Fabrication and characterization of thermal conductivity detectors(TCDs) of different flow channel and heater designs

Y.E. Wua, K. Chenb,*, C.W. Chena, K.H. Hsua

aDepartment of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, TaiwanbDepartment of Mechanical Engineering, University of Utah, 50 S. Central Campus Dr., Rm. 2202, 84112 Salt Lake City, UT, USA

Received 19 October 2001; received in revised form 8 April 2002; accepted 14 April 2002

Abstract

Different flow channel designs and heaters made from different materials were tested for improving the performances of silicon-based

thermal conductivity detectors. One of the designs involved an electric heater sandwiched between two identical flow channels for high heat

transfer rates. The heater of the other design was suspended over a slot to reduce heat losses. The flow channels were etched in silicon wafers

and nickel heating elements were deposited on Pyrex glass, polyimide, and silicon nitride membranes. The transient behaviors of the heaters

and the wafer temperatures were measured and analyzed for different voltages. The effects of flow channel design and membrane material on

the heat transfer characteristics and sensitivities of the detectors were examined. Simple heat transfer models were developed to aid in

understanding and diagnosing detector behaviors and performances. The polyimide heater had the best signal conditions. The warm-up times

of the TCDs were found to be primarily dependent upon the package dimensions and properties. The double-channel TCD exhibited 20%

higher heat transfer rate compared to the single-channel design, but the sensitivities of these two designs differed only slightly.

# 2002 Published by Elsevier Science B.V.

Keywords: Micro GC; Response time; Sensitivity; Thermal conductivity detector

1. Introduction

A variety of thermal sensors [1] have been developed for

the measurements of heat flux, mass flow rate, velocity, as

well as physical and chemical properties (e.g., thermal

conductivity, chemical composition, etc.) of a fluid flow.

Examples of thermal sensors include hot-wire and hot-film

anemometers, thermal-pulse and other convective-type

flowmeters [2], TCDs, and so on. These sensors generally

involve a fluid flow over electrically heated filaments or thin

films. Various fluid and flow properties can be determined by

measuring the heat transfer rate or temperature change of the

heating elements. For most thermal sensors, the sensitivity

can be improved by increasing the heat transfer rate between

the heater and the fluid. A short response time is often

desired for reduced warm-up period and better temporal

resolution. Although attention in the present investigation

was limited to TCDs, results of this study are also useful to

other sensors that utilize heat transfer in a fluid flow for

property measurement or identification.

TCDs have been used in gas analysis for more than a

century [3]. In a TCD the change in gas thermal conductivity

due to the injection of a gas sample into the carrier gas

stream can be detected by measuring the change in heat

transfer rate of an electric heater in the flow. The flow

channel of a TCD is very long and lateral heat transfer is

almost exclusively by conduction. In recent years silicon

micromachined TCDs have been widely used in micro gas

chromatography (GC) systems. These micro GCs have the

size of a briefcase [4,5] and are capable of performing most

of the tasks a large chemical analyzer can do. The compact-

ness and portability of micro GCs make them extremely

suitable for environmental testing such as leakage detection

of hazardous chemicals, monitoring of various chemical

processes, and gas emission analysis of power plants,

Although TCDs may not be as sensitive as ionization

detectors for GC applications, they are concentration sensi-

tive devices while ionization detectors are mass sensitive. As

the detector size reduces, so does the fluid mass, but the

concentration remains unchanged. The TCD is therefore,

more advantageous to use than other types of detectors for

micro GCs [6,7].

A review of TCD heat transfer was given in Chen and

Wu’s paper [7]. Extensive studies of conventional TCDs

Sensors and Actuators A 100 (2002) 37–45

* Corresponding author. Tel.: þ1-801-581-4150; fax: þ1-801-585-9826.

E-mail address: chen@mech.utah.edu (K. Chen).

0924-4247/02/$ – see front matter # 2002 Published by Elsevier Science B.V.

