Modal response and frequency shift of the cantilever in a noncontact atomic force microscope

Abstract

The force-sensing cantilever in a noncontact atomic force microscope is a continuous system with infinite number of eigenmodes. Although the frequently used point mass model was found sufficient in many cases, its conditions for validity and the insights on how higher eigen-modes could affect the selection of operation parameters were not established. In this letter, we formulate the cantilever motion using modal response analysis, a powerful means enabling an efficient numerical solution and a first order analytical solution. The origins and impacts of the higher eigenfrequency oscillation are then investigated, which sheds lights on achieving optimal imaging conditions.