Pulsed Force - Kelvin Probe Force Microscopy
Surface potential is a physical property of the material that is related to the work function of materials and the presence of surface residual charges. A popular type of SPM method for surface potential measurement is the Kelvin probe force microscopy which was invented in the 1990s. The underlying principle of KPFM is to use a DC voltage bias to compensate for the difference in surface potential to prevent electron migration upon electrical contact.
KPFM has its conceptual origin in the Kelvin method, by Lord Kelvin.
Consider a pair of plates of different metal types close in space: if there is an electrical connection between them, e.g., through a wire, then the Fermi level alignment occurs and electrons move from low work function metal to the high work function metal. A net result is the emergence of charges between two metal plates, and Coulombic forces.
If a DC voltage is applied between two plates and the voltage value matches the difference in work functions, then the migration of electrons is negated, and no charge or Coulombic force shall emerge. The contact potential difference between the metal surfaces due to the difference in work functions can be measured by searching for the DC voltage. This configuration allows for macroscopic measurement of the work function.
In KPFM, the Coulombic force between the sample and the AFM metallic tip is measured and used to recover the contact potential difference. Current representative KPFM techniques (amplitude modulated KPFM and frequency modulated KPFM) usually use an AC voltage to drive the electrons between the AFM tip and sample; the resulting periodical Coulombic forces cause the AFM cantilever to oscillate. A DC voltage is used to minimize the cantilever oscillations or the frequency shifts of the cantilever from the periodical Coulombic force.
For KPFM operations under ambient conditions, a large magnitude of AC voltage is usually needed. To avoid possible electrical damage between the tip and sample, a lift mode operation is usually adopted by KPFM, including the original amplitude-modulated KPFM and a more popular frequency-modulated KFPM. First, the AFM scans the topography of the sample, and then the tip is lifted from the sample surface with a constant offset from the topography. The AC and DC voltages are only applied during the lift without direct tip-sample contact.
Illustration of lift mode (by Bruker) The AFM first scan the topography of the sample, then lift to a specified height, and then retrace the topography plus the lift height.
However, the current KPFM has limitations due to its lift mode operation. At the nanoscale, the Coulombic force is long-range and can extend hundreds of nanometers. If the tip is lifted 50 ~ 100 nm, the dominant force that drives the cantilever oscillation in KPFM is not just from the tip apex. Coulombic forces between the sample and AFM cantilever and tip cones are present. As a result, the spatial resolution suffers.
A simulation by Colchero, Gil, and Baró (PRB 64, 245403, (2001)) shows the force contribution from the AFM tip apex, tip cone, and cantilever.
As their simulation revealed, in order to have the tip apex as the dominant source of Coulombic force, the tip-sample distance has to be less than ~ 2 nm. This is much smaller than the usual 50 nm lift mode of AM-KPFM and FM-KPFM under ambient conditions.
Pulsed force Kelvin probe force microscopy
The invention of the pulsed force Kelvin probe force microscopy (PF-KPFM) is to utilize the short tip-sample distance configuration in the peak force tapping mode for surface potential measurement. Moreover, PF-KPFM uses a field-effect-transistor (FET) to switch ON and OFF the electrical connectivity between the AFM tip and sample and track the Coulombic force generated by Fermi level alignment.
The peak force tapping mode of AFM has a deterministic contact region and detachment region. When the tip is just detached from the sample surface, the tip-sample distance is separated but still very close (< 2 nm), which is a good spot for inducing the Fermi-level alignment. The Coulombic force is mainly generated between the AFM tip apex and the sample, which is a requirement for high spatial resolution.
The schematics of the PF-KPFM are shown in the right figure. The AFM is operated in the peak force tapping mode (pulsed force mode). A FET is used to switch ON/OFF and electrical connectivity between the sample and the metallic AFM tip. The ON/OFF state of the FET is controlled by a function generator.
The timing of the FET switching happens when the tip and sample are just detached in a peak force tapping cycle.
When the FET is switched ON, it acts as a wire to collect the tip and sample. Charges emerge if their surface potentials are different. When the FET is switched OFF, it cuts off the electrical connection and acts as a capacitor. Small charges between the sample and tip migrate to the residual capacitor between the source and drain.
If the FET is switched ON/OFF multiple times, the Coulombic force causes the AFM cantilever to oscillate. In PF-KPFM the period of FET switching matches that of the cantilever free-space resonant oscillation.
The cantilever resonant oscillations are induced by switching the FET a few times. The high quality factor of the AFM cantilever means that the oscillations persist during the detachment phase of the peak force tapping cycle. The oscillations are then extracted using gate triggered digitalization and a fast Fourier transform is used to extract the amplitude of the oscillations. The stronger the Coulombic force from the Fermilevel alignment, the stronger the cantilever oscillations.
The Coulombic force induced cantilever oscillations depend on the relative position of the Fermi levels. If the DC voltage is swept between the tip and sample, the amplitude of the cantilever oscillation exhibits a characteristic V-shape. The intercept between two branches gives an accurate measurement of the contact potential difference (CPD) between the AFM tip and the sample.
To enable the spatial scan of PF-KPFM, a negative feedback loop is used to regulate the cantilever oscillation amplitude to an external set point as the AFM tip is scanned over a sample in the peak force tapping mode (pulsed force mode). The output of the DC voltage is then offset with information of the setpoint and the V-shape slope. The spatial distribution of the CPD is then obtained with the PF-KPFM. The details of the construction and operation of the PF-KPFM is described in our paper ACS Nano, 14, 4, 4839-4848 (2020).
We have benchmarked the PF-KPFM on a calibration sample of Al/Si/Au versus the commercial FM-KPFM of a Multimode AFM (Bruker). The comparison is shown below. 10 nm spatial resolution is observed for PF-KPFM versus ~40 nm of that of FM-KPFM.