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ScienceDirectProcedia Engineering 00 (2014) 000–000

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EUROSENSORS 2014, the XXVIII edition of the conference series

3D Multiphysics Modelling of an SOI CMOSMEMS Thermal Wall Shear Stress Sensor

C. Falco1*, A. De Luca1, S. Sarfraz1, I. Haneef2, J Coull1,S.Z. Ali3, F. Udrea1

1Department of Engineering, University of Cambridge, Cambridge, UK2 Institute of Avionics & Aeronautics Air University, Islamabad, Pakistan

3Cambridge CMOS Sensors Ltd, Cambridge, UK

Abstract

This work presents for the first time a 3-D model of an SOI CMOS MEMS thermal wallshear stress sensor using multiphysics approach. The model involves three differentphysical domains and, when compared with the experimental results, shows an excellentagreement in every condition.

After the validation process, the model has been used to perform a transientanalysis on the device. The electro-thermal transient time, defined as the timerequired from the device to change its temperature from 10 to 90% of the steady statevalue when a step is applied to the biasing current, has been evaluated.

© 2014 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of the scientific committee of Eurosensors 2014.

Keywords: flow sensor, modeling, MEMS, 3D model, wall shear stress

1. Introduction

The introduction of the MEMS (micro electro-mechanical systems) technologyhighly improved the capabilities of integrated devices. The MEMS technologyis based on two technological steps: thin layer deposition of a wide range of

** Corresponding author. Tel.: +44 (0)1223 748311.E-mail address: cf361@cam.ac.uk

1877-7058 © 2014 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of the scientific committee of Eurosensors 2014.

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materials and etching with different grades of selectivity and isotropy.Those devices shows better performances compared to the bulk ones in termsof: reduced inertia, higher spatial resolution, smaller power consumptionrequired to reach the same sensitivity and higher cut-off frequency [1]. MEMS technology is extensively used for sensors in a wide range of

applications; two different approaches can be used for the sensing process:direct when the quantity to measure is directly related to the signal output(often using moving elements) or indirect where the two signals are relatedvia a third physical quantity, often temperature (this kind of devices arecalled “thermal MEMS sensors”). This paper analyses a thermal SOI MEMS CMOS sensor for the wall shear stress

τ, defined as the stress that a viscous fluid exerts on a surface because ofthe friction. The working principle for this device involves several coupledphysical domain: joule heating, thermal conduction, natural and forcedconvection.While a number of thermal wall shear stress sensors have been reported in

the literature [2,3], there are few examples of numerical modelling, but theyare not 3-D [4] or they do not include the heat dissipation [5], whereas thiswork overcome both the limits.The device, the technology used to produce it and the working principle will

be described in §2, together with the characterization results in stagnantand moving air. Later, in §3, the numerical model is described in details,including all the approximations and assumptions done during the developmentprocess. §4 presents the numerical results, compared to the experimentalones. Eventually, a transient simulation has been performed and the resultspresented in §5.

2. Device

The device presented here is a thermal MEMS flow sensor, thus it contains aheater – a 2 μm×400 μm metal hot-wire placed perpendicular to the flowdirection and biased with a constant current up to 10mA reaching atemperature up to 300oC identified as R3 – and one or more thermal sensorsaround it, in this case four identical resistors (R1, R2, R4 and R5) parallelto the heater at a distance of 200 and 400 μm on both sides, using the metalTCR to evaluate the temperature. Every resistor is connected to four tracks:two are wide (amperometric) and inject the biasing current, two are narrow(voltmetric) and measure the voltage across the resistor with high precision.The device has been produced with a standard SOI CMOS technology, with the

tungsten resistors embedded in a layer of silicon dioxide above the siliconwafer. The whole structure is then covered with silicon nitride to protectthe device from the atmospheric impurities. In order to improve the thermalinsulation from the heating element to the environment, the substrate is

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locally removed from the central region using a deep RIE (Reactive IonEtching) obtaining a membrane configuration. After a dicing step, the chip isglued to a golden substrate using a metal-based die attach. A top view of thecomplete chip and a schematic cross-section (not to scale) are presented inFig.1When placed in stagnant air, the temperature profile obtained inside the

membrane is symmetric, and the resistors output is the same for the couplesR1-R5 and R2-R4. Two effects can be identified when adding the flow: the heatremoved from the chip will increase (reducing the temperature in the heaterand thus the voltage across it) and the temperature profile will lose itssymmetry (the heat will be removed more efficiently from the upstream regionthan from the downstream one). The flow direction can be detected with adifferential measure on the lateral resistors, whereas it is undetectablefrom the voltage on R3.

Fig. 1 – (a) optical micrograph of the SOI CMOS wall shear stress sensor chip, with someimportant dimensions.. (b) Schematic diagram showing the sensor cross section (not to scale).

