A transmission-line theory for heat conduction in multilayer thin films

This paper presents a general formulation for the heat conduction problem in multilayer thin film structures with laser-induced surface-heating, using the transmission-line techniques. The transient heat diffusion equation in the space-time domain is transformed into the spectral domain by using the Laplace transform with respect to time and the Hankel transform with respect to the radial coordinate. Equivalent transmission-line models are utilized to describe the heat diffusion in the direction perpendicular to the plane of the layers and to obtain the transformed temperature. Examples of applications of this technique to obtain space-time distributions of temperature for various thin film structures with different boundary conditions are given. For the evaluation of the temperature excursions, a technique associated with the inverse Laplace transform has been developed to improve the convergence of the inverse Hankel transform. Numerical results are presented to illustrate the effectiveness of this transmission-line approach, using examples of diamond films on silicon substrates which are currently of great interest in the literature