Domain epitaxy: A unified paradigm for thin film growth

We present a unified model for thin film epitaxy where single crystal films with small and large lattice misfits are grown by domain matching epitaxy (DME). The DME involves matching of lattice planes between the film and the substrate having similar crystal symmetry. In this framework, the conventional lattice matching epitaxy becomes a special case where a matching of lattice constants or the same planes is involved with a small misfit of less than 7%–8%. In large lattice mismatch systems, we show that epitaxial growth of thin films is possible by matching of domains where integral multiples of major lattice planes match across the interface. We illustrate this concept with atomic-level details in the TiN/Si(100) with 3/4 matching, the AlN/Si(100)with 4/5 matching, and the $\mathrm{ZnO}\mathrm{/\alpha -}{\mathrm{Al}}_2{\mathrm{O}}_3\text{(0001)}$ with 6/7 matching of major planes across the film/substrate interface. By varying the domain size, which is equal to intregral multiple of lattice planes, in a periodic fashion, it is possible to accommodate additional misfit beyond perfect domain matching. Thus, we can potentially design epitaxial growth of films with any lattice misfit on a given substrate with atomically clean surfaces. In situ x-ray diffraction studies on initial stages of growth of ZnO films on sapphire correctly identify a compressive stress and a rapid relaxation within 1 to 2 monolayers, consistent with the DME framework and the fact that the critical thickness is less than 1 monolayer. DME examples ranging from the Ge–Si/Si(100) system with 49/50 matching (2% strain) to metal/Si systems with 1/2 matching (50% strain) are tabulated, strategies for growing strain-free films by engineering the misfit to be confined near the interface are presented, and the potential for epitaxial growth of films with any lattice misfit on a given substrate with atomically clean surfaces is discussed.