I'm trying to understand whether the Black's equation is only true for mortal wire / interconnections or it is also applicable to immortal wires (essentially when its $jL$ product is less than $jL_{blech}$ where $j$ and $L$ are the current density and the length of the wire respectively).


  • $\begingroup$ I am sorry but I do not understand what a mortal/immortal wire is. Can you give a link? $\endgroup$
    – anna v
    Jul 15 '13 at 6:45
  • $\begingroup$ @annav Refer to the section "wire length" synopsys.com/Tools/Verification/CapsuleModule/… $\endgroup$ Jul 15 '13 at 7:33
  • $\begingroup$ thanks, but completely out of my data base. I think this should be asked in the electronics.stackexchange if it gets no response here. $\endgroup$
    – anna v
    Jul 15 '13 at 10:57
  • $\begingroup$ "immortal" is not a technical term. I think you are asking "why does electromigration not effect wires shorter than the Blech length?" (To which I do not, unfortunately, know the answer.) $\endgroup$ Jul 15 '13 at 11:54
  • $\begingroup$ @WanderingLogic Thanks for contribution, but what I am asking is, whether the Black's equation gives a correct Mean Time To Failure (MTTF) estimation for the wires which do not suffer from electromigration (e.i. the wires with the $jL$ product smaller than $jL_{blech}$). $\endgroup$ Jul 15 '13 at 23:02

While I'm not an expert on electromigration, it seems obvious to me that the answer is "Black's equation does not apply to very short wires".

  • Black's equation is an empirical model to estimate the MTTF (mean time to failure) of a wire due to electromigration. The equation does not mention length, and so it predicts the same MTTF no matter what the length of the wire.

  • Wikipedia says of the Blech length "Any wire that has a length below this limit will not fail by electromigration."

  • Black's equation predicts that even very short wires will fail due to electromigration, which contradicts the discovery of Mr. Bleck that such wires actually don't fail due to electromigration.


  • Black's equation doesn't apply to wires shorter than the Blech length.

My understanding is that Black's equation is a very useful and practical rule of thumb that was used long before anyone understood the physical mechanisms of eletromigration, and is still used today. Much like Newton's second law ("F=ma") is still used today, even though "F=ma" is known to be incorrect over very small distances or at very high velocities.

R.L. de Orio et. al. have have developed physics-based models to estimate MTTF of a wire. As you might have expected, those models give approximately the same MTTF as Black's equation for long wires in the kind of environment Mr. Black worked in, and a much longer MTTF ("immortal") for very short wires.

R.L. de Orio, H. Ceric, S. Selberherr. "Physically based models of electromigration: From Black’s equation to modern TCAD models" Microelectronics Reliability journal. 2010.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.