Thermal simulation of a micromachined thermopile-based thin-film gas flow sensor

MicroelectronicsJournal29 (1998) 291-297 © 1998 Published by Elsevier Science Limited Printed in Great Britain. All rights reserved 0026-2692/98/$19.00

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Thermal simulation of a micromachined thermopile-based thin-film gas flow sensor U. Diillner*, E. Kessler, S. Poser, V. Baier and ,J. MOiler Institutefor Physical High Technology e. V., Helmholtzweg 4, P.O. Box 100239, D07702 Jena, Germany

FEM calculations of a thermal gas flow sensor based on thermopiles made of thin films of Bi0.87Sb0.13 as n-type material and Sb as p-t3q0e material are presented. The results of thermal simulations concerning the response of the signal voltage to variations of the flow velocity at constant gas temperature as well as to variations of the gas temperature at constant :flow velocity are compared with experimental data. The good agreement between calculated and experimental results confirms the proposed two-dimensional thermal model. The design as a classical delta-T-type flow sensor did not result in a complete suppression of the influence of gas temperature variations to the sensor response. © 1998 Published by Elsevier Science Ltd. All rights reserved.

hermal flow sensors o f the boundary layer type rely on the flow-induced cooling o f a heated sensor region. The fluid flow changes the temperature distribution in this region,

which can be detected by measuring either the temperature o f the heater (conventional anemometer type sensor) or a flow-induced lateral temperature difference (delta-T-type flow sensor). Resistive strips (in the simplest case the heater itself) or thermopiles are primarily employed to transduce the temperatures into signal voltages using the thermoresistive or the Seebeck effect, respectively. During the last decade, micromachined thermal flow sensors have been developed for mass flow controlling, volume flow and flow velocity measurements (see [1-3] and the references in the corresponding chapters o f these books). The features o f these micro flow sensors such as small size, low cost, fast response time, low heating power and possible integration o f read-out electronics make them promising devices in a variety o f industrial, domestic and scientific applications.

*Author to whom all con:espondence should be addressed. Tel: +49-3641-657711. Fax: +49-3641-657700. E-mail: [email protected] ena.de.

In this paper thermal modeling calculations o f a micromachined thermal gas flow sensor o f the

1. Introduction

T

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U. Dillner et al./Thin-film gas flow sensor

delta-T-type based on thermopiles are presented. The sensor is aimed at measuring the gas flow in a portable, battery-operated device. Contrary to previous work on thermopile-based micromachined flow sensors [4-6] where the thermopiles were fabricated in standard IC technology using doped silicon, Bi0.87Sb0.13 was employed for the n-type thermopile layer and Sb for the p-type layer. These materials show a high thermoelectric figure of merit Z=S2a2 -1 (S is the Seebeck coefficient, a is the electrical conductivity and )[ is the thermal conductivity), e.g. Z is about 0.5 x 10 -3 K -I for thin films of Bi0.87Sb0.13 [7]. Owing to the low thermal conductivity of these films (about 3 W K -1 m -1) this Z value is nearly one order of magnitude higher than the corresponding one of polysilicon. A sensor for battery operation should be highly sensitive for a low power consumption. This design goal is supported by the thermoelectric materials chosen. A low heating power means, on the other hand, a relatively low temperature difference between the heater and the gas, resulting in a more pronounced effect of gas temperature variations on the sensor's response. Therefore, this effect is investigated in this paper. 2. Sensor design

The sensor layout is illustrated in Fig. 1. A 50 #m wide heater of NiCrSi is arranged in the middle on a 0.8 #m thick free-standing stress-compensated membrane of an area of 3.6x1.15mm 2 made by anisotropic etching of a Si wafer covered with a Si3N4/SiO2/Si3N4 sandwich system. The temperature at two symmetrical locations upstream (Tu) and downstream (TD) of the heater is measured by two thermopiles patterned microlithographically by wet chemical etching applying a multi-layer technology [8], i.e. arranging the n-type and p-type legs one on the top of the other separated by an insulating photoresist layer. Each thermopile consists of 100 thermocouples with legs of 20#m width and 10#m spacings. The distance between the edges of the heater and the thermopiles is 20 #m.

