Semiconductor Electronics: Materials, Devices and Simple Circuits

Physics · Class 12

Simulation · Physics · Class 12

Doping: electrons and holes

From the lesson Carrier concentration and band levels in Semiconductor Electronics: Materials, Devices and Simple Circuits. Change the values and watch what happens.

Doping: electrons and holesPhysics · Class 12

The idea behind it

NCERT §14.4

  • 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.