Modeling and uncertainty quantification of non-contact scanning thermal microscopy
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Since its introduction, Scanning Thermal Microscopy (SThM) has been widely used to measure surface temperature and thermal properties of nano-scale materials and structures with high spatial resolution. However, discrepancy exits between the temperature read by the SThM probe and the actual temperature of sample measured. In addition, the temperature of the measured sample can be affected by the presence of the SThM probe. In this thesis work, we used Ansys Fluent to develop a SThM model to establish calibration between the temperature read by the SThM probe and the actual temperature of measurement. The effects of the probe on the temperature of sample is also quantified. We use Bayesian inference to calibrate the unknown thermal conductivities of the polymer (substrate). This model is validated by comparing its predictions with experiment observations. We also quantify the uncertainties in the Quantity of Interest (QoI), the probe tip temperature, due to the uncertainty in the simulation input parameters. This is accomplished by using a generalized polynomial chaos (gPC) formalism. A response surface relating the QoI to model inputs is constructed through stochastic collocation. A Smolyak sparse grid is used to reduce the computation expense. The response surface is sampled based on the PDFs of the input parameters to obtain the PDF of the QoI. We find the uncertainty in the cross-plane thermal conductivity of the liquid polymer and the diameter of the probe tip have large contributions to the overall uncertainty in the QoI.