Experimental quantitative study into the effects of electromigration field moderation on step bunching instability development on Si(111)

Abstract

We experimentally studied the effects of a moderated electromigration field on the dynamics of the step bunching process on the Si(111) surface at 1130 \ifmmode^\circ\else\textdegree\fi{}C (regime II) and 1270 \ifmmode^\circ\else\textdegree\fi{}C (regime III). The surfaces with step bunch morphologies were created by annealing vicinal Si(111) at fixed temperatures while the applied electric field $E$ was adjusted for every experiment. Scaling relations, ${y}_{m}~{h}^{\ensuremath{\alpha}}{E}^{q}$, between the slope of a step bunch ${y}_{m}$, step bunch height $h$, and electromigration field $E$ were experimentally probed. Scaling exponents $\ensuremath{\alpha}$ \ensuremath{\approx} 2/3 and $q$ \ensuremath{\approx} 1/3 were extracted from the step bunch morphologies created by annealing Si(111) in the regime III (1270 \ifmmode^\circ\else\textdegree\fi{}C), which are in good agreement with the predictions of the generalized BCF theory. Scaling exponents $\ensuremath{\alpha}$ \ensuremath{\approx} 3/5 and $q$ \ensuremath{\approx} 1/3 were extracted from the morphologies created by annealing in regime II (1130 \ifmmode^\circ\else\textdegree\fi{}C). This result was compared to the scaling relations derived within the frame of the transparent step model, which correctly predicts the formation of the step bunching instability by step-up adatom electromigration. The scaling relation obtained by experiment was found to differ from the model predictions. We measured values of critical electric field (${E}_{\mathrm{cr}}$), i.e., minimum electric field required for the step bunching to take place. A relatively weak field of $E$ > 0.5 V/cm was found to be sufficient to initiate the step bunching process in regime II. This contrasts with regime III, where ${E}_{\mathrm{cr}}=1.0$ and 2.0 V/cm were measured for Si miscut from the (111) plane by 1.1\ifmmode^\circ\else\textdegree\fi{} and 2.5\ifmmode^\circ\else\textdegree\fi{}, respectively. The increased values of ${E}_{\mathrm{cr}}$ were attributed to the enhanced step-step repulsion in regime III. The theoretically predicted formation of compressed step density waves was observed upon annealing in both regimes with $E<{E}_{\mathrm{cr}}$.