Thermomechanical Stresses in Copper Films at Elevated Temperature

Abstract

Thermomechanical stresses in metallic films are a root cause for material fatigue which limits the lifetime of electronic devices. Since the yield stress of metals is temperature dependent, plastic deformations during thermal cycling are increased at elevated temperature. This effect reduces the reliability of electronic parts. In order to investigate this problem, a 20μm thick copper film was deposited on a silicon wafer. After annealing at 400°C, the sample was exposed to thermal cycles in the temperature range between room temperature and 600°C. The different values for the CTE of copper and silicon lead to a curvature of the sample. The wafer curvature was measured by a multi-laser beam method. On the basis of the experimental results, a new theoretical model was developed, which describes the stress evolution in the film during thermal cycling. In this investigation, the relation between wafer curvature and film stress is calculated by analogy to a model by Freund [1] which is an improvement to the well known Stoney formula. In addition to the elastic response, the new model considers plasticity of the copper film as well as temperature dependence of creep. It is demonstrated that the model can well describe the experiment and thus thermomechanical stress in copper films.