Intrinsic Semiconductors

Definition. An intrinsic semiconductor is a semiconductor crystal (silicon or germanium) in a chemically PURE state, with no deliberately added impurity atoms at all. Each atom in the crystal lattice is tetravalent (four valence electrons) and forms four covalent bonds with its four nearest neighbours, so that, at absolute zero, every valence electron is locked into a completed bond and the material behaves exactly like an insulator -- no free carriers exist.

Thermal generation of electron-hole PAIRS. At any temperature above absolute zero, ordinary thermal vibration of the lattice occasionally supplies enough energy to break one of these covalent bonds, freeing the bond's electron to wander through the crystal as a mobile conduction electron. The vacancy this leaves behind in the broken bond -- a missing electron in an otherwise complete arrangement of bonds -- behaves, for almost every practical purpose, like a mobile particle of POSITIVE charge, called a hole: a neighbouring bond's electron can hop into the vacancy, filling THAT hole but creating a new one exactly where the hopping electron used to be, so the hole appears to migrate through the crystal, in the direction opposite to the actual electron motion, exactly as if it were a real, independently moving positive charge.

Equal numbers, always. Because every single broken bond releases exactly one free electron AND leaves exactly one hole, thermal generation in an intrinsic semiconductor always produces electrons and holes in EXACTLY EQUAL numbers: $n_e = n_h = n_i$, where $n_i$ is called the intrinsic carrier concentration. $n_i$ itself rises steeply with temperature (more thermal energy breaks more bonds) and depends on the size of the material's own energy gap $E_g$ (Section 9.6) -- a smaller gap gives a larger $n_i$ at any given temperature, which is why germanium ($E_g \approx 0.7\ \text{eV}$) has a substantially higher intrinsic carrier concentration than silicon ($E_g \approx 1.1\ \text{eV}$) at the same temperature. …