# Design of a Piezoelectrically Actuated Ultrananocrystalline Diamond (UNCD) Microantilever Biosensor
## 4 Conclusions  
This work presented the theoretical design and modeling of high-sensitivity piezoelectrically actuated microcantilevers for biosensing applications. The modeling approach was validated against experimental data from nanocrystalline diamond (NCD) microcantilevers with integrated AlN piezoelectric actuators. Given the similarity in Young's modulus between NCD and ultrananocrystalline diamond (UNCD), this system provided a suitable reference for validating both the frequency and time domain numerical models developed in this study. The simulated resonant frequencies and quality factors showed strong agreement with the experimental values, with deviations below 3%, likely due to numerical damping and microfabrication tolerances. Following this validation, the models were applied to design UNCD-based and Si-based microcantilevers aimed at detecting an added mass of 1 picogram (pg) uniformly distributed over the cantilever's active area. The design methodology centered on the integration of a Pt/AlN/Pt piezoelectric actuator, which served as the foundational component. The design process was standardized to enable scalability across different operational frequency ranges and target masses. By tuning the actuator's resonant frequency and subsequently optimizing the beam length, the microcantilevers were tailored to exhibit measurable resonance frequency shifts in response to added mass. Subsequently, a Gaussian distribution was used to confine the mass distribution to a certain area on the microcantilever. Three positions were used to observe the impact of the mass location on the resonant frequency shift of the UNCD and Si microcantilevers. It was observed that the resonant frequency shift decreases in comparison to when the mass is considered uniformly distributed on the surface. The resonant frequency shifts were reduced by 4 times. Furthermore, the resonant frequency shift decreases as the mass distribution center is nearer the border of the piezoelectric actuator and increases as the mass distribution center moves towards the tip of the microcantilever. Both the UNCD and Si microcantilevers show slightly similar resonant frequency shifts upon positioning the mass distribution at the same points on the microcantilever (Tables 9 and 12). Nonetheless, the relative trends between materials (UNCD vs. Si) and the overall design methodology remain valid. These results confirm the robustness of the modeling framework while acknowledging that precise mass distribution patterns would ultimately require experimental validation. Future work will further incorporate spatially resolved biomolecular adsorption data to improve accuracy. Although environmental damping models, such as thermoacoustic effects, were not included in this phase of analysis, the structural response of the system was thoroughly characterized. This provided a critical first step in the design of reliable MEMS-based biosensors. Furthermore, the integration of COMSOL's Heat Transfer in Solids module \begin{table}
\begin{tabular}{c c} \hline \hline \(y_{0}\)**Coordinate (\(\upmu\)m)** & **Resonant Frequency Shift (Hz)** \\ \hline
40 & 600 \\
30 & 300 \\
20 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Resonant frequency shift (Hz) for a mass distribution function described by Equation (7), with radius \(r=5\upmu\)m, positioned at \(y_{0}\) on the Si beam while keeping \(x_{0}\) at 0 \(\upmu\)m.  
enabled the inclusion of thermoelastic damping, which allowed for physically realistic quality factor (\(Q\)) estimation through time domain simulations. To evaluate biosensing performance, both the UNCD and Si microcantilevers were designed with identical geometries and actuator structures to isolate the impact of the base material. The results indicated that UNCD microcantilevers exhibit superior sensitivity and higher natural frequencies compared to their Si counterparts for the same active sensing area.