A New Diaphragm Material for Optical Fibre Fabry-Perot Pressure Sensor

2009 Fifth International Conference on MEMS NANO, and Smart Systems

A New Diaphragm Material for Optical Fibre Fabry-Perot Pressure Sensor

Muzalifah Mohd Said#1, Syafeeza Ahmad Radzi#2, Zarina Mohd Noh#3, Siti Aisah Mat Junos@Yunus#4, Siti Normi Zabri @ Suhaimi#5 Faculty of Electronic and Computer Engineering Universiti Teknikal Malaysia Melaka 76109 Durian Tunggal, Melaka,Malaysia [email protected], [email protected], [email protected], [email protected] [email protected] Abstract—Fibre optic Fabry-Perot interferometric pressure sensors have proved many orders of excellent measurements system, but they suffer from limitations in sensitivity and resolution caused by the trade-off in designing the sensor when very thin diaphragm is needed. By reducing the diaphragm thickness increases the deflection range, but reduces the diaphragm strength and therefore increases the risk of mechanical failure. The pressure sensor has been designed and its fabrication process using MEMS techniques is explained. This paper proposes a new diaphragm material for the fibre optic Fabry-Perot pressure sensor. Using a Polydimethylsiloxane (PDMS), the limitation on sensor resolution and sensitivity are overcome. The goal of this research is to design and analyze the PDMS diaphragm to enhance the consistency and sustainability of fibre optic FabryPerot pressure sensor for medical measurements which require a minimum resolution of ~1 mmHg over all the physiological pressure range (~300 mmHg) [1,2]. Comparisons of theoretical and simulation with Coventor Ware simulator on mechanical part of the pressure sensor are made. Also, an explanation viewing the sensor’s diaphragm stability is provided. Keywords-MEMS, Fabry-Perot, polydimethylsiloxane, resolution.

I.

2. 3.

4.

II.

THEORY

In this section, theory on fibre optic pressure sensor are briefly explained and reviewed. A. Fabry- Perot Interferometry One of the areas of greatest interest has been in the development of high performance interferometric fibre optic sensors. Fabry-Perot interferometer (variable-gap interferometer) consists of two highly reflective and strictly parallel plates [1-9]. Fabry-Perot interferometry pressure sensor is a MOEMS technology device which consists of mechanical and optical part. The basic principle of fibre optic Fabry Perot pressure sensor operation is involving two components of mechanical and optical. When light is introduced into the Fabry-Perot cavity through the optical fibre, the light beam is reflected back and forth between the fibre end face and mirror (cavity), but at each reflection only a small fraction of the light is transmitted and carried back through the fibre. A broadband light emitting diode (LED) centered at 850 nm is used as the illumination source for the sensor with the pressure range 0-40kPa.

interferometric.

INTRODUCTION

In this paper, an improved version of a micro-electromechanical systems (MEMS) pressure sensor interrogated by light propagating in an optical fibre is being visualized, designed, and simulated. The improvement involves use of PDMS diaphragm in the MEMS sensing structure. In designing the mechanical part of Fabry-Perot pressure sensor, there is a trade-off exists when optimizing the diaphragm thickness. Reducing the diaphragm thickness increases the deflection range, but reduces the diaphragm strength and therefore increases the risk of mechanical failure. Use of this PDMS diaphragm is believe to provide significantly enhanced sensor sensitivity and to perform high consistency functionality for a very thin diaphragm pressure sensor compared to previous versions utilizing silicon, silica, polymer and SU-8 for the Fabry-Perot pressure sensor diaphragm. The associated purposed of this research include: 1. MEMS design and fabrication of Fabry-Perot cavity based pressure sensors attached with fibre optic.

978-0-7695-3938-6/09 $25.00 © 2009 IEEE DOI 10.1109/ICMENS.2009.15

Realizing pressure sensors system based on diaphragm design principles. To investigate the feasibility of micro-machining Fabry-Perot diaphragm through the using of PDMS as diaphragm material. To simulate the sensor tip for the analysis of diaphragm’s deflection using Coventor Ware simulator and do the comparison with theoretical analysis.

