A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy

Abstract

The spring constant of microfabricated cantilevers used in scanning force microscopy (SFM) can be determined by measuring their resonant frequencies before and after adding small end masses. These masses adhere naturally and can be easily removed before using the cantilever for SFM, making the method nondestructive. The observed variability in spring constant—almost an order of magnitude for a single type of cantilever—necessitates calibration of individual cantilevers in work where precise knowledge of forces is required. Measurements also revealed that the spring constant scales with the cube of the unloaded resonant frequency, providing a simple way to estimate the spring constant for less precise work.