PII: S 0 9 2 4 - 4 2 4 7 ( 0 2 ) 0 0 1 4 4 - 9

have been carried out and published in various books (e.g.,

[3]) and technical journals (e.g., [8–11]). On the other hand

few research results of TCDs that were fabricated using the

lithography technique were published despite the fact that

silicon-based TCDs have become commercially available

for years. Early research of silicon-based GCs and TCDs

was performed at Stanford University [6,12]. Shallow chan-

nels were etched on a silicon wafer and thin metallic films

were used as heaters. Convective heat transfer was neglected

and a lumped thermal model was developed in Jerman’s

thesis [6] for heat transfer analysis of their silicon-based

TCD. The TCD, Jerman and co-workers developed was

found to be very sensitive to pressure difference due to

the shallow channels they used. The entrance effect of TCDs

of planar structure was found to be confined to a distance

about four times the thermal entry length of a circular tube

subject to a uniform thermal boundary condition [7].

The present investigation was motivated by the lack of

detailed experimental data for flow channel and heater

designs and their effects on the performances of silicon-

based TCDs. In this paper nickel (Ni) heating elements were

deposited on different membranes and their transient beha-

viors and noise levels were recorded and studied. A one-

dimensional heat transfer analysis was applied to different

flow channel designs: one with the gas flow above the heater

only and the other comprised of an upper and a lower flow

channel. Electricity consumption rates of the two designs

were measured and their sensitivities compared. The signal

conditions of our TCDs were influenced by the supplied

voltage and the membrane material. The warm-up time

depended primarily on the silicon package dimensions.

The double-channel design had a higher heat transfer rate,

but the sensitivities of the double- and single-channel

designs were very close to each other.

2. Design and fabrication of silicon-based TCDs

The simplest TCD design that can be batch-fabricated

using the lithography technique involves a thin film depos-

ited on a substrate as a resistor to generate heat. Above the

heater is an etched flow channel bonded or glued to the

substrate surface. The major drawback of this single-channel

design is the conductive losses through the substrate. To

reduce the conductive losses, a deep channel, evacuated or

opened to the atmosphere, is often fabricated underneath the

heater. Fabrication and test results of the single-channel

TCD can be found in Jerman’s thesis [6].

From the heat transfer point of view, a better TCD design

is the one with the electric heater sandwiched between

two flow channels identical in dimensions, material, and

configuration. The heat generated by the heater will pass

through the gas volumes in the upper and lower flow channels

equally. The conductive losses beneath the heater can be

almost totally eliminated. However, since most metallic thin

films do not have very good mechanical properties, the thin

heating element suspended over the lower flow channel may

not have sufficient strength to prevent it from being deflected.

Although deflection of the heating element can be alleviated

by reducing the channel width or by increasing the film

thickness, the former will increase the heat losses to the

channel sidewalls while the latter will result in a lower

electric resistance of the heater. The remedy we devised

was to deposit the heating element onto a membrane of better

mechanical properties. The membrane must be made of an

electrically insulating material. It must have sufficient

strength to remain un-deflected when suspended over a wide

flow channel. A low thermal conductivity is also desired for

reducing the conductive loss from the membrane to the

channel sidewalls. Due to the presence of a membrane

beneath the heating element, heat transfer to the lower flow

channel is less than that to the upper channel and the TCD

performance is somewhat compromised.

In the present investigation both single- and double-

channel designs were tested. In the single-channel design

a silicon wafer with the flow channel etched in was bonded

to a membrane that forms the channel floor. A thin film of Ni

was deposited on the top surface of the membrane. Below

the membrane was another silicon channel open to the

atmosphere. The air in the open channel reduced the heat

losses from the bottom of the heater. The double-channel

design had the same membrane, heating element, and upper

flow channel as the single-channel one. The bottom of the

membrane, however, was bonded to another silicon wafer

with an identical flow channel etched in. The equivalent

thermal circuits of these two designs are depicted in Fig. 1.

