Logarithmic sensitivity ratio elucidates thermal transport physics in multivariate thermoreflectance experiments

Abstract

We mathematically derived a sensitivity-based method that identifies the thermal transport physics and parameters suitable for multivariate nonlinear fits in a frequency-domain thermoreflectance (FDTR) experiment. Modern electronic devices often consist of heterogeneous nanolayers with multiple unknown thermal transport properties. However, simultaneous fitting in a single experiment for these unknown parameters will produce unreliable results if they are correlated. Current methods to identify such correlations are unreliable. This unreliability has impeded the accuracy and speed of characterizing the unknown thermal properties of such multilayer stacks. Our proposed logarithmic sensitivity ratio (LSR) analysis can evaluate the feasibility of fitting a pair of unknown parameters and clarify the governing thermal transport physics. The effectiveness and convenience of this analysis were studied using Monte Carlo simulations and actual FDTR experiments for fitting up to three unknown parameters. The principle behind this method can be extended to other techniques where multivariate fits are needed.