Experimental performance and potential improvements

{100}

Ψ = 0.67 Ψ = 0.90

[010]

[100]

[001]

{100}

Ψ = 0.81

Ψ = 1.00 sphere

Figure 4.9.The notion about the pore morphology is supported by the visualization of different cubic crystal habits. The sphericity quantifies the similarity to a sphere.

of Ψ = 0.85. This contradiction is solved by the consideration of concavities in the pore morphology (arrows in figure 4.5). The coalescence of two pores is supposed which leaves these recesses in the surface. Hence, this fine detail has to be emphasized as valuable hint for the understanding of the pore shape.

The treatment of the pore as 3D body is convenient but the general difference between a usual, convex crystal form and a pore has to be mentioned. The concave surface of the crystal matrix surrounding the pore is the substantial matter. The approach is assumed to be valid as long as the bounding facets dominate over the impact of edges comparing a crystal and the pore. This limitation implies a possible size effect, i.e the size dependent change of the pore morphology.

4.1.2.2. Experimental performance and potential improvements

This section is dedicated to the discussion of technical aspects of the experiment. In the first place, advantages of the applied experimental conditions are highlighted. A critical consideration of resolution limits follows and, finally, potential improvements are outlined.

The specimen shape enables the acquisition of projections over the tilt range of 180^◦. Thereby, the missing wedge problem [143] and the elongation of the reconstructed volume [134] are circumvented. The silhouette of the specimen is directly observed in the recon-structed volume represented by, for instance, the isosurface viewed along the [00¯1] direction (figure 4.5). Of course, this viewing direction is inaccessible in the microscope. It is exclu-sively attained in the visualization of the 3D evaluated data set. Consequently, irregularities caused by the specimen preparation are easily told apart from reconstruction artefacts.

A systematic decrease of intensity toward the centre of the specimen is not detected in figure 4.6. Hence, the selection of the HAADF imaging conditions with a collection angle range of 60 mrad to 160 mrad avoids the cupping artefact that has been described by den

Broeket al.[156]. This artefact arises from a non-linear increase of intensity with thickness and results in the underestimation of the intensity within the volume of interest. The maximal thickness of 170 nm encountered here remains approximately in the linear regime for GaSb which is consistent with the preliminary considerations illustrated in figure 3.11.

(a) (b)

AlSb

Si GaSb

50 nm

Figure 4.10.The HAADF image (a) is compared to the reprojection of the reconstructed volume (b). The direction of the reprojection corresponds to the viewing direction of the HAADF micrograph.

In figure 4.10(a) and (b), an HAADF image is compared to the reprojected volume in the respective direction. The general similarity is apparent, i.e. structural features are repro-duced in the tomogram. The enhanced contrast in the reprojection image is in agreement with the intention of the polytropic montage [137] which has preceded the development of electron tomography. On the other hand, the spatial resolution is downgraded: The dark vertical border that parts the surface damage in the right from the specimen volume appears broader and blurred. The transition from the GaSb to the AlSb layer is less abrupt. Besides, this blurring exacerbates with increasing distance to the small pore. The overall loss of res-olution is a consequence of data binning and low-pass filtering before the application of the reconstruction algorithm. These measurements are applied to reduce the noise in the tomo-gram. A compromise between resolution and SNR is made for the data evaluation. A further impact originates from inaccuracies of the image alignment and uncorrelated distortions in individual images. The distortions cause the gradient of blurring with respect to the small pore to which all images have been aligned.

The facet determination relies on the angular resolution in addition to the spatial resolu-tion. The latter limits the size of detectable facets. The former is important to distinguish between crystallographic planes separated by a certain angleα. In principal, the determina-tion of angles in the tomogram can be inaccurate because of residual image distordetermina-tions and the wrong allocation of tilt angles to the individual frames. Matobaet al.[175] quantified deviations of the actual goniometer tilt and the computer readout. For the presented results, the deviation of the vicinal substrate surface from the (001) plane by 4^◦ (figure 4.3) shows that the angular resolution is not a limitation for the discrimination of low indexed facets (hkl) withh, k, l≤2.

