Non-fourier Thermal Conduction In Nano-scaled Electronic Structures

When very fast phenomena and small structure dimensions are involved, the classical law of Fourier becomes inaccurate. A more sophisticated model is then needed to describe the thermal conduction mechanisms in a physically acceptable way. In this paper the according diffusion equation is solved for a nano-scaled semiconductor substrate, in order to gain physical insight in the problem. Analytical solutions for the temperature and heat flux distributions are presented. The complex thermal impedance and thermal step response of the structure are discussed. The most remarkable fact is that the temperature inside the substrate can go below the ambient temperature for a short amount of time. The results also clearly demonstrate the wave character of the heat propagation and the analogy with RLC transmission lines