The fringe capacitance formula of microstructures

Chuang, Wan-Chun; Wang, Changwen; Chu, Wen-Chang; Chang, Pei‐Zen; Hu, Yuh-Chung

doi:10.1088/0960-1317/22/2/025015

Cited by 27 publications

(23 citation statements)

References 12 publications

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“…As a result the fringing electric field lines have a significant impact on overall capacitance. 17 For this reason the device was fabricated on a thin film of gelatin, allowing the capacitor's fringing electric field will pass through the gelatin film below the electrodes. Additionally, the patterned gelatin is much thicker than the electrodes to allow fringing electric field lines above the device to pass through gelatin rather than air.…”

Section: Discussionmentioning

confidence: 99%

Gelatin as a new humidity sensing material: Characterization and limitations

2014

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The goal of this work is to assert the utility of collagen and its denatured counterpart gelatin as cost-effective alternatives to existing sensing layers comprised of polymers. Rather than producing a material that will need to be discarded or recycled, collagen, as a by-product of the meat and leather industry, could be repurposed. This work examines the feasibility of using collagen as a sensing layer. Planar electrodes were patterned with lift-off process to work with the natural characteristics of gelatin by utilizing metal vapor deposition, spin coating, and photolithography. Characterization methods have also been optimized through the creation of specialized humidity chambers that isolate specific characteristics such as response time, accuracy, and hysteresis. Collagen-based sensors are found to have a sensitivity to moisture in the range of 0.065 pF/%RH. Diffusion characteristics were also analyzed with the diffusion coefficient found to be 2.5 × 10−5 cm2/s. Absorption and desorption times were found to be 20 seconds and 8 seconds, respectively. Hysteresis present in the data is attributed to temperature cross-sensitivity. Ultimately, the utility of collagen as a dielectric sensing material is, in part, due to its fibrous macrostructures as well its hydrophilic sites along the peptide chains. Gelatin was patterned between and below interdigitated copper electrodes and tested as a relative humidity sensor. This work shows that gelatin, which is inexpensive, widely available, and easy to process, can be an effective dielectric sensing polymer for capacitive-type relative humidity sensors.

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Section: Discussionmentioning

confidence: 99%

Gelatin as a new humidity sensing material: Characterization and limitations

2014

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“…The experiment results are listed in the sixth column of Tables 7-9. The authors of this paper had published a two-dimensional capacitance formula for determining the capacitance of the micro-beam without etching hole [11], we can use that formula to calculate the capacitance difference of the present two test beams, that is:…”

Section: Experiments Verificationmentioning

confidence: 99%

“…a C 1 ∆ L is given by Equation (8); b ∆C is given by the Equation (8) in [13]; c ∆C is given by Equation (7). [11] Reference [13] This work …”

Section: Experiments Verificationmentioning

confidence: 99%

“…As a result, etching holes make evaluating the capacitance of microstructures becomes much more difficult. There was some literature that evaluated the two-dimensional [7][8][9][10][11] or three-dimensional [8,9,12] fringe capacitances of the microstructures without etching holes. However, no literature mentioned the evaluation of the capacitance of perforated microstructures.…”

Section: Introductionmentioning

confidence: 99%

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The Fringe-Capacitance of Etching Holes for CMOS-MEMS

Wang

Chu

et al. 2015

Micromachines

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Movable suspended microstructures are the common feature of sensors or devices in the fields of Complementary-Metal-Oxide-Semiconductors and Micro-Electro-Mechanical Systems which are usually abbreviated as CMOS-MEMS. To suspend the microstructures, it is commonly to etch the sacrificial layer under the microstructure layer. For large-area microstructures, it is necessary to design a large number of etching holes on the microstructure to enhance the etchant uniformly and rapidly permeate into the sacrificial layer. This paper aims at evaluating the fringe capacitance caused by etching holes on microstructures and developing empirical formulas. The formula of capacitance compensation term is derived by curve-fitting on the simulation results by the commercial software ANSYS. Compared with the ANSYS simulation, the deviation of the present formula is within˘5%. The application to determine the capacitance of an electrostatic micro-beam with etching holes is demonstrated in a microstructure experiment, which agrees very well with the experimental data, and the maximum deviation is within˘8%. The present formula is with simple form, wide application range, high accuracy, and easy to use. It is expected to provide the micro-device designers to estimate the capacitance of microstructures with etching holes and predominate in the device characteristics.

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“…Thus, it is necessary to consider the influence of the fringing effect when calculating the dynamic characteristics of the variable geometry microbeam. Many different formulas for computing fringing fields have been proposed in [26,27] and we compared the difference of dynamic behavior of the microbeam among four typical fringing effect models. The revised formulas of electrostatic force of different models are depicted in appendix.…”

Section: Fringing Effectsmentioning

confidence: 99%

Dynamic Characteristics of Electrostatically Actuated Shape Optimized Variable Geometry Microbeam

Zhang

Peng

et al. 2015

Shock and Vibration

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We mainly analyze the dynamic characteristics of electrostatically actuated shape optimized variable geometry microbeam. A nonlinear dynamic model considering midplane stretching, electrostatic force, and electrical field fringing effects is developed. Firstly, we study the static responses of the optimized microbeams under DC polarization voltage. The generalized differential quadrature method (GDQM) is used. Secondly, the dynamic responses of the shape optimized microbeams driven by DC and AC voltages are investigated using GDQM in conjunction with Levenberg-Marquardt optimization method. The results show that the more gradual change in width, the larger the resonant frequency and the maximum amplitude at resonance. Then we further discuss in detail how do the maximum width, midsection width, and curvature of the width function affect the frequency response of the microbeams. We find that the amplitude and resonant frequency of the dynamic response are not monotonically increasing as the curvature of the width function increases and there exists a critical curvature. This analysis will be helpful in the optimal design of MEMS actuators. Finally, for more consideration, different residual stress, squeeze-film damping, and fringing effect models are introduced into the governing equation of motion and we compare the corresponding dynamic response.

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The fringe capacitance formula of microstructures

Cited by 27 publications

References 12 publications

Gelatin as a new humidity sensing material: Characterization and limitations

Gelatin as a new humidity sensing material: Characterization and limitations

The Fringe-Capacitance of Etching Holes for CMOS-MEMS

Dynamic Characteristics of Electrostatically Actuated Shape Optimized Variable Geometry Microbeam

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