Effect of Surface Stress on Micromechanical Cantilevers for Sensing Applications

Three models for surface stress loading effect on a micromechanical cantilever are proposed as concentrated moment acting at the free end (Model I), concentrated moment plus axial force acting at the free end (Model II), and uniformly distributed surface force acting along the microcantilever (Model III). Solution to Model I loading is based on the Stoney formula, assuming that the microcantilever is subjected to pure bending and deformed with a constant curvature. Model II takes into account the clamping effect in such a way that an additional axial force is introduced. The deflections resulting from Models I and II surface stress loading effect are solved by Euler-Bernoulli beam theory. In Model III, the effect of surface stress is modeled as uniformly distributed surface force that causes both uniformly distributed bending moment and axial force acting along the axis of the microcantilever. The energy method is then used to obtain the governing equation and boundary conditions for Model III displacement. Comparison of the results obtained by the three models with those by the finite element method and experiment indicates that Model III is the most realistic model for surface stress loading effect to obtain the deflection of a microcantilever.

Model III for surface stress loading effect is then used to demonstrate the applications of a microcantilever in sensor technology through the measurement of tip deflection under an atomic adsorption as the source of surface stress. Dual attractive or repulsive characteristics of interactions between a pair of mercury atoms are described in terms of Lennard-Jones potential. The force per unit atomic spacing induced by the adjacent free surface atoms of a monolayer is then computed using the potential. The sensitivities of atomic spacing and monolayer thickness to the tip-deflection of a microcantilever are studied in this research.