Coupling and nonlinear effects of cantilever deflection and torsion encountered when simultaneously measuring vertical and lateral forces using the scanning probe method

Abstract

Coupling and nonlinear problems arising in the large-scale deformation of a cantilever due to vertical and lateral forces exerted by the scanning probe microscope (SPM) are quantified and clarified. For this purpose, two types of cantilevers in practical use—rectangular and V-shaped—are selected. Calculations are performed using the nonlinear finite element method. Sensitivity to lateral force is found to decrease with increasing vertical force, until the critical value of zero is reached. Then, the sensitivity becomes negative with further increases in the vertical force. As for the nonlinear effect, the torsional stifness against the lateral force is found to exhibit soft spring characteristics for a small vertical force range, and hard spring characteristics for a larger range. At the point of the transition, the nonlinear effect appears to diminish. It is interestng to note that at the precise point of transition, the coupling effect between the deflection and torsion is also elimated, which constitutes the optimum condition for simulataneous measurement of the vertical and lateral forces.