  We approach the old-standing problem of vicinal crystal surfaces destabilized
by step-down and step step-up currents from a unified modelling viewpoint with
focus on both the initial and the intermediate stages of the instability. We
develop further our atomistic scale model of vicinal crystal growth (Gr)
destabilized by SD drift of the adatoms in order to account for also the
vicinal crystal sublimation (Sbl) and the SU drift of the adatoms as an
alternative mode of destabilization. In order to study the emergence of the
instability we use the number of steps in the bunch (bunch size) N as a measure
and probe with small-size systems the models stability against step bunching
(SB) on a dense grid of points in the parameter space formed by the diffusion
rate/step transparency, surface miscut and drift direction, for each of the
four possible cases - Gr+SD, Gr+SU, Sbl+SD, Sbl+SU. The obtained stability
diagrams show where the system is initially most unstable and provide a ground
to study there the intermediate stages of the developed instability quantifying
the surface self-similarity by the time-scaling of N. For each of the four
enumerated cases we show that it reaches the universal curve N=2sqrt(T/3),
where T is the time, properly rescaled with the model parameters. We confirm
the value of the numerical pre-factor with results from a parallel study of
models based on systems of ordinary differential equations (ODE) for the step
velocity.
