Figure 1

(Color online) (a) Step region (shaded) for which the number of atoms, their positions, and the location of the step edge are to be determined. The region shown corresponds to the $\left[\overline{1}10\right]$-down step configuration and is surrounded by reconstructed terraces with the unit cell marked by rectangles. (b) Crossover operation through which the genetic pool of step structures is evolved. The step energies used in the selection process are computed after relaxing a padding zone (in addition to the step region) with the support kept fixed.Reuse & Permissions

Figure 2

(Color online) Finding the structure of $\left[22\overline{1}\right]$-normal steps on Si(114). (a) Step energy $\Lambda$ of the lowest-energy structure (solid line) and averaged across the pool (dashed line) during the genetic evolution. The lowest energy structure is shown after 0, 200, 500, and 800 crossover operations; the atoms subjected to optimization are shown as darker spheres in the insets. (b) Evolution of the average number of atoms across the pool (dashed line) and of the atom number corresponding to lowest-energy member (solid line). (c) Step energies before and after the final relaxation of all members of the genetic pool. The formation energies decrease upon full relaxation unless bonds are broken in the process (as found in the case of structure No. 28).Reuse & Permissions

Figure 3

(Color online) Low-energy step structures of $\left[\overline{1}10\right]$-oriented steps on the Si(114) surface. The atoms subjected to optimization are represented by dark spheres, while the atoms making up the terrace reconstructions are the lighter ones. The remaining atoms are shown as smaller gray spheres. The structural motifs on the terraces are rows of dimers (d), rebonded atoms (r), and tetramers (t). Some or all of these motifs also make up the shown step structures with the exception of the most favorable down-step models [panels (a) and (b)] which include hexagon rows denoted by “h.” A schematic contour of the step topology was included in each side view to aid the eye.Reuse & Permissions

Figure 4

(Color online) Results of the genetic algorithm (a, b) and experimental observations of steps on Si(114) surfaces (c, d). (a) Lowest step energies attained at various atom numbers in the step zone. (b) Final step formation energies of the top-ranking structures for each of the four types of steps described in text. The $\left[\overline{1}10\right]$ steps have consistently lower energies than similarly ranked $\left[22\overline{1}\right]$ structures. (c) STM image of a vicinal Si(114) surface obtained after cleaning and brief annealing (reproduced from Ref. 11 with permission from the American Institute of Physics). (d) STM image taken after flashing at $1225°\mathrm{C}$ followed by $30\min$ annealing at $450°\mathrm{C}$ (courtesy of D. E. Barlow, A. Laracuente, and L. J. Whitman). The experiments show that the $\left[\overline{1}10\right]$ steps are preferentially longer than the $\left[22\overline{1}\right]$ ones, which is consistent with the calculated step formation energies shown panel (b).Reuse & Permissions