Notice that the double-channel design has an additional

conduction resistance for the heat flow path from the mem-

brane bottom to the surroundings. However the total heat

flux to the gas is qu þ ql in comparison with just qu in the

single-channel TCD.

Fabrication and packaging of our TCDs are now briefly

described. A silicon wafer was first thoroughly cleaned

using a procedure similar to RCA 1 and 2 [4]. A positive

photo resist (Hoechst AZ 4903) was then spin-coated onto

the wafer. Hexamethyldisilazane (HMDS) was used as an

adhesion promoter to improve photo resist (PR) adhesion.

The aligner we used was Karl Suss JB3 UV 300/400 with

the g-line (wavelength ¼ 436 nm) light source. The flow

channels were wet-etched [4,13] in the silicon wafer using

a mixture of KOH and de-ionized water. The gas entry and

exit ports were etched using ethylene diamine-phrocatechol

water (EDP). The flow channels were only 20 mm deep and

smooth surfaces were desired. On the contrary the gas entry

and exit ports were much deeper (175–250 mm) for the

insertion of commercial capillaries and surface roughness

was not important. Therefore, EDP was used as the etchant

to speed up the wet etching process. The open channel

beneath the membrane of the single-channel TCD was

fabricated in a similar fashion. Since the lower channel

was etched through the silicon wafer, no etch stop was

needed and the faster etchant EDP was used.

38 Y.E. Wu et al. / Sensors and Actuators A 100 (2002) 37–45

The same PR (Hoechst AZ 4903) and pattern transfer

process were used for the deposition of the Ni heating

element on different membrane materials. After spin coat-

ing, softbaking, exposuring, and developing of the PR, a

chrome (Cr) layer of 15–25 nm was coated before Ni film

deposition for better adhesion. The heating element pattern

was transferred onto the Ni film by liftoff instead of etching

since lift-off has better line-width control of the transferred

pattern. Removal of the unwanted Ni film was accomplished

by immersing the membrane in acetone for 2 h, followed by

1–2 min of ultrasonic agitation. Shown in Fig. 2 is the laser

scanning microscope (LSM) image of the snaking heating

element. The width of the heating element was approxi-

mately 14 mm and the average thickness, measured by a

Tencor a-step profile meter, was around 1.5 mm. After the

heating element was fabricated, gold leads were deposited

onto the membrane in a similar process.

Three different materials were tested for the membrane on

which the Ni heating element was deposited using the

thermal evaporation method. They are polyimide, Pyrex

glass, and silicon nitride. The solidified polyimide sheet

(Kapton-FN by DuPont) was 50.8 mm thick and coated with

12.7 mm Teflon on both sides. The polyimide sheet was soft

and deposition of a uniform metallic film on it proved to be

challenging. To avoid deformation and over-softening, the

rinse temperature and time of the polyimide sheet cannot

exceed 80 8C and 5 min. A gray film was observed (Fig. 3)

when thin PR (Hoechst AZ 1500) was used. We suspected

the gray film was Cr that diffused through the PR layer

and stuck to the polyimide surface. After switching the

PR to AZ 4903 and reducing the spin coating speed from

5000 to 4000 rpm, the gray film no longer appeared. Four

identical heating elements on the polyimide surface can be

seen in Fig. 3. These heating elements form the four resistors

in a Wheatstone-bridge circuit [14] that can detect slight

imbalances between the two resistors in the testing channel

and the other two resistors in the reference flow channel of

a TCD.

Pyrex glass has good mechanical properties and a low

thermal conductivity. It was therefore, also tested as a

membrane material of the heater. Slots or shallow channels

were first etched in a silicon wafer. Corning # 7740 Pyrex

glass 500 mm in thickness was then anodically bonded

[15,16] to the wafer. The Pyrex glass/silicon wafer was

immersed in 49% HF with ultrasonic agitation for 40 min

to reduce its thickness to about 33 mm. The rough Pyrex

glass surface after etching was polished to 20 mm using

aluminum-oxide powders. Cr and Ni layers were then

deposited on the Pyrex glass surface, and the heating ele-

ment pattern was transferred by lift-off. The same pattern

transfer process was repeated for the deposition of gold leads

onto the Pyrex glass surface.

