Temperature distribution on thin-film metallizations

Abstract

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.