Analysis of asymmetric resonance response of thermally excited silicon micro-cantilevers for mass-sensitive nanoparticle detection

Abstract

In this paper, the asymmetric resonance frequency (f0) responses of thermally in-plane excited silicon cantilevers for a pocket-sized, cantilever-based airborne nanoparticle detector (Cantor) are analysed. By measuring the shift of f0 caused by the deposition of nanoparticles (NPs), the cantilevers are used as a microbalance. The cantilever sensors are low cost manufactured from silicon by bulk-micromachining techniques and contain an integrated p-type heating actuator and a sensing piezoresistive Wheatstone bridge. f0 is tracked by a homemade phase-locked loop (PPL) for real-time measurements. To optimize the sensor performance, a new cantilever geometry was designed, fabricated and characterized by its frequency responses. The most significant characterisation parameters of our application are f0 and the quality factor (Q), which have high influences on sensitivity and efficiency of the NP detector. Regarding the asymmetric resonance signal, a novel fitting function based on the Fano resonance replacing the conventionally used function of the simple harmonic oscillator and a method to calculate Q by its fitting parameters were developed for a quantitative evaluation. To obtain a better understanding of the resonance behaviours, we analysed the origin of the asymmetric line shapes. Therefore, we compared the frequency response of the on-chip thermal excitation with an external excitation using an in-plane piezo actuator. In correspondence to the Fano effect, we could reconstruct the measured resonance curves by coupling two signals with constant amplitude and the expected signal of the cantilever, respectively. Moreover, the phase of the measurement signal can be analysed by this method, which is important to understand the locking process of the PLL circuit. Besides the frequency analysis, experimental results and calibration measurements with different particle types are presented. Using the described analysis method, decent results to optimize a next generation of Cantor are expected.

Fabrication of ZnO Nanorods on MEMS Piezoresistive Silicon Microcantilevers for Environmental Monitoring

“…The ZnO-covered cantilevers were then operated in a temperature-and humidity-controlled climatic chamber for the investigation of humidity sensing. Fano-resonance based model fitting [6] results indicated that multi-layer ZnO-NRs-patterned piezoresistive micro-cantilevers sensor have a sensitivity value of 6.35 ± 0.27 ppm/RH% at 25 °C in the range from 30% RH to 80% RH (Figure 4). This sensitivity is higher than 0.05 ppm/RH% and 0.12 ppm/% reported for sol-gel ZnO nanowires and nanoparticles, respectively, on a quartz crystal balance [7] and ZnO quantum dots on a QCM with 5-10 ppm/% [8].…”

In-Plane and Out-of-Plane MEMS Piezoresistive Cantilever Sensors for Nanoparticle Mass Detection

“…A resonant cantilever, as a gravimetric-based sensor, represents a mass-concentration detector. As shown in Equation (1), a calibration factor (CF) in units of µg × min/(m 3 × Hz) is needed to convert the measured resonance-frequency shift rate (∆f R /t CT ) into a mass-concentration regime, which is done against the FMPS as a standard reference instrument [27,30]:…”

“…The resonance frequency decrement due to particle collection and its frequency-shift rate determined over a 10-min sampling time is delineated in Figure 10. In contrary to our previous design [27,30], we did not operate the EtPCS under cyclic switching between separated particle-sampling and frequency-tracking modes but measured frequency shift under continuously maintained particle collection, i.e., at applied high voltage. In addition, fluctuation of temperature and humidity in the chamber were maintained at nearly constant values fluctuating by less than ~0.2 °C and ~0.6%, respectively.…”

“…It was subsequently connected to a negative high direct current voltage, i.e., −115 V. Furthermore, a copper ring (Figure 2a) was connected to +115 V and placed around the cantilever. Consequently, positively charged (and uncharged) nanoparticles would be attracted (and polarized/attracted) to the selected cantilever surfaces by electrophoresis and dielectrophoretic mechanisms, respectively [27,29,30]. This nanoparticle sampling method has been proven to be effective not only for larger silicon microcantilevers but also for smaller nanoscale silicon pillars [17,31,32].…”

“…This numeral reference was then implemented in a phase-locked loop (PLL) system (LabVIEW-based) to keep the optimized state for phase locking and easily facilitate resonance-frequency tracking in real-time ( Figure 4). Due to the existence of direct-thermal parasitic coupling effects on the sensing part resulting in an asymmetric amplitude shape and a reverse phase response (Fano resonance) [30], a referencesignal subtraction method is embedded in our LabVIEW system. This method has successfully been demonstrated to remove the parasitic effect on the EtPCS output signal and construct an optimized frequency response [24,33,34].…”