Suppression of thermoelastic damping in MEMS beam resonators by piezoresistivity

Microelectronic mechanical (MEM) beam resonators with high quality factors are always preferred in practical applications. As one of the damping sources, thermoelastic damping (TED) caused by irreversible heat flows is usually considered as an upper limit of the overall damping effect. A new method is proposed in this work to compensate TED by taking advantage of the piezoresistive effect. Such a method is implemented by applying an electrostatic field along the beam length with a negative piezoresistive coefficient. During a resonance, the stretched part of the beam generates a higher electrical power density and thus a higher temperature, while the compressed region leads to a lower temperature. Such a temperature distribution is opposite to the temperature change caused by the thermoelastic effect. The working principle is described by a set of coupled differential equations, which are subsequently solved by the finite element method. The result indicates that the TED in the beam resonators can be completely compensated when the strength of electrical field is tuned to a critical value, namely CEF. The value of the CEF is further analyzed by a series of parametric studies on various material properties and geometric factors. Silicon microelectronic mechanical (MEM) beam resonators are being developed aggressively for a variety of applications nowadays, such as sensing [1–3], time application and frequency controls [4,5] due to their advantages of high frequency and high quality factor. The miniaturized scale is also capable of batched fabrication for cost reduction. As one of the most important design characters, a high mechanical quality factor (i.e. Q-factor or Q-value) or less energy loss in a resonator means a better precision to operate as a sensor or a frequency filter. Therefore, it is of great importance to understand the dominating energy loss in the mechanical vibration to identify those factors that impose an upper limit of the Q-value and those factors that could be eliminated to improve the design. The dominant mechanisms from which the resonator dissipate energy include air damping, support loss [6,7] and thermoelastic damping (TED) [8–14]. Among them, air damping can be eliminated by packaging in vacuum because of the small size of the devices. But the support loss and TED can impose an upper limit on the design of micro resonators with high quality factors. In vibrations of resonators, the non-equilibrium state of the temperature field is generated by the change of the strain field. Hence, the irreversible …