Introduction

Atomic force microscopy (AFM) has been developed to a nearly ubiquitous tool for studying physics, chemistry, biology, medicine and engineering at the nano-scale [1-5]. AFM could signifi cantly impact many fabrication and manufacturing processes due to its advantages such as 3D topography of nano-fabrication and metrology for MEMS [2]. As a typical dynamic mode, the tapping mode (TM) is widely used in the operation of AFM where the cantilever is driven at a fi xed frequency close or equal to the fundamental resonance frequency of vertical bending [4,6]; a schematic of the TM-AFM setup is shown in Fig. 1. Moreover, the vibration amplitude of the cantilever is much bigger than the equilibrium separation between the tip and the sample.