Carrier concentration and band levels

Doping adds energy levels inside the gap: a donor level ED just below EC in n-type material, and an acceptor level EA just above EV in p-type material.

n-type: very little energy lifts electrons from ED into the conduction band. At room temperature most donors are ionised while only about 10¹² Si atoms are, so almost all conduction electrons come from donors.

p-type: a small energy lets a valence electron jump up to EA and ionise the acceptor negatively; equivalently, a hole drops from EA into the valence band. Electrons rise and holes sink when they gain energy.

At room temperature most acceptors are ionised, so the holes in the valence band come mainly from the impurity.

In thermal equilibrium, nₑnₕ = nᵢ² (Eq. 14.5), whatever the doping.

Band gaps: C (diamond) 5.4 eV, Si 1.1 eV, Ge 0.7 eV. Tin (Sn) is also in group IV but is a metal, because its gap is 0 eV.

Example 14.2: pure Si with 5 × 10²⁸ atoms m⁻³ is doped with 1 ppm arsenic, so ND = 5 × 10²⁸ × 10⁻⁶ = 5 × 10²² m⁻³. Since nᵢ = 1.5 × 10¹⁶ m⁻³ is negligible beside this, nₑ ≈ ND = 5 × 10²² m⁻³.

Then nₕ = nᵢ²/nₑ = (2.25 × 10³²)/(5 × 10²²) ≈ 4.5 × 10⁹ m⁻³: over ten trillion times fewer holes than electrons.

In compound semiconductors, shifting the ratio of elements can also change the type. Ideal GaAs has Ga : As = 1 : 1, but Ga-rich or As-rich crystals such as Ga₁.₁As₀.₉ or Ga₀.₉As₁.₁ act as defects that alter its properties.

EC and EV are not located at any particular place in the solid; drawn as straight lines, they just mark the bottom of the conduction band and the top of the valence band.