10
10
EXAMPLE: ELECTRICAL FORCE
EXAMPLE: ELECTRICAL FORCE
MICROSCOPE
MICROSCOPE
In this chapter, Electrical Force Microscopy (EFM) is briefly presented as an example for the
application of lock-in amplifiers.
EFM is one of the detection technique used to enhance the capabilities of 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, work functions, surface charges or different dopant concentrations
in
semiconducting
materials.
The schematic diagram sketches an AFM operated the non-destructive dynamic non-contact mode.
The cantilever (with the metallic tip) is oscillating in its 1
st
mechanical Eigenmode ωr
perpendicularly to the surface. For position sensing of the cantilever, a laser beam deflection
detection with a position-sensitive photo-detector is employed. A lock-in amplifier analyses the
detector signal at the cantilever resonance frequency ωr and passes the determined amplitude
value to a feedback control system that re-adjusts the tip-sample distance. The required
displacement of the z-piezo can be recorded as topography signal.
In addition to the topography, EFM detects electrical forces. These forces are proportional to the
derivative of the capacitance
C
of the tip-sample arrangement with respect to the tip-sample
distance
z
and proportional to the potential difference
U
squared:
F
el
= −
1
2
d
C
d
z
U
2
.
(5)
A possible voltage dependency of
C
is neglected in this consideration.
Manual Anfatec PCI-Lockin Amplifier AMU2.4 – Rev. 1.10 dated 30/09/20
Page 62 (70)
Figure 58: Schematic diagram of the EFM experimental setup.
Lock-In 1
Feedback
2
nd
harmonic
1
st
harmonic
Lock-In 2
2
ω
ref
ω
ref
U
bias
~
U
ac
cos(
ω
ref
t
)
+
z
y
x
ω
r
ω
ref
Sample
Photo-
detector
Tip
Lock-In 3
