# Pressure dependence of electric conductivity of solid semiconductors

For semiconductors, if we increase the temperature, the band gap of a solid is reduced and more electron-hole pairs are generated -> greater motion of charge carriers in the bands -> greater conductivity.

However, how does pressure affect the electric conductivity of solid semiconductors? I guess the energy of the filled bands will be increased because the average distance of the atoms will be decreased so this will increase electric conductivity?

• You seem to be speaking of semiconductors in your first paragraph - metals tend to have decreased conductivity (increased resistivity) with increasing temperature as scattering increases. Are you focused only on semiconductors for the second paragraph and question? Have you looked at the pressure dependence of semiconductor band gaps? Jun 22, 2021 at 12:40
• Yeah sorry I am referring to semiconductors/insulators. Jun 22, 2021 at 12:58

I'll start with a metal first to get that out of the way. Looking at Dugdale and Gugan (Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences Vol. 241, No. 1226 (Aug. 20, 1957), pp. 397-407) one finds that the resitivity of copper at constant temperature monotonically increases a bit going from 1 to 2000 atm of pressure. The resistance of the sample in their Figure 1 increased from 0.09345$$\Omega$$ to 0.09357$$\Omega$$. A small, but real increase.
Semiconductors are more varied, particularly with respect to the question of doping. For example, one brief overview states "for most semiconductors the fundamental gap increases with applied pressure", which is certainly true for silicon and germanium. However, that is far from the full effect, particularly for doped vs intrinsic material. For example, the conductivity of $$p$$-type germanium increases with pressure, while $$n$$-type decreases with pressure. That is explained by interband scattering. All in all, one can end up with complex behaviors of the resistivity/conductivity of semiconductors as the pressure changes, depending on type and amount of doping, as well as temperature.