Measuring and testing – Surface and cutting edge testing – Roughness
Reexamination Certificate
2000-06-05
2002-12-24
Larkin, Daniel S. (Department: 2856)
Measuring and testing
Surface and cutting edge testing
Roughness
C310S309000
Reexamination Certificate
active
06497141
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates, in general, to microelectromechanical (MEM) structures, and particularly to sensors, filters, switches and the like which utilize variable capacitors for driving and for measuring displacement, as well as to circuitry for measuring output signals produced by such capacitors and for producing drive signals at frequencies selected to produce parametric resonances having sharp transitions between stable and unstable motion of MEM structures.
The generic term “microelectromechanical system” (or MEMS) has been applied to the broad field of micromachining and refers to structures such microsensors, microactuators, microinstruments, microoptics, and microfluidics. The applications of these devices are wide-ranging and include accelerometers, which may be used, for example, to deploy automobile airbags, inkjet printer heads and other fluidic devices, arrays of movable mirrors for color projection displays, atomic probes for imaging and transporting atoms, and the like. MEMS devices typically use silicon as a structural material, with the devices being fabricated using integrated circuit technology and more particularly using the single crystal reactive etch and metalization (SCREAM) process which is described, for example, in U.S. Pat. No. 5,719,073, issued Feb. 17, 1998, the disclosure of which is hereby incorporated herein by reference.
Although the use of MEM systems is becoming widely accepted, these micrometer-scale devices present challenges in the real time measurement of device motion, for such devices exhibit multiple modes of motion, have nonlinearities in their spring constants and damping, and exhibit other deviations from the simple models which are often used to describe the motion of mechanical structures. Precise real-time measurements of these devices are needed to understand, to model, and to control these effects. The measurement of device motion and parameters at the nanometer-scale has been done using microinstrumentation fabricated on the same chip as the test devices through the use of variable capacitor motion sensors. However, the use of variable capacitors to measure motion assumes the capacitor structure is stable throughout the measurement; that is, that the gap remains constant and the capacitor electrodes do not rotate or move in a direction perpendicular to the direction of the desired motion to be measured.
One reason for the difficulty in measurements is that in many resonant microelectromechanical systems with electrostatic actuation, the application of a voltage to the device for driving it or for measuring changes in capacitance, changes the effective stiffness of the system. In certain systems, the application of a periodic voltage causes the stiffness to be changed periodically. The equation of motion for such a system is the Mathieu equation:
ⅆ
2
θ
ⅆ
τ
2
+
(
β
+
2
δ
cos
2
τ
)
θ
=
0
Mathieu equation has been studied extensively in many physical contexts because it governs the pumping of a swing, the stability of ships and columns, Faraday crispations in surface waves on water, electrons in Penning traps, and parametric amplifiers based on electronic or superconducting devices. Many theoretical studies have been carried out on the Mathieu equation, but most of them have been macroscopic, and in these cases damping limits the obtainable experimental results.
SUMMARY OF THE INVENTION
The present invention is directed to MEM structures which may be parametrically driven to provide stable operation and to permit precise switching between stable and unstable operations by very small changes in the drive frequency or by very small changes in the characteristics of the structure itself so as to provide improved control and sensing. Although the techniques of the present invention are applicable to a wide variety of microstructures, including parallel plate linear actuators, reduction and augmentation actuators, and linear force comb actuators, the invention will be described herein in terms of torsional devices, and in particular to torsional scanning probe z-actuators having an integrated tip, such as the device described in the above-mentioned U.S. Pat, No. 6,000,280. This device is a micromechanical torsional resonator which incorporates capacitive actuators, or drivers, for producing mechanical motion, and more particularly is a structure which incorporates an improved comb-type actuator structure which consists of high aspect ratio MEM beams fabricated as interleaved fixed and movable capacitor fingers. The device is fabricated from single-crystal silicon and includes a cantilevered beam connected to an adjacent substrate by a torsion bar, within an atomically sharp tip formed on the beam. The capacitive actuator structure can be used either for sensing displacements or inducing motion, the capacitive plates of the fixed and movable fingers allowing a wide range of motion and high amplitudes without failure. This type of actuator generates out of plane motion forces between the fixed and movable fingers due to a phenomenon known as comb-drive levitation, wherein a voltage is applied to the fixed electrodes on the silicon substrate, while the substrate and the adjacent movable electrodes are grounded. This causes asymmetrical fringing electric fields between the movable and fixed electrodes which induce motion in the movable electrodes. Such a micromechanical torsional resonator obeys the Mathieu equation:
(&thgr;″+
a
&thgr;′+(&bgr;+2&dgr; cos 2&tgr;)&thgr;=0
where
a=c/
2
&ohgr;I
&bgr;=(
k+&ggr;A
DC
)/4&ohgr;
2
I
and
&dgr;=(&ggr;
A
AC
)/4&ohgr;
2
I
where I is the mass moment of inertia of the torsional cantilever, c is the torsional damping constant, k is torsional stiffness, and M is the applied torque, &ggr; is a parameter that corresponds to the drive strength, &ohgr; is the driving frequency, and A is the input strength under normal operation.
It has been found that such a MEM resonator exhibits unique stability properties, wherein multiple regions in the &bgr;-&dgr; parameter space have unstable solutions so that the resonator exhibits resonance-like behavior under several different conditions. The boundaries between these conditions of instability and regions where stable behavior is exhibited are extremely sharp so that a very small change in the frequency of a drive signal and, the characteristics of the MEM device, or a change in a parameter being measured can switch the vibrational motion of the MEM device from a stable to an unstable condition, or vice versa. It has been found that a to frequency change of as little as 0.001 Hz at 114 kHz in the drive signal can effect this change.
When operating in an instability region, the MEM devices of the invention provide increased sensitivity to changes in measured parameters, such as force measurements in an atomic force microscope (AFM). For example, in conventional atomic force microscopes, a high Q in the sensor device leads to higher sensitivity, but at the expense of bandwidth. By utilizing the parametric resonance instability of the present invention, the effect of Q can be decoupled from sensitivity. Further, since the device has such a high sensitivity to changes in frequency between its stable and unstable vibratory conditions, a small force; i.e., the force to be measured, applied to the MEM device can change its characteristics and cause it to “jump” across the boundary from an unstable to stable condition. Because the boundary is so sharp, very small force interactions can be measured. The forces being measured in such a device manifest themselves as changes in the torsional stiffness k of the device. Thus, a change in k will shift the position of the sharp boundary, changing the state of the resonator from “on” to “off”, or vice versa. In addition, small changes in the voltage or frequency can be used independently to move the operating state from stable
MacDonald Noel C.
Turner Kimberly L.
Cornell Research Foundation Inc.
Jones Tullar & Cooper P.C.
Larkin Daniel S.
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