Measurement and modelling of non-contact atomic force microscope cantilever properties from ultra-high vacuum to normal pressure conditions

Abstract

The resonance frequency and Q-factor of cantilevers typically used for non-contact atomic force microscopy (NC-AFM) are measured as a function of the ambient pressure varied from 10 −8 mbar to normal pressure. The Q-factor is found to be almost constant up to a pressure in the range of 10 −2-10 −1 mbar and then decreases by about three orders of magnitude when increasing the pressure further to normal pressure. The decrease in the resonance frequency measured over the same pressure range amounts to less than 1% where a significant change is observed in the range of 10-10 3 mbar. The pressure dependence of the effective Q-factor and resonance frequency is approximated by analytical models accounting for different processes in the molecular and viscous flow regimes. By introducing a heuristic approach for describing the pressure dependence in the transition regime, we are able to well approximate the cantilever properties over the entire pressure range.

Design and Fabrication of a Vacuum Chamber for a Commercial Atomic Force Microscope

“…The quality factors in air (solid line) and in a 8×10 -3 vacuum (broken line) were calculated to be 397 and 4325, respectively. A clear quality factor enhancement was observed along with a shift in the resonance frequency typical for a non-contact AFM cantilever [11].…”

“…Generally, the lower the pressure, the higher the values of the quality factors which are observed. However, for a pressure level below the molecular flow regime (＜1×10 -4 torr), the quality factor improvement becomes nearly stagnant [11].…”

Imaging pulsed laser deposition oxide growth by in situ atomic force microscopy

“…Typical PLD conditions involve substrates at elevated temperatures and process pressures up to several mbar, a pressure regime where cantilever response is known to alter dramatically 28 . The cantilever resonance frequency f 0 and the cantilever quality Q factor are nearly constant at pressures ranging from 10 −6 -0.1 mbar 29 .…”

Determination of exposure to engineered carbon nanoparticles using a self-sensing piezoresistive silicon cantilever sensor

“…3 Realized full Wheatstone bridge consisting of p-type resistors on the cantilever including shielding layer (FE-SEM image, right part). In the left part a schematic view of the cantilever sensor with its large pads for wire bonding, the circuit diagram of the strain gauge resistors connected into a Wheatstone bridge, and an integrated resistor for temperature control are displayed caused by several sources that are either intrinsic factors, e.g., material damping, phonon-phonon interaction, phonon-electron interaction, thermoelastic damping, anchor losses or extrinsic factors, e.g., air or other surrounding media (Lübbe et al 2011). Dissipation is the inverse of the quality factor (Q-factor) and can be expressed as the sum of the relevant contributions due to above effects according to:…”