Semiconductors

In a single atom, an electron has sharp energy levels. In a solid, billions of atoms sit close together and their levels spread into bands of allowed energies. Two bands matter:

• the valence band: filled with the electrons that bond the atoms;
• the conduction band: where electrons are free to move and carry current.

Between them is the energy gap E_g, where no electron can be.

The size of the gap sorts materials into three groups:

In a semiconductor, a little heat lets some electrons jump the gap into the conduction band. Each one leaves behind an empty place in the valence band, called a hole. A hole behaves like a positive charge: a neighbouring electron can fill it, so the hole moves the other way.

Intrinsic (pure) semiconductor: electrons and holes come only in pairs, so n_e = n_h = nᵢ. Warming it frees more pairs, so its resistance falls with temperature, unlike a metal.

Pure silicon conducts poorly. Doping, adding a tiny amount of another element (about one atom in a million), raises its conductivity enormously. This gives extrinsic semiconductors:

• n-type: add a pentavalent atom (5 outer electrons: arsenic, antimony, phosphorus). Four bond with silicon; the fifth is nearly free. Electrons are the majority carriers. The dopant is a donor.
• p-type: add a trivalent atom (3 outer electrons: boron, aluminium, indium). One bond is short of an electron, leaving a hole. Holes are the majority carriers. The dopant is an acceptor.

Either type is still electrically neutral overall: each dopant atom brought its own matching nuclear charge.

In any semiconductor at equilibrium, n_e × n_h = nᵢ². Adding donors raises n_e, so n_h must fall: the majority carriers swamp the minority ones.