Another membrane material we tested was silicon nitride

(Si3N4). This material is very hard and strong, and is easier

to work with for metallic pattern transfer. Prior to the

deposition of the Ni heating elements, a layer of 0.5 mm

Si3N4was deposited on the silicon wafer using the LPCVD

(low-pressure chemical vapor deposition) technique. A gold

film about 1000 A thick was then fabricated by lift-off to

protect the desired silicon nitride regions. The undesired

silicon nitride was washed out in 85% phosphoric acid

(H3PO4) at 140 8C. Due to its high stiffness, silicon nitride

had a higher success rate than polyimide for the fabrication

of the heater assembly (heatingþ element þ membrane).

This extremely thin membrane, however, lasted only a

few experiments in our tests.

The upper half of the TCD, which was comprised of the

upper flow channel and the heater, and the lower half which

consisted of the lower flow channel or a slot in a silicon

wafer, were glued together using EPO-TEK 301-2 by Epoxy

Technology. During the packaging process cautions must be

Fig. 1. Cross sections of the (a) double- and (b) single-channel TCDs, and

the corresponding thermal circuits. Conduction resistances ¼ L/k and

convection resistances ¼ 1/h, where L is the thickness; k the thermal

conductivity; h the heat transfer coefficient.

Y.E. Wu et al. / Sensors and Actuators A 100 (2002) 37–45 39

taken to prevent the adhesive from seeping into the flow

channels, which may block the gas flow and/or shorten the

heating elements.

Before packaging, the heater was placed in a furnace to

measure its electric resistances at different temperatures.

The temperature–electric resistance relationships of the

heaters we fabricated were found to be fairly linear for

temperatures ranging from 20 to 200 8C, with the tempera-

ture coefficient of resistance very close to 0.003 O cm/8C.

3. Test results and discussion

3.1. Transit-time measurements

The goal of this test is to determine the time required for

the TCD output signal to reach a steady state. The tested

TCDs were the single-channel type (Fig. 1(b)), but their

heaters were made from different materials. The TCDs were

placed on a metallic rack in an evacuated stainless-steel

Fig. 2. LSM image of the deposited heating element.

Fig. 3. Gray film on the surface of the polyimide membrane during pattern transfer.

40 Y.E. Wu et al. / Sensors and Actuators A 100 (2002) 37–45

chamber during the test. Attention was focused on heat

conduction from the heating element to the membrane

and the silicon wafers. Results of this test can be used to

determine the warm-up time of a TCD. The information is

also useful to TCDs and TCD-like structures using a voltage

excitation to measure fluid properties or to improve the

sensor sensitivity. For instance, in Lacey’s patent [17], a

sinusoidally alternating voltage was applied to the Wheat-

stone bridge, or the sensor resistor was alternatively

operated at two different temperatures to eliminate the

influence of wall temperatures. Bonne and co-workers mea-

sured the time responses of DC excited filaments in their

flowmeter and pressure sensor [18,19] for fluid composition

correction.

The electric current of the heating element was monitored

during the transient test for a supplied voltage. Test results of

three membrane materials are shown in Figs. 4 and 5. In the

transient period the heating element temperature rose and its

resistance increased. The current of the heating element

therefore, decreased and eventually approached a constant

value when the heater reached thermal equilibrium with its

surroundings. The output currents were very noisy when the

supplied voltages were low, as shown in Fig. 4. High-voltage

results (Fig. 5) showed much better signal conditions. This is

because the background temperature fluctuations had less

effect on the heater temperature when it was heated to a

higher temperature. These current plots also reveal that the

times required for a TCD to reach a steady state were about

the same for different voltages. The transit times of the three

membranes we tested were very close. The output current of

the polyimide membrane had the lowest noise level, espe-

cially at low voltages. It was therefore, selected in the heat

transfer test of different flow channel designs.

