TMPM5200-2
5-75
eration
■
Principle of SKPM op
Kelvin Force Microscopy (KFM) is designed to observe a surface-potential image of a
specimen by detecting the electrostatic force generated between a cantilever and a
specimen using an AC-mode atomic force microscope (AFM) and controlling the bias
potential of the specimen so that the electrostatic force becomes a minimum.
The following states the principle of KFM.
If U is the potential difference between a cantilever and a specimen, the electrostatic
force generated between them is given by the following equation:
z
∂
2
Here, z is the distance between the cantilever and the specimen, and C is the electrostatic
capacitance. An AC voltage with amplitude V
C
∂
2
1
U
F
⋅
⋅
−
=
AC
and angular frequency
ω
, superimposed
on DC voltage V
DC,
is given by the following equation:
t
V
V
V
AC
DC
t
ω
sin
⋅
+
=
This superposed voltage is applied between the cantilever and the specimen. If the
contact potential difference is
∆
φ
/q
q
AC
DC
φ
∗
, the potential difference U is :
t
V
U
t
t
t
V
ω
V
q
φ
s
/
/
⋅
+
Fr
on, the el
in
∆
−
∆
−
=
om the above equati
ectrostatic force F is given as follows:
(
)
z
C
t
V
AC
∂
q
V
F
DC
∂
⋅
⋅
+
2
sin
ω
as follows:
∆
−
⋅
−
=
/
2
1
φ
This equation can be expanded
(
)
(
)
t
V
z
C
AC
ω
2
cos
4
1
2
⋅
⋅
∂
∂
⋅
+
t
z
z
V
F
DC
φ
/
2
1
∂
∂
⎢⎣
⎡
∆
−
⋅
−
=
The
frequ
equation (1). These components are detected as the
teristic
frequ
V
q
V
C
AC
DC
ω
φ
sin
/
⋅
⋅
∆
−
⋅
∂
−
C
V
q
AC
2
1
2
2
∂
⋅
⎥⎦
⎤
+
Electrostatic force F has both a static component and components at angular
encies
ω
and 2
ω
, as shown in
change of the vibration amplitude (F: Force) of the cantilever and the charac
ency (
z
F
∂
∂
: Z-component of Force gradient). The
ω
component is removed using the
Lock-in Amplifier. In the case of Force, the
ω
component corresponds to
(
)
AC
DC
V
q
V
z
C
⋅
∆
−
⋅
∂
∂
/
φ
, as shown in the second term of equation (1).
In the case of Force gradient the
ω
component corresponds to
(
DC
q
V
z
C
∆
−
⋅
∂
∂
/
2
2
φ
)
AC
V
⋅
.
value
beco
•
RE
Japan, 49, 281 (1994)
457 (1996)
The specimen surface potential
is measured by controlling
DC
V
so that this
mes zero.
FERENCE:
Hiroshi Yokoyama, et al., Journal of The Physical Society of
acuum Science Technology, B14,
T. Hochwitz, et al., Journal of V
) is the Work Function Difference (WFD) and
∆
φ
/q(units: V) is the Contact Potential Difference
∗
∆
φ
(units: eV
(CPD).
（１）
