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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.

A thermodynamically consistent continuum theory for single-species, step-flow epitaxy that extends the classical Burton-Cabrera-Frank ͑BCF͒ framework is derived from basic considerations. In particular, an expression for the step chemical potential is obtained that contains two energetic contributions-one from the adjacent terraces in the form of the jump in the adatom grand canonical potential and the other from the monolayer of crystallized adatoms that underlies the upper terrace in the form of the nominal bulk chemical potential-thus generalizing the classical Gibbs-Thomson relation to the dynamic, dissipative setting of stepflow growth. The linear stability analysis of the resulting quasistatic free-boundary problem for an infinite train of equidistant rectilinear steps yields explicit-i.e., analytical-criteria for the onset of step bunching in terms of the basic physical and geometric parameters of the theory. It is found that, in contrast with the predictions of the classical BCF model, both in the absence as well as in the presence of desorption, a growth regime exists for which step bunching occurs, except possibly in the dilute limit where the train is always stable to step bunching. In the present framework, the onset of one-dimensional instabilities is directly attributed to the energetic influence on the migrating steps of the adjacent terraces. Hence the theory provides a "minimalist" alternative to existing theories of step bunching and should be relevant to, e.g., molecular beam epitaxy of GaAs where the equilibrium adatom density is shown by Tersoff, Johnson, and Orr ͓Phys. Rev. B 78, 282 ͑1997͔͒ to be extremely high.

We revisit the step bunching instability without recourse to the quasistatic approximation and show that the stability diagrams are significantly altered, even in the low-deposition regime where it was thought sufficient. In particular, steps are unstable against bunching for attachment-detachment limited growth. By accounting for the dynamics and chemical effects, we can explain the onset of step bunching in Sið111Þ-ð7 × 7Þ and GaAs(001) without resort to the inverse Schwoebel barrier or step-edge diffusion. Further, the size-scaling analysis of step-bunch growth, as induced by these two combined effects, agrees with the bunching regime observed at 750 °C in Sið111Þ-ð7 × 7Þ.