Biomedical Engineering Reference
In-Depth Information
scanners for AFM may be constructed from other types of electromechanical devices such
as flexure stages [27, 28], voice coils [29], etc. All that is important is that the electro-
mechanical device must have very accurate positioning.
2.2.1.1 Piezoelectric scanners
The most common types of piezoelectric materials in use for AFM scanners are constructed
from amorphous lead barium titanate, PdBaTiO
3
or lead zirconate titanate, Pb[Zr
x
Ti
1-
x
]O
3
,
0
1 (usually abbreviated as PZT). The ceramics may be 'hard' or 'soft', depending on
the formulation. This affects howmuch they can expand, versus the applied voltage, as well
as the linearity of the relationship between applied voltage and expansion. Hard ceramics
have smaller coefficients of expansion, but are more linear. Soft ceramic formulations have
more non-linearities and have greater expansion coefficients. After fabrication, piezoelec-
tric ceramics are polarized. Polarization may be lost by elevating the piezos to a tempera-
ture above their critical temperature or by applying too high a voltage.
Electronically, piezos act as capacitors and store charges on their surface. Capacitances
of ceramics may be as large as 100 microfarads. Once a charge is placed on the piezo-
ceramic, the piezoceramic will stay charged until it is dissipated. Electronic circuits used
for driving the piezoceramics in an AFM must be designed to drive large capacitive loads.
All piezoceramics have a natural resonance frequency that depends on the size and
shape of the ceramic. Below the resonance frequency, the ceramic will follow an oscil-
lating frequency, at resonance there is a 90
8
phase change, and above resonance there is a
180
8
phase change. To a great extent, the resonance frequencies of the piezoelectric
ceramics limit the scan rates of atomic force microscopes. As a rule of thumb, the higher
the resonant frequency of the scanner, the faster you can scan.
Piezoelectric materials can be fabricated in several shapes such that they have more or
less motion. As an example, a disk, as illustrated in Figure 2.2, gets longer and narrower
when a voltage is applied. The piezoelectric ceramic changes geometry such that the
volume is preserved during extension. Another configuration for a piezoelectric ceramic is
a tube, with electrodes on the inside and outside. This configuration gives a lot of motion,
and is very rigid. Another configuration is the bimorph, constructed from two thin slabs of
piezomaterial that are polarized in opposite directions. When a voltage is applied the
ceramic expands in a parabolic fashion. The motions of these geometries, along with the
equations of motion are illustrated in Figure 2.8.
Ideally, the piezoelectric ceramics would expand and contract in direct proportion to the
driving voltage. Unfortunately, this is not the case, and all piezoelectric materials show non-
linear behaviour. They show two primary non-ideal behaviours, hysteresis and creep [30].
Hysteresis, derived from the word history, causes the ceramic to tend to maintain the shape
that it was in previously. As the ceramic is expanding, there is a negative shaped non-
linearity, and as thematerial is contracting, there is a positive shaped non-linearity. Hysteresis
causes a 'bending' distortion in the images obtained, unless corrected. Creep occurs when the
ceramic is subjected to a sudden impulse such as a voltage step function. This means that
when the piezo is used to move to a different part of the scan range by applying an offset
voltage to it, it will tend to continue moving in the same direction as the offset, even after the
voltage has stopped changing. Both these effects are illustrated in Figure 2.9. Real examples
of the effects of these non-linearities on AFM images can be found in Chapter 6. These non-
ideal behaviours must be corrected to avoid such distortions in the AFM images.
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