Biomedical Engineering Reference
In-Depth Information
The forces applied to the surface by the probe in contact mode are given by Hooke's law:
F
¼
k
D
ð
3
:
1
Þ
where
F
deflection distance (m).
The basis of contact-mode AFM is that the microscope feedback system acts to keep the
cantilever deflection at a certain value determined by the instrument operator. This point is
known as the set-point. The set-point is one of the important control parameters that the
operator must adjust to optimize imaging, and there are equivalent parameters for all other
AFM imaging modes as well. Equation 3.1 shows that either a probe with a high force
constant (one with a stiff cantilever), or a greater deflection (i.e. a higher set-point), will
lead to a higher applied force. Because the feedback system of the AFM cannot have
instantaneous response, the vertical deflection will actually vary somewhat during
imaging (indicated by the red region of the curve in Figure 3.2). The amount it varies
will depend on the topography of the sample, flexibility of the cantilever, scanning speed,
and how well the feedback circuit has been optimized. Optimization of these parameters is
discussed in Section 4.2. The AFM software may display the deflection signal as a line plot
as the tip passes over the sample, or as an image. The deflection signal in contact-mode
AFM is the error signal, that is, the size of the deflection is a measure of how much the
cantilever is deflecting
before
the deflection is 'corrected' by the feedback circuit via
height adjustment by the piezo. Therefore, in the ideal situation, there would be
no
contrast
in the deflection image. The more contrast exists in the deflection signal, the more 'errors'
will be present in the height image, because regions of high contrast in the deflection
image correspond to regions in the height image, where the feedback has not yet corrected
for cantilever deflection. However, usually it is not possible to have the feedback signal
respond perfectly, and the deflection signal will show the slope of the sample, because it is
regions where there is high slope, or more precisely, a great rate of change of slope with
distance, that give rise to large cantilever deflections.
The imaging mode described so far is known as
constant-force
contact-mode AFM. If the
user turns off feedback altogether while imaging, then they are effectively using
constant-
height
contact-mode AFM rather than
constant-force
contact-mode AFM. Because
constant-force mode is by far the most widely used mode, in general any reference to
contact-mode AFM will mean constant-force mode unless specified otherwise, and this is
the convention we follow in this topic. In constant-height mode, with no feedback active,
the image signal comes entirely from cantilever deflection, rather than from the voltage
applied to the
z piezo
(which would be typically set at a constant value). Height measure-
ments will therefore require specific calibration of the cantilever deflection, to extract real
sample topography. Constant-height mode AFM does have some specific applications: it
can be useful in conditions where scanning is carried out so fast that the feedback system
cannot cope [9, 36]. However, under these conditions, AFM is in fact acting rather like a
stylus profiler as the tip-sample force is not fully controlled. Typically, to carry out these
measurements, the feedback system is initially used to determine the location of the sample
surface, and the approximate topography, before being turned off, or just reduced to a very
low level.
However, even using constant-force AFM, the software typically will allow the user to
save the deflection image, and some operators choose to publish this image, as it is often a
¼
force (N),
k
¼
probe force constant (N/m) and
D
¼
