Adaptive Mechanics Provides Multi Axis Motion with Sub Nanometer Flatness and Sub Rad Yaw, Pitch and Roll

Typical applications of scanning probe microscopes (SPM) are surface structure and feature sizes measurement with high resolution capability in both vertical and lateral directions.  The SPM accuracy and resolution (3-D image or profile lines) strongly depend on the accuracy of the scanning apparatus.  Therefore it is important that the scanning apparatus provide sufficient X, Y, Z positioning resolution while limiting unwanted motion to a minimum [1]. The SPM tip and its mounting parts are generally several orders of magnitude larger (dependent on the SPM type used [2]) than the scanning range.  Due to this arrangement, Abbe errors introduced by unwanted rotations (φx, φy, φz) of the scanning apparatus cannot be neglected, even after calibration.  For example to achieve 0.1 nm Z measurement accuracy with a tip offset of [xtip , ytip] = [100,100] µm from the ideal tip position, the rotational error (φx, φy) must be less than 1 µrad (0.2 arcsec) [3].  The ideal tip position is the coordinate at which the Z motion is calibrated (Fig. 1) [1][3].

Principle of a profile scan with SPM.

Figure 1. Principle of a profile scan with SPM.

Most critical for XY scanning is the Z out-of-plane motion.  For example the sampled measurement data of an X-scan is generally

Z(x)  = zsample(x) + kx

zspm(x) + xtip φxry(x)

where zsample(x) is the true profile of the sample. Non-parallelism between the sample and the stage is described by the line kx. The total unwanted motion is the SPM out-of-plane error zspm(x) plus the nonlinearity of the Abbe error xtipφxry(x) .

Unwanted out-of-plane motion and rotation of conventional XY scanning stages (flexure arrangements, etc.) are on the order of a few nm and arcsec due to cross talk induced by the two-axis arrangement and other mechanical parameters.  The out-of-plane motion cannot simply be compensated for since it exhibits hysteresis and strongly depends on scanning direction and range.  Fig. 2 shows out-of-plane motion hysteresis for a 100 µm scan and several 10 µm scans, respectively.

Dependence of out-of-plane motion on scanning range and offset.

Figure 2. Dependence of out-of-plane motion on scanning range and offset.

Adaptive XY-Stage with 6 Degrees of Freedom

To eliminate unwanted motion, it is necessary to measure and control all six degrees of freedom (X, Y, Z, φx, φy, φz).  For an XY-scan (a typical usage of the SPM), X and Y are commanded by the user (signal generator, etc.) while Z, φx, φy, φz are commanded to be zero by the active error compensation system.  The accuracy of this technology is only limited by performance of the control system and displacement sensors.  Since the accuracy of the system is scanning range independent, individual range calibration is no longer required.

To realize a 6 axes closed-loop positioning system, PI developed a new multi-axis flexure stage, a digital position controller and a two plate capacitive displacement sensor consisting of a PROBE [4] and a slightly larger TARGET plate.  This type of sensor was chosen because of its sub-nanometer resolution and insensitivity to lateral motion.  Six TARGET plates form a coordinate reference (Fig. 3). The sensors Sx1 and Sx2 measure the X-displacement and the rotation φz while the sensor Sy measures the Y-position. The sensors Sz1, Sz2, Sz3 measure the z-position and rotations φx and φy.

Arrangement of the capacitive sensors.

Figure 3. Arrangement of the capacitive sensors.

Two 3-axis DSP-based digital controllers (A, B) control the 6-axis positioner. The digital controller provides flexibility and the computing power for digital filtering, linearization of the sensor signals and calculating the individual axis information from multiple sensor inputs as well as the individual PZT actuator drive signals (e.g. 4 actuators for the Z axis).  Each controller provides inputs (A/D converted) for 4 capacitive sensors (three for closed loop position control plus one Z position monitor sensor) and outputs (D/A converted) for 4 PZT actuators (2 to 4 actuators have to be driven for any single axis movement).

After A/D conversion the sensor signals are filtered and then linearized with a 4th order polynomial.  The digital filter and linearization parameters can be user modified.  Each controller provides a standard serial interface (RS-232) and a parallel interface (IEEE 488).  For XY-scans communication with only one controller is sufficient.  Controller A drives the actuators producing the X, Y and φz motion based on the feedback of the capacitive sensors Sx1, Sx2, and Sy.  The nominal range of X, Y and φz (rotary error compensation) is 100 x 100 µm2 and ±500 µrad, respectively.