A lumped-system analysis was first applied to the mem-

brane beneath the heating element. The thermal time con-

stant [20] (the time required for the temperature of a lumped

system to come within 37% of its steady-state value) of the

polyimide membrane was found to be in the millisecond

range. Thermal time constants of the other two membranes

were even smaller due to their small thicknesses and high

Fig. 4. Time variation of the heater current for a supplied voltage of 4 V. (Membrane material: polyimide.)

Fig. 5. Time variations of the heater currents for a supplied voltage of

12 V. (Membrane materials: (a) Si3N4; (b) Pyrex glass; (c) polyimide.)

Y.E. Wu et al. / Sensors and Actuators A 100 (2002) 37–45 41

thermal diffusivities. The slow warm-up periods observed

in the test therefore, must be due to the large thermal

capacitance of the silicon package. This explains why the

required times for the three TCDs to reach a steady state were

very close to one another. Although the membranes in these

TCDs were different, the silicon packages were identical.

Time variation of the average temperature of the silicon

package can be estimated from the following equation for a

lumped system:

rVcdT

dt¼ Qmembrane�wafer � h Awafer�airðT � TairÞ

� Qwafer�rack (1)

where r, V, c, T are the density, volume, specific heat, and

average temperature of the silicon wafers; h is the heat

transfer coefficient; and t the time variable. The three terms

on the RHS represent the heat input to the silicon package

from the heater, the convective heat loss from package

surfaces, and the conductive heat loss to the metallic rack

beneath the TCDs during the transient heat transfer test. The

conductive loss term can be expressed as:

Qwafer�rack ¼ ðT � TrackÞRcond

(2)

The conduction resistance, Rcond, is proportional to the length

and inversely proportional to the thickness and thermal

conductivity of the silicon package. The rack temperature

remained nearly constant during the test.

Since the test chamber was evacuated, there was no

convective heat loss during the transient test. The complete

solution to the heat equation with h ¼ 0 consists of a steady-

state and a transient solution:

T�Track ¼ ys þ yt (3)

where

ys ¼ Qmembrane�waferRcond (4)

yt ¼ ðTinitial � Track � ysÞ exp�t

RcondrVc

� �(5)

The thermal time constant of the transient process is there-

fore, equal to RcondrVc. The package was made up of two

4 in:� 4 in. silicon wafers glued together. There are two sets

of flow channels and heaters fabricated at the center of the

silicon wafers. As a result only one half of the package was

considered in the transient conduction analysis.

The thermal capacitance was computed from:

ðrcÞðVÞ ¼ ð1:6� 106 Jm�3 K�1Þð2� 350mm� 4 in:� 2in:Þ¼ 5:78JK�1 (6)

The conduction resistance was estimated from:

The thermal time constant calculated from the above

estimation is about 28 s for the three TCDs. This estimate

is in good agreement with the transient current plots in

Figs. 4 and 5. The noise levels in these current measurements

seemed to be dependent primarily upon the thermal capa-

citances of the heaters. The good signal conditions of the

polyimide membrane are probably attributed to its large

volume.

3.2. Heat transfer in TCDs of different flow-channel

designs

Heat transfer characteristics of single- and double-chan-

nel TCDs were compared and analyzed in this test. The

polyimide membrane was selected since it exhibited the best

signal conditions in the transit time test. A single-channel

TCD and a double-channel TCD made from the same

materials were placed in the stainless-steel chamber. The

chamber was filled with helium gas—a carrier gas com-

monly used in GC applications. The stagnant gas in the flow

channels simulated the conduction-dominant heat transfer

process in TCD operations. A thermocouple was attached to

the lower channel surface of the double-channel TCD for

measuring the silicon wafer temperature. The measured

surface temperature of the double-channel TCD together

with the electric currents of both TCDs is presented in Fig. 6.

