Thermomechanical noise of a free v-shaped cantilever for atomic-force microscopy.

We have calculated the thermal noise of a v-shaped AFM cantilever (Microlever, Type E, Thermomicroscopes) by means of a finite element analysis. The modal shapes of the first 10 eigenmodes are displayed as well as the numerical constants, which are needed for the calibration using the thermal noise method. In the first eigenmode, values for the thermomechanical noise of the z-displacement at 22 degrees C temperature of square root of u2(1) = A/square root of c(cant) and the photodiode signal (normal-force) of S2(1) = A/square root of c(cant) were obtained. The results also indicate a systematic deviation ofthe spectral density of the thermomechanical noise of v-shaped cantilevers as compared to rectangular beam-shaped cantilevers.