There are three key questions that we would like to address in this section:
· What is the positioning system precision, including systematic errors and feedback system resolution?
· What speed can the positioning system reach while being in feedback?
· Is the positioning system suitable for scanning probe microscopy imaging?
An actuator can, in principle, have many different errors. Here, we concentrate on two main problems: it can move in a different direction than expected and it can bend during the motion. The system guidance errors for the crossed roller bearing (CRB) stage and the flexure stage were evaluated using an interferometer and a digital autocollimator. The latter was based on a position-sensitive detector combined with a laser beam reflection from a mirror on the stage. For comparison, the same guidance errors were measured on a stack piezoceramic element representing a typical solution that is used in some microscopes (mechanical guidances are used only rarely in commercial AFMs) and also on a xy system of an older commercial AFM. The results are summarized in Table . The crosstalk (a parasitic motion in the second axis due to the motion in the first one) and the rotation (a dependence on the deviation of the orientation of the positioner’s moving part from the direction of the motion) were evaluated. We can see that the mechanical errors of both guidances are lower than those of piezoceramic solutions. A properly constructed piezoceramic AFM scanner will have probably better metrological parameters than the presented stack actuators; however, it can be seen that the presented approach is fairly within the limits of present microscope technology.
Comparison of metrological properties of different systems
The feedback algorithm, as run on the microchip, has itself a bandwidth higher than 100 kHz, which is far more than what we can get from the hardware parts used in the rest of the system. The final feedback speed is influenced, namely, by two other factors: the moving mass and the force that can be generated. The masses are 2 and 6 kg for the x and y axes of the CRB stage, respectively, while for the flexure stage, these are 16 and 20 g, respectively. The maximum force is 0.8N for the first stage and 0.02N for the second stage. As we can see, the smaller system could be approximately ten times faster, which was also observed in practice. While the large system needs some 300 ms to reach any position (with almost no dependence on the distance), the smaller one needs some 30 to 80 ms, depending on the distance (this is the effect of the proportional term of the algorithm).
As we have seen, the moving mass has a big influence on the feedback algorithm performance, and the algorithm is expected to be tuned with respect to it. In practice, this means that we need to keep the mass of the samples well below the mass of the moving part of the positioner, if we do not want to change the feedback parameters with every sample. Typically, we have scanned samples with a mass of up to 1/10 of the moving part of the positioner mass, which means some 200 g for the CRB stage and some 1.6 g for the flexure-based stage. Even if it might look as a small number, this is relatively easy, as the mass of our typical samples is very small - 1.6 g, which corresponds to a silicon wafer piece of some 10 cm2.
The big advantage of the feedback based on the force is that in the absence of the counter-force, the system is not dependent on its position. At every position, the system can reach the same accuracy, given only by the interferometric sensor accuracy. There is no need for large-bit depths of the DAC output to the coils as the force itself is not connected with the final resolution. This is a rather different system compared to the system using piezoceramic components, where the DAC bit depth is directly connected with the scanner resolution. Of course, when we have to produce a large compensation of the counter-force, we lose some of these advantages as the counter-force usually depends on the position. It is therefore important to preserve the counter-force as low as possible at the scanner design and manufacturing phase. The system resolution is based on the two interferometer and feedback loop imperfections; it is typically around 15nm for both systems, but it could be tuned even to some 5nm if the parameters were adjusted with greater care. Note that the resolution does not mean accuracy, which is determined by more factors, including laser stability, geometrical errors (like the Abbe error), interferometer non-linearities, etc. However, from the first estimates, it looks that the feedback loop noise determining the above resolution is by far the biggest uncertainty component of the whole positioning system uncertainty budget.
The suitability of the system for the SPM imaging is another important parameter. The fact that the positioning stage is able to move with a certain resolution and accuracy, it still does not necessarily implicate that it is suitable for these purposes. Some actuators used for the nano- and microscale positioning do not move smooth enough to enable a tip-sample feedback loop. In some cases, there are significant vibrations or acoustic noise during the motion. A typical example is a stick-slip actuator, which is often featuring both effects. As there is a rather independent and quickly randomly changing force applied on the stage by the voice coils in our system, it could be easily possible that our system has similar errors. The easiest way to determine whether an actuator is suitable for this application is to use it. In Figure , we show results of measurements of a microchip surface using both systems. We can see that the systems are suitable for SPM imaging, even if the mechanical combination of the xy positioning systems with AFM head was very far from the optimum and we can still see some noise and thermal drifts.
Images of a microchip surface acquired using both systems. (A) AFM measurement using CRB stage. (B) AFM measurement using flexure-based stage.
The aim of this article was to present the positioning control approach, not to compare the developed stages to other systems. However, if we compare both stages to an existing commercial system for large-area SPM scanning (described in [10
]), it is important to note that they offer a similar range, even if their cost is several orders of magnitude lower. On the other side, the total positioning uncertainty of commercial stages is smaller by approximately an order than for the two presented stages as the presented proof-of-concept systems were still not optimized for minimising mechanical and thermal drifts and mechanical vibrations.