Electrostatic force microscope

Force measurement

For example, consider a conductive cantilever tip and sample which are separated a distance z usually by a vacuum. A bias voltage between tip and sample is applied by an external battery forming a capacitor, C, between the two. The capacitance of the system depends on the geometry of the tip and sample. The total energy stored in that capacitor is U = C⋅ΔV2. The work done by the battery to maintain a constant voltage, ΔV, between the capacitor plates (tip and sample) is -2U. By definition, taking the negative gradient of the total energy Utotal = -U gives the force. The z component of the force (the force along the axis connecting the tip and sample) is thus:

:F_{electrostatic} = \frac{1}{2} \frac{\partial C}{\partial z} \Delta V^2 .

Since * CPD* This causes the apex of the parabola to rest at ΔV = Vtip − Vsample − VCPD = 0. Typically, the value of VCPD is on the order of a few hundred millivolts. Forces as small as piconewtons can routinely be detected with this method.

Non-contact atomic force microscopy

A common form of electric force microscopy involves a noncontact AFM mode of operation. In this mode the cantilever is oscillated at a resonant frequency of the cantilever and the AFM tip is held such that it only senses with long range electrostatic forces without entering the repulsive contact regime. In this non-contact regime, the electric force gradient causes a shift in the resonance frequency of the cantilever. EFM images can be created by measuring the cantilever oscillation, phase and/or frequency shift of the cantilever in response to the electrostatic force gradient.

Immersion

With an electrostatic force microscope, like the atomic force microscope it is based on, the sample can be immersed in non-conductive liquid only, because conductive liquids hinder the establishment of an electrical potential difference that causes the detected electrostatic force.

References

• L. Kantorovich, A. Livshits, and M. Stoneham, J. Phys.:Condens. Matter 12, 795 (2000).
• "Electrostatic Force Microscope for Probing Surface Charges in Aqueous Solutions" by S. Xu and M.F. Arnsdorf, PNAS 92 (1995) 10384