Degenerate epitaxy, coincidence epitaxy and origin of “special” boundaries in thin films

Abstract

When the substrate crystal is of a higher symmetry than the crystal of the overgrown film, a finite number of differently oriented island-nuclei ( n) develop, which ensues a finite number of misorientations ( m) across boundaries in the film where m = C( n,2). This phenomenon of degenerate epitaxy is observed in the double positioning of the [111] f.c.c. metal films on MoS 2 with (112) twin boundaries and the triple positioning of the tetragonal YBa 2Cu 3O 7− x (YBCO) on lattice matched cubic SrTiO 3 with 90°-boundaries of Σ3. The in situ growth of YBCO films on (001) MgO is a good example of coincidence epitaxy, where the lattice misfit is large. Differently oriented island-nuclei form to minimize interfacial energy by maximizing the lattice coincidence according to the Near Coincidence Site Lattice (NCSL) model and minimizing the misfit and strain energy across the film/substrate interface. Thus the number of possible misorientations ( m) from the number of differently oriented island-nuclei ( n) is given as m = n 2/2 when n is even and m = ( n − 1)( n + 1)/4 when n is odd. Only nine misorientations have been observed compared to the calculated value of 64; extensive grain growth and grain annihilation are believed to be responsible for the disappearance of many misorientations. Those [001] tilt boundaries corresponding to Σ5, Σ17, Σ29, off-Σ13 and 45° have all been observed.