Kelvin Probe Microscopy

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Kelvin probe force microscopy (Kelvin mode of Scanning Probe Microscopy) was invented for measuring contact potential difference between the probe and the sample [1]. At present time Kelvin mode is based on the two-pass technique. In the first pass the topography is acquired using standard Semicontact mode (mechanical excitation of the cantilever). In the second pass this topography is retraced at a set lift height from the sample surface to detect the electric surface potential Ф(x). During this second pass the cantilever is no longer excited mechanically but electrically by applying to the tip the voltage V_tip containing dc and ac components


V_tip=V_dc + V_ac sin(wt)

The resulting capacitive force F_cap between the tip and a surface at potential V_s is

F_cap =(1/2) (V_tip - Ф(x))²(dC/dz)

where C(z) is the tip-surface capacitance. The first harmonic force

F_{cap w} = (dC/dz(V_dc- Ф(x)V_ac)sin(wt)

leads to suitable cantilever oscillations. The feedback then changes the dc tip potential V_dc until the w component of the cantilever (and accordingly w component of the tip-force) vanishes, e.g. V_dc (x) became equal to Ф(x). So mapping V_dc (x) reflects distribution of the surface potential along the sample surface. If no special tip-sample bias voltage is applied this distribution is Contact Potential Difference distribution.

References 

1. Appl. Phys. Lett. 58, 2921 (1991).