Finally, some approaches are supposed that improve the tomography performance. Three aspects are considered comprising the sample preparation, the data acquisition and the raw data evaluation:

1.) The investigation of the pore succeeded in spite of the damage layer on the (110) surface. Nevertheless, it is assumed that the avoidance of surface features is beneficial in order to reduce noise in the reconstructed volume. This damage layer occurred during SEM monitoring of the preparation progress with an acceleration voltage of 20 kV. The surface features might form due to electron beam induced redeposition of sputtered material or they are remains of molten material. Of course, the question arises why 20 kV electrons harm the material and the TEM investigations at 200 kV do not alter the material. Beam damage due to TEM investigations are not observed although three different tilt series have been acquired. The energy dependence of the interaction of charged particles with matter in SEM and TEM have been studied by Egertonet al.[176]. They have found that there is a minimum at energies in between the regimes of electron-electron and electron-nucleus interactions explaining the counterintuitive behaviour observed in this work. Moreover, the work of Yasuda et al.[177] suggests a careful consideration of electron beam induced creation and clustering of vacancies in GaSb. This effect is excluded as origin for pores during FIB based sample preparation because the pores are also observed in conventionally prepared specimen. In general, the aspect of irradiation damage in TEM and SEM observations has to be reconsidered for each object under investigation because the energy dependence is specific to the material system.

Two further preparation related points concern the size and the shape of the sample. A cylindrical specimen with a diameter as small as possible is aspired to focus on the object of interest. This reduction maximizes the control of the experiment, especially by exclud-ing or reducexclud-ing artefacts. This requirement is limited by the performance of FIB sample preparation. The resolution of the ion beam microscope, the precision of site control and the stability of the ion optics. The irregular shape of the presented specimen is, for instance, the consequence of beam drift during the intended transform of the specimen into a cylindrical object. Moreover, the reaction of the Ga-ion beam with the GaSb has to be kept in mind.

Lugstein et al. [178, 179] described the reaction of GaSb as well as the formation of Sb nanowires under Ga ion irradiation. That is, a balance between specimen shaping and ion beam interaction with the sample has to be found in order to avoid surface features.

The second optimization proposal is related to the later image alignment of the tilt series.

The introduction of markers allows a more precise image alignment as well as a correction of image distortions and the nominal tilt angle. Gold particles are applied in electron tomog-raphy on biological objects for this purpose [142] which might be feasible by a dip of the needle shaped specimen into an adequate suspension. The ultimate control and application of marker has been demonstrated by Hayashida et al. [180] who deposited tungsten dots with a helium ion microscope.

2.) The data acquisition in STEM benefits from shorter scan times. Random image distor-tions arise due to sample stage movements and magnetic disturbance fields. A higher beam current at the object plane is required for this improvement because a faster scan reduces the SNR. An enhancement of the beam current will occur if the microscope is equipped with a C_S-corrector for the condenser system or a higher gun brightness (e.g. a cold field emitter or a higher acceleration voltage [107]). The urgency to increase the beam current and to reduce the scan time will grow if larger collection angles for HAADF imaging are needed due to higher sample thicknesses or if an EDX signal has to be exploited for direct chemical maps.

For instance, Kotulaet al. [9] reported an acquisition time of 1 h for one EDX map in a tilt

series.

3.) The last aspect addresses the software based data evaluation. The necessary alignment of tilt series images preceding the 3D reconstruction relies on distinct features that are visible in subsequent images. Presented results are improved by the usage of the small pore instead of larger objects as the whole needle shape, the AlSb layer or the big pore. Consequently, a feature which is even smaller in size and which provides a stronger contrast in all images, contributes to an improvement of the tomogram. The digital image correction with help of a set of small markers has been described above.