Measuring the dimensions of the tip and its lever by Scanning Electron Microscopy

In order to determine the force out of the beam deflection, the precise optics as well as the spring constants of the cantilever have to be known.

The calibration procedure is one of the essential parts of FFM-experiments. Each cantilever should be characterized accurately. Manufacturer's data are usually not sufficient and can lead to errors of up to a factor 10. Thus, each cantilever has to be characterized. One way is to use an electron microscope and to deterimine all the relevant parameters, such as: Tip radius R; heigth of tip h ; width, thickness and length of cantilever (w/, t, l) and position of tip on the cantilever. In addition, elastic constants are needed: Youngs modulus E, shear modulus G. Having determined all these parameters, the normal spring constant cB and the torsion spring constant ct for a rectangular cantilever are given by:

    

From Scanning Electron Microscopy the dimensions of the cantilever can be determined in order to compute its spring constant. One can get more precise results by making use of the resonance frequency instead of the thickness of the lever, since the thickness is a very important property which can be determined only with troubles.