We experimentally investigated step bunching induced by direct current on vicinal $\mathrm{Si}\mathrm{}\left(111\right)\mathrm{}“1\times 1”$ 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, $l_b\sim N^{-\alpha },$ was determined for four step-bunching temperature regimes above the $7\times 7-“1\times 1”$ transition temperature. The step-bunching rate and scaling exponent differ between neighboring step-bunching regimes. The exponent α is 0.7 for the two regimes where the step-down current induces step bunching (860–960 and 1210–1300 °C), and 0.6 for the two regimes where the step-up current induces step bunching (1060–1190 and >1320 °C). The number of single steps on terraces also differs in each of the four temperature regimes. For temperatures higher than 1280 °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.

• Received 27 January 2000

DOI:https://doi.org/10.1103/PhysRevB.62.8323