Current carrying capacity of dendrites

Dendrites are sometimes found on electronic hardware during failure analysis or trouble shooting activities. Problems due to dendrite formation can vary from catastrophic failure to occasional electronic glitches. If a dendrite is thought of as a fuse in a circuit, then it is apparent that it can have, depending on size, a wide range of current carrying capability. Mathematical modeling and experimental analyses were conducted to determine the reasons for the wide range of observed behavior. Mathematical modeling indicates that the resistivity of the dendrite and the thermophysical characteristics of the substrate on which it is grown determine its current carrying capacity. More specifically, the modeling indicates that maximum dendrite size and time to failure are determined by the power loss within the dendrite and the rate at which heat can be transferred away from the dendrite. Small dendrites are stable and can grow until they reach a size at which internal heat generation cannot be accommodated by the heat loss due to conduction through the substrate. Dendrites in low voltage applications on substrates with high thermal diffusivity are more likely to lead to failures with high power loss, whereas dendrites in high voltage applications on low thermal diffusivity substrates (e.g. tin on glass/epoxy circuit board material) are more likely to lead to high resistance shorts. Experimental results and failure analysis observations agree qualitatively and semi-quantitatively with the results of the idealized dendrite model