Controller B takes care of error compensation.  It drives the actuators canceling the unwanted Z-motion (6 µm) and rotations φx and φy (±100 µrad) based on the feedback of the sensors Sz1, Sz2 and Sz3.

Calibration and Measurement Results

The capacitive sensors are calibrated in situ using a differential plane mirror interferometer [5].  Differential interferometers allow reduction of the dead-path to 20 mm and mounting of the reference mirror directly to the frame of the stage.  A sensor pre-calibration is performed to match the gain of each sensor in a group (sensors contributing to the position information of one individual axis, e.g. Sz1, Sz2 and Sz3 contribute to the Z position and at the same time also to φx, φy).  The pre-calibration reduces tilt errors to less than 5 µrad while moving in X, Y and Z.  After pre-calibration, every sensor is measured again (sensor and interferometer axes coaxial or in the same plane).  Based on these results the linearization parameters for each sensor are calculated and the result is stored in an EEPROM. The linearization process improves overall system linearity to 0.003%.  Fig 4 shows the X-axis position error before and after linearization.

Positioning error before and after sensor linearization.

Figure 4. Positioning error before and after sensor linearization.

XY-position repeatability was tested to be better than 0.5 nm (RMS) over the full 100x100 µm2 range.  Z-direction stability is better than 0.033 nm (RMS).

The positioning resolution and repeatability of the system is mainly limited by the ADC and DAC resolution and stability.  The prototype was equipped with 16 bit ADC's and DAC's.  The test results below indicate a limitation of the converters rather than the concept of the adaptive stage.

Fig 5 shows Z out-of-plane motion over a 100 x 100 µm XY scan with the active compensation on.  The out-of-plane error is less than 0.5 nm peak to peak (measured with a small range capacitive sensor).

Out-of-plane motion (Z) over a 100 x 100 µm2 scanning range.

Figure 5. Out-of-plane motion (Z) over a 100 x 100 µm2 scanning range.

The residual out-of-plane error mainly depends on the deformation of the sensor carrying frame rather than the distortion of the capacitive sensor itself. 

The TARGET part (Fig 3) was chosen as the reference.  TARGET electrodes were designed larger then PROBE electrodes to eliminate influences of non-parallelism (between TARGET plane and PROBE plane) on the position accuracy during lateral parallel motion of the PROBE to the reference.

Since XY-plane and the YZ-plane are defined by more than one sensor, all TARGET electrodes defining an individual plane are diamond milled in one step. 

The influence of the sensor surface finish on the results can be neglected (flatness ≤ 0.5 µm over a 50 mm2 area).  To simplify the calculation, the surface of the capacitor plates developed by PI can be assumed as a spherical distortion.  The radius of the sphere is approximately r = 1.1x106 mm.  That means when one electrode of the Z-sensor moves across dx, the distance between the Z-sensor plates changes by dz = (dx)2/(2r).

For typical position changes dx = ±50 µm, the residual error dz is only ±1.1x10-3 nm.

Improvements of the above concept have already been started.  New FEM models of the sensor frame promise less distortion.  Since Z-out-of-plane motion is mainly dependent on the XY position, a modified digital controller can further improve accuracy by correlating Z actuator drive signals with the XY position.


1.   O. Jusko, X.Zhao, H. Wolff and G. Wilkening. Design and three dimensional calibration of a measuring scanning tunneling microscope for metrological applications, Rev. Sci. Instrum. 65(8), 2514 (1994).

2.   H. Rohrer: STM. 10 years after. Proc. 6th Int. Conf. on STM, Interlaken, Swissland, 1991, 10 Years of STM, 1 (1992).

3.   X. Zhao. Hochauflösende Dreidimensionale Positionierungsbestimmung bei Rastersondenmikroskopen mittels kapazitiver Aufnehmer. PTB-Bericht, PTB-F-20, ISSN 0179-0609, Braunschweig, 1995

4.   PI Products for micropositioning, Catalogue Edition E, CAT.112/D/05.95/13, Physik Instrumente, Waldbronn, Germany, 1995

5.   ZYGO.ZMI System Documentation, Zygo Corporation, Middlefield, CT, USA, 1995



This information has been sourced, reviewed and adapted from materials provided by PI (Physik Instrumente) LP, Piezo Nano Positioning.

For more information on this source, please visit PI (Physik Instrumente) LP, Piezo Nano Positioning.


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