Quantitative analysis of nanoripple and nanoparticle patterns by grazing incidence small-angle x-ray scattering 3D mapping

3D reciprocal space mapping in the grazing incidence small-angle x-ray scattering geometry was used to obtain accurate morphological characteristics of nanoripple patterns prepared by broad beam-ion sputtering of Al${}_2$O${}_3$ and Si${}_3$N${}_4$ amorphous thin films as well as 2D arrays of Ag nanoparticles obtained by glancing angle deposition on Al${}_2$O${}_3$ nanorippled buffer layers. Experiments and theoretical simulations based on the distorted-wave Born approximation make it possible to determine the average 3D shape of the ripples and nanoparticles together with crucial information on their in-plane organization. In the case of nanoparticle arrays, the approach was also used to quantify the growth conformity of an additional capping layer, which proceeds by replication of the buried ripple pattern.

Figure 1

Schematic drawing of the scattering geometry used to perform 3D GISAXS reciprocal space mapping. ${\alpha }_{\mathrm{i}}$ denotes the angle of incidence, $\varphi$ is the in-plane rotation angle, and $(2{\theta }_{\mathrm{f}},{\alpha }_{\mathrm{f}})$ are the in-plane and out-of-plane angles of emergence. The $z$ direction is normal to the sample surface, while the $x$ and $y$ directions are in the surface plane.

Figure 2

Representation of the shape used to model the form factor of the ripples. The direction of the Xe${}^{+}$ ion beam is also indicated.

Figure 3

GISAXS intensity calculated at $\varphi =0^{\circ }$ for periodic nanoripples with $W=20$ nm, $H=4$ nm, $L=100$ nm, and ${\sigma }_{\mathrm{W}}=0$. (a) Out-of-plane ($2{\theta }_{\mathrm{f}},{\alpha }_{\mathrm{f}}$) map with $A=0$ and ${\xi }_{\mathrm{y}}=250$ nm. (b) Line profiles (logarithmic scale) drawn at ${\alpha }_{\mathrm{f}}=0.3^{\circ }$ for different ${\xi }_{\mathrm{y}}$ values ($A=0$). (c) Out-of-plane ($2{\theta }_{\mathrm{f}},{\alpha }_{\mathrm{f}}$) map with $A=0.3$ and ${\xi }_{\mathrm{y}}=250$ nm. (d) Line profiles (linear scale) drawn at ${\alpha }_{\mathrm{f}}=1.5^{\circ }$ for different $A$ values (${\xi }_{\mathrm{y}}=250$ nm). Curves in (b) and (d) are shifted upward for clarity.

Figure 4

In-plane GISAXS maps ($2{\theta }_{\mathrm{f}},\varphi$) calculated at (a) ${\alpha }_{\mathrm{f}}=0.3^{\circ }$ and (b) ${\alpha }_{\mathrm{f}}=1.5^{\circ }$ for periodic nanoripples with $W=20$ nm, $H=4$ nm, $L=100$ nm, ${\xi }_{\mathrm{y}}=250$ nm, ${\sigma }_{\mathrm{W}}=0$, and $A=0.3$. (c) and (d) Corresponding GISAXS maps ($q_{\mathrm{y}},q_{\mathrm{x}}$).

Figure 5

Asymmetry ratio $AR(\varphi ,{\alpha }_{\mathrm{f}})$ calculated with (a) $A=0$ and (b) $A=0.3$ ($W=20$ nm, $H=4$ nm, $L=100$ nm, ${\xi }_{\mathrm{y}}=250$ nm, and ${\sigma }_{\mathrm{W}}=0$). The dotted lines represent the position ${\alpha }_{\mathrm{f}}={\alpha }_{\mathrm{i}}=0.3^{\circ }$.

