= Semiconductor
{wiki}
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> as
$$
\sigma=q(n\mu_n+p\mu_p).
$$
Here $q>0$ 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>.
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