The National Physical Laboratory (NPL) is the United Kingdom's national standards laboratory, an internationally respected and independent centre of excellence for R&D, and knowledge transfer in measurement and materials science.

NPL maintains world-class metrology facilities and offers calibration services with the highest available accuracy. Each year NPL carry out thousands of UKAS-accredited calibrations for measurement and instrumentation companies. They also deliver innovative, specialised measurement services, tailored to new and demanding applications. Atomic force microscopy is one such application, used by many R&D sectors.

The Atomic force microscope (AFM) is a very high resolution-scanning microscope and is used at NPL laboratories for imaging the surface of materials in the micrometer to nanometer length scales. The AFM consists of a microscale cantilever with a sharp tip at its end, which is used to scan the specimen surface, with the tip radius being in the order of nanometers. The microscope determines surface topography by measuring the displacement at the tip of a micro fabricated cantilever spring. This technique can also be used to measure forces on particles attached to a spring. Knowledge of the spring constant on the AFM is therefore a vital parameter. This can be obtained from calculating the modal frequency response of the cantilever as a whole.

Atomic force microscopy is a popular method used by many industrial R&D sectors to measure surface topography and materials properties. This provides a 3-D image of the surface from which line profiles may be extracted. An important advantage compared with other methods is that it can operate in ambient and liquid environments. This opens possibilities for the study of biological samples, polymers, electronic materials and coatings.

NPL required a parametric model of the AFM to be generated, which would allow the user of the macro to select the shape of the cantilever, followed by the calculation of natural frequencies and mode shapes using finite element analysis during the calibration procedure.

In order to accurately simulate the static and dynamic response of the cantilever the following properties had to be accounted for: radii of curvature, the level of residual stress in the coating, coating thickness and the mass of the tip.

created a parametric model using ANSYS where the AFM probe was modelled by means of 8- noded 3D elements with large strain large deflection capability. The top surface of the cantilever was then coated with 4 noded shell elements to simulate the 30-50 nm thick layer which coats the device. The effect of the AFM tip was modelled with an offset mass element.

A full model of the AFM was generated in order to capture any torsional or unsymmetrical modes.

The analysis work was carried out in two stages. The macro for the first stage was written to allow for the following options:

Subsequent work required an additional parametric macro to be written, which allowed for the shape and fixity options as described above but also included the presence of surrounding fluid, modelled with FLUID136 elements, to account for fluidic damping effects. A semi-sphere of fluid was modelled, the dimensions of which were very large compared to the dimensions of the structure. Keeping the size of the fluid domain relatively large created the effect of a far field domain. In addition, infinite elements on the fluid boundary were included to render the shape and size of the domain less important. Graphics illustrating the semi-sphere of fluid are shown in below.

As a part of this work NPL also carried out experimental investigations. There was an excellent agreement between the FEA modelled versus experimentally determined frequencies and displacements. Details of the results from FEA and experimental work can be found in the publication "Dynamic Properties of AFM Cantilevers and the calibration of their Spring Constants" by David-A Mendels et al.

The parametric ANSYS macros written by IDAC to carry out calibration analyses gave excellent agreement with experimental results. Altering the values of parameters gave researchers a better understanding of the driving factors in the simulation. For example, NPL learnt that the coating layer and the wall interaction were important features that affected the solution, whilst the tip mass could be ignored completely. This helped improve the quality and accuracy of the experiments. Setting up the analysis parametrically also allowed NPL to carry out analyses under different loading conditions for two separate geometric shapes, with the Fluid Structure interaction either being switched on or off. This meant that the time associated with setting up laboratory experiments was greatly reduced.

There is also potential for NPL customers to further use this technology. It is envisaged that using this technology a NPL customer could carry out web enabled calibration and print a calibration report on a pay per use basis.