Novel High-Resolution Lateral Dual-Axis Quad-Beam Optical MEMS Accelerometer Using Waveguide...
Malayappan, Balasubramanian;Krishnaswamy, Narayan;Pattnaik, Prasant Kumar
hv photonics Article Novel High-Resolution Lateral Dual-Axis Quad-Beam Optical MEMS Accelerometer Using Waveguide Bragg Gratings 1 2 Balasubramanian Malayappan and Narayan Krishnaswamy 1, and Prasant Kumar Pattnaik * Department of Electrical and Electronics Engineering, BITS-Pilani, Hyderabad Campus, Hyderabad 500078, India; email@example.com Department of Electronics and Communication Engineering, Sai Vidya Institute of Technology, Bengaluru, Karnataka 560064, India; firstname.lastname@example.org * Correspondence: email@example.com; Tel.: +91-40-66303612 Received: 8 June 2020; Accepted: 4 July 2020; Published: 18 July 2020 Abstract: A novel lateral dual-axis a-Si/SiO waveguide Bragg grating based quad-beam accelerometer with high-resolution and large linear range has been presented in this paper. The sensor consists of silicon bulk micromachined proof mass suspended by silica beams. Three ridge gratings are positioned on the suspending beam and proof mass to maximize sensitivity and reduce noise. Impact of external acceleration in the sensing direction on the Bragg wavelength of gratings and MEMS structure has been modelled including the effects of strain, stress and temperature variation. Acceleration induces stress in the beam thus modifying the grating period and introducing chirp. The differential wavelength shift with respect to reference grating on the proof mass is the measure of acceleration. To compensate for the effect of the weight of the proof mass and increase the sensitivity of the sensor, electrostatic force of repulsion is applied to the proof mass. For the chosen parameters, the designed sensor has a linear response over a large range and a sensitivity of 30 pm/g. The temperature of surroundings, which acts as noise in sensor performance is compensated by taking differential wavelength shift with respect to reference grating. By design and choice of material, low cross-axis sensitivity is achieved. The proposed design enables a high-resolution well below 1 g/ Hz and is suitable for inertial navigation and seismometry applications. Keywords: accelerometers; high-resolution; quad-beam MEMS; differential measurement; coupled-mode theory; nano-grating 1. Introduction Microelectromechanical systems (MEMS) technology ﬁnds various applications because of low cost, small size, ease of fabrication and reliable performance. Sensing is arguably the most prominent application of MEMS with branches that have developed into full-ﬂedged ﬁelds like RF-MEMS, BioMEMS, microﬂuidics and optical MEMS. MEMS sensors based on capacitive, piezoelectric and piezoresistive effects are limited in their performance due to electromagnetic interference (EMI). Capacitive and piezoelectric sensing requires that the electronic sensing must be placed nearby the sensor itself. Integrated sensors using optical readout methods, however, are unaffected by EMI and also do not add to the electromagnetic radiation acting as noise for the other sensors and devices in the vicinity, thus improving device performance [1–5]. Optical readout techniques offer very high sensitivity and resolution. Among optical components, Bragg gratings are widely used for various sensing applications because their response characteristics can be made sensitive to different external conditions like Photonics 2020, 7, 49; doi:10.3390/photonics7030049 www.mdpi.com/journal/photonics Photonics 2020, 7, 49 2 of 18 temperature, material, stress and pressure. Bragg gratings act as guided-wave optical reﬂection ﬁlters. The ﬁlter characteristics from centre frequency/wavelength, full-width at half maximum (FWHM), main lobe power and side-lobe powers are dependent on the properties of the gratings and its surroundings. Coupled-mode theory is used to analyze the Bragg grating properties. By design, Bragg gratings are not point sensors as their response depends on the conditions throughout its length. This makes Bragg gratings and particularly ﬁbre Bragg gratings (FBG) an economically attractive solution for various sensing applications [6–8]. Optical MEMS sensors based on the interaction of MEMS structure with free space light or light in the optical ﬁbre are limited in scope as they cannot be subject directly to vibration or acceleration. However, the integration of optical devices with MEMS enhances the performance of the sensor. Photonic-Integrated-Circuits (PIC), which hold promise of vastly improved performance with much reduced cost and power consumption by miniaturization of optics, are rapidly maturing for silicon platforms with standardization of various photonic library components . Optical MEMS based PICs, which rely on a change in optical properties of a waveguide by electromechanical actuation, have been found to have excellent potential for scalability due to low optical loss and device footprint in addition to low power consumption . Thus, optical MEMS sensors based on integrated light guidance are an attractive avenue for further research and development. An accelerometer is a sensor used to measure acceleration forces and are used for applications ranging from seismic prospecting, vibration measurement, constant/static force measurement to inertial navigation. Accelerometers are needed in several areas, where the change in speed or vibration in an object needs to be monitored or measured. Quad-beam-mass accelerometer is a popular MEMS accelerometer design commonly used with piezoresistive sensing elements . In the quad-beam accelerometer design, due to acceleration experienced by the device frame, stress is introduced into the suspending beams. By integrating sensing components to the beams, the acceleration is measured. Table 1 presents a summary of various optical sensing techniques for accelerometers. Encoding of acceleration in intensity of the output optical signal is a simple and efﬁcient mechanism for optical sensing suitable for harsh environmental conditions. In this technique, movement of proof-mass either modiﬁes the coupling between light input and output paths [12–14] or blocks the optical path [15,16]. It is a process amenable to integration into PIC. However, these designs have poor fundamental resolution limits. Integrated optical MEMS accelerometers based on microring resonators and racetrack resonators with a sensitivity of 0.015 m/g have been proposed for seismic prospecting [17,18]. The dynamic range of ring resonator based sensors is limited by the small displacement range over which optical coupling takes place. A high-resolution integrated resonant accelerometer based on an optical microdisk resonator was demonstrated in  where the photoelastic effect caused a shift in resonance frequency. To increase sensitivity, the microdisk was integrated with resonant tether of resonant accelerometer instead of the suspending arm. By using a narrow linewidth laser locked to an operating wavelength close to the resonance peak, a linear range of operation with a DC sensitivity of 6 g/ Hz for device natural frequency of 16.3 kHz has been obtained. In [20,21], ﬁbre is drawn and wound into microrings, which are positioned on sensitive regions of MEMS structures. This eliminates the need for light input and output coupling. For ring resonator based sensors, the acceleration is encoded in the resonance wavelength of the ring. Table 1. Commonly used optical sensing techniques for accelerometers. Sensing Technique Sensitivity Range Bandwidth Remarks Intensity Modulation [12–16] Low Low Medium Amenable to integration; free-space light propagation; source noise is crucial Ring resonators [17–21] High Low High Small footprint; non-linear sensor output; guided-wave propagation; wavelength shift due to acceleration Photonics 2020, 7, 49 3 of 18 Table 1. Cont. Sensing Technique Sensitivity Range Bandwidth Remarks Photonic Crystals [22,23] High Low High Coupling light into and out of sensor is challenging; guided-wave propagation; photonic bandgap is modiﬁed Diffraction Gratings  High Low Low to High Free-space light propagation; complex packaging; high sensitivity requires complex detection mechanism Interferometers [3,25–29] Low to High High Low to High Free-space light propagation; precise positioning and alignment needed Bragg gratings [30–36] Medium High Low Guided-wave propagation; wavelength-encoded acceleration; advanced interrogation schemes allow sub-pico strain detection In , the authors demonstrated a high-resolution integrated accelerometer using photonic-crystal nanocavity. A resolution in the order of ng/ Hz has been demonstrated based on the coupling of the optical ﬁeld from delicately tapered ﬁbre held in the evanescent region of the photonic-crystal zipper cavity. In , a nano-g accelerometer based on sub-wavelength diffraction gratings has been demonstrated. Although by optimizing the detection circuit, resolution close to the limits of optical sensing that were shown for this sensor requires