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Numerical solution of the electromigration boundary value problem under pulsed dc conditions

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3 Author(s)
Xiang Gui ; Department of Electrical Engineering, University of Alberta, Edmonton, Alberta T6G 2G7, Canada ; Dew, Steven K. ; Brett, Michael J.

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The one‐dimensional electromigration boundary value problem under pulsed dc conditions is numerically investigated by utilizing the transmission‐line matrix modeling method. A perfectly blocking boundary, where void formation and failure occur, is assumed at one end of an interconnection line. At the other end, two physically plausible boundary conditions are considered. From the design‐rule point of view, an approach is proposed to convert conveniently the pulsed stress into an equivalent dc stress that would produce electromigration damage at a similar rate. Based on the fundamental diffusion‐drift model, we show that the vacancy buildup behavior under a pulsed dc stress γp can be described accurately by the dc stress γdc scaled according to the duty factor r of the current pulse, namely, γdc=rγp. This study also represents a theoretical confirmation for the (jr)-2 dependence of the pulsed electromigration failure (where j is the current density), which has been observed in a number of experimental studies. © 1996 American Institute of Physics.

Published in:

Journal of Applied Physics  (Volume:80 ,  Issue: 9 )