Growth of Step Bunches on a Si(001) Vicinal Face with Drift of Adatoms

Abstract

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 ∝ t β with \(\beta \lessapprox 1/2\). 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 l b decreases as l b ∝ 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...