[On the thermal responses of a rectangular AFM cantilever coupled surface by the elastic biological specimens]

Atomic force microscopy (AFM) is a very important tool in studying biological problems at the level of cell and molecules. In an AFM experiment to measure the mechanical properties of biological specimens, the measurement accuracy will be reduced by the environmental thermal noise. Here, we have characterized the thermo-mechanical responses of a rectangular AFM cantilever with the tip coupled to the surface by an elastic biological specimen, showed that the cantilever and the specimen behave as springs in parallel, and derived a relationship between the mean square deflection and the mean square inclination. Furthermore, we have presented an approximate expression for the specimen spring constant in terms of contributions to the mean square inclination from the first few vibration modes and suggested a new method for determining the elasticity of the specimen by measuring the change in the tip fluctuations in the presence of coupling.