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Kelvin Probe Force Microscopy (KPFM)
fundamentals
Kelvin Probe Force Microscopy (KPFM), also known as Surface Potential
Microscopy, is a non-contact mode AFM technique capable of imaging local
variations in the Work Function of a sample (see Figure a). The work function
is defined as the binding energy of the outermost electron of a given material
with regards to the vacuum level. Since KPFM uses a probe (AFM tip) with its
own work function, overlapping with the sample’s work function (see Figure
b), KPFM yields information about the difference between the two, called
contact potential difference (U CPD ).
Substituting U = U CPD +U ext in the force expression above allows us to calculate
the electrostatic force acting on the tip. Among other terms, one component
Fω is proportional to sin(ωt): F ω = dC/dz [U DC − U CPD ] U AC sin(ωt). This term
vanishes when U DC equals U CPD (see Figure c). So, modifying the DC voltage
until the force is zero allows to measure the contact potential difference.
To achieve this, F ω simply needs to be recorded using a lock-in amplifier. Its
output can then be used for a feedback that tries to modify U DC so that the
vibration amplitude is zero. This is the measurement scheme behind a Kelvin
Probe Measurement: to always adjust U DC so, that the force on the tip and
therefore its vibration at frequency ω are zero.
To model the KPFM geometry for quantification of the results, one can think
of the AFM tip and the sample as two sides of a capacitor. The force between
these sides can be expressed as F = 1/2 dC/dz U 2 , where C is the effective
capacitance and U is the total potential difference between the sample and
tip. This difference U can be split up in two terms:
i) The first term is the Contact Potential Difference (U CPD ); as mentioned
above, this is the difference between the work function of tip and sample
(Figure b).
By recording the applied U DC , one can image the Contact Potential Difference
directly, and hence one is able to extract nanoscale spatial information
about work function variations of the sample.
Kelvin Probe Force Microscopy has wide spread use in many different areas
of surface science. In case of semiconductors it allows to investigate local
electrical potentials and band bending distribution. It can image the
electrical properties of metallic nanostructures, and help to investigate the
local charge transfer of catalyst nanostructures for example.
U CPD
ii) The second term is the additional voltage that is applied to the tip relative
to the sample. Typically, one applies a DC voltage as well as a AC component
with frequency ω. This potential is hence written as U ext = U DC + U AC sin(ωt).
Work Function
U CPD
Work Function
Sample
Sample
(a)
Tip
(b)
Tip
(c)
U AC
U AC
U CPD
Optical fiber
Work Function
+ ++
++
+ ++
++
V
Dither piezo
Tip
Sample
V U
Tip
AC
Sample
Tip
Sample
Sample
U AC U DC
U AC
+ ++
++
V
U AC U DC
Tip
Sample