Ordering mechanism of stacked $\mathrm{Cd}\mathrm{Se}∕\mathrm{Zn}{\mathrm{S}}_x{\mathrm{Se}}_{1-x}$ quantum dots: A combined reciprocal-space and real-space approach

The vertical and lateral ordering of stacked CdSe quantum dot layers embedded in $\mathrm{Zn}{\mathrm{S}}_x{\mathrm{Se}}_{1-x}$ has been investigated by means of grazing incidence small angle x-ray scattering and transmission electron microscopy. Different growth parameters have been varied in order to elucidate the mechanisms leading to quantum dot correlation. From the results obtained for different numbers of quantum dot layers, we conclude on a self-organized process which leads to increasing ordering for progressive stacking. The dependence on the spacer layer thickness indicates that strain induced by lattice mismatch drives the ordering process, which starts to break down for too thick spacer layers in a thickness range from $45\text{to}80\mathrm{\AA }$. Typical quantum dot distances in a range from about $110\text{to}160\mathrm{\AA }$ have been found. A pronounced anisotropy of the quantum dot correlation has been observed, with the strongest ordering along the $\left[1\overline{1}0\right]$ direction. Since an increased ordering is found with increasing growth temperature, the formation of stacking faults as an additional mechanism for quantum dot alignment can be ruled out.

Figure 1

Schematic of the sample structure. $N$ quantum dot containing CdSe layers are embedded in $N+1$ strain compensating ZnSSe layers, each of thickness $d$.

Figure 2

Scattering geometry (top) and 2D grey scale representation of spectra recorded from sample A with a position sensitive detector (PSD) in dependence of grazing incident angle ${\alpha }_i.(1\mathrm{r.l.u.}=2\pi ∕5.67\mathrm{\AA })$. Superlattice Bragg peaks (SL), Yoneda peak (Y), and specularly reflected intensity are indicated.

Figure 3

Scattering geometry (right) and GISAXS pattern obtained from sample A (left). Superlattice Bragg peaks (SL), Yoneda peak (Y), and specularly reflected intensity are indicated. Additionally, satellite spots are observed at $q_{\Vert }\approx \pm 0.04\mathrm{r.l.u.}$ (marked by white circles; $1\mathrm{r.l.u.}=2\pi ∕5.67\mathrm{\AA }$).

Figure 4

GISAXS pattern obtained from (top to bottom) samples A $(N=10)$, B $(N=5)$, and C $(N=3)$.

Figure 5

$Z$-contrast cross-section TEM image of sample A (tenfold QD stack) taken in ⟨110⟩ zone axis. The growth direction is from the bottom to the top of the image.

Figure 6

GISAXS pattern obtained from (top to bottom) samples D $(d=20\mathrm{\AA })$, E $(d=45\mathrm{\AA })$, and F ($d=80\mathrm{\AA })$.

Figure 7

Cross section {220} dark-field TEM images of (a) sample E $(d=45\mathrm{\AA })$ and (b) sample D $(d=20\mathrm{\AA })$, each taken in ⟨110⟩ zone axis.

Figure 8

Cross section TEM images of sample F $(d=80\mathrm{\AA })$ taken in ⟨110⟩ zone axis, for two different dark-field conditions: (a) {220} dark field and (b) {002} dark field.

Figure 9

GISAXS patterns obtained from sample A (tenfold stack) for different orientations. The azimuthal angle $\phi$ (see sketch in the middle left) is indicated in each image, as well as the crystallographic direction being parallel to ${\vec{q}}_{\Vert }$.

Figure 10

Left: GISAXS profiles in $q_{\Vert }$ direction obtained from sample A (tenfold stack) for different azimuthal angles $\phi$. Fits to the data are shown as solid black lines. The inset reveals the components fitted to the data: central Gaussian, central Lorentzian (${\mathrm{Lor}}_0$, shaded), and satellite Lorentzians. Right: Intensity of the central Lorentzian (∎), as well as satellite peak intensity (▴), position (▾), and full width at half maximum (●) as a function of azimuthal angle $\phi$. The intensity parameters have been normalized to their maximum value. The open symbols represent results obtained from a fivefold QD stack.

Figure 11

Cross section {220} dark-field TEM images of sample E taken in two perpendicular ⟨110⟩ zone axes.

Figure 12

GISAXS patterns obtained from (top to bottom) samples G $(T=310°\mathrm{C})$, H $(T=280°\mathrm{C})$, and I $(T=230°\mathrm{C})$.