Modeling of thermal stresses in passivated interconnects

Abstract

Analytical modeling is performed to obtain closed-form solutions for the thermal stresses in passivated interconnects in microelectronic devices. A periodic unit cell of a planar passivated interconnect on a substrate is considered. When the aspect ratio of the cross section of the interconnect line has a limiting value, zero or infinity, closed-form solutions for the volume-averaged thermal stresses in the interconnect can be readily derived. These analytical solutions agree with existing finite element calculations. Using the modified shear lag model, the general closed-formed solutions for the thermal stress distributions in the cross section of the unit cell normal to the interconnect line are derived. Specific results are calculated for the system of Al interconnect lines on Si substrate with SiO2 passivation. The effects of the geometrical parameters in the system (e.g., interconnect aspect ratio, distance between interconnect lines, and passivation thickness) on the thermal stress distributions are examined.