B. B. PDMS as Sensor Diaphragm The development of high-performance diaphragm is of critical importance in the successful realization of the devices. The most essential property for use in membrane diaphragm as pressure systems is high elasticity. Particularly, diaphragms capable of linear deflection are needed in many pressure sensors. A pressure sensor with a PDMS diaphragm is believed to achieve much larger deformation than other conventional silicon diaphragms under low pressure because of the lower Young's modulus of PDMS. The mechanical properties of PDMS (10:1) are having Young’s modulus ( E) of 750 kPa, Poisson’s ratio(v) of 0.5, 154

Density of 920 Kg/m3, refraction index of 1.415 and yield strength (σ) of 20kPa. PDMS is a biocompatible, ultra-violet transparent, and gas permeable elastomer that can withstand a wide temperature range (-100 to 100°C). PDMS is easy to process and has been widely applied in the micromachining field [3]. III.

Where ,

r12 =

METHODOLOGY

( nair − ndiaphragm ) (nair + ndiaphragm ) Eq. 3

2π .nair .L

Eq. 4

λ0

r is the Fresnel reflection coefficient of the Fabry–Perot interferometer; r12 and r23 are the Fresnel reflection of the fibre-end–air and air–gold interfaces, respectively, at normal incidence; L is the air cavity depth/thickness, Ø is the phase and λ0 is the centre wavelength of the light source that illuminates the Fabry–Perot interferometer.

A. Design of Ideal Fabry-Perot Pressure Sensor The Fabry-Perot interferometer is an optical instrument which uses multiple-beam interference. For the pressure sensor design, the radius of the circular diaphragm has chosen as, a = 62.5 μm which is compatible with the fibre optic tip size. A multi-mode 62.5/125 μm (core diameter/cladding diameter) is used for pressure sensor operating at 850 nm.

In order to decide the initial cavity depth of the sensor, we need to decide the sensor’s diaphragm thickness first. Next step is to find the diaphragm thickness. A. Diaphragm thickness calculation: The cavity depth has two limiting values and should lie between them. The lower bound is imposed by the diaphragm thickness and the upper bound is imposed by the spectral width Δλ of the light source. The diaphragm thickness should be such that it does not deflect more than λo/4 at maximum designed pressure which implies that cavity depth [9, 12]:

Fig. 1 The proposed MEMS based Fabry-Perot pressure sensor

The Fabry-Perot cavity-based pressure sensor as shown in Fig. 1 is a Fabry-Perot interferometer consisting of two parallel, partially reflecting surfaces separated by a gap as illustrated in Fig. 2.

L ≥ λ0 / 4

Zhou et al. stated that since the cavity is circular in shape, the pressure sensing diaphragm is modeled as a circular membrane [14]. The deflection of the diaphragm due to the application of pressure, P is given by [4-12] 2 2 r ⎤ r ⎤ 3(1 − μ 2 ) Pa 4 ⎡ ⎡ w( r ) = w − = − 1 ( ) 1 ( ) 0⎢ ⎢ Eq. 5 a ⎥⎦ a ⎥⎦ 16 Eh 3 ⎣ ⎣ Where r: distance from the centre of the diaphragm plate w(r): deflection at r , wo: deflection at r=0 P : normal pressure, a : radius of the cavity; h: diaphragm thickness, μ : Poisson’s ratio of diaphragm E: Young’s modulus of diaphragm

Fig. 2 The dielectric layers contributing to the effect of FP pressure sensor and reflection coefficients when the sensor is illuminated with a broad spectrum source like LED.

