In this study, we investigate the performance of two piezoresistive micro-electro-mechanical system (MEMS)-based silicon cantilever sensors for measuring target analytes (i.e., ultrafine particulate matters). We use two different types of cantilevers with geometric dimensions of 1000 × 170 × 19.5 µm³ and 300 × 100 × 4 µm³, which refer to the 1st and 2nd types of cantilevers, respectively. For the first case, the cantilever is configured to detect the fundamental in-plane bending mode and is actuated using a resistive heater. Similarly, the second type of cantilever sensor is actuated using a meandering resistive heater (bimorph) and is designed for out-of-plane operation. We have successfully employed these two cantilevers to measure and monitor the changes of mass concentration of carbon nanoparticles in air, provided by atomizing suspensions of these nanoparticles into a sealed chamber, ranging from 0 to several tens of µg/m³ and oversize distributions from ~10 nm to ~350 nm. Here, we deploy both types of cantilever sensors and operate them simultaneously with a standard laboratory system (Fast Mobility Particle Sizer, FMPS, TSI 3091) as a reference.

The asymmetric resonance response in electro-thermal piezoresistive cantilever resonators causes a need of an optimization treatment for taking parasitic actuation-sensing effects into account. An electronic reference circuit for signal subtraction, integrated with the cantilever resonator has the capability to reduce the effect of parasitic coupling. Measurement results demonstrated that a symmetric amplitude shape (Lorentzian) and an optimized phase characteristic (i.e., monotonically decreasing) were successfully extracted from an asymmetric resonance response. With the monotonic phase response, real-time frequency tracking can be easier to implement using a phase-locked loop (PLL) system. In this work, an electro-thermal piezoresistive cantilever resonator functionalized with self-assembled monolayers of chitosan-covered ZnO nanorod arrays as sensitive layers has been investigated under different relative humidity (rH) levels. Enhancement of resonance phase response has been demonstrated by implementing the reference signal subtraction. Subsequently, a lock-in amplifier integrated with PLL system (MFLI, Zurich Instruments, Zurich, Switzerland) was then employed for continuously tracking the resonant frequency. As a result, we find a good correlation of frequency shift (∆f₀) with change in rH monitored using a commercial reference sensor.

The asymmetric resonance response in thermally actuated piezoresistive cantilever sensors causes a need for optimization, taking parasitic actuation–sensing effects into account. In this work, two compensation methods based on Wheatstone bridge (WB) input voltage (V_{WB_in}) adjustment and reference circuit involvement were developed and investigated to diminish those unwanted coupling influences. In the first approach, V_{WB_in} was increased, resulting in a higher current flowing through the WB piezoresistors as well as a temperature gradient reduction between the thermal actuator (heating resistor: HR) and the WB, which can consequently minimize the parasitic coupling. Nevertheless, increasing V_{WB_in} (e.g., from 1 to 3.3 V) may also yield an unwanted increase in power consumption by more than 10 times. Therefore, a second compensation method was considered: i.e., a reference electronic circuit is integrated with the cantilever sensor. Here, an electronic reference circuit was developed, which mimics the frequency behavior of the parasitic coupling. By subtracting the output of this circuit from the output of the cantilever, the resonance response can thus be improved. Both simulated and measured data show optimized amplitude and phase characteristics around resonant frequencies of 190.17 and 202.32 kHz, respectively. With this phase optimization in place, a phase-locked-loop (PLL) based system can be used to track the resonant frequency in real time, even under changing conditions of temperature (T) and relative humidity (RH), respectively. Finally, it is expected to enhance the sensitivity of such piezoresistive electro-thermal cantilever sensors under loading with any target analytes (e.g., particulate matter, gas, and humidity).

Cantilever-based sensors have attracted considerable attention in the recent past due to their enormous and endless potential and possibilities coupled with their dynamic and unprecedented sensitivity in sensing applications. In this paper, we present a technique that involves depositing and vaporizing (at ambient conditions) a particle-laden water droplet onto a defined sensing area on in-house fabricated and commercial-based silicon microcantilever sensors. This process entailed the optimization of dispensing pressure and time to generate and realize a small water droplet volume (V_d = 49.7 ± 1.9 pL). Moreover, we monitored the water evaporation trends on the sensing surface and observed total evaporation time per droplet of 39.0 ± 1.8 s against a theoretically determined value of about 37.14 s. By using monodispersed particles in water, i.e., magnetic polystyrene particles (MPS) and polymethyl methacrylate (PMMA), and adsorbing them on a dynamic cantilever sensor, the mass and number of these particles were measured and determined comparatively using resonant frequency response measurements and SEM particle count analysis, respectively. As a result, we observed and reported monolayer particles assembled on the sensor with the lowest MPS particles count of about 19 ± 2.

Resonance-based sensors ordinarily show a symmetrical amplitude shape, which is accompanied by a monotonic transition as its phase response. At its resonance state, there is a 90° phase difference between the excitation force and the system response. Nevertheless, due to some parasitic factors, resonance-based sensors might show non-ideal frequency response as seen in in-plane electro-thermal piezoresistive cantilever sensors (EtPCSs). Because of a direct thermal parasitic coupling from the excitation part to the sensing part, the sensor output shows an asymmetric amplitude shape and a reversing phase response. In some EtPCS that have relatively lower thermal exposure on their sensing part, a symmetrical amplitude shape could be demonstrated but was still accompanied with a low magnitude of monotonical phase response. In this work, a method of reference subtraction was introduced to enhance the frequency response of the EtPCS at changing ambient conditions (e.g. humidity, temperature, smoke exposure). As a result, we obtained optimized frequency responses suitable for a phase-locked loop-based system to carry out resonant-frequency tracking in real-time.

This study presents a measurement approach suitable for the simultaneous determination of both the mass m_p and magnetic moment µ_p of magnetic particles deposited on a micro electro mechanical system (MEMS) resonant cantilever balance, which is operated in parallel to an external magnetic field-induced force gradient F′(z). Magnetic induction B(z) and its second spatial derivative δ²B/δz² is realized, beforehand, through the finite element method magnetics (FEMM) simulation with a pair of neodymium permanent magnets configured in a face-to-face arrangement. Typically, the magnets are mounted in a magnet holder assembly designed and fabricated in-house. The resulting F′ lowers the calibrated intrinsic stiffness k₀ of the cantilever to k₀-F′, which can, thus, be obtained from a measured resonance frequency shift of the cantilever. The magnetic moment µ_p per deposited particle is determined by dividing F′ by δ²B/δz² and the number of the attached monodisperse particles given by the mass-induced frequency shift of the cantilever. For the plain iron oxide particles (250 nm) and the magnetic polystyrene particles (2 µm), we yield µ_p of 0.8 to 1.5 fA m² and 11 to 19 fA m² compared to 2 fA m² and 33 fA m² nominal values, respectively.