Electric-current-induced step bunching on Si(111)

Abstract

We experimentally investigated step bunching induced by direct current on vicinal $\mathrm{Si}(111)``1\ifmmode\times\else\texttimes\fi{}1''$ surfaces using scanning electron microscopy and atomic force microscopy. The scaling relation between the average step spacing ${l}_{b}$ and the number of steps N in a bunch, ${l}_{b}\ensuremath{\sim}{N}^{\ensuremath{-}\ensuremath{\alpha}},$ was determined for four step-bunching temperature regimes above the $7\ifmmode\times\else\texttimes\fi{}7\ensuremath{-}``1\ifmmode\times\else\texttimes\fi{}1''$ transition temperature. The step-bunching rate and scaling exponent differ between neighboring step-bunching regimes. The exponent \ensuremath{\alpha} is 0.7 for the two regimes where the step-down current induces step bunching (860\char21{}960 and 1210\char21{}1300 \ifmmode^\circ\else\textdegree\fi{}C), and 0.6 for the two regimes where the step-up current induces step bunching (1060\char21{}1190 and g1320 \ifmmode^\circ\else\textdegree\fi{}C). The number of single steps on terraces also differs in each of the four temperature regimes. For temperatures higher than 1280 \ifmmode^\circ\else\textdegree\fi{}C, the prefactor of the scaling relation increases, indicating an increase in step-step repulsion. The scaling exponents obtained agree reasonably well with those predicted by theoretical models. However, they give unrealistic values for the effective charges of adatoms for step-up-current-induced step bunching when the ``transparent'' step model is used.