A Comprehensive TCAD Approach for Assessing Electromigration Reliability of Modern Interconnects

Interconnect reliability dependence on fast diffusivity paths

“…The capacity of the grain boundary to accept trapped vacancies is expressed by the stress-dependent equilibrium concentration [6,7] …”

“…3 we show characteristic curves of the EM related vacancy concentration build-up for an extended simulation time. Here a parametrized continuum-level EM model is used [6]. All three curves are obtained for the same layout and operating conditions, but they differ because of a different copper microstructure.…”

“…The continuum Eqs. (6) are solved, until a stress threshold (r th ) for void nucleation is reached at some triple point (c.f. Fig.…”

“…If the stress is above the threshold value (r > r th ), the free energy monotonically decreases with the void volume, and the energy barrier vanishes. If we now assume an adhesion free patch with a radius of 10 nm (about 20 atoms), we obtain r th % 344 MPa [6].…”

Physically based models of electromigration: From Black’s equation to modern TCAD models

“…The impact of the complex structure of modern interconnects and general constraints imposed by the surrounding layers on the stress evolution cannot be obtained. Therefore, the development of TCAD approaches has become more and more important, as they have allowed numerical simulations of complete two- [16,[37][38][39][40][41][42] and three-dimensional [43][44][45] interconnect structures taking into account various physical effects related to electromigration in a consistent manner.…”