This confirms that the dissertation titled “Design and Analysis of a Wearable MEMS Piezoresistive Accelerometer with Low Transverse Sensitivity for Neurological Disease Diagnosis” submitted by SONALI BIS, Research Scientist at the Department of Electronics and Electrical Engineering, Indian Institute of Technology Guwahati, has been awarded a B.Sc. Doctor of Philosophy, she performed under my supervision and guidance. The sensitivity of the transverse axis should be as low as possible, especially for the detection of weak tremor shocks.
Introduction
MEMS accelerometers can be used to measure inclination, body movements for a given frequency range, and amplitude of human body movements that occur as a result of voluntary and involuntary actions. There are various transduction mechanisms such as capacitive, piezoelectric and piezoresistive which can be used for the design of such accelerometers [6].
Brief Literature Survey
This improved the symmetry of the structure and gave a sufficient reduction in the sensitivity of the transverse axis. Although various designs have been presented, the proof mass structure with support beams is still one of the most popular as reported by [10], [12] and [13].
Motivation
The worst cross-axis sensitivity of either axis (except the sensor axis) determines performance. In general, the motivation is to design a wearable MEMS sensor for high sensitivity low g applications with low cross-axis sensitivity.
Thesis Contribution
The design to arrive at a suitable aspect ratio of the proof mass for simultaneous reduction of transverse axis sensitivity in both outer axes is motivated by the same. Reduction of cross-axis sensitivity at the circuit level has been proposed in the literature, but simultaneous reduction at the sensor level has not been studied in the literature.
Thesis Organization and summary of each chapter
In Chapter 5 the performance improvement through reduction in cross-axis sensitivity was discussed. While performing the test mass optimization, it is ensured that the mass of the test mass is kept the same so that the prime axis sensitivity is not adversely affected.
Extended Literature Survey
Accelerometers have a proof mass that experiences an inertial force in the opposite direction of the acceleration to be measured. The mechanical noise is due to the Brownian motion of the proof mass suspension or anchors.
Introduction
Design Approach
Let x be the displacement of the mass relative to the rest frame and y the displacement of the housing relative to the same rest frame. It should also be emphasized that any other parameter proportional to the displacement amplitude (Z) can also be used to detect the acceleration. The change in resistance of a piezoresistive material is directly proportional to the voltage, so it is important to place the piezoresistors in a position where the maximum voltage can be sensed.
As soon as the resistance of piezoresistors changes due to the voltage caused by the applied acceleration, it must be detected to establish the amplitude of the applied acceleration.
Proposed Design configuration of the MEMS accelerometer
It can be seen that the induced voltage decreases as the thickness of the beam increases, indicating that it is beneficial to reduce the thickness of the beam. In this section, we examine the impact of beam placement on developed voltage and subsequently on sensitivity. The impact of the placement of these beams on the cross-axis sensitivity is also being investigated.
The proposed structure therefore places the beams in line with the edge of the test mass.
Wheatstone bridge as signal pick up circuit
Assume that the magnitude of the voltage is the same for all resistors and denote the magnitude of the change in resistance by ∆R. Let us also assume that the no-voltage resistance of all piezoresistors is the same and is denoted by R. In practical cases, the change in resistance will not be exactly the same, in this case Eq.
Simulation Results and Analysis
In the piezoresistive sensing mechanism, whenever there is a change in the resistance value, this change is proportional to the developed voltage which in turn is proportional to the displacement of the proof mass. The longitudinal stress values are obtained to be maximum near the fixed points and minimum at the center of the beams. The rhythmic pattern or oscillations of tremor may be related to the movement of the mass and spring [3].
For p- and n-type silicon, the value of the piezoresistive coefficient decreases with increasing temperature and doping concentrations.
Conclusion
Introduction
Bao has detailed the squeeze film air damping of thick holes made in the plate, provided that the holes in the plate have the same cross-sectional area. The squeeze film analysis of most MEMS devices is generally performed using the 2D isothermal compressible Reynolds equation [36] and [38]. Different mathematical models with different assumptions have been proposed by different researchers to determine the squeeze film damping model [48] and [49].
Since the dynamic behavior is significantly affected by the pressure film-air damping, correct prediction of damping ratio becomes significantly important.
Theoretical Background
Therefore, the damping ratio caused by the compressed air of the film can be obtained by measuring atoMp and ts from the step response of the mass spring damper system. The air film acts as a damper and this type of damping is called Squeeze film air damping. The softening effect of the Squeeze film is the interaction of the resistive silicone mass and the air film trapped in the gap between the mass and the encapsulation.
Continuum-based models can break down when the mean free path is greater than the gap thickness.
Analysis of damping for the proposed structure
Time domain Analysis
Conclusion
80 5.3 Proposed Aspect Ratio for Simultaneous Reduction of Cross-Axis Sensitivity 825.4 Proposed Scheme for Further Reduction of Cross-Axis Sensitivity by Grain- 5.4 Proposed Scheme for Further Reduction of Cross-Axis Sensitivity by Grain -.
