Disc-like copper vias fabricated in a silicon wafer: Design for reliability

Simple formulas have been obtained for the evaluation of the 1) elastic stability of thin-and-large-diameter ("disc-like") copper vias fabricated in a silicon wafer and subjected, at elevated temperatures, to thermally induced compression, as well as of the level of the 2) cumulative stresses in an array of vias. Based on the computed data, we have concluded that, when the spacing between the vias in a via array is twice as large as the via diameter, the maximum cumulative tensile stress in the silicon wafer could be assessed by multiplying the "hoop" pressure due to a single via by the factor of 2.25.