Figure 1

Surface morphologies created on Si(111) by extended annealing at 1270 °C. (a) AFM image of Si(111) annealed with electric field $E$ $=$ 3.6 V/cm, showing 10- (middle terrace) and 14-nm-high antibands located close to terrace edges. Antibands are indicated by arrows. (b) AFM image of Si(111) obtained by annealing with $E$ $=$ 2.0 V/cm showing two neighboring terraces, where the antibands developed by sublimation spirals (lower terrace) and bending of crossing steps (upper terrace).Reuse & Permissions

Figure 2

Surface morphologies created on Si(111) by extended annealing at 1270 °C with different electric fields applied in the step-down direction. The step bunches are aligned along the [1-10] direction, while the down-step [11-2] direction is toward the right in all images. For weakened electromigration fields, wider terrace widths were required to initiate development of the step-bunching instability. Circled are the terrace areas containing crossing steps in a steady-state symmetric S shape. (a) A derivative image of a surface annealed for 15 min with $E$ $=$ 3.6 V/cm and current $I$ $=$ 3.8 A. The crossing steps on the narrower sections of the terraces are less developed toward the antiband. (b) A derivative image of a sample annealed for 30 min with $E$ $=$ 2.8 V/cm ($I$ $=$ 2.9 A). (c) A derivative image of Si(111) annealed for 60 min with $E$ $=$ 1.7 V/cm ($I$ $=$ 1.8 A). (d) A derivative image of a sample annealed for 60 min with $E$ $=$ 1.4 V/cm ($I$ $=$ 1.5 A).Reuse & Permissions

Figure 3

(Color online) The width of the narrowest terrace segments containing crossing steps in the steady-state shape ($L_{\mathrm{m}}$) vs electromigration field $E$, demonstrating the $E$ ∼ $L_{\mathrm{m}}$${}^{-2}$ dependence. The shaded area in the graph indicates terraces where the minimum requirements for $E$ and $L$ are not satisfied and, consequently, the formation of antibands cannot be achieved. The graph points obscure the error bars along the $E$ axis. Ten to 15 sites of 50 × 50 μm${}^2$ were randomly selected across the entire step-bunched area of each sample. The minimum width $L_{\mathrm{m}}$ was drawn from 30–40 separate terraces containing crossing steps in the steady-state S shape.Reuse & Permissions

Figure 4

The step-bunching morphology on a Si(111) surface created at 1130 °C by annealing with different electromigration fields. The surface is off cut 2° toward the [11-2] direction. The direction of the miscut is from left to right in all images, as shown by a stairway symbol in Fig. 4a. Darker areas correspond to step bunches. (a) Phase AFM image of a step-bunched Si(111) surface obtained entirely by dc annealing with $E$ $=$ 3.9 V/cm. (b) Phase AFM image of Si(111) after annealing with $E$ $=$ 1.0 V/cm. (c) Phase AFM image demonstrating that the step bunches expand and occupy most of the surface after annealing at $E$ $=$ 0.6 V/cm. (d) Phase AFM image of Si(111) after annealing with $E$ $=$ 0.5 V/cm; the applied electric field is below critical and is insufficient to initiate the step-bunching process.Reuse & Permissions

Figure 5

(Color online) Dependence of the critical electric field $E_{\mathrm{cr}}$ on the initial average interstep distance $l$ at 1130 and 1270 °C (temperature regimes II and III, respectively). The annotated angles next to experimental points indicate the corresponding degree of miscut off the Si(111) plane in the [11-2] direction. Some error bars are obscured by the graph points.Reuse & Permissions