Intrinsic semiconductors

Pure Si and Ge form a diamond-like lattice: every atom has four nearest neighbours. The lattice spacing a is 3.56 Å for carbon, 5.43 Å for silicon and 5.66 Å for germanium.

Each atom shares one of its four valence electrons with each neighbour and takes a share of one from each. Such a shared pair is a covalent (valence) bond.

At low temperature every bond is intact. As temperature rises, thermal energy frees a few electrons, which become conduction electrons and leave behind a vacancy in the bond.

The freed electron carries charge −q; the vacancy it leaves behaves like a particle of charge +q, called a hole.

In an intrinsic (pure) semiconductor the numbers are equal: nₑ = nₕ = nᵢ (Eq. 14.1), where nᵢ is the intrinsic carrier concentration.

Holes move: an electron from a neighbouring bond jumps into the vacancy, so the hole appears to shift to the site the electron left. This is really bound electrons moving, described as a hole moving; the originally freed electron plays no part.

In an electric field, free electrons give an electron current Iₑ and holes drift towards the negative potential giving a hole current Iₕ. The total current is I = Iₑ + Iₕ (Eq. 14.2).

Electron-hole pairs are also destroyed when an electron meets a hole (recombination). At equilibrium, generation and recombination go on at equal rates.

At T = 0 K an intrinsic semiconductor behaves as an insulator; above 0 K thermal energy puts some electrons in the conduction band and an equal number of holes in the valence band.

Example 14.1: C, Si and Ge share one lattice structure, but their four bonding electrons sit in the 2nd, 3rd and 4th orbits. The energy to free one is highest for C and least for Ge, so C has negligible free electrons (an insulator) while Si and Ge have significant numbers.