# Nanopositioning - Sub-Nanometer Position Noise Measurements - Supplier Data by Mad City Labs

## Topics Covered

Background

Position Noise in Nanopositioners

Thermal Johnson Noise

High Resolution Nanopositioning

## Background

Nanopositioning systems, widely used in nanotechnology research, typically have a total range of motion of several microns to a couple of hundred microns with positioning resolutions in the nanometer range.  An important and relevant specification not commonly listed in sales literature is the degree to which a nanopositioner can locate a specific position and maintain that position under closed loop control.

## Position Noise in Nanopositioners

Random noise effects in the sensing system combined with control electronics noise combine to produce the physical characteristic called position noise.  Position noise is the ultimate limiting factor in any nanopositioner’s ability to accurately move in the nanometer realm.  Minimizing position noise is critical to the design of nanopositioners and determines the smallest useful range of motion that can be expected for a given system.  Accurate determination of position noise - which may be in the picometer range – requires special techniques and knowledge of the underlying system design parameters.

## Thermal Johnson Noise

A technique developed by Mad City Labs uses the nanopositioner’s own internal piezoresistive position sensors to supply the basic data used to compute position noise.  Viewed as simple, low impedance, variable resistors the piezoresistive sensors generate a form of low level noise called Johnson noise.  Thermal Johnson noise produces random voltage fluctuations across a resistive element as a result of thermally induced electron motion.  Thermal noise is intrinsic to all resistors and cannot be avoided.  Johnson noise is considered white noise and is spread evenly across the frequency spectrum with its amplitude proportional to the absolute temperature.  To calculate the Johnson noise component:  V2rms = 4kTRΔF where k=Boltzman’s constant, T = temperature in °K, R = sensor resistance, and ΔF = nanopositioner effective bandwidth.  At room temperature, the calculated Johnson noise is approximately equal to 0.04 μvolts rms.  This translates to approximately 1 part in 7 million of the full amplitude sensor signal.  Equating this to position noise, the Johnson noise would represent approximately 0.014 nanometers (14 picometers) of noise on a full range motion of 100 microns.  Based on these numbers, Johnson noise in the piezoresistive sensing elements is not a significant contributor to position noise at the nanometer level.  Quantifying other sources of noise in the electronic controller involves direct measurement of the voltage variations present on the sensor while the nanopositioner is held in a steady reference position by the controller.  Digitizing the sensor output at a given position and performing an FFT on the resulting data gives a plot of the frequency distribution of the system noise.  As expected, the observed noise spectrum is relatively low frequency since the mechanical nature of a nanopositioner causes it to perform like a low pass filter on the noise.  Mad City Labs controller design avoids the common problems of 60Hz power line noise by using high frequency switching power supplies instead of linear power supplies.  High frequency noise coming from the controller power supply is effectively filtered out by the low frequency mechanical characteristics of the nanopositioner and adds nothing to the position noise calculation.  A second FFT is performed on sensor data acquired while the nanopositioner is driven with a sine wave signal to produce a 1 nanometer peak-to-peak motion.  This second FFT allows a comparison to be made between the amplitude of the spectrum of random noise and the amplitude of the narrow peak resulting from the input signal.  Observed peak amplitude ratios of 10/1 demonstrate that the random noise amplitude is approximately 1/10 of the one nanometer input signal - equivalent to 0.1 nanometers of position noise.  Since Johnson noise is less than a third of the measured system position noise, the primary noise components derive from other sources present in the system.

## High Resolution Nanopositioning

Direct noise measurements on Mad City Labs nanopositioning systems as described above have shown that positioning resolutions in the sub-nanometer range are well within the capabilities of the system.  Whether the nanopositioner’s ultimate resolution and position noise is of critical importance depends completely on the application.  Typical uses for nanopositioners in optical microscopy are far less demanding than, for example, the use of nanopositioners in the production of Bragg diffraction gratings.  As nanotechnology research pushes the practical limits of atomic level manipulation, it is certain that nanopositioners with high positioning resolution will be increasingly needed to locate, move, and fabricate the necessary components.