Micro mechanical devices

Active Frequency Tuning of Microresonators

 

Richard Syms

We have developed a simple method for active frequency tuning of microresonators, based on the use of constrained thermal expansion. A small current is passed through the suspension of the microresonator, so that the suspension is locally heated. The remainder of the structure then exerts a stress on the suspension, which alters its stiffness. A simple model has been developed to predict the power sensitivity obtained with folded and unfolded geometries, including the effects of electrothermal heating, and conduction and convection cooling. We have shown that shown the sensitivity of folded structures can change sign as the ambient gas pressure is lowered, in contrast to the behaviour of unfolded structures. Tuning is then by tensile axial stress rather than compressive stress. Using folded, laterally-resonant, bulk micromachined comb-drive electrostatic actuators, we have obtained tuning ranges of -25% and +50% (at atmospheric pressure and at 10 mT, respectively, with powers of 10 mW and 1.5 mW, respectively). We have also developed a nested coupled resonator, in which the frequency of one resonator may be tuned without effecting that of the other, allowing frequency matching to be obtained.
 
Arrangement for electrothermal
Arrangement for electrothermal tuning of single-axis resonator.
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Variation of resonant frequency
Variation of resonant frequency with tuning power, at different external gas pressures.
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Bulk-micromachined Thermo-hydraulic Microactuator

 

Jun Su Lee and Stepan Lucyszyn

Paraffin wax exhibits a volumetric expansion of ~15%, at around its melting point. A high performance bulk-machined hydraulic electrothermal microactuator activated using paraffin wax has been fabricated. As applications, the actuators have been applied to Braille cells, microfluidic valves, microgripper and micropipette. The paraffin wax is contained within a bulk micromachined silicon container. The container is sealed using an elastic diaphragm of PDMS. The container is heated using gold microheaters located on an underlying glass substrate. All the layers used to make up the containers are bonded together using an overglaze paste and PDMS. The all application devices were successfully operated at around 10 or 15 V.

 
Expanded structure of the basic bulkmicromachined actuator, and cross section of the actuator.
Expanded structure of the basic bulkmicromachined actuator, and cross section of the actuator.
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Assembled devices: (a) microvalve, (b) micropipette, (c) microgripper of type A and (d) type B.
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Electrostatic and Mechanical Modelling of Electroformed Structures

 

Andrew Holmes, Kin Wei Lee

Resist moulds formed by UV lithography generally have sloping sidewalls, which are transferred to electroplated structures. As a result key elements in resonant electrostatic devices, such as support beams and comb-drive electrodes, are trapezoidal rather than rectangular in cross-section. We have investigated the effects of non-vertical sidewalls on the mechanical constants of nickel beams, and on the performance of electrostatic comb-drives. In the former case, the effect is to reduce the torsional stiffness of the beam. In the latter, asymmetry of the fringing fields above and below the electrodes, and in the field in the gap, causes out-of-plane actuation forces to arise. These may be used to excite torsional motion in suspensions normally driven in-plane. The figures below show the variation of the normalised torsional stiffness, and the vertical force, with wall angle in trapezoidal cross-sections.

 
Trapezoidal features in a typical torsional mirror microstructure.
Trapezoidal features in a typical torsional mirror microstructure.
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Variation with wall angle
Variation with wall angle of a) the normalised torsional stiffness kt x L/a3bG (where L = beam length, and G = shear modulus), and b) out-of-plane electrostatic force (with a = 15 microns, b = 4 microns, and minimum gap = 4 microns).
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Improved Design of Micromachined Lateral Suspensions using Intermediate Frames

 

Tom Pike and Sunil Kumar

Lateral suspensions are one of the most common types of structures used in MEMS devices. We have performed the first complete analysis of the translational and rotational modes of a model lateral suspension. The derived formulas quantify spurious-mode resonant frequencies for cross-axis translation and rotation, and on-axis translation, and can provide very simple expressions for the rejection ratios in terms of the geometry of the suspensions. It is shown that the introduction of intermediate frames, coupling equivalent points of the lateral suspension either side of the suspended mass, can provide much improved dynamics.