3. 3-D Model

The model has been created using Comsol Multiphysics 4.4, that has thecapability to couple analysis performed on a structure in different physicaldomain. In order to create a complete model, all the physical aspects hasbeen taken into account: joule heating for the electrical power dissipationand heat transfer via both conduction and convection (natural in stagnantair, forced when the flow is included).The model has to include, together with the chip, the air volumes above and

below the active region. Furthermore, die attach and package has to beincluded because of their important role in defining the temperature profile:they add a non-negligible thermal resistivity (22W/K) in series on the heat

(a)

(b)

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dissipation path, with an important effect (up to 10%) on the temperatureprofile inside the structure.In order to reduce the mesh count in the model (directly related to the

computational time), some approximations and assumptions has been made: All the pads are neglected: they are above the substrate where the

temperature is assumed constant; Only the amperometric tracks are included: the voltmetric ones are

narrower and don’t dissipate energy; The structure is halved along a plane parallel to the flow: the

structure is symmetric under every point of view, with the properboundary conditions on the cutting plane the results can be extended inthe other half.

The final structure can be seen in Fig. 2a, the chip (without air volume andpackaging elements) in figure 2b. The last critical point to consider is thedefinition of the boundary conditions.For the electric domain, the external surface of all the tracks is defined

as ground (reference for the voltage) and a current density is applied on theopposite edge.For the thermal domain, the environmental temperature has to be fixed as

reference in the structure, the surfaces considered here are the bottom ofthe package and the flow entrance surface .The last domain is the fluid-dynamic, and the conditions applied in this

case are: velocity fixed in the entrance and the top surfaces with aparabolic profile, and no slip (null velocity) at the bottom surface.

4. Numerical Results and model validation

The model has been validated in all the different physical domains. Firstly,the temperature in all the sensing point for 3 different values of current(6.5, 8.5 and 10mA) and wall shear stress ranging from 0 to 0.3Pa, with aremarkable agreement between numerical data and reality (an error lower than5%, Fig. 3a).

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Also the electric output has been validated, considering both the change inthe voltage across the heater (anemometric approach, Fig. 3b) and thedifferential voltage in the resistor couples 1-5 and 2-4 (calorimetricapproach, Fig 3c). Those results shows the capability of the model toaccurately describe the device answer for every value of biasing power andwall shear stress up to 0.3[Pa].

Fig. 2 – 3-D view of the structure included in the model, complete (a) and without air and

packaging elements (b)

Fig. 3 – Comparison between numerical and experimental data: temperature profile for a biasingcurrent of 10mA and different wall shear stress values (a); output voltages for the anemometric(b) and calorimetric (c) configurations as a function of the wall shear stress. Lines identifythe numerical data, markers are for the experimental data point.

5. Transient Analysis

Once validated with the process described above, the numerical results canbe assumed to be an excellent description of the reality. Thus, the numericalresults can be used to gather more data about the device behaviour thatcannot be obtained experimentally.A transient analysis is presented here, for determining the turn on time

defined as the time required for the temperature to go from the 10 to the 90%of the steady state value. To analyse this, a step change in the biasingcurrent has been applied without any fluid motion, and the value obtained is15ms. This is high compared to other devices reported in literature, and twopossible reasons can be found for that:

The high membrane diameter dramatically increases the response time;

(a)(b)

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The constant current (CC) driving mode, chosen for its simplicity,requires a longer time than the constant temperature (CT) one toreach the steady state

This parameter can be used to configure another driving system, with apulsed current signal. The pulses has to be longer than the rise time toreach the steady state temperature profile, with a consistent reduction inthe power consumption (depending on the duty cycle, and as high as 50%).

6. Conclusions

The model presented in this paper has proven to give a perfect descriptionof the actual device, despite the approximation introduce to reduce the meshcount.The device has been presented first in §2, then the model has been

presented in details in §3. The results obtained has been compared with theexperimental during the whole developing process, and the matching levelreached is impressive as reported in §4.The numerical model has then been used to perform a transient analysis. The

response time has been evaluated in both the electro-thermal and the fluid-dynamic domain. Results are reported in §5 and will help in evaluating theoptimum driving signal for a pulsed mode configuration.

References[1] Kuo, Jonathan TW, Lawrence Yu, and Ellis Meng. "Micromachined thermal flow sensors—A

review." Micromachines 3.3 (2012): 550-573.[2] I. Haneef, S. Z. Ali, F. Udrea, J.D. Coull, H. P. Hodson, High Performance SOI-CMOS Wall Shear Stress

Sensors, IEEE Sensors conference 2007, 1 (2007) 1060-1064[3] A. De Luca, I. Haneef, J. Coull, S. Z. Ali, C. Falco, F. Udrea, A thermopile based SOI CMOS MEMS wall

shear stress sensor, Sensor Conference CAS 2013 International, 1 (2013) 59-62.[4] Lin, Q., Jiang, F., Wang, X.-Q., Han, Z., Tai, Y.-C., Lew, J., and Ho, C.-M., MEMS Thermal Shear-

Stress Sensors: Experiments, Theory and Modeling, Proceedings of Solid-State Sensor Actuator Workshop(2000), 304–307.

[5] P. Fürjes, G. Légrádi, Cs. Dücső, A. Aszódi, I. Bársony, Thermal characterisation of a direction dependentflow sensor, Sensors and Actuators A, 115 (2004) 417-423.