  The functionalization of an Atomic Force Microscope (AFM) cantilever with a
colloidal bead is a widely used technique when the geometry between the probe
and the sample must be controlled, particularly in force spectroscopy. But some
questions remain: how does a bead glued at the end of a cantilever influence
its mechanical response ? And more important for quantitative measurements, can
we still determine the stiffness of the AFM probe with traditional techniques?
In this article, the influence of a colloidal mass loading on the eigenmodes
shape and resonant frequency is investigated by measuring the thermal noise on
rectangular AFM microcantilevers with and without a bead attached at their
extremities. The experiments are performed with a home-made ultra-sensitive
AFM, based on differential interferometry. The focused beam from the
interferometer probes the cantilever at different positions and the spatial
shapes of the modes are determined up to the fifth resonance, without external
excitation. The results clearly demonstrate that the first eigenmode almost
doesn't change by mass loading. However the oscillation behavior of higher
resonances present a marked difference: with a particle glued at its extremity,
the nodes of the mode are displaced towards the free end of the cantilever.
These results are compared to an analytical model taking into account the mass
and the inertial moment of the load in an Euler-Bernoulli framework, where the
normalization of the eigenmodes is explicitly worked out in order to allow a
quantitative prediction of the thermal noise amplitude of each mode. A good
agreement between the experimental results and the analytical model is
demonstrated, allowing a clean calibration of the probe stiffness.
