Iodine Vacancy Formation Energy in CH₃NH₃PbI₃ Perovskite

Iodine vacancies and their behavior in the MAPbI ₃ perovskites are determining factors in the stability of the perovskite to light. In this article, we investigate the formation of iodine vacancy in the CH ₃ NH ₃ PbI ₃ perovskite analytically and calculate its required energy. Iodine vacancy formation needs a certain amount of energy to separate an iodine ion from its lattice position and transfer it to another lattice position at crystal surface, grain boundaries, and/or dislocations. When a lattice position becomes vacant in a crystal, the atoms around this position lose their equilibrium state and will no longer remain in their primary lattice position. The neighbor ions of the vacancy move slightly from their lattice position to reach a new stable state. This transition from unstable to steady state is called relaxation, and the released energy from this process is called relaxation energy. So, first, we calculate the energy needed to separate an iodine ion from its primary lattice position, and then, to estimate the relaxation energy, the new equilibrium positions and energy changes of the neighbor ions are determined. The vacancy formation energy is equal to the difference between these two energies.