The refractive index of the material is n. Assuming normal incidence, Fresnel reflection coefficient, r, is given by [9, 12]: ( n − n2 ) 2 r= 1 Eq.1 ( n1 + n2 ) 2 where n1 and n2 are the refractive indices of the two media forming the boundary. For the sensor configuration shown in Fig. 2, the Fabry– Perot effect comes from the two partially reflecting mirrors formed by the interface of an optical-fibre-end-to-air cavity; the reflectivity is about 0.04, and of an air-cavity-toreflective metal layer (gold) as shown in Fig. 2. The reflectance of the Fabry sensor is given by [7, 10]: r12 + r23 exp( − 2 jφ ) 1 + r12 r23 exp( −2 jφ )

r12 =

(nair + ndiaphragm ) φ=

An analysis on the obligation and principle to design the optical fibre FP pressure sensor is described in this section. The transmittance and reflectance of a FP cavity sensor as a function of cavity gap is discussed here.

R =| r |2 =

( nair − ndiaphragm )

The maximum diaphragm deflection is obtained from Eq. 4 when r = 0 3(1 − μ 2 ) Pa 4 Eq. 6 w0 = 16 Eh 3 The diaphragm thickness should be such that it does not deflect more than λo/4 at maximum designed pressure is by substituting wo= λo/4 as the deflection for the maximum designed pressure and is expressed by the following equation: 4 Eh 3λ0 P= 4 Eq. 7 3a (1 − μ 2 )

2

Eq. 2

155

Re-arrange Eq.7, then will get Eq.8 below: 1/ 3

Eq. 8

Eq. 8 is used to calculate the membrane thickness which will deflect by λo /4 at the maximum designed pressure. The optical pressure sensor operating at 850 nm is chosen to respond over the pressure range 0 - 40kPa. Calculation on Eq. 8 indicate that 1.93 μm of diaphragm thickness is required for making a diaphragm’s centre deflection of λ0/4 at 40 kPa. Therefore, by using Eq. 6 the maximum diaphragm deflection is calculated to be 0.212 um. The intention of this design is to use a thinner sensor diaphragm in order to obtain a greater response. The ratio between the deflection and the pressure difference is defined as the diaphragm pressure sensitivity (ω). When the optical fibre is positioned to face the centre of the diaphragm, only the centre deflection ωc is of interest [2,4, 6]. w 3(1 − μ 2 ) a 4 (um/kPa) Eq. 9 ωc = 0 = P 16 Eh 3 For the pressure design, the calculated sensitivity using Eq. 9 is ~0.0055um/kPa. The upper bound on the cavity depth is imposed by the spectral width of the LED source, ‘ΔλLED ’. The free spectral range ΔλFSR of the Fabry Perot interferometer must be greater the line-width of LED to avoid any ambiguities [9]. Free spectral range is the working range where there are no overlapping orders and for FPI illuminated with LED having centre wavelength λo is expressed as [3, 9, 12]:

λ0

Fig.3 shows the reflectance as a function of cavity depth. Diaphragm with gold coated has shown higher reflectance compared to none coated. A cavity depth at L= 1.7μm is chosen to satisfy the constraints of upper and lower bound. By choosing the cavity depth of 1.7μm, the reflectivity lies in the linear range and as the applied pressure increases, the reflectance from the sensor is increases as well (Fig. 3). As stated before, since the calculated maximum diaphragm deflection is 0.222 μm, therefore cavity depth varied from 1.7 μm for zero pressure to 1.49 μm for maximum pressure of 40kPa. Fig. 4 below shows the predicted membrane deflection and the pressure sensor response using the sensor parameters which are; membrane thickness, h: 1.93μm, cavity radius, a: 62.5 μm and cavity depth, L: 1.7 μm. Diaphragm deflection and reflectivity in respond to applied pressure 2.5E-07 0.45

2

Λ OPL The free spectral range ‘ΔλFSR’ should be greater than the line-width ‘ΔλLED’ of the LED, the requirement can be written as [3, 7, 9]: Eq. 11 Δλ ≤ Δλ LED

FSR

2) Cavity depth selection: A. Saran et al, explained as the cavity depth increases, ΔλFSR narrows down, reduce the fringe visibility and leads to a situation where consecutive orders will overlap. As the value of cavity depth approaches λ 2 fringe visibility 0 approaches zero. 2n Δλ cavity

2 n

cavity

Δ λ

LED

By combining upper and lower bound, the limiting values between which the cavity depth should lie, is expressed as [9]:

