281 Introduction to surface processes

units, dimers, adatoms and stacking faults, and is hence known as a DAS model. The 7 37 is just one possible structure of this type, all of which have odd numbers of multiples between the surface and bulk meshes. The LEED or THEED patterns of the 737 structure contains 49 superstructure spots (or beams) of diVerent intensity, which needed to be analyzed to solve the structure in detail.

1.4.6Various `root-three' structures

These structures arise in connection with metals and semi-metals (B, Cu, Ag, Au, In, Sb, Pb, etc.) on the (111) face of semiconductors, and adsorption of gases on hexagonal layer compounds such as graphite. Here again we have three domains, but they are positional, as well as sometimes orientational, in nature. One can put the atoms in three positions on the substrate, but if you put them on one lattice (A), the other two (B and C) are excluded, in the case of rare gases on graphite because of the large size of the adatoms, as indicated earlier in ®gure 1.16. Studies of such structures have a long history in statistical mechanics, as in the `three-state Potts model', where the three equivalent positions leads to a degenerate ground state, and interesting higher temperature properties. Adsorption is discussed here in more detail in chapter 4.

Figure 1.20 shows the reported structure of Ag adsorbed on Si or Ge(111), which has been determined by surface X-ray diVraction (Howes et al. 1993), with the surface and bulk lattices indicated. The interesting point in the present context about this Aginduced structure is to realize how much has to happen at the surface, to produce these structures. Deposition of metal atoms alone is not nearly enough to produce it starting from Si(111)737 or Ge(111)238. Substantial diVusion of both metal and semiconductor is required. The same consideration applies to producing Si(111) surfaces by cleavage, which results in the 231 structure. This p-bonded structure, which does not require any long range atomic motion is, however, metastable. Heating to around 250°C causes it to transform irreversibly into the 73 7, which is the equilibrium structure below the reversible 737 to `131' transformation at 830°C; these transformations involve major movement of atoms at the surface.

1.4.7Polar semiconductors, such as GaAs(111)

When lower symmetry structures are combined with the lower symmetry of the surface, various curious and interesting phenomena can occur. For example, GaAs

Å

and related III±V semiconductors are cubic, but low symmetry (43m point group). Looked at along the [111] direction, the atomic sequence is asymmetric, as in (Ga, As, space) versus (As, Ga, space). This results in `polar faces', with (111) being diVerent

Å Å Å V

from (111). These are the A and B faces, and can have di erent compositions and charges on them. Atomic composition and surface reconstruction interact to cancel out long range electric ®elds. For `non-polar' faces, e.g. GaAs (110), this composition/charge imbalance does not occur, and these tend to have (131) surfaces. This