Comparison Between Torsional Spring Constants of Rectangular and V-Shaped AFM Cantilevers

The properties of force-sensing micro-cantilevers are of fundamental importance for measurements employing atomic force microscopy (AFM) techniques. Due to the well-known arguments of Sader, it is generally accepted that V-shaped cantilevers are more sensitive to lateral forces than rectangular ones. We present results of numerical (finite element modelling) and experimental comparison between torsional spring constants of rectangular and V-shaped commercial AFM cantilevers. As representative example of such beams, we considered AFM probes available commercially. In particular, we tested scaled-up models of V-shaped cantilevers which had the same geometrical shapes as commercial AFM cantilevers. Both the rectangular and the V-shaped larger scale models were made of the same material; they had the same length, thickness, normal spring constant, as well as the same location and shape of the tip base. In the experiments and the simulations, an external lateral load was applied to the free end of the tip. A good agreement between the experimental work and finite element method (FEM) simulations was observed. The results show that the torsional spring constant of the V-shape cantilevers considered here was greater than that of the equivalent rectangular beams by up to 45%. The discrepancy with the results from Sader should be caused by differences in both the load transfer scheme and the geometrical shapes of the V-shaped beams.