ANEXOS

C (nF)

+x - x + y -y _2::

0.658 0.615 0.645 0.630 2.55 before poling

0.666 0.623 0.654 0.630 2.57 after 8 h 19 min re-poling at + 180 V

0.674 0.640 0.654 0.623 2.59 after 13.5 min re-poling at +500 V Table 3.1: Measured Capacitance of Quadrants: The capacitance of each quadrant of the center actuator was measured with a d igital multimeter ( Dick Smith Q- 1426). All quadrants have equal capacitance to within 7%. The capacitance was measured before and after re-poling the piezoelectric ceramic. Re-poling only changed the measured capacitance by small amounts. The total rise in capacitance was 1 .5%. In a l l cases the total capacitance of all quadrants agreed with the calculated value of (2.50 ± 0.43) nF from equation (A.2). It can be assumed that the ceramic was well poled before re-poling, since a depoled ceramic measures capacitances that are about 30% lower than in a poled state.

To find out whether the piezoelectric actuator was properly and evenly poled, the capacitance of the individual quadrants was measured. This was also rec­ ommended by Hines [96] and W. Smith [173] . The capacitances between each electrode and the grounded inside electrode was found to be (0.64 ± 0.02) nF for all electrodes. The measured values are listed in the first row in table 3. 1 , the total value of the electrode capacitance is listed i n the fifth column (headed 2::) . In the appendix, equation (A.2), a total capacitance of (2.50 ± 0.43) nF was calculated, which agrees with the measured result of 2.55 nF. Table 3.1 also shows the result of re-poling the ceramic of the center actuator, discussed below. These results suggest that the actuator has not been degraded.

Groos [81] drew attention to proper grounding and shielding. If the tip had a resistive path to ground, while not being adequately shielded from the

ample, then influence charges are induced, which can be measured as a voltage6.

This is also discussed in several electronics and instrumentation books [135, 19] . R. Smith [1 72] suspected a short circuit in the electrodes of the actuator, while Hipps [97] suggested to make certain that there was no leakage current between tip and actuator electrodes as well as clean th insulator between them if necessary 7 .

A s a result of these suggestions the resistance between any electrode of the center actuator and the tip was re-examined. The resistance was found to be not less than 6 x 1013 n. Short circuits between individual electrodes and tip were also ruled out. This did not solve the problem however.

Other suggestions to test the sensitivity of the actuators came from Tr­ uscott [184], W. SmithS and Ramaswamy9 .

6Groos also suggested to turn the actuator or the sample by 900 or 1800 and to estimate the necessary offset voltages that would cause the observed behavior.

7Hipps also made the interesting point that a tip that is bent due to impact on the sample may exhibit the problematic behavior. The im pact would make a pit in the sample, which could have a steep slope. The bending of the tip gives a certain direction to the effect . Hipps noted that a bad approach algorithm could produce a bent tip every time that an approach is attempted.

sW. Smith [1 73] suggested the application of a low-frequency (2 Hz) sine wave to the actuator and observation under a optical microscope with a magnification of about 4 0 x .

9 Ramaswamy [160] devised a capacitive method to measure the length change of the piezo­ electric actuator, thereby measuring their sensitivity. The technique seems to be similar to the one described in an article of Vieira [190J.

Double Pielo Effect 1.5 0.5 -0.5 + -1.5 -2 '" + . i · • • • + -x electrode .""-. _{+x electrode} -200 -150 -100 -so 0 50

I/(<t/- y) (V) lOO ISO 200

Figure 3.6: Double-Piezoelectric Effect (y): Following the method of measuring the double piezoelectric effect advised by Truscott (184) and also described by Chen (44) . a voltage was applied to two opposing quadrants of the center actuator. Resulting voltages, generated via the double piezoelectric effect, were measured individually at the remaining quadrants. The applied voltages are ± 160 V on the two y q uadrants a nd are shown here. The data when applying voltages to the two x quadrants is shown in figure 3.7. The strain created in the remaining quadrant is symmetric even if the quadrants with voltages applied to them do not response equally to these voltages. The resulting double piezoelectric voltage is in the range of a few millivolts. This measurement provides data that a l low comparison between the i ndividual quadrants. In principle the values can be i nterpreted q uantitatively if the input resistance of the voltmeter is known. As a superior technique for a quantitative measurement, however, a current measuring method should be employed , since the equivalent output i mpedance of the quadrants is very high. The output voltage measured shows the sensitivity differences between actuator quadrants. In the two measurements the -x quadrants exhibit a double piezoelectric effect with almost twice the strength of the +x quadrants.

Following a recommendation by Truscott the double piezoelectric effect for the cent er actuator was measured. This effect is the result of using the piezo­ electric effect to cause a strain and the converse effect to generate a voltage. A voltage is applied to one or more but not all electrodes of the actuator. The strain in turn generates a voltage on the remaining electrodes. The measurement should be done symmetrically, i.e. a voltage should be applied to an opposing electrode pair, for instance the ±x pair, and the resulting voltage should be measured on the orthogonal pair, which is the ±y electrode in this example. The procedure is described in the introductory book of Chen [44]. The recorded data are graphically presented in figures 3.6 and 3.7. The measurements were meant to provide data that would allow comparison between the individual quadrants. The graphs show that two quadrants, -x and +y, respond almost twice as strongly to the applied voltages as the other quadrants.

After finding unequal response from the quadrants, the actuator was re­ poled. Firstly the ceramic was re-poled at + 180 V, which agrees with a recom­ mendation in [44] , where a re-poling field of about

_E

for more than 8 hours is suggested. Lregsgaard [122] described a technique of re-poling depoled piezoelectric actuators, where the actuator ceramic is poled at 1000 V via a 10 Mrl resistance10 for a few minutes. His actuators had wall thickness between 0.5 mm and 0.7 mm. For the actuator used in this micro-

3. 1. MOVING THE MICROSCOPE AND THE SCANNING TIP

Double PteZO Eftec:I

.

/

V(+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.