λ0 4

≤L≤

λ20 2 ncavity Δλ LED

0.35 0.3

1.5E-07

0.25 0.2

1.0E-07

5.0E-08

deflection

0.15

Reflectivity

0.1 0.05

0.0E+00

0 0

9,911

19,822

29,734

39,645

49,556

Pressure (pascal)

Fig. 4 Plot of the deflection and predicted response of the Fabry-Perot pressure sensor for pressure range of 0-40kPa

LED

To avoid the overlapping of consecutive orders, the cavity depth of FPI should be less than . λ 20

0.4

2.0E-07

Eq. 10

Diaphragm deflection (m etre)

Δλ FSR ≈

Fig. 3 Plot of the periodic change in reflectivity RF with change in cavity depth, L

Reflectance

⎡ 3a 4 (1 − μ 2 ) ⎤ h=⎢ Pmax ⎥ ⎣ 4 E λ0 ⎦

B. The Dynamic Properties of the Fabry-Perot Pressure Sensor Title and Author Details 1) Frequency response: The natural/resonant frequency, fn of the circular plate is a function of the dimensionless parameter κ [13]

which is 0.2125um ≤ L ≤ 10.32um

fn = Where

156

Eh3 κ 2 ij 2π .a 2 12ρ (1 − μ 2 )

Eq. 12

a is the radius of the sensor diaphragm, h is the diaphragm thickness,

E is the Young’s modulus of silicon dioxide, ν is the Poisson’s ratio and ρ is the mass per unit area for silicon dioxide. κ2 = 10.22 for the fundamental mode of the circular plates with clamped edge [13]. Calculation in Eq.12 indicates that the natural frequency of the fundamental mode for Fabry-Perot pressure sensor is 1.405MHz (radius of the diaphragm: a = 62.5μm, thickness of diaphragm: h = 2 μm, mass density of silicon dioxide: ρ =2200 kg/m2 ). 2) Operating Frequency Range: Generally, operating frequency range for the sensor should be selected well below (at least 60%) or above the natural frequency [5]. Hence, the operating frequency range of the Fabry Perot pressure sensor is 740 kHz – 2.94 MHz. 3) Resolution: Here the resolution means the minimum detectable cavity change this cavity length resolution corresponds to a pressure resolution. The resolution of the sensor can then be stated in terms of the wavelength and the finesse, F, of the resonator as [18]: Resolution = F (2nL /λ) Eq. 13 where F = coefficient of finesse = [2r / (1 - R2)] 2 Eq.14

suffers the creeping behaviour of the polymeric-based materials when pressure is applied [3, 15, 16]. IV.

RESULTS AND DISCUSSIONS

Here, simulation of the basic structure has been done in order to evaluate the optimal lateral dimensions of the diaphragm. Coventor Ware simulator enable to depict the mechanical behaviour of the sensor for the real-life application. The design pattern of Fabry-Perot pressure sensor (radius of the diaphragm: a = 62.5μm, thickness of silicon dioxide diaphragm: h = 2μm, cavity depth: 1.7μm) A. Simulation Results: PDMS effects on diaphragm’s deflection Sensor diaphragm is simulated using Coventor Ware simulator for two different cases. In the first cases, the diaphragm is combined with PDMS layer. In the second case, the same simulation was performed on the diaphragm structure formed using the thin layer silicon dioxide diaphragm alone. As the pressure increases, the diaphragm deflection increases, as seen in Fig. 5. Diaphragm deflection Vs Applied pressure (simulation)

0.0000002

Diaphragm deflection (m)

The finesse is 0.948; thus the resolution of the Fabry Perot pressure sensor is 10.37 Pa. C.

