Prediction of orientation relationships and interface structures between α-, β-, γ-FeSi₂ and Si phases

A pure crystallogeometrical approach is proposed for predicting orientation relationships, habit planes and atomic structures of the interfaces between phases, which is applicable to systems of low-symmetry phases and epitaxial thin film growth. The suggested models are verified with the example of epitaxial growth of α-, γ- and β-FeSi₂ silicide thin films on silicon substrates. The density of near-coincidence sites is shown to have a decisive role in the determination of epitaxial thin film orientation and explains the superior quality of β-FeSi₂ thin grown on Si(111) over Si(001) substrates despite larger lattice misfits. Ideal conjunctions for interfaces between the silicide phases are predicted and this allows for utilization of a thin buffer α-FeSi₂ layer for oriented growth of β-FeSi₂ nanostructures on Si(001). The thermal expansion coefficients are obtained within quasi-harmonic approximation from the DFT calculations to study the influence of temperature on the lattice strains in the derived interfaces. Faster decrease of misfits at the α-FeSi₂(001)||Si(001) interface compared to γ-FeSi₂(001)||Si(001) elucidates the origins of temperature-driven change of the phase growing on silicon substrates. The proposed approach guides from bulk phase unit cells to the construction of the interface atomic structures and appears to be a powerful tool for the prediction of interfaces between arbitrary phases for subsequent theoretical investigation and epitaxial film synthesis.