Mapping quantum dot-in-well structures on the nanoscale using the plasmon peak in electron energy loss spectra

Plasmon energy losses experienced by fast electrons passing through a thin specimen are readily measured using electron energy loss spectroscopy. We describe a simple model of the shape and energy of the single scattering distribution plasmon peak, which relates the energy loss spectrum to the material parameters of average band gap ${\overline{E}}_g$, lattice parameter $a$, core ion dielectric constant ${\epsilon }_c$, and plasmon lifetime $\tau$. This model is used to interpret maps of plasmon energy and full width at half maximum taken from an $\mathrm{In}\mathrm{As}∕{\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum dot-in-well structure. We find that the bulk plasmon peak shifts are mainly determined by the strain in the structure, which may provide a new means of mapping strain on the nanoscale. The regions of maximum plasmon peak width appear to correspond to regions of high strain gradient. It is possible to separate the effects of plasmon lifetime from the other factors, leaving a parameter which is a combination of ${\overline{E}}_g$, $a$, and ${\epsilon }_c$. We have been able to map this parameter with a spatial resolution of a few nm.

Figure 1

Dark field 002 TEM image, showing the InAs DWELL layers.

Figure 2

STEM dark field image of one layer in the $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ heterostructure. The area analyzed by EELS is marked as “spectrum image.” Spatial drift corrections were measured, and corrected during acquisition of the EELS data.

Figure 3

A measured SSD plasmon peak in bulk GaAs (bold) and a least squares fit (dotted) according to Eq. (12).

Figure 4

(a) A map of plasmon energy $E_{\max }$ for the region shown in Fig. 2. Also marked are lines which show the position of the data $A$, $B$, and $C$ plotted in Fig. 5. (b) A map of FWHM $\Gamma$ and (c) $E_p^{\prime }$, extracted from the data in (a) and (b).

Figure 5

Data extracted from Fig. 4 along the lines $A$, $B$, and $C$ shown in Fig. 5a. (a), (b) energy $E_{\max }$; (c), (d) FWHM $\Gamma$; and (e), (f) the parameter $E_p^{\prime }$.

Figure 6

Variation in plasmon peak position predicted from Eqs. (11, 12) as a function of change in (a) lattice parameter, (b) $E_g$, (c) ${\epsilon }_c$, and (d) $\Gamma$. In all cases the theoretical change is shown as a thick solid line: the measured peak position of GaAs is shown as a horizontal dashed line which crosses the theoretical curve in the center of the data range. The plasmon energy in the quantum dot is shown as a dashed line, and that in the ${\mathrm{In}}_{0.2}{\mathrm{Ga}}_{0.8}\mathrm{As}$ well is shown as a line of diamond data points. The expected plasmon energy in the well is shown in (a) as a line of square data points.

Figure 7

Comparison of the spatial resolution of the map of the parameter $E_p^{\prime }$, the dark field 002 image of Fig. 1, and the ADF image of Fig. 2. The resolution of all images is of the order of a few nm.