Design and Analysis of Nonuniformly Shaped Heaters for Improved MEMS-Based Electrothermal Displacement Sensing

Fowler, Anthony; Bazaei, Ali; Moheimani, S. O. Reza

doi:10.1109/jmems.2013.2240261

Cited by 22 publications

(25 citation statements)

References 26 publications

(31 reference statements)

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“…This measure is experimentally hard to characterize, especially for highly linear MEMS position sensors, due to interfering effects such as noise and limited resolution of micro-system analyzers and also nonlinearities in displacement source such as quadratic dependency of force on actuator voltage in comb drives [32]. The model can also predict the sensor response for much larger displacements than those achievable by limited stroke comb drives in [14] and [30]. Compared to the previously reported models, the proposed first-principles-based model incorporates the following nonlinear phenomena in the heat equation:…”

Section: Motivationmentioning

confidence: 99%

“…To roughly estimate the temperature profile of resistivity, we first neglect the minor effect of the heat-sink on the heater resistance and use the following static boundary value problem reported in [30] to predict the I-V characteristic of the heaters.…”

Section: Static Analysismentioning

confidence: 99%

“…is the local cross-section of the heater, G is the heat conductance to ambient from each end point of the heater connected to a pad, and K a (x) is the local per-unitlength thermal conductance of the heater to ambient, which in the absence of the heat-sink is described as [30]:…”

Section: Static Analysismentioning

confidence: 99%

“…8]). By appropriately shaping the heater width profile for a more uniform temperature distribution, the sensitivity, noise, and linearity of the sensor can be improved [30]. An important step before fabrication is to predict the sensor response by reliable models capturing the various nonlinearities involved [31].…”

mentioning

confidence: 99%

“…The schematic in Fig. 2 simultaneously shows two position sensors, each using a pair of identical heaters, one sensor with uniform beam width (straight) and the other one with nonuniform width (shaped), as described in [30]. To measure the displacement d of the heat-sink, which results in a variation in the individual heat conductances between the heaters and ambient in opposite directions, the resulting small difference between the resistances of the heaters is electronically amplified as the output voltage V o .…”

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A Comprehensive Analysis of MEMS Electrothermal Displacement Sensors

Bazaei

Moheimani

2014

IEEE Sensors J.

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Abstract-For electrothermal microelectromechanical system position sensors, we introduce a novel analytical model that captures the nonuniform distribution of temperature as well as the nonlinear dependence of resistivity on temperature. The proposed model also captures the effects of contoured beam heaters and the nonuniformity of the air gap between the heatsink and the heaters, which varies with heat-sink position and is differentially transduced into the output voltage. The model accurately predicts the experimentally obtained I-V data and the corresponding sensor output. It also explains the considerable improvement achieved in the linearity of the sensor response when the beam profiles are appropriately shaped to yield a more uniform temperature distribution. The shaped sensor is compared with conventional uniform electrothermal sensors under two different operating conditions, voltage, and current bias modes. Improved linearity is observed in both cases. The model is also applicable to predict the dynamic response of the sensor. An iterative procedure is developed to solve the additional complexity in voltage mode, which is a nonlinear partial integro-differential equation. Considering different bias modes and heater profiles, we evaluate the sensor bandwidth and linearity using the model and conduct experiments to validate the results. Based on first principles, the proposed model is more transparent than sophisticated software-based approaches and compatible with traditional solvers in MATLAB.Index Terms-Electrothermal, position sensor, MEMS, nonlinear analysis. I. MOTIVATIONI N MANY micro-electro-mechanical systems (MEMS), it is highly desirable to measure the displacement of moving components accurately [1]-[8]. This is particularly important in applications such as probe-based data storage and scanningprobe microscopy, where the required high positioning accuracies are achieved by feedback control and displacement sensing In [25], electrothermal position sensors were analyzed using a system approach. The effect of nonuniform temperature distribution along the heaters was not considered in this analysis. This effect was considered for heaters with uniform width and dopant concentration using first principles in [29] and through a software-based lumped capacitance model in [19]. The nonuniform heat distribution causes the central area of the sensing resistor to reach temperatures much higher than the outer areas ([20, Fig. 8]). By appropriately shaping the heater width profile for a more uniform temperature distribution, the sensitivity, noise, and linearity of the sensor can be improved [30]. An important step before fabrication is to predict the sensor response by reliable models capturing the various nonlinearities involved [31]. In contrast to commercial modeling software, first-principles-based models provide more transparent, flexible, and reliable tools for analysis, especially when the nonlinear phenomena are dominant.In this paper we develop analytical models for electrothermal position sensor...

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Section: Motivationmentioning

confidence: 99%

Section: Static Analysismentioning

confidence: 99%

Section: Static Analysismentioning

confidence: 99%

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