 
A lateral suspension incorporating an intermediate frame
A lateral suspension incorporating an intermediate frame
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Below are shown how the rejection ratio falls off rapidly for all the off-axis modes as more folded cantilevers are added to the suspension without frames, while with frames the rejection ratio is maintained.

 
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To investigate the derived relationships suspensions have been fabricated using through-wafer deep reactive-ion etching (DRIE). Using analysis of the suspension dynamics under the rastered beam of a scanning electron microscope, the various modes of the suspension have been visualized and quantified. These observations are in good agreement with the derived formulas, taking into account the actual profile of the beams fabricated in DRIE. Further finite element analysis across a broad range of suspensions is consistent with the derived formulas. A design heuristic is provided for rapidly optimizing micromachined lateral suspensions by incorporating intermediate frames.

Micro Dynamics

 

Richard Syms, Ty Harness

The dynamics of single-axis resonant comb-drive microactuators are well understood. They consist of a single dominant mass - the moving half of the electrode and its supporting shuttle - suspended on elastic flexures and constrained to move along a single axis. Due to the span of the electrode, its mass is distributed, but the shuttle is designed to be sufficiently rigid that the assembly can be considered a pointlike mass for in-plane motion. The suspension is often small enough compared with the shuttle that it can be considered massless. More complicated behaviour is expected in multi-axis stages, since these contain several masses, independently suspended but linked by coupling beams. Conseqently they are multi-DOF systems even for in-plane motion. We have carried out detailed investigation of x-y stage dynamics, using a combination of analytic theory, finite element modelling and experiment. Good agreement has been obtained between the predictions of simple coupled-mode models and finite element modelling using the commercial FEM package ANSYS.
 
 56521
 Bulk micromachined x-y stage.
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56522
CAD layout of 2-axis comb-drive electrostatic microactuator.
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56523
ANSYS plot of lowest order hybrid resonant mode of 2-axis microresonator.
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Passive Frequency Tuning of Microresonators

 

Richard Syms, David Moore (Cambridge University)

Vibrating resonators are important components of micromechanical systems, with applications in sensors and actuators. However, defects and stresses can cause resonance shifts, and it is important to develop methods of tuning. Active tuning is based on electrically-induced stress. We have developed simple electrothermal tuning methods, and have used them to demonstrate wide-range, reversible tuning of single resonators (up to 50% change in resonant frequency), and also independent frequency tuning and matching of coupled resonators.

 
56512
In-plane microresonator, after FIB tuning.
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Passive methods are based on dimensional trimming, and are potentially more economic, since they avoid the need for control circuitry. However, care is needed to optimise the tuning process. We have demonstrated precise tuning of in-plane microresonators by using focused ion beam (FIB) micromachining to remove material at the roots of flexure suspensions, and hence effectively lengthen the flexures.

 
56514
Layout of in-plane microresonator.
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56516
Frequency response, before and after FIB micromachining.
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Silicon Electrostatic Microactuators

 

Richard Syms, Ty Harness, Ron Lawes (Rutherford Appleton Laboratory) 

Because electrostatic forces scale relatively advantageously with reducing size, electrostatic actuators are promising alternatives to electromagnetic devices in the microstructure size domain. Silicon-based surface micromachined actuators have already been demonstrated, using polysilicon mechanical parts on a silica sacrificial layer. We have developed an alternative fabrication process, based on bulk micromachining of silicon. A 7 microns deep p+ etch stop layer is first formed by boron ion implantation and diffusion into an n-type wafer. This layer is then patterned with a Cr metal mask, and reactive ion etching is used to transfer the pattern through the etch stop layer. A wet chemical etch (EDP) is then used to remove bulk silicon to a considerable depth (100 microns) beneath the mechanical parts, to create an undercut structure that is free to move on a flexure suspension system. Mechanical motion is obtained by applying electrostatic forces through pairs of comb-drive electrodes, using electrode isolation provided by inbuilt p-n junction diode structures. Single-axis devices have been constructed which have displacements as large as 20 microns at resonance, using drive voltages of ~15 V.

 
56505
Bulk micromachined electrostatic microactuator.
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56507
Detail of comb electrodes.
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56508
View of comb electrodes in motion.
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