can reduce thermal conductivity, thereby improving the efficiency of thermoelectric devices. However, despite significant efforts, phonon-localization has not yet been observed experimentally in real materials. Here we propose that surface-roughness dominated nanowires are ideal candidates to observe localization of phonons, and show numerically that the space and time evolution of the energy generated by a heat-pulse injected at a given point shows clear signatures of phonon localization. We suggest that the same configuration might allow experimental observation of localization of phonons. Our results confirm the universality in the surface-roughness dominated regime proposed earlier, which allows us to characterize the strength of disorder by a single parameter combining the width of the wire as well as the mean height of the corrugation and its correlation length.
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Experimental observation of highly reduced thermal conductivity in surface-roughness dominated silicon nanowires have generated renewed interest in low-dimensional thermoelectric devices. Using a previous work where the scattering of phonons from a rough surface is mapped to scattering from randomly situated localized phonons in the bulk of a smooth nanowire, we consider the thermal current across a nanowire for various strengths of surface disorder. We use non-equilibrium Greens function techniques that allow us to evaluate the thermal current beyond the linear response regime, for arbitrary cold and hot temperatures of the two semi-infinite connecting leads. We show how the surface-roughness affects the frequency dependence of the thermal current, eventually leading to a temperature dependent reduction of the net current at high temperatures. We use a universal disorder parameter to describe the surface-roughness as has been proposed, and show that the dependence of the net current on this parameter provides a natural explanation for the experimentally observed differences between smooth vs rough surfaces. We argue that a systematic study of the thermal current for different values of the temperature difference between the two sides of a surface-roughness dominated nanowire for various strengths of disorder would help in our understanding of how best to optimize the thermoelectric efficiency.
We analyze, both theoretically and numerically, the temperature dependent thermal conductivity k{appa} 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 k{appa} 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 k{appa} on the diameter d.
Suppressing phonon propagation in nanowires is an essential goal towards achieving efficient thermoelectric devices. Recent experiments have shown unambiguously that surface roughness is a key factor that can reduce the thermal conductivity well below the Casimir limit in thin crystalline silicon nanowires. We use insights gained from the experimental studies to construct a simple analytically tractable model of the phonon-surface roughness interaction that provides a better theoretical understanding of the effects of surface roughness on the thermal conductivity, which could potentially help in designing better thermoelectric devices.
Andos model provides a rigorous quantum-mechanical framework for electron-surface roughness scattering, based on the detailed roughness structure. We apply this method to metallic nanowires and improve the model introducing surface roughness distribution functions on a finite domain with analytical expressions for the average surface roughness matrix elements. This approach is valid for any roughness size and extends beyond the commonly used Prange-Nee approximation. The resistivity scaling is obtained from the self-consistent relaxation time solution of the Boltzmann transport equation and is compared to Prange-Nees approach and other known methods. The results show that a substantial drop in resistivity can be obtained for certain diameters by achieving a large momentum gap between Fermi level states with positive and negative momentum in the transport direction.
A modeling approach, based on an analytical solution of the semiclassical multi-subband Boltzmann transport equation, is presented to study resistivity scaling in metallic thin films and nanowires due to grain boundary and surface roughness scattering. While taking into account the detailed statistical properties of grains, roughness and barrier material as well as the metallic band structure and quantum mechanical aspects of scattering and confinement, the model does not rely on phenomenological fitting parameters.
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