FRICTION FORCE MICROSCOPY MEASUREMENTS - NORMAL AND TORSIONAL SPRING CONSTANTS FOR V-SHAPED CANTILEVERS

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