Abstarct: In this paper, size-dependent behavior of Atomic force microscope microbeam made of functionally graded materials (FGMs) in both contact and tapping mode, is investigated on the basis of the strain gradient theory. The material properties of the microbeam are varying in the direction of the microbeam thickness, baxsed on a power law. General presented governing equation and the boundary conditions have been specialized for a cantilever beam using in atomic force microscopes (AFMs), with silicon in mid-plane and piezoelectric in both sides through thickness. The electric excitation loading on the beam is considered to be generated by AC and DC interactions; and this point, separates this analysis into two different segments. The effect of the tip position, on the vibration of the micro cantilever are also analyzed. The analysis of the nonlinear motion of the microbeam is carried out with the employment of perturbation theory and multiple scales method. As a Conclusion, the nonlinear behavior of the system baxsed on frequency response equation is discussed.