Modelling and analysis of fringing and metal thickness effects in MEMS parallel plate capacitors

Abstract

This paper presents a detailed design and analysis of fringing and metal thickness effects in a Micro Electro Mechanical System (MEMS) parallel plate capacitor. MEMS capacitor is one of the widely deployed components into various applications such are pressure sensor, accelerometers, Voltage Controlled Oscillator's (VCO's) and other tuning circuits. The advantages of MEMS capacitor are miniaturisation, integration with optics, low power consumption and high quality factor for RF circuits. Parallel plate capacitor models found in literature are discussed and the best suitable model for MEMS capacitors is presented. From the equations presented it is found that fringing filed and metal thickness have logarithmic effects on capacitance and depend on width of parallel plates, distance between them and thickness of metal plates. From this analysis a precise model of a MEMS parallel plate capacitor is developed which incorporates the effects of fringing fields and metal thickness. A parallel plate MEMS capacitor has been implemented using Coventor design suite. Finite Element Method (FEM) analysis in Coventorware design suite has been performed to verify the accuracy of the proposed model for suitable range of dimensions for MEMS capacitor Simulations and analysis show that the error between the designed and the simulated values of MEMS capacitor is significantly reduced. Application of the modified model for computing capacitance of a combed device shows that the designed values greatly differ from simulated results noticeably from 1.0339pF to 1.3171pF in case of fringed devices.

A modified capacitance model of RF MEMS shunt switch incorporating fringing field effects of perforated beam

“…Relative error performance of the models with respect to FEM value is given in Tables 8-10 and also graphically represented in Fig. 14. The proposed model shows very good accuracy in larger air gap with smaller dielectric layer but fails in reverse condition due to it is more precise on metal thickness effects [10] especially in larger air gap.…”

“…The difference with simulated value is due to the surface roughness and dielectric charging effect. Palmer Yang combined model is valid in very small air gap range 0.25-0.75 lm [10] which is not desirable for MEMS switch to achieve high isolation. It makes this model inaccurate for 2-4 lm range of air gap.…”

“…Analytical model of capacitance per unit length for the parallel plate with thickness 't' [9,10] as shown in Fig. 5 was proposed by Yang [9] as …”

“…Insertion loss, isolation, and other high frequency performance parameters of the switch depend on the up-state to down-state capacitance ratio [8]. Very few works related to modeling of parallel plate 3D capacitance are reported till date [9][10][11][12][13][14][15][16]. The technical report [9] has summarized various analytical and empirical models of capacitance in different types of parallel plate structures with different ranges of validity.…”

“…But none of them is applicable to MEMS capacitive switch owing to the fact that small dielectric layer on the lower plate is ignored in this analysis. A hybrid model [10] for computing capacitance by combining Palmer's formula [11] to account the edge fringing effect and Yang's formula [14] to account fringing effect due to metal plate thickness has been reported. But it has not considered perforated plates and hence, fringing field through perforations is not taken into account.…”