In order to measure noise spectra, the resulting data should be divided by the square-root of the used
bandwidth.
The integrated spectrum is taken with a time constant of 10 ms and
a slope of 24 dB (4
th
order) – bandwidth factor ~ 1,03. The related
bandwidth is then 1/10 ms = 100 Hz. In order to interpret the
result as noise in units of V/Hz
0.5
, the spectrum should be divided
by 10 Hz
0.5
(= sqrt(100 Hz)).
E
XAMPLE
: E
LECTRICAL
F
ORCE
M
ICROSCOPE
In this chapter electrical force microscopy (EFM) is briefly presented as an example for the
application of lock-in amplifiers.
EFM is a related technique to the well-established atomic force microscopy (AFM). Its special aim
is to detect electrical forces to learn something about the electrical properties of a surface, for
example about the local distribution of surface potentials on electronic devices or different dopant
concentrations in semiconducting materials.
The fundamental experimental setup shown in Figure 6 is based on a conventional atomic force
microscope: In the non-destructive dynamic non-contact mode, an oscillating metallic tip fixed to a
cantilever is scanning over the surface by means of a piezo scanning device. The distance between
tip and sample can be controlled by monitoring the oscillation amplitude of the cantilever, because
its value is influenced by short-range van der Waals forces. Therefore a reflected laser beam and a
position-sensitive photo-detector are used. A lock-in amplifier analyzes the detector signal at the
cantilever resonance frequency
ω
r
and passes the determined amplitude value to a feedback control
Manual Anfatec PCI-Lockin Amplifier AMU5.0 – Rev. 1.01
Page 13 (34)
Figure 6: Schematic diagram of the EFM experimental setup.
