Application of triangular atomic force microscopy cantilevers to friction measurement with the improved parallel scan method

The atomic force microscopy (AFM) can provide tribological information in micro/nanoscale. However, the general measurement techniques require rigorous value of stiffness and relationship between AFM cantilever deformation and corresponding photodetector response. In this study, triangular AFM cantilevers with different dimensions are applied to quantitatively measure the coefficient of friction with the improved parallel scan method [Y. L. Wang, X. Z. Zhao, and F. Q. Zhou, Rev. Sci. Instrum. 78, 036107 (2007)]. An analytical model is first presented with the plan-view geometrical dimensions of cantilevers. Finite element analysis (FEA) models are set up to validate the analytical model. The results show good agreement between analytical calculation and FEA simulation. More importantly, the coefficient of friction obtained with different cantilevers on silicon surface shows a good consistency. At last, the factors which may affect measurement are discussed. The advantage of the model presented here is that the general uncertainties of thickness and Young's modulus are not necessary to be known for the friction force calibration in AFM application.