Vacancy Formation Energy for the Charged and Neutral States of TlGaSe$_{2}$ Crystal

Electronic band structure and defect formation energy of TlGaSe 2 are studied using density functional method within the Local Density Approximation.Calculated band structure shows that the top of valence band and the bottom of conduction band locate at the symmetry point  and along the symmetry line -Y, respectively.The defect formation energy is calculated as the difference between the total energy of a stable structure and the relaxed defect structure at constant volume.Calculation is done for the five charge states: 2, 1, 0, 1, 2.Energies of vacancies' (V Tl , V Ga , V Se ) formation are determined for the TlGaSe 2 crystal consisting of 63 atoms for the various charge states as a function of Fermi energy.The calculated optical properties indicate that the optical energy gap is increased due to the Se and Tl vacancies.