The average electric resistances of the heating elements

were 822 and 773 O for the single- and double-channel

TCDs at a supplied voltage of 14 V. Deduced from the

temperature coefficient of resistance, the heating element

temperatures of the single- and double-channel TCDs were

193.5 and 176.3 8C, respectively at this supplied voltage.

Assuming the outer surface temperatures of the upper and

lower flow channels were close to each other, the heat fluxes

through the upper and lower flow channels can be calculated

from:

qu ¼ ðTNi � TSiÞsum of ðthickness=thermal conductivityÞ

¼ ðTNi � TSiÞðL=kÞhelium in upper channel þ ðL=kÞupper Si wafer

¼ 1:33 MW m�2 (8)

Rcond ¼ wafer length=2

silicon thermal conductivity � 2 � wafer thickness � wafer width

¼ 4 in:=2

148 W m�1 K�1 � 2 � 350 mm � 4 in:Þ¼ 4:83 K W�1 (7)

42 Y.E. Wu et al. / Sensors and Actuators A 100 (2002) 37–45

ql ¼ðTNi �TSiÞ

ðL=kÞmembraneþðL=kÞheliumin lowerchannelþðL=kÞlowerSiwafer

¼ 0:237MWm�2 (9)

And the total heat transfer rate of the double-channel TCD

is the sum of qu and ql multiplied by the channel floor area.

The calculated heat transfer rate of 0.283 W is 12% higher

than the power consumption of the electric heater, which

was determined from the product of the heater current and

voltage.

A couple of causes may contribute to the discrepancy

between the heat transfer model and experimental measure-

ments. For one thing, the back of the thermocouple bead was

exposed to the cool surroundings and the bead diameter was

larger than the flow channel width. As a result the thermo-

couple temperature was slightly lower than the temperature

of the channel surface it measured. The major reason is

probably the overestimation of the membrane surface tem-

perature. Since the heating element did not cover the entire

floor of the flow channel, the average floor temperature

should be lower than the heating element temperature.

The 12% higher heat transfer rate of the theoretical solution

indicates the average floor temperature should be about

18 8C lower than the heating element temperature TNi.

It is very difficult to accurately measure the gas tempera-

ture in the channel under the polyimide membrane or the

membrane surface temperature for the single-channel TCD.

It was assumed in our analysis that the outer surface

temperature of the open silicon channel and the gas tem-

perature at the channel opening (point o in Fig. 1(b)) were

close to the lower channel surface temperature of the double-

channel TCD. The calculated heat fluxes through the closed

and open channels of the single-channel TCD are:

qu ¼ ðTNi � TSiÞðL=kÞhelium in upper channel þ ðL=kÞupper Si wafer

¼ 1:49 MW m�2 (10)

ql ¼ðTNi � TSiÞ

½ðL=kÞmembrane þ ðL=kÞhelium in open channel�¼ 0:0118 MW m�2 (11)

The power consumption is : Q ¼ ðqu þ qlÞA ¼ 0:271 W

(12)

Results of the above heat transfer analysis changed only

slightly if the gas temperature at the channel opening was

assumed to be the surroundings’ temperature of 24 8C.

When the single-channel TCD is operated in atmosphere,

the open channel will be filled with air. If the thermal

conductivity of air were used in Eq. (11), ql would change

to 0.0582 MW m�2, but the TCD power consumption, Q,

would increase by 3% only.

Just like the double-channel results, the calculated heat

transfer rate of the single-channel TCD is 14% higher than

the measured one, indicating the average floor temperature

was again slightly lower than the heating element tempera-

ture. If the floor temperatures could be more accurately

determined, the one-dimensional heat transfer model should

yield better agreement with the experimental data. Never-

theless our model showed the heat transfer to the helium gas

in the double-channel TCD was about 20% higher than that

in the single-channel design at a supplied voltage of 14 V.

The difference in heat transfer rates agreed well with

experimental measurements.

