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Experimental Techniques - Electronic Force Microscope

The Electrostatic Force Microscopy (EFM) is a non-contact method which allows us to measure the electronic potential difference between the cantilever tip and the sample with a horizontal resolution of ~100nm and to within a few tens of milliVolts. The technique generally only works with conductive samples, or, at least, samples supported on large conductive substrates reasonably close beneath them.

As in standard noncontact modes, the cantilever is oscillated about it's resonance and held a small distance (~100nm) above the sample. Although the cantilever is oscillated by applying a sinusoidal voltage to a piezo upon which it is mounted (see the SFM page for an explanation of noncontact techniques), the cantilever is electrically isolated from the piezo. We exploit this fact by applying another AC signal, this time directly to the cantilever and at a different frequency from the mechanical resonance of the cantilever. In addition, we apply a DC signal to the tip along with the AC one.
So we now have two AC signals and one DC signal. The first AC signal is applied to the piezo and shakes the cantilever at resonance. The second is applied to the cantilever itself and is of a markedly different frequency.

Now, consider what happens when the sample is at ground potential and the tip isn't (due to the DC signal--the AC signal is, on average, zero). There will be a force between them (due, to a first approximation, by a net charge difference between the tip and the sample). Since the charge on the tip varies sinusoidally at a fixed frequency, the force will vary at the same frequency. This will cause the tip to vibrate at the same frequency. Just as we can pick out the amplitude of vibration at mechanical resonance with a lockin amplifier, we can pick out this electronic vibration with a second lockin.
At first blush this may seem overly complicated. Since it is the DC signal that results in a net charging of the cantilever (from which the force appears), why not just stick with a DC signal?

The answer is a question: How would you measure the electric force? Applying a DC offset to the cantilever will cause it to bend toward the surface, but we have no way to directly measure that since we're shaking the tip at it's mechanical resonance and we have an active feedback loop running to keep the tip a fixed distance from the sample.
By applying an AC signal on top of the DC signal, we make the tip wiggle at the AC frequency. Then we can use the same kind of equipment to measure the amplitude of that wiggle that we use to measure the amplitude of mechanical oscillation.

A detailed discussion of EFM can be found in Steve Howell's PhD thesis. In particular, it discusses how the DC signal effects the amplitude of the AC vibration.
As the tip is scanned over the surface, the amplitude of vibration at the electronic driving frequency is recorded. In this way a 3D image is constructed of the magnitude of the electronically driven oscillation. If different portions of the sample have, say, a net charge, this will effect the electronic force between the tip and sample at that point, this will then show up on the scanned image.

One can also make single point measurements. By holding the tip above a fixed position on the sample and varying the DC offset applied to the tip, we can map out the magnitude of the elctronic force over a range of voltages. This technique can provide a very sensitive measure of the potential of the sample.
We have used this technique to measure the electronic potential of self assembled monolayers of molecules on gold surfaces as well as the photovoltage developed by the protein bacteriorhodopsin under illumination by a diode laser.

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