complex packaging. Fabry-Pérot interferometric cavities formed with MEMS structures are popular for accelerometers as the accelerometer proof-mass itself can act as a reﬂecting end-face to form the cavity. The sensitivity of this class of sensors has been enhanced by increasing mechanical sensitivity [3,27–29] and moving from intensity based detection to coherence demodulation  to phase-generated-carrier (PGC) modulation . As the FP cavity length is mechanically modiﬁed due to acceleration, this method is based on free-space or unguided propagation of light which poses challenges in terms of quality of alignment and packaging and incurs high optical losses. Fibre Bragg grating (FBG) based accelerometers have been extensively researched and have been shown useful for high sensitivity measurement over a large range [30,32,33]. High resolution FBG based accelerometers have been demonstrated when used in combination with other resonant structures like ring resonators , a Fabry-Pérot (FP) cavity , -shifted ﬁbre Bragg gratings (PSFBG) , ultrastable lasers [34,39] and actively locked lasers using radio-frequency modulation [35,40]. Though silicon-on-insulator (SOI) based planar waveguide Bragg gratings have been applied to other sensing applications like pressure sensors [41,42], the integration of silicon based Bragg grating into PIC has not matured after the initial excitement based on silicon-nitride waveguides . Polymers are an attractive option for planar optical MEMS sensors as waveguides and Bragg gratings can be written directly onto a substrate. Polymer planar Bragg gratings based on materials like polymethylmethacrylate (PMMA) and TOPAS have been used to demonstrate strain sensors [36,43]. Properties of polymer Bragg gratings depend on humidity apart from temperature and strain and humidity immunity is important for robust performance . The major challenge with using Bragg gratings as strain sensors/accelerometers is that for high resolution (requires sharp Bragg peak), long grating length is required. Thus, the integration of planar waveguide Bragg gratings into MEMS requires relatively large structures. Waveguide Bragg grating based accelerometers are suited for high sensitivity quasi-static acceleration measurements like in seismometry. Since PIC components are generally based on a silicon/SOI platform, we present a planar Bragg grating high-resolution dual-axis accelerometer on silicon substrate. In this paper, we present the design and analysis of high-resolution integrated waveguide Bragg grating based optical MEMS quad-beam lateral two-axis accelerometer with a large linear range. Photonics 2020, 7, 49 4 of 18 The silicon wafer based accelerometer has silicondioxide beams and amorphous-silicon(a-Si) optical waveguide and gratings on these beams for the sensing elements. In our earlier works [45,46], we reported a simulation model of single axis accelerometer based on waveguide Bragg gratings. In this work, the design of a novel conﬁguration of lateral quad-beam optical MEMS accelerometer for multi-axis sensitivity with suppressed cross-axis sensitivity and immunity to environmental effects is presented. Further, detailed analysis of the mechanical and optical response of the proposed optical MEMS device has been done. In Section 4, plausible fabrication steps for realizing the proposed device and set-up for interrogating the sensor are detailed. Finally, results and conclusions are presented in Sections 5 and 6. 2. Sensor Conﬁguration Figure 1 shows a schematic of the proposed waveguide Bragg grating based MEMS quad-beam accelerometer with multi-axis sensitivity. The sensor consists of an amorphous-silicon (a-Si) waveguide with three Bragg gratings, Grating-1, Grating-2 and Grating-3 of different Bragg wavelengths such that their ﬁlter characteristics do not overlap, as shown in Figure 2. Grating-1 and Grating-3 are each integrated with two perpendicular suspending beam of the accelerometer. Transmitted Light Grating-3 Reflected Light Bulk Silicon SiO Amorphous Silicon Grating-1 Grating-2 Incident Light Figure 1. Schematic design of waveguide Bragg grating based Quad-Beam accelerometer: (Inset shows a cross-section view of one beam with amorphous-silicon(a-Si) waveguide and grating). Figure 2. Reflection spectra of proposed sensor showing Bragg peaks of Grating-1, Grating-2 and Grating-3. Normalized Power Photonics 2020, 7, 49 5 of 18 Grating-2 is integrated on the proof-mass and acts a reference for acceleration measurement. The Bragg gratings are in series