Optical micro mechanical accelerometer with double grating: design and simulation

Yu Zhang; Honghao Ma

doi:10.1364/AO.491536

Applied Optics
Vol. 62,
Issue 22,
pp. 6016-6024
(2023)
•https://doi.org/10.1364/AO.491536

Optical micro mechanical accelerometer with double grating: design and simulation

Yu Zhang and Honghao Ma

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Yu Zhang and Honghao Ma, "Optical micro mechanical accelerometer with double grating: design and simulation," Appl. Opt. 62, 6016-6024 (2023)

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Related Topics
Table of Contents Category
- Optical Devices, Sensors, and Detectors
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: March 23, 2023
- Revised Manuscript: May 28, 2023
- Manuscript Accepted: July 11, 2023
- Published: July 27, 2023

Abstract

A double-grating-based optical micro mechanical accelerometer with differential detection structure is reported in order to enhance the optical scale factor. A theoretical model is established based on the multi-slits Fraunhofer diffraction model. According to the calculation and analysis, the normalized optical scale factor is improved from 5.491E6 with the single-side detection structure to 10.98E6 with the differential detection structure. Mechanical sensitivity with 4.04 nm/g and natural frequency with 7756.8 Hz of the optical accelerometer are shown by finite element simulation. The results of simulations show a novel scheme for an optical micro mechanical accelerometer with high resolution, to the best of our knowledge. Furthermore, micro-opto-electro-mechanical system fabrication flow is given in this work, which provides a reference for other kinds of optical sensors.

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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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Element	Material	Parameter	Symbol	Value
Proof mass	Silicon	Length of the square in proof mass	L	3000 µm
		Thickness of the proof mass	H	120 µm
		Mass of the proof mass	m	2.5 mg
		Young’s modulus of silicon	E	170 GPa
		Poisson ratio of silicon	$ν$	0.28
		Density of silicon	$ρ$	$2320 {k g / m}^{3}$
Supported beam	Silicon	Length of the supported beam	$L_{b}$	795 µm
		Width of the supported beam	$W_{b}$	300 µm
		Thickness of the supported beam	$H_{b}$	20 µm
Grating	Aluminum	Period of the micro grating	$Λ$	4 µm
		Ratio of the micro grating	r	0.5
		Grating area	$A_{G}$	$1000 µ m \times 1000 µ m$
		Thickness of the grating	$H_{G}$	100 nm
Mirror	Aluminum	Length of the mirror	$L_{M}$	3000 µm
		Width of the mirror	$W_{M}$	3000 µm
		Thickness of the mirror	$H_{M}$	100 nm
Laser	--	Wavelength	$λ$	632.8 nm
		Power	$I_{i n}$	1 mW

Stiffness	Optical Sensitivity		Natural Frequency		Mechanical Sensitivity
6496.0 N/m	Calculated value	Simulated Value	Calculated value	Simulated Value	Calculated value	Simulated Value
	10.98 E6/m	10.76 E6/m	8107.9 Hz	7756.8 Hz	3.8 nm/g	4.04 nm/g
	Error (%)		Error (%)		Error (%)
	2.004		4.330		6.316

Characteristics	This Work	Ref. [18]	Ref. [22]	Ref. [5]	Ref. [23]
Schematic	Double grating Based	Grating based	Grating based	Fabry–Perot cavity based	Fabry–Perot cavity based
Mechanical sensitivity	4.04 nm/g	2555.5 nm/g	169 nm/g	190 nm/g	6.52 nm/g
Measurement range	$\pm 9 g$	$\pm 20 g$	$\pm 1 g$	$\pm 5 g$	$\pm 1 g$
Resonance frequency	7756.8 Hz	312 Hz	24.8 Hz	1141 Hz	1372 Hz
Resolution (Noise floor)	$59.2 n g / \sqrt H z$ ( $Q = 1000$ ) Calculated mechanical thermal noise	$6.4 n g / \sqrt H z$ ( $Q = 1000$ ) Calculated mechanical thermal noise	$15 n g / \sqrt H z$ @ 1 Hz Measured value	--	153 µg (Resolution) Measured value
Dimensions of proof mass	$3000 µ m \times 3000 µ m \times 120 µ m$	Radius: 1500 µm Thickness: 350 µm	Radius: 2650 µm Thickness: 500 µm	$4020 µ m \times 3020 µ m \times 75 µ m$	$4020 µ m \times 3020 µ m \times 75 µ m$

Element	Material	Parameter	Symbol	Value
Proof mass	Silicon	Length of the square in proof mass	L	3000 µm
		Thickness of the proof mass	H	120 µm
		Mass of the proof mass	m	2.5 mg
		Young’s modulus of silicon	E	170 GPa
		Poisson ratio of silicon	$ν$	0.28
		Density of silicon	$ρ$	$2320 {k g / m}^{3}$
Supported beam	Silicon	Length of the supported beam	$L_{b}$	795 µm
		Width of the supported beam	$W_{b}$	300 µm
		Thickness of the supported beam	$H_{b}$	20 µm
Grating	Aluminum	Period of the micro grating	$Λ$	4 µm
		Ratio of the micro grating	r	0.5
		Grating area	$A_{G}$	$1000 µ m \times 1000 µ m$
		Thickness of the grating	$H_{G}$	100 nm
Mirror	Aluminum	Length of the mirror	$L_{M}$	3000 µm
		Width of the mirror	$W_{M}$	3000 µm
		Thickness of the mirror	$H_{M}$	100 nm
Laser	--	Wavelength	$λ$	632.8 nm
		Power	$I_{i n}$	1 mW

Stiffness	Optical Sensitivity		Natural Frequency		Mechanical Sensitivity
6496.0 N/m	Calculated value	Simulated Value	Calculated value	Simulated Value	Calculated value	Simulated Value
	10.98 E6/m	10.76 E6/m	8107.9 Hz	7756.8 Hz	3.8 nm/g	4.04 nm/g
	Error (%)		Error (%)		Error (%)
	2.004		4.330		6.316

Abstract

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Applied Optics