Phase shifts and energy dissipations of several modes of AFM: Minimizing topography and dissipation measurement errors

For clear interpretation of a sample's surface properties, several simple and general relations between phase shifts of atomic force microscopy (AFM) and sample's properties are derived. The topography and dissipation measurement errors due to some inherent uncertainties are investigated. For derivation of these simple and general relations among measuring signals and sample's properties, the dynamic behavior of a cantilever is simulated into a mass-spring-damper model. In general, the conventional model can determine the first mode only. The dynamic effective spring theory is introduced here. Based on this theory, the conventional model can be modified to accurately determine the dynamic motions of higher modes of a cantilever. If the dynamic behavior is almost harmonic, the exact dynamic response of the general system subjected to arbitrary tip-sample force is derived. Moreover, several simple and general relations among dynamic responses of AFM and sample's properties are discovered. Based on these relations, the errors of measuring a sample's surface properties due to the inherent measuring uncertainties are investigated. Finally, some methods to minimize the error of measurement are proposed.