Growth of step bunches on a Si(001) vicinal face with drift of adatoms

On a Si(001) vicinal face, where the direction of fast surface diffusion alternates on consecutive terraces, step bunching has been observed under direct current heating. By using a one-dimensional step model with drift of adatoms, we study growth laws of step bunches. If evaporation is negligible, the average number N of steps in a bunch increases with time as N ∝ tβ with β less than and double approximate 1/2. The growth exponent β weakly depends on the repulsive interaction potential between steps. When steps at a distance l interact with the repulsive potential ζ ∝ 1/l ν, the average step distance in a bunch lb decreases as lb ∝ N-α with α ≈ 3/2(ν + 2). The exponents α and β are related as β ≈ 1/(2 + α). The simulation results are consistent with experiment if we take account of both logarithmic and ν = 2 potentials, which are expected in this system. The growth rate of the bunch size with step-down drift is faster than that with step-up drift. If evaporation of adatoms is significant, the difference of the growth rate in the opposite drift directions becomes small. The apparent exponent β depends on the drift direction, and is larger with step-up drift.