Piezostack

In combination with the ferrule (i.e. the fiber–end, § 4.3.2), the actuator (dither) and the cantilever itself, the piezo elements form the heart of the setup. The ensemble is often referred to as the scanhead. The piezo elements used here are PZT piezos that consist of a lead zirconate titanate ceramic. The entire piezo stack is build up of six elements; three piezo elements are used for the 3D coarse approach and are called the positioning piezos or short positioners. The other three piezos are used for the scanning of the sample and are called the scanner piezos. The ones used here are provided by attocube; the ANPxyz100 LT piezo positioners and the ANSxyz100 LT piezo scanners, which are especially designed to perform under LT conditions. The main characteristics of the various elements are listed in table 4.2. Piezoelectric ceramics have a perovskite crystal structure and a Curie temperature, which is used to permanently polarize and elongate the piezo element. The maximum elongation of the elements is linearly depend on temperature and is reflected by a linear decrease in capacitance. A piezo element can lose its piezoelectric properties from large electric fields and/or temperatures above the critical temperature. Like ferromagnetic materials, piezo elements also experience hysteresis under influence of an external electrical field. This hysteresis curve changes when the piezo is cooled down. The maximum polarization will remain the same, but there is less thermal motion and the domains within the piezo tend to interact longer. Therefore, a change in electric field will respond to a smaller change of the polarization and therefore smaller steps as function of applied piezo voltage.

Piezo

Volt. Range Scan Range Calibration RCL^¶ ANC300 Impedance Z

RT 77/4.2 K RT 77 K 4.2 K RT 77 K 4.2 K RT 77 K 4.2 K RT 77 K 4.2 K RT 77 K 4.2 K

[V] [V] [µm] [µm] [µm] [nm/V] [nm/V] [nm/V] [nF] [nF] [nF] [nF] [nF] [nF] [Ω] [Ω] [Ω]

Pos

x 0..60 0..150 4000 4000 5000 – – – 994^k 351 173 990 351 166 160 453 922

y 0..60 0..150 4000 4000 5000 – – – 951 340 167 980 340 164 167 468 953

z 0..60 0..150 5000 4000 5000 290^⊳ – 65^⋄ 1078 395 192 1100 396 191 147 402 828

Scan

x 0..60 0..150 45 47 30 693 343 196 4588 1889 922 5000 1740 944^⊲⊳ 34.7 1005 1024

y 0..60 0..150 45 49 30 803 370 209 5039 1775 921 5100 1790 969 31.6 1004 1019

z 0..60 0..150 21 24 15 250 120 71.4 1244 514.5 278 1200 578 305 128 1047 1159

Dither 0..60 0..150 2.3^♣ – 1.2 – – – 513 140 72.4 490 137 71 325 − 2199

⋆Maximum scan range values for the positioners adapted from the attocube specificationsheet [72].

†Calibration values for the scanners are determined at the center position of the piezo element.

‡Capacitance values have a tolerance of ±10 nF.

§For low temperature values, the impedance of the scanners starts to dominate over the capacitance characteristic.

¶Capacitance values were both read out by a Philips 6303A Auto RCL meter and by the internal capacitance meter of the attocube ANC300.

kCalibration values for the z positioner adapted from the attocube specificationsheet [73].

⊳The step size in upward direction ∆zup= 290 nm @ V = 35 V and in the downward direction ∆zdown= 500 nm @ V = 35 V.

⋄The step size in upward direction ∆zup= 65 nm @ V = 65 V and in the downward direction ∆zdown= 180 nm @ V = 65 V.

⊲⊳Tolerance for the (x,y) scanners is larger due to design flaw in electrical shielding. Values may vary ±40 nF.

♣Dither stroke values adapted from the attocube specification sheet [74].

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Figure 4.4: (a) Three steps of the movement cycle of the positioner piezos. m1 is the main body and m2 is the inertial weight attached to the piezo. Ξ is the displacement of the main body and X is the extension length of the piezo. (1) Starting position of the positioner. (2) Piezo is extended as function of the applied voltage, m1

follows the piezo movement. (3) The piezo retracts so rapidly that m1 does not follow the movement. (b) The four possible scan directions. The arrows indicate the positive (or ‘forward’) scan direction for each angle (top).

