Temperature distribution on thin‐film metallizations

The time‐dependent temperature distribution of a thin‐film stripe has been solved rigorously using two successive Laplace transforms on both time and coordinate. For a good conducting stripe with a δ‐shaped crack it is shown that the temperature distribution can be very adequately described by the steady‐state solution provided only that the time scale involved is of the order of 10−3 sec or longer. No localized hot spot is possible, for whatever reasons, for a good conductor. However, if heat generation outpaces heat conduction, as would be the case for a poor conductor, a localized temperature becomes quite realizable. Finally, if stripe cracking is developed via grain‐boundary grooving processes somewhere along the stripe, in particular near the anode, void formation there is simply a natural consequence of the temperature‐grandient effect.