Resonant MEMS microsensor for the measurement of fluid ... - UMEL

Resonant MEMS microsensorfor the measurement of fluid density and viscosityO. Vancauwenberghe 1 , A.R.H. Goodwin 2 , E. Donzier 1 , M. Manrique 2 , and F. Marty 31 Schlumberger Doll Research, 36 Old Quarry Road, Ridgefield CT 06877, USAemail: vanco@slb.com2 Schlumberger Cambridge Research, High Cross Madingley Road, Cambridge CB3 0EL, UK3 Groupe ESIEE, SMM, Cité Descartes, BP 99, F-93162 Noisy-le-Grand, FranceSummary: A resonant MEMS microsensor was developed to measure fluid density and viscosity. Itconsists of a thin plate made of a SOI top layer vibrating at resonance in its first bending mode. Its workingprinciple is based on the resonance frequency and quality factor affected by the surrounding fluid densityand viscosity. Measurements have been done in a series of gases and liquids at different pressures andtemperatures. The resonant MEMS is able to measure densities to ± 1% in the range of 1 to 1100 kg/m 3 andviscosities to ± 5% in the range of 10 to 10 5 µPa s.Keywords: Density, viscosity, Resonant MEMS, vibrating plate, SOICategory: 4 (Non-magnetic physical devices)1 IntroductionIn the petroleum industry, measurements of densityand viscosity are required to determine the value ofthe produced fluid and production strategy. Densityand viscosity measurements are also important inindustrial process control, especially in chemicaland food industries.We took advantage of the fact that the vibrationof a plate is affected by the surrounding fluid todesign a resonant MEMS microsensor using SOIwafers and DRIE micromachining. In this paper,we will describe our sensor working principle andfabrication, and report the measurements obtained.to control and measure the resonance frequency f aswell as the amplitude or equivalently the qualityfactor Q.Fig. 1. Picture of the whole Si resonant MEMSmicrosensor with main components indicated.2 Principle of operationThe resonant MEMS microsensor, shown in Figure1, consists of a thin vibrating plate made of the topsilicon layer of a Fusion-Bonded SOI wafer. Theuse of SFB SOI wafers allows us to choose at willthe thickness of the vibrating plate and simplifiesthe DRIE micro-machining steps by providing anetch stop with the buried oxide (BOX).To drive into resonance the vibrating plate,magnetic forces are used as illustrated in Figure 2.The device is placed in a constant magnetic field Bgenerated by an external electromagnet or apermanent magnet. With an alternating current Iinjected in a coil fabricated on the plate top surface,alternating Laplace forces F put the plate in forcedoscillations. When the current is at the plate firstnatural frequency, the plate vibrates in resonance inits first bending or flexion mode with maximumamplitude. Piezoresistive gauges configured inWheatstone bridges and placed close to theclamped edge are used to sense the varying strainsin the plate as it oscillates. These bridges allows usFig. 2. Actuation principle by Laplace forcesWhen the MEMS sensor is placed in a givenfluid, its resonance characteristics, f and Q, will beaffected by the surrounding fluid as follows. Thefluid in proximity to the oscillating plate is movedby the body’s motion, adding effective mass orinertia to the intrinsic mass of the plate, hencedecreasing f. The shearing associated with the fluidmotion around the plate gives rise to viscous energyloss per cycle, and so makes Q < Q vacuum . Thus, thedensity ρ and viscosity η of the fluid may beobtained by measuring f and Q of the vibratingplate in resonance.BFI18

3 MEMS fabricationThe starting wafer is a 4” SFB SOI wafer with a topSi layer 20 µm thick. A thermal oxide is firstgrown, then a 0.4 µm PolySi layer is deposited,implanted with boron and patterned to define anRTD for temperature in-situ measurement and thepiezoresistive gauges for resonance control and fand Q measurements. After passivation and contactopenings, a 1 µm thick aluminum layer is sputterdeposited and patterned to define the coil and otherinterconnections.DRIE is then used to etch from the front side theSOI layer around the plate and from the back sidethe Si substrate all underneath the plate. A final HFetch of the BOX layer releases the vibrating plate.Figure 3 shows a completed resonant MEMSsensor in its package specifically designed to allowit to be dipped in various fluids, liquids or gases, atvarious pressures (up to 70 MPa or 10 kpsi) andtemperatures (up to 150 °C).4 MeasurementsFig. 3. MEMS in its packageTable 1 shows f and Q measured in vacuum and invarious fluids, namely inert gas (Ar), natural gas(CH 4 ), reservoir oil, formation water, and siliconeoil. In vacuum and at 298 K, f 0 is 5.3 kHz, in goodagreement with FEM simulations with ANSYS.Fluid ρ (kg/m 3 ) η (mPa⋅s) f (Hz) QP → 0 5326 4556CH 4 7.23 0.011 4722 127Ar 671 0.049 1429 60Crude oil 774 1.02 1160 10Brine 1060 0.99 1005 12Si oil 1910 2200 527 2Table 1. f and Q in vacuum and various fluids.With some approximations, simple relations canbe derived to describe the dependency of f and Q onthe fluid density ρ and viscosity η:ff⎛πwρ= ⎜1+4h ρ⎝0 Si⎞⎟⎠−1232and Q f ηρ = CSTwhere ρ si is the Si density, w and h are the platewidth and thickness and CST is a constant [1, 2, 3].However, a more elaborate model [3] wasnecessary to account for the f and Q variations overthe whole range of densities and viscosities for bothgases and liquids.To calibrate the microsensor, three parametersdefined in the model need to be adjusted by fittingthe measures taken with argon. After this rathersimple calibration, densities in the range of 1 to1100 kg/m 3 can be measured to ± 1%, andviscosities in the range of 10 to 10 5 µPa s to ± 5%.These accuracies on ρ and η were obtained bycomparing measured values with either acceptedliterature or experimental values.Figures 4 and 5 show the error on measureddensities and viscosities for Ar, N 2 , CH 4 , heptane,crude oil, formation water and reference standards.10 2 Dr /rh (expt.)/(mPa.s)210-1-2100000Ar 333 KAr 353 KAr 373 KAr 393 KN2 333 Kn-heptane 333 KCrude OilFormation waterVis + den STD0 200 400 600 800 1000 1200r /(kg/m 3 )100001000100Fig. 4. Relative error on measured densities10N2CH4ArHeptaneCrude oilFormation waterVis + den STD10 100 1000 10000 100000h (lit.)/(mPa.s)Fig. 5. Comparison between measured viscosities andreferenced valuesReferences[1] J.E. Sader, “Frequency response of cantileverbeams immersed in viscous fluids with applicationsto the atomic force microscope”, J. Applied Physics84 (1998) 64-76, and references therein.[2] L.D. Landau, E.M. Lifshitz, Fluid mechanics,Pergamon (Oxford, 1989).[3] A.R.H. Goodwin, E. Donzier, M. Manrique, O.Vancauwenberghe, to be published.19