Sensors and Materials, Vol. 8 , No. 6 (1996) 345-35 6
MYUTokyo
S &M0250

A New Heat Flux Sensor: From Microvolts
to Millivolts
Vital M. Meyer and Bruno Keller
Chair of Building Physics,
Institute of Building Technologies,
ETH Hi:inggerberg, CH-8093 Zurich, Switzerland(Received March 29, 1995; accepted December 22, 1995)
Key words:

heat flux sensor, heat transfer, thermocouples, building physics

A newly developed heat flux sensor of very high sensitivity is presented. It is based on
the well-known Seebeck effect. We made use of the technique of anisotropic siliconetching, the thermoelectric material properties of Bi/Sb and the photolithography used for
microelectronics. The resulting sensor has a sensitivity of about 10 mV-m2 I W whichcorresponds to a responsivity ofabout 20 V /W. This is higher by a factor ofabout 100 thanthat of the best commercially available heat flux sensors.

1.

Introduction

Heat flux measurements are of interest in various fields: in some applications, likecalorimetric measurement of specific heat, melting heat etc., the integral of the heat flux
over time is of primary interest.
In building physics, we are interested in the heat flux density, e.g. as a criterion ofa wallconstruction under steady state thennal conditions. In real-world buildings, however,steady state thermal conditions are never reached. The shortwave radiation of the sun,stochastic changes ofexternal temperatures and internal heat sources, rapidly changing air
flux patterns, etc., influence the thermal behavior of a room. In such a complex thermal
environment, it is necessary to measure the heat fluxes directly instead of measuring
temperatures and calculating heat fluxes by the use of more or less well-known thermal
film coefficients.

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Sensors and Materials, Vol. 8, No. 6 (1996)

346

The main reason why there are so few heat flux measurements is the poor behavior of
the commercially available heat flux sensors. They tend to be thick and thus have highthermal resistance. Moreover, the signal density (signal per active area) is low. This makes
it impossible to perform measurements with high spatial resolution.

2.

Design of Conventional Heat Flux Sensors

Most heat flux sensors Ct -4) consist of a thin layer of material (rubber, plastic) in which atherniopile is encapsulated (see Fig. 1). A heat flux perpendicular to the substrate inducesa small temperature difference L1 iJ over each thermocouple. These temperature differences
are summed by a number of thermocouples connected in parallel thermally and in series
electrically. In this manner, we measure an integral heat flux signal over the sensor area.
All existing heat flux sensors have one or more serious drawbacks:- large substrate thickness and therefore high thermal resistance disturbs the heat flux
measured- the intrinsic three-dimensional structure of the thermopile complicates production andis prohibitive for microtechnological structuring methods- the use of wires severely restricts the choice of thermoelectric materials

3.

New Design

3.1 Design criteria

Our aims for the new sensor design were the following.
- maximizing the sensitivity of the sensor- minimizing the thermal resistance of the sensor

heat flow q
isotherms

Useebecksubstrate = thermal resistanceFig. 1. Conventional heat flux sensor.

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Sensors and Materials, Vol. 8, No. 6 (1996)- physical thickness of the sensor less than 1 mm
- sufficient robustness of the design- low production costs

3.2 Sensitivity of the sensor

The output signal U of a heat flux sensor is a de-voltage. In a linear approximation:(1)

where N: number of thermocouples, £Xp0 : Seebeck coefficient between the positive and thenegative thermoelectric materials and �19-: temperature difference over the thermocouples
1(see Fig. 1). �17-is proportional to the he t flux::(2)�17- Rth · q
where Rth [K-m2 /W]: effective thermal resistance of substrate and thermocouple and q[W /m2]: heat flux.
To characterize a heat flux sensor, we have to distinguish between two important
quantities. First, the sensitivity S [V-m2/W] is the output voltage per unit of heat flux:Su= - = N · a n · Rili = n · Asensor · a n · Rili
q

p

p

(3)

where n is the density of thermocouples per active area Aensor (the sensitive area of thesensor). This quantity is usually given in the heat flux sensor literature. Another very
important quantity is the responsivity R [V /W] which is simply the sensitivity divided by
the active area of the sensor:s

