(a) shows a HAADF image of a specimen prepared by FIB following the procedure described above. As it can be observed, the needle has a shape close to cylindrical and its diameter is small enough so that the different QDs layers are visible, showing that the proposed fabrication method was successful.
Figure 1 Cross-sectional HAADF images of the needle-shaped specimen taken at different rotation angles. Note that the angles between the stacking of QDs and the growth direction are different for the three images: (a) 0°, (b) 5°, and (c) 11°. (more ...)
In this image, the InAs QDs can be clearly observed as they exhibit brighter contrast than the GaAs matrix because of the higher average Z
number. However, in HAADF images, the static atomic displacements of the atoms, because of the strain in the epitaxial layers, also play an important role in the observed contrast
]. Because of the rounded shape of the QDs, they are not expected to show sharp upper interfaces when observed by HAADF but with diffused boundaries, in which the contrast is gradually reduced at the edge, as it is shown in the image. Regarding the vertical stacking of the QDs, it is worth mentioning that we have not found a stacking running across all the 50 layers as expected, but only up to approximately 12 to 15 QDs. This could be detrimental to the functional properties of this structure, and it is a consequence of the strain fields in the structure.
About the vertical alignment of the QDs, from the micrograph in the inset of Figure
(a) it seems to be parallel to the growth direction. In many cases, this is the expected distribution of the QDs since the non-perfect alignment of the QDs has been reported to influence the electron wavefunction
] and to reduce the exchange energy between electronic states
]. However, it should be highlighted that TEM cross section images are 2D projections of the sample and therefore, the volume information is lost; this should be taken into account to avoid the misinterpretation of the images. In this regard, (b) and (c) in Figure
show HAADF images of the same needle-shaped specimen as in (a) in Figure
but taken at different rotation angles, 90° apart from each other, and −10° and 80° from the micrograph in (a) in Figure
, respectively. The unusual geometry of the needle-shaped specimen fabricated by FIB in this study allowed us to obtain a higher number of projections than possible from the conventional thin foils, providing interesting additional information of the sample. As it can be observed, at these rotation angles, the stacking of QDs is not vertically aligned anymore. Instead, deviation angles of 5° and 11° with respect to the growth direction have been measured. Other values for the vertical alignment of the QDs have been measured from different rotation angles. These experimental results to evidence that the conclusions obtained from the conventional 2D analysis of the stacking of QDs often found in the literature are not reliable and would mislead the interpretation of the functional properties of these nanostructures, being the 3D analysis of the sample as an essential step.
In order to obtain 3D information from the sample, we have acquired a tilt series of HAADF images, and we have computed the tomogram using these images. The results are shown in Figure
shows a general view of the needle, including the upper stacking of QDs and the platinum deposition. For the analysis of the distribution of the QDs, a segmentation of the reconstructed structure was carried out, as shown in Figure
. This figure reveals that the real distribution of the QDs consist of a stacking that follows a straight line that deviates 10° from the growth direction Z, which is quite different from the results obtained from Figure
. From this analysis, we have also observed that there is an asymmetry in the size of the QDs, being around 30% smaller in one direction than in the perpendicular one in the growth plane.
Figure 2 The surfaces render of the reconstructed volume and an axial slice through the needle. (a) Semi-transparent external surface of the tomogram of the needle with opaque surfaces for the QDs below the platinum deposition. A projection of one of the central (more ...)
It is worth mentioning that often the 3D information obtained from tomography analyses suffers from the missing wedge artifact due to a lack of information for high rotation angles. This causes an elongation of the features in the sample along the microscope optical axis (in our case, parallel to the wetting layers). Figure
shows an axial slice through the reconstructed needle, where this elongation is observed. We have superimposed a circle along the surface of the needle to evidence this elongation more clearly. From this figure, we have calculated an elongation percentage due to the missing wedge of 1.14%. We have measured the vertical alignment of the dots using the location of the center of each dot and because of the calculated elongation, this position will be displaced from its real location. The maximum error in the location of the QDs would occur for dots placed close to the surface of the needle, and where the QDs alignment has a component parallel to the optical axis of the microscope. In this case, the error in the angle between the QDs vertical alignment and the growth direction would be of 3.5°. This error could be minimized using needle-shaped specimens in combination with last generation tomography holders that allow a full tilting range. On the other hand, for QDs stacking included in a plane perpendicular to the microscope optical axis located in the center of the needle (as shown in Figure
), there would be no error in the measurement of the angle. In our case, the vertical alignment of the dots is closer to this second case. In Figure
we have included the position of the upper QD in the stacking with a white dotted line, and of the lower QD with a black dotted line. As it can be observed, both dots are very close to the center of the needle, and the vertical alignment forms an angle close to 90° with the optical axis; therefore, the error in the measurement of the QDs vertical alignment is near to 1°.
The observed deviation from the growth direction of the stacking of QDs is caused by the elastic interactions with the buried dots and by chemical composition fluctuations
]. However, other parameters such as the specific shape of the QDs
], elastic anisotropy of the material
], or the spacer layer thickness
] need to be considered as well to predict the vertical distribution of the QDs. Understanding these complex systems needs both a strong theoretical model and precise experimental measurements to compare the obtained results. Our work provides these experimental data. The correlation of these results with the growth design and with the functional properties of these structures will allow closing the loop to optimize the performance of devices based in stacking of QDs.