The voltage
U
contains a direct voltage part
U
DC
and an alternating voltage part
U
AC
:
U
=
U
DC
U
AC
⋅
cos
ref
t
.
(6)
U
DC
consists of an additional applied bias voltage and, what is especially interesting from the
physical point of view, potential differences caused by different electronic work functions and
charges. For separating the impact of these electrical forces from other forces (e.g. van der Waals
forces),
U
has to be modulated at the frequency
ω
ref
.
As a result of this, the photo-detector signal is
modulated at this frequency as well.
Inserting equation (6) in (5) and using power-reduction formulae of trigonometric functions one
can expect a force between tip and sample at the frequency
ω
ref
as well as at
2·
ω
ref
.
Figure 59
confirms this prediction: It shows the frequency spectrum of the cantilever oscillation with clear
signals at the mechanical excitation frequency
ω
r
and at the frequencies of the first and second
harmonic of the electrical excitation.
Now two additional lock-in amplifiers (see Figure 58) can be used to analyse the photo-detector
signal at the frequency ω
ref
and 2·ω
ref
simultaneously. The measured amplitudes of the signals are
proportional to the strength of the electrical force components.
Manual Anfatec PCI-Lockin Amplifier AMU2.4 – Rev. 1.10 dated 30/09/20
Page 63 (70)
Figure 59: Frequency spectrum of the oscillating cantilever
10
20
30
40
50
1E-5
1E-4
1E-3
0.01
A
m
p
lit
u
d
e
[
V
]
Frequency [kHz]
ω
r
ω
ref
2·ω
ref
