Editing Electromigration (section)

=== Forces on ions in an electrical field ===
Two [[force]]s affect ionized [[atom]]s in a conductor: 1) The direct [[Electrostatics|electrostatic]] force ''F<sub>e</sub>'', as a result of the electric field <math>E</math>, which has the same direction as the electric field, and 2) The force from the exchange of momentum with other [[charge carrier]]s ''F<sub>p</sub>'', toward the flow of charge carriers, is in the opposite direction of the electric field. In metallic conductors ''F<sub>p</sub>'' is caused by a so-called "electron wind" or "[[ion wind]]".

The resulting force ''F<sub>res</sub>'' on an activated ion in the electrical field can be written as

:<math>F_{res}=F_e-F_p=q\cdot (Z_e-Z_p) \cdot  E = q\cdot Z^*\cdot E=q\cdot Z^*\cdot j\cdot \rho
</math>
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where <math>q</math> is the [[electric charge]] of the ions,<math>Z_e</math> and <math>Z_p</math> the valences corresponding to the electrostatic and wind force respectively, <math>Z^*</math> the so-called effective valence of the material, <math>j</math> the current density, and <math>\rho</math> the resistivity of the material
.<ref>{{cite journal
| last1      = Lodder
| first1     = A.
| last2      = Dekker
| first2     = J. P.
| date       = 1998
| title      = The electromigration force in metallic bulk 
| url        = https://aip.scitation.org/doi/abs/10.1063/1.54652
| journal    = AIP Conference Proceedings
| volume     = 418
| issue      = 1
| pages      = 315–328
| doi        =  10.1063/1.54652
| access-date = 2021-01-15
| arxiv= cond-mat/9803172
| bibcode = 1998AIPC..418..315L
| s2cid = 18376825
}}</ref>
Electromigration occurs when some of the [[momentum]] of a moving electron is transferred to a nearby activated ion. This causes the ion to move from its original position. Over time this force knocks a significant number of atoms far from their original positions. A break or gap can develop in the conducting material, preventing the flow of electricity. In narrow interconnect conductors, such as those linking transistors and other components in integrated circuits, this is known as a ''void'' or ''internal'' ''failure'' ([[Electric circuit|open circuit]]). Electromigration can also cause the atoms of a conductor to pile up and drift toward other nearby conductors, creating an unintended electrical connection known as a '''hillock failure''' or '''whisker failure''' ([[short circuit]]).  Both of these situations can lead to a malfunction of the circuit.