How to set-up Kelvin Probe Feedback (FM-KPFM) with Direct Sideband Detection

HF2 users can already find valuable information on the HF2LI-MOD option in earlier blogs such as in Exploring the HF2LI-MOD: Measuring Bessel Functions for the difference between tandem and (direct) sideband detection or even schematics of various KPFM configurations in HF2PLL for KPFM Applications.

Here, I would like to get a bit more practical and walk the way through setting up a real KPFM measurement in FM modulation.

Why direct sideband detection?

Every SPM user has experienced it: Kelvin Probe imaging is slow, sometimes really slow, even more so in the original LiftMode™ or Multipass technique, where the tip scans the same line for a second time to record ‘pure’ electrostatic forces. That is why single-pass techniques are becoming increasingly popular with a plethora of new modes originating from a simple idea: different cantilever frequencies can be used for simultaneously accessing different information originating from the same tip-sample interaction. Information obtained in that way can be related to nanomechanical, electrical or magnetic properties of the sample. This being said, single-pass techniques still often remain fairly slow because the lowest PID bandwidth limits the overall scanning speed. In FM-KPFM in particular, many users will demodulate the AC-component of the frequency shift from the output of the PLL, with a PID regulating the bias, which then acts as an additional low-pass filter in the complete loop. In practice, the KPFM bandwidth has to be smaller than the PLL bandwidth, which by SNR consideration would hardly exceed let’s say 400 Hz. For stiff sensors such as Tuning Fork, qPlus™ sensors or KolibriSensors™ this is even more challenging because typical PLL demodulation bandwidth will remain below 50 Hz for good atomic resolution imaging.

All these considerations rely on the fact that most lock-in amplifiers or PLLs can track only one frequency at a time (one internal reference or VCO) and therefore devices need to be cascaded with tandem demodulation. The HF2LI-MF option allows to track 6 arbitrary frequencies simultaneous and independently. Each sideband (from bias modulation) and carrier (cantilever resonance tracked by PLL) will be measured with its own time constant independent from each other. The benefits are 3-fold:

  1. Faster bias modulation possible (independent of PLL demodulation)
  2. Optimization of PLL settings for better resolution (narrow band) regardless of AC modulation
  3. Potential increase of SNR for the Kelvin feedback since both sidebands are measured and added (twice the X-component).

Let’s see now how this applies for FM-KPFM and especially how to set this up in a HF2PLL.

Kelvin probe parabola, first CPD determination

Here we already locked the PLL to the 77 kHz cantilever resonance frequency with PID1 for Amplitude control (AGC) on Signal Output 1 (please also refer to Chapter 3.8 of the User Manual on how to set-up the PLL). The tip is therefore already approached and we lift it by let’s say 50 nm above the surface to be sensitive to only electrostatic interactions. If you cannot lift the tip, as not every SPM Controller allow this, simply reduce the gain of Z-feedback over a point or a tiny scan area. The HF2PLL’s Aux 4 channel acts as the pure DC bias voltage and is used as ‘Manual’ offset. With a T-BNC we also feed this offset to the ‘Add’ on Signal Output 2 to excite the cantilever electrostatically with an AC+DC bias voltage. By manually shifting the Aux 4 value with computer’s cursor keys, we can display the CPD (Contact Potential Difference) parabola as shown in Figure 1. Let’s stay away from CPD in the beginning to be sensitive to more electrostatic force.

Figure 1: First encounter with CPD parabola

Figure 1: First encounter with Contact Potential Difference (CPD) parabola

Alternatively, you can also check the effect of cantilever amplitude as a function of bias voltage: amplitude will be minimal at CPD with a linear dependence below and above this minimum. In such case, the Sweeper will be more convenient than the Spectroscope.

FM detection of AC bias modulation

Now that we know where the CPD lies, we can add an AC modulation to the bias voltage, which will also be sensed by the cantilever. This modulation will results in 2 sideband peaks on each side of the resonance. This can be set-up directly in the Modulation tab with ‘FM Demodulator’ mode selected and Oscillator 1 (from the PLL) and 2 for each sideband. This action will automatically use the first 3 demodulators in the Lockin-MF tab described in Figure 2. Since we are interested in the X-component of the demodulated signal (i.e. the monotonic behavior as a function of bias), make sure to optimize the phase to minimize Y-Component (the auto-phase button at the right of the phase value should work just fine for that). Phase adjustment should be done when the Z-feedback is off and with a large bias voltage so that the measured signal comes mainly from the electrostatic tip-sample interaction. Note that since both sidebands use the same oscillator, the phase should be the same so you can adjust the phase for demodulator 2 and copy it in demodulator 3. For better phase measurements, you can reduce the BW of the demodulator and increase it again when scanning.

MF tab-sidebands X2X3-settings-comments

Figure 2 (click to enlarge): set-up modulation and detection with correct phase adjustment.

Please note that the phase of the sidebands is not equivalent to the phase of the modulation, that’s why it is necessary to auto-phase both oscillators 1 & 2 (and not just the sidebands). Only then will you have maximum X components with opposite phase (180° between each sideband) and therefore opposite sign as can be seen below. In the Numerical tab, this would look like this:

Signal strength

 

Optimizing the bandwidth with the zoomFFT Spectrum Analyzer

At this stage, one might wonder how this looks like in the frequency domain, especially to see the strength of the electrostatic interaction compared to the resonance and decide for an appropriate bandwidth. The spectrum speaks for itself but since it is also acquired in real-time, one can play with the parameters and change bias modulation, tip sample distance and eventually PID feedback loop on the DC bias. All the measured values from these peaks are directly displayed in the Numerical tab for a given filter setting (i.e. bandwidth and roll-off).

zoomFFT-sidebands 2kHz comments

Closing the PID loop

If all the above behavior has been observed and predictably reacts to the DC value when changed manually, we are ready to close the loop. The feedback will regulate only the DC component of bias and send the output value to Aux 4. It is recommended to start well away from CPD where the slope is steeper and the signal is stronger. When the PID is enabled, monitor the bias voltage to make sure the value goes in the right direction (if not, change the slope!). You may start with only I-gain (around 10 kV/Vs) and slowly increase P-gain to the desired noise level but below feedback oscillation, watch the DC bias value moving more or less slowly toward CPD depending on the gain. Compare forward and backward scan line for fine gain adjustment and to optimize scan speed.

Figure 4: PID settings to control DC bias voltage from sideband input

Figure 4: PID settings to control DC bias voltage from sideband input

Voilà ! You are all set to make wonderful KPFM images. Here is just an example on Graphene flakes, courtesy of Thilo Glatzel from Universität Basel:

Figure 5: Direct FM-KPFM on Graphene

Acknowledgements

I am greatly indebted to Thilo Glatzel (Uni Basel) and Tino Wagner (ETH Zurich) for on-site measurements on their very well prepared sample & microscope as well as for fruitful discussion and feedback. Thanks also to Sadik Hafizovic to clarify with me the effect of phase between the carrier and its sidebands.

Disclairmer

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