Anomalous thermal behaviour in small electronic devices: non-uniformity and overshoot in dynamic temperature distributions

Abstract

This paper presents a theoretical investigation of the temperature distributions generated by a small heat source mounted on or embedded in semiconductor material. The dynamic thermal behaviour of the structures is studied in the frequency domain using phasor notation for the temperature and heat flux fields. Both classical and hyperbolic thermal conductions are considered. The latter accounts for the finite heat propagation speed, which is necessary for accurately describing very fast transitions. Although a uniform power density is applied, the temperature distribution inside the source is spatially non-uniform. As is already well known, this even holds for steady state conditions. For high frequencies, however, the maximum magnitude (i.e. largest oscillations) of the temperature occurs near the edges and corners of the heat source, rather than in the centre where it could intuitively be expected. This anomalous behaviour is observed for a wide variety of configurations, ranging from a simple 1D analytical slab model to numerical results for a 3D multi-layered electronic package. The classical theory clearly underestimates the edge effect, particularly for submicrometre structures. The substantial deviation from the distributions obtained by non-Fourier theory illustrates that special care should be taken when analysing fast heat transfer in small electronic devices.