Efficiency modeling of a CMOS MEMS convective accelerometer

2012 International Conference on Design & Technology of Integrated Systems in Nanoscale Era

EFFICIENCY MODELING OF A CMOS MEMS CONVECTIVE ACCELEROMETER B. Mezghani, F. Tounsi, M. Masmoudi

A.A.Rekik*, F. Mailly, P. Nouet

*University of Sfax, National Engineering School of Sfax EMC Research Group TUNISIA

LIRMM - CNRS/Univ. Montpellier 2 161 Rue Ada 34095 Montpellier Cedex 5, FRANCE

In contrast to the 2D model widely used in FEM simulations of convective accelerometers [5,8], the new alternative 3D model offers a more realistic modeling. This is because the real shape and size of all accelerometer elements are respected. Therefore, 3D FEM simulations, where all geometrical forms are volumes describing real situations, will enable the understanding of the sensitivity evolution in relation with various physical and geometrical parameters. This will allow to optimize the accelerometer geometry and in particular the heater and detector lengths. It should be noted that the modeling of these two specific parameters is only possible thanks to the 3D FEM simulations. Moreover, this particular study gives opportunity to better predict not only sensor sensitivity but also power dissipation. Being able to study this latter parameter in convective accelerometers is considered extremely important since power dissipation is the main disadvantage in this type of sensors.

Abstract— This paper reports efficiency modeling using 3D FEM simulation of a convective accelerometer obtained by FSBM of a die fabricated using standard CMOS technology. In such sensors, best sensitivity is obtained by placing temperature detectors where air temperature is the most sensitive to acceleration. This will obviously depends on 3D effects. In a previous work, a behavioral model of the sensor including only 2D effects was developed. This work investigates 3D effects which give the opportunity to better predict not only sensor sensitivity but also power dissipation. Experimental sensitivity values and 3D FEM ones are verified for two different sensors and two different heater temperatures. For a prototype having a heater-cavity border distance of 340μm and a heater length of 230μm, maximum sensitivity point is obtained for detectors localized at a distance of 125μm from heater center. Using this 3D geometry in FEM simulations, we show that electrical power decreases more rapidly than sensitivity when heater length is reduced. Moreover, when detectors are shortened, the sensitivity will be quite higher with an optimal value obtained for a detector implemented on one third of the side bridge.

Using 3D model of the convective accelerometer in FEM simulations with the Ansys© software, this paper presents the study of heater and detector lengths variations effect on sensitivity and power dissipation. This paper is organized as follows:

Keywords— CMOS, MEMS, Convective accelerometer, FEM simulation.

I.

INTRODUCTION

Accelerometer detailed presentation is given in section 2. This includes its description and a brief explanation of the operation mode.

Standard monolithic CMOS fabrication technology makes the MEMS convective accelerometer suitable for miniaturization and low cost sensors [1,2]. In addition, the micromachined convective accelerometer offers the superiority to sense very high shocks compared to the commonly used capacitive ones [3,4]. Both the design rigidity and the absence of any proof mass make this possible. Unfortunately, the strict requirements for process compatibility usually limit the performance level and application choice [5,6,7].

In section 3 the proposed model is validated through a comparison between experimental and simulation values of sensor sensitivity. In section 4, heater length and its variation effect on sensor sensitivity and power dissipation are studied. The impact of detector length variations on sensor sensitivity is studied in section 5.

One way to enhance and optimize the performance of this monolithic sensor resides in studying the system geometry to choose the best compromise between different key parameters. This can be done through accurate models which should be carefully used in simulations. These simulations could be made on the sensor to evaluate the influence of geometrical and material properties on sensitivity and bandwidth. In such mechanical sensor, Finite Element Modeling (FEM) simulation is considered to be the best alternative. This is true provided that the developed model is accurate.

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Finally, a brief conclusion is given in section 6. II.

CONVECTIVE ACCELEROMETER PRESENTATION

The device under study is a convective accelerometer obtained by Front-Side Bulk Micromachining of a CMOS die fabricated in a 0.8μm technology from Austria Microsystems® (Fig.1) [9].The three thin bridges are composed of the CMOS process back-end layers (oxide, polysilicon, aluminum, and nitride). In particular, polysilicon is used to implement

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2012 International Conference on Design & Technology of Integrated Systems in Nanoscale Era

TABLE I.

resistors, for both heating (RH) and temperature sensing (RD1, RD2).The heater is powered by an electrical voltage (UH) to create a temperature gradient in both bottom (i.e. etched silicon) and top (i.e. package) cavities: the temperature is then maximum at the heater location and minimum at the cavity boundaries. When no acceleration is applied, the temperature detectors (RD1, RD2) are located on identical temperature isotherms, obtained for symmetry reasons. Therefore, the common-mode temperature (TCM) will be indicated by both detectors such as RD1=RD2=f(TCM). The detector temperature reading is made feasible thanks to the high resistivity dependence to temperature of polysilicon (Temperature Coefficient of Resistance, TCR=9×10-4/C). Under acceleration along the sensitive x-axis, the cavity temperature distribution deforms due to free convection and each detector can now measure the differential temperature, TD.

