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Dual-Frequency Resonance Tracking (DFRT)

Related Products: HF2LI with the HF2LI-MF, HF2LI-PID, HF2LI-MOD options, UHFLI with the UHF-MF, UHF-MOD, UHF-PID options


  • PFM
  • piezo
  • ferro-electric materials
  • nanomechanical properties


Track a resonance in a situation where the phase flips or does not provide enough sensitivity (low Q).


  • perform frequency tracking where the use of a PLL is not possible
  • simple add-on to existing SPM microscope: only sensor deflection (detection) and bias voltage (drive) needs to be accessible
  • faster and more effective measurements

As multi-layer thin films and multi-ferroic materials become thinner, the need for resonant enhanced measurements are necessary to increase sensitivity for reduced polarization voltage. While lock-in measurements at a fixed low frequency was the norm for bulk material, the nano-mechanical response to a mechanical or electrostatic excitation can be greatly enhanced at the contact resonance of an AFM sensor. Within the same Zurich Instruments unit, bi-modal excitation, sideband detection and PID feedback on the difference of amplitude is readily available for both in-plane and out-of-plane components measurements simultaneously.

Dual-frequency Resonance Tracking (DFRT) Graph

Description of the Method

A PID controller internal to the lock-in amplifier is used to regulate the difference between two amplitudes measured at frequencies f1 and f2 around the resonance. The magnitude and the sign of the difference can be used to calculate the error signal for the PID controller to modify the drive frequency (f1+f2)/2.

At resonance there is no difference between A1 and A2 and there is no resulting error signal. If the resonance frequency decreases like the in picture above, A2' - A1' is negative and the drive frequency is decreased.

LabOne Supports Imaging

The LabOne Software Trigger is equipped with the grid mode which serves to align the measured samples to a grid of pixels in order to depict the measured parameter in a 2D plot. All within the same user interface it is therefore possible to modify experiment parameters and immediately see the result in another tab. With the power to stream up to a sustainable 800 kSa/s over multiple channels in a triggered fashion, LabOne is strong for image acquisition up to video rate (8 frames * 256 * 256 pixel/s). Saving of acquired images into SXM format is possible as well. See also a recent blog of Daniel Wright when working with one of the LabONE APIs.

Advanced DFRT

Measuring with Zurich Instruments electronics presents a series of advantages with respect of standard PFM acquisition.

Criteria Standard PFM DFRT-PFM with HF2LI or UHFLI
Bias modulation frequency 100 Hz to few kHz up to 50 / 600 MHz, at or near contact resonance (CR)
Frequency deviation none (static frequency) frequency tracking, reference frequency for lock-in measurement always at resonance
Multiple frequencies yes, up to 2 frequencies (with 2 lock-ins or one HF2LI) yes, up to 6 frequencies or 2 contact resonances
Lock-in measurements single lock-in measurement of amplitude and phase carrier and sideband amplitude and phase (in total 12 measurements)
Feedback signal none (open loop) difference of sideband amplitudes (A2-A1)
Tuning manual tuning, low repeatability resonance enhancement, SNR improvement, vector field reconstruction from in-plane & out-of-plane contributions

Image Resources

An image created using the LabOne grid mode using DFRT. Image courtesy of Ehsan Esfahani, University of Washington, Seattle. The images show the amplitude and phase measured on nanocrystalline Sm-doped Ceria sample using 4th harmonic response for DFRT mode. Such samples exhibits higher concentration of mobile species near grain boundaries.

Amplitude measured in nanocrystalline Sm-doped Ceria sample using 4th harmonic response for DFRT mode
Phase measured in nanocrystalline Sm-doped Ceria sample using 4th harmonic response for DFRT mode

Further Applications of DFRT

DFRT can also be used for ESM (Electrochemical Strain Microscopy) which relies on the same principle of PFM but is sensitive to the ionic current induced strain or STIM (Scanning Thermo-Ionic Microscopy) to measure strain induced by thermal oscillations.


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