Lattice Stability and Point Defect Energetics of TiSi2 and TiGe2 Allotropes from First-Principles Calculations

This work determines the phase stabilities and point defect energetics of TiSi2 and TiGe2 allotropes using density functional theory. The primary focus is on the C49 and C54 allotropes, which compete during TiSi2 phase formation. It is found that the ground state structure for TiGe2 is the C54 allotrope, desirable for its low sheet resistance, while the less desirable, higher resistance C49 allotrope forms the ground state structure of TiSi2. A first attempt to understand the Ge atom's role in lowering the enthalpy of formation for the C54 structure is made from the perspective of the extended Born model. Charge density differences, the density of states, and Bader charge analysis show that these systems are predominantly ionically bonded, with the Ge atoms introducing additional covalent bond stability for the C54 allotrope. It is known that higher temperatures favor C54 formation in TiSi2. Helmholtz free energy calculations for TiSi2 suggest that the vibrational free energy does not drive the system to the C54 phase. The formation energies of certain point defects within the C49 structure of TiSi2 are less than 1 eV, which is consistent with experiments that show high defect concentrations. Thus, the driving force for C54 formation at higher temperatures may be related to the high defect concentration in the C49 allotrope.