NW 4

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(a) (b)

Fig. 6.23: (NW 3) (A)Q_y Q_z projection of a RSM measured in the middle of the NW. Indicated in white is the center of mass position with the variance of the intensity distribution. (B) Bending of the NW with the NW tip as reference.

• core NW tip diameter: 64 nm

• core NW foot diameter: 140 nm

• NW length: 2700 nm

• shell NW foot diameter: 230 nm

• shell NW length: 1600 nm

• NW elongation in [111] direction: 17 nm

• NW elongation towards the sample surface: 70 nm

Raman shifts were calculated and compared with the measurements. Unfortunately, the agreement is again poor. On the other hand the strain values obtained from the Raman measurement using the linear dependency factor k agree quite well. The necessary displacement of the NW tip in surface direction to reproduce the bending in the FEM simulation is very high and most probably not describing reality. However, it is hard to investigate whether the bending was induced by the synchrotron radiation during the experiment or not, we have to leave this question unfortunately still open.

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Fig. 6.24: (NW 3) On the top left the measured strain in [110] direction is plotted in blue. The NW bending with respect to its tip is plotted as a blue line in the bottom left graph. On the right hand side FEM results are shown. The red, and green lines overlayed in the graphs on the left hand side are the simulation results according to the measurements. All the strain values are given in %. The elongation of the NW in the FEM simulation was 17 nm.

(a) (b)

Fig. 6.25: (NW 3) (A) Comparison of the FEM results with the strain values from Johannes Greil (top), together with the comparison of the Raman simulation with the measured Raman shift (bottom).

(B) Top view SEM image of the investigated wire along with the simulated geometry in FEM.

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(a) (b)

Fig. 6.26: (A) Resulting real space map of scanning X-ray diffraction microscopy at the Si (220) and Ge (220) Bragg reflections. (B) Overlay of the Ge (220) map and a SEM image of NW 4.

are indicated, where 430 is the thin tip and 593 the thick foot of the NW. The interesting positions are the tip and the middle of the wire, therefore Fig.6.27 (B), and Fig.6.28 show Q_y Q_z projections of this RSMs with cuts through the thickness oscillations. The RSM at position 514 is not shown here, since no thickness oscillations were observed, this is probably due to the amorphous shell wrapped around the base of the NW, which can alter the surface of the crystalline NW core and destroy phenomena like thickness oscillations. The RSM of the tip position and its remarkable features demand a more detailed discussion. The distance between the thickness oscillations changes withQ_y. Q_y is more or less the NW growth direction, and therefore the changing thickness oscillations reflect the tapering of the NW within the illuminated NW segment. Figure6.28 shows the evaluation of the RSM of the NW tip at different Q_z positions. Please note that the intensity of Fig.6.28 is higher for lower Q_y values, whereas in Fig.6.27 (B) more intensity was scattered to higherQ_y values, reflecting the fact that different segments of the bended NW give raise to scattering intensity at differentQ_y positions. This is a nice feature, however, it also shows us that still considerable diffracted intensity due to the tails of the nano-focused synchrotron beam is collected, since the distributed intensity along Q_y is always observable over the whole range according to the NW’s bending.

The measured strain values of this NW are very small, as can be seen in Fig6.27 (A), and in the line plot of _[110] in Fig6.29. This line plot was created by averaging the calculated strain values perpendicular to the NW direction. In the strain map of this measurement a rather high strain gradient in piy direction, which is perpendicular to the NW growth direction, showed up. This gradient is actually slightly higher than the estimated precision of the method. We always assumed that the different values in beam direction (the convolution between NW thickness and vertical beam size gives rise

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(a) (b)

Fig. 6.27: (NW 4) (A) Real space image of of the strain distribution evaluated from the (220) Bragg peak position. Indicated are the NW’s tip (position 430), the middle (514), and the foot (593). In (B) the RSM recorded in the middle (position 514) of the NW is plotted. The slice where the thickness oscillations are evaluated is indicated in the map as a grey area. The comparison between measurement and shape function gives a NW thickness of 120 nm at this position.

to this broadening) are physically the same, i.e. the values have to be equal, which was also the case for the other NWs. The position of the Bragg reflections was calculated as the center of mass position of the intensity distribution, from the whole NW’s scattered intensity at each real space point. The somehow highly pronounced effect of “seeing”

scattered intensity from the tails of the focused beam during the investigation of NW4, as seen from the thickness oscillations, is assumed to cause this effect. The calculated values seem to be averaged over a higher volume, and therefore intensity from something else than the NW can be involved too. The problem is that one has to evaluate the intensity maxima of the Bragg peak, and when the Bragg peak intensity is a mixture of several volume elements of the NW with additional intensity from something beside the NW which actually needs not even fully be in Bragg condition, data evaluation becomes really hard, especially when one wants to measure small lattice plane changes. However, bare in mind that the strain values of NW4 are quite small, presumably there was almost no elongation of the NW due to the cantilever. The FEM simulation agreed with this assumption, the elongation necessary to get a comparable strain in [111] direction was only 5 nm, whereas the displacement towards the sample surface providing a agreement between the bending values of simulation and measurement was 60 nm. This NW was not investigated with µ-Raman scattering, and therefore no Raman simulation was calculated.

• core NW tip diameter: 90 nm

• core NW foot diameter: 160 nm

• NW length: 2700 nm

• shell NW foot diameter: 310 nm

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(a) (b)

(c) (d)

Fig. 6.28: (NW 4) (A,B,C) RSM collected at the NW tip. i.e. when the beam was hitting the NW tip. The thickness oscillations were evaluated at three differentQy positions as indicated with a gray area in (A), (B), and (C). The trend from the thin tip with 95 nm diameter to a diameter of 115 nm somewhere close to the middle of the NW can be seen nicely. (D) is a comparison of a SEM image and the FEM model of NW4.

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Fig. 6.29: (NW 4) On the top left the measured strain in [110] direction is plotted in blue. The NW bending with respect to its tip is plotted as a blue line in the bottom left graph. On the right hand side FEM results are shown. The red, and green lines overlayed in the graphs on the left hand side are the simulation results according to the measurements. All the strain values are given in %. Almost no NW elongation along [111] was necessary in the FEM simulation, however, a displacement of the NW tip towards the sample surface to reproduce the NW’s bending.

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• shell NW length: 1000 nm

• NW elongation in [111] direction: 5 nm

• NW elongation towards the sample surface: 60 nm

Figure6.28 (D) shows the wire geometry of the FEM model with a SEM image. The measurement and simulation results are shown in Fig.6.29, where the strain results agree rather poor, but the bending of the NW is described quite well.