Accurate force measurement in the atomic force microscope: a microfabricated array of reference springs for easy cantilever calibration

Calibration of atomic force microscope (AFM) cantilevers is necessary for the measurement of nanonewton and piconewton forces, which are critical to analytical applications of AFM in the analysis of polymer surfaces, biological structures and organic molecules. We have developed a compact and easy-to-use reference artefact for this calibration. This consists of an array of dual spiral-cantilever springs, each supporting a polycrystalline silicon disc of 170 mum in diameter. These were fabricated by a two-layer polysilicon surface micromachining method. Doppler interferometry is used to measure the fundamental resonant frequency of each device accurately. We call such an array a microfabricated array of reference springs (MARS). These devices have a number of advantages. Firstly, modelling the fundamental resonant frequencies of the devices is much more straightforward than for AFM cantilevers, because the mass and spring functions are isolated in different parts of the structure. Secondly, the spring constant of each spring is in linear proportion to the mass of the device, given that the resonant frequency is measured accurately. The thickness and hence the mass can be measured accurately by AFM or interferometry. The array spans the range of spring constant important in AFM, allowing almost any AFM cantilever to be calibrated easily and rapidly. The design of the MARS makes it much less sensitive to uncertainties in its dimensions, which is expected to lead to an improvement, in principle, of approximately a factor of three compared to the most accurate previous methods of spring constant calibration, because the spring constant is proportional to the a critical thickness (after resonant frequency has been measured) rather than the cube of a critical thickness, as for a reference cantilever.