Sazzadur Chowdhury

A closed-form model for the pull-in voltage of electrostatically actuated cantilever beams

A simple computationally efficient closed-form model has been developed to determine the pull-in voltage of a cantilever beam actuated by electrostatic force. The approach is based on a linearized uniform approximate model of the nonlinear electrostatic pressure and the load deflection model of a cantilever beam under uniform pressure. The linearized electrostatic pressure includes the electrostatic pressure due to the fringing field capacitances and has been derived from Meijs and Fokkemas highly accurate empirical expression for the capacitance of a VLSI on-chip interconnect. The model has been verified by comparing the results with published experimentally verified 3D finite element analysis results and also with results from similar closed-form models. The new model can evaluate the pull-in voltage for a cantilever beam with a maximum deviation of ±2% from the finite element analysis results for wide beams, and a maximum deviation of ±1% for narrow beams (extreme fringing field).

Pull-in voltage study of electrostatically actuated fixed-fixed beams using a VLSI on-chip interconnect capacitance model

A highly accurate computationally efficient closed-form model has been developed to determine the pull-in voltage of an electrostatically actuated fixed-fixed beam. The approach includes the electrostatic spring softening effects due to the fringing field capacitances along with the nonlinear spring hardening effects associated with the load-deflection characteristics of a uniformly loaded fixed-fixed beam. Meijs and Fokkemas highly accurate empirical formula for the capacitance of a VLSI on-chip interconnect has been used to determine the spring softening effects due to the fringing field capacitances. The developed model has been verified by comparing the results with published experimentally verified three-dimensional (3-D) finite element analysis (FEA) results and with those from other published representative closed-form models. The developed model can determine the pull-in voltage with a maximum deviation of 1.27% from the FEA results for small deflections and for large deflections (airgap-beam thickness ratio =12), the deviation from the FEA results is 2.0%. A maximum deviation of 0.5% from the FEA results has been observed for extreme fringing field cases (beamwidth-airgap ratio /spl les/0.5). The models accuracy range is better compared to the other published models.

Nonlinear effects in MEMS capacitive microphone design

An analytical method is presented that provides a better approximation for design parameter values of a MEMS capacitive microphone. The spring softening effect associated with the nonlinear characteristics of the electrostatic pressure due to a bias voltage, and the spring hardening effect associated with nonlinear stretching of the central region of a uniformly loaded fully clamped diaphragm with residual stress are both considered. The method allows a more accurate determination of the developed electrostatic pressure, maximum diaphragm deflection and the pull-in voltage. The resulting electrostatic pressure, pull-in voltage and deflection profile of the diaphragm are in close agreement with finite element analysis results.

Design of a MEMS acoustical beamforming sensor microarray

This paper describes the design methodology for a microelectromechanical systems (MEMS)-based acoustical beamforming sensor microarray. The proposed acoustical array offers the potential of controlled directional sensitivity with constant beamwidth when used in conjunction with the appropriate digital signal processor. The array has been designed for use in a hearing instrument with a digital beamsteering engine to provide controlled directional sensitivity and constant beamwidth over the audio frequency range to improve speech intelligibility in noisy and reverberant environments. A MEMS-based packaging solution that allows the sensor array to be mounted in the ear canal is also described. The MEMS sensor-package interface features microspring contacts that enable low impedance connectivity between the sensor array and the related microelectronics. This allows the array to be easily removed for cleaning or replacement purposes.

Design of a MEMS discretized hyperbolic paraboloid geometry ultrasonic sensor microarray

Design of a discretized hyperbolic paraboloid geometry beamforming array of capacitive micromachined ultrasonic transducers (CMUT) has been presented. The array can intrinsically provide a broadband constant beamwidth beamforming capability without any microelectronic signal processing. A mathematical model has been developed and verified to characterize the array response. A design methodology has been presented that enables determination of the arrays physical dimensions and CMUT modeling in a straightforward manner. Developed methodology has been used to design two discretized hyperbolic paraboloid geometry beamforming CMUT arrays: one in the 2.3 MHz to 5.2 MHz frequency range and another in the 113 kHz to 167 kHz frequency range. CMUTs have been designed using a cross-verification method that involves lumped element modeling, 3D electromechanical finite element analysis (FEA), and microfabrication simulation. The developed array has the potential to be used in real-time automotive collision-avoidance applications, medical diagnostic imaging and therapeutic applications, and industrial sensing.

