Growth law of step bunches induced by the Ehrlich–Schwoebel effect in growth

We study growth law of step bunches formed in growth due to the Ehrlich–Schwoebel effect by using a one-dimensional step flow model. We neglect evaporation of adatoms and assume that the repulsive interaction potential between steps is given by Al−ν, where A is the strength of the repulsion and l is the step distance. When the adatoms attach to the step more easily from the upper terrace than from the lower terrace, an equidistant train of steps is unstable to bunching instability in growth. The terrace width between bunches increases as the bunches grow via collision and coalescence. Time dependence of the terrace width is given by L∼tβ with β≈1/2. The value of β is independent of the power of the step interaction potential ν, which affects L dependence of the step distance in a bunch.