Electrical resistance of metallized via−holes

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Abstract
The resistance of a via−hole laser−drilled through an alumina substrate depends on the hole geometry, the type of probe, the deposition technique, and the properties of the film. If the walls of the hole constitute a truncated cone, the resistance is Rs/π[ln(d2/d1)]{1/4 + [h/(d2 − d1)]2}1/2, where Rs is the sheet resistance, h is the substrate thickness, and d1 and d2 are the diameters. Increasing the larger diameter helps by (a) reducing the rim−to−rim resistance, (b) reducing the ’’spreading’’ resistance, and (c) making the walls more accessible for metallization. A four−point probe, on the other hand, measures the rim−to−rim resistance as approximately (Rs/π) ln cosh (h/d), where d is an average diameter. If the hole is partially bare, the four−point reading will depend on probe orientation. A comparison of calculation and measurement indicates Rs in the hole to be between two and forty times Rs outside, depending on the thickness. Electrical probing of broken−open holes showed this to be due to thickness differences, not roughness or ledge resistance.

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