Coarse-to-fine optical MEMS accelerometer design and simulation

Mojtaba Rahimi; Majid Taghavi; Mohammad Malekmohammad

doi:10.1364/AO.439762

Applied Optics
Vol. 61,
Issue 2,
pp. 629-637
(2022)
•https://doi.org/10.1364/AO.439762

Coarse-to-fine optical MEMS accelerometer design and simulation

Mojtaba Rahimi, Majid Taghavi, and Mohammad Malekmohammad

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Mojtaba Rahimi, Majid Taghavi, and Mohammad Malekmohammad, "Coarse-to-fine optical MEMS accelerometer design and simulation," Appl. Opt. 61, 629-637 (2022)

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- Optical Devices, Sensors, and Detectors
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About this Article
History
- Original Manuscript: August 16, 2021
- Revised Manuscript: December 15, 2021
- Manuscript Accepted: December 19, 2021
- Published: January 10, 2022

Abstract

A coarse-to-fine optical microelectromechanical systems (MEMS) accelerometer based on the Fabry–Pérot (FP) interferometer is proposed. The mechanical structure consists of a proof mass that is suspended by four L-shaped springs. The deflection of the proof mass due to the applied acceleration is detected using two FP cavities that comprise the system’s optical system. Using coarse-to-fine measurement and the dual wavelength method simultaneously increases the sensitivity of the accelerometer as well as the linear measurement range. The optical simulation shows that the sensitivity of the proposed device is 10 times as high as that of a similar optical MEMS accelerometer with one FP cavity. In addition, the proposed optical system is insensitive to the displacements of the proof mass in the orthogonal directions, which considerably reduced the cross-axis sensitivity. The minimum feature size of the structure is 15 µm and the optical signal is conducted completely through the optical fibers, facilitating the device fabrication. Here are the results of the simulation: mechanical sensitivity of 190 nm/g, optical sensitivity of 8 nm/g, linear measurement of ${{\pm 5}}\;{{\rm g}}$, and first resonance frequency of 1141 Hz.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Symbol	Description	Value
$D_{0 - c o a r s e}$	Coarse cavity length	36.30 µm
$D_{0 - f i n e}$	Fine cavity length	36.58 µm
$λ$	Source wavelength	1.5–1.6 µm
$a$	Optical fiber core radius	4.5 µm
$n_{c o}$	Optical fiber core refractive index	1.446
$n_{c l}$	Optical fiber clad refractive index	1.441
$R$	Optical fiber surface reflection coefficient	0.04
$T$	Optical fiber surface transmission coefficient	0.96
$n$	Refractive index of the cavity medium	1

		Coarse Cavity			Fine Cavity
Region	Acceleration Range	Mechanical Displacement (nm)	Spectrum Shift(nm)	Measurement Wavelength	Mechanical Displacement(nm)	Spectrum Shift(nm)	Measurement Wavelength
I	0 to 1 g	0 to 19	0 to 0.8	First wavelength	0 to 190	0 to 8	First wavelength
II	1 g to 2 g	19 to 38	0.8 to 1.6		190 to 380	8 to 16	Second wavelength
III	2 g to 3 g	38 to 57	1.6 to 2.4		380 to 570	16 to 24	First wavelength
IV	3 g to 4 g	57 to 76	2.4 to 3.2		570 to 760	24 to 32	Second wavelength
V	4 g to 5 g	76 to 95	3.2 to 4		760 to 950	32 to 40	First wavelength

Symbol	Description	Value
L	Proof mass length	4020 µm
W	Proof mass width	3020 µm
$L_{1}$	Length of the springs along the X axis	1270 µm
$W_{1}$	Width of the springs along the Y axis	15 µm
$L_{2}$	Length of the springs along the Y axis	45 µm
$W_{2}$	Width of the springs along the Y axis	15 µm
$L c$	Coarse cavity location	1010 µm
$t$	Thickness	75 µm
$E$	Young’s modulus of silicon	170 GPa
$ρ$	Density of silicon	$2329 k g / m^{3}$

Symbol	Description	FEM
$k_{y}$	Spring constant along the Y axis	81.96 N/m
$k_{x}$	Spring constant along the X axis	$1.25 \times 1 0^{6} N / m$
$m$	Mass of the proof mass	$1.59 \times 1 0^{- 6} k g$
$k_{z}$	Spring constant along the Z axis	$7.79 \times 1 0^{4} N / m$
$f_{y}$	Resonance frequency along the Y axis	1.141 kHz
$f_{x}$	Resonance frequency along the X axis	141.5 kHz
$f_{z}$	Resonance frequency along the Z axis	35.2 kHz
$S_{y}$	Mechanical sensitivity along the Y axis	190.11 nm/g
$S_{x}$	Mechanical sensitivity along the X axis	0.012 nm/g
$S_{z}$	Mechanical sensitivity along the Z axis	0.2 nm/g
$C_{x y}$	Cross-axis sensitivity between the X axis and Y axis	0.01 %
$C_{z y}$	Cross-axis sensitivity between the Z axis and Y axis	0.1 %

Characteristics	CFMA	2020 [22]	2020 [13]	2019 [27]	2019 [23]	2017 [21]
Measurement range	$\pm 5 g$	$\pm 0.517 g$	$\pm 217 g$	$\pm 1 . 56 g$	$\pm 1 g$	$\pm 156 g$
Mechanical sensitivity ( $Δ x / Δ a$ )	190 nm/g	242 nm/g	0.612 nm/g	781.64 nm/g	70 nm/g	1.6 nm/g
Optical sensitivity ( $Δ λ / Δ a$ )	8 nm/g	1017 nm/g	2.07 nm/g	964.35 nm/g	3.2 nm/g	0.0756 nm/g
Resonance frequency	1141 Hz	1037 Hz	20911 Hz	562.85 Hz	1676 Hz	12935 Hz
Footprint of the proof mass	$4020 µ m \times 3020 µ m$	$2000 µ m \times 2000 µ m$	$116 µ m \times 116 µ m$	$4207 µ m \times 4207 µ m$	$8000 µ m \times 6000 µ m$	$200 µ m \times 200 µ m$
Cross-axis sensitivity	0.01% (X) 0.1% (Z)	9.67% (X) 2.6% (Z)	0.86% (X) 0.96% (Z)	7% (X) 1% (Z)	1.02% (X) 1.36% (Z)	Not mentioned
Main structure	Fabry–Pérot cavity	1D photonic crystal	1D photonic crystal	1D photonic crystal	Fabry–Pérot cavity	2D photonic crystal
Minimum feature size	15 µm	109.8 nm	109.8 nm	109.8 nm	70 µm	240 nm
Fabrication complexity	Simple	Difficult	Difficult	Difficult	Simple	Difficult

Abstract

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Applied Optics