A resonant pressure MEMS sensor based on levitation force excitation detection

Abstract

This paper proposes a MEMS resonant pressure sensor through implementing an out-of-plane repulsive (levitation) force to enhance the sensor detection threshold and consequently widen its sensing range. 2D and 3D finite-element simulations are conducted and compared to some available experimental data. The simulated results show an increase in the generated levitation force as outstanding merit owing to the added side upper electrodes. The levitation force is then further increased by lateral spacing optimization in association with the assumed applied voltage, which decreases the overall size (footprint) as well. The dynamical behavior around the static equilibrium is first numerically solved using the so-called shooting technique and then compared with an available online simulation tool: the “Matcont” package. The simulated results prove the capability of the online simulator to capture the dynamic response of the resonant micro-sensor when approaching its respective bifurcation points where the stable and unstable branches collide, when in contrary, the shooting technique failed to get the dynamic responses when passing by these bifurcations. Thanks to the fast converging outcomes of the “Matcont” online simulation equipped with simultaneous stability analysis, a comprehensive analysis of the micro-sensor dynamical response is conducted. Three sensing mechanisms as: measurements of frequency shift, amplitude alternation, and amplitude rise/fall near a bifurcation region are evaluated and characterized. Along with enumerating the strengths of the proposed sensor over the conventional capacitive pressure sensors, the advantage of measuring the amplitude rise/fall near the corresponding bifurcation region comparing to the two other sensing mechanisms is detailed, and its possible failure for performance repeatability is resolved by means of the slow-varying frequency sweep. Unlike the traditional parallel-plate configuration in which only one-side frequency shift is observed, in this proposed design, two-sides frequency shift is detected, and accordingly, the reinitialization is categorized based on that. As compared to the conventional MEMS pressure sensor, this revisited design equipped with the suggested sensing mechanism offers wider tunability and sensing range, resolution power enhancement, and simplification of the signal processing circuit.

Appendix

$$\begin{aligned} \delta _1= & {} \frac{r_1V_\mathrm{DC}^2}{{\mathcal {K}}_{11}}\sum _{j=1}^{5}j {\mathcal {A}}_j {\bar{x}}^jx_0^{j-1}\int _{0}^{1}\varphi ^{j+1} \hbox {d}x \end{aligned}$$

(12)

$$\begin{aligned} \delta _2= & {} \frac{r_1V_\mathrm{DC}^2}{{\mathcal {K}}_{11}}\sum _{j=2}^{5}\frac{j(j-1)}{2} {\mathcal {A}}_j{\bar{x}}^j x_0^{j-2}\int _{0}^{1}\varphi ^{j+1} \hbox {d}x \end{aligned}$$

(13)

$$\begin{aligned} \delta _3= & {} \frac{r_1V_\mathrm{DC}^2}{{\mathcal {K}}_{11}}\sum _{j=3}^{5}\frac{j(j-1)(j-2))}{6}{\mathcal {A}}_j{\bar{x}}^j x_0^{j-3}\int _{0}^{1}\varphi ^{j+1} \hbox {d}x \nonumber \\\end{aligned}$$

(14)

$$\begin{aligned} F_0= & {} \frac{-2r_1V_\mathrm{DC}V_\mathrm{AC}}{{\mathcal {K}}_{11}}\sum _{j=0}^{5}{\mathcal {A}}_j {\bar{x}}^jx_0^{j}\int _{0}^{1}\varphi ^{j+1} \hbox {d}x \end{aligned}$$

(15)

$$\begin{aligned} f_1= & {} \frac{2r_1V_\mathrm{DC}V_\mathrm{AC}}{{\mathcal {K}}_{11}}\sum _{j=1}^{5}j{\mathcal {A}}_j {\bar{x}}^jx_0^{j-1}\int _{0}^{1}\varphi ^{j+1} \hbox {d}x \end{aligned}$$

(16)

$$\begin{aligned} f_2= & {} \frac{2r_1V_\mathrm{DC}V_\mathrm{AC}}{{\mathcal {K}}_{11}}\sum _{j=2}^{5}\frac{j(j-1)}{2} {\mathcal {A}}_j {\bar{x}}^j{\hat{x}}_0^{j-2}\nonumber \\&\int _{0}^{1}\varphi ^{j+1} \hbox {d}x \end{aligned}$$

(17)

$$\begin{aligned} f_3= & {} \frac{2r_1V_\mathrm{DC}V_\mathrm{AC}}{{\mathcal {K}}_{11}}\sum _{j=3}^{5}\frac{j(j-1)(j-2)}{6} {\mathcal {A}}_j {\bar{x}}^jx_0^{j-3}\nonumber \\&\int _{0}^{1}\varphi ^{j+1} \hbox {d}x \end{aligned}$$

(18)