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Mechanical properties in MEMS and NEMS are very sensitive to changes in the environment. For the studied membranes, it is known that for example, a global temperature change influences the eigenfrequency [1]. Besides external heating, internal processes due to the vibration (e.g. local friction) could lead to local changes in temperature. Silicon nitride membranes (side length: 450 μm, thickness: 500 nm) are used as resonators, which makes it possible to fabricate thermometers directly on their surface. Local temperature measurements are performed using the thermoelectric effect. Gold and permalloy (Ni81Fe19) can be used to form thermocouples of micrometer size. That provides a sensitivity of 20 μV/K [2]. The system is driven with a piezoelectric actuator and monitored using a digital holographic microscope (DHM), allowing local probing of the vibration [3]. To improve the signal-to-noise ratio of the periodic temperature signal, the measurement is carried out with a lock-in amplifier. The expected signal frequency is twice the drive frequency and is therefore used as the reference for the lock-in measurement. With this setup, sub-millikelvin sensitivity can be achieved.
Measurements are carried out with a strong drive, resulting in vibration amplitudes on the order of hundreds of nanometers and temperature differences of up to 0.5 mK. The signal depends strongly on the thermometer position, both at different locations on the membrane and at positions aside the membrane. In addition, driving strength and vibrational mode also affect the temperature difference. An increase in temperature can also be seen when a neighbouring membrane is vibrating. This coupling between the membranes is confirmed as a change in the frequency response.
[1] F. Yang et al., Sens. Actuators A Phys. 354, 114307 (2023).
[2] F. L. Bakker et al., J. Appl. Phys. 111, 084509 (2012).
[3] G. Coppola et al., Meas. Sci. Technol., vol. 15, 529 (2004)