Analytical Calculation of Metallized-Hole Resistance

The resistance of metallized holes which connect diffcrent levels of metallization in an electronic package, is calculated by solving the 3-dimensional Laplace equation. The metallized hole considered is cylindrical with current flowing in and out through conducting lines. Four configurations are studied. Extensive tables giving normalized values of resistance haw; been obtained through computer calculation. The dimensions of the metallized hole and conductors are normalized with respect to the height of the hole, and in this way a wide range of geometries is dealt with. One important observation from these calculations is the strong dependence of the resistance on the geometry of the conductors carrying the current in and out of the metallized hole. An average current density can be obtained through the use of an equivalent conductor resistance for the metallized hole.