Electric Field
An electric field is the region of influence that electric charge creates around itself, defined at any point as the force that a small test charge would feel per unit of its charge. Its units are newtons per coulomb or, equivalently and more useful in electronics, volts per metre. The field is what pushes charge carriers through wires and semiconductors, and in a transistor it is the control mechanism itself.
The field concept grew from Michael Faraday's lines of force and was made mathematical by James Clerk Maxwell. Faraday, in the 1830s and 1840s, pictured space around charges and magnets as filled with lines of force, with density showing strength, an idea some contemporaries thought naive. Maxwell, in the 1860s, turned it into a set of equations in which electric and magnetic fields change into each other and propagate as waves at the speed of light, uniting electricity, magnetism and optics. Field lines are a drawing convention: they begin on positive charge, end on negative charge, never cross, and are packed more closely where the field is stronger. A field has direction as well as size, which is why it is a vector.
The field and the voltage are two views of the same thing, related by a simple slope. Voltage is the integral of the field along a path, so in the simplest uniform case the field equals the voltage difference divided by the distance: E = V / d. One volt across one metre is one volt per metre, but across a micrometre it is a million volts per metre. This is why microelectronics is dominated by fields: tiny distances turn ordinary supply voltages into enormous fields. Inside a conductor in equilibrium the field is zero, since mobile charge rearranges to cancel it; only at insulating gaps and boundaries can a strong field persist.
The strongest fields in daily technology sit across thin insulators, and every insulator has a breakdown limit. When the field in an insulator becomes large enough, electrons are torn loose or avalanche, and the material conducts destructively. For silicon dioxide, the insulator of the MOS transistor, the breakdown field is generally of the order of megavolts per centimetre, and designers keep operating fields well below it, since long-term stress degrades oxide even short of outright failure. The same physics sets the ratings of capacitors, limits flash memory endurance, where charge is forced through thin oxide, and explains why a thin gate dielectric forces a low supply voltage: a gate only a few atomic layers thick sees a large field from even a small voltage.
In semiconductors, three fields recur, and they play different roles. In a capacitor, the field between plates stores energy. In the depletion region of a pn junction, fixed ionised dopant atoms create a built-in field that points from the n side to the p side, opposes diffusion and sweeps minority carriers across, which underlies diodes, solar cells and the bipolar transistor. At the gate of a field-effect transistor, the field reaches through an oxide into the silicon, attracts or repels carriers at the surface and so opens or closes a channel; that is the basis of the modern chip. A frequent misconception is that a field must carry current to do anything: a gate field acts without current flowing through the insulator, which is why a transistor can be controlled by voltage with almost no input power.
Read electric field as voltage spread over distance: the invisible agent that moves charge, stores energy and, across a few nanometres of oxide, switches the transistors of every modern chip.