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Sub-Nanometer Motion


Mad City Labs nanopositioners have unmatched precision and resolution capabilities due to the inherent low-noise properties of proprietary PicoQ® sensor technology. A relevant application for nanopositioning is atomic force microscopy (AFM). Imaging calibrated samples using an AFM is a demanding application of nanopositioning systems.

The following tests involve a Mad City Labs long range, low-profile nanopositioning system equipped with PicoQ® sensor technology (model Nano-LP100) performing a 1nm peak-to-peak sine wave and steps of 0.095 nm (95 pm), externally verified with a calibrated AFM.

The results of these tests are significant; if a nanopositioner's inherent position noise is larger than 0.1 nm, it cannot move in externally-detectable 95 pm step intervals. The AFM measurements below are yet another confirmation that Mad City Labs nanopositioners with PicoQ® sensor technology set the standard for the lowest position noise on the market. Inherent position noise of nanopositioning systems with PicoQ® sensors has already been shown to be in the 10s of pm/√Hz [MacKay, James F. Understanding noise at the nanometer scale." Laser Focus World, 43.3, (2007)].

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  Testing Principle


block diagram of SPM-M kit

Block Diagram of SPM-M Kit. In the experiment discussed below, the actual AFM configuration consisted of an XYZ probe nanopositioner with a separate sample nanopositioner.
Mad City Labs manufactures high-resolution AFM instruments consisting of nanopositioning systems and the MadPLL® controller that can be used with a variety of resonant probes such as a tuning fork with an etched Tungsten tip or an Akiyama probe. As an example, see the SPM-M kit.

The AFM probe tip is positioned in proximity to the sample surface using the Z-axis of a nanopositioner. The distance between the probe tip and the sample surface is directly related to the magnitude of the force between the tip and sample. The nanopositioner is moved to maintain constant force between the tip and the surface. In a typical experiment, the tip is scanned along the X and Y axes. In this experiment, the Z-axis position is measured directly to provide a height measurement of the sample.

Mad City Labs nanopositioners include integrated, direct measurement position sensors with PicoQ® sensor technology, already calibrated using NIST-traceable interferometric methods. Any displacement of the moving portion of the nanopositioner will yield a change in position sensor output, with the resolution ultimately limited by the noise of the nanopositioning system. Total AFM noise must be sufficiently low in order to externally measure sub-nanometer motion. Measuring the output of the nanopositioner's absolute position sensors assures accurate scan size and Z-axis position of the probe as it scans over the surface.

Test Setup


In the following tests, the AFM instrument consisted of a Nano-HS3 nanopositioning system with PicoQ® sensor technology for XYZ probe motion mounted on a SPM-MZ for Z axis coarse approach. A MadPLL® was used for closed loop feedback to maintain probe position in Z and an etched Tungsten tip attached to a quartz tuning fork was used as the imaging probe. Data were acquired using AFMView™ software, and analyzed and presented using SPIP® software.

  1nm Sine-Wave Motion Performed by a 100 Micron Range Nanopositioner


A Silicon (111) substrate of single atomic layer steps was mounted to a Nano-LP100 with PicoQ® sensor technology, operating in closed loop, which was placed underneath the AFM described in the Test Setup section, above.

The Z-axis of the Nano-LP100 was commanded with a 1nm peak-to-peak sine wave at approximately 0.8 Hz using a 20 bit digital interface, causing the Silicon substrate to move in a 1nm peak-to-peak sine wave in the Z direction. No XY scanning was involved in this test while the sample nanopositioner (Nano-LP100) and the AFM maintained constant XY position. The sine-wave motion of the Nano-LP100 Z-axis carrying the Silicon substrate caused the MadPLL® to adjust the Z-axis position of the probe in order to maintain a constant force between the probe and Silicon substrate, and the probe's Z-axis position was measured and recorded. The test was performed over 600 iterations. The data result in a two dimensional colored image, with the X-axis representing time, Y-axis representing the iteration number, and the colors representing the displacement of the AFM probe [Figure 1].

