The description of friction of silicon MEMS with surface roughness: virtues and limitations of a stochastic Prandtl–Tomlinson model and the simulation of vibration-induced friction reduction

• W. Merlijn van Spengen,
• Viviane Turq and
• Joost W. M. Frenken

Beilstein J. Nanotechnol. 2010, 1, 163–171, doi:10.3762/bjnano.1.20

• frequency. The results obtained agree very well with measurement data reported previously. Keywords: MEMS; microscale friction reduction; normal force modulation; stochastic Prandtl–Tomlinson model; surface roughness; Introduction With the invention of the friction force microscope (FFM) by Mate et al. [1

• zero at a negative apparent normal force is due to the contribution to the effective normal load of adhesion between the two surfaces. The new stochastic Prandtl–Tomlinson model To describe the microscale irregular stick-slip behaviour, we have extended the well-known Prandtl–Tomlinson model [4][5][7

• surface roughness. The characteristic length scale is related to the surface roughness correlation length of the MEMS sidewalls. We refer to our description as the ‘stochastic Prandtl–Tomlinson model’ (Table 1). ξ(x) is a realization of a stochastic function, where x is the space variable (position). It