why does the doping with pentavalant or trivalent impurities reduce the energy gap Eg?
Answers
The band-gap is a region in energy with no allowed states. The density of states versus energy depends on the chemical composition of the material; if the chemical composition is changed, at least, in principle, the state density distribution should change. Dopants are impurities, so, the chemical composition changes by doping. The change in the energy distribution of the allowed states cannot have a general rule such as: the band-gap will decrease after introduction of impurities. Generally, those impurities are called dopants, which create allowed shallow states in the band-gap. Shallow states have small ionisation energies; and, when the doping density is high, the dopant states generate a band. If this band is very close to the valence or conduction band edge, the band-gap will decrease.
The question was not well defined. Were these observations made for any impurities? Impurities have to satisfy a number of criteria to qualify as dopants.