Stress Distribution and Mass Transport Along Grain Boundaries During Steady-State Electromigration

Abstract

ABSTRACTStress distribution and mass flux in the plane of each grain boundary within a polycrystalline thin-film conductor have been calculated during electromigration for zero flux divergence (steady state) and various boundary conditions. Steady state, representing a balance between the (applied) electric and (induced) stress driving forces, is assumed to develop after a short transient time. Boundary conditions at the intersection of grain boundaries with the top and bottom conductor surfaces (surface junctions) and with the conductor edges (edge junctions) are assumed to be of two types: open (flux passes freely) and closed (zero flux). Flux is assumed to pass freely at the intersection of grain boundaries with each other (triple Junctions). Several grain boundary configurations are considered, including individual boundaries, single triple junctions, and combinations thereof, assuming that bottom surface junctions (conductor/ substrate interface) are closed and that top surface junctions are either open (bare conductor) or closed (passivation layer). Results clearly show the formation of incipient holes and hillocks near the intersection of triple junctions and/or closed (blocked) edge junctions with open surface junctions.