Hysteresis curves of the x and y piezo scanners (bottom). The picture reflects the relative transverse displacement as function of the applied voltage in all four directions. ∆ξ/ξ denotes the measured transverse displacement scaled against a known grating of width ξ. V/Vc denotes the applied voltage against the center voltage (Vc,RT = 30 V, Vc,LT= 75 V).

Piezo positioners

The principle of operation of the positioners is seen in Fig. 4.4a. The piezo element is fixed on one side to the piezostack and the other side is attached to a mass m2, the inertial weight. m1 is the main body that tightly surrounds m2. If a voltage is applied to the piezo, the piezo tube is slowly extended. If the inertial force is smaller than the friction force between m2 and the main body, the main body will follow the piezo (step 1 and step 2). If after the movement a fast voltage drop is applied to the piezo, the inertial force will exceed the friction force. Therefore, piezo tube will be shortened, but the main body will stay behind (step 3). The displacement of the main body after one cycle is called Ξ. Ξ depends on the extension of the piezo and on the masses m1and m2. For the piezo to follow an ideal sawtooth voltage the piezo has to be able to retract very fast, this means that m2≪ m1. The piezo displacement can be expressed by

Ξ = m1

m1+ m2

X, (4.5)

with X is the extension length of the piezo. This motion cycle can be repeated several times so the main body will move a large distance while the piezo element only has a limited range. Now the sample can move in three directions over quite large distances (table 4.2.2).

Piezo scanners

The piezo scanners are used for scanning and therefore need to be very accurate in terms of transverse displacement as function of applied voltage. As explained in the previous paragraph, the piezos suffer from

5 mm

60 nm

2 1

-53 nm

(a) x and y calibration

1 m m

44 nm

2 2

–34 nm

(b) z scanner calibration (c) Line views Figure 4.5: (a) Picture of the UMG01 sample taken at room temperature, used for calibration of the x and y scanner piezos. The width of the grains is 2 µm. The picture was obtained by scanning in the 180^◦ direction in CE lock–in mode, with a resonance frequency of 84.8 kHz and a drive amplitude of 2.0 mVp. The Q factor of the Multi75–G Budgetsensors AFM tip was 705. The applied filter was 200 Hz 6 dB/Oct. The scan speed vscan = 14 µm/s and the total image size is 43 × 44 µm² imaged in a 512 × 512 resolution frame. (b) Image of the TGZ01 sample, used for the z scanner calibration. The image was taken at room temperature with a Budgetsensors Multi75–G AFM tip. The drive frequency was 77.7 kHz with a drive amplitude of 17.0 mVp. The Q factor of the cantilever was 124 and the used scan speed was 4.0 µm/s over a total area of 4 × 4 µm²in a 512 × 512 resolution frame. The setup was operated in CE lock–in mode with an applied loop filter of 4 kHz 30 dB/Oct.

(c) The corresponding line views for the two images.

hysteresis due to polarization non–linearity as a function of applied electric field^¶. For the attoANSxyzscanners the typical hysteresis curves can be seen in Fig. 4.4. These curves were obtained by calibrating the piezos against a known grating, such as displayed in Fig. 4.5a. The hysteresis of the piezo not only depends on the temperature, but also on the scan direction. For optimization of the calibration, the sample should be calibrated in all four scan directions at all of the temperatures of interest. By measuring the transverse displacement relative to the known distance ξ = 2 µm, the scanners can be calibrated. The calibration values for each scanner can be derived from the intersection of the curve with the V/Vc axis, with Vc the center voltage. From Fig. 4.4b, scanning in the ±x direction might appear to be most obvious choice, since these directions show the less hysteresis. This would imply scanning in the 0^◦ or 180^◦ direction. Scanning in these directions means that the x direction is the ‘fast’ axis, whereas y is the ‘slow’ axis. However, from a stability point of view, it is much more sensible to have a slow axis with the least hysteresis. Therefore, the scan direction of choice should be the 90^◦ direction since the calibration value does not deviate much around the center voltage and the slow axis has the least hysteresis^k. The calibration values for each of the piezos can be found in table 4.3. The z scanner piezo has been calibrated against the TGZ01 sample from µMasch^∗∗. The result for the measurement at RT can be seen in Fig. 4.5b. The grating has a step height of 24.0 ± 1.0 nm.

The image was obtained at room temperature while operating the setup in CE lock–in mode. The calibration value for the z scanner was set at 250 nm/V. As one can see, this calibration is in agreement with the observed step–height of the TGZ01 sample.