Atomic Force Microscopy and Spectroscopy - Dynamic Force Spectroscopy and Biomolecular Recognition - page 54

2004; Green et al., 2004; Cook et al., 2006). Today, most commercial AFM setups
include already software routines to calibrate the vertical spring constant via thermal
noise analysis (Hutter and Bechhofer, 1993; Butt and Jaschke, 1995; Cook et al.,
2006) in a convenient way.

Detection methods. Today, nearly all commercial AFMs use the so-called laser beam
deflection scheme shown in Figure 2.2. The bending and torsion of cantilevers can be
detected by a laser beam reflected from their backside (Alexander et al., 1988; Meyer
& Amer, 1988), while the reflected laser spot is detected with a sectioned photodiode.
The different parts are read out separately. Usually a four-quadrant diode is used to
detect the normal and the torsional movements of the cantilever. With the cantilever
at equilibrium, the spot is adjusted such that the upper and the lower sections show
the same intensity. If the cantilever bends up or down, the spot moves, and the differ-
ence signal between upper and lower section is a measure of the bending. A detailed
analysis of the optimal position where to focus the laser spot on the back side of the
cantilever was given by Schaffer and Fuchs (2005).
The sensitivity can be even improved by interferometer systems adapted by sev-
eral research groups (Rugar et al., 1989; Moser et al., 1993; Allers et al., 1998;

Photodiode

Laser

Mirror

Torsion

A B
C D

Deflection

Set-point

Cantilever

Error signal

PID

z

Scanner

y

x

z-position

FIGURE 2.2 Principle of an atomic force microscope working with the laser beam deflection
method. Deflection (normal force) and torsion (friction) of the cantilever are measured simul-
taneously by measuring the lateral and vertical deflection of a laser beam while the sample is
scanned in the x-y plane. The laser beam deflection is determined using a four-quadrant photo
diode. If A, B, C, and D are proportional to the intensity of the incident light of the corre-
sponding quadrant, the signal (A+B)-(C+D) is a measure for the deflection and (A+C)-(B+D)
is a measure for the torsion of the cantilever. A schematic of the feedback system is shown
by solid lines. The actual deflection signal of the photodiode is compared with the set-point
chosen by the experimentalist. The resulting error signal is fed into the PID controller, which
moves the z-position of the scanner to minimize the deflection signal.