Finite Element Calculations of Thermal Stresses in Passivated and Unpassivated Lines Bonded to Substrates

Abstract

ABSTRACTThermal stresses in passivated and unpassivated aluminum lines bonded to substrates have been calculated using the MARC finite element code. Stresses in the unpassivated lines increase with increasing line width, with increasing substrate rigidity, and with decreasing distance from the substrate. Edge effects become significant for small line widths. Stresses in passivated lines increase with decreasing aspect ratio, with increasing passivation thickness, and with increasing Young's modulus of the passivation. Allowing plastic deformation to occur in the lines homogenizes and reduces the stresses. The calculated stresses in passivated lines are compared to recent measurements of stresses in encapsulated aluminum lines. The measured values are about a factor of four smaller than the calculated stresses, indicating that some deformation process besides plasticity, such as voiding or cracking, must have occurred to relieve the stresses.