Energy dissipation and frequency shift of a damped dynamic force microscopy

The closed-form solution of the transient response of damped dynamic force microscopy subjected to the nonlinear interatomic force is derived. The frequency shift and the decay rate of a V-typed probe can be determined easily and precisely by the proposed method. If the taper ratio is zero, a uniform cantilever is obtained. Moreover, the transient response of a non-uniform cantilever can be determined also in the same way. The complex Youngʹs modulus is used to describe the viscoelastic material property. In the modulus, the loss factor is introduced. The relation between the Q-factor and the loss factor is discussed. Moreover, the relation between the energy dissipation and the frequency shift is revealed. Finally, the effects of several parameters on the Q-factor, the frequency shift and the decay rate are investigated. The proposed method can be easily applied to investigate the tapping mode of AFM.