# Design of a Piezoelectrically Actuated Ultrananocrystalline Diamond (UNCD) Microantilever Biosensor
## 4 Conclusions
This enhancement is attributed to the superior mechanical properties of UNCD, making it a strong candidate for next-generation biosensor platforms. In terms of time domain analysis, simulations using a Backward Differentiation Formula (BDF) solver of orders 2 and 5 revealed that a lower solver order (2) produced results more consistent with the experimental \(Q\) values reported in [27]. This is likely due to the suppression of higher-order vibrational modes by the numerical damping introduced at lower solver orders. Attempts to implement the generalized alpha solver did not yield conclusive results, particularly for microcantilevers with natural frequencies approximately three orders of magnitude higher than the validation case. Further work is required to refine these damping models and improve simulation accuracy under high-frequency operation. Table 13 summarizes studies of cantilever simulations found in the literature. Compared to previously reported methodologies for modeling microcantilever biosensors, the approach presented in this work offers a more comprehensive and experimentally validated framework by integrating both frequency and time domain finite element \begin{table}
\begin{tabular}{c c c} \hline \hline
**Modeling** & **Representative Study** & **Description** \\ \hline \hline \multirow{4}{*}{Analytical Modeling} & \multirow{4}{*}{[PERSON] et al. (2024) [31]} & Used classical beam theory to estimate resonant frequency shifts due to biomolecular interactions. Analytical results were validated through finite element analysis and experiment \\  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Comparison of other modeling approaches for microcantilever simulations. simulations using COMSOL Multiphysics. While analytical models, such as those by [PERSON] et al. (2018) and [PERSON] and [PERSON] (2018), provide useful insights for initial estimations or device optimization, they are limited in their ability to account for complex material stacks and damping mechanisms. Stochastic models, like those by [PERSON] et al. (2018) and [PERSON] et al. (2018), focus on noise and thermal fluctuations, but they do not provide structural performance evaluation under piezoelectric actuation. In contrast, the study described in this article not only models a realistic multilayer actuator structure (Pt/AlN/Pt) integrated on ultrananocrystalline diamond (UNCD), but it also validates the model using published experimental data on nanocrystalline diamond (NCD) microcantilevers. This dual-domain, experimentally benchmarked simulation strategy allows for accurate estimation of key performance indicators, such as resonant frequency shifts and quality factor (\(Q\)), making it more suitable for guiding the design of next-generation MEMS biosensors with picogram-level sensitivity. In conclusion, this study demonstrates a robust simulation framework for designing and analyzing piezoelectrically actuated UNCD-based microcantilevers. The methodology is validated, scalable, and adaptable, laying a solid foundation for the development of MEMS biosensors capable of detecting extremely small mass changes with high precision. Future work will focus on the fabrication and experimental testing of the proposed devices to validate their biosensing performance under realistic conditions. One critical aspect will be the experimental investigation of how the mechanical properties of thin films--particularly UNCD and AlN--vary with thickness at the nanoscale, as such variations can significantly influence resonant behavior. Additionally, the effect of atmospheric pressure on the quality factor and sensitivity will be studied by simulating and testing device performance under different environmental damping conditions, including operation in air and vacuum.