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Calculation of deflection and mechanical stresses in plates of therectangular form by variational and numerical methods [for pressuresensor design]
Abstract
The influence of tensile and compressive in-plane stresses of silicon plates are investigated. The cases of square and rectangular shaped elastic elements are considered. It is shown that in-plane stresses can have a great influence on plate deflection and stress distribution, and should be taken into account when designing piezoresistive pressure sensors
This paper gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The bibliography at the end of the paper contains more than 1330 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1999-2002.
A CMOS stress sensor is merged with a delta-sigma modulator to produce a sensor with a low frequency RF output. A PMOS current mirror with two orthogonal transistors is used as the stress sensor. The delta-sigma modulator generates an output signal that can be processed digitally or monitored by a communications receiver. The frequency shift of the DSBSC output of the modulator is directly proportional to the stress induced mismatch in the sensor cell. A test chip demonstrating the sensor has been fabricated using the 1.5 mum MOSIS CMOS process.
The results of elastic element (EE) modeling by the Ritz
variational method (RVM) for the silicon pressure sensors are compared
with the results by the finite element method (FEM) using program
package such as ANSYS. The influence of types of the shape functions in
RVM for the analysis of the deflection and stress distributions on
rectangular diaphragms is studied for 1⩽m⩽5 where size ratio
m=a/b. The comparison of calculated results of the deflection and stress
distribution by RVM with those by FEM shows little difference for m=1,
but for m>2 all kinds of the shape functions give errors, for example
with Hermite polynomials, such as a saddle form on deflection
distribution. For m⩽2 the difference by the two methods is less than
10%. For the evaluation of displacement of piezoresistors at the most
interesting points on the diaphragm, the RVM shows that the deflection
and stress distribution can be estimated easily and accurately
This paper discusses some factors which affect the dimensional limits of miniature piezoresistive catheter pressure sensors, analyses the influence of silicon wafer thickness and piezoresistor area dimensions on the sensitivity of the sensor on the basis of the mechanism of anisotropic etching of (100) silicon and the stress-distribution curve of a rectangular silicon diaphragm, and presents the design, process and passivation technology of a miniature piezoresistive catheter pressure sensor. The size of the sensor chip is 1.0 mm × 2.5 mm, its sensitivity is about 100 μV/V kPa and its resonance frequency is more than 350 kHz. The processing technology is suitable for batch manufacture.
Die Aufstellung von zulässigen oder Vergleichsfunktionen für das Ritzsche Verfahren wird erheblich vereinfacht, wenn man hermitesche Interpolationspolynome benutzt. Für Differentialgleichungen mit konstanten Koeffizienten werden fertige Integrationsmatrizen angegeben, so daß die ganze Methode auf bloße Matrizenmultiplikationen hinausläuft und daher leicht programmierbar ist.
The disposition of admissible or comparison functions for the Ritz-method will be essentially simplified by using the polynoms of Hermite approximation expression function. For differential equations with constant coefficients ready made integral matrices will be given thus that the whole method is a mere multiplication of matrices and consequently suitable for digital computers.
The mechanical behaviour (deflection and eigenvalues) of orthotropic micromachined sensor membranes under the combined action of out-of-plane pressure and internal in-plane stresses is discussed in this paper. Hermite polynomials of eighth order are used in combination with a Ritz method in order to solve the specific mechanical problems mentioned above. The solution procedure is presented and the results show excellent agreement with those obtained by other methods. In particular, simulations that have been carried out with the finite-element program ANSYS confirm this fact. The method presented here results in a quick, flexible and very accurate approximation of the mechanical behaviour. Furthermore, measurements of the centre deflection of sensor membranes are presented. A comparison with the theoretical results shows that the method used here leads to a sufficient prediction of the real deflection behaviour. Additionally, eigenfrequencies are evaluated and excellent agreement with the literature is also found in this case.
This paper mainly presents the experimental determination of the small deflection behaviour of boron-implanted silicon-nitride and highly boron-doped silicon diaphragms for micromachined silicon subminiature microphones. The additional implantation of boron into silicon-nitride diaphragms reduces the intrinsic stress in the deposited amorphous films. The minimum detectable deflection, using a Mach-Zehnder interferometer, is about 0.02 nm for dynamic measurements (A-weighted filtering). The largest measurable deflection (where nonlinearities of the interferometer are negligible) is strongly influenced by the wavelength of the laser and is about 10 nm. Thus, applying this method to pressure sensors and gas flow meters, the pressure range is restricted. In order to achieve a high sensitivity of the measuring apparatus and a low detectable deflection amplitude a feedback configuration stabilizes the interferometer in the most sensitive operation points.
Single-crystal silicon is being increasingly employed in a variety of new commercial products not because of its well-established electronic properties, but rather because of its excellent mechanical properties. In addition, recent trends in the engineering literature indicate a growing interest in the use of silicon as a mechanical material with the ultimate goal of developing a broad range of inexpensive, batch-fabricated, high-performance sensors and transducers which are easily interfaced with the rapidly proliferating microprocessor. This review describes the advantages of employing silicon as a mechanical material, the relevant mechanical characteristics of silicon, and the processing techniques which are specific to micromechanical structures. Finally, the potentials of this new technology are illustrated by numerous detailed examples from the literature. It is clear that silicon will continue to be aggressively exploited in a wide variety of mechanical applications complementary to its traditional role as an electronic material. Furthermore, these multidisciplinary uses of silicon will significantly alter the way we think about all types of miniature mechanical devices and components.
Die Mechanischen Eigenschaften von Membranen aus Silizium, Siliziumkarbid und Siliziumnitrid
- W Lang