conﬁguration with reﬂected light showing three peaks as in Figure 2 when broadband input is launched. Light is launched into the device through an integrated directional coupler which acts as a circulator  to enable collection of reﬂected light as the output. When the device frame is subject to a force, the proof mass displaces thus inducing stress in the suspending beams, which eventually results in a shift of Bragg wavelengths and reﬂection spectrum characteristics for Grating-1 and Grating-3. Depending on the direction of acceleration, the beams are either subject to compressional or tensile stress corresponding to blue or red shifts in the Bragg peaks. Grating-2 is insensitive to any external acceleration and acts as reference for noise cancellation due to variation of temperature experienced by the device. 3. Sensor Design and Mathematical Modelling Figure 3a shows the side view of the portion of the sensor showing beam dimensions and compositions. The waveguide core material is taken as amorphous silicon (a-Si) based on the proposed fabrication procedure detailed in Section 4. A silicon wafer is used as substrate for the sensor instead of SOI platforms. The buried-oxide (BOX) layer thickness in typical SOI platforms is limited to below 5 m. Also, the device layer silicon of such waveguides is thick (in range of 5–10 m) and would require ﬁne lapping, patterning and etching to realize the required dimensions. Instead, using a thermally oxidized silicon wafer of required thickness, a simple LPCVD process is sufﬁcient to deposit silicon of the required thickness, which can then be easily patterned using IC photolithography. Hence, to simplify the fabrication process, the core material has been chosen as a-Si. Figure 3b shows typical stress and consequently the strain proﬁle along beam length when subject to external acceleration. The sensor design and modelling will be discussed in following four subsections; mechanical properties of structure under acceleration studied using continuum mechanics, optical properties of waveguide Bragg grating due to stress and strain using coupled-mode theory, opto-mechanical coupling and sensitivity, cross-axis sensitivity and noise cancellation. 3.1. Mechanical Design of Quad-Beam Accelerometer Figure 3a shows the beams suspending the proof mass to be composed of silicondioxide (SiO ). Silicon proof mass is taken as a truncated pyramid with a square base, with a top side (L ) 4 mm and thickness (t ) 400 m. A truncated pyramid is considered to account for bulk-micromachined silicon proof mass. The density of silicon is taken as 2329 kg/m . SiO has much lower Young’s modulus and Poisson ratio than crystalline silicon. Strain induced in a material in response to applied stress/force is proportional to its Young’s modulus. Poisson ratio gives information of a material’s strain in a direction perpendicular to applied stress. Thus, a lower Young’s modulus and Poisson ratio is preferred for a multi-axis accelerometer, as it would yield higher response and lower cross-axis sensitivity. Under its own weight, the proof-mass of the quad-beam accelerometer displaces downwards inducing normal stress on the beam surface, T ¹zº given by , ow-normal 3¹l 2zº ¹ º T z = mg (1) ow-normal 2bh where b, h, l are the width, thickness and length of the beam respectively, g is the acceleration due to gravity and m is the mass of the proof-mass. The length of the beam is considered to be along the z-direction with z = 0 representing the position near the foot of the beam. For lateral acceleration of 1g applied parallel to one set of beams and perpendicular to the other, the in-plane stress components for the same amount of force are T ¹zº and T ¹zº, which can be taken as , ow-k ow-? ¹t hº ¹1.5L + lº T ¹zº = l 3z mg (2) ow-k bh L ¹L + lº p Photonics 2020, 7, 49 6 of 18 3¹l 2zº T ¹zº = mg (3) ow-? 