LIST OF SENSOR MAIN LATERAL DIMENSIONS AND PARAMETERS WITH THEIR VALUES AND DETAILS

Symbol

Description

Value

Unit

RH RD TCR d r1 r2 h1 h2 w

Heater electrical resistance Detector electrical resistance Temperature Coefficient of Resistance Distance heater-detector Heater half-width Distance heater-cavity border Cavity Depth Package Height Package side length

0.35 50 9×10-4 175 20 350 390 1 2

kΩ kΩ 1/°C μm μm μm μm mm mm

III.

EXPERIMENTAL VS 3D FEM SENSITIVITIES

As a first step, we use the available characterization values to verify the accuracy of the 3D FEM results and specifically the meshing which is being used in simulations. Here, heater length is taken to be one third of the middle bridge length. This specific proportion is used so that more than 90% of the electrical power (PH), supplied to the heating resistor, is dissipated by heat transfer into the fluid (conduction & convection). The remaining power is lost by conduction in the suspended bridge towards the substrate [9]. In simulations, this fraction is then assumed to be at constant temperature and the conduction towards the substrate along the other parts of the bridge is neglected. In addition, the same fraction of lateral bridges is used for detectors’ length. Furthermore, temperature profile found from a 3D geometry decreases faster with distance from heater than for a 2D geometry (Fig.2). Therefore, to achieve optimal sensitivity, the detector location should be closer to the heater than for a 2D geometry modeling. Other sensor 3D geometry and FEM simulation steps and sensitivity evaluation procedure are presented in [11].

Figure 1. SEM picture of a CMOS-MEMS convective accelerometer (top view) and associated geometrical parameters (bottom, cross-sectional view).

Then, the temperature variation (ΔTDi) of each detector can be evaluated by taking the difference between the two previous readings (ΔTDi=TDi-TCM). The differential temperature, proportional to the sensor sensitivity is obtained from both detectors, and will be given by ΔTD=ΔTD1-ΔTD2. Finally, the thermal signal is converted into an output voltage by means of an integrated Wheatstone bridge. This voltage is then amplified by an on-chip instrumentation amplifier. For more details on sensor please refer to previous works from some of the authors [9,10]. The sensor main lateral dimensions and parameters with their nominal values and details are given in Table I [9].

Figure 2. Temperature profile along the sensitive x-axis for 2D and 3D geometry models.

In Table II, we show experimental sensitivities, SExp, and 3D FEM ones, SSim, for two different devices (prototype 1 and prototype 2) and two different heater temperatures (TH). We clearly see that both experimental and simulation sensitivity values are found to be approximately the same.

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2012 International Conference on Design & Technology of Integrated Systems in Nanoscale Era

TABLE II.

EXPERIMENTAL VS 3D FEM SENSITIVITIES FOR 2 DIFFERENT PROTOTYPES AND TWO DIFFERENT HEATER TEMPERATURES.

Parameters

Prototype 1

Prototype 2

h1 (μm) h2 (μm) r2 (μm) d (μm) TH(K) SExp(mK/g) SSim(mK/g) SSim / SExp

300 1000 340 125

300 1000 570 200 600 200 189.63 0.95

IV.

500 33.5 34.93 1.04

600 64 66.49 1.04

effect on the sensor sensitivity, a number of 3D FEM simulations are performed using Ansys© software. Table III gives sensitivity (S=ΔTD) values evaluated for the range of heater lengths previously set. In all these simulations, heater temperature is set at 600K and detectors are placed at 125μm from the heater center; this location ensures maximum sensitivity for a device with maximum heater length (230μm). Table III shows also that the location of detectors that gives maximum sensitivity shifts slightly closer to the heater as the heater length shrinks. This could be also deduced from the lower common mode temperature (TCM) readings. Sensitivity reduction is due to isotherms contraction produced when heater length reduces. Therefore, if acceleration is applied, the hot bubble displacement will be quite lower, as shown in the cross section of Fig.3.

HEATER LENGTH VARIATION EFFECT

In the previously developed behavioral model of the sensor (based on 2D FEM results), both heater and detectors lengths were not included [10]. This was the case since both of these lengths are perpendicular to the 2D plane of study (the plane passing from the sensing axis in Fig. 1 and perpendicular to the bridges). To be able to study heater length effect, a geometry based on volumes has to be used.

(b)

(a)

Figure 3. Isotherms within cavity for two different heater lengths: a) LH=50μm ; b) LH=230μm.

