Analysis of thermal behavior in multi-layer metal thin films based on hyperbolic two-step model

Abstract

This work theoretically analyzes non-equilibrium thermal behavior in multi-layer metal films with the hyperbolic microscopic two-step model. It is necessary to solve the coupled energy equations or an equation containing higher-order mixed derivatives in both time and space for such problems. The difference in the relaxation times of dissimilar materials introduces the complexity and causes some mathematical difficulties at the interfaces. A numerical scheme is developed in this work and is applied to the examples in double-layer and triple-layer films with an ultrashort pulse heating. To evidence the efficiency of the present numerical scheme, the analytical solutions for the illustrated examples are presented. The effects of the thermal property ratios of dissimilar metals on heat transfer are investigated. It lends the theoretical insight to hyperbolic microscale heat transfer in multi-layer metal films. Results show the difference in the thermal properties of dissimilar materials and the hyperbolic nature of heat transfer in electron gas sufficiently affect the thermal behavior in multi-layer films at early times.