attoMICROSCOPY
PAGE 100
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 (UCPD).
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 U2, 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 (UCPD); as mentioned above,
this is the difference between the work
function of tip and sample (Figure b).
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 Uext = UDC + UAC
sin(ωt).
Substituting U = UCPD +Uext 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): Fω = dC/dz [UDC −
UCPD] UAC sin(ωt). This term vanishes when
UDC equals UCPD (see Figure c). So, modifying the DC voltage չѥ