Quality factors in micron- and submicron-thick cantilevers

Abstract

Micromechanical cantilevers are commonly used for detection of small forces in microelectromechanical sensors (e.g., accelerometers) and in scientific instruments (e.g., atomic force microscopes). A fundamental limit to the detection of small forces is imposed by thermomechanical noise, the mechanical analog of johnson noise, which is governed by dissipation of mechanical energy. This paper reports on measurements of the mechanical quality factor Q for arrays of silicon-nitride, polysilicon, and single-crystal silicon cantilevers. By studying the dependence of Q on cantilever material, geometry, and surface treatments, significant insight into dissipation mechanisms has been obtained. For submicron-thick cantilevers, Q is found to decrease with decreasing cantilever thickness, indicating surface loss mechanisms. For single-crystal silicon cantilevers, significant increase in room temperature Q is obtained after 700°C heat treatment in either N2 or forming gas. At low temperatures, silicon cantilevers exhibit a minimum in Q at approximately 135K, possibly due to a surface-related relaxation process. Thermoelastic dissipation is not a factor for submicron-thick cantilevers, but is shown to be significant for silicon-nitride cantilevers as thin as 2.3 μm.