Least-Squares Parameter Estimation Algorithm for a Microelectrothermal Bridge Circuit

A least-squares parameter estimation algorithm is designed to extract the thermal conductivity of metallic nanowires using a nanofabricated microelectrothermal test structure. The device is a thermal analog of a bridge circuit, such as is commonly used to measure electrical impedance. A resistive heater is positioned symmetrically between two temperature sensors. A nanowire array extends from the heater to one sensor, unbalancing the bridge temperatures. The least-squares cost function exploits the underlying symmetry of the thermal bridge circuit, reducing sensitivity to parasitic thermal conductances and other uncertain parameters. The algorithm is demonstrated on a series of aluminum nanowire arrays with varying nanowire widths. The results are shown to be consistent with predictions made using the electron thermal transport analogy.