A grain structure based statistical simulation of temperature and current density dependence of electromigration

Although current density exponents and activation energies are well-known for the elemental processes (like void nucleation due to electromigration generated stress) there is no consensus on which apparent activation energy or current density exponent values should be used in reliability estimates for realistic line structures comprising regimes of both bamboo and polycrystalline sections. In this contribution a Monte-Carlo approach was used to generate realistic-like line structures, and their electromigration lifetimes were simulated. For a given grain structure distribution, the stress evolution along the line was simulated, letting voids nucleate and grow until the largest one reached the specified critical size, resulting in a “failure”. By repeating this process for various current densities and temperatures, it was possible to extract the apparent activation energies and current density exponents from the simulation data