292

pile2

~ile 3

]ne

Fig. 1. Layoutof the flow sensor chip. The thermopower of Bi0.87Sb0.13 against Sb is 135#V/K for our thin films of 0.5#m thickness. This yields a signal voltage of 13.5 mV per 1 K signal temperature difference TD--Tu. Owing to the differential temperature measurement TD--Tu the offset of the flow-dependent signal is, ideally, zero and disturbances caused by varying gas temperature are, at least partially, suppressed [9]. 3. Thermal modeling

A 2D finite element analysis (x-axis, parallel to the flow direction, y-axis perpendicular to the membrane) using the FEM code ANSYS/ FLOTR_AN was performed to model the temperature distribution in the flow channel and the free-standing membrane. A schematic view of the sensor arrangement in the flow channel is illustrated in Fig. 2. The sensor chip

Microelectronics Journal, Vol. 29, Nos 4-5

package

~0.8 v

inlet

outlet

0.6 >

v,_

0.2

er I (.;i-~ I l e a d e r

~r-:

0.4

merrnopile 0

Fig. 2. Flow sensor arrangement.

0

1

2

3

4

distance along the line K3-K4 (mm)

at temperature Ts is mounted on a T O - 8 header put into a package at temperature Tp. Containing a flow channel of a diameter D=4 mm, the package is to be in good thermal contact with the sensor, i.e. Tv=Ts. The gas at the inlet is at temperature TG, which may be different from Ts. The sensor chip consists of a silicon rim supporting the flee-standing membrane with the thermopiles (TP) and the centrally located heater (H). Generally, the temperature difference ATs=TD-Tu is a function of the average flow velocity v and the gas temperature Tc. For the FEM calculations, v is to vary from 0 to 2 m/sec, while To is to lie between 286 and 303 K. Moreover, we assume a constant heating power NH=I m W and a fixed temperature of the ,;ensor chip Ts=293 K. The y-component of the flow velocity is set to zero in the whole flow channel. The inlet velocity profile is assumed to be parabolic (cf. Fig. 3).

Fig. 3. Local flow velocity at the inlet versus distance

from the bottom of the flow channel for an average flow velocity v=0.66m/see. Inlet

Tp

outlet

Ts = temperature boundary condition

T

= c o n v e c t i o n surface load

Fig. 4. FE model of the membrane and the flow channel (not to scale). The numbers 1-4 denote regionsof different materials.

With v=2m/sec maximally, the Reynolds number Re=vDpGti-c((/~o is the air viscosity, Pc the air density) does; not exceed 540, which is far enough away from Re=2300, where the flow in a duct becomes turbulent. This means the problem is laminar and does not require any turbulence model to be activated for the A N S Y S / F L O T R A N 2D element FLUID141.

elements in four different regions and the boundary conditions. Regions 1-3 belong to the flee-standing membrane, while region 4 comprises the flow channel. Regions 1 and 3 are the parts of the membrane covered by the heater and the thermopiles, respectively, whereas region 2 is the membrane area between the heater and the thermopiles. The dimensions of the FEM modeling area and the location of some keypoints are given in Fig. 5.

Figure 4 is an illustration of the finite element model of the arrangement showing the finite

The width of the membrane w=1.15 m m is related to the width of the three regions wi (i=1, 2, 3) by

293

U. Dillner et al./Thin-film gas flow sensor

20 mm

YJ

>

20 mm

T [K]

>

293 293,5 "mm' 294 294.5 Bill 295 BIB 295.5 BB 296 lib 296.5 BB 297 BB 297.5 BB 298

1.15 ~

mm

~

7g K3

E Kn:

keypoint n

I total FEM modeling area zoomed FEM modeling area

membrane Sl rim

Fig. 5. Geometric size of the FEM modeling area.

