A Quantitative and Predictive Model of Electromigration-Induced Breakdown of Metal Nanowires

An isothermal model of electromigration breakdown of metal nanowires 80-700 nm in diameter is developed and validated using experimental data obtained from isolated cylindrical Au nanowires. The model considers electromigration from an applied current producing a net flux of metal atoms, reducing the nanowire radius and conductivity precipitously and accounting for both mass and electronic carrier transport. The model successfully predicts the observed critical failure current, the correct scaling with nanowire radius to 3/2 power, and the impedance evolution prior to breakdown. Application to the case where feedback control is employed to limit the rate of nanowire thinning reproduces key features, including slowed necking, a threshold current and voltage after which lower bias is required to advance formation, and the dependence of these values on feedback parameters.