The effect of pressure on band gap can be understood in quite simple terms. Pressure changes the lattice parameters and therefore average distance between electrons/holes and ions. This results in change in the magnitude of the electron/hole - ion potential. This potential plays a significant role in determining the band gap at the Brillouin zone. Besides, average distance between electrons/holes also changes. This modifies the overlap integral. Change in overlap integral changes the band width, and consequently the band gap.
Generally the hydrostatic pressure on a crystal narrows the energy bandgaps because approaches the atomic orbitals allowing an easy electronic hopping and hence the matter could transform from insulator to semiconductor or from (Mott) semiconductor to metal. However not always that is true,e.g, in some IV-VI and III-V binary compound, such as GaN and SiC,
pressure induced phase transitions, which are not so simple as from Mott semiconductor to metal.
But, in general, enough pressure allows to get a metal from a semiconductor or an insulator.
The effect of pressure on band gap can be understood in quite simple terms. Pressure changes the lattice parameters and therefore average distance between electrons/holes and ions. This results in change in the magnitude of the electron/hole - ion potential. This potential plays a significant role in determining the band gap at the Brillouin zone. Besides, average distance between electrons/holes also changes. This modifies the overlap integral. Change in overlap integral changes the band width, and consequently the band gap.
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The energy gap of material is inversely proportional to lattice constant ,d,and to the the dielectric constant, epsilon. The dielectric constant itself is proportional to density of atoms N in the solid material and their polarizability, alpha. That is
Eg is proportional to 1/ epsilon *d = consatnt/ N alpha * d,
d decreases with compression in all direction or it decreases with compression in the direction of the compression and increases increases on the normal direction. So, the the change in the Eg with pressure depends on the direction of the measurement. N also increases with compression. So, we have to competing factors N and d. Therefore the different behavior of the materials with pressure.