Creep after TiJ}--Sample Approach
2.5
2
� tiJ}--sample distance (s)
E � 1 .5
0.5
/
tunneling current (It)• • 0" .0 0° . 0 ""'" • "' • • ••• ".. . ','
setpoint
o 5 1 0 1 5 20 25 30 35 40 45
t (s)
35
Figure 3.2 : Creep of Center Actuator: The tip-sample distance (s) and the tunneling current (It) are shown simultaneously j ust after the approach mechanism has encountered tunneling current and switched on feedback control. The tunneling current is kept at the desired setpoint, while the controller adjusts the voltage of the center actuator so as to keep a constant tip-sample distance. Creep follows approximately a logarithmic behavior. After 40 s the center actuator expanded by approximately 20 n m .
quadrant
Inner
electrode
Figure 3.3: Polarization of the Ceramic: The piezoelectric ceramic of the actuators has been polarized with a positive voltage on the outside electrodes. After poling a permanent polarization is left , shown in the diagra m . With the inner electrode grounded , the ceramic wall will contract if a negative voltage is applied to a ny of the quadrants.
observed [84, 1 56, 190] . Vieira [190] reports that the length change follows the equation
6.[
T = a + ,B ln t
very accurately, where a and ,B are parameters that depend on the electric field and the temperature. The logarithmic behavior can qualitatively be seen in figure 3.2. According to Dirscherl [59] all three quantities: field, strain and temperature, interact with each other. Vieira continues by summarizing the experimental findings of other researchers who found logarithmic time depen dence. He suggests that creep is associated with thermally activated processes having different activation energies.
3 . 1 .2 P iezoelectric Actuators
The actuators used in the probe head are tube shaped following the design first published by Binnig and Smith [29] . A diagram of a typical tube-shaped actuator is shown in figure 2.9. The microscope tip is attached to the lower end of the tube. Applying voltages to the tube quadrants generates strains in the tube and make it possible to move the attached tip in all six directions of space. Instead of pressing or extruding the actuators, the manufacturer [175] ma chined them to achieve high precision. The tubes are electroplated on the inside and outside with a thin film of silver. The outer coating is segmented into four quadrants, which serve as four electrodes. The coating on the inside is used as a counter-electrode. The counter-electrode is kept at ground potential, while each of the quadrants is independently driven by a high-voltage control signal. The tube design uses the transverse piezoelectric effect and so the important piezoelectric strain constant is d3 1 . The piezoelectric ceramic has been poled with a positive voltage on the outside, so that the resulting permanent polariza tion of the ceramic is pointing from the inside of the tube radially outwards as shown in figure 3.3. An applied negative voltage on any of the quadrants results in an electric field opposed to the poling field and in line with the permanent
3. 1. MOVING THE MICROSCOPE AND THE SCANNING TIP
37
polarization. The electric field causes the tube wall to contract and the tube length to elongated. The opposite is true for positive voltages.
Since opposite fields tend to depole the ceramic, it is generally recommended that the tube be expanded rather than contracted5 , which means the actuator should preferably be used with the tip retracted from the sample rather than extended towards the ample. This is indeed possible if the actuator is used with a certain offset.
When a common voltage is applied to all four electrodes, the actuator tube elongates or contracts, which lowers or lifts the tip. This way the tip is moved vertically, which is denoted as the z direction.
When a voltage is applied between the counter-electrode and only one of the four outer electrodes, then the tube will bend towards or away from this electrode. In the current design, equal and opposite voltages are applied to opposing electrodes to improve linearity. In addition, with just one electrode activated the tip would move horizontally as well as vertically. The vertical
movement is cancelled, if two opposing quadrants are driven simultaneously with equal and opposite voltages. In this manner the tip is moved horizontally in either the
±x
or±y
direction.When calculating the horizontal and vertical deflections of the two different actuators used in this microscope the actual lengths of the electrodes of the actuator and the attached pieces have to be taken into account. A detailed diagram of the center actuator is shown in figure
3.4,
where it can be seen that the electrode length is only part of the overall actuator length. When a voltage is applied to all outer electrodes of the center actuator only the ceramic covered by the electrodes experiences an electric field. The resultant straintlie!
le!
relates only to the electrode length. For a horizontal deflection of the tip the actuator bends, carrying the tip holder and tip with it. The bending is discussed in appendix A.4. Figure A.I in the appendix shows the bent actuator.
Elongation or contraction of the piezoelectric actuator can be calculated from the vertical sensitivity, which is defined as
v
r;;
=
\1;; ,where v is the amount of vertical length change and
V;;
is the applied common voltage. The z direction is arbitrarily defined as the direction along the tubeaxis, which is more or less perpendicular to the sample. Cross-coupling between the different axes is disregarded. The sensitivities of the actuators are approx imately constant for small deflections. The vertical sensitivity is calculated in appendix A.4, equation
(A. 12)
asr;; =
(-3.36 ± 0.23) om/v.
The horizontal sensitivity rh of the actuator is the amount of horizontal deflection of the tip h per unit of applied voltage That is
h 7'h = --;- .
� h
SI am indebted to Kai Dirscherl [59) from the Danish Institute for Fundamental Metrology for this information.
unit = 1 mm
Pi = 12. 7
lel = 9. 9
macor insulator
steel tip holder tungsten tip
t = 0. 51
= 3. 1 75 Cc = 2. 0
steel clamp ring
,silver electrodes
w = 1.2 m = 2. 0 t = 3 .. .4
Figure 3.4: Center Actuator: The complete actuator is shown i n cross-section a nd as a side view. The compound actuator consists of the piezoelectric ceramic tube, the tip holder plus tip and an electric insulator between tube and tip holder. The dimensions of each actuator component are shown i n the diagram and are also listed in table A . I of the appendix along with other tube properties. This information will be referred to when calculating the sensitivity, vibrational modes and thermal drift of the actuator. A diagram of the complete probe head plus sample holder is shown in figure 3 . 1 6 .
3. 1 .