Minority Carrier
A minority carrier is the less abundant type of mobile charge in a doped semiconductor: electrons in p-type material, holes in n-type material. In a p-type silicon region doped to about 10^16 acceptors per cubic centimeter, holes number about 10^16 per cubic centimeter while electrons number only about 10^4, a gap of twelve orders of magnitude fixed by the mass-action law, n × p = ni². Minority carriers are therefore rare at equilibrium, but they are the carriers that matter whenever a junction is forward biased, light is absorbed, or a transistor is switched on, because any excess of them stands out against such a tiny background.
Minority carriers are created by injection or by photons, and each one lives a short, finite life before it disappears. Forward-biasing a pn junction pushes electrons into the p side and holes into the n side, and absorbing a photon above the band gap creates an electron-hole pair, so either way the minority population on one side jumps far above its equilibrium value. Those excess carriers then wander by diffusion until they recombine with a majority carrier; the average time this takes is the minority-carrier lifetime, and the average distance covered is the diffusion length, L = √(D × τ), with D the diffusion coefficient and τ the lifetime. In device-grade silicon the lifetime can range from nanoseconds in heavily doped or contaminated regions to milliseconds in pristine float-zone material, so diffusion lengths run from under a micrometer to several hundred micrometers or more.
The bipolar junction transistor works only because minority carriers can cross the base before they die. In an npn device the emitter injects electrons into the thin p-type base, where they are minority carriers; most of them diffuse across and are swept into the collector, so the collector current is set by minority-carrier transport and the transistor gain depends on how few recombine on the way. This is why the base must be made much narrower than the diffusion length, often a fraction of a micrometer or less in modern devices. The idea was developed by Shockley in 1948-49 in his theory of the junction transistor, and the Haynes-Shockley experiment of 1949 at Bell Labs directly measured the drift, diffusion and lifetime of injected minority carriers in germanium, turning what had been theory into a quantity that could be measured.
The flip side of minority-carrier devices is storage: charge that was injected must be removed again before the device can switch off. A saturated bipolar transistor or a forward-biased pn diode holds a cloud of excess minority carriers, and when the drive reverses, that stored charge keeps current flowing for a time set by the lifetime, which is the storage time and the reverse-recovery time. It was a main speed limit of early transistor logic. Designers attacked it by deliberately shortening the lifetime, for example by doping silicon with gold, and by keeping transistors out of saturation, as in Schottky-clamped TTL logic, where a Schottky diode, a majority-carrier device, diverts base drive. Power electronics still faces the same trade-off in PIN diodes and in insulated-gate bipolar transistors, whose minority-carrier tail causes switching loss.
Minority-carrier lifetime is also the quality score of silicon itself. Metal impurities such as iron, copper and gold, crystal defects and surface states all create recombination sites that shorten the lifetime, so fabs and solar manufacturers measure lifetime on wafers, using methods such as photoconductance decay, as a sensitive monitor of contamination long before a device fails. In a solar cell, photons generate minority carriers that must diffuse to the junction before they recombine, so a diffusion length longer than the wafer thickness is a design requirement, and a long lifetime is why high-efficiency cells use ultrapure float-zone or high-grade Czochralski silicon. A frequent misconception is that minority carriers carry little current because there are few of them; in fact, once injected they can outnumber the equilibrium majority carriers in lightly doped regions, which is the very mechanism by which a transistor amplifies.
Read minority carrier as the rare charge that does the active work in a bipolar device: it is made by injection or light, it survives only for a lifetime and a diffusion length, it carries the transistor's gain across the thin base, and its stored cloud is the reason bipolar switching is slower than majority-carrier switching.