Comb-drive resonator

We can estimate the mass of the released elements by considering the shuttle mass and support beams to be concentrated at one point. The mass of the eight polysilicon support beams would be 

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Lay out a comb-drive resonator in the Poly MUMPS process using L-Edit in MEMS Pro as shown in Figure 2.20. Use the Polyl layer (h = 2 pm) for fabrication of the comb-drives and folded springs. 

Calculate the resonant frequency for the comb-drive resonator in Problem 1 above. 

The comb-drive resonator shown in Figure 3.7 is a common device in surface micromachining processes [4]. We will estimate the resonance frequency by calculating the spring constant of the folded spring and the mass of the released elements that are driven into resonance by electrostatic actuation. 

Often the supplier will include one of their own test structures in the customer s layout space. For example the PolyMUMPs die will have a comb-drive resonator added into the layout after the customer turns it in, so long as they have followed the design guidelines that specify leaving a space on the layout for the inclusion of the comb-drive resonator. The comb-drive can be inspected for the fidelity of the patterning since the combs of the comb-drive use the minimum space to achieve the maximum force. The comb-drive can also be driven into electrical resonance by the application of the appropriate biasing conditions [3]. 

The comb drive microresonator used for this study is shown in top and side view in Fig. 1. The main components of the resonator are a shuttle structure comprised of the connected back-to-back combs, two suspended folder beams with one end anchored to the substrate, and fixed comb drives. Table 1 lists some key dimensions of the resonator. 

An example of the library elements for active elements, passive elements, and resonator elements is shown in Figure 1.26. This library includes shuttle plates, folded springs, rotary torsional springs, linear comb-drives and rotary comb-drives, rotary motors, and test circuits. Having these standard components available at the click of a mouse can significantly accelerate layout. 

W.C. Tang, T.-C.H. Nguyen, M.W. Judy, and R.T. Howe, Electrostatic-comb drive of lateral polysilicon resonators, Sensors and Actuators A21-23,... 

Starting from the analytical description, we can create a first rough design of the sensor system, including the resonant frequencies for drive and detection and the sizes of the sensing element, the electrostatic comb structures, and the detecting capacitors. While this work is done, the physical properties of the technology already have to be considered. 

The mechanical resonance frequency is mainly determined by the masses and the coupling stiffness between the masses, here 6 kHz. For the detection an acceleration sensor is placed on each of the two masses, arranged in a comb structure by surface micromachining. The drive works electrodynamically. A permanent magnet causes a magnetic field vertical to the surface of the sensor element. Conductors on the masses, stimulated by an electrical current, experience a Lorentz force, which drives the masses. 

Figure 18.14(a) shows a schematic of the electrostatically driven mirror with two directions of deflection. The fast moving mirror is fixed by torsion springs at a gimbal and is excited to oscUlate by an electrostatic drive, realized by stacked comb electrodes. The gimbal itself is also fixed by torsion springs to the MEMS chip and is excited to oscillate more slowly to perform the vertical sweep. In one of the test designs realized in the author s lab, the mirror has a diameter of 0.9 mm and oscillates in resonance with 32 kHz as fast axis frequency and with 0.6 kHz as slow axis frequency. 

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