Design and tuning of MEMS based cantilevers and combs differential capacitive acceleeometer

Abstract

Micro electro mechanical systems (MEMS) are devices made utilizing sensors, actuators, electronic read out circuits on a suitable base called substrate with packages for its protection from external environment. Along with electrical counterpart, major role is played by Mechanical components which is mainly composed of Cantilevers, beams, different shape suspensions, proof mass and anchors. Cantilevers contribute its vital role in almost all MEMS structure bearing compression, tension, bending and twisting mode. So, utilizing a simple cantilever, to help form a complex device like accelerometer is studied in details in this research work. Along with various type of loads acting on cantilevers like lateral pointed and distributed force, residual mean stress, gradient causing out of plane deflection, compression and tension loads are used to axially tune the performance of the cantilever. An initial judgement of behaviour is studied for materials like Silicon, Aluminium, Gallium Nitride (GaN) and Silicon carbide (SiC) for harsh environment and futuristic applications. Dynamic behaviour pertaining resonant frequency of MEMS resonator and its shift by axial tuning mechanism is studied in advance to lay the foundation for complex device like micro accelerometer. MEMS devices require active mechanism for tuning in field operation because post fabrication, design parameters may change due to residual stress, fabrication imperfections, temperature etc. Application of axial compressive (C) or tensile forces (T) allows one to implement this tuning. Effects of compressive and tensile forces, stress gradient (SG) and transverse loading is analysed for futuristic materials like Gallium Nitride (GaN) and Silicon Carbide (SiC) for use in high temperatures and harsh environments. The effects of above forces on pull in voltage (VPI), bandwidth (BW) and resonance frequency (RF) are analyzed. Results for Aluminum cantilever beam show, that VPI decreases by ~1.2 times at low beam lengths of 200 μm and about 5 times at higher length of 800 μm when tensile force is changed to compressive under loading. Similar trends are holding for GaN and SiC except that pull in voltage scales up in proportion to material‘s Young‘s modulus, E. An analytical relation of pull in voltage VPI vs. Young‘s modulus E and Poisson‘s ratio ‗‘ are predicted. Effect of stress gradient is also studied and it is found that although it affects pull in voltage within 10% range, application of axial compressive or tensile forces further change it within 20% range. Comparison of analytical results for pull in voltage,VPI with Coventorware software shows a better agreement for low loading of 10% compared to full loading of 100%. Also, Log-Log plot of pull in voltage vs. length is derived and predicted that it can be used to estimate the contribution of charge re-distribution and fringing field. Furthermore, bandwidth decreases by 16 Hz when compressive force is applied and increases by 66 Hz when tensile force is applied for Aluminium cantilever with 400 μm length and 50 μm width. Similarly, RF decreases by 165 Hz in compression and increases by 623 Hz for tension loading. The predictions of our model agree well with experimental and finite element method (FEM) results (within 4.54% and 6.46% respectively). Acceleration is measured where ever there is a change in velocity of an object in a particular motion to control its dynamics. MEMS based micro accelerometers sensors have been evolved from the last two decades. The advantages embedded in the MEMS technology surpasses the traditional accelerometer used which were bulky, less sensitive and quite costly for intended applications. The amalgamation of IC fabrications technology in MEMS fabrication paves the strong foundation for reliable, robust and state of the art devices in MEMS domain. For applications like defence sectors, aerospace, medical, automobiles, consumers applications various grades of accelerometers are used. Various sensing techniques like Piezo, thermal, tunnelling, optical, resonant, capacitive are major contributors in the design, fabrications of sensors. All the techniques have their respective advantages as well as disadvantages. Capacitive sensing method employed is very useful and high in demand due to its simplicity, compatibility and easy to fabricate using MEMS foundry. Using capacitive methods of sensing, three parameters area, gap between plates (electrodes) and dielectric needs to be changed. The two parameters viz. area and gap change are very common in various sensing devices. Two plates and three plates methods have been utilized using gap change approach in designing micro accelerometers. A differential capacitive approach can be used using three plate methods where centre plate proof mass, suspension springs and lower and upper electrodes play vital role in deciding sensitivity, resolutions, range of operations. A very big fundamental problem associated with gap change approach is Pull down phenomenon common in MEMS plate, diaphragm-based designs. Apart, readout integrated circuit (ROIC) used for signal reading follows complex closed loop architecture for better performances. Till date no simple, easy to realise differential capacitive design has been evolved and utilized for area changing approach in micro accelerometers. A dissolved wafer process (DWP) technology-based design where area changing scheme has been used which had its own limitations in exhibiting directions which is a fundamental essential requirement of any accelerometer. A novel design approach for detecting acceleration using COMBS structural design is presented for catering various requirement for navigational and defence applications. Mechanical structures with proof mass and compliant suspension beams offers different approaches for design of micro accelerometer. Gap change method and Area change methods provide their various advantages and disadvantages for accelerometer design. Enhanced sensitivity, bandwidth, operational range are key parameters on stake The concept utilizes area change of vertical combs- based structure in such a way that a very simple, easy to use and state of the art device is proposed for futuristic MEMS accelerometers. The BOX layer embedded in SOI wafers provides two separate zones for utilizing the differential capacitive concept. The fixed fingers set is cut in SOI wafer and movable fingers are made from a separate silicon wafer. The acceleration acting on the proof mass of movable structure ensures movement of silicon fingers in SOI wafer cut fixed fingers thereby providing change in capacitance. This change in capacitance is read using application specific integrated circuit (ASIC). This SOI comb-based accelerometer is able to identify the direction of acceleration simply in differential form in addition to numerous other advantages in performance parameters. A very significant improvement (almost double) in sensitivity has been found in