Generation of an ordered Ge quantum dot array in an amorphous silica matrix by ion beam irradiation: Modeling and structural characterization

We studied the generation of an ordered Ge quantum dot array in an amorphous silica matrix by ion beam irradiation. In particular we investigated the influence of the irradiation process on the nucleation of Ge clusters, on the correlations in their positions and on the crystalline quality of Ge quantum dots formed after subsequent annealing. We have developed a method for the description of the intensity of grazing-incidence x-ray small-angle scattering from irradiated multilayers, which enables a precise determination of the arrangement of quantum dots as well as their position correlation and size distribution. The analysis shows that the irradiation causes an ordering of Ge clusters along the irradiation direction, which substantially improves the correlations of the Ge dot locations in their three-dimensional array. The observed phenomena are explained and simulated by a Monte Carlo model based on the modification of local Ge density induced by ion tracks in the irradiated multilayers.

Figure 1

(Color online) Geometries used for the GISAXS and TEM measurements. The irradiation direction is indicated by the dashed arrows. The probing beam is (a) perpendicular $(\perp )$ and (b) parallel $(\parallel )$ to the irradiation plane.

Figure 2

TEM cross sections of the (a) as-deposited and (b) irradiated multilayers before annealing taken in the $\perp$ direction. (c) and (d) TEM cross sections in the $\perp$ direction of the irradiated multilayer after annealing obtained with two different magnifications. The insets show the Fourier transformations of the corresponding TEM images.

Figure 3

(Color online) GISAXS maps of the annealed multilayers: (a) nonirradiated and (b) irradiated taken in the $\perp$ configuration; (c) simulation of the map of the irradiated multilayer. $Q_{y,z}$ are the scattering vectors in the detector plane.

Figure 4

(Color online) Schematic sketch of the 3D paracrystal model used for the analysis of the GISAXS data.

Figure 5

(Color online) (a) The simplified lateral profile of the density of Ge atoms in the $\text{Ge}+{\text{SiO}}_2$ layer around a single ion track used for the numerical simulation of the nucleation. A constant Ge density assumed before the irradiation is denoted by the dotted line; $L$ is the coordinate parallel to the layer surface. (b) The simulated profile of the Ge density in the same layer after the irradiation with the fluence of $1\times {10}^{15}\text{ions}/{\text{cm}}^2$. (c) TEM cross section of the annealed multilayer. (d) The simulated Ge density obtained assuming a formation of spherical Ge QDs during annealing.

Figure 6

(Color online) Raman spectra of the irradiated and nonirradiated multilayers (a) before and (b) after annealing. In the spectra measured before annealing, amorphous Ge bands close to 80 and $275{\text{cm}}^{-1}$ (denoted by a-Ge and dashed lines) are visible. The inset in (b) shows the enlarged TO Ge peak at $300{\text{cm}}^{-1}$.

Figure 7

(Color online) Diffraction curves of the nonirradiated and irradiated multilayers. The inset shows the first three diffraction peaks corrected for background stemming from the substrate scattering.

Figure 8

(Color online) Infrared absorption spectra of the irradiated and nonirradiated samples. The inset shows the difference of the measured curves. The spectra are corrected to the contribution of pure Si substrate.