Study of lateral mode SOI-MEMS resonators for reduced anchor loss

MEMS resonators fabricated in silicon-on-insulator (SOI) technology must be clamped to the substrate via anchoring stems connected either from within the resonator or through the sides, with the side-clamped solution often employed due to manufacturing constraints. This paper examines the effect of two types of commonly used side-clamped, anchoring-stem geometries on the quality factor of three different laterally-driven resonator topologies. This study employs an analytical framework which considers the relative distribution of strain energies between the resonating body and clamping stems. The ratios of the strain energies are computed using ANSYS FEA and used to provide an indicator of the expected anchor-limited quality factors. Three MEMS resonator topologies have been fabricated and characterized in moderate vacuum. The associated measured quality factors are compared against the computed strain energy ratios, and the trends are shown to agree well with the experimental data. © 2011 IOP Publishing Ltd.

Direct parameter extraction in feedthrough-embedded capacitive MEMS resonators

This paper presents a method for fast and accurate determination of parameters relevant to the characterization of capacitive MEMS resonators like quality factor (Q), resonant frequency (fn), and equivalent circuit parameters such as the motional capacitance (Cm). In the presence of a parasitic feedthrough capacitor (CF) appearing across the input and output ports, the transmission characteristic is marked by two resonances: series (S) and parallel (P). Close approximations of these circuit parameters are obtained without having to first de-embed the resonator motional current typically buried in feedthrough by using the series and parallel resonances. While previous methods with the same objective are well known, we show that these are limited to the condition where CF ≪ CmQ. In contrast, this work focuses on moderate capacitive feedthrough levels where CF > CmQ, which are more common in MEMS resonators. The method is applied to data obtained from the measured electrical transmission of fabricated SOI MEMS resonators. Parameter values deduced via direct extraction are then compared against those obtained by a full extraction procedure where de-embedding is first performed and followed by a Lorentzian fit to the data based on the classical transfer function associated with a generic LRC series resonant circuit. © 2011 Elsevier B.V. All rights reserved.

A moving-coil designed micro-mechanics tester with application on MEMS

A moving-coil designed micro-mechanics tester, named as MicroUTM (universal testing machine), is in-house developed in this paper for micro-mechanics tests. The main component is a moving coil suspended in a uniform magnetic field through a set of springs. When a current passes through the coil, the electromagnetic force is proportional to the magnitude of the current, so the load can easily be measured by the current. The displacement is measured using a capacitive sensor. The load is calibrated using a Sartorius BP211D analytical balance, with a resolution/range of 0.01 mg/80 g or 0.1 mg/210 g. The displacement is calibrated using a HEIDENHAIN CT-6002 length gauge with an accuracy of +/- 0.1 mu m. The calibration results show that the load range is +/- 1 N and the displacement range is +/- 300 mu m. The noise levels of the load and displacement are 50 mu N and 150 nm, respectively. The nonlinearity of the load is only 0.2%. Several in-plane load tests of the MEMS micro-cantilever are performed using this tester. Experimental results, with excellent repeatability, demonstrate the reliability of the load measurement as well as the flexible function of this tester.

Deflections and curvatures of a film-substrate structure with the presence of gradient stress in MEMS applications

The close form solutions of deflections and curvatures for a film-substrate composite structure with the presence of gradient stress are derived. With the definition of more precise kinematic assumption, the effect of axial loading due to residual gradient stress is incorporated in the governing equation. The curvature of film-substrate with the presence of gradient stress is shown to be nonuniform when the axial loading is nonzero. When the axial loading is zero, the curvature expressions of some structures derived in this paper recover the previous ones which assume the uniform curvature. Because residual gradient stress results in both moment and axial loading inside the film-substrate composite structure, measuring both the deflection and curvature is proposed as a safe way to uniquely determine the residual stress state inside a film-substrate composite structure with the presence of gradient stress.

Stability and bifurcation behaviour of electrostatic torsional NEMS varactor influenced by dispersion forces

The influences of Casimir and van der Waals forces on the nano-electromechanical systems (NEMS) electrostatic torsional varactor are studied. A one degree of freedom, the torsional angle, is adopted, and the bifurcation behaviour of the NEMS torsional varactor is investigated. There are two bifurcation points, one of which is a Hopf bifurcation point and the other is an unstable saddle point. The phase portraits are also drawn, in which periodic orbits are around the Hopf bifurcation point, but the periodic orbit will break into a homoclinic orbit when meeting the unstable saddle point.