this design strategy. Along with this good dynamic behaviour (Bandwidth), improved operational range and better figure of merit (FOM) has been reported. A new designed fabrication scheme has been proposed for the micro accelerometer mentioned. The design of  30g operation shows the enhanced linear range is achievable in SOI approach beating the limitations of diffusion layer depth in Silicon based dissolved wafer process (DWP) technology for fabrication of MEMS accelerometers. Two technological approaches are compared, one having same thickness of fixed and movable interdigitated fingers (for DWP) and the other having different thickness using an SOI wafer. Remarkable sensitivity improvement by a factor of upto two is achieved for capacitance change per unit g (del C/g) in new differential SOI design presented here. Bandwidth of the device is also improved significantly in SOI compared to DWP design. Furthermore, effect of temperature (-40 °C to 125 °C) has almost negligible influence on (del C) due to in built differential concept of comb type fingers compared to DWP technology. Cross axis sensitivity is also very low due to stable, robust design of the accelerometer offering less stiction sideways and better pull in stability. Simple analytical relations for dynamically changing overlap capacitance are derived and presented. These analytical results are compared with simulations using Coventorware software and agree within 1.8% in linear range of operation upto tip deflection of 8.5 μm. Effect of fabrication tolerances, including all process steps, on sensitivity delC/g and bandwidth (BW), are also studied and results presented. An overall figure of merit (FOM) is included which is better in this study compared to available literature. Further, only two wafers are needed to fabricate the proposed differential capacitive sensing compared to conventional push pull three plate system using three wafers. Separate Deep Reactive Ion Etching (DRIE) step on two different wafers offers better debris removal as compared to interdigitated fingers cut by single DRIE step. Residual stress is an inherent part of the MEMS fabrication processes which needs to be addressed in such a way that its effect could be minimised if not nullified. Stress analysis for mean and gradient induced deflections and warping in the new Micro accelerometer is done both analytically as well as by simulation. A thorough comparison between DWP technology and SOI technology-based accelerometer is presented with advantages of SOI technology with promising results. Theoretical formulations developed for residual and working stress which can be utilized for optimizing the performance of micro accelerometer. Maximum reported experimental mean stress (500MPa) and stress gradient (0.1MPa/μm) is also studied in detail. A comparison of analytical and simulations for stress induced deflections are in good agreement (within 5.29 % and 3.97 %) for residual planar and axial stress respectively. Working shear stress in torsional beams at 30g in proposed new differential vertical SOI comb type accelerometer is lesser by 20.9 MPa compared to DWP technology. For 1000g shock, the SOI case, stress of 0.55 GPa having a better safety margin by a of factor of 2 compared to fracture limit (FL) of 1.1GPa of silicon. In contrast to this, DWP has a stress of 1.25GPa and hence it crosses FL value and has no safety margin. Warping stress induced in restrained torsional beam have been analyzed and compared with simulation results and found to be in good agreement within 1.87% for SOI technology case and 11.25% for DWP technology case. The effect of initial tip deflection (3.4 μm due to 500 MPa stress and 0.1 MPa/μm stress gradient) on sensitivity has marginal effect on milli g range but has moderate influence on limiting high g operational range. Finally, to tune the effect of stress gradient post fabrication in field which hamper the overall performance of the accelerometer, SOI based electrodes and Cantilevers ears (attached to proof mass) are utilized harnessing electrostatic actuation tuning. A new conceptual utilization of Silicon on Insulator (SOI) wafer is reported for bi-directional vertical electrostatic fringe field tuning of the Micro Electro Mechanical Systems (MEMS) micro accelerometer for compensating stress induced curling (up and down), sensitivity and mechanical dynamic response. The buried oxide (BOX) layer based SOI wafer provides bi-directional electrodes for applying bias voltages independently. Residual stress induced curved deflection due to stress gradient is targeted for tuning and reducing its effects using fringe field electrode configuration in SOI wafer technology. Movable silicon structure is electrostatically (utilizing fringe field) brought back near to original mean position with softened stiffness (increase in sensitivity) and reducing drastically the effects of stress gradients. The simulations are carried out using Coventorware and COMSOL Multiphysics softwares. The deflection results obtained by both softwares agree within 7.69% for maximum deviation. There is a deviation in change in capacitance (del C) of 5.89 % when stress gradient of 0.1 MPa/μm and 17.62% when stress gradient of 4 MPa/μm is applied on the structure at 30g. This deviation can be tuned by above mentioned Bi directional tuning. Additionally, non-linearity induced by stress gradient in sensitivity can also be tuned by electrostatic fringe field effectively upto 18.64% when higher stress gradient (4MPa/μm) was affecting the structure. The proposed tuning concept can be utilized for other MEMS devices suffering from stress gradient issues. Coventorware, MEMS+ and COMSOL Multiphysics software tools have been used for cantilever and acceleration design and electrostatic actuation tuning simulations. The technical parameters for micro accelerometer viz. sensitivity, bandwidth, range of operations, cross axis sensitivity, pull in voltage characteristics etc. have been designed, simulated and analysed during this research work. A significant improvement seen in majority of these parameters particularly sensitivity and figure of merit (FOM). It may be argued that the advantages obtained in our design may be at the cost of some other parameters. It may be stressed here that major advantages of our proposed design are obtained by using SOI technology which is mature enough and doable. The tolerance level defined for micro accelerometer structure mainly combs fingers and torsion beams is achievable using state of the art high precision mask aligner (MA) and bond aligner (BA) technology present today. The SOI wafer tuning based concept introduced in the ending work, has the possibilities of reducing the gaps between three electrodes islands proposed (two SOI fixed and one movable cantilever on proof mass). So, there is a trade-off between voltage applied and stress gradient correction or compensation in the micro accelerometer structure. For small magnitude gradient tuning voltage requirements are low as compared to higher stress gradients.