Determining Young's modulus via the eigenmode spectrum of a nanomechanical string resonator

Abstract

We present a method for the in situ determination of Young's modulus of a nanomechanical string resonator subjected to tensile stress. It relies on measuring a large number of harmonic eigenmodes and allows us to access Young's modulus even for the case of a stress-dominated frequency response. We use the proposed framework to obtain Young's modulus of four different wafer materials, comprising three different material platforms amorphous silicon nitride, crystalline silicon carbide, and crystalline indium gallium phosphide. The resulting values are compared with theoretical and literature values where available, revealing the need to measure Young's modulus on the sample material under investigation for precise device characterization.