Density functional theory DFT is a computational method used to study the electronic structure of materials, including semiconductors. The band gap of a semiconductor material is the energy difference between the valence band highest occupied energy level and the conduction band lowest unoccupied energy level . This band gap determines the electrical and optical properties of the material.Doping is the process of introducing impurities dopants into a semiconductor material to modify its electrical properties. There are two types of doping: n-type adding electron donors and p-type adding electron acceptors . The doping concentration refers to the number of dopant atoms per unit volume.As the doping concentration increases, the band gap of the semiconductor material can be affected in several ways:1. Band gap narrowing: As the doping concentration increases, the added impurities introduce new energy levels within the band gap. These new energy levels can cause the conduction band to shift downwards and the valence band to shift upwards, leading to a narrowing of the band gap. This effect is more pronounced in heavily doped materials.2. Band gap widening: In some cases, the interaction between the dopant atoms and the host material can lead to a widening of the band gap. This is less common and depends on the specific material and dopant combination.3. Band gap renormalization: In heavily doped materials, the interaction between the added charge carriers electrons or holes can lead to a renormalization of the band structure, which can either increase or decrease the band gap, depending on the material and doping concentration.DFT calculations can be used to predict the changes in the band gap of a semiconductor material as a function of doping concentration. These calculations involve solving the Kohn-Sham equations for the doped material, which provide the electronic structure and energy levels. By comparing the energy levels of the doped and undoped material, the change in the band gap can be determined.In summary, the band gap of a semiconductor material can change with its doping concentration, and density functional theory calculations can be used to predict these changes. The specific effect on the band gap depends on the material, dopant type, and doping concentration.