Pattern formation in the instability of a vicinal surface by the drift of adatoms

We study the behavior of steps in a vicinal face with drift of adsorbed ato ms (adatoms) by an external field. When the drift is in the downhill direct ion and its velocity exceeds critical values, nu(c)(x) and nu(c)(y), the vi cinal face is linearly unstable to long-wavelength fluctuations parallel an d/or perpendicular to the steps. By taking the continuum limit of the step- flow model, we derive an anisotropic Kuramoto-Sivashinsky equation with pro pagative terms, which describes the motion of an unstable vicinal face. Its numerical solution shows ripples or a zigzag pattern expected from the lin ear analysis. Nonlinearity becomes important in the late stage and, dependi ng on the condition, various patterns are formed: regular step bunches, a h ill and valley structure tilted from the initial step direction, mounds, an d a chaotic pattern. [S1063-651X(99)03612-0].