In-plane thermal conductivity measurement on nanoscale conductive materials with on-substrate device configuration

Abstract

In this study, we measure the in-plane thermal conductivity of palladium (Pd) nanowire with varying length (3-50 m) and width (100-250 nm). The bridges are fabricated by electron beam lithography with an on-substrate measurement configuration. The measurements are performed on substrates with 190 nm and 2.9 μm thick thermal oxide using a 4-probe steady-state DC Joule heating method, and several suspended structure are also prepared to investigate the accuracy of the on-substrate results. For the on-substrate measurements, the thermal conductivity is estimated for short nanowires assuming the magnitude of the heat loss to the substrate from measurements of longer nanowires. As a result, the measured thermal conductivity is 30  5 W/mK for suspended short nanowires at room temperature, and the estimated thermal conductivity for the on-substrate samples are consistent with this value. The measurements on the substrate with 2.9 μm oxide result in small variations between samples (± 5 W/mK), while the results on 190 nm thick oxide has a larger variation and uncertainty (> ± 20 W/mK) due to the uncertainty in the magnitude of the heat loss to the substrate. Sufficient measurement accuracy is only achieved if the heat loss to the substrate can be estimated or measured with high accuracy.

Continuous Carbon Nanotube-Based Fibers and Films for Applications Requiring Enhanced Heat Dissipation

“…The emissivity of the samples is 0.86 ± 0.02 measured through a calibration procedure described in the Supporting Information. Heat transfer along the specimen is governed by the steady-state 1D heat diffusion equation: 32,33 α…”

“…Heat transfer along the specimen is governed by the steady-state 1D heat diffusion equation: , with the boundary condition of where k , A , L , and α are the thermal conductivity, cross-sectional area, length, and TCR of the specimen, respectively, h ′ is the convective heat loss per unit length to the air (with units of W m –1 K –1 ), T ( x ) is the temperature profile along the length of the specimen, T 0 is the room temperature (295.15 K), T L /2 is the temperature of the ends of the specimen, p ′ = I 2 R 0 / L is the heat generation per unit length in the specimen, and I and R 0 are current amplitude and the electrical resistance of the specimen at T 0 , respectively. The analytic solution of eq is where m 2 = ( h ′ – αp ′)/ kA , when h ′ – αp ′ > 0.…”

Enhanced Electrical and Thermal Conduction in Graphene-Encapsulated Copper Nanowires

“…To analyze the thermal transport in these NWs, we use a heat diffusion equation 35 that incorporates the heat generation from Joule heating, the heat flow along the NW and the heat loss to the substrate (Supporting Information, Figure S8). Joule heating-induced relative change in resistance can be expressed using a closed-form expression 36 for on-substrate NWs…”