Trends and strain in the structures of two-dimensional rare-earth silicides studied using medium-energy ion scattering

The surface structures of the two-dimensional (2D) rare-earth (RE) silicides formed by Gd and Tm on Si(111) have been determined using medium-energy ion scattering (MEIS). These data have been taken together with those from earlier MEIS studies of the 2D silicides formed by Dy, Ho, Er, and Y to investigate the existence of trends in the structural parameters of this class of surfaces. It was found that the Si-RE bond length associated with the surface bilayer in the 2D silicides followed the same trend as the bond length in the bulk silicide compounds which is simply related to the size of the RE atom. In contrast, changes in the Si-RE layer spacing in the 2D silicides were found to be too large to be accounted for by a size effect alone. It was found that the strain that results from the expansion or compression of the overlayer to fit the Si(111) surface is compensated by changes in the Si-RE layer spacing. Finally, there is a systematic variation in the rumple of the surface bilayer in the 2D RE silicides which appears to increase with the magnitude of the lattice mismatch suggesting that strain in the overlayer results in a weakening of the $\mathrm{Si}\text{−}\mathrm{Si}$ bond in the surface bilayer.

Figure 1

Diagram showing the surface structure of the 2D rare-earth silicides.

Figure 2

The origin of the blocking dips in the RE scattering yield for the $\left[\overline{1}00\right]$ incidence geometry. The filled and open circles represent Y atoms and Si atoms in the surface bilayer, respectively.

Figure 3

(Color online) Angle-dependent RE scattering yield for the $\left[\overline{1}00\right]$ incidence geometry in the region of the dip $\gamma$ for a range of 2D silicides. A curve drawn through a smoothed version of raw experimental data has been added to guide the eye. Data shown for Gd and Tm not previously reported; others from Refs. 12, 13, 14.

Figure 4

Plot illustrating the origin of contributions to the ${\chi }^2$ $R$-factor (weighted square of the residuals) when comparing experimental data to a simulation for (a) the optimum model selected by the $R$-factor and (b) the structurally correct model. (Experimental data corresponds to 2D yttrium silicide, Ref. 14.)

Figure 5

(Color online) The angle-dependent RE scattering yield from $\mathrm{Si}\left(111\right)1\times 1\text{−}\mathrm{Gd}$ for the $\left[\overline{1}00\right]$ incidence geometry shown along with the simulation for the optimum model.

Figure 6

(Color online) The angle-dependent RE scattering yield from $\mathrm{Si}\left(111\right)1\times 1\text{−}\mathrm{Tm}$ for the $\left[\overline{1}00\right]$ incidence geometry shown along with the simulation for the optimum model.

Figure 7

(Color online) Variations in the RE-Si layer spacing in the bulk RE silicides and the RE-Si2 layer spacing in the 2D silicides plotted against bulk RE-Si bond length (a measure of the size of the RE atom). Lines are drawn between the points to guide the eye. The data relating to the bulk silicides is from Ref. 4.

Figure 8

(Color online) Variations in the effective $c$-axis strain ${\epsilon }_{\mathrm{eff}}$ in the 2D RE silicides plotted as a function of the lattice mismatch between the bulk silicide and the Si(111) surface. The $a$-axis strain (which is defined by the lattice mismatch) is plotted as an aid to the illustration. Each line plotted is a straight-line fit to the associated data points.

Figure 9

Variations in the surface bilayer rumple (Si1-Si2 layer spacing) in the 2D RE silicides plotted as a function of the lattice mismatch between the bulk silicide and the Si(111) surface.