Determination of Elastic Modulus of Silicon Carbide (SiC) Thin Diaphragms via Mode-Dependent Duffing Nonlinear Resonances

We report on a non-destructive, on-chip technique for determining the elastic modulus ( E_{\mathrm {Y}} ) of silicon carbide (SiC) thin diaphragms by measuring their nonlinear resonances. Departing from the conventional static load-deflection techniques ( e.g. , beam bending, membrane bulging and nanoindentation), the nonlinear resonance approach enables characterizing mechanical properties without risk to the microdevices, bypassing complicated contact-mode sample preparation, and bulky, expensive apparatus. We derive the mode-dependent Duffing resonances of the diaphragms in the 'membrane' regime, and correlates E_{\mathrm {Y}} with the Duffing 'backbone' curve. To verify our model, we fabricate SiC square diaphragms (1mm \times 1 mm \times 2~\mu \text{m} ) that exhibit multimode resonances up to 500kHz and quality ( Q ) factors up to 16,000. Taking the device's (2,2) mode as an example, we obtain E_{\mathrm {Y}} = 436\,\,\pm \,\,27 GPa via its Duffing nonlinear response. The technique can be readily and widely extended to other thin films and MEMS/NEMS resonators. [2020-0209]