2hb From the above equations, it is evident that beam geometry with a large width to height ratio is needed to minimize cross-axis sensitivity. The dimensions of proof-mass determine its mass and for maximizing the strain along beams, the mass must be maximized. Hence, based on practical considerations , the dimensions have been decided. The beams have a width of 210 m and height 5 m. The variation of all stress components along the length of the beam will follow the pattern of Figure 3b. As seen in Figure 3b, along the length of the beam suspending proof-mass, there is a change in sign of the strain (compressive to tensile or vice versa) with a portion of zero strain in the central region of the beam. The position where zero strain occurs and the amplitude and symmetry of stress distribution depends on the net magnitude and direction of acceleration experienced by the proof-mass. 5 µm 1200 µm 400 µm Bulk Silicon SiO Amorphous Silicon (a) Stress on beam surface (ı ) -ı L/2 0 L Position along length of beam (b) Figure 3. (a) Side view of portion of the sensor showing beam dimensions; (b) variation of stress along the length of the beam. The actuation of the waveguide Bragg grating depends on the strain along its length. To realize a lateral accelerometer, an electrostatic repulsive force equal to the weight of proof-mass is applied to minimize the normal stress. This can be achieved by metallizing the bottom surface of the proof mass, bonding the device with another wafer carrying an electrode and maintaining the same potential on both surfaces using external electrical supply. The separation(s) between electrodes determines the capacitance between two surfaces (C) and thus the potential to be applied for compensating the effect of weight. The electrostatic force, F for applied potential, V is given by, 1 dC F = V (4) 2 ds Photonics 2020, 7, 49 7 of 18 Amorphous silicon on top of the SiO layer represents the optical waveguide and has cross-section 2 2 dimensions in only the order of 4 m in contrast to the 1000 m cross-section area of the SiO . By rule of mixtures for the composite beam of individual Young’s modulus E and E having volume 1 2 fractions V and V respectively, for stress applied laterally to the stack of materials, the effective 1 2 moduli E is , eff E E 1 2 E = (5) eff E V + E V 1 2 2 1 Since the volume contribution of silicon waveguide in the structure is very low, it has a negligible impact on the effective Young’s modulus and thus the mechanical response of the device under acceleration. The fundamental vibration frequency ( f ) of the sensor is for out-of-plane vibration and is found using Rayleigh’s quotient as, 1 2E bh eff f = (6) 2 ml For the design values, f is found as 92.43 Hz and veriﬁed by ﬁnite element analysis using COMSOL Multiphysics. 3.2. Waveguide Bragg Grating Waveguide Bragg grating with surface-relief is designed for wavelengths around 1550 nm using TM mode for propagation. A rib waveguide with a core of a-Si height (d) of 1.5 m (slab thickness is 0.8 m and width 5 m), waveguide width 1.6 m runs over the SiO beam of 5 m thickness, which also acts as the cladding for the waveguide.The single-mode waveguide with the above dimensions satisfy the Soref condition  and have been reported earlier for realizing narrow bandwidth tunable Bragg grating based ﬁlters [50,51]. The slab of width 5 m is considered so that it does not adversely impact either the optical or mechanical properties of the sensor. The refractive indices of the core and cladding are 3.545 and 1.45, respectively. The mode proﬁle for fundamental mode propagating in this waveguide obtained by beam propagation method (BPM) is given in Figure 4. The dotted line in Figure 4 shows the transverse cross-sectional dimensions of the waveguide. E Mode Profile (m=0, n =3.486) y eff 1.6μm 0.7μm 0.8 μm 5 μm Figure 4. Mode proﬁle of the waveguide (dotted line shows the cross-sectional dimensions of the waveguide core). Photonics 2020, 7, 49 8 of 18 The longitudinal cross-section view of the Bragg grating is shown in Figure 5. For a grating of period , the Bragg wavelength, is (7) = 2n (7) B ef f where n is the effective refractive index of the waveguide calculated using waveguide analysis . ef f Period, Λ Air, RI =1 Incident Light Amorphous-silicon Transmitted n =3.545 core Light Reflected Light SiO n =1.45 clad Figure 5. Longitudinal cross-section view of surface-relief waveguide Bragg grating. As light propagates along the grating, due to the periodic corrugations, partial reﬂection occurs at each period. For light in which the wavelength satisﬁes the Bragg condition, the reﬂected and transmitted ﬁelds are in phase and thus the backward and forward propagating waves couple. The theoretical determination of this is performed using coupled mode theory [53,54]. Z-direction is the direction of propagation of light with grating boundaries at z = 0 and z = L . For all calculations, only the ﬁrst order diffraction and fundamental mode have been considered. Coupled mode equations of a Bragg grating with R and S as complex-amplitudes of forward-running and backward-running modes considered for analysis are (8) and (9). dR = i ˆ R¹zº + iS¹zº (8) dz dS = i ˆ R¹zº