This paper discusses computational simulations of the evolution of stresses and deformation in unpassivated and SiO2-passivated Al lines on Si substrates. The finite element model accounts for elastic-plastic deformation in the Al lines during etching, passivation, and subsequent thermal cycling, by recourse to a generalized plane strain formulation within the context of a unit cell with appropriately constrained boundary conditions. The effects of different controlled variations in thermal history, and in the width, height, spacing, and yield behavior of the Al lines are analyzed; all these factors are seen to have potentially strong effects on the evolution of stresses within the lines. The predictions of the computations presented in this work are amenable for direct comparisons with experiments of curvature evolution along and perpendicular to the lines upon patterning, passivation, and thermal loading. The predicted stresses in metal interconnects can be directly used for reliability modeling purposes.
Exact Solution of Thermoelastic Problem for a One-Dimensional Bar without Energy Dissipation
