Incommensurate phase near (√3&times√3)R30&deg structure on a face-centered cubic (111) surface

抄録

An incommensurate structure or a commensurate structure with very long periodicity is difficult to handle, because the unit cell cannot be defined or contains a lot of surface atoms. One way to tackle the problem is to start with a nearby commensurate structure with short periodicity and consider the deviation from it. For example, (22&times√3) ("herringbone") reconstruction on a clean Au(111) surface can be considered as slight deviation from bulk-truncated, (1&times1) structure. Due to tensile stress on the surface, the topmost Au layer is compressed in [-110] direction, and 23 Au atoms in the direction are accommodated within 22 periods on the substrate. After the reconstruction, all surface Au atoms cannot occupy stable fcc sites, but some are pushed to metastable hcp sites and even Au atoms on bridge sites are produced at the boundaries between fcc and hcp domains. The reconstruction is imaged by STM as bent atom rows with two brighter stripes corresponding to Au atoms on bridge sites. (Note that so-called herringbone reconstruction contains two steps: one is uniaxial compression along <-110> resulting in (22&times√3) and the other is connection of two domains which differ in compression directions by 120&deg. We focus on the first step.)

In this paper, we consider what happens if the initial structure is (√3&times√3)R30&deg with four surface atoms in a unit cell, and compare the result with the structure derived from (1&times1). Figure illustrates the initial (1&times1) (a) and (√3&times√3)R30&deg (b) structures. As for the (1&times1) structure (a), surface atoms are close-packed in [-110] direction, and occupy only fcc sites. We numbered the leftmost fcc sites with black letters along the [-110] direction, and also numbered surface atoms with red letters. Both numbers correspond to each other due to the (1&times1) periodicity. When the surface layer is compressed in [-110] direction, e.g., the 17th surface atom is pushed to the 16th fcc site. Note that only the shift by full one period is allowed. At the same time, middle atoms numbered 8 or 9 are moved by half a period, and become very close to hcp sites. Thus, bent atom rows travel through fcc-hcp-fcc sites.

In (√3&times√3)R30&deg case illustrated in Fig. (b), surface atoms occupy four different sites including the most stable fcc site, and the close-packed direction is changed to [11-2] due to 30&deg rotation of the √3 unit cell. In [-110] direction, three substrate fcc sites correspond to four horizontal surface atom rows. When the overlayer is compressed in [-110], a shift by half a period is sufficient to produce the surface atom row which is energetically-equivalent to the 0th row. For example, the shift of the 22nd (4N+2 where N is an integer) surface row to the 16th fcc site produces the same arrangement of surface atoms as the 0th row. Moreover, a half-period shift of the 20th (4N) row generates the equivalent but antiphase arrangement to the 0th row. These half-period shifts are in marked contrast with full-period shifts required in the (1&times1) case. The half-period shift causes a quarter period shift of the 9th and 11th atom rows, and places them near hcp sites. The mechanism is similar to that on the (1&times1) surface. However, the resultant arrangement is different. Surface atoms form stripes which run perpendicular to [-110] and parallel to [11-2]. Surface atoms are aligned along [-12-1] direction in one stripe, and aligned in [2-1-1] in the other, and form a chevron-like pattern as a whole. The reconstruction may be considered as two-dimensional twinning which has a symmetry axis of [11-2]. We will show that the above model can be applied to striped incommensurate (SIC) phases of Pb on Si(111) and Pb on Ge(111) systems.