Line-Width Dependence of Stress in Passivated Al Lines During Thermal Cycling

Abstract

ABSTRACTWe have obtained theoretical stress-temperature curves for passivated Al lines undergoing thermal cycling. A finite element plane-strain cross-sectional analysis with a time-dependent constitutive property for Al, based on equations for discreteobstacle controlled plasticity, was performed. The parameters for this Al constitutive relation were obtained by fitting with experimentally obtained stress-temperature curves for Al blanket films on silicon. Theoretical results agree well with the x-ray diffraction experimental data of Besser et al.1 Using a time-dependent property for Al helps match the data better than a time-independent property. Theoretical stress-temperature curves were also obtained for the longitudinal, transverse, and normal stress components in aluminum lines for line-widths ranging from 0.5 to 10 µm. The hysteresis of the stress-temperature curve of Al gets less as the line-width gets smaller. All stress components in the Al line change substantially with linewidth for the same oxide thickness.