Evaporation and growth of crystals: Propagation of step-density compression waves at vicinal surfaces

We studied the step dynamics during crystal sublimation and growth in the limit of fast surface diffusion and slow kinetics of atom attachment-detachment at the steps. For this limit, we formulate a model free of the quasistatic approximation in the calculation of the adatom concentration on the terraces at the crystal surface. Such a model provides a relatively simple way to study the linear stability of a step train in the presence of step-step repulsion and the absence of the usual destabilizing factors (as Schwoebel effect, surface electromigration, impurities, etc.). The central result is that a critical velocity of the steps in the train exists, which separates the stability and instability regimes. Instability occurs when the step velocity exceeds its critical value Vcr=12KΩA∕kTl³, where K is the step kinetic coefficient, Ω is the area of one atomic site at the surface, and the energy of step-step repulsion is U=A∕l², where l is the interstep distance. Integrating numerically the equations for the time evolution of the adatom concentrations on the terraces and the equations of step motion, we obtained the step trajectories. At V>Vcr, step-density compression waves propagate on the vicinal surface (small step bunches which move but do not manifest any coarsening). This instability is a consequence of the retardation effect in the relaxation of the adatom concentration on the terraces due to the slow attachment kinetics.