Step bunching with general step kinetics: stability analysis and macroscopic models

The stability of a vicinal surface with respect to step bunching is analyzed during growth or sublimation, in presence of adatom migration, and with general step kinetics, i.e. with arbitrary Ehrlich–Schwoebel effect and step transparency. It is found that: (i) The stability only depends on the sign of the product of the electromigration force with the incoming flux, not only for perfectly transparent steps, but also for instantaneous attachment kinetics. (ii) The inversion of stability shifts towards the sublimation regime as step kinetics becomes slower. (iii) When elastic interactions are weak, short wavelength modes, such as pairing, introduce an additional stability threshold in the regime of non-local mass transport (i.e. strong transparency, and slow attachment kinetics). Macroscopic models are built, that allow one to recover quantitatively the stability criteria, and to understand them within a simple physical picture. Experiments on Si(1 1 1) are discussed in the light of these results.