Direct Measurement of Thermal Conductivity of Gold from Meso- to Nano-Scale

Abstract

Abstract Body: Conductors having at least one dimension at the nanoscale have properties that differ substantially from their bulk counterparts. In particular, electrical resistivity increases significantly when size is reduced while thermal conductivity (κ) decreases. These factors present a critical technological barrier to miniaturization, since the former increases self-heating when current is driven while the latter limits dissipation of that heat from device-active regions. Despite the prominent role of metallic nanostructures in current and future electronics and photonics, large gaps exist in understanding the influence of “size effects” on thermal characteristics at small dimensions. In particular, there is a paucity of direct measurements of thermal conductivity for technologically-relevant materials. This study focuses on development and test of a method for directly measuring κ for conducting nanofilms and nanowires. We report on design, fabrication, test, and application of this approach to 50 and 100 nm thick evaporated gold structures with lateral dimensions ranging from 74 to 720 nm, thereby spanning the nano- to meso-scale. Measurements are carried out at ambient room and 100° C temperatures, i.e., in the standard operating range of low-power electronics. A decrease in κ is observed as gold thickness is reduced. At large lateral width, corresponding to the microscale and analogous to thin films, κ values are found to be 200 and 280 W/mK for thicknesses of 50 and 100 nm, respectively (room temperature). These are to be compared with the accepted value of 317 W/mK for κ of bulk gold. In addition, as the width is reduced, for either thickness, a dramatic decrease in κ is observed beginning at ~ 300 nm width. For the smallest nanowire investigated, 50 nm in thickness and 74 nm in width, a value of κ = 56 W/mK is obtained. At higher test temperature, the thermal conductivities are found to decrease, as expected. The decrease in κ with diminishing size are primarily attributed to grain boundary and surface/interface scattering of electrons—that conduct most of the heat in gold—and quantitatively interpreted using the Boltzmann Transport Equation (BTE).