Under the conditions of high current densities and high temperatures in metals, there is momentum transfer between conducting electrons and diffusing metal atoms. This causes gradual drift of the ions in the metal in the direction of electron flow and result in mass transport. This process of material transfer is called Electromigration(EM). The affect of EM in integrated circuits is open circuit(void) or short circuit(Hillock) failures.
The mean time to failure(MTTF) of an interconnect is the expected time that it will operate before the first failure. MTTF of the interconnect under constant current stress and temperature, subjected to EM affects, is given by Black’s equation as

(1)  

where
Activation energy for failure(0.5 to 0.7 eV for Al)
Constant based on interconnect properties and geometry. Calculated emprically
Current density in the metal interconnect
Constant vary between 1 ~ 7
Boltzmann constant
Temperature in K

Eq (1) indicates that temperature and current density are the key factors that contribute to electromigration mechanism. Electromigration mechanisms are accelerated by current density as well as temperature.

Factors affecting Electromigration

• Temperature: There will be changes in the interconnect temperature due to power dissipation of neighbouring interconnects or transistors on the chip, self heating of interconnect due to current flow, poor thermal conductivity to the ambient. Whatever the cause of temperature rise, electromigration occurs and reduces MTTF.

  Once a void begins to develop it enters positive feedback to reduce the width of metal wire. A void causes the metal width to reduce, means increase in local current density. As a result of it due to Joule heating the temperature of the wire increases. The rise in temperatures accelerates the growth of the void, and this cycle continues, and eventually it results in open circuit.

  

  Thermal acceleration loop during electromigration¹
  
• Metal Width: Wider metal lines have lower current density for the same current, hence have high resistance to electromigration. But if the width of the metal line is reduced below the grain size of the metal material, increases the resistance again to EM. Example is Bamboo wires[more…]

  

• Metal Length: There is a lower limit on the length of metal line below which EM does not occur for a given current density and material choice. This length is called Blech length. Any interconnect length below Blech length can be treated as EM proof.

Rules of Thumb

• Physical layout tips to avoid EM
• avoid 90 degree corners on high current nets
• even distribution of multiple vias

Bibliography

Signal Electro-migration Analysis and Fixing Research in IC Compiler
Electromigration and copper metallization