Friction force microscopy measurements: Normal and torsional spring constants for V-shaped cantilevers

A combination of finite element analysis (FEA) calculations and resonant frequency measurements are applied for determining normal and lateral spring constants of microfabricated ceramic/gold cantilevers for friction force microscopes. The cantilever Si3N4 and Au layers are combined analytically into an equivalent single composite layer. Bending and torsion behavior of the cantilever under typical operating forces are determined through FEA. Effective Young's modulus for the composite Si3N4-Au beam from 172 to 185 GPa is determined through assimilation of FEA and fundamental resonant frequency measurements. Several current analytical solutions are compared to the full FEA evaluation. A new analytical expression is derived for obtaining the ratio of lateral to normal spring constants and thereby evaluation of absolute values of friction coefficients. Calibration plots are presented for assessment of both vertical and torsion spring constants of bicomponent cantilevers by measuring their resonant frequencies and thickness of gold overlay.