1) Heater length values To be able to model the effect of heater length, none of the other parameters should be changed, and in particular, the cavity half width, r2. For that, we will use dimensions of prototype 1 from Table II. In our study, the effective heater length has to be physically meaningful. Therefore, we should find an estimation of both highest and lowest possible heater lengths.

3) Impact of heater length on power dissipation During normal operation, the heating bridge is powered by a dc voltage (UH) in order to set an initial temperature distribution in the cavity. The average heater temperature (TH) is directly linked to the electrical power (PH) with a linear relationship:

As explained above, in order to minimize power loss, maximum heater length should be set to one third of the middle bridge length, which is 680μm. This gives a value of approximately 230μm.

ܶு ൌ ܶ஺ ൅ ܴ‫݄ݐ‬ு Ǥ ܲு

(1)

Where TA is the ambient temperature and RthH is the thermal resistance of the heater, which depends not only on heater dimensions but also on its geometrical environment. This thermal resistance is given by:

The minimum possible heater length is set by the technological limit on the resistor per square value given by the foundry. The heating resistor is fabricated using a polysilicon meander on a fixed bridge proportion. Here, the minimum heater length is set to 50μm. If the technological limit cannot be met, then we can implement this resistor on two or multiple layers of the suspended central plate. In this case, we have to make sure that the original symmetric design is respected. This means that the biasing line of the heater resistor have to be implemented on both sides of the plate. This will produce central isotherms giving equal common mode temperature reading from detectors.

ܴ‫݄ݐ‬ு ൌ ௛

ଵ ಹ ௌ೐

(2)

Where hH (in W.m-2.K-1) is the heat transfer coefficient and Se is the exchange surface between the heater beam and surrounding fluid (air) given by: ܵ௘ ൌ ሾʹሺʹ‫ݎ‬ଵ ൅ ݁ሻሿ‫ܮ‬ு

Heater length has a major impact on both sensor sensitivity and electrical power dissipation. This will be detailed in the following two sections.

(3)

With r1, e and LH are respectively, the half-width, thickness and length of the heater. From the above equations, the electrical power is expressed as:

2) Impact of heater length on sensor sensitivity ܲு ൌ οܶு ݄ு ܵ௘

We assume that the volume of heated air in the cavity will be much less if the heater length is reduced. This will produce smaller isotherms surrounding the heater, thus, affecting the convective behavior of the sensor. To prove this and study its

(4)

Where ΔTH = TH - TA is the heater temperature change and TA is the ambient temperature

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2012 International Conference on Design & Technology of Integrated Systems in Nanoscale Era

TABLE III.

IMPACT OF HEATER LENGTH ON SENSITIVITY IN A 3D GEOMETRY MODELING FOR PROTOTYPE 1. LH VARIES FROM 7% (50μm) UP TO 1/3 (230μm) OF THE MIDDLE BRIDGE LENGTH (2.R2).

LH (µm)

230

210

190

170

150

130

110

90

70

50

S (mK/g) for d=125µm

66.72

64.22

61.64

58.09

57.18

51.9

47.01

40.79

35.77

30.25

TCM (K) for d=125µm

371.8

371.8

369.2

367.5

364.7

359.9

356.1

350.7

344.7

337.7

TABLE IV.

IMPACT OF HEATER LENGTH ON POWER CONSUMPTION IN A 3D GEOMETRY MODELING FOR PROTOTYPE 1.

LH (µm)

230

210

190

170

150

130

110

90

70

50

hH (kW/m²/K)

1.36

1.41

1.43

1.47

1.53

1.57

1.65

1.77

1.9

2.15

PH (mW)

8.67

8.2

7.52

6.96

6.43

5.72

5.14

4.55

3.84

3.19

Using 3D FEM simulations, the effect of heater length on PH is investigated for the range of heater lengths previously set. Computed values are summarized in Table IV. This study shows that, for fixed values of r1, e and heater temperature, the electrical power decreases when heater length shrinks. Moreover, electrical power decreases slightly more rapidly than sensitivity when heater length is reduced. To illustrate this phenomenon, figure 4 presents the sensitivity according to heater power for constant heater temperature but different heater lengths. The straight line represents the best heating efficiency which is obtained for a shorter heater. Since the curve is below the straight line, it shows that the heating efficiency decreases when both heater power and length increase. Figure 5. Heating efficiency as a function of heater length.

V.

DETECTOR LENGTH VARIATION EFFECT

Detectors are implemented on side bridges which lengths are, due to the square cavity, equal to LDB=2(r2-d). For prototype 1, LDB = 430μm. Each temperature detector length, LD, can only be a fraction of LDB. Sensor sensitivity is extracted from average differential temperature readings obtained by integrating over the detectors’ length. An average value should be evaluated since, in a real situation, detector’s temperature should not be taken at a single central point where differential temperature is at its maximum value. Therefore, LD will have a direct effect on sensitivity. Here again, we assume that thermal conduction along the detectors’ bridge is negligible or that the presence of detectors do not disturb the local temperature gradient due to fluid thermal conduction and its variation due to acceleration. Table V presents computed sensitivities when detectors’ length is varied. It is clear that if the detector is shortened, the sensitivity will be quite higher. Sensitivity saturation is observed starting from a detector length set to the third of the lateral bridge.

