Heat generation transport in micro and sub- micro scale in electronic packaging - Ooi, Chun Keang (2003)
Energy exchange takes place in extremely small dimension and time scale in the process of micro-electronic packaging. For fast heating response. Fourier conduction law is inadequate to explain the phenomena. Thus. compensate the Fourier law, named as Non-Fourier law. Non-Fourier law, based on two-phase-lag model has introduced two from classical Fourier heat conduction equation when applied to rapid heating process. These assumptions are finite thermal wave propagation speeds and time of equilibrium between electron and lattice. From previous research on dual phase-lag model, different governing equations have to employ for different boundary conditions, but with a proposed two phase-lag model only a single governing equation is adequate. These phase lags are the phase lag for temperature gradient (xT) and heat flux (xq). A finite element method and Runge-Kutta method are applied in the development of threelower temperature values as compared with one-dimensional and two-dimensional model. The application of two phase-lag model to very-large-scale-integrated (VLSI) interconnect thermal analysis, illustrates that circuit open failure occurs at current pulse of 300ns. An implementation of Asymptotic Waveform Evaluation (AWE) scheme in first and second order ordinary differential equation shows a break through as compared with conventional methods. This advanced, powerful and efficient scheme shows excellent results compared with Runge-Kutta method, central difference method and ANSYS* 5.4, and is several orders faster.