TECHNICAL PAPER

Electro-thermal analysis of an embedded boron diffusedmicroheater for thruster applications

Pijus Kundu • Tarun Kanti Bhattacharyya •

Soumen Das

Received: 17 October 2012 / Accepted: 19 February 2013

� Springer-Verlag Berlin Heidelberg 2013

Abstract One of the important design criteria of micro-

propulsion systems in particular VLM is the type of mi-

croheater, its layout and placement with a view to achieve

uniform heating of propellant, fast heat transfer efficiency

with minimum input power. Thrust produced by mic-

rothruster not only depends on the structural geometry of

the thruster and propellant flow rate, but also on the

chamber temperature to produce super saturated dry stream

at the exit nozzle. Detailed design of microheater in ther-

mal and electrical domains using co-solvers available in

MEMS software tools along with material’s thermal

property, temperature dependence of electrical resistivity

and thermal conductivity have been considered in the

present work to achieve precise modeling and experimental

accuracy of heater operation. The chamber temperature

was analytically calculated and subsequently the required

resistance and power were estimated. The boron diffused

microheaters of meanderline configuration in silicon sub-

strate has been designed and its finite element based elec-

tro-thermal modeling was employed to predict the heater

characteristics. The variation of microheater temperature

with time, applied voltage and along chamber length has

been determined from the modeling. Subsequently the

designed microheater was realized on silicon wafer by

lithography and boron diffusion process and its detailed

testing was evaluated. It was found that boron diffused

resistor of 820 X can generate 405 K temperature with

applied input power 2.4 W. Finally the simulated results

were validated by experimental data.

1 Introduction

Recent development of solid-state miniature sensors and

actuators based on semiconductor materials leads to

attractive solutions for various applications, ranging from

healthcare and safety to process and quality control in

industrial implementation (Gajda and Ahmed 1995; Fung

et al. 1996; Briand et al. 2000; Puigcorbe et al. 2003 and

Baroncini et al. 2004), inertial navigation systems, etc.

Micropropulsion systems are indispensable in miniaturized

spacecrafts for attitude control; delta-V maneuvers, station

keeping, and orbit adjust (Rossi et al. 1997; Lewis et al.

2000; Zhang et al. 2005). Moreover similar high perfor-

mance complex devices based on microscale explosive

boiling are explored thermal bubble jet printers, biology,

medicine, space exploration, and microelectronic cooling

(Iida and Okuyama 1994; Glod et al. 2002). Besides that

gas sensors and flow sensors (Xua et al. 2005; Wang et al.

2007, 2009) such as microfluidic PCR chip (Lien et al.

2009) are being extensively deployed in safety control, and

healthcare diagnosis systems etc. Microscale heating is one

of the important criteria for efficient functioning of the

above devices. This leads to a thorough investigation of

microscale heaters over the decades with the wire heater

and the thin film heater being the two primary variants of

heater design. With the advancement of microfabrication

technology thin film heaters are more efficient compared to

P. Kundu (&)

Advanced Technology Development Centre,

Indian Institute of Technology, Kharagpur 721302, India

e-mail: pijusknd82@gmail.com

T. K. Bhattacharyya

Department of Electronics and Electrical Communication

Engineering, Indian Institute of Technology,

Kharagpur 721302, India

S. Das

School of Medical Science and Technology,

Indian Institute of Technology, Kharagpur 721302, India

123

Microsyst Technol

DOI 10.1007/s00542-013-1759-2

their wire-based analogues due to the lower heat mass, ease

of integration and compatibility with MEMS-based trans-

ducer devices.

Among various micropropulsion systems vaporizing

liquid microthrusters (VLM) that produces thrust by

changing its propellant from liquid to gaseous phase has

received considerable attention of researchers in the

recent past (Ye et al. 2001; Mukerjee et al. 2000; Mueller

et al. 1997). One of the important design criteria of a

VLM is the type of microheater, its layout and placement

with a view in achieving uniform and fast heat-transfer

efficiency with minimum input power (Kundu et al.

2012). A polysilicon thin film resistor and diffused/

implanted resistor on the outer surface of the vaporizing

chamber have been used as the microheater in some

VLMs reported earlier (Mukerjee et al. 2000). Such mi-

croheaters are not directly exposed to the liquid propellant

and hence have a longer working life. However this

configuration leads to substantial loss of heat that reduces

the thermal efficiency. Ye et al. (2001) have reported a

VLM with an internal Ti-film resistor as the microheater,

yielding higher heat-transfer efficiency. However, the

wire-bonded electrical contacts are exposed to the pro-

pellant and the holes in the top substrate through which

the bonding wires emerges are sealed by ‘glue’. These are

not desirable for long-term use of the device. Maurya

et al. (2005a) implemented silicon-based VLMs with two

bonded micromachined chips integrated with a p-diffused

microheater and were able to achieve thrust of 5–120 lN

with heater power between 1 and 2.4 W at a water flow

rate of 1.6 ll s-1 and presented its thermodynamic,

electrothermal and microfluidic analysis in a semi-ana-

lytical way (Maurya et al. 2005b).