1nm sine wave performed by Nano-LP100 and measured by Mad City Labs AFM
Figure 1. 2D representation of 1 nm peak-to-peak sine wave motion measured by the AFM over 600 iterations. X-axis represents time, each Y-axis line represents one measurement iteration, and color represents measured probe displacement in nanometers.


The experimental question is: can the Nano-LP100 perform a 1 nm peak to peak motion? The data confirm that it can, as externally detected and measured by the AFM.

Figure 2 shows a single test cycle of the 1 nm sine wave probe displacement measurements:

1nm sine wave performed by Nano-LP100 and measured by Mad City Labs AFM
Figure 2. 1D representation of a single test iteration of measured probe displacements. X-axis represents time and the Y-axis represents nanopositioner displacement of 1 nm peak-to-peak.

95 pm Steps Performed by a 100 Micron Range Nanopositioner

A Silicon (111) substrate of single atomic layer steps was mounted to a Nano-LP100, with PicoQ® sensors, operating in closed loop and placed underneath the AFM described in the Test Setup section, above.

For a 100 micron range nanopositioning system with a 20 bit DAC, 95 pm represents a 1 bit change in the DAC output. The Z-axis of the Nano-LP100 was commanded in 95 pm square wave, i.e. in repeated 95 pm steps between two positions, at approximately 0.8 Hz. No XY scanning was involved in this test while the sample nanopositioner (Nano-LP100) and AFM maintained constant XY position. The stepping motion of the Nano-LP100 Z-axis carrying the Silicon substrate caused the MadPLL® to adjust the Z-axis position of the probe in order to maintain a constant force between the probe and Silicon substrate, and the probe's Z-axis position was measured and recorded. The test was performed over 600 iterations. The data result in a two dimensional colored image, with the X-axis representing time, Y-axis representing the iteration number, and the colors representing the Z axis displacement of the AFM probe [Figure 3].

95pm step performed by Nano-LP100 and measured by Mad City Labs AFM
Figure 3. 2D representation of 95pm step motion. X-axis represents time, each Y-axis line represents one measurement iteration, and color represents measured probe Z axis displacement of 95 pm.


The experimental question is: can the Nano-LP100 perform repeated 95 pm steps? The data confirms that it can, as externally detected and measured by the AFM.


860 pm Steps Performed by a 450 Micron Range Nanopositioner


A Silicon (111) substrate of single atomic layer steps was mounted to a 450 micron range Z axis nanopositioner with PicoQ® sensors, operating in closed loop and placed underneath the AFM described in the Test Setup section, above.

For a 450 micron range nanopositioning system with a 20 bit DAC, 860 pm represents a 2 bit change in the DAC output. The Z-axis nanopositioner was commanded in a 860 pm square wave, i.e. in repeated 860 pm steps between two positions. No XY scanning was involved in this test while the sample Z axis nanopositioner and AFM maintained constant XY position. The stepping motion of the Z-axis nanopositioner carrying the Silicon substrate caused the MadPLL® to adjust the Z-axis position of the probe in order to maintain a constant force between the probe and Silicon substrate, and the probe's Z-axis position was measured and recorded. The test was performed over 256 iterations. The data result in a two dimensional colored image, with the X-axis representing time, Y-axis representing the iteration number, and the colors representing the Z axis displacement of the AFM probe [Figure 4].

95pm step performed by Nano-LP100 and measured by Mad City Labs AFM
Figure 4. 2D representation of 860 pm step motion. X-axis represents time, each Y-axis line represents one measurement iteration, and color represents measured probe Z axis displacement of 860 pm.


The experimental question is: can the 450 micron range Z axis nanopositioner perform repeated 860 pm steps? The data confirms that it can, as externally detected and measured by the AFM.


Additional Information

Laser Focus World Article
article on low-cost AFM built with MadPLL and nanopositioning systems
NANOPOSITIONING: Piezo­electric nano­positioners forge low-cost atomic force microscope
AFM Video Tutorial
Build your own AFM tutorial video

MadPLL® Brochure
MadPLL brochure



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