Kelvin probe force microscopy (KFM), which is based on atomic force microscopy
(AFM), was proposed by Nonnenmacher in 1991, and allows us to obtain not
only topographic images but also potential images. The term Kelvin is used
for the reason that the principle of KFM is analogous to that of Kelvin method. Potential is obtained by detecting a cantilever deflection caused by
an electrostatic force between a tip and a sample. This potential means contact potential difference (CPD) between a tip and
a sample, namely the work function difference between a tip and a sample,
as shown in Fig. 1.
[1] M. Nonnenmacher, M. P. O'Boyle and H. K. Wickramasinghe: "Kelvin
probe force microscopy", Appl. Phys. Lett.58, 2921 (1991).
Principle
General KFM system is shown in Fig. 2. We applied an ac modulation bias
VAC (frequency fAC) with a dc offset bias VDC between a tip and a sample to generate an electrostatic force between
the tip and the sample as shown in Fig. 2(1). The cantilever deflection
by an electrostatic force is detected by a photo detector, and then the
component signal of frequency fAC is derived by a lock-in amplifier as shown in Fig. 2(2). The signal is
transferred to a feedback controller as shown in Fig. 2(3), and there,
the intended potential, that is, CPD is obtained by adjusting the dc offset
bias VDC so that the component signal of frequency fAC becomes zero as shown in Fig. 2(4).
We consider the band diagrams of the tip and the sample shown in Fig.
1. The band gap between the vacuum and the Fermi levels, namely the work
function, differs from one material to another. Therefore, we define the
work functions of the tip and the sample as φ1, φ2, respectively as shown in Fig. 1. The Fermi levels of the tip and the
sample correspond by them being in touch, and the electric field φ2-φ1 is generated between the tip and the sample. Furthermore, by applying an
ac modulation bias VAC, the induced electrostatic force FES between the tip and the sample by the electric field is given by,
where C and z are the capacitance and distance between the tip and the sample, respectively,
and this equation leads to,
.
If we applied a dc offset bias VDC between the tip and the sample, which is equal to the electric field φ2-φ1 between the tip and the sample, the vacuum levels of the tip and the sample
becomes same height, and simultaneously the second term of the right side
of the equation mentioned above, namely the f2 component signal, becomes zero. Therefore, we can obtain the intended
potential by adjusting dc offset bias VDC to nullify the f2 component signal.
In Kelvin method, contact potential difference (CPD) is obtained by adjusting
a dc bias so that current, which is generated by capacitance change with
actuator between two plates, becomes zero as shown in Fig. 4. In Kelvin
method, current is used for potential determination. On the other hand,
an electrostatic force is used for potential determination in Kelvin probe
force microscopy (KFM).
Overview
.
Kelvin Probe Force Microscopy (KFM)