• Cheneler, David
• Vicary, James
• Bowen, James

Abstract

Atomic force microscopy (AFM) employs microfabricated cantilevers as sensing elements, which are used to measure surface topography and interaction forces. The flexible free end of a cantilever often presents either a pyramidal tip or a colloid probe particle. Cantilevers are traditionally V-shapedor rectangular, and are generally fabricated from Si or SixNy. Laser light is reflected off the free end of the cantilever onto a position-sensitive photodetector (PSD). AFM force measurement studies began in earnest during the early 1990s, followed by significant efforts to accurately calibrate the mechanical properties of the cantilever. These efforts centred on understanding the beam mechanics, in particular the flexibility of the free end, where the tip or colloid probe is situated.Force measurements have been applied to a wide variety of scientific and engineering disciplines, and across many industrial sectors. For many studies, the use of colloid probes or chemical functionalisation permits the selective study of a particular material/material interaction, often under non-ambient environments. Force measurements can provide information regarding sample mechanical properties, during the tip/sample approach, as well as adhesive properties, during the tip/sample separation. The spring constant is a measure of the cantilever stiffness, i.e. the resistance to bending. The spring constant of a rectangular cantilever can be estimated using Euler-Bernoulli beam theory. Once calibrated, the spring constant is used in calculations in order to convert normal (i.e. vertical) deflections into normal forces using Hooke's law.The range of AFM cantilevers commercially manufactured means that spring constants in the approximate range 0.001 to 100 N/m are available. Deflections in the range 0.1-100 nm are typically measurable on the PSD, and hence forces can be measured in the picoNewton to microNewton range. Accurate control of the beam thickness during fabrication is particularly difficult to achieve, due to the nature of the etching process employed. The width and length of the beam are generally much more reliable and repeatable. Given the sensitivity of the spring constant to the beam thickness, typically proportional to (thickness)3, accurate calibration is a necessity for accurate force measurements.We are currently calibrating 40 different designs of rectangular AFM cantilever, designed using Timoshenko beam theory, manufactured from Si. The various designs incorporate a range of widths, lengths, and thicknesses. These cantilevers are expected to exhibit spring constants in the range 100 to 10,000 N/m. This would afford researchers the opportunity to perform adhesion, indentation, and tribological testing with normal loads approaching 1 mN, whilst retaining the displacement resolution of the AFM. We present the latest results of this project, including measured cantilever resonant frequencies and calculated spring constants, which are compared to analytic expressions and finite element models.

Topics

• impedance spectroscopy
• surface
• theory
• atomic force microscopy
• etching