Fractal Concepts in Surface Growth

We have seen that surfaces grown by MBE are rough at large length scales. Moreover, the dynamics of the roughening process follows simple power laws that are predictable if one uses the correct growth equation. In our previous discussion, we neglected a particular property of the diffusion process, the existence of the Schwoebel barrier, biasing the atom diffusion (see §12.2.4). In this chapter we show that this diffusion bias generates an instability, which eventually dominates the growth process. The growth dynamics do not follow the scaling laws discussed in the previous chapters and the resulting interface is not self-affine.

Diffusion bias and instabilities

We saw in §12.2.4 that the existence of an additional potential barrier at the edge of a step generates a bias in the diffusion process, making it improbable that an atom will jump off the edge of the step. Next we investigate how one can incorporate this effect into the continuum equations.

A nonzero local slope corresponds to a series of consecutive steps in the surface (see Fig. 20.1). Suppose an atom lands on the interface and begins to diffuse. If it reaches an ascending step, it sticks by bonding with the atoms of the step. If it diffuses toward the edge of a descending step, there is only a small probability the particle will jump down the step, since the edge barrier will reflect the particle back.