Thin film microheaters are evaluated by their low power

consumption, fast response, good heat confinement,

excellent mechanical stability, and reliable fabrication

yield. Heavily doped p-type silicon is extensively used as

the microheater material because of its excellent mechan-

ical properties (Fung et al. 1996). However, the main issue

of this kind of microheater is its relatively high power

consumption. For thin film microheater, modeling is a good

way to predict its performance, especially its detailed

temperature profile (Fung et al. 1996; Puigcorbe et al.

2003; Baroncini et al. 2004; Rossi et al. 1997), spatial and

temporal fluctuation, etc. Unfortunately, the thin film

material properties required for efficient design of micro-

heater are rarely discussed in details, which are essential to

the microheater performance prediction. To improve the

microheater performance, recent studies have employed

dielectric membrane to ensure low power consumption

(Briand et al. 2000; Puigcorbe et al. 2003; Baroncini et al.

2004; Rossi et al. 1997). Although dielectric membrane can

provide improvement in terms of microheater power

consumption the material is not highly reliable for harsh

environmental applications. The dependence of tempera-

ture variation on electrical resistivity and thermal con-

ductivity of thin film materials are often ignored. It should

be noted that these are the key material properties required

for any thin film microheater modeling and realization.

Also, the literature survey reveals that detailed studies on

accurate design of microheater in thermo fluidic and

electrical domains using co-solvers of various available

software tools and calibration and testing procedures of

fabricated heaters are seldom despite their usefulness in

understanding the modeling and experimental accuracy of

microheater operation.

The present work reports the design, fabrication and

testing of microheaters used in the microthruster with the

aim to achieve uniform heat distribution in the thruster

chamber and fast heat transfer efficiency with minimum

input power. Considering the heat transfer by conduction

and convection processes the required heater energy was

analytically estimated for a specific amount of propellant to

be vaporized. Subsequently the heater geometrical dimen-

sion was obtained and its finite-element based electro-

thermal modeling was presented to predict the microheater

performance. The boron diffused microheater of mean-

derline configuration in silicon substrate has been realized

by lithography and boron diffusion process and its detailed

testing was evaluated. Finally the simulated results were

validated with experimental data.

2 Analytical calculation

2.1 Design of microheater

Due to scaling down of structural dimensions and its crit-

ical geometrical configuration, the hydrodynamic behavior

is highly complex inside the MEMS thruster. The operating

principle of a VLM thruster is the electrical heating of the

liquid propellant using an embedded microheater to gen-

erate a hot gas which can be passed through a nozzle to

provide thrust. Thruster performance is evaluated from

generated thrust and specific impulse which are governed

by the propellant inlet flow rate and exit velocity (Kundu

et al. 2012). The exit velocity is a function of vaporizing

chamber temperature (Tc) and pressure (Pc).

Since Pc will linearly increase with Tc, both will lead to

an increase of gas exit velocity (Vexit) and hence thrust. The

heater should be designed to supply adequate power to

achieve necessary Tc with minimum time span. This may

be achieved by employing a uniformly spreading resistor

over the entire chamber surface. With increase of heater

surface area, the heat transfer rate will improve but the

conduction loss will also increase.

Microsyst Technol

123

Either thin film resistor (Ye et al. 2001; Lewis et al.

2000) or diffused/implanted resistors (Mukerjee et al.

2000; Maurya et al. 2005a, b; Robert and Kenneth 2001)

are used as resistive heating element in microthruster

applications (Kundu et al. 2012). The device configuration

was designed consisting of two silicon layers having

miniature propellant chamber sandwiched between two

heaters embedded at top and bottom exposed surfaces of

silicon layer located at a fixed distance from the chamber

surface as shown in Fig. 1. In the present study boron

diffused p-type resistor in n-Si substrate has been consid-

ered for microheater. Instead of using one, two similar

resistors located at the top and bottom surface of a micro

chamber are designed for efficient heating of liquid pro-

pellant that flows through the chamber. The resistors are

embedded in the wafer surface as shown in Fig. 1 and

passivated by SiO2 film to provide electrical insulation and

corrosion resistance. The diffused resistor is powered by

electrical voltage that provides thermal heating surround-

ing the heater and as a result temperature of the sur-

rounding zone will increase. In the present configuration

heaters are located at the exposed surface of wafer whereas

propellant that flows through VLM chamber is in contact

with the other surface of the wafer and thus they are sep-

arated by wafer thickness. Thus the heat energy flows from

microheater to propellant by conduction process through

wafer thickness followed by convection process through

the liquid propellant.

2.2 Heater energy and power requirement

The total energy (QT) required to vaporize the liquid is the

sum of the energy required to raise the temperature of the

propellant to the vaporization point (Q1) and the energy for

vaporization (Q2) at that temperature neglecting heat loss.

Hence

QT ¼ Q1 þ Q2 ð1Þ

Q1 and Q2 are given by

Q1 ¼ mcDT ð2ÞQ2 ¼ mLv ð3Þ

where m