Introduction
In addition to geometric modification, another approach to increase stiffness was by depositing heavy metal on top of the test mass. In [13] and [16], the upper part of the test mass was electroplated with 20 μm thick gold, which reduced the sensitivity of the cross axis in the lateral axes. In the present work an attempt has been made to reduce the sensitivity of the cross axis without the use of any costly metal.
The chosen proof-mass aspect ratio provides equal and reduced cross-axis sensitivity on both the x- and y-axis simultaneously.
Theoretical Background
In order to maintain an equivalent mass, we reduced the thickness of the proof mass and then deposited metallic gold [17]. The cross-axis sensitivity of the proposed accelerometer was evaluated based on the given theory. Here, ∆z denotes the vertical displacement of the masses when the normal acceleration is applied, and kz is the stiffness in the Z direction.
Thus to ascertain the figure of merit of the device in terms of the highest sensitivity of the primary axis and the lowest sensitivity of the cross axis, the normalized parameters kkθx.
Proposed aspect ratio for simultaneous reduction in cross-axis sensitivity
Stiffness of beam in X direction normalized to stiffness in major axis is given by (m2/rad) kθx. To increase the sensitivity in the major axis, the stiffness in the axis must be reduced, and to decrease the cross-axis sensitivity, the stiffness of girders in that direction must be increased. The higher the value of these parameters, the better the device is in terms of transverse axis.
This maintains the natural frequency and sensitivity of the original 1:1 aspect ratio design.
Proposed Scheme for further reducing Cross-axis Sensitivity by Wheatstone bridge
The proposed design has a dimension similar to that shown in Figure 5.1, except that the dimension of the proof mass is different, namely µm3. Eight piezoristors connected in the form of a Wheatstone bridge are shown in the figure. Because of this opposing nature, these piezoresistors can be connected in the form of a Wheatstone bridge, as shown in Fig.
When the acceleration is applied in y direction, R1f, R2f, R3m and R4m undergo tension and R1m,R2m,R3f and R4f undergo compression as shown in Fig.
Conclusion
In practical cases the voltages induced will not be exactly equal in magnitude, so there will be very small output. This helps to reduce cross-axis sensitivity even when stress is induced in the structure with the application of off-axis acceleration. For the proposed structure, to obtain the sensitivity, stress was observed upon application of ±6 g acceleration in all three axes.
Introduction
Electrical thermal noise is caused by the agitation of the charge carriers by lattice thermal vibrations and is present regardless of the bias voltage. However, a higher temperature causes more movement of the carriers, hence the Johnson sound is temperature dependent. The designed microaccelerometer has a silicon square proof mass with four bars, two on either side of the proof mass. The whole structure is surrounded by a fixed frame.
Eight p-doped monocrystalline silicon piezoresistors are implanted, four at the junction of the beam and the proof mass, and the other four at the junction of the beam and the fixed frame.
Noise in the accelerometer
Here the effective spring constant is taken for parallel beams which is given by four times the spring constant for each. Given the high value of Q, it can be assumed that most of the energy is confined around ωn and F¯n2= ¯Fn2(fn). Since the result does not depend on the frequency, the spectral density of the fluctuating sound power related to attenuation is given.
Hz. The noise equation 6.16 can be rewritten in terms of the quality factor as in equation (6.17).
Proposed model for noise reduction
In this way we get increased efficiency, as the quantization noise can now be pushed to frequencies far from the signal band. Noise shaping is applied as a second step to improve the signal-to-noise quantization ratio. The amount of quantization noise is not changed by this process, but the signal-to-noise ratio is increased in the low-frequency region of the spectrum.
In a sigma-delta modulator (SDM), the techniques of oversampling and noise shaping are combined, resulting in increased efficiency, as the quantization noise can now be pushed to frequencies far from the signal band.
Results
Damping determines the thermal fluctuations, so the device design must have an effective and controlled damping mechanism to have an improvement in the signal-to-noise ratio. For the piezoresistive sensor with proof mass and the top and bottom lids, damping is determined by both the spacing between them and the viscosity of the fluid used. In the present case, the piezoresistive accelerometer senses the acceleration in the vertical z-axis, therefore pressure film damping is considered.
The damping force arises from the effect of the compressive film of the test mass and the air film trapped in the gap between the mass and the encapsulation.
Conclusion
Conclusion
Further work
Theories and Numerical Procedure Applied in COMSOL for Modelling Damping
For the square test measure the value is 0.42. The thin film gap is taken for the proposed structure as 18.6µm. The response characteristic shows that the damping coefficient obtained for the 18.6µm height was slightly greater than 0.7. Therefore, the procedure was repeated simulating it for higher height in order to achieve a desirable damping ratio of 0.7.
With this gap value, the damping coefficient is calculated using other models and also estimated by simulation.
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