R = -- = n · lXpn • Rfh.
Asensor(4)

With sensors of high responsivity, measurements are possible with a small active area
and therefore with high spatial resolution.
To express the efficiency of a heat flux sensor in terms of measurements we areinterested in, we define a "quality number" Q:

Asensor(5)

where d5 : thickness of the sensor. The quality number takes into account not only theSensors and Materials, Vol. 8, No. 6 (1996)

348

responsivity but also the effective thermal resistance and the thickness of the sensor which
disturbs the heat flux.

3.3 The material: figures of merit and noise

In order to select the best thermoelectric materials for our purpose, we consider thesignal-to-noise ratio of our sensor. The noise U0 of a thermopile is mainly thermal noiseand determined by its internal resistance R. It is given by the well-known Johnson formula:,

Un, = -,j4 · k · T · R · N(6)where k: Boltzmann constant, R: electrical resistance of the thermopile and /:,,f frequency
bandwidth.
Assuming a thermopile with N thermocouples composed of two equal legs withdimensions l, ATc (length of thermocouple leg, thermocouple cross section) with resistivity
pp, p0 respectively, the internal resistance is equal to
,

(7)

l

= N·- · P,um
ATCwith Psum = (pp + Pn ) ·To analyze the thermal behavior of a heat flux sensor, we use a simple I-dimensionalmodel as illustrated in Fig. 2.
We assume that?.,,=\= IL-Tc and IL-Tc = A.substrate· In this model, the effective thermal
resistance is given by the resistance of the thermocouple leg(8)With these assumptions and eq. (2), the output voltage of the sensor is
U

= N-a

pn

l
·q·-

ATC

(9)

and the generated noise voltageUn,=�4 · k · T · N · _Al ·Psum · /:,,f.
TC

(10)

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Sensors and Materials, Vol. 8, No. 6 (1996)

Asubstrate

Fig. 2. Thermoelectric leg.

This leads to a signal-to-noise ratio SNR ofuapn

SNR = - = q · --==
Uns
lvrc · -,JPsum

N·l·ATc
4-k·T·N(11)

Finally, the noise equivalent heat flux NERF is:
NEHF =

4 ·k ·T·N
ATC -vr-::--p/J,um . �----�.
N · l · ATc
apn

(12)

From eq. (11), it is clear that the material figure of merit to be maximized is
Zsensora(13)This is in contrast to the definition commonly used in connection with thermoelectric
power generation. A comparison of the material figures of merit Zsensor of different
materials in use in thermoelecttic applications is shown in Figs. 3 and 4, using values fromSensors and Materials, Vol. 8, No. 6 (1996)

350

Te, Bi, Se, Sb

0.05
0.045

Bi2Te3(+Bi)

0.04
0.035
0.03
0.D25
0.02
0.015
0.01
0.005

Sb
Cu

Fe

p-Polysilicon0Fig. 3.

Thermoelectric materials, p-type.

0.05

Te,Bi,Se,Sb

0.045

Bi2Te3 (+Cul)

0.04
0.D35
0.03
0.025
0.02
O.DI5

Sb/Bi

O.DI
0.005

Al

CuNi

n-Polysilicon

0 ..L----�-----�-----�Fig. 4.

Thermoelectric materials, n-type.

literature at T= 20/25° C. The materials from the Bi/Sb/Te group are the most interestingfor our purposes; other materials, like polysilicon, which are used in standard CMOS
processes, have much lower values. The deposition of thin films of alloys of Bi/ Sb/Te,
however, is rather complicated.
Therefore, we select 90%Bi-10%Sb as the negative and pure antimony as the positive
thermoelectric leg.