Design consideration of PDMS diaphragm. During operation, it is important to ensure that the diaphragm works well without failure. To make it possible, the maximum force applied by the actuator mechanism must not exceed the elastic limit force of the PDMS diaphragm [15]. According to the Tresca yield criterion (maximum yielding stress criterion) for the plane stress case, the elastic limit forces of the diaphragm can be expressed as: 4 πk 2 Flmt = h2σ y ( 2 ),− − − > when_ 1 ≤ k ≤ 1.6 Eq.15 3 2k −1 2 8 πk Flmt = h2σ y ( ),−− > when_ k ≥ 1.6 3 (1+ v)(4k 2. ln k +1)

where σy is the yield strength of the diaphragm material (PDMS=20kPa). k = a/b, in which a is the radius of the diaphragm b is the radius of the embossed diaphragm. h is the thickness of the diaphragm. v is the Poisson’s ratio Obviously, PDMS diaphragm cannot stand alone as pressure sensor diaphragm as they will easily collapse. At least 150 μm thick of PDMS diaphragm for having elastic limit pressure of 50.2 kPa is needed to withstand the maximum pressure for the detection of the physiological pressure range 0~300 mmHg/ 0~40 kPa [2]. If the PDMS diaphragm is too thick, most probably it will extremely

0.00000015

0.0000001

Without PDMS With PDMS 0.00000005

0 0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Pressure (Pascal)

Fig. 5 Deflection of the diaphragm on the presence and absence of the PDMS.

As seen in Fig. 5, the presence of the PDMS with 10um thick on the top of oxide diaphragm has less significant on the sensor’s diaphragm deflection. But PDMS is important to support the micro-thin silicon dioxide from disintegrate during the sensor operation. PDMS enhance the flatness of a deflecting diaphragm in the active device area, with the optimization of the degree of parasitic signal averaging effect, the intensity of the detecting output signal, and the mechanical stability of the micro-cavity structures [17]. This is the reason why PDMS layer is neglected during the sensor design process. Fig. 6 a) and b) shows the stress distribution at the diaphragm surface when a maximum pressure of 40kPa is applied on it. The maximum stress is at the centre of the diaphragm and the minimum stress is at the diaphragm’s clamp edges.

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ACKNOWLEDGMENT The authors would like to thank Universiti Teknikal Malaysia Melaka (UTeM) for the financial support in the research activities among the staffs. An appreciation is also dedicated to colleagues and those who involved directly or indirectly in producing this paper.

Fig. 6 Deformation map on the central area of the movable diaphragm at maximum deflection, generated by the residual stress gradient; a) top view b) centre-slice view.

REFERENCES [1]

B. Theoretical and simulation results for diaphragm’s deflection. Diaphragm deflection trend is compared between theoretical and simulation as shown in Fig. 7.

[2]

Diaphragm deflection Vs Applied pressure

[3]

Diaphragm deflection (metre)

0.00000025

0.0000002

[4]

0.00000015

0.0000001

Calculation

[5]

Simulation

0.00000005

0 0

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20000

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30000

35000

40000

45000

Pressure (Pascal)

[7]

Fig. 7 Simulated and calculated deflection of the membrane as a function of applied pressure.

Graph in Fig. 7 shows that the theoretical and simulation results on sensor’s diaphragm deflection are almost identical. As the pressure increases the discrepancy increases. The simulation result is approximately 10% lower than the modeled value at maximum pressure of 40kPa. This approves the theoretical results previously done. V.

[6]

[8]

[9]

[10]

CONCLUSIONS

This research has successfully design and simulates an optical fibre Fabry-Perot pressure sensor with PDMS diaphragm which has the potential of detecting low pressure for medical application. A simple micromachining process compatible with MEMS was presented in fabricating Fabry-Perot cavitybased pressure. Pressure sensors is designed to respond over the pressure range 0 ~ 40kPa and operating at 850 nm. Good agreement of the data from the theoretical and the data from the simulation shows the excellent performance of the novel pressure sensors for accurate pressure measurement. The optimum conditions for having a PDMS layer underneath silicon dioxide diaphragm as a composite diaphragm of the pressure sensor were determined. This PDMS-Oxide composite diaphragm is designed for improving the sustainability of pressure sensors. The sensor’s pressure sensitivity is 0.0056 um/kPa and the resolution is 10.37 Pa, which are an adequate achievement in comparison to existing pressure sensors for medical application.

[11]

[12]

[13] [14] [15]

[16] [17]

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