Fractal description of dendrite growth during electrochemical migration

Abstract

In this paper, the usability of fractal description of dendrites in failure analysis is discussed. Dendrites grow during electrochemical migration (ECM) causing failures in the form of short circuits between conductive wirings and leads in microcircuit interconnection and packaging elements, especially on printed wiring boards. The parameters of the dendrite growth process are influenced by functional (electrical) and environmental conditions as well as by the material composition of metallisation stripes and surface finishes. Mathematically, dendrites can be described as fractals and therefore they can be characterised with fractal dimension values calculated by various computerised pattern processing methods. We have found relationship between chemical composition of surface finishes and fractal dimensions of dendrites grown from them. This hypothesis has been proved in three steps: first, dendrites were grown by simple water drop test (WDT) series in order to get good quality, reproducible test specimens; in the second step, optical photomicrographs were taken from the dendrite structures and finally these micrographs were analysed using computerised algorithms. The result is that fractal dimensions are material specific and so they can be used to describe the material composition. This is not only an important theoretical result in understanding dendrite growth mechanisms, but it also has a useful practical aspect: short detection and optical inspection can be combined with simple calculations to identify materials involved into electrochemical migration failures without making more complicated elemental chemical analysis.