What it Takes for High-Speed AFM Measurements

Typically for biological and catalysis applications, time matters! And AFM images that record in 10 minutes or more are not acceptable. We often receive inquiries about what constitutes a complete solution for ‘fast AFM’ and what Zurich Instruments can offer in this area. Therefore, I would like to describe here all necessary conditions (if not always sufficient) to achieve ‘High-Speed’ (HS) AFM applications, which include the high-speed demodulation offered by Zurich Instruments such as the HF2LI or UHFLI lock-in amplifier.

What do we mean by High-Speed AFM ?

First, let me state what we mean by ‘High-Speed’: it’s the scanning speed at which one can capture a complete AFM image with enough pixel resolution (let say at least 128×128) without noticeable change of the physical phenomena under investigation. It then usually requires many images to track changes up to a certain ‘video rate’. Such parameters can vary a lot from system to system, so the most critical scanning parameter is the pixel dwell time or time during which tip oscillations can be measured to record a single pixel. There is also a trade-off between speed and resolution which has already been addressed in a previous blog on: Resolution, Scanning Speed and Demodulation Bandwidth.

Obviously HS might mean different things for different applications but, in practice, it refers to AFM images acquired in the order of 1s or less. From a naive perspective, everything is the same (i.e. the same AFM set-up), just faster, but in reality everything is different (many different components)! This is what I would like to show here, so let’s see what it takes to build a fast AFM.

1. Fast Probe Sensors

At first, this might look like an easy fix: let’s just buy a cantilever with a high-resonance frequency; it is indeed possible to get good commercial probes near the 2 MHz, such as the Arrow-UHF Cantilever. The higher the frequency, the less time it takes to measure the change in oscillations and the faster the tip moves to the next pixel. This is however not always as trivial as it seems, for at least 4 reasons:

  • a higher frequency cantilever usually means much smaller dimensions and needs to have the laser spot size reduced accordingly (for beam-deflection set-up).
  • a stiffer cantilever means less sensitivity (in N/m) and therefore requires an improvement in sensitivity on the detector side to maintain reasonable SNR (Signal-to-Noise Ratio).
  • a stiffer cantilever usually come with higher Q, thus reducing the ‘natural bandwidth’ of the probe (f0/Q). For operation in AM mode (tapping), this means a longer relaxation time for the cantilever to reach equilibrium, which is counter-productive. This might require a different demodulation scheme (FM mode for instance).
  • when the sensor oscillates rapidly, one might not detect all oscillations with good enough resolution. This is even more so in situations when higher flexural modes and harmonics matter.

These possible issues bring us to the next 2 points.

2. Detector Bandwidth

This is often the first stumbling block in HS-AFM: insufficient photo-diode (PD) detection bandwidth for beam deflection set-up or the fast pre-amplifier for self-sensors e.g. quartz resonators, MEMS, etc. This is not always the easiest component to change, it is often the whole AFM head that has to be modified. For older AFM set-ups, typical PD bandwidth is of the order of 500 kHz. Most new commercially available AFM microscopes will now be delivered with 10 MHz bandwidth which is not always sufficient but is at least more reasonable.

3. Demodulator / Lock-in Amplifier **

All these fast oscillations have to be processed to measure changes in amplitude (AM mode) or in phase (FM mode). The most critical parameter is then the demodulation bandwidth or lock-in time constant. This is independent from the actual AFM set-up and a lock-in amplifier is easily exchanged, being a stand-alone device. If the cantilever oscillates slowly there is no real benefit from fast demodulation since the lock-in will still need to wait for at least 3 oscillation cycles to make a realistic measurement. But already with a 1 MHz resonator a single oscillation will only take 1 µs and so for 10 oscillations per pixel, which will give a reasonable SNR (Signal-to-Noise Ratio), a 10 µs lock-in time constant is a must. With today’s MEMS-based SPM sensors reaching a few MHz or more, it now make sense to consider lock-in amplifiers that minimize the pixel dwell time by measuring changes in amplitude and phase as fast as possible.

A second advantage of fast demodulation is the integration of digital feedback loops for better resonance tracking. In particular, for high Q factors there are advantages to having feedback on the phase (phase-locked loop) rather than the amplitude, which exhibits a slow relaxation time. PLL feedback circumvents the problem of high-frequency resonators with lower natural bandwidth (f0/Q):  the relaxation of the cantilever does not depend on Q factor but on the PLL bandwidth, which can be set by the user as a trade-off between speed and resolution. All integrated feedback loops can provide a faster response, and also for Z, as addressed in the next point.

4. Z-Feedback (PID) loop **

Z-Controller feedback is in fact not always necessary as some HS-AFMs work in an open-loop (constant height) or with simple tilt compensation but without actual surface tracking.  This is however only possible for fairly flat surface. When possible, it makes sense to have the loop digitally integrated together with the demodulator for faster reaction (reduced latency and data communication as well as ADC/DAC conversion). This integration can also be offered by Zurich Instruments’ lock-in amplifiers

5. Fast Scanner

Standard piezotube scanners typically have a resonance frequency in the order of 1 kHz. For ‘not-so-demanding’ high-speed applications, this might suffice – let’s say to scan no more than 512 lines per second. Above that regime, it is necessary to look for a scanner with higher resonance frequency, eithe ra smaller scan-tube (less mass, hence higher f0)  but usually at the expense of smaller scan size. That’s why there are recent developments in this field for scanners that are not based on piezo-ceramic tubes, such as high frequency flexural stages.

6. Fast Acquisition System

Finally, all the nice mega-bytes (MB) of data generated per second have to eventually be captured to process the actual AFM image, change parameters on the fly and save all necessary data to the hard-drive. The fastest operation, such as demodulation of cantilever amplitude and phase would already have been done with an internal or external lock-in amplifier, so the minimum bandwidth requirement is the amount of pixel information that is going to be received per second. For a minimalist approach of 256×256 frame per second, this require a controller bandwidth (real-time acquisition loop) of at least 70 kHz and goes up very quickly with higher pixel resolution or more frames per second, or both. Most standard commercial SPM controllers cannot exceed an acquisition bandwidth of more than 100 kHz. It therefore requires a fast data acquisition card but as well as some programming, or some analogue control electronics available commercially.

Conclusion

The purpose of this blog was to describe the building blocks of a microscope that changes a ‘standard’ AFM set-up into a ‘high-speed’ one. HS-AFM is still an emerging field and not all the points raised above are yet fully optimized, especially when taken together. I have attempted here to show the benefit of Zurich Instruments’ high-speed lock-in amplifiers and PLL/PID options in a more general context, which may help instrumentalists to focus on other harder aspects of their set-up.

** : Points 3&4 can be addressed by Zurich Instruments lock-in amplifier with or without options such as PLL and PID.