A model of electromigration failure under pulsed condition

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Abstract
A model of electromigration failure under pulsed constant-current excitation is derived. Starting with Black’s expression for electromigration failure under dc conditions, the fractional lifetime consumed per infinitesimal time interval is defined as a function of film temperature. The fractional lifetime consumed per pulse is then computed assuming that temperature in the film is an exponentially increasing function of time while the pulse is on. Damage relaxation during the pulse off time is characterized by a time constant exhibiting the same activation energy as the dc electromigration lifetime. Film temperature during the pulse off time is assumed to be an exponentially decreasing function of time. On the basis of the choice of the time-temperature dependence, the model presented here is strictly valid only when the pulse on time and pulse off time exceed characteristic thermal response time of the film. Application of the model to the experimental conditions of Miller yields good agreement between the predicted and measured lifetime as a function of pulse duty cycle for a pulse repetition rate of 250 kHz.

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