Spring constants of composite ceramic/gold cantilevers for scanning probe microscopy

A combination of finite element analysis (FEA) calculations and resonant fr equency measurements are applied for determining the normal and lateral spr ing constants of microfabricated ceramic/gold cantilevers for friction forc e mode of scanning probe microscopy (SPM). The cantilever Si3N4 and Au laye rs are combined analytically into an equivalent single composite layer. Ben ding and torsion behavior of the cantilever are determined through FEA. Eff ective Young's modulus for the composite Si3N4-Au beam is determined throug h assimilation of FEA and fundamental resonant frequency measurements. Seve ral current analytical solutions are compared with the full FEA evaluation. A new analytical expression is derived for obtaining the ratio of lateral to normal spring constants and thereby the evaluation of absolute values of friction coefficients. Calibration plots are presented for the assessment of both vertical and torsion spring constants of bi-component cantilevers b y measuring their resonant frequencies and thickness of gold overlay. The c omplex relationship between resonant frequency, f(0), and spring constants, k, can be presented in scaling form k similar to f(0)(alpha) with alpha ap proximate to 2.60 for a wide range of compositions of cantilever beams. Dev iations from the simple cubic relationship k similar to f(0)(3) known for a homogeneous beam are related to the bi-component nature of cantilevers wit h ceramic layer and gold overlay. The calibration plots are proposed and an alytical expression is derived to make more accurate assessment of spring c onstants for composite SPM cantilevers. (C) 1999 Elsevier Science S.A. Air rights reserved.