The band gap of a semiconductor material can be altered by doping it with impurities such as boron or phosphorus. Density functional theory DFT calculations can help predict these changes. Doping introduces new energy levels within the semiconductor's band structure, which can affect the band gap.When a semiconductor is doped with boron a group III element , it becomes a p-type semiconductor. Boron has one less electron than the semiconductor's atoms, creating an "acceptor" level near the valence band. Electrons from the valence band can easily move to this acceptor level, leaving behind a positively charged "hole." This process effectively narrows the band gap, as the valence band's top energy level shifts closer to the conduction band.On the other hand, when a semiconductor is doped with phosphorus a group V element , it becomes an n-type semiconductor. Phosphorus has one more electron than the semiconductor's atoms, creating a "donor" level near the conduction band. Electrons from the donor level can easily move to the conduction band, effectively narrowing the band gap as the conduction band's bottom energy level shifts closer to the valence band.In summary, doping a semiconductor material with impurities such as boron or phosphorus can change its band gap by introducing new energy levels within the band structure. Density functional theory calculations can help predict these changes, providing valuable insights for designing semiconductors with specific electronic properties.