Determination of the maximum speed of AFM systems
What determines the maximum speed of AFM systems

On a first view, this seems very easy to be answered, but let's take a close look. The precondition is, the tip must be able to follow the surface while scanning, which has two preconditions:

  1. The scan mechanics must be able to position the tip fast enough
  2. The sensor must be able to deliver the information from the surface fast enough

The first point is determined by the eigenfrequency of the scanning system. One has to differ between X,Y and Z movement. The Z movement must be about two orders of magnitude faster than the X,Y movement (the Z response time should be at least in the range of the pixel time), as the tip has to follow the surface during one scan line. In X,Y direction one only needs the relatively slow X,Y movement. In typical AFM scanners, the eigenfrequency of the Z movement is higher than in X,Y direction. The eigenfrequency in Z direction is strongly influenced by the type of scanner, i.e. whether the tip is moved up and down or the sample.
It is easy to see that a sample larger than 1 cm is slower to be moved up and down than the AFM tip. That is why many sample scanners, where the sample is moved during the scan and the tip is fixed, have the Z movement on the tip side (separated X,Y, and Z scanner).

The eigenfrequency of the X,Y scanner is much less critical. When scanning very fast, one can see on flat samples sometimes at the side of the image vertical lines running perpendicular to the scan direction. These lines result from the turn around at the borders of the scan which induce oscillations in the X,Y scanner. If you can see these lines, the line distance in relation to the time-per-line shows the eigenfrequency of the scanner.

As a basic rule, a smaller scanner has a higher eigenfrequency than a larger scanner. So, to make a fast scanner is straight forward. But what determines the scan speed of a small scanner?

Speed of information flow

We look at the problem from the information theoretical point of view: The faster the information flow from the surface, the faster the maximum scan speed. Unfortunately, one can not get more information per time unit for free. In AFM context, information from the surface means interaction, so more information means more interaction i.e. more force. So, if the tip interacts more with the surface, one can scan faster. By thinking about that, this seems quite obvious. In the extreme case of an infinitely small cantilever this is the only limit. Of course, in reality the cantilever has a certain mass and force constant, and a smaller cantilever should deliver information with less interaction or deliver information faster with similar interaction. But for a smaller cantilever, the noise of the bending detection becomes larger, therefore the information transfer from the cantilever to the detector will for very small cantilevers limit the information flow. As always, one can choose between high speed or low noise, but not get both at the same time.

One can also see this information limit in AC mode: A cantilever with a high Q factor is more sensitive to surface interaction than a cantilever with a small Q factor. At the same time, a cantilever with high Q factor needs less energy to keep a certain amplitude than a cantilever with low Q factor. If now the oscillations of a low Q and a high Q cantilever are totally dampened, and then allowed to restore, which cantilever will have its original amplitude restored faster? The one with the lower Q factor, because it is shaked stronger. The extreme case is here a cantilever with a Q factor of 0.5, corresponding to DC mode operation, which reacts fastest. And in this state, the eigenfrequency of the cantilever is the limiting factor. So also here, a more sensitive cantilever with a higher Q, using less force, works slower than a cantilever with lower Q.

You can easily test this limit yourself: Scan in AC mode a very flat sample (untilted), switch off the feedback look setting the loop gain to zero and record an amplitude image. By that, you remove the influence of the feedback loop and Z piezo, but you will still see at some very fast speed that the image becomes blurry. This speed is higher for a cantilever with low Q factor than for one with a high Q factor, if the other properties are identical.

This results in the following rules:

  1. The scan speed of the speed optimized AFM is limited by the response time of the sensor.
  2. For similar image quality, a higher scan speed requires more information per time unit from the surface and therefore more interaction between tip and sample is needed
  3. A rule of thump for the response time of the sensor is Q factor / (π * eigenfrequency)

State-of-the-art high speed cantilevers have their absolute speed limit in the order of magnitude of 1 mm/s. A scan of (2 µm)² at 400 lines, which is about TV resolution, takes with this speed about 1.6 s. To reach real live AFM of 25 Hz framerate at that resolution, one would need much higher speeds, which can in principal not be reached with state-of-the-art cantilever and detector techniques.

Experimentally, cantilevers with about 4 MHz eigenfrequency have been realized. With such a cantilever, for an optimal scanner for the scan parameters above a frame rate of 6 Hz could be realized or when only taking 100 lines even nearly the 25 Hz. Unfortunately, these types of cantilevers, which are only 1 to 2 µm wide, come with worse signal to noise ratio than standard cantilervers and are in general more hard to handle, also from the adjustment point of view.

We at DME have decided to manufacture our standard AFMs as probe scanners, where all movements are done on the tip side, for benefit of flexibility. Because the tip holder in our scanners have a low mass, our AFMs belong to the fastest scanning systems on the market, the scan speed is independent from the sample size. Looking at our standard AFM, for (50 µm)² or smaller scanners, the eigenfrequency of the scanner becomes unimportant in comparison to the other effects, so we have decided to use (50 µm)² as the smallest available scanner size. When you compare maximum scan speeds of our (50 µm)² scanner with our (200 µm)² scanner, to get an equivalent image quality one can scan two to three times faster with the (50 µm)² scanner. The resolution is in this case quite independent of the scanner size and in both cases atomic.

For more information about high-speed AFMs see for example Ando et al., Eur J Physiol (2008) 456, p. 211-225