Effect of Undercut on the Characterization of the Mechanical Properties of Silicon Nanocantilevers with Dynamic and Static Test

Abstract

The elastic mechanical properties of silicon nanocantilevers are of prime importance in biotechnology and nanoelectromechanical system (NEMS) applications. In order to make these applications reliable, the exact evaluation of the effect of the undercut on the mechanical properties of silicon nanocantilevers is essential and critical. In this paper, a numerical-experimental method for determining the effect of the undercut on resonant frequencies and Young’s modulus of silicon nanocantilevers is proposed by combining finite element (FE) analysis and dynamic frequency response tests by using laser Doppler vibrometer (LDV) as well as static force-displacement curve test by using an atomic force microscope (AFM). Silicon nanocantilevers test structures are fabricated from silicon-on-insulator (SOI) wafers by using the standard complementary metal-oxide-semiconductor (CMOS) lithography process and anisotropic wet-etch release process based on the critical point drying, which inevitably generating the undercut of the nanocantilever clamping. Combining with three-dimensional FE numerical simulations incorporating the geometric undercut, the dynamic resonance tests demonstrate that the undercut obviously reduces resonant frequencies of nanocantilevers due to the fact that the undercut effectively increases the nanocantilever length by a correct value ΔL. According to a least-square fit expression including ΔL, we extract Young’s modulus from the measured resonance frequency versus the effective length dependency and find that Young’s modulus of a silicon nanocantilever with 200-nm thickness is close to that of bulk silicon. However, when we do not consider the undercut ΔL, the obtained Young's modulus is decreased 39.3%. Based on the linear force-displacement response of 12μm long and 200nm thick silicon nanocantilever obtained by using AFM, our extracted Young’s modulus of the [110] nanocantilever with and without undercut is 169.1GPa and 133.0GPa, respectively. This error reaches 21.3%. Our work reveals that the effect of the undercut on the characterization of the mechanical properties of nanocantilevers with dynamic and static test must be carefully considered.