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

TL;DR

This paper introduces a method to determine Young's modulus of nanomechanical string resonators by analyzing their eigenmode spectrum, enabling accurate material characterization even under high tensile stress.

Contribution

The paper presents a novel in-situ approach to measure Young's modulus using harmonic eigenmodes, applicable to stress-dominated nanomechanical resonators.

Findings

Measured Young's modulus for four wafer materials.

Compared experimental results with theoretical and literature values.

Highlighted the importance of sample-specific measurements for precision.

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 to access Young's modulus even for the case of a stress-dominated frequency response. We use the proposed framework to obtain the Young's modulus of four different wafer materials, comprising the 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.