# Design of a Piezoelectrically Actuated Ultrananocrystalline Diamond (UNCD) Microantilever Biosensor
## 1 Introduction  
Microantilevers provide the basis for the simplest/fundamental device structure within the field of microelectromechanical systems (MEMSs) [1,2]. Rectangular microcantilevers can be modeled as a planar beam that lies in a single plane (e.g., plane XY in Figure 1). The microcantilever lies in a plane parallel to a substrate where films to produce the microcantilever were grown, with the free tip capable of moving perpendicular to the substrate, such that the lateral in-plane motion of the free end would encounter more resistance [3]. Microantilevers are extensively used as key components of physical, chemical, and biological sensors. The sensing application is based on the changes in bending (static mode) [4] or in resonance frequency (dynamic mode) [5] produced by the action induced by molecules or other materials adsorbed on the surface of the cantilever [6]. Although microcantilevers have been extensively explored for biosensing applications, several limitations persist in the existing literature. Most conventional designs rely on silicon (Si) or silicon-based materials (see Table 1), which, while widely available, exhibit moderate mechanical properties that constrain sensitivity--especially in dynamic operation modes. The relatively low Young's modulus of Si limits the achievable resonant frequency, reducing the cantilever's capacity to detect extremely small mass changes, such as those in the picogram range. Furthermore, many prior studies treat the actuator and cantilever design as separate entities, lacking a clear correlation between the piezoelectric actuator's resonant frequency and the cantilever's mechanical response. This disjointed approach leads to suboptimal energy transfer and reduced sensitivity. In addition, environmental damping and mechanical losses are often overlooked in simulation models, impacting predictive accuracy under real-world conditions. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Property** & **Si** & **SiC** & **Si\({}_{3}\)N\({}_{4}\)** & **UNCD** \\ \hline Young’s Modulus (GPa) & 130 & 450 & 166–297 & 916–980 \\ Shear Modulus (GPa) & 80 & 149 & 65.3–127 & 577 \\ Hardness (kg/mm\({}^{2}\)) & 1000 & 3500 & 800–3050 & 10,000 \\ Fracture Strength (GPa) & 1.0 & 5.2 & 0.18–0.65 & 5.3 \\ Poisson’s Ratio & 0.22–0.278 & 0.183–0.192 & 0.23–0.28 & 0.07 \\ Density (kg/m\({}^{3}\)) & 2329 & 3210 & 3170 & 3500 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of mechanical properties of Si, SiC, and Si\({}_{3}\)N\({}_{4}\)[7,8], with UNCD [9, 10, 11, 12]. Figure 1: Structure of a microcantilever with one free end, where L is the length, W is the width, and t is the thickness of the beam. This study introduces a unified and systematic design methodology that begins with optimizing the piezoelectric actuator and then designing the microcantilever based on the novel ultrananocrystalline diamond (UNCD) to match the actuator's resonant frequency. This matching ensures efficient vibrational excitation. UNCD offers a higher Young's modulus, shear modulus, and hardness and lower damping (characterized by Poisson's ratio) compared to prior materials used for microcantilevers (Table 1). The unique UNCD properties enable enhanced resonant frequencies and superior sensitivity. The simulation framework incorporates both frequency and time domain analyses, including thermoelastic damping, to realistically predict quality factors and oscillation amplitudes. This integrated approach directly addresses the key challenges found in previous designs and provides a robust foundation for next-generation, high-sensitivity MEMS biosensors. Table 1 summarizes the key mechanical properties of the materials previously used as bases for producing MEMS microcantilevers [7; 8]. These include ultrananocrystalline diamond (UNCD) films, as developed by [PERSON] and colleagues [9; 10; 11; 12], grown on Si substrates. UNCD exhibits the highest Young's modulus among the listed materials.