An electro-thermo-mechanical coupling phase-field model of defect evolution induced by electromigration in interconnects

Abstract

In this paper, the defect evolution caused by electromigration induced surface diffusion in interconnects is investigated using a newly-developed electro-thermo-mechanical coupling phase-field model. The Joule heat and its resulting thermomigration are included into the phase-field model. The governing equation of the phase-field is solved by semi-implicit spectral methods and the accompanied governing equations of applied physics fields are solved by finite volume methods. Comparative investigation into defect evolution with and without the influence of Joule heating is conducted. It is deduced that thermomigration facilitates local elongation of the defect in the “current crowding” region and exerts a substantial influence on the defect morphological evolution. Subsequently, the effect of the inclination angle of the electric field on the void morphology evolution and crack propagation is discussed. We find that the defect achieves the largest characteristic length when the electric field direction is perpendicular to the uniaxial tension direction, implying a higher threat to the circuit safety. This study may help to deepen people's understanding of how the thermal effect functions in electromigration process and sheds light on different modes of defect evolution in interconnects.