Failure mode analysis of MEMS suspended inductors under mechanical shock
Introduction
Micro-electromechanical system (MEMS) inductors have been widely studied in the recent decades due to their benefits in improving the performance of radio frequency integrated circuits (RFICs) [[1], [2], [3], [4]]. Compared with CMOS on-chip inductors, MEMS suspended inductors have a much higher Q factor and have been used for high performance RFICs. Typically, a high Q factor is achieved through a suspended spiral coil, which is used to suppress the energy coupling between the coil and the substrate. For example, the Q factor of the MEMS suspended inductor proposed by Yoon [5] in 2002 is as high as 70.
RFICs integrated with MEMS inductors can be used in many applications, such as consumable electronic devices and military systems. In military applications, high performance RFICs with MEMS inductors have been employed in artillery fuses to improve the detection sensitivity. In general, artillery fuses can withstand high mechanical shock of the order of 104 to 105 g [6]. A suspended structure is susceptible to damage under high mechanical shock, although it has the advantage of a high Q factor. For this purpose, failure analysis of MEMS inductors should be carried out.
Extensive studies have been performed in order to improve the reliability and mechanical performance of MEMS suspended inductors. Jiang et al. [7] briefly discussed the mechanical robustness of suspended inductors, the analysis of which was based on a simple equivalent cantilever beam model. Wang et al. [8] used pillars to sustain the inductor coil to improve the mechanical performance of the suspended inductor. Sagkol et al. [9] studied the self-heating effects in suspended inductors. Lin et al. [10] designed a robust suspended inductor by using a cross-shaped sandwich membrane support. Many contributions have also been made on the modeling and simulation of MEMSs under shock. Corigliano et al. [11] developed a two-dimensional geometrical model for polycrystals by using Voronoi tessellation. Mariani et al. [12] presented a multi-scale, finite element approach to assess the effects of polysilicon morphology on the failure mode of MEMSs under shock. However, these studies focused on MEMSs of polysilicon. Few studies have been completed on the failure analysis of suspended MEMS inductors.
In this investigation, the failure mechanisms of MEMS suspended inductors are studied and shock experiments with a Machete hammer are carried out. First, MEMS suspended inductors are designed and fabricated. Then, a theoretical analysis is performed. Based on the theoretical results, the failure modes and criteria of the suspended inductors are discussed. For the purpose of verification and comparison, shock test experiments are carried out and the results are discussed.
Section snippets
MEMS suspended inductor sample and fabrication
In this study, we chose the 1.5 turns inductor in [13] as the inductor sample. This inductor has a good performance, the inductance is designed as 1.5 nH and the Q factor is higher than 20 at the frequency band of 1–7.6 GHz and reaches 38 at 7.4 GHz. A schematic of the MEMS suspended inductor is shown in Fig. 1 and the geometry parameters of the inductor are shown in Fig. 2.
The MEMS suspended inductors consist of a suspended spiral coil, an insulating layer, pillars (used as electrical ports)
Shock loads and acceleration response of inductor
Shock pulses that occur in actual applications are very complex but they can be considered as a series of simple pulses, such as half-sine waveforms, as widely used in theoretical analysis [14,15]. The half-sine waveform shock pulses can represent shock environments, such as the hammer test, Hopkinson bar and so on, and they can be expressed as:where a0 is the amplitude of the shock and τ is the duration of the shock load. As Fig. 5 shows, various half-sine shock loads can
Shock test and discussion
To verify the theoretical analysis, the MEMS suspended inductors are tested by using a Machete hammer. The test machine is shown in Fig. 14. By changing the lifting height of the hammer, we can obtain different shock load amplitudes. The amplitude of the shock pulses generated by the Machete hammer range from 8500 to 20,400 g and the durations range from 100 to 120 μs.
The suspended MEMS inductors were fabricated on a wafer and the wafer was separated into a number of dies. The size of each die
Conclusions
In this study, we analyze the failure mode of MEMS suspended inductors by theoretical and experimental methods. We combine the SDOF model and the method of solving a statically indeterminate structure to calculate the distributions of the equivalent stress and the deformation of the suspended inductor under shock. According to the theoretical analysis, the criterion for the failure of the suspended inductor under shock is the critical stress and the critical positions of the inductor coil are
Acknowledgments
This work was supported by NSAF (No. U1630119). We thank Chongying Lu and Feng Zhu for their great assistance in experiments and measuring the performances of the inductors.
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