Validating the Critical Point of Spontaneous Parametric Downconversion for Over 600 Scanning MEMS Micromirrors on Wafer Level

Sensors and actuators based on resonant microelectromechanical systems (MEMS), such as scanning micromirrors, are well established in automotive and consumer products. As the areas of application broaden toward highly automated driving and augmented reality, the performance requirements for the MEMS are also increasing. Devices outside of the performance specifications have to be rejected, which is costly due to the high processing times of MEMS technologies. In particular, nonlinear system behavior is often found to cause unexpected device failure or performance issues. Thus, accurate simulation or rather system models, which account for nonlinear sensor dynamics, can not only increase process yield, but, more importantly, also lead to a comprehensive understanding of the underlying physics and, consequently, to improved MEMS design. In a recent work by Nabholz et al. “Spontaneous parametric down-conversion induced by non-degenerate three-wave mixing in a scanning MEMS micro mirror” (Sci. Rep., vol. 9, 2019, Art. no. 3997), we have studied the possibility of a rather drastic device failure induced by nonlinearities on the example of a resonant scanning MEMS micromirror. On the level of a few selected chips, we have carefully measured the complex nonlinear system behavior and modeled it by a nonlinear mode-coupling phenomenon known as spontaneous parametric downconversion (SPDC). The most intriguing feature of SPDC is the sudden change from a rather linear to a highly nonlinear system behavior at the threshold or rather critical oscillation amplitude of the mirror. However, the threshold only lies within the range of the mirror's operational amplitude if certain frequency resonance conditions regarding the modes of the mechanical structure are met. As a direct consequence, the critical amplitude strongly depends on the frequency spectrum of the MEMS design, which, in turn, is largely influenced by fabrication imperfections. In this letter, we validate the dependence of the critical amplitude on the resonance condition by measuring it for over 600 micromirrors on wafer level. Our work does not only validate the theory of SPDC with measurements on such a large scale but also demonstrates modeling strategies, which are essential for MEMS product design.