Q3(a)(ii). Semiconductors: n-type, p-type and the effect of temperature

1. Semiconductor: a solid whose filled valence band is separated from an empty conduction band by a small gap E_g (Si 1.110 eV, Ge 0.664 eV, GaAs 1.441 eV). At room temperature a few electrons are excited across the gap; each leaves a positive hole behind, and both carry current.
2. Intrinsic (pure Si, Ge): equal numbers of electrons and holes, all from thermal excitation; conductivity is small.
3. n-type: Si doped with a group 15 element (P, As). The dopant uses four electrons in bonds; the fifth sits in a donor level just below the conduction band and is easily released. Electrons are the majority carriers (n for negative).
4. p-type: Si doped with a group 13 element (B, Al). One electron short, it creates an empty acceptor level just above the valence band. Electrons enter it from the valence band and leave holes: holes are the majority carriers (p for positive).

Effect of temperature

INTRINSICn∝ T^(3/2)e^(-E_g/2kT)SLOPE-E_g/2k on σ vs 1/T

1. The number of carriers grows exponentially with T, n∝ T^(3/2)e^(-E_g/2kT) (kT=0.0259 eV at 300 K). For Si, warming from 300 K to 350 K multiplies it by 27. Conductivity therefore increases with temperature, the opposite of a metal (whose conductivity falls as lattice vibrations scatter the electrons).
2. In a doped semiconductor the dopant carriers are all released at ordinary temperature, so the conductivity changes little; at high temperature intrinsic excitation takes over and the doped and pure curves merge (dashed and red lines).
3. A plot of σ against 1/T for the intrinsic range is a straight line of slope -E_g/2k, which is how the band gap is measured.

Application. the thermistor (temperature sensor) uses the steep rise of conductivity with T; a junction of p- and n-type silicon is the diode and the solar cell.