Density functional theory applied toVN∕TiNmultilayers

Abstract

By means of a density functional theory approach, materials properties of $\mathrm{V}\mathrm{N}[001](100)\ensuremath{\parallel}\mathrm{Ti}\mathrm{N}[001](100)$ multilayers are studied focusing on the elastic and mechanical properties of the interface. For the isolated bulk phases of TiN and VN, elastic constants and moduli are derived in order to analyze the matching conditions at the interface. Modeling of the mechanical properties was done in terms of brittle cleavage by calculating cleavage energies and critical stresses for the bulk phases as well as for the multilayer system. The interface energy of $\ensuremath{-}0.054\phantom{\rule{0.3em}{0ex}}\mathrm{J}∕{\mathrm{m}}^{2}$ was derived for the lateral lattice parameter of MgO(100) according to the multilayer growth on this substrate. For this case, also atomic interlayer distances and critical stresses are determined and a Poisson ratio of the VN[001] and TiN[001] was evaluated. The values of $\ensuremath{\nu}=0.279$ and $\ensuremath{\nu}=0.235$, respectively, agree very well with the available experimental data. The strain energy and the interfacial cleavage properties of the multilayer are calculated as a function of the lateral lattice parameter illustrating growth conditions on different substrates. The cleavage energy at the interface considerably changes with respect to the lateral lattice parameter, but the critical stress of $\ensuremath{\approx}27\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ remains rather unchanged. The relaxation of atoms following an epitaxial strain of VN layers transforms VN into the structure with tetragonal-like stacking. This fact is an indication that stoichiometric VN is metastable against tetragonal distortion.