Electro-thermal considerations dedicated to 3D integration; noise coupling

3D integration is considered the most promising solution to overcome current challenges in planar technologies. As an emerging technology, electrical compact models are notably required for 3D interconnects, including Through-Silicon Via (TSV), to accurate 3D-system performances. More generally, analytical substrate extraction methods, relying on the Transmission Line Matrix (TLM) method, or the use of Green kernels, are proposed to model multilayers substrates on an electrical, but also thermal, points of view. An important problem for designers of complex heterogeneous circuits, combining digital and analog parts, is also to predict the perturbations coming from commutating logical gates, flowing through the substrate to reach some sensitive analog blocks. We then present, in this paper, an application of a stochastic model based on Markovian processes; the digital switching activity is modeled as functions defined as Markov Chains. The final goal is to grasp the noise power density of such perturbations. As an example, we extract an actual interference signal resulting from the modulation of parasitic injected waveforms for instance into some circuit supply driven by the discrete stochastic process.