Although more heat was transferred to the helium gas in

the double-channel TCD, the double-channel design con-

sumed more electricity for a desired heater temperature.

Theoretically heat transfer to the gas flow in an ideal double-

channel TCD is 100% more than that in an ideal single-

channel TCD, and the sensitivity is doubled too. In reality

the sensitivities of the two designs do not differ as much

as the heat transfer rates due to thermal resistances other

than the gas resistances in the heat flow paths. The TCD

sensitivity is a measure of the influence of the change in gas

Fig. 6. Measured wafer temperature and heater currents at different voltages.

Y.E. Wu et al. / Sensors and Actuators A 100 (2002) 37–45 43

thermal conductivity on the heater power. A comparison of

the sensitivities of the two flow channel designs is presented

in Fig. 7. This comparison was made for TNi ¼ 500 K and

TSi ¼ To ¼ 300 K. The abscissa of the plot is the gas

thermal conductivity normalized by helium thermal con-

ductivity at 400 K. Fig. 7 shows that while the heat flux of

the double-channel TCD maintains approximately 20%

higher when the gas thermal conductivity varies from 0.9

to 1.1 of khelium, the changes in heater power consumptions

of the two TCDs are very close. In this comparison dq00 of the

double-channel TCD is only about 3% higher than that of the

single-channel TCD. Better sensitivity improvement over

the single-channel design can be achieved if the double-

channel TCD uses thinner membrane and silicon wafers.

4. Conclusions

TCDs of different flow channel designs and heater mate-

rials were fabricated and their performances and transient

behaviors characterized. One-dimensional heat transfer and

lumped system models were developed and compared with

experimental observations. It was found in the transient test

that the TCD response time depended primarily on the

dimensions of the silicon package. The power input affected

only the signal’s noise level. The double-channel design

transferred more heat to the gas flow than the single-channel

design, but the increase in sensitivity due to the additional

flow channel was not as significant as the increase in heat

transfer rate. The average heater surface temperature was

slightly lower than the heating element temperature deduced

from the resistance measurement.

Acknowledgements

This research was supported by the Chung Shan Institute

of Science and Technology (CSIST). The advice and

information provided by Dr. S.W. Ko of CSIST is greatly

appreciated.

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Fig. 7. Heat fluxes and heat flux changes of single- and double-channel TCDs. [dq00 ¼ q00ðkÞ � q00ðk ¼ kheliumÞ].

44 Y.E. Wu et al. / Sensors and Actuators A 100 (2002) 37–45

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Biographies

Ye-Ee Wu received the PhD degree from the Department of Chemical

Engineering and Material Science, Syracuse University, in 1983. He has

been an Associate Professor in the Mechanical Engineering Department,

National Taiwan University of Science and Technology, since 1985. Prior

to that he worked for the China Steel Corporation for 2 years as a research

scientist. Dr. Wu’s research interests include microfabrication technology,

non-destructive evaluation, and mechanical metallurgy.

Kuan Chen received his PhD degree from the University of Illinois at Urbana-

Champaign in 1981. Immediately thereafter he jointed the Faculty of

Mechanical Engineering of the University of Utah, and became an Associate

Professor in 1988. He was a professor in the Mechanical Engineering

Department, National Taiwan University of Science and Technology, from

1997 to 1999. His current research interests include microfabrication, thermal

plasmas, thermoelectrics, and microscale thermal systems and phenomena.

Chao-Wen Chen received his MS degree from the Department of

Mechanical Engineering, National Taiwan University of Science and

Technology, in 2000. He is now serving in the Army as a Lieutenant to

fulfill his military obligation.

Keng-Hao Hsu received his MS degree from the Department of

Mechanical Engineering, National Taiwan University of Science and

Technology, in 2000. He is now serving in the air force as a Sergeant to

fulfill his military obligation.

Y.E. Wu et al. / Sensors and Actuators A 100 (2002) 37–45 45