Self-assembling of Ge quantum dots in an alumina matrix

In this work we report on a self-assembled growth of a Ge quantum dot lattice in a single 600-nm-thick $\text{Ge}+{\text{Al}}_2{\text{O}}_3$ layer during magnetron sputtering deposition of a $\text{Ge}+{\text{Al}}_2{\text{O}}_3$ mixture at an elevated substrate temperature. The self-assembly results in the formation of a well-ordered three-dimensional body-centered tetragonal quantum dot lattice within the whole deposited volume. The quantum dots formed are very small in size (less than 4.0 nm), have a narrow size distribution and a large packing density. The parameters of the quantum dot lattice can be tuned by changing the deposition parameters. The self-ordering of the quantum dots is explained by diffusion-mediated nucleation and surface-morphology effects and simulated by a kinetic Monte Carlo model.

Figure 1

(Color online) Structure of the grown films. (a) TEM cross section of film A. The substrate surface is parallel to the bottom edge of the shown cross section. The inset shows the corresponding FT, (b) TEM cross section of film A with a better resolution, showing an ABAB type of QD ordering. (c) AFM image of a film A surface showing squarelike in-plane ordering of QDs. [(d)–(f)] GISAXS maps of films A–C grown under different conditions (Table ).

Figure 2

(Color online) The EDXS spectra of sample A. The measurements were performed in area 1 closer to the layer surface and in area 2 closer to the layer/substrate interface. The areas are indicated in the TEM cross-section image of the film shown in the inset. The hatched parts of the bars denote the amount of surplus (nonstoichiometric) oxygen.

Figure 3

(Color online) (a) X-ray diffraction curves: the vertical dashed lines show the positions of the diffraction peaks for crystalline Ge. (b) Raman spectra: amorphous (a-Ge) and crystalline (c-Ge) frequency modes are indicated by vertical dashed lines.

Figure 4

(Color online) Explanation and Monte Carlo simulations of the growth of a bcc-like QD lattice. (a) In-plane arrangement of QDs in various 2D dot arrays, $n$ is the array index starting from the bottom of the layer. (b) Cross-sectional view of the positions of QDs. The insets show simulated (sim) and experimentally measured by TEM (exp) QD arrangements. (c) If the initial disorder in a 2D hexagonal lattice is low (left panel, $\sigma =0.15$) six well-separated minima exist at the surface around each buried dot. For the higher disorder degree (right panel, $\sigma =0.30$), some of the minima are very close or overlap (indicated by arrows).