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In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. [1] The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point.
The typical current density at which electromigration occurs in Cu or Al interconnects is 10 6 to 10 7 A/cm 2. 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 AC current density J in a conductor decreases exponentially from its value at the surface J S according to the depth d from the surface, as follows: [4]: 362 = (+) / where is called the skin depth which is defined as the depth below the surface of the conductor at which the current density has fallen to 1/e (about 0.37) of J S.
Silver, although it is the least resistive metal known, has a high density and performs similarly to copper by this measure, but is much more expensive. Calcium and the alkali metals have the best resistivity-density products, but are rarely used for conductors due to their high reactivity with water and oxygen (and lack of physical strength).
The electron mobility is defined by the equation: =. where: E is the magnitude of the electric field applied to a material,; v d is the magnitude of the electron drift velocity (in other words, the electron drift speed) caused by the electric field, and
The arrows indicate the direction of the electric field E and the electric current density j. ... which limits their ... ×10 −8 V 2 K −2 for copper at 0 °C to L ...
The slowing carriers also increases the space charge density and resulting potential. In addition, the potential developed by the space charge can reduce the number of carriers emitted. [16] When the space charge limits the current, the random arrivals of the carriers are smoothed out; the reduced variation results in less shot noise. [15]
This ongoing current in both directions is called the exchange current density. When the potential is set more negative than the formal potential, the cathodic current is greater than the anodic current. Written as a reduction, cathodic current is positive. The net current density is the difference between the cathodic and anodic current density.