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Sensors and Materials, Vol. 8, No. 6 (1996)

3.4 Geometrical design

In drder to profit from the common methods known from microelectronics, it is ofprimar}t importance to create a planar thermocouple structure. Therefore, we disturb theheat fluk field in such a way that it induces temperature differences in the plane.
To kchieve this, we use the technology of anisotropic silicon etching, known fromthermoelectric IR-sensors and other types of sensors: <5l an anisotropic etchant, e.g. KOH,
has a significantly higher etch rate for (100) crystal planes than for (111) planes. There­
fore, it is possible to generate window-like openings in a silicon wafer, protected by a Si02
/Si3N4 mask (see Figs. 5 and 6).
In this type of design, we have to adapt the thermal analysis of the sensor. For
membranes with length much greater than width, the I -dimensional model illustrated inFig. 7 holds. <6l
A consideration of the energy balance for a volume element V of the membrane resultsin the following differential equation for the temperature difference AT(x) = Tz(x) - T1
1

- - d 2 T( x)q = a,;c · AT( x ) - A· d
2

ax

with

Aai,

a,;c = 4 ·CJ· T0 · £ + -.
s
3

(14)
(15)

a,1c is a thermal film coefficient containing a radiation and conduction part; ;\, · d is theeffective thermal conductivity of the membrane and the thin-film thermocouples (seebelow); CJis the Boltzmann constant; £ is the emissivity of the membrane; ands is the wafer
thickness. The solution of eq. (15) under the obvious boundary conditions is:

Fig. 5.

Anisotropic etching.

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Sensors and Materials, Vol. 8, No. 6 (1996)

thermoelectric materials

500 µmt
membrane SiO /Si N

substrate Si

'

'

4

Fig. 6. New design.

ti,.T(x) = _!l_.

a,;c

· x)
(i - cosh(p)
cosh(p · l)_ � a,;c

p-

(16)

-·

},,-d

The temperature difference over the thermocouple is ti,.T(x= 0). To choose a reasonable
membrane width, we have to consider the temperature difference over the thermocouple as
a function of the length of the thermocouple leg l, ti,.T(x = 0, l)q (ti,.T(x = O,l ) = - 1---ar;c1 )cosh(pl)(17)

With our design parameters (thermocouple film thickness: dBi/Sb= 0.5 µm, dsb = 0.5 µm,},,Bi/Sb = 4 WI (mK) A.sb = 13 WI (mK), thermocouple width wBi/sb = wsb = 20 µm,
thermocouple leg distance a = 5 µm, membrane thermal conductivity Amern, dmem> and(18)

we find the dependence of 1 - 1 / cosh (pl) from the length of the thermocuple leg l (T0 =25C, },,Air = 0.026 WI (mK), s = 500 µm, £ = 1) (Fig. 8).

Sensors and Materials, Vol. 8, No. 6 (1996)

353

Volume element V-BT-A·d·- '
Bx x

\

-BT

-A·d·-'

ax xMx)Fig. 7.

Thermal model.

We see that at a length of the thermocouple leg of 570 µm., as in our design, we obtained
a temperature difference which is about 70% of the maximum possible value. This result
is in good agreement with those which we obtained from 2-dimensional finite-element
simulations.
For our measurement purposes, we need a relatively large sensitive area. The dimen­
sions of our nitride/oxide membranes are 1140 µm x 25000 µm with a thickness of about 1µm. A sensor contains 10 membranes, each containing 889 thermocouples. The thermo­
couple array is generated by thermal evaporation of the Bi / Sb-Sb thermocouples. The
silicon chip is then bonded on a ceramic substrate of 35 mm x 35 mm x 0.254 mm. This
results in a total sensor thickness of 0. 75 mm. Around the chip, we constructed a ceramic
rectangular frame of 0.5 mm thickness (see Fig. 9). A synopsis of the parameters of oursensor is given in Table l.

