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]

中文翻译：

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通过模式相关的 Duffing 非线性谐振确定碳化硅 (SiC) 薄隔膜的弹性模量

我们报告了一种用于确定弹性模量的非破坏性片上技术（ $E_{\mathrm {Y}}$ ) 的碳化硅 (SiC) 薄膜通过测量其非线性共振。与传统的静载荷偏转技术（例如、梁弯曲、膜膨胀和纳米压痕），非线性共振方法能够在不危及微器件的情况下表征机械性能，绕过复杂的接触模式样品制备和笨重、昂贵的设备。我们推导出了“膜”状态中隔膜的依赖于模式的达芬共振，并关联 $E_{\mathrm {Y}}$ 与 Duffing 的“骨干”曲线。为了验证我们的模型，我们制造了 SiC 方形隔膜 (1mm $\times 1$ 毫米 $\times 2~\mu \text{m}$ ) 表现出高达 500kHz 的多模共振和质量 ( $Q$ ) 因子高达 16,000。以设备的 (2,2) 模式为例，我们得到 $E_{\mathrm {Y}} = 436\,\,\pm \,\,27$ GPa 通过其 Duffing 非线性响应。该技术可以很容易地广泛扩展到其他薄膜和 MEMS/NEMS 谐振器。[2020-0209]