Nanopositioning and Nanometrology
PI offers the widest range of high-dynamics and high-resolution nanopositioning systems worldwide. The precision and repeatability achieved would not be possible without highest-resolution measuring devices. Capacitive sensors are the metrology system of choice for the most demanding nanopositioning applications. The sensors and the equally important excitation and read-out electronics are developed and manufactured at PI by expert teams with long-standing experience.

Measurement Principle
The measurement principle in both cases is the same: two

Test and Calibration
PIs nanometrology calibration laboratories are seismically, electromagnetically and thermally isolated, and conform to modern international standards.

PI calibrates every capacitive measurement system individually, optimizing the performance for the customers application. Such precision is the basis of all PI products, standard and customized, and assures optimum results in the most varied of applications.

For capacitive sensors, resolution is in principle unlimited, and is in practice limited by electronic noise. PI signal conditioner electronics are optimized for high linearity, bandwidth and minimum noise, enabling sensor resolution down to the picometer range.

Electronic noise and sensor signal bandwidth are interdependent. Limiting the bandwidth reduces noise and thereby improves resolution. The working distance also influences the resolution: the smaller the working distance of the system, the lower the absolute value of the electronic noise.

Figure 1 shows measurements of nanometer-range actuator cycles taken with a D-015, 15 m capacitive position sensor and a laser interferometer. The graphs clearly show the superior performance of the capacitive position sensing technique.

Figure 2 illustrates the influence of bandwidth upon resolution: the PISeca single electrode sensors show excellent resolution down to the sub-nanometer range, even at high bandwidths.


Linearity and Stability of PI sensors
The linearity of a measurement denotes the degree of constancy in the proportional relation between change in probe-target distance and the output signal. Usually linearity is given as linearity error in percent of the full measurement range. A linearity error of 0.1% with range of 100 m gives a maximum error of 0.1 m. Linearity error has no influence whatsoever upon resolution and repeatability of a measurement.

Linearity is influenced to a high degree by homogeneity of the electric field and thus by any non-parallelism of the probe and target in the application. PI capacitive position sensor electronics incorporate a proprietary design providing superior linearity, low sensitivity to cable capacitance, low background noise and low drift. The Integrated Linearization System (ILS) compensates for nonparallelism influences.

A comparison between a conventional capacitive position sensor system and a PI ILS system is shown in Figure 3. When used with PI digital controllers (which add polynomial linearization) a positioning linearity of up to 0.003 % is achievable.

Figure 4 shows the linearity of a P-752.11C piezo flexure nanopositioning stage with integrated capacitive position sensor operated in closed-loop mode with an analog controller. All errors contributed by the mechanics, PZT drive, sensors and electronics are included in the resulting linearity of better than 0.02 %. Even higher linearity is achievable with PI digital controllers like the E-710.

Stability of the measurement is limited mainly by thermal and electronic drift. For accuracy and repeatability reasons, it is thus necessary to maintain constant environmental conditions. The exceptional long-term stability of the PI capacitive position sensor and electronics design is shown in Figure 5.


Principle of the Measurement
Signal/Displacement Proportionality
When a voltage is applied to the two plates of an ideal capacitor, it creates a homogenous electric field. This principle is the basis of measuring displacement with capacitive position sensors. For small gaps, the applied voltage is proportional to the plate distance. The planes of the sensor surface (probe) and the target form the two capacitor plates. The target should not be below a certain size because of boundary effects. This is important for applications with, say, a rotating drum as target. For metallic materials, the thickness of the target has no influence on the measurement.


Guard Ring Geometry/Design
The proportionality referred to is based on the homogeneity of the electric field. To eliminate boundary effects, the superior PI design uses a guard-ring electrode that surrounds the active sensor area and is actively kept at the same potential (see Fig. 7). This design shields the active sensor area and provides for excellent containment of the measurement zone. Thus optimum measuring linearity over the full range is achieved within the specified accuracy.


Calibration for Best Accuracy
PIs nanometrology calibration laboratories offer optimum conditions for factory calibration. As references, ultra-highaccuracy incremental sensors like laser interferometers are used.

PISeca systems are calibrated at PI with a NEXLINE positioning system having a closed-loop resolution better than 0.01 nm in a test stand with friction-free flexure guidance and an incremental reference sensor featuring a resolution better than 0.1 nm (Fig. 8 and 9).


Special Design Eliminates Cable Influences
When measuring distance by detection of capacitance changes, fluctuations in the cable capacitance can have an adverse effect on accuracy. This is why most capacitive measurement systems only provide satisfactory results with short, well-defined cable lengths.

PI systems use a special design which eliminates cable influences, permitting use of cable lengths of up to 3 m without difficulty. For optimum results, we recommend calibration of the sensor-actuator system in the PI metrology lab. Longer distances between sensor and electronics can be spanned with special, loss-free, digital transmission protocols.


Electrode Geometry, Sensor Surface Flatness and Finish
During sensor production, great care is taken to maintain critical mechanical tolerances. Measuring surfaces are diamond machined using sophisticated process control techniques. The result is the smooth, ultra-flat, mirrored surfaces required to obtain the highest resolution commercially available.


Parallelism of Measuring Surfaces
For optimum results, target and probe plates must remain parallel to each other during measurement. For small measurement distances and small active areas, any divergence has a strong influence on the measurement results. Tilt adversely affects linearity and gain, although not resolution or repeatability (see fig. 12). Positioning systems with multilink flexure guidance reduce tip and tilt to negligible levels (see Fig. 13) and achieve outstanding accuracy.


Fig. 10: Capacitive position sensors in an ultra-high-accuracy, six-axis nanopositioning system designed by PI for the German National Metrology Institute (PTB). Application: scanning microscopy



Fig. 11: Digital sensor-signal transmission (DST) allows a distance up to 15 m between positioning unit and controller, here an E-710 multi-axis digital piezo controller