Effects of Domain Boundaries on the Diffraction Patterns of One-Dimensional Structures

Abstract

Motivated by diffraction experiments on the 2 √ 3 × √ 3 R30 • reconstructed Si(111) surface due to deposition of rare earth elements (Dy, Tb) and silicide formation, we analyse the splitting and non-splitting of superstructure diffraction spots. For this purpose, we model diffraction patterns for one-dimensional structures generated by the binary surface technique and use supercell models to keep the analysis simple. Diffraction patterns are calculated in the framework of the kinematical diffraction theory, and they are analyzed as a function of the domains and domain boundaries. Basic properties of the diffraction pattern are analyzed for model systems of a two-fold and a three-fold periodicity. The rules derived from these calculations are applied to the "real-world" system of Si (111)Depending on the combination of domains and domain boundaries of different types, a plethora of different features are observed in the diffraction patterns. These are analyzed to determine the sizes of both domain boundaries and domains from experimentally observed splitting of specific superstructure spots.

On the diffraction pattern of bundled rare-earth silicide nanowires on Si(0 0 1)

“…First of all, it can be seen that introducing DBs between adjacent NWs leads to additional peaks in the diffraction pattern for small values of the scaled variance M −1 regardless of the periodicity considered. This is analogous to the observations we made in our previous study [15] and can be explained by the so-called supercell approach in which all supercells are composed of domains (in this case ≡ NWs) with the same size γ and DBs of uniform size forming a supercell of pγ + 1 unit cells, introducing the periodicity parameter p (one-fold ≡ p = 1 and two-fold ≡ p = 2), leading to the additional diffraction spots. Their position (in the reciprocal space) is given by…”

“…This is somewhat counter-intuitive considering the fact that the distance between adjacent peaks ∆H is only a function of the domain size γ in the framework of the supercell approach. As a matter of fact, the results obtained here only converge to the results expected from the supercell approach [15]…”

“…Only peaks at or near the nominal peak positions H nom = µ/p (with μ ∈ Z) remain. This is due to the fact that the structure factor of the domains of the average size γ is very similar to the structure factor of the unit cells it is composed of [15]. The position of the (remaining) peaks depends on whether the DBs exhibit in-phase or anti-phase character and the exact makeup of the DBs.…”

“…Consequently, it is also applicable to large unit cells where a dynamical approach would be infeasible. In our previous studies [15] we only considered the influence of DBs embedded in domains of uniform length on the diffraction pattern (supercell approach) in the framework of the binary surface technique [15][16][17].…”