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+yelectrodeV(+I_ x) (V)
Figure 3.7: Double- Piezoelectric Effect (x): The graph shows the second half of the results presented in figure 3.6. The applied voltages are between - 1 0 V and 160 V for the two x quadrants. Similar to the results in figure 3.6, the +y q uadrants exhibit a double-piezoelectric effect twice that of the -y quadrants.
scope, which has a wall thickness of 0.51 mm, the applied voltagel l should be approximately +200 V. The ceramic of the cent er actuator was also re-poled at high voltages over several hours. For the second re-poling a high-voltage supply was used with a voltage of +500 V as mentioned in table 3 . 1 . The capacitance of the actuator electrodes increased by only 1 .5%. Since all electrodes show relatively even capacitance and the re-poling is very small, it can be assumed that the ceramic is poled as well as it can be.
Although the observed tilt during a linescan appeared to be smaller after re-poling, the actuator behavior remained a ymmetric. By using a graphite sample and scanning an area of roughly one hundred nanometers squared, the center actuator was calibrated. A scan was taken and displayed without slope correction. After a few repetitions, multiplication factors for the quadrants were found that rendered a reasonably flat image of the sample. The control voltage for the +x and the -y quadrant had to be multiplied by 2.2, which agrees well with the above finding of the double piezoelectric effect.
The fact that re-poling had hardly any effect on the actuator may be due to irreversible changes in the piezoelectric ceramic. Probably the only solution is to replace the actuator. It is not clear why a change in polarization should not be measurable as a accompanied change in capacitance.
3 . 1 .3 Movement of the Probe Head
The probe head can be moved sideways by a concerted 'skip' of the outer tubes: all outer tubes contract, bend in the wanted direction and then elongate again to their initial length. A sideways movement can be either circular or horizon tal relative to the sample holder. When th microscope moves in the circular direction, the three outer actuator tubes 'walk' up or down the ramps they sit
1 1 The field strength mentioned is also the one that will cause depoling of the ceramic if
applied opposite to the polarization direction of the ceramic, i .e. if -200 V is applied to the outer electrodes.
O.8 �m
Figure 3.8: Typical Step Size: By moving horizontally along the sample holder ra mp, the probe head is slowly lifting or lowering itself. The typical horizontal step size is approximately 0.8 /Lm, which results in a vertical shift of 17 nm.
on. As a result, a clockwise circular movement lowers the microscope and an anti-clockwise movement raises the microscope.
The cent er actuator can also be moved horizontally and vertically. Movement in all three dimensions are needed when scanning the tip over the sample surface and adjusting the distance between the tip and sample surface. In general one would move the microscope as a whole to cover greater distances of hundreds of micrometers and use the center actuator alone to position the scanning tip on a finer scale of less than 4 j.lm. The coarse approach and the search for a region of interest would require movement of the microscope as a whole, whereas the fine approach and all scanning activities of the tip is done by the center actuator.
Typical Step Size of the Probe Head
Any circular movement of the tunneling unit standing on the sample holder ramps gets translated into a vertical lowering or rising of the tunneling unit by:
6.y = 6.x tan a ,
where 6.x is the horizontal movement, 6.y the vertical movement and a the slope of sample holder ramp. The ramp has a small inclination of a � 1 .3°. A diagram is shown in figure 3.8, which shows the typical step size. Note that moving the probe-head down or up the ramp is usually done in many small steps rather than a single big step. The outer tubes have a horizontal sensitivity of
rh = ( - 18.9 ± 5. 7) nm/v,
which was deduced in appendix A.4 as equation ( A . 14). With a voltage of typically 40 V the typical horizontal step size turns out to be 18.9 nm/v x 40 V =
760 nm. Such a step will ideally lower the probe head by 760 nm x 0.022 = 1 7 nm.
With the experimental set-up described here the outer actuators are cur rently driven from just one high-voltage control signal, which has been dis tributed via a resistive network to the electrodes of the outer actuators. The step size in this case is only half of the above, i.e.
9
nm for a 40 V voltage step. The voltage can of course be increased to compensate for this.Step Size Calibration of the Probe Head
The vertical motion of the probe head has been calibrated using the vertical sensitivity of the center actuator. The probe head was brought into a position where tunneling current could be detected. The tip was retracted from the sample and the probe head moved either up or down the ramp. After moving the