Figure 4. Sensitivity according to heater power.

This relationship between heating efficiency and heater length can be clearly seen on figure 5 where this efficiency (S/PH) is plotted as a function of heater length. This is very important for convective accelerometer optimization since one of the foremost disadvantages of convective accelerometers is their power dissipation.

TABLE V.

As a conclusion, heater length should be chosen depending on the application where the sensor is intended to be used in. Moreover, if in a specific application both power dissipation and sensitivity should be optimized, then a compromise could be found to achieve the best efficiency.

LD(µm)

IMPACT OF DETECTOR LENGTH ON SENSITIVITY FOR PROTOTYPE 1.

LDB

S(mK/g) 43.79

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1/2 LDB

1/3 LDB

1/6 LDB

1/24 LDB

62.45

66.49

69

69.5

2012 International Conference on Design & Technology of Integrated Systems in Nanoscale Era

VI.

[3]

T.K. Sethuramalingam, A. Vimalajuliet, Design of MEMS based capacitive accelerometer, 2nd International Conference onMechanical and Electrical Technology (ICMET) 2010, Singapore. [4] W.T. Latt, U-X. Tan, C.N. R., W.T. Ang, Placement of accelerometers for high sensing resolution in micromanipulation, Sens. Actuators A, 167(2) (2011), pp. 304-316. [5] O. Leman, F. Mailly, L. Latorre and P. Nouet, HDL Modeling of convective accelerometers for system design and optimization, Sens. Actuators A 142 (2008), pp. 178-184. [6] X.B. Luo, Z.X. Li, Z.Y. Guo and Y.J. Yang, Study on linearity of a micromachined convective accelerometer, Microelectronic Engineering 65 (2003), pp. 87-101. [7] J S. Billat, H. Glosch, M. Kunze, F. Hedrich, J. Frech, J. Auber, H.Sandmaier, W. Wimmer and W. Lang, Micromachined inclinometer with high sensitivity and very good stability, Sens. Actuators A 97-98 (2002), pp. 125-130. [8] A.A. Rekik , F. Azaïs, N. Dumas, F. Mailly, P. Nouet, Modeling the influence of etching defects on the sensitivity of MEMS convective accelerometers, Proc. IEEE Int’l Mixed-Signals, Sensors and Systems Test Workshop (IEEE IMS3TW) 2010. [9] A. Chaehoi, F. Mailly, L. Latorre and P. Nouet, Experimental and finite element study of convective accelerometer on CMOS, Sens. Actuators A 132(1) (2006), pp. 78-84. [10] O. Leman et al., Modeling and system-level simulation of a CMOS convective accelerometer, Solid-State Electronics, Volume 51, Issues 11-12, pp. 1609-1617, 2007. [11] B. Mezghani, A. Brahim, F. Tounsi, A.A. Rekik, M. Masmoudi, P. Nouet., From 2D to 3D FEM simulations of a CMOS MEMS convective accelerometer, Proc. International Conference on Microelectronics (ICM) 2011, Hammamet, Tunisia.

CONCLUSION

This paper presents FEM simulation results obtained using new 3D model of a CMOS MEMS convective accelerometer. Using this model, evaluated sensitivity values are found to be very close to the experimental values. Moreover, we were able to study the effect of heater and detector lengths variations on sensitivity and power dissipation. It is shown that detectors optimal position shifts closer to the heater as the heater length shrinks. In addition, it is concluded that electrical power decreases more rapidly than sensitivity when heater length is reduced. Detector length has a direct influence on the sensitivity and an optimum detector length is found lower or equal to the third of the lateral bridge. ACKNOWLEDGMENT Authors would like to acknowledge their teammate at LIRMM, F. Azaïs, for background work and discussions. REFERENCES [1]

[2]

V. Milanovic, E. Bowen, M.E. Zaghloul, N.H. Tea, J.S Suehle, B. Payne, M. Gaitan, Micromachined convective accelerometers in standard integrated circuits technology, Applied Physics Letters , vol.76, no.4, pp.508-510, Jan 2000. A.A. Rekik , F. Azaïs, N. Dumas, F. Mailly, P. Nouet, A MEMS convective accelerometer equipped with on-chip facilities for sensitivity electrical calibration, Proc. IEEE Int’l Mixed-Signals, Sensors and Systems Test Workshop (IMS3TW) 2011, Santa Barbara, California, USA.

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