Dimension- and shape-dependent thermal transport in nano-patterned thin films investigated by scanning thermal microscopy.

Scanning thermal microscopy (SThM) is a technique which is often used for the measurement of the thermal conductivity of materials at the nanometre scale. The impact of nano-scale feature size and shape on apparent thermal conductivity, as measured using SThM, has been investigated. To achieve this, our recently developed topography-free samples with 200 and 400 nm wide gold wires (50 nm thick) of length of 400-2500 nm were fabricated and their thermal resistance measured and analysed. This data was used in the development and validation of a rigorous but simple heat transfer model that describes a nanoscopic contact to an object with finite shape and size. This model, in combination with a recently proposed thermal resistance network, was then used to calculate the SThM probe signal obtained by measuring these features. These calculated values closely matched the experimental results obtained from the topography-free sample. By using the model to analyse the dimensional dependence of thermal resistance, we demonstrate that feature size and shape has a significant impact on measured thermal properties that can result in a misinterpretation of material thermal conductivity. In the case of a gold nanowire embedded within a silicon nitride matrix it is found that the apparent thermal conductivity of the wire appears to be depressed by a factor of twenty from the true value. These results clearly demonstrate the importance of knowing both probe-sample thermal interactions and feature dimensions as well as shape when using SThM to quantify material thermal properties. Finally, the new model is used to identify the heat flux sensitivity, as well as the effective contact size of the conventional SThM system used in this study.