W=Wl+2(W2+W3).wl=50/im

is the width o f the heater, w2 is exactly defined as the sum o f the distance between the edges of the heater and the thermopiles and half the width o f the hot junctions o f the thermopiles: thus w2--45/*m=(20+50/2) #m. The thermal conductivity data for the various components o f the membrane including the thermopiles and photoresist layers given in [10] were used in the calculations. For the heater material, a thermal conductivity of 1 2 W K - l m -1 was assumed. The heat transfer from the membrane to the T O - 8 header through the air-filled etch pit o f a depth d=0.5 m m was included in the analysis by a heat transfer coefficient h=d.Gd-1 (/~G is the air thermal conductivity), i.e. h = 5 0 W K - l m -2 applied to the membrane finite elements as a convection surface load (cf. arrows in Fig. 4).

Fig. 6. 2D temperature distribution over the free-standing membrane at z e r o f l o w velocity. NH=1 mW, TG=Ts=293 m.

T [K] mm

mll BIBI lib IBm Ill Ill BB mm mll

I membrane

293 293.5 294 294.5 295 295.5 296 296,5 297 297.5 298

SI rlm

Fig. 7. 2D temperature distribution over the free-standing membrane at an average flow velocity v=0.66m/sec. NH=I roW, Tc=Ts=293K.

4. Results of t h e F E M c a l c u l a t i o n s

First we present modeling results for the case TG=Ts . In Fig. 6 the calculated temperature distribution at v=0 and Tc=293 K is shown in a zoomed part o f the FEM m o d d i n g area over the sensor membrane (cf. hatched area in Fig. 5). As expected, the distribution is completely symmetric. This symmetry is broken with a nonzero flow velocity as indicated by Fig. 7. It can be

294

seen that the temperature distribution generated by the heater is shifted downstream by the flow. The temperature o f the membrane along the line connecting keypoints K1 and K2 is illustrated in Fig. 8. The three curves corresponding to three different average flow velocities show the distortion o f the temperature profile by the flow. In the enlarged picture o f Fig. 9 we see that the signal

Microelectronics Journal, Vol. 29, Nos 4-5

299 E

T [K]

298

293 294 " 295 lib 296 == 297 rail 298 i 299 Ill== 3OO i 301 I

/\

IE e 296297 Q" '~ 295 ~294

/ / ~~/', 1, , /X~k,N / : , ,-,,, / / / / . . / ~ """

0

'"""" %'~

0.25 0.5 0.75 1 distancealongthe lineK1-K2(ram)

1.25

Fig. 8. Local membrane temperature versus distance from the upstream edge at v=0 (dashed curve), v=0.66m/sec (solid curve) and v=2m/sec (dotted curve). N.=I mW, To=Ts=293 K.

I membrane

Fig. 10. 2D temperature distribution over the free-standing membrane at an average flow velocity v=0.66m/sec. NH=I mW, Tc=303K, Ts=293K.

299

/

/A\ I/ I/ I /

\

SI rlm

298

I

/"i

[ "i /

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i

"

Fig. 9. Enlarged detail of Fig. 8 with triangles depicting the signal temperature difference. temperature difference depicted by a black triangle rises with increasing flow velocity. N e x t we present the F E M results for the case o f an inlet gas temperature, which generally differs

0.25

0.5

0.75 1 distance along the lineK1-K2(turn)

I

1.25

Fig. 11. Local membrane temperature versus distance from the upstream edge at TG=286K (dashed curve), TG=293K (solid curve) and TG=303K (dotted curve). NH=I mW, v=0.66m/see. from the sensor temperature (TG#Ts). In Fig. 10 the calculated temperature distribution at v=0.66m/sec and TG=303K is shown. The three curves in Fig. 11 correspond to three different gas temperatures at the inlet. O n e can s e e that the temperatures o f both the upstream and downstream hot junctions o f the thermopiles are shifted upwards with increasing To. In

295

U. Dillner et al./Thin-film gas flow sensor

5

,,' i /

.... lid

-

.-"" '

.

\ 4 --

" ',

41,"

.-O ......

.....

..O

...Q.

