Parallel beam approximation for V-shaped atomic force, microscope cantilevers

Due to its simplicity, the parallel beam approximation (PBA) is commonly used in the analytical evaluation of the spring constant of V-shaped atomic force microscope (AFM) cantilevers. However, the point of contention regarding the validity of the PBA is as yet an unresolved issue, which has been exacerbated by some recent contradictory reports. In this paper, we present a detailed investigation of the deflection properties of the V-shaped AFM cantilever, and in so doing, show mat the PBA is in fact a valid and accurate approximation, provided the width and length of the parallel rectangular arms are chosen appropriately. As a direct consequence of this finding, we obtain exceedingly simple yet accurate formulas for the V-shaped cantilever, which will be of value to the users of the AFM.