Optical bandgap in various impurity-Si systems from the metal–insulator transition study

In different impurity-Si systems, our expressions for spin-polarized ground-state energy, spin-polarized chemical potential energy, and spin susceptibility have been investigated and also compared with other theoretical-and-experimental results. That gives rise to a satisfactory description of some physical properties such as: metal–insulator transition of the first (or second) order, explored from the spin-polarized ground-state energy (or spin susceptibility), and optical bandgap, obtained from the spin-polarized chemical potential energy obtained in the metallic phase