Effects of slots on thermoelastic quality factor of a vertical beam MEMS resonator

Abstract

the resonance occurs in the mechanical domain. MEMS resonators have already started to use in various applications from wrist watches to the state of the art communications, due to their extremely features. However developing a MEMS resonator with high quality factor in MHz frequency ranges, which would be compatible with CMOS integrated circuits (Dragoi et al. 2012) is very important in view of different applications. In integrated circuits, applications such as filters (Bannon et al. 2000;Lopez et al. 2009), timing and reference frequency devices (Lin et al. 2004;Nguyen 2007), microprocessors (Abdelsalam et al. 2010) and sensors such as pressure and humidity sensors (Shi et al. 2013;Muniraj 2011) facing an important challenge either from scientific or engineering viewpoint that must be well addressed. As an important property, Quality factor (Q) is a scaled ratio between stored energy and damped energy per cycle, which is associated with frequency. In a MEMS resonator, Q is an indication of mechanical energy damping in the system that directly influences sensitivity and resolution of the device Hao et al. 2003). Theoretically, quality factor can be calculated for every frequency, whereas in practice, it is obtained for a specific resonance.In a beam type MEMS resonator, to understand and analyze the energy loss mechanisms, it is important to know the sources of energy loss. The latter could be consisted of support loss, thermoelastic loss and surface loss (Hao et al. 2003). Compression and decompression of an oscillating structure results an irreversible heat flow that is called thermoelastic damping (TED). In Clamped-Clamped (C-C) beam MEMS resonator, the beam in bending experiences a variation on temperature which causes a thermal gradient through the beam. The latter should be well adjusted to maintain the thermal equilibrium. To do this, energy must be intelligently dissipated while the quality factor of the Abstract Thermoelastic damping is one of the dominant mechanisms of structural damping in vacuum-operated microresonators. A three dimensional numerical model based on the finite element method is used for simulating thermoelastic damping in clamped-clamped microelectromechanical beam resonators. In this regards, both simple and slotted beam are considered. To understand the effect of slot positions and sizes on the resonator performance, resonant frequency and thermoelastic quality factor are calculated for both simple and slotted beams for a wide range of beam length from 10 to 400 µm. Punching slots in the resonator beam reduces the stiffness and mass of the beam which affect the resonant frequency. In addition thermomechanical coupling mechanisms of the resonator are affected by the slots which improve the thermoelastic quality factor. For most of the beam lengths, it is shown that the slots at the beam-anchor interface region, where the strain is high, are more effectively enhanced the thermoelastic quality factor than one at the centre of the beam region. However, the highest resonance frequency i...

Vibrational and thermoelastic behavior of punched-beam micro resonators containing odd-number of slots

“…Lengths of the beams are considered to be 30.5 µm, 100 µm, and 400 µm. The place of two outer slots (L as ) is determined based on results of Asadi and Sheikholeslami, 26 where Q TED achieves its maximum amount. The length of these two outer slots (L s1 ) is considered to be 0.1 L b , because for this length, the Q TED increases and the reduction of f res is not a lot.…”

“…Their analysis led to an expression for TED in the form of rapidly converging infinite series. Asadi and Sheikholeslami 26 by punching two slots in C–C beam MEMS resonators studied variations of the Q TED and the resonant frequency ( f res ) versus slot places for different slot lengths in 3D case. Their results showed that there are three critical points for f res and Q TED in a C–C beam MEMS resonator, one point is in the middle of the beam and two points are at the anchor-beam interfaces.…”

“…The previous studies have presented variations of the f res and the Q TED versus slot positions and have shown the places where the f res and the Q TED are maximum or minimum. In this work based on the previous work of authors, 26 by using 3D simulations (in COMSOL Multiphysics), three slots have been punched together in the critical points of C–C beam resonators in order to increase both f res and Q TED . Also, in order to study the effects of distribution of the slots along the beam length on the Q TED and f res , at places where strain is low, five slots have been punched in the beam.…”

Analysis of Frequency Stability and Thermoelastic Effects for Slotted Tuning Fork MEMS Resonators

“…Having shown how to minimize the by adjusting the orientation of the resonator with respect to the silicon wafer and the doping level, the main goal of this section is to point-out a good strategy to maximize the quality factor of the MEMS resonator. Since it is known from the literature (see e.g., [ 20 , 21 , 22 , 23 ]) that slots may significantly reduce the thermoelastic damping, we now focus on the new model-geometry for a SETF depicted in Figure 9 . Clearly, a multiplicity of slots could be included in the model, but the potentialities of the proposed approach are better put in evidence with a single one.…”

“…However, the rather low thermoelastic quality factor is a strong limit for practical applications. A known strategy for improving Q consists in adding slots along the beams to reduce heat conduction (see [ 20 , 21 , 22 , 23 ]). Regrettably, slots may also sensibly increase the frequency drift in temperature.…”