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

Abstract

Calibration of atomic force microscope (AFM) cantilevers is necessary for themeasurement of nanonewton and piconewton forces, which are critical to analyticalapplications of AFM in the analysis of polymer surfaces, biological structures andorganic molecules. We have developed a compact and easy-to-use referenceartefact for this calibration. This consists of an array of dual spiral-cantileversprings, each supporting a polycrystalline silicon disc of 170 µmin diameter. These were fabricated by a two-layer polysilicon surfacemicromachining method. Doppler interferometry is used to measure thefundamental resonant frequency of each device accurately. We call such an array amicrofabricated array of reference springs (MARS).These devices havea number of advantages. Firstly, modelling the fundamental resonantfrequencies of the devices is much more straightforward than for AFMcantilevers, because the mass and spring functions are isolated in differentparts of the structure. Secondly, the spring constant of each spring isin linear proportion to the mass of the device, given that the resonantfrequency is measured accurately. The thickness and hence the mass can bemeasured accurately by AFM or interferometry.The array spans therange of spring constant important in AFM, allowing almost any AFMcantilever to be calibrated easily and rapidly. The design of the MARSmakes it much less sensitive to uncertainties in its dimensions, whichis expected to lead to an improvement, in principle, of approximatelya factor of three compared to the most accurate previous methods ofspring constant calibration, because the spring constant is proportional tothe a critical thickness (after resonant frequency has been measured)rather than the cube of a critical thickness, as for a reference cantilever.