Current density

Amount of charge flowing through a unit cross sectional area per unit time

In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. 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. In SI base units, the electric current density is measured in amperes per square metre.

Current density is important to the design of electrical and electronic systems. Circuit performance depends strongly upon the designed current level, and the current density then is determined by the dimensions of the conducting elements. For example, as integrated circuits are reduced in size, despite the lower current demanded by smaller devices, there is a trend toward higher current densities to achieve higher device numbers in ever smaller chip areas. See Moore's law. At high frequencies, the conducting region in a wire becomes confined near its surface which increases the current density in this region. This is known as the skin effect. High current densities have undesirable consequences. Most electrical conductors have a finite, positive resistance, making them dissipate power in the form of heat. The current density must be kept sufficiently low to prevent the conductor from melting or burning up, the insulating material failing, or the desired electrical properties changing. At high current densities the material forming the interconnections actually moves, a phenomenon called electromigration. In superconductors excessive current density may generate a strong enough magnetic field to cause spontaneous loss of the superconductive property. The analysis and observation of current density also is used to probe the physics underlying the nature of solids, including not only metals, but also semiconductors and insulators. An elaborate theoretical formalism has developed to explain many fundamental observations. The current density is an important parameter in Ampère's circuital law (one of Maxwell's equations), which relates current density to magnetic field. In special relativity theory, charge and current are combined into a 4 vector.

Since charge is conserved, current density must satisfy a continuity equation. Here is a derivation from first principles.

In electrical wiring, the maximum current density (for a given temperature rating) can vary from 4 A⋅mm−2 for a wire with no air circulation around it, to over 6 A⋅mm−2 for a wire in free air. Regulations for building wiring list the maximum allowed current of each size of cable in differing conditions. For compact designs, such as windings of SMPS transformers, the value might be as low as 2 A⋅mm−2. If the wire is carrying high frequency alternating currents, the skin effect may affect the distribution of the current across the section by concentrating the current on the surface of the conductor. In transformers designed for high frequencies, loss is reduced if Litz wire is used for the windings. This is made of multiple isolated wires in parallel with a diameter twice the skin depth. The isolated strands are twisted together to increase the total skin area and to reduce the resistance due to skin effects. For the top and bottom layers of printed circuit boards, the maximum current density can be as high as 35 A⋅mm−2 with a copper thickness of 35 μm. Inner layers cannot dissipate as much heat as outer layers; designers of circuit boards avoid putting high current traces on inner layers. In the semiconductors field, the maximum current densities for different elements are given by the manufacturer. Exceeding those limits raises the following problems:
The Joule effect which increases the temperature of the component. The electromigration effect which will erode the interconnection and eventually cause an open circuit. The slow diffusion effect which, if exposed to high temperatures continuously, will move metallic ions and dopants away from where they should be. This effect is also synonymous with ageing. The following table gives an idea of the maximum current density for various materials. MaterialTemperature Maximum current densityCopper interconnections(180 nm technology)25 °C 1000 μA⋅μm−2 (1000 A⋅mm−2)50 °C 700 μA⋅μm−2 (700 A⋅mm−2)85 °C 400 μA⋅μm−2 (400 A⋅mm−2)125 °C 100 μA⋅μm−2 (100 A⋅mm−2)Graphene nanoribbons25 °C 0.1–10 × 108 A⋅cm−2 (0.1–10 × 106 A⋅mm−2)

Even if manufacturers add some margin to their numbers, it is recommended to, at least, double the calculated section to improve the reliability, especially for high quality electronics. One can also notice the importance of keeping electronic devices cool to avoid exposing them to electromigration and slow diffusion. In biological organisms, ion channels regulate the flow of ions (for example, sodium, calcium, potassium) across the membrane in all cells. The membrane of a cell is assumed to act like a capacitor. Current densities are usually expressed in pA⋅pF−1 (picoamperes per picofarad) (i. e., current divided by capacitance). Techniques exist to empirically measure capacitance and surface area of cells, which enables calculation of current densities for different cells. This enables researchers to compare ionic currents in cells of different sizes. In gas discharge lamps, such as flashlamps, current density plays an important role in the output spectrum produced. Low current densities produce spectral line emission and tend to favour longer wavelengths. High current densities produce continuum emission and tend to favour shorter wavelengths. Low current densities for flash lamps are generally around 10 A⋅mm−2. High current densities can be more than 40 A⋅mm−2.