Figure 6

GISAXS analysis of the as-etched Al${}_2$O${}_3$ thin film. (a) Experimental out-of-plane ($2{\theta }_{\mathrm{f}},{\alpha }_{\mathrm{f}}$) map at $\varphi =0^{\circ }$. (b) In-plane ($2{\theta }_{\mathrm{f}},\varphi$) map at ${\alpha }_{\mathrm{f}}=0.{425}^{\circ }$. (c) Simulated out-of-plane map. (d) Simulated in-plane map. The direction of the Xe${}^{+}$ ion beam is indicated by the arrow in (a).

Figure 7

GISAXS analysis of the as-etched Si${}_3$N${}_4$ thin film. (a) Experimental out-of-plane ($2{\theta }_{\mathrm{f}},{\alpha }_{\mathrm{f}}$) map at $\varphi =0^{\circ }$. (b) In-plane ($2{\theta }_{\mathrm{f}},\varphi$) map at ${\alpha }_{\mathrm{f}}=0.{425}^{\circ }$. (c) Simulated out-of-plane map. (d) Simulated in-plane map. The direction of the Xe${}^{+}$ ion beam is indicated by the arrow in (a).

Figure 8

HAADF-STEM images of Al${}_2$O${}_3$-capped Ag nanoparticles grown on rippled Al${}_2$O${}_3$ thin films. (a) Plan view, Ag amount of 2.8 nm, and (b) cross-section view, Ag amount of 1.4 nm. The dark and bright dotted lines are guides to the eye, which mark the buffer/capping and capping/air interfaces, respectively.

Figure 9

GISAXS intensity calculated at $\varphi =0^{\circ }$ for Al${}_2$O${}_3$-capped Ag nanoparticles grown on rippled Al${}_2$O${}_3$ thin films (linear color scale). (a) $\chi =0^{\circ }$, no correlated roughness. (b) $\chi =21.8^{\circ }$, no correlated roughness. (c) $\chi =21.8^{\circ }$, correlated roughness with ${\delta }_{\mathrm{y}}=0$. (d) $\chi =21.8^{\circ }$, correlated roughness with ${\delta }_{\mathrm{y}}={\Lambda }_{\mathrm{y}}/4$. The corresponding configurations are also sketched in cross-section view.

Figure 10

Line profiles drawn at $2{\theta }_{\mathrm{f}}=-0.{44}^{\circ }$ and $2{\theta }_{\mathrm{f}}=0.{44}^{\circ }$ corresponding to the simulated GISAXS patterns shown in Figs. 9a, 9b, 9c, 9d. Curves are shifted upward for clarity.

Figure 11

GISAXS analysis of Al${}_2$O${}_3$-capped Ag nanoparticles grown on a rippled Al${}_2$O${}_3$ thin film (Ag amount of 1.4 nm). Experimental out-of-plane ($2{\theta }_{\mathrm{f}},{\alpha }_{\mathrm{f}}$) maps at (a) $\varphi =0^{\circ }$ (x-ray beam parallel to the $x$ direction) and (b) $\varphi ={90}^{\circ }$ (x-ray beam parallel to the $y$ direction). The directions of the Xe${}^{+}$ ion beam and Ag atomic flux are indicated by the black and gray arrows in (a). (c), (d) Simulated out-of-plane maps. (e) Schematic picture of the capping-layer surface corresponding to the configuration described in Fig. 9d.

Figure 12

GISAXS analysis of Al${}_2$O${}_3$-capped Ag nanoparticles grown on a rippled Al${}_2$O${}_3$ thin film (Ag amount of 2.8 nm). Experimental out-of-plane ($2{\theta }_{\mathrm{f}},{\alpha }_{\mathrm{f}}$) maps at (a) $\varphi =0^{\circ }$ and (b) $\varphi ={90}^{\circ }$. The directions of the Xe${}^{+}$ ion beam and Ag atomic flux are indicated by the black and gray arrows in (a). (c), (d) Simulated out-of-plane maps.

Figure 13

(a) AFM image of the surface morphology obtained with Al${}_2$O${}_3$-capped Ag nanoparticles grown on a rippled Al${}_2$O${}_3$ thin film (Ag amount of 1.4 nm). (b) Corresponding 2D (inset) and 1D power spectral densities (PSD).