Missing rows and atomic steps

Irregularities in the form of missing rows and atomic steps are frequently observed. Each of these break the∼25 ˚A periodicity. However, the geometry of these features is not random. Examples of missing rows and atomic steps are depicted in figures 6.13 and 6.15. In this section it is demonstrated that the geometry of these irregularities can be understood by considering that the

{111}-nanofacet coverage, at the atomic steps or missing rows, is maximised.

In the presence of missing rows ridge-to-ridge separations of∼34 ˚A,∼42 ˚A and ∼50 ˚A have been observed. These distances correspond to 4, 5 and 6 times the (110) unit cell parameter of 8.4 ˚A, respectively. When these fea- tures are present the separation of the rows is always observed to be an integer multiple of 8.4 ˚A. The vertical ridge-to-trough depth increases with

Figure 6.13: (a) and (b): 60 nm×60 nm STM images. (c) and (d): line profiles corresponding to green line segment in (a) and (b). In the presence of missing rows the ridges can be separated by ∼34, ∼42 and∼50 ˚A which corresponds to 4, 5 and 6 times the unit cell parameter of 8.4 ˚A. With the increasing ridge-to-ridge distance the ridge-to-trough depth increases. The reason for such relationships, which maximises the (111) coverage, can be understood by viewing figure 6.14.

6.2. Atomic and electronic structure 125

the row separation as seen in figure 6.13(d). It is important to note that as the tip probes the trough it will collect current from other segments of the reconstruction due to its finite size and this results in an underestimated ridge-to-trough depth.

The geometry of the missing rows can be understood by examining the structure of this reconstruction. If one starts with the ansatz that the{110}

and {111} sections of the reconstruction are always terminated by the same (110) and (111) planes and the (111) surface coverage is maximised, then is follows that the distance between rows must be a multiple of 8.4 ˚A. This is illustrated schematically in figure 6.14 which demonstrates examples of

Figure 6.14: The ridge-to-ridge distance in (a) and (c) are 25.2 ˚A and 33.6 ˚A and the corresponding ridge-to-trough depths are 4.5 ˚A and 7.5 ˚A, respec- tively. Experimentally, when the regular 25 ˚A periodicity is broken by miss- ing rows, the ridge-to-ridge distance is always an integer multiple (greater than 3) times 8.4 ˚A. The STM line profile in (b) illustrates a ridge-to-ridge distance of ∼34 ˚A. Note that the ridge-to-trough depth increases with the ridge-to-ridge separation.

126 Chapter 6. (1×3) row-reconstruction

25.2 ˚A (3×8.4 = 25 ˚A) and 33.6 ˚A (4×8.4 = 25 ˚A) ridge-to-ridge separations. The model in figure 6.14 is a stoichiometric slab terminated by {111}Fetet1-

and {110}B-planes. Figure 6.14 also demonstrates that with increasing row separation the facets between them increase in size, and hence, the ridge-to- trough depth increases, in agreement with the experimental observations. If the distance between rows is a non-integer times 8.4 ˚A, either the two facets will not be the same (111) termination or the{110} segments will be larger or of a different (110) termination.

Figure 6.15: (a) 80 nm×80 nm STM. (b) Line profile corresponding to the green line segment in (a). When the rows step up by 3 ˚A the lateral separation of the rows is observed to be equal to 21 ˚A or 29 ˚A, these distance correspond to 21₂ and 31₂ times the unit cell parameter of 8.4 ˚A, respectively. (c) Line profile corresponding to the blue line segment in (a). When the rows step up by 6 ˚A the lateral separation of the rows is observed to be equal to 25 ˚A which corresponds to 3 times the unit cell parameter of 8.4 ˚A. The reason for such relationships, which maximising the (111) coverage, can be understood by viewing figure 6.16.

6.2. Atomic and electronic structure 127

This analysis can also be applied to the atomic steps. The rows are routinely observed to step up of down by 3 or 6 ˚A as seen in figure 6.15. 3 ˚A corresponds to the distance between like (110) planes, A to A-plane or B to B-plane. If we enforce the conclusion drawn from the missing rows, that is, the (111) coverage is maximised, we find that the ridge-to-ridge distance must be an integer and a half times 8.4 ˚A when their vertical separation is

Figure 6.16: (a) and (b) illustrate that if the step height is equal to 3 ˚A, the lateral distance between ridges is an integer and a half times the unit cell distance. (c) illustrates that if the step height is equal to 6 ˚A, the lateral distance between ridges is an integer times the unit cell distance. The models are compared to the experimental STM line profiles. Note the comparison between the models and line profiles ridge-to-trough depth between the step.

128 Chapter 6. (1×3) row-reconstruction

3 ˚A. Furthermore, if the vertical separation is 6 ˚A the ridge-to-ridge distance must be an integer times 8.4 ˚A. This is depicted schematically in figure 6.16 and is always observed experimentally.

At irregularities in the form of missing rows and atomic steps, the {111}- facets are present and are maximised. The analysis is in agreement and adds weight to the work of Parkinson et al., who determined on the basis of RHEED that faceting occurred [143]. The question arises as to why the reconstruction is (1×3) and not (1×4) or greater, as a larger unit cell will increase the {111} coverage. In section 5.1.3, on the basis of RAS measure- ments and DFT calculations, it is concluded the terminating layers of the

{111}-nanofaceted row reconstruction are stained. Increasing the periodic unit increases the facet size, and hence, the facet height (surface normal di- rection). With increased facet height the strain in the terminating planes will be greater: the strain in any layer is constrained by the strain in the layer below it, hence, will greater facet height the strain in the terminating plane will increase. It is suggested that the reduction in surface energy associated with increasing {111} coverage, is at odds with the resultant strain energy. (1×3) periodicity is likely a balance between the two.