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Dual-Frequency Resonance Tracking (DFRT)


Application Description

Dual-frequency resonance tracking (DFRT) is a contact mode atomic force microscopy (AFM) technique used to measure weak electrical or mechanical responses from a sample. Traditional resonance tracking techniques rely on a phase-locked loop (PLL) to keep the phase constant, but such an approach fails with ferroelectric or other materials that exhibit a phase reversal depending on the domain orientation. The advantage of DFRT lies in the ability to measure phase reversal while using solely the resonant amplitude for feedback. Applications related to the DFRT technique include piezoresponse force microscopy (PFM), electrochemical strain microscopy (ESM), which is sensitive to the ionic-current-induced strain, and scanning thermo-ionic microscopy (STIM) – which measures the strain induced by thermal oscillations.

DFRT is particularly relevant for thin-film characterization of ferroelectric and multiferroic materials, where resonance-enhanced measurements enable the measurement of weaker signals and the use of lower polarization voltages to avoid film breakdown. While lock-in measurements at a fixed low frequency is the norm for bulk materials, the nano-mechanical response to a mechanical or an electric excitation can be greatly enhanced by turning to a contact resonance technique.

Measurement Strategies

Setup for dual-frequency resonance tracking (DFRT) with HF2LI Lock-in Amplifier

The first step is to identify the contact resonance (CR) by sweeping the output frequency that is either electrically or mechanically driven when the AFM tip is in contact with the sample. It is then possible to generate an amplitude-modulated signal (on the signal output) that gives rise to two sideband amplitudes A1 and A2 on either side of the CR. In the figure, the red curve illustrates the difference A2 - A1 as a function of the drive frequency: this exhibits a monotonic behavior around the resonance with good gain sensitivity and is thus used for feedback. A PID controller – internal to Zurich Instruments lock-in amplifiers and optimized with the PID Advisor – regulates the difference A2' - A1' between the sideband amplitudes measured at frequencies fc+/-fm. This amplitude difference is used as the error signal for the PID controller and acts upon the center frequency fc. If the resonance frequency changes due to tip-sample interactions, the measured amplitude difference A2' - A1 varies and the drive frequency is shifted as a result, as shown in the figure. At resonance, A1 and A2 coincide and the chosen setpoint is thus zero.

For multiferroic measurements and related PFM modes, the driving signal output is directed to the bias voltage. The same measurement principle applies when the signal output goes to a shaker piezo mechanically coupled to the sample, which leads to the observation of a nano-mechanical response.

Standard PFM versus DFRT-PFM

This table highlights how using Zurich Instruments for DFRT-PFM measurements leads to several advantages compared to standard PFM measurements:

Criterion Standard PFM DFRT-PFM with HF2LI or UHFLI
Bias modulation frequency 100 Hz to few kHz Up to 50 / 600 MHz at CR
Frequency tracking None (static) Frequency tracking topography, used as a reference for lock-in measurements
Frequency generation Up to 2 frequencies (with 2 lock-ins or 1 HF2LI) Up to 6 frequencies or 2 CRs
Lock-in measurements Single lock-in measurement of amplitude and phase Center and sideband amplitudes and phases, PID error, frequency shift
Feedback signal None (open loop) Difference of sideband amplitudes (A2-A1), PID Advisor
Choice of drive frequency Manual tuning, fixed frequency Always at CR, higher signal-to-noise ratio (SNR)

The Benefits of Choosing Zurich Instruments

  • Bimodal excitation, sideband detection, and PID feedback on the amplitude difference are all accessible through the same Zurich Instruments lock-in amplifier.
  • Both inputs of the HF2LI Lock-in Amplifier can be used for the simultaneous measurement of in-plane and out-of-plane components, enabling the study of the complete piezoelectric vector field (magnitude, orientation, and polarity).
  • You can increase the sensitivity of your measurements with resonance enhancement techniques – even when the use of a PLL is not possible. The same PID Advisor can optimize any linear feedback loop.
  • Zurich Instruments offers a solution in the form of a simple add-on to any third-party AFM microscope: only the sensor deflection (vertical and lateral) and the bias voltage (drive) need to be accessible.
  • All internal channels can be recorded as multiple images by synchronizing the data acquisition (DAQ) module with an End-of-Line (EOL) trigger from the Scan Engine.
  • Use higher harmonic components with DFRT to be sensitive to ionic current (e.g., ESM), to thermally induced strain (e.g., STIM), or to other harmonic-related phenomena.
  • Tracking the resonance frequency leads to lower topographical cross-talk, which is especially important for samples with high surface roughness.

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Application Notes

Park Systems, Zurich Instruments

Stabilizing the piezoresponse for accurate and crosstalk-free ferroelectric domain characterization via dual frequency resonance tracking


Rodriguez, B.J., Callahan, C., Kalinin, S.V. & Proksch, R.

Dual-frequency resonance-tracking atomic force microscopy

Nanotechnology 18, 475504 (2007)

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