Evidence for diffusion-limited kinetics during electromigration-induced step bunching on Si(1 1 1)

We have measured how the initial terrace width l₀ on vicinal Si(1 1 1) surfaces influences the rate of step bunching and the minimum terrace width within a bunch when direct-current heated at 940-1290 °C. A comparison of this data with analytic solutions and numerical simulations of the conventional “sharp-step” model give strong evidence that the kinetic length d is relatively small (d < ∼20 nm) in both temperature regime I (∼850-950 °C) and regime III (∼1200-1300 °C), in which step-down current is required for step bunching. This indicates that surface mass transport is diffusion-limited in both regimes I and III when l₀ > 20 nm, and hence that the adatom attachment- and terrace diffusion-hopping rates are of comparable magnitude. We also observe similar scaling with initial terrace width in temperature regime II (∼1040-1190 °C), in which step-up current is required for bunching, suggesting a similar step bunching mechanism in all three temperature regimes.