Structure and growth of crystalline superlattices: From monolayer to superlattice

Abstract

We discuss the physical phenomena fundamental to the understanding of the structure and growth of crystalline superlattices: (i) the growth mode as determined by surface energies, supersaturation, and lattice misfit; and (ii) the dependence of epitaxial orientation on lattice matching, atomic bonding, and film thickness, in the topical case of epitaxy at (111) fcc/(110) bcc interfaces. For uniformity monolayer-by-monolayer [Frank--van der Merwe (FM)] growth is desirable. This may be adversely affected by the formation of misfit dislocations. Continued FM growth may be achieved with alternate A and B layers at moderate supersaturation, provided that the surface energies ${\ensuremath{\gamma}}_{A}$ and ${\ensuremath{\gamma}}_{B}$ are compatible. The suggestion that it is possible otherwise at sufficiently high supersaturation is a misconception. The main epitaxial orientations in the present case---the Nishiyama-Wassermann (NW) and the Kurdjumov-Sachs (KS) orientations---have been previously predicted on the (energetically justified) basis of geometrical relationships alone. The predictive power of this model is demonstrated for hexagonal interfaces. Ideally, to predict the evolution of the structure and orientation of a growing (thickening) film atomic forces must be allowed for. We model these forces by means of crystallinity and harmonicity of film, and by a truncated--Fourier-series adsorbate-substrate interaction. Various forms of homogeneous and oscillatory film strains, affecting orientation and structure, are illustrated graphically. We conclude that a good guideline for superlattice formation is the following: (a) growth at moderate supersaturations of metal pairs with comparable \ensuremath{\gamma}'s in the unique NW orientation (0.8\ensuremath{\lesssim}b/a\ensuremath{\lesssim}1.0, a and b are nearest-neighbor distances); or, possibly, (b) nucleation and growth along unidirectional steps.