Pull-in voltage calculations for MEMS sensors with cantilevered beams

MEMS sensors, such as acoustic, noise and vibration transducers often employ a diaphragm or cantilevered structure as part of a variable capacitance sensor geometry. A bias voltage is necessary to ensure a linear force-capacitance range of operation. The calculation of the pull-in voltage whereby the sensing structure collapses due to electrostatic forces is an important design requirement. A linearized, uniform approximate model of the nonlinear electrostatic pressure has been developed and used in conjunction with the load deflection model of a MEMS cantilever beam under uniform pressure to develop a highly accurate model to calculate the pull-in voltage. The new model improves sensor design methodology by evaluating the pull-in voltage for a cantilever beam with a maximum deviation of less than 1% from the finite element analysis results for wide beams and for narrow beams with extreme fringing fields.

Square Diaphragm CMUT Capacitance Calculation Using a New Deflection Shape Function

A new highly accurate closed-form capacitance calculation model has been developed to calculate the capacitance of capacitive micromachined ultrasonic transducers (CMUTs) built with square diaphragms. The model has been developed by using a two-dimensional polynomial function that more accurately predicts the deflection curve of a square diaphragm deformed under the influence of a uniform external pressure and also takes account of the fringing field capacitances. The model has been verified by comparing the model-predicted deflection profiles and capacitance values with experimental results published elsewhere and finite element analysis (FEA) carried out by the authors for different material properties, geometric specifications, and loading conditions. New model-calculated capacitance values are found to be in excellent agreement with published experimental results with a maximum deviation of 1.7%, and a maximum deviation of 1.5% has been observed when compared with FEA results. The model can help in improving the accuracy of the design methodology of CMUT devices and other MEMS-based capacitive type sensors built with square diaphragms.

A new deflection shape function for square membrane CMUT design

A new deflection shape function that can predict the deflection profile of a uniformly loaded microfabricated clamped square membrane with a much higher accuracy compared to existing models has been presented. The model has been developed by using an empirical data fit technique to identify new terms and new parameter values that compensate for the deviation of the existing deflection shape functions for square membranes from experimental and FEA results. The model has been optimized for typical design space of square diaphragm capacitive micromachined ultrasonic transducers (CMUT). The new model predicted deflection profiles exhibit excellent agreement with experimental and 3-D FEA results. CMUT capacitance values calculated after pressure loading using the new deflection shape function show a maximum deviation of 3.4% from the FEA results compared to −7–21% maximum deviations when existing models are used. The new model will be helpful to implement a much higher accuracy design methodology for CMUTs.

A Highly accurate method to calculate capacitance of MEMS sensors with circular membranes

A highly accurate analytical method to calculate capacitance of MEMS capacitive type sensors with circular membranes has been presented. The method determines the center deflection of the membrane by taking account of the electrostatic pressure due to the bias voltage, external pressure, residual stress, and nonlinear spring hardening effect during large deflection. A new deflection shape function uses this center deflection to calculate a highly accurate deflection profile of the membrane which is then used to calculate the capacitance between the deformed membrane and the fixed backplate for any deformed profile of the membrane. The model has been verified by comparing the results with experimental and 3-D electromechanical finite element analysis (FEA) results with excellent agreement. The model predicted values deviate by a maximum of 2.2% for the membrane center deflection and 3.4% for capacitance values for different external pressure loading and electrostatic bias voltage.

Microelectromechanical systems and system-on-chip connectivity

The interconnection of microelectromechanical systems (MEMS) and other devices to a system-on-chip (SoC) implementation is described. MEMS technology can be used to fabricate both application specific devices and the associated micropackaging system that will allow for the integration of devices or circuits, made with non-compatible technologies, with a SoC environment. In the primary example presented, MEMS technology has been used to develop an acoustical array sensor for a hearing instrument application and also to provide a custom micropackaging solution suitable for in-the-ear canal implantation. A MEMS based modular micropackaging solution consisting of MEMS socket submodules and an insertable/removable microbus card has been developed to provide the necessary packaging and connectivity requirements. The modular socket concept can also be used for many other purposes, such as temporarily connecting a CMOS die to a SoC implementation of a die tester using MEMS based cantilevered bridge-type microspring contacts to provide connectivity to the die under test.