Adhesion of growing nanoparticles at a glance: Surface differential reflectivity spectroscopy and grazing incidence small angle x-ray scattering

This paper compares the capability of surface differential reflectivity spectroscopy (SDRS) and grazing incidence small angle x-ray scattering (GISAXS) to characterize in situ, “at a glance,” a collection of nanoclusters by statistically defining the geometry of an average particle (diameter, height, and interparticle distance). SDRS and GISAXS are run simultaneously on Ag/MgO(001) films during their growth. They are shown to lead to consistent values of the morphological parameters, with a particular good agreement about the aspect ratio (height/diameter) which, thanks to the basic physics underlying the two measurements, is determined in both cases. By modeling silver particles by truncated spheres, close estimates of the wetting angle and of the adhesion energy are derived ($0.75\pm 0.08\text{J}{\text{m}}^{-2}$ for SDRS and $0.85\pm 0.20\text{J}{\text{m}}^{-2}$ for GISAXS). This demonstrates that the very flexible laboratory SDRS can be used to study the growth of a film in a similar way as the well-documented small angle x-ray scattering provided it is analyzed in an appropriate framework.

Figure 1

(Color online) Principle of the coupled SDRS and GISAXS measurements. In SDRS, the relative variation in the sample reflectivity in the UV-visible range is recorded. The incident and reflection angles are related by the Snell-Descartes law: $i_i=i_r$. In GISAXS, the incident x-ray beam of wave vector ${\mathit{k}}_i$ impinges on the surface at a grazing angle ${\alpha }_i$. The scattered intensity (wave vector ${\mathit{k}}_f$) is recorded on a plane as function of the exit angle ${\alpha }_f$ (with respect to the surface plane) and of the in-plane angle $2{\theta }_f$. The wave vector transfer is noted $\mathit{q}=\left(q_x,q_y,q_z\right)$.

Figure 2

(Color online) SDRS optical spectra recorded in situ during the growth of the Ag/MgO(001) film at (a) 300 and (b) 640 K. Deposited thicknesses are given—Open circles: experiment; line: simulation (see text).

Figure 3

(Color online) Evolution of the morphological parameters $H$, $D$, and $L$ (a) and (b) at 300 (c) and (d) at 640 K. Filled symbol: GISAXS; open symbol: SDRS—Estimates of the thickness obtained from $H$, $D$, $L$ are shown in (b) and (d) as a function of the quartz measurements. The SDRS integrated signal (filled circles) over the whole spectral range is shown on the right scale of (b) and (d). To first approximation, it depends linearly on the film thickness (Ref. 42).

Figure 4

(Color online) Values of the aspect ratio of Ag/MgO(001) clusters grown at 300 and 640 K. They are directly determined in the case of SDRS data. In the case of GISAXS, they are derived from the particle heights and diameters shown in Fig. 3.

Figure 5

(Color online) Evolution of the 2D GISAXS patterns recorded in situ during the Ag/MgO(001) growth at 300 K (simultaneously with SDRS), with the incident beam parallel to the MgO[010] direction, as a function of the deposited thickness: (a) 1 nm, (b) 1.8 nm, (c) 2.2 nm, (d) 3.6 nm, (e) 4.4 nm, (f) 6.2 nm, (g) 7 nm, and (h) 10 nm. The intensity is represented on a logarithmic scale. Black contours between colors correspond to order of magnitude in intensity. The $q_y$ (respectively, $q_z$) axis ranges from 0 to $2.5{\text{nm}}^{-1}$ (respectively, $2.6{\text{nm}}^{-1}$).

Figure 6

GISAXS cut (a) parallel and (b) perpendicular to the surface for the 3.6-nm-thick Ag deposit on MgO(001) at 300 K. Dots: cuts of the experimental GISAXS pattern; thin line: best fits of the experimental cuts. The results of the best fit are as follows: $L=14.2\text{nm}$, $D=8.8\text{nm}$, and $H=6.3\text{nm}$. The intensity is represented on a logarithmic scale.

Figure 7

Interference function $S\left(q_y\right)$. Filled squares: $L=14.2\text{nm}$. This case corresponds to the 3.6-nm-thick Ag deposit on MgO(001) at 300 K. The corresponding GISAXS cut parallel to the surface is displayed in Fig. 6. Filled triangles: $L=7.1\text{nm}$.