**4. Conclusions**

We reported the impact of bottom electrode designs on electromechanical properties, such as *Q*, *k*2, and FOM of 230 MHz and 1.1 GHz AlN CMRs. Both measurements and FEA calculation results showed that the change in bottom electrode coverage rates impact CMRs. Such an e ffect is largely due to the change in the amount of mechanical damping, which was more dominant in lower-frequency CMRs, and led to large fluctuations in *Q*. For 1.1 GHz CMRs, *Q* decreased with increasing bottom electrode areas as the damping towards supporting substrate increased. To validate our claims, we measured CMRs at 10 K, confirming that the experimental results match the theoretical predictions. Compared to mechanical damping or anchor loss, the e ffect of TED remained constant regardless of changes in bottom electrode designs. This is because TED depends on the ratio of metal-to-piezoelectric material coverage only in the active region of the resonator. We believe our findings can contribute to the enhancement of the current state of AlN CMRs and possibly other types of piezoelectric MEMS resonators by improving their electromechanical properties. These finding will directly impact applications in which CMRs are used as the main components, such as in oscillator and sensor systems.

**Author Contributions:** Conceptualization, G.P. and H.J.K.; Experiment, S.I.J., C.R., and H.J.K.; writing—original draft preparation, S.I.J., C.R. and H.J.K.; writing—review and editing, G.P. and H.J.K.; funding acquisition, G.P. and H.J.K.

**Funding:** This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2018R1C1B6008041), KIMM of the Ministry of Science and ICT of South Korea (2018010152), and DARPA Dynamics Enabled Frequency Sources (DEFYS) program (FA86501217264).

**Acknowledgments:** Authors would like thank sta ff members from CMU Nanofab and DGIST CCRF device cleanroom for their assistance in device fabrication and characterization.

**Conflicts of Interest:** The authors declare no conflict of interest.
