Resolving fast dynamics through measurement in the frequency domain

The advent of multifrequency lock-in amplifiers has made possible the development of AFM methods that are explicitly designed to exploit the nonlinear nature of the tip-surface interaction. These methods capture information in the frequency domain with high signal-to-noise ratio through measurement of intermodulation between two or more drive tones.

Intermodulation electrostatic force microscopy (ImEFM) [1] is an open-loop alternative to Kelvin-probe force microscopy (KPFM), where the potential of the surface is obtained from a measurement of four frequency components of the force which fall within the cantilever resonance.

We have recently developed a time-resolved variant of ImEFM [2], where the cantilever drive intermodulates with a series of voltage pulses on the sample to produce force components at multiple frequencies around resonance. Measuring these force components we reconstruct dynamic processes in the material with time resolution of 30 nanoseconds, dispite of the limited bandwidth (~500 Hz) of the cantilever resonance.

Intermodulation conductive AFM (ImCFM) [3] measures the current-voltage characteristic (IVC) at every pixel of an AFM scan with a speedup of four orders of magnitude in comparison to the traditional time-domain methods. Frequency-domain analysis allows for complete separation of the galvanic current from displacement current in the tip-sample capacitance. The technique also maps the voltage dependence of the tip-sample capacitance, allowing for the investigation of phenomena such as quantum capacitance.

[1] Borgani, Appl. Phys. Lett. 105, 143113 (2014).
[2] Borgani, Rev. Sci. Instrum. 90, 013705 (2019).
[3] Borgani, Phys. Rev. Appl. 11, 044062 (2019).