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 $V_{\mathit{cr}}=12K\Omega A∕kT{l}^3$, where $K$ is the step kinetic coefficient, $\Omega$ is the area of one atomic site at the surface, and the energy of step-step repulsion is $U=A∕l^2$, 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 $V>V_{\mathit{cr}}$, 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.

• Received 9 February 2007

DOI:https://doi.org/10.1103/PhysRevB.76.035443