Multispecies epitaxial growth on vicinal surfaces with chemical reactions and diffusion

Abstract

We derive, in the form of coupled partial differential equations, the evolution equations for the epitaxial growth, via step flow, of a multispecies crystal on a stepped surface. Both adsorption–desorption on the terraces and attachment–detachment along the step edges are accompanied by chemical reactions and adatom diffusion. Moreover, we account for deposition from either a vacuum, e.g., in molecular beam epitaxy, or a gas, e.g., during vapour phase epitaxy (chemical or physical). Our theory (i) endows the steps with a thermodynamic structure whose main ingredients are a free-energy density and species edge chemical potentials, (ii) incorporates anisotropy into the terrace species diffusion as well as into the edge free energy, species mobilities, attachment–detachment and reaction-rate coefficients, (iii) allows for large departures from local equilibrium along the steps, and (iv) ensures the consistency of the constitutive relations for the terrace and edge chemical rates with the second law. In particular, a configurational force balance at each step yields a generalization of the classical Gibbs–Thomson relation. Finally, the special case of steady-state growth of a binary compound is discussed.

Epitaxy of Binary Compounds and Alloys

“…For a generalization to the case of N species (N Q 3) and multiple terrace and edge reactions in the absence of bulk atomic diffusion and direct adsorption-desorption onto the steps, cf. Cermelli and Jabbour [26].…”

“…26 25 Since chemical reactions on the terraces are ignored, the only adatoms present there are those of the A and B species. 26 Note that equations (39), (44) and (51) imply the following constraints on É c and É t as prescribed by equations (43) and (48) respectively:…”

“…Instead, the bulk and terrace configurational forces balances (26) and (27), augmented by the Eshelby identities (31) and (32), respectively, serve to specify f c and f t : 23 Here we assume, somewhat formally, that all three species, i.e., A; B, and AB, are present in the bulk. Sections 7 and 8 pertain to special cases, the former corresponding to that of a binary compound with only AB-particles present in the bulk, the latter to the case of a binary alloy such that only atoms of the A-and B-species are present in the crystalline phase.…”

The effect of kinetics in the surface evolution of thin crystalline films

“…Ref. [6]. In the vapour, however, the grand canonical potential is negligible and what remains is the grand canonical potential in the solid C þ À rm þ , with C þ the free energy density in the solid, r the density in the solid and m þ the chemical potential in the solid.…”

Step bunching during the epitaxial growth of a generic binary-compound thin film

“…Gurtin (1995Gurtin ( , 2000. We adhere to this viewpoint on the ground that the aforementioned balance law, when constitutively augmented, serves to generalize the classical, variationally derived Gibbs-Thomson relation along steps-cf., e.g., Bales and Zangwill (1990), Krug (2005), and Jeōng and Williams (1999)-to the dissipative, nonequilibrium setting of multispecies epitaxy, see also Cermelli and Jabbour (2005). Indeed, it is not clear if, in the presence of dissipation, a variational principle exists or what form it should take.…”