""

/

g ~

{3) t~

3

o >

calcu latio n experiment

"',

/'"

'

/,

/

2a,

0

' "x

I 0

I 0.4

I

I i I I I 0.8 1.2 1.6 average flow velocity (m/s)

I

I 2

i

I 2.4

Fig. 13. Signal voltage Us versus average flow velocity v. NH=I mW, Tc=Ts=293 K.

5

-

Fig. 12. Enlarged detail of Fig. 11 with triangles depicting the signal temperaturedifference. 4

the enlarged picture of Fig. 12, however, we see that the upstream and the downstream shifts are not equal. This results in a signal temperature difference that clearly depends on Tc, i.e. it rises with increasing inlet gas temperature. Hence there is no full compensation of inlet gas temperature variations in the sensor signal.

5. Comparison with experimental data Figure 13 shows the calculated and the measured signal voltage Us=13.5mVK-lx(TI)-Tu) of the sensor as a function o f the average gas flow velocity v at T G = T s . From the slope o f the measured Us(v) curve at small flows, a sensitivity o f 5 . 9 v w - l m - l s e c is obtained, which compares to the sensitivity values o f high sensitivity C M O S gas flow sensors [5]. Figure 14 illustrates measured effect o f the on the response o f plotted as a function velocity v=0.66 m/sec.

296

the calculated and the gas temperature variation the flow sensor. Us is o f T c - T s at a constant Dividing the slope o f the

g 8) 3 o

1-

2

0

ca Icu latio n experiment

•

I -8

=

I -4

I

gas temperature

I 0

I

I 4

I

- sensor temperature

I 8

I

I 12

(K)

Fig. 14. Signal voltage Us versus temperature difference Tc-Ts. NH=I mW, v=0.66 m/sec.

measured Us(Tc-Ts) curve by Us at T c - T s = 0 , we get a temperature coefficient of the signal voltage with respect to gas temperature variations of 0.016 K -1. From the good agreement between the calculated and experimental data illustrated in Figs 13 and 14, it can be concluded that the employed 2D FEM model is adequate for describing the temperature field within and over the flow sensor membrane.

Microelectronics Journal, Vol. 29, Nos 4-5

6. Conclusion By employing a 2D finite element analysis to model the temperature distribution in the flow channel and the free-standing m e m b r a n e o f a thermal gas flow sensor we calculated the signal voltage as a function o f the flow velocity at constant gas temperature and as a function o f the gas temperature at constant flow velocity. T h e calculated functions fit the experimental data reasonably well. T h e design as a classical delta-T-type flow sensor did not result in a complete suppression o f the influence o f gas temperature variations to the sensor response.

Acknowledgement This w o r k was supported by the C o m m i s s i o n o f the European Corrmaunities, D G XII, contract n u m b e r M A T 1 - C T 940028.

References [1] Middelhoek, S. and Audet, S.A. Silicon Sensors, Academic Press, London, 1989, Chapter 4.3, pp. 189-191. [2] Hohenstatt, M. Sensors, a comprehensive survey, in W. G6pel, J. Hesse and J.N. Zemel (eds), Thermal

Sensors, VCH Verlag, Weinheim, 1990, Vol. 4,

Chapter 9, pp. 323-343. [3] van Oudheusden, B.W. Thermal Sensors, G.C.M. Meijer and A.W. van Herwaarden (eds), Institute of Physics, Bristol, 1994, Chapter 5.2, pp. 134-152. [4] van Oudheusden, B.W. and van Herwaarden, A.W. High-sensitivity 2-D flow sensor with an etched thermal isolation structure, Sensors and Actuators, A21A23 (1990) 425-430. [5] Moser, D. and Bakes, H. A high sensitivity CMOS gas flow sensor on a thin dielectric membrane, Sensors and Actuators, A37-A38 (1993) 33-37. [6] Mayer, F., Paul, O. and Baltes, H. Influence of design geometry and packaging on the response of thermal CMOS flow sensors, Transducers '95.Eurosensors IX, Digest of Technical Papers, Stockholm, 1995, Vol. 1, pp. 528-531. [7] V61klein, F. and Kessler, E. Thermal conductivity and thermoelectric figure of merit of Bil_xSbx films with 0
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