Because an important part of the AFM scan head consists of piezoelectric ele-ments, the basics of piezoelectrics will be discussed first. Piezoelectric materials become polarized when they are subjected to a mechanical force, resulting in a voltage proportional to the applied force. On the other hand an electric field lengthens or shortens the piezoelectric material depending on the polarization of the field. Only small length differences can be obtained (even with large volt-ages) which is good for the actuation application such as AFM scanners where only small surface areas need to be scanned at a time.
The piezo elements used here are PZT piezos and consist of a lead zirconate titanate ceramic. Piezoelectric ceramics have a perovskite crystal structure.
Above a critical temperature, the Curie temperature, the perovskite crystals have a cubic symmetry and no dipole moment as is shown in figure 3.1a. If the temperature is below the Curie temperature the crystal structure is slightly distorted and gets a tetragonal symmetry as is shown in figure 3.1b. The central T i4+ or Zr4+ is closer to the top than to the bottom of the unit cell creating a dipole moment. These dipole moments tend to align and form domains. The di-rection of polarization of the different domains is random so the net polarization of the piezo element is zero. By exposing the element to a direct electric field the domains that are aligned with the electric field increase and the domains that are not aligned decrease. This means the piezo element lengthens in the
direc-Pb
Figure 3.1: a) A perovskite crystal with the temperature above the Curie perature having a cubic crystal structure. b) A perovskite crystal with a tem-perature that is lower than the Curie temtem-perature. The crystal structure is tetragonal and has an electric dipole moment.
tion of the applied electric field. When the electric field is removed the domains remain aligned and the piezo now has a permanent polarization and elongation.
Ferromagnetic materials show hysteresis and the same behavior can be seen for ferroelectric materials. In figure 3.2 the polarization can be seen as a function of the electric field. In figure 3.3 the strain, or the relative increase(decrease) in size can be seen as a function of the electric field. The relative increase in the direction of the applied electric field is accompanied by a corresponding but smaller decrease in the direction perpendicular to the applied field. This is no problem for the used actuators because they can only move the piezostack in the direction of the applied field. In the other direction the piezo is fixed with only one end while the other end is free so deformation in this direction will not move the piezo stack.
A piezo element can depolarize and loose its piezoelectric properties. This occurs when the temperature approaches, or is higher than, the Curie tempera-ture, or when a large voltage creating an opposite electric field is applied or due to a large force that is applied to the piezo. The piezo thus has to be treated with care to avoid damage. If the temperature is decreased the hysteresis graph will change. The maximum polarization will remain the same but when the electric field is decreased there is less thermal motion and the domains tend to remain intact longer. Therefore at zero electric field the polarization is higher.
A change in electric field now responds in a smaller change of the polariza-tion. This means that the scan area at low temperatures will get smaller for the same applied voltage. The range over which the sample can move is very small. Moreover when the system is prepared for measurements the sample can move a bit with respect to the tip and a tip crash can easily occur. To get to the interesting areas of the sample there are three additional piezo elements, the positioners, that provide a much larger movement of the sample. So the scanners for the x-, y- and z-direction are used for small continuous movements whereas the positioners are used to make discrete larger steps.
P(a.u.)
E(a.u.)
Figure 3.2: Hysteresis curve of the polarization P versus the electric field E. The arrows indicate how the polarization changes when the electric field changes.
The principle of operation of the positioners is seen in figure 3.4. The piezo element is fixed on one side to the piezostack and on the other side to a mass m2, the inertial weight. There is also a main body, m1, that tightly surrounds m2. If the piezo tube is slowly extended the inertial force is smaller than the friction force between m2 and the main body so the main body will follow the movement of the piezo. This is shown in figure 3.4(a) and (b). If afterwards a fast voltage drop is applied to the piezo the inertial force is larger than the friction force and the piezo will shorten but the main body will stay behind.
This can be seen in figure 3.4(c).
The displacement of the main body after one cycle is called ∆x. ∆x depends on the extension of the piezo and on the masses m1 and m2. For the piezo to follow an ideal sawtooth voltage the piezo has to be able to retract very fast, this means that m2cannot be large. However m1has to be large in comparison to m2 in order to overcome the frictional force. ∆x can be expressed by the following equation:
∆x = m1
m1+ m2d (3.1)
here d is the extension of the piezo from figure 3.4 a to b. This 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(∼6 mm) while the scan range is still small and accurate.
E(a.u.) S(a.u.)
Figure 3.3: Hysteresis curve of the strain, S, (which is proportional to the relative increase in length) versus the electric field E. The arrows indicate how the strain changes when the electric field changes.