X-ray diffuse scattering study of vacancy nanoclusters in homoepitaxial Ag(001) films

The analysis of x-ray diffuse scattering measurements on Ag homoepitaxial films is presented. The experiments, which establish that a low concentration of large vacancy clusters can be incorporated into noble metals during homoepitaxial growth, were performed on 100 monolayer films of Ag deposited on Ag(001) at low temperature. The diffuse scattering of this film was measured, in situ, near several in-plane Bragg positions in grazing-incidence geometry. Because of the large dilatation from the vacancy clusters, the usual approximations of Huang and Stokes-Wilson scattering cannot be made and it is shown that numerical integration of the diffuse scattering equations leads to good agreement between the data and a point-defect scattering model.

Figure 1

Schematic diagram in reciprocal space showing the measurement and calculation details. Experimental measurements were carried out along the [0, K, 0.1] direction as shown by the thin horizontal lines. The shaded rectangular region schematically shows the resolution function of the detector at one measurement point, indicating that the intensity is integrated along the surface normal, from $L=0.005$ to $L=0.15$. The thick solid lines on the K axis show where the numerical calculation of diffuse scattering intensity was performed. Note that the scale is exaggerated in the diagram: it is highly elongated along $L$ and compressed along $K$.

Figure 2

Diffuse x-ray scattering data for Ag/Ag(001) obtained along [0, K, 0.1] in the vicinity of four Bragg positions, $K_n$. It was measured for the clean starting surface (squares) and with 100 MLs of deposited Ag (diamonds).

Figure 3

The x-ray diffuse scattering intensity is shown for the 100-ML Ag(001) film. It was obtained by subtracting the diffuse scattering measured on the clean starting substrate from the total scattering measured on the substrate containing the deposited film. Note that the distribution of diffuse scattering around the Bragg positions is asymmetric toward lower $K$ and that the intensity decreases rapidly with increasing $K_n$.

Figure 4

The symmetric diffuse intensity, $I_{\mathrm{sym}}\left(q_{\left|\right|}\right)=[I(Q_n-q_{\left|\right|})+I(Q_n+q_{\left|\right|})]/2$, is plotted for all measured orders of Bragg position $K_n$. Notice that the intensity decreases rapidly with increasing $K_n$, indicating a large static Debye-Waller factor. Also plotted are resolution-corrected $1/q^2$ and $1/q^4$ lines that show the Huang and Stokes-Wilson scattering, respectively, predicted in the small displacement approximation.

Figure 5

The effect of resolution is shown by comparing the diffuse intensity calculated for $q_z=0$ (dotted line) with the same intensity integrated over the experimental resolution, $q_z=0.005\sim 0.15$ (solid line).

Figure 6

Comparison of the measured diffuse scattering intensity (circles) and the numerically calculated intensities (lines). Dotted (blue), solid (black), and dashed (red) lines are for $-b=30$, 60, and 100, respectively.

Figure 7

The symmetric and antisymmetric components of the experimental diffuse intensities are shown on a logarithmic scale for the four measured Bragg positions, along with the same calculated curves as shown in Fig. 6.

Figure 8

Calculated diffuse scattering intensity at $q=0.02$ as a function of $K_n$ for different defect cluster sizes. For a monovacancy, the intensity initially increases with $K_n$, but for larger clusters the diffuse intensity decreases monotonically. The lines are a guide for the eye.

Figure 9

Diffuse scattering intensity as a function of $K$ at $L$ = 0.02 for two different growth temperatures: 285 K (squares) and 150 K (circles).

Figure 10

Contour map of the diffuse scattering intensity near the (0, 4, 0) Bragg peak which shows the arc-shaped intensity distribution of powder peaks. The white strip at the center of the map is an artifact because no data were taken there.