The working principle of lift-mode EFM is based on the fact that van der Waals and electrostatic forces have a different dependence on the tip-sample distance. While van der Waals forces act in tip-samples distance between 1 nm and 10 nm, electrostatic forces have a range of more than 1 μm. Thus, when the tip is close to the sample, van der Waals forces govern the tip-sample interaction. As the tip moves away from the sample, van der Waals forces rapidly decrease, and electrostatic forces become dominant.

Therefore, lift-mode EFM uses a dual pass approach: in the first pass scan, the tip maps the sample topography in a tip-sample distance, where van der Waals forces dominate. Then, the tip is lifted to a distance with negligible van der Waals forces, where electrostatic forces govern the tip-sample interaction. This distance is typically between 50-100 nm. In the second pass scan, the tip follows the topography scan of the first pass to achieve a constant tip-sample distance and thereby detects only the electrostatic force for EFM imaging, without topography crosstalk (figure 2a). Here, an additional tip bias increases the electrostatic interaction between tip and sample. To avoid drift effects between the topography and EFM scan, both passes are performed subsequently at each scan line.

For improved sensitivity and signal-to-noise ratio, both scans are performed in dynamic mode using lock-in detection. During the first pass, the tip oscillates at the cantilever’s resonance frequency in the attractive van der Waals force regime in Park’s true Non-contact mode, ensuring tip and sample preservation. In the second pass scan at constant tip-sample distance, the tip oscillation at resonance is now only sensitive to the electrostatic forces. The oscillation amplitude and phase on the second pass scan give the magnitude and sign of the sample surface potential. This single frequency EFM is easy to operate even with single lock-in amplifier. However, because of the property of the lift mode, it measures the EFM in far distance from surface and scan twice. This method is more time consuming and loses spatial resolution in the EFM amplitude and phase, compared to dual frequency EFM (see below).

Dual frequency EFM in current Park AFMs is designed to provide an efficient single pass method to acquire both topography and the EFM signals simultaneously, without loss of sensitivity. Dual frequency EFM allows complete separation of topography and EFM signals, as each of the signals is obtained at vastly different frequencies detected with two different lock-in amplifiers (figure 2b). The tip scans the surface topography by oscillating at the cantilever resonance ω0 to obtain a Non-contact mode topography image. At the same time, an AC bias with a frequency of ωtip is applied to the tip via the second lock-in amplifier as well as a DC bias. The electrical excitation of the tip leads to an oscillating electrostatic force between the biased tip and the charged surface. The second lock-in amplifier decouples the motion of the tip introduced by the electrostatic force at the AC frequency ωtip from the topography signal detected at resonance ω0. The amplitude and phase at ωtip contain information on the magnitude and sign of the surface charge. The frequency ωtip should be small compared to cantilever’s mechanical oscillation frequency ω0 to avoid interference between the two signals. Typically, Park AFMs use frequencies of ωtip~10 to 20 kHz for the AC excitation.

A schematic diagram of the experimental setup of dual frequency EFM is shown in figure 3. The additional lock-in amplifier for the EFM signal is embedded in the AFM controller and serves two purposes: the first the application of the AC voltage with the frequency ωtip, in addition to the DC bias. The second is the separation of the signal component at ωtip, which carries the EFM data, from the topography signal detected at the cantilever resonance ω0. In the dual frequency EFM, the tip and the sample can be viewed as a capacitor, with an oscillating electrostatic interaction force Fel given as:

With tip-sample capacitance C in a distance d and the total voltage V. Since both AC and DC voltages are applied simultaneously between the tip and the sample, the total voltage V between the tip and the sample is expressed by the following equation:

Where VDC is the DC tip bias, VS is the surface potential on the sample and VAC and ωtip are the amplitude and frequency of the applied AC voltage, respectively. The combination of equation 1 and 2 results in three terms that describe the electrostatic force:

These terms can be referred to as static DC term (a), and two AC terms at ωtip (b) and 2ωtip (c). Whereas the static DC term is difficult to detect, the second lock-in amplifier used for EFM can accurately decouple the AC term at ωtip to image the electrostatic properties of the sample. The amplitude at ωtip contains information on the magnitude of the electrostatic charging of the sample, while the phase contains information on the sign of the surface charge.

The key advantages of dual frequency EFM compared to lift mode EFM are as follows:

An EFM measurement of Au patterns on a SiO2 substrate is shown in figure 5. The sample consists of two microcomb-shaped electrodes. One of the Au electrodes is connected to the ground while the other is connected to the sample bias. The electrodes are 30 nm high (25 nm Au and 5 nm Ti) on a 100 nm thick oxide layer on Si substrate for insulation between the interdigitated electrodes.

By applying a DC bias of +0.5 V to the sample, the EFM signals between grounded and biased electrodes are clearly distinguishable.