Estimation of temperature coefficient of resistance for microfabricated platinum thermometers in thermal conductivity measurements of one-dimensional nanostructures

Abstract

The suspended-microdevice method is widely used in thermal conductivity measurements of one-dimensional nanostructures, in which microfabricated platinum coils are used as thermometers to determine temperature rises of both the heat source and heat sink. The error in the estimated temperature coefficient of resistance (TCR) of thermometers usually dominates the total error in this measurement. In this paper, we compare different methods to calculate TCR of platinum resistance thermometers (PRT) in thermal conductivity measurement of an individual boron nanoribbon performed on the suspended-microdevice setup. Our results show that electrical resistances of PRTs deviate from the Bloch–Grüneisen formula due to the high defect and impurity concentration in the resistance thermometer. This deviation cannot be fully compensated by considering the interference between electron–phonon scattering and electron–impurity scattering. It is also shown that simple numerical differentiation can give an accurate TCR since the random error in the measured electrical resistance is small enough. High-order polynomial fitting can also work well except at the boundary of temperature range.