B. Krijnen

A single-mask thermal displacement sensor in MEMS

This work presents a MEMS displacement sensor based on the conductive heat transfer of a resistively heated silicon structure towards an actuated stage parallel to the structure. This differential sensor can be easily incorporated into a silicon-on-insulator-based process, and fabricated within the same mask as electrostatic actuators and flexure-based stages. We discuss a lumped capacitance model to optimize the sensor sensitivity as a function of the doping concentration, the operating temperature, the heater length and width. We demonstrate various sensor designs. The typical sensor resolution is 2 nm within a bandwidth of 25 Hz at a full scale range of 110 μm.

Flexures for large stroke electrostatic actuation in MEMS

The stroke of a microelectromechanical systems (MEMS) stage suspended by a flexure mechanism and actuated by electrostatic comb-drives is limited by pull-in. A method to analyze the electrostatic stability of a flexure mechanism and to optimize the stroke with respect to the footprint of flexure mechanisms is presented. Four flexure mechanisms for large stroke are investigated; the standard folded flexure, the slaved folded flexure, the tilted folded flexure and the Watt flexure. Given a certain stroke and load force, the flexures are optimized to have a minimum wafer footprint. From these optimizations it is concluded that the standard folded flexure mechanism is the best flexure mechanism for relatively small strokes (up to ±40 μm) and for larger strokes it is better to use the tilted folded flexure. Several optimized flexure mechanisms have been fabricated and experimentally tested to reach a stroke of ±100 μm. The displacement of the fabricated stages as a function of the actuation voltage could be predicted with 82% accuracy, limited by the fairly large tolerances of our fabrication process.

Deflection of an eccentric tooth of a comb drive in an electrostatic field

The elastic deflection of a comb drive tooth in an electrostatic field is considered. The tooth can be symmetrically located between two rigid teeth of the matching comb, in which case the problem reduces to a pure bifurcation problem for which the critical voltage can be determined. Alternatively, due to an ap- proximate straight-line mechanism, the tooth can have a uniform initial lateral displacement and a smooth curve of equilibria is found which has a limit point, after which pull-in occurs. An assumed deflection shape and a series expansion of the electrostatic capacity yield the deflection curves for the case with a uniform initial lateral displacement. This shows that pull-in occurs at a voltage that is reduced by a factor that is about pro- portional to the two-third power of the relative lateral initial dis- placement. The theoretical results have been experimentally tested. The results show a qualitative agreement, but the experimental de- flections are larger and the pull-in voltages are lower. These differences can be explained from neglected fringe fields and de- viations from the nominal shape.

A Large-Stroke 3DOF Stage With Integrated Feedback in MEMS

In this paper, we design, fabricate, and validate a large-stroke 3-degree-of-freedom (DOF) positioning stage with integrated displacement sensors for feedback control in a single-mask microelectromechanical systems (MEMS) fabrication process. Three equal shuttles exactly define the position of the stage in x, y, and Rz. The kinematic relation between the shuttle positions and the stage position is given by the geometric transfer function. By increasing the order of this geometric transfer function, the stage error can be reduced. Each shuttle consists of a flexure mechanism, a position sensor, and electrostatic comb drive actuators for actuation along a straight line. The range of motion of the stage is limited by electrostatic pull-in of these comb drives. Three parameters of the stage, the leafspring length, the eccentricity, and the tangential arm, have been varied to find their influence on the stage range of motion. These simulation results can be used to design stages with different specifications. Position control of the individual shuttles is applied to control the position of the stage. The stroke of the 3DOF stage is verified up to 161 μm in x, 175 μm in y, and 325 mrad in Rz. This exceeds the range of motion of existing stages.

Deflection and Pull-In of a Misaligned Comb Drive Finger in an Electrostatic Field

The elastic deflection of a comb drive finger in an electrostatic field is considered. The finger can be symmetrically located between two rigid fingers of the matching comb, in which case the problem reduces to a pure bifurcation problem for which the critical voltage can be determined. Alternatively, due to the nonlinear motion of an approximate straight-line guidance mechanism, the base of the finger can have a lateral and angular displacement, which results in a smooth curve of equilibria with a limit point, after which pull-in occurs. An analytic model is derived, which is validated by 2-D and 3-D finite-element analyses and experiments. For the analytic model, an assumed deflection shape and a series expansion of the electrostatic capacity yield the deflection curves. This shows that the pull-in occurs at a voltage that is reduced by an amount that is about proportional to the two-third power of the relative base displacement. The theoretical results for the case of a lateral base displacement have been experimentally tested. The results show a qualitative agreement with the analytic model, but the experimental deflections are larger and the pull-in voltages are lower. The finite-element analyses show that these differences can be explained from neglected fringe fields and deviations from the nominal shape.

Erratum to “A Large-Stroke 3DOF Stage With Integrated Feedback in MEMS”

In the above paper [1] , references [32]–[38] were inadvertently removed and are as follows.