Semiconductor

A semiconductor has an electronic band gap and a conductivity strongly affected by temperature, impurities and carrier injection. Optical absorption can create mobile electrons and holes, enabling a photodiode.

The useful feature of a semiconductor is that its charge carrier population can be controlled. Semiconductor doping changes the supply of mobile electrons or electron holes; carrier injection changes their population away from thermal equilibrium. A transistor turns that control into an electronic amplifier: a small input signal controls a larger flow of supplied energy.

For a uniform semiconductor in a weak electric field, a simple drift model writes its electrical conductivity asHere $q>0$ is the elementary charge, $n,p$ are the number densities of mobile electrons and electron holes, and ${\mu }_n,{\mu }_p$ their positive charge carrier mobilities. The two contributions add because opposite electric charges drift in opposite directions and therefore carry electric current in the same direction. This model assumes fixed temperature and mobilities and omits diffusion from density gradients.

An original dimensionless example isolates the effect of carrier injection. Suppose initially $p\ll n=n_0$ and ${\mu }_n=2{\mu }_p$. Adding equal excess populations $\Delta n=\Delta p=0.1n_0$ gives $\Delta \sigma /{\sigma }_0=0.15$, even though the added electron holes remain a minority carrier population. A semiconductor can respond strongly to a small injected population without changing its underlying band gap.