Size and frequency dependence of effective thermal conductivity in nanosystems

Abstract

A single phenomenological expression is proposed to describe thermal transport in a wide variety of nanoscale devices. Size and frequency dependence is studied for some nanosystems from the diffusive to the ballistic regimes. In a single expression we obtain the effective thermal conductivity of cross-plane thin layer experiments where the device has a size limitation in the direction of the flux, and nanowire and in-plane experiments where the size limitation is in a transversal direction from the flux in terms of the effective size of the device. For nonzero frequencies, the size dependence has a maximum which becomes narrower at higher frequencies. For a given size, the effective thermal conductivity decreases for increasing frequency. These features may be limited in the design of nanoscale devices, because of the accumulation of dissipated heat.