Simulation of the effect of surface roughness on the mechanical properties of a microbeam

Surface flaw is harmful for the quality of microelectromechanical device, because it could affect the mechanical response of the micro structure inside. In this paper, we simulate the effect of surface roughness on the mechanical properties of a micro beam by a two-dimensional finite element analysis. The random surface is generated in one dimension by a gauss correlation function with two major parameters, root mean square (RMS) s and correlation length λ. The effect of s and λ on the bending deflection and eigenfrequency of a 0.5μm (height)×5μm (length) beam is investigated for the cases of one fixed end and two fixed ends, with the following results. Firstly, with a same load, the bending deflection of the microbeam increases with both RMS and correlation length, while the eigenfrequencies (the first to the sixth) of the microbeam decrease with the increase of both RMS and correlation length. In another word, the roughness of the surface softens the microbeam. Secondly, by generating numbers of microbeams with a same s and λ, we find that the increase of the s and λ causes the increasing instability degree of the microbeam for the bending deflection U_max and the eigenfrequencies ω in both cases. In the case of two fixed ends, a RMS of 60nm and a correlation length of 300nm lead to a ΔU_max/U_max=7% instability degree of the bending, while in the case of one fixed end, they would lead to a value of ΔU_max/U_max=11%. In the mean time, they lead to Δω/ω=2.9% instability degree of the first frequency in the case of two fixed ends, and Δω/ω=4.25% in the case of one fixed end. The simulation would be helpful in the fabrication design of microelectromechanical device.