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Stress migration is a failure mechanism that often occurs in integrated circuit metallization (aluminum, copper). Voids form as result of vacancy migration driven by the hydrostatic stress gradient. Large voids may lead to open circuit or unacceptable resistance increase that impedes the IC performance.
Black's Equation is a mathematical model for the mean time to failure (MTTF) of a semiconductor circuit due to electromigration: a phenomenon of molecular rearrangement (movement) in the solid phase caused by an electromagnetic field. The equation is: [1] = ()
For solder joints (SnPb or SnAgCu lead-free) used in IC chips, however, electromigration occurs at much lower current densities, e.g. 10 4 A/cm 2. It causes a net atom transport along the direction of electron flow. The atoms accumulate at the anode, while voids are generated at the cathode and back stress is induced during electromigration.
Electrochemical migration (ECM) is the dissolution and movement of metal ions in presence of electric potential, which results in the growth of dendritic structures between anode and cathode. The process is most commonly observed in printed circuit boards where it may significantly decrease the insulation between conductors.
eFuses can be made out of silicon or metal traces. In both cases, they work (blow) by electromigration, the phenomenon where electric flow causes the conductor material to move. Although electromigration is generally undesired in chip design as it causes failures, eFuses are made of weak traces that are designed to fail before others do. [3] [4]
Feedback-controlled electromigration (FCE) is an experimental technique to investigate the phenomenon known as electromigration. By controlling the voltage applied as the conductance varies it is possible to keep the voltage at a critical level for electromigration .
The Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It extends Fick's law of diffusion for the case where the diffusing particles are also moved with respect to the fluid by electrostatic forces.
Stress analysis is specifically concerned with solid objects. The study of stresses in liquids and gases is the subject of fluid mechanics.. Stress analysis adopts the macroscopic view of materials characteristic of continuum mechanics, namely that all properties of materials are homogeneous at small enough scales.