  We study the step bunching kinetic instability in a growing crystal surface
characterized by anisotropic diffusion. The instability is due to the interplay
between the elastic interactions and the alternation of step parameters. This
instability is predicted to occur on a vicinal semiconductor surface Si(001) or
Ge(001) during epitaxial growth. The maximal growth rate of the step bunching
increases like $F^{4}$, where $F$ is the deposition flux. Our results are
complemented with numerical simulations which reveals a coarsening behavior on
the long time for the nonlinear step dynamics.
