The Design, Modeling and Experimental Investigation of a Micro-G Microoptoelectromechanical Accelerometer with an Optical Tunneling Measuring Transducer

Abstract

This treatise studies a microoptoelectromechanical accelerometer (MOEMA) with an optical measuring transducer built according to the optical tunneling principle (evanescent coupling). The work discusses the design of the accelerometer's microelectromechanical sensing element (MSE) and states the requirements for the design to achieve a sensitivity threshold of 1 µg m/s² at a calculated eigenvalue of the MSE. The studies cover the selection of the dimensions, mass, eigenfrequency and corresponding stiffness of the spring suspension, gravity-induced cross-displacements. The authors propose and experimentally test an optical transducer positioning system represented by a capacitive actuator. This approach allows avoiding the restrictions in the fabrication of the transducer conditioned by the extremely high aspect ratio of deep silicon etching (more than 100). The designed MOEMA is tested on three manufactured prototypes. The experiments show that the sensitivity threshold of the accelerometers is 2 µg. For the dynamic range from minus 0.01 g to plus 0.01 g, the average nonlinearity of the accelerometers' characteristics ranges from 0.7% to 1.62%. For the maximum dynamic range from minus 0.015 g to plus 0.05 g, the nonlinearity ranges from 2.34% to 2.9%, having the maximum deviation at the edges of the regions. The power gain of the three prototypes of accelerometers varies from 12.321 mW/g to 26.472 mW/g. The results provide broad prospects for the application of the proposed solutions in integrated inertial devices.

Keywords: evanescent coupling; microoptoelectromechanical accelerometer; microoptoelectromechanical sensing element; optical measuring transducer; positioning system; proof mass; sensitivity threshold; tunneling effect; waveguides.

Figure 1

Functional scheme of an MOEM accelerometer with an OMT.

Figure 2

MSE displacements along the Y axis; (a) Frequency range from 10 to 500 Hz; (b) Frequency range from 500 to 1000 Hz.

Figure 3

Dependence of the spring suspension stiffness on the MSE’s mass at different frequencies; (a) Mass change from 1 × 10⁻⁹ to 1 × 10⁻⁵ kg; (b) Mass change from 1 × 10⁻⁹ to 1 × 10⁻⁷ kg.

Figure 4

Types of MSEs (spring suspension is not given); (a) Type 1 MSE; (b) Type 2 MSE.

Figure 5

Dependence of an MSE’s dimensions on its mass; (a) Mass change from 1 × 10⁻⁸ to 1 × 10⁻⁵ kg; (b) Mass change from 1 × 10⁻⁸ to 1 × 10⁻⁶ kg.

Figure 6

Dependencies of the a_BR on the MSE’s mass; (a) Mass change from 1 × 10⁻⁸ to 1 × 10⁻⁵ kg; (b) Mass change from 1 × 10⁻⁸ to 1 × 10⁻⁷ kg; (c) Mass change from 1 × 10⁻⁷ to 1 × 10⁻⁶ kg; (d) Mass change from 1 × 10⁻⁶ to 1 × 10⁻⁵ kg.

Figure 7

Spring-type elastic elements of the suspension.

Figure 8

Dependence of the displacement Δz and length G of the elastic elements on the dimensions b and b₁.

Figure 9

Design of the accelerometer’s MSE (optical waveguides are not shown).

Figure 10

Model of the OMT’s directional coupler.

Figure 11

Dependence of the optical transmission coefficient of the directional coupler’s through port on the coupling length and gap at a wavelength of 1550 nm.

Figure 12

Power maps at different gaps obtained via the FDE method.

Figure 13

Dependence of the OMT’s S21 on the gap at a wavelength of 1550 nm obtained via the FDTD method.

Figure 14

S-parameters of the OMT for a gap of 360 nm; the waveguide cross-section is 350 nm × 850 nm and the coupling length is 100 µm; (a) S21, S31, S42, S43, S12, S13, S24, S34; (b) S11, S22, S33, S44, S41, S14, S32, S23.

Figure 15

MSE fabrication process flow: (a)—formation of the optical waveguides and metallic plates; (b)—separation of functional elements; (c)—bonding to the carrier wafer; (d)—thinning of the device wafer; (e)—etching of the reverse side of the device wafer; (f)—bonding to the base wafer; and (g)—debonding of the carrier wafer.

Figure 16

Formed optical waveguides.

Figure 17

Prototype of the accelerometer’s MSE.

Figure 18

Experimental setup: 1—accelerometer prototype; 2—triaxial positioner; 3—six-axis automatic positioner; 4—six-axis manual positioner; 5—fiber holder; 6—laser; 7—joystick; 8—personal computer; 9—power meter; 10—sources of electric voltage; 11—sources of electric voltage; 12—polarizer.

Figure 19

Connection scheme of the positioning system electrodes.

Figure 20

Dependence of the simulated acceleration on the calculated voltage U₃.

Figure 21

Dependence of the accelerometer’s output optical power on the acceleration; (a) Range from minus 0.03 g to plus 0.05 g; (b) Range from minus 0.01 g to plus 0.01 g.

Figure 22

Dependence of the accelerometer’s output optical power on the acceleration; (a) Range from minus 0.001 g to plus 0.001 g; (b) Range from minus 0.0001 g to plus 0.0001 g.

Figure 23

Dependence of the accelerometer’s output optical power on the acceleration in a range from minus 0.00001 g to plus 0.00001 g.