Mass sensitivity of co-resonantly coupled dynamic mode cantilever sensors

I. Lampouras, J. Körner
Leibniz University Hannover,

Keywords: mass-sensitivity, co-resonant cantilever sensors, silicon nitride, dynamic-mode


Dynamic mode cantilever sensors are widely employed for materials characterization in scanning probe methods, or as sensitive mass and gas sensors [1]. The cantilever beam’s oscillatory state, which is influenced by external interactions (i.e. force gradient, mass load), is detected by laser-based methods, such as deflectometry or interferometry. The change of the oscillation parameters is then used to quantify the interaction. Measures to increase the sensitivity of these sensors include reducing the geometric dimensions to lower the cantilever’s spring constant and effective mass. This, in turn, requires the use of very sophisticated concepts to ensure reliable oscillation detection of these (nano)cantilevers [2]. Therefore, these detection approaches are typically not compatible with commercially available equipment. The co-resonant concept addresses these contradicting requirements of highest sensitivity and robust detectivity by mechanical coupling and eigenfrequency matching of a micro- and a nanocantilever. This configuration creates a co-resonant state that combines and harnesses the favorable properties of both resonators to enable: (i) high sensitivity based on the nanocantilever’s properties and (ii) stable oscillation detection by established and widely available methods for the microcantilever [3]. The challenge for this concept is the adjustment of both cantilevers’s eigenfrequencies to match to a certain degree, while keeping the spring constant k and effective mass of the nanocantilever very low (i.e. k in the order of mN/m or below) and the dimensions of the microcantilever within a range suitable for stable oscillation measurements (i.e. width ideally at least 10 µm width, thickness ~1m µm). We have recently developed a process that enables the creation of predefined cantilever geometries fulfilling the aforementioned requirements and inherent eigenfrequency matching through choice of cantilever dimensions. The developed process is batch-compatible and the co-resonantly coupled system is fabricated monolithically from low-stress silicon with good accuracy and reproducibility for the target parameters [4]. The fabricated sensors have been characterized through vibration experiments to determine their sensor properties and mass-sensitivity by scanning electron microscope (SEM) studies with defined mass deposition of amorphous carbon. It was found that a co-resonantly coupled system made from low-stress silicon nitride comprising a microcantilever (kmicro = 1.6 N/m) and a nanocantilever (knano = 3.9 mN/m) with an eigenfrequency deviation of 4 % exhibits a sensitivity of 1.35 Hz/fg and 0.004 Hz/fg for each of the coupled system’s resonance peaks. This is comparable to that of ultra-sensitive nanocantilevers which require advanced oscillation detection [2]. The study was conducted with an SEM to realize the mass deposition, but the same sensor was also measured with a standard environmental atomic force microscope to validate the compatibility with commonly used equipment for oscillation detection. With a reliable fabrication process at hand, these preliminary results are the basis for future work aimed at further investigating the sensitivity potential of the co-resonant concept. [1] B. N. Johnson et al., Biosens Bioelectron 32:1, 2012; [2] N. V. Lavrik et al., Appl Phys Lett 82:2697, 2003; [3] J. Körner, J Mater Res 33(17):2504, 2018; [4] I. Lampouras et al., J Micromech Microeng 34:015005, 2024;