Setup characterization

The typical method for testing the bending mechanism for MCBJ is recording opening and closing traces and collect data for a statistical analysis. An exemplary result is shown in Fig. 6.3, which depicts a conductance histogram of sample B0057K at 80 K. The ac-quisition of the traces took about 3 h at an applied voltage of 5 mV.

Altogether 160 opening and closing curves serve as base of this histogram. A very promi-nent peak is located at 1 G₀, but also the peaks at 2 G₀ and 3 G₀ are obvious and close to the exact multiplies of G₀. The shift towards lower conductances can be explained by backscattered electrons on defects near to the contact. These findings are in good agreement with other results [81, 90, 91].

A closer look on the raw data provides Fig. 6.4. There, some opening (top) and closing (bottom) traces are shown, where the conductance plateaus nicely appear. The opening traces show more small steps, presumably due to more mechanical load to the mechanics, than the closing traces. The long plateaus at 1 G₀ and the prominent peak in the con-ductance histogram point out the generation of Au chains during the stretching process.

0 1 2 3 4 5 6 7 8 9 10

0.5 1 1.5 2 2.5

x 10

Conductance [G

]

Counts [arb. u.]

Figure 6.3: Conductance histogram of gold measured at 80 K. The 160 opening and closing traces, which served as base, were recorded with an applied voltage of5 mV.

0 1 2 3 4 5 6 7 8 9

Conductance[G 0]

Displacement [arb. u.]

0 1 2 3 4 5 6 7 8 9

Conductance[G 0]

Displacement [arb. u.]

Opening curves

Closing curves

Figure 6.4: Opening curves (top) and closing curves (bottom) performed at 80 Kwith the developed breaking mechanism, described in section 4.2.1.

Optical setup

Position determination of the laser spot on the sample The used optical setup, a modification of a 4f configuration which was already described in section 4.2.3, enables the controlled positioning of the laser spot on the sample within a window of more than 500µm×500µm in steps smaller than 1µm on the sample. To enhance the accuracy and the repeatability of the motion of the spot, two step motors tilt the mirror precisely.

Fig. 6.5 proves the assumption that the relation between tilting the mirror and the

-200 -100 0 100 200

Figure 6.5: a) Within a window of more than500µm×500µma precise positioning of the laser spot is possible. For every position an optical picture was taken and tagged with red dots for the x-directions and blue dots y-direction. The coordinates were read out and plotted against the expected position in b) and c).

position on the sample is linear in the measured window. Hence, as shown in Fig. 6.5a), the sample was scanned fromy=−285µm to 301µm andx=−253µm to 250µm, whereas the contact is located at (0/0). The points were read out manually from the optical pictures and tagged with red dots for x and blue dots for the y-axis. Moreover, the size of the dots indicates the spot diameter.

In Fig. 6.5b) and c) the positions of the spots are plotted against the expected position for the x and the y direction, respectively. The distance between two expected positions was calculated by the distance of the two outer spots divided by the number of dots minus 1. Linear fits of the curves in Fig. 6.5b) and c) exhibit slopes with 0.996±0.003 for the x-axis and 1.000±0.002 for the y-axis. The slopes very close to 1 and residual sum of squares (RSS) of 34µm with 18 points in y-direction and a RSS of 96µm with 24 points in x-direction demonstrate that tilting the mirror by a certain angle leads to an equidistant position change on the sample over the whole interval.

7

Figure 6.6: Analysis of position of the illumination spots. a) illustrates the illumination spot of the cross-section, which were tagged with green dots after manual read out. On the right-hand side, eight original pictures of the laser spot are shown, whereas the labeling starts on the left-hand side with 1. b) and c) reveal the analysis of the position in x and y direction, respectively. The constriction is located at position (0/0).

Another, more difficult example of a recorded cross-section is shown in Fig. 6.6. There, it is a challenge to identify the laser spot positions in the optical pictures. In a) the studied cross section is depicted after read out, whereas the positions were tagged with green dots. On the right-hand side, original pictures of the spots are shown, labeled from the left most position (1) to the rightmost (19). The position of the spots 2-4 on the Kapton are hard to identify, while the spots 1, 18, and 19 are clear.

A possible reason for this extremely different appearance of the spot can be the residual roughness of the substrate although many efforts were taken (see section 4.1.1) to avoid this.

Furthermore, spot 7 and 8 illustrate that inconclusive pictures occur often close to gold structures, which have a different reflection coefficient compared to Kapton [79, 88].

Summarized, although it is hard to identify always all spots on the sample, this setup allows the precise motion of the laser spot on the sample and the determination of the position, since linear movement is given based on a few clear spots combined with the reliable positioning due to the mirrors.

Determination of the laser spot size The knife-edge technique was used to estimate the laser spot diameter. To this end, a photodiode detects the reflected intensity while the laser spot is moved across a 36µm wide stripe of gold. There is an intensity profile corresponding to the convolution of a box function for the stripe and a 2D Gauss profile for the laser caused by the differences in reflectivities of gold and Kapton. The direction parallel to the stripe does not influence the result, so the convolution reduces to a 1D integral, which leads to a difference of two error functions, which is used to fit the curve.

Fig. 6.7 depicts the reflected intensity I_R with the fit I_R=A·

The formula to calculate the spot diameter leads to d= 2·√

ln 2·s= 12.7µm.

10 20 30 40 50 60 70 80

Reflectedintensity[arb.u.]

Position [µm]

36 µm

Figure 6.7: Reflected intensity versus the position of the laser spot across the36µmwide gold stripe.

The spot diameter was determined by the knife-edge technique to12.7µm. The red curve is the fit with Eq. 6.1.