text: In SKP the probe and sample are held parallel to each other and electrically connected to form a parallel plate capacitor. The probe is selected to be of a different material to the sample, therefore each component initially has a distinct Fermi level. When electrical connection is made between the probe and the sample electron flow can occur between the probe and the sample in the direction of the higher to the lower Fermi level. This electron flow causes the equilibration of the probe and sample Fermi levels. Furthermore, a surface charge develops on the probe and the sample, with a related potential difference known as the contact potential (V). In SKP the probe is vibrated along a perpendicular to the plane of the sample. This vibration causes a change in probe to sample distance, which in turn results in the flow of current, taking the form of an ac sine wave. The resulting ac sine wave is demodulated to a dc signal through the use of a lock-in amplifier. Typically the user must select the correct reference phase value used by the lock-in amplifier. Once the dc potential has been determined, an external potential, known as the backing potential (V) can be applied to null the charge between the probe and the sample. When the charge is nullified, the Fermi level of the sample returns to its original position. This means that V is equal to -V, which is the work function difference between the SKP probe and the sample measured.
  The cantilever in the AFM is a reference electrode that forms a capacitor with the surface, over which it is scanned laterally at a constant separation. The cantilever is not piezoelectrically driven at its mechanical resonance frequency ω as in normal AFM although an alternating current (AC) voltage is applied at this frequency.
  When there is a direct-current (DC) potential difference between the tip and the surface, the AC+DC voltage offset will cause the cantilever to vibrate. The origin of the force can be understood by considering that the energy of the capacitor formed by the cantilever and the surface is
  plus terms at DC. Only the cross-term proportional to the V·V product is at the resonance frequency ω. The resulting vibration of the cantilever is detected using usual scanned-probe microscopy methods (typically involving a diode laser and a four-quadrant detector). A null circuit is used to drive the DC potential of the tip to a value which minimizes the vibration. A map of this nulling DC potential versus the lateral position coordinate therefore produces an image of the work function of the surface.
  A related technique, electrostatic force microscopy (EFM), directly measures the force produced on a charged tip by the electric field emanating from the surface. EFM operates much like magnetic force microscopy in that the frequency shift or amplitude change of the cantilever oscillation is used to detect the electric field. However, EFM is much more sensitive to topographic artifacts than KPFM. Both EFM and KPFM require the use of conductive cantilevers, typically metal-coated silicon or silicon nitride. Another AFM-based technique for the imaging of electrostatic surface potentials, scanning quantum dot microscopy, quantifies surface potentials based on their ability to gate a tip-attached quantum dot.