Higher-mode free-free beam micromechanical resonators

Abstract

However the need for further size reduction to attain even higher frequencies can conjure up scaling-induced problems [6], such as higher motional impedance and greater susceptibility to contaminants. To avoid these limitations, a method for raising frequency without the need for excessive scaling is desired.Pursuant to reducing the amount of size reduction needed for increasing frequency, this work investigates higher-mode operation of vertical free-free beam micromechanical resonators. With larger dimensions than previous fundamental-mode counterparts at the same frequency, and with slightly higher Q's (as will be seen), these higher-mode free-free beam resonators provide several key advantages over the former, including (1) lower series motional resistance R x ; (2) higher dynamic range and power handling; and (3) multiple ports that permit the 0 o input-to-output phase-shift often preferred for high impedance micromechanical oscillators and invertible bandpass mixer-filters targeted for wireless applications. This paper first develops a complete model for design and simulation of higher-mode freefree beam micromechanical resonators in Sections II and III,

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“…This last device is similar to the one presented in [8], but in that case the matched supports were torsional rods.…”

Mechanical Vibrations of Thermally Actuated Silicon Membranes

“…Even though these outputs will provide information on the vibrating behavior of the structures, they do not provide information on the shape of the structure during this vibration. In some cases this is not important as the vibration behavior is still affected by what is being measured [8]. In other applications, such as in rheology, the vibrating shape is important to determine the effectiveness of the measurement technique.…”

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“…In equation form, assuming identical resonators, the equivalent motional resistance of the array is given by (35) From a parameter perspective, when a number of these resonators are coupled into an array, the overall effective electrode area increases by a factor of . From (22)- (25) in Section III, since an increase in the electrode-to-resonator overlap area always leads to an increase in power at the third-order input intercept point , this arraying strategy reduces series motional resistance without degrading linearity. This is in contrast to other available approaches to lowering , such as reducing the electrode-to-resonator gap spacing , raising the effective permittivity , or raising the dc-bias , all of which eventually begin to degrade the .…”

“…Inserting (19) into (20) and assuming that or (which is the case, here), a compact expression for can be written as the "parallel" combination of several power terms (22) where and are terms emanating from nonlinear voltage and displacement interactions, given by (23) (24) and derives from purely nonlinear displacement interactions, and is given by (25) Each of the previous terms competes to constrain the , and each will surface as the dominant constraint over different parameter spaces. For example, for large values of , the term is often the smallest of the three terms, so dominates over the other terms to constrain the .…”