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Sensors and Materials, Vol. 8, No. 6 (1996)

1

1-1/cosh(pl)

0.8
0.6
0.4
0.2

570µm

0
500

0
Fig. 8.

l[µm]

1000

1500

Temperature difference over thermocouple.

Ah03

35mm

0.75mmFig. 9.

4.

Heat flux sensor mounted on ceramic substrate.

Comparison with Conventional Heat Flux Sensors

In Table 2 we show a comparison of the characteristic constants of our sensor withthose of commercially available heat flux sensors.

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Sensors and Materials, Vol. 8, No. 6 (1996)
Table 1
Synopsis of sensor parameters.
Active area
Film thickness Bi/Sb
Film thickness Sb
Thermocouple length
Thermocouple width
Number of thermocouples
Responsivity
Sensitivity
Resistance

5.

[cm2]

5.55
0.5
0.5
1140
20
8890
20±2
11000 ± 1100
8±1

[µm]

[µm]
[µm]
[µm]
[-]
[V/W]
[µV/(W/m2)][MQ]

Discussion

Our new heat flux sensor is the first which takes full advantage of modern
microtechnological developments. Using these fabrication techniques we have managed
to improve the responsivity by almost two orders of magnitude and the quality number Q isincreased by several orders of magnitude.
In a further step, we will coat our sensors to make them selective for different heattransfer mechanisms: convection, thermal infrared and short wavelengths. This will allow
us to measure each of these mechanisms separately at the same location.

Table 2Comparison with other commercially available heat flux sensors.

Active area
[cm2]
Thickness[mm]
Thermal[m2K/W]
resistanceDensity of[cm-2]
thermocouples
Responsivity[V/W]
Sensitivity[µV/(W/m2)]· Quality number [V2 /(m3KW)]
Price
[DM]
(*) partially defective

TNO,
PUl.1

Isover
St. Gobain

CSEM

ETH
Prototype 1

3

1.5 X 1Q-2

100
0.8

4 X 1Q-3

209-0.5
2.5 X 10-3

2.2(*)
0.75
1.6 X 10-s

?

2

30

1,600

0.2
50
8.8 X 102550.-

0.0012 - 0.0015
12-15
0.7
600.-

0.001
20
0.8
?

20±2
4,400 ±450
3.3 X 1010
-300.-

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Sensors and Materials, Vol. 8, No. 6 (1996)

Acknowledgment
The authors wish to thank Prof. F. Volklein from the Engineering College in Wiesbaden
for his important contribution to this work; Dr. E. Kessler from the Institute for PhysicalHigh Technology in Jena for device fabrication and Prof. H. Melchior and Dr. J. Schmidfrom the Institute for Quantum Electronics of the Swiss Federal Institute of Technology formany fruitful discussions. We thank also the research fund of the Swiss Federal Institute ofTechnology in Zurich for financial' support.

References

2
3
4
5
6

M. Degree and S. Klarsfeld: A New Type of Heat Flowmeter for Application and Study ofInsulation and Systems in Building Applications of Heat Flux Transducers, ed. E. Bales, M.
Bamberg and G. E. Courville (ASTM, Philadelphia, 1985) p. 163.
Y. Miyake and U. Eguchi: Development ofa Large Area Heat Flow Meter in Guarded Hot Plateand Heat Flux Meter Methodology, ed. C. J. Shirtliffe and R. P. Tye, (ASTM, Philadelphia,
1985) p. 171.
F. van der Graaf: Heat-flux sensors, in Sensors, Volume 4: Thermal Sensors, ed. T. Ricolfi and
J. Scholz (VCH, Weinheim 1992), Chap. 8.
F. Porret: Capteurs fluxmetrique de chaleur en technologie couches minces, Rapport Final,
Centre Suisse d'Electronique et de Microtechnique S. A. (1986).
F. Volklein and W. Schnelle: Sensors and Materials 3 (1991) 41
F. Volklein: private communication.