4. Conclusion

This chapter has reviewed the basic mechanisms behind electrostatic MEMS comb-drives. The design and simulation of comb-drive actuators incorporating gray­scale technology to tailor actuator properties (without increasing the device footprint) was presented using both analytical approximations and finite element analysis (in FEMLAB).

Multiple comb-drive actuators with reduced height comb-fingers and suspensions were then fabricated and tested to experimentally confirm the predicted behavior of improved resolution and reduced driving voltages. Specifically, for variable height comb-fingers, the displacement resolution at 20^m was improved from 344nm/V to 227nm/V with little effect on resolution at smaller displacements. On a separate device, suspension spring constants were reduced from 7.7N/m to 2.3N/m to enable lower driving voltages, achieving >3 times the deflection at 100 V.

These results have clearly illustrated the value of using gray-scale technology within electrostatic MEMS actuators to modify device behavior without increasing overall actuator footprint. Measurements of static and dynamic actuator behavior confirm that our FEA model and iterative displacement calculation techniques are able to accurately predict 3-D actuator behavior. These results serve as the foundation for developing the tunable resonator devices presented in Chapter 4, as well as for the optical fiber alignment systems developed in Chapters 5 and 6.

CHAPTER 4: VERTICALLY-SHAPED TUMABLE MEMS RESONATORS

1. Introduction

Micromechanical resonators have received significant attention over the past 20 years due to their applications in thin film characterization [138], signal processing (RF and IF filters) [65, 67, 139], gyroscopes [68], electrostatic charge and field sensors [69], mass sensors for bio-chemical sensing [140], and vibration-to-electric energy conversion [141-144]. Laterally driven comb-resonators are often preferred due to their reduced damping and large travel range [49]. Vacuum sealing techniques have been used to increase the quality (Q) factor of comb-resonators to >2,000 in some cases [67].

This chapter is devoted to presenting an additional important application for the variable-height comb-drive structures presented in Chapter 3: voltage-tunable MEMS resonators. Previous MEMS tuning methods will be reviewed briefly, and the principle of vertically-shaped gray-scale electrostatic springs is introduced as a tuning mechanism. Design and simulation of vertically-shaped comb-fingers as electrostatic springs will be followed by testing results that demonstrate their bi-directional tuning capability of MEMS resonators in the 2 kHz range.

2. Tunable mems Resonator Operation

Since the inception of MEMS resonators, as far back as 1967 [70], the natural progression has been towards developing tunable resonators for use in tunable filters and other frequency dependent applications. The most popular technique is the use of an additional electrode beneath a suspended cantilever, as shown in Figure 4.1, to tune the resonant frequency down [66, 70-72, 139]. The situation can be best described using the where k_eff is the effective spring constant, k_mech is the mechanical spring constant, z is the deflection magnitude, and C and V are the capacitance and voltage on the tune electrode, respectively. Assuming the voltage is constant, taking the 2^nd derivative of Equation 49 yields an expression for keff, where the second term represents an electrostatic spring ^(kelec^):

For the cantilever example in Figure 4.1, C can be approximated as a parallel-plate capacitor using the electrode area (A), gap (d), and dielectric constant of air (e₀):

^ ^£₀ A

ELECTROSTATIC MEMS ACTUATORS USING GRAY-SCALE TECHNOLOGY 1

Brian Carl Morgan, Doctor of Philosophy, 2006 1