Multi-Frequency Atomic Force Microscopy (MF-AFM)

Multi-frequency techniques in atomic force microscopy (MF-AFM) can discriminate many different contributions from the tip-sample interaction in the form of mechanical, electric, magnetic, or optical responses. MF-AFM is also sensitive to non-linear effects causing a harmonic distortion from the steady-state motion of the oscillating cantilever. As most AFM sensors exhibit different eigenmodes up to a few MHz, the ability to actuate and detect such modes separately can be exploited and adapted to measure various physical phenomena. For example, bimodal excitation, dual-harmonic Kelvin probe, multi-harmonic mode, and many SNOM or tip-enhanced techniques often make use of higher harmonic generation.

Demodulating many frequency components simultaneously from one or multiple inputs is a key requirement for multi-frequency techniques. The choice of a measurement setup depends on whether information is mostly contained in the eigenmodes (that is, the natural modes of vibration of the resonator), in the harmonics (i.e., integer multiples of the fundamental tone), or in both. We can nonetheless distinguish three different measurement strategies for MF-AFM:

• Drive and measure multiple eigenmodes that map force contribution from different interactions (electrical and mechanical, for instance). This type of measurement can be performed in open- or closed-loop configurations to actively track the resonance.

• Higher eigenmodes exhibit a different quality factor Q and stiffness k, and can be driven at a different amplitude A: this leads to distinct coupling strengths and responses between the resonator and the tip-sample interaction. Use different eigenmodes to detect short-range forces with a small amplitude on the first mode and keep feedback stable with a large amplitude on the 2nd mode.
• Record the tip-sample interaction over as many harmonic components as possible to fully reconstruct the non-linear interaction from an inverse FFT transformation.

Broad measurement capabilities and tunable modulation parameters are therefore crucial for the design and optimization of the experimental setup.

• Multi-frequency actuation and multi-demodulation detection are built into all Zurich Instruments products for fast set-up and reconfiguration. For instance, driving linear superpositions of sine waves on single or dual outputs can be achieved with an upgrade based on the MF-MD, HF2LI-MF, UHF-MF options depending on the instrument platform.
• A single instrument allows you to measure all frequency components at once, for various eigenmodes and harmonics. Input signals can originate from vertical or lateral deflection, and they can be measured simultaneously.
• When imaging the surface or in force spectroscopy mode, all measured signals can be acquired at the same time thanks to the LabOne Data Acquisition (DAQ) module (recording phases, amplitudes, frequencies, PID error, etc.).

• The signal strength can be maximized with phase shifters between drive and detection or by adjusting the phase between two drive signals. This is particularly relevant for phase-dependent signals such as those studied in dissipation Kelvin probe force microscopy (D-KPFM), Q-Control or magnetic resonance force microscopy (MRFM).
• The multi-frequency capability can be successfully combined with high-speed scanning thanks to lock-in time constants as low as 30 ns on the UHFLI Lock-in Amplifier.
• The number of input and output channels grows with your needs: multiple instruments can be seamlessly integrated to behave as one thanks to multi-device synchronization (MDS).