Intrinsic semiconductors
A pure semiconductor such as silicon or germanium (both tetravalent) is intrinsic. Each atom forms four covalent bonds with its neighbours. At room temperature, a few bonds break; each freed electron leaves behind a hole (a vacancy that behaves like a positive charge). In an intrinsic semiconductor the electron and hole concentrations are equal: nₑ = nₕ = nᵢ. Compound semiconductors such as GaAs and CdS also exist.
Extrinsic semiconductors (doping)
Adding a very small amount of a suitable impurity (doping) greatly increases conductivity.
- n-type: doped with a pentavalent element (phosphorus, arsenic, antimony). Four of its electrons form bonds; the fifth is loosely held and easily freed. These impurities are called donors. Electrons are the majority carriers and holes the minority carriers.
- p-type: doped with a trivalent element (boron, aluminium, gallium, indium). One bond is incomplete, creating a hole. These impurities are acceptors. Holes are the majority carriers.
In the band picture, a donor level lies just below the conduction band and an acceptor level just above the valence band, so very little energy is needed to create carriers.
Although one type of carrier is in the majority, the doped crystal as a whole is electrically neutral, because every free carrier is balanced by a charged impurity ion.
Mass-action law
At equilibrium, nₑnₕ = nᵢ². Example: silicon (nᵢ = 1.5 × 10¹⁶ m⁻³) doped with arsenic to give nₑ ≈ 5 × 10²² m⁻³. Then nₕ = (1.5 × 10¹⁶)²/(5 × 10²²) = 4.5 × 10⁹ m⁻³, far fewer holes than electrons.
Key points
- Intrinsic: nₑ = nₕ.
- Pentavalent donor → n-type; trivalent acceptor → p-type.
- Doped semiconductors remain electrically neutral.
- nₑnₕ = nᵢ².
Exam tips
- "n" and "p" refer to the sign of the majority carriers, not to the net charge of the crystal.
- In mass-action problems, the dopant concentration gives the majority carrier density directly.