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Sensors (Basel). 2017 May 23;17(6). pii: E1191. doi: 10.3390/s17061191.

Thermal Characterization of Dynamic Silicon Cantilever Array Sensors by Digital Holographic Microscopy.

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Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
Laboratoire d'Acoustique de l'Université du Maine (LAUM, UMR CNRS 6613), 72000 Le Mans, France.
Graduate School of Engineering, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aoba-ku, 980-8579 Sendai, Japan.
Lyncee Tec SA, PSE-A, CH-1015 Lausanne, Switzerland.
Institut für Chemie, Martin-Luther-Universität Halle-Wittenberg, Kurt-Mothes-Straße 2, 06120 Halle (Saale), Germany.
Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.


In this paper, we apply a digital holographic microscope (DHM) in conjunction with stroboscopic acquisition synchronization. Here, the temperature-dependent decrease of the first resonance frequency (S₁(T)) and Young's elastic modulus (E₁(T)) of silicon micromechanical cantilever sensors (MCSs) are measured. To perform these measurements, the MCSs are uniformly heated from T₀ = 298 K to T = 450 K while being externally actuated with a piezo-actuator in a certain frequency range close to their first resonance frequencies. At each temperature, the DHM records the time-sequence of the 3D topographies for the given frequency range. Such holographic data allow for the extracting of the out-of-plane vibrations at any relevant area of the MCSs. Next, the Bode and Nyquist diagrams are used to determine the resonant frequencies with a precision of 0.1 Hz. Our results show that the decrease of resonance frequency is a direct consequence of the reduction of the silicon elastic modulus upon heating. The measured temperature dependence of the Young's modulus is in very good accordance with the previously-reported values, validating the reliability and applicability of this method for micromechanical sensing applications.


digital holography; micromechanical cantilever sensors; temperature coefficient of elastic modulus; temperature coefficient of resonance frequency; thermal load

Conflict of interest statement

The authors declare no conflict of interest. In addition, the founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results. Yves Emery is co-founder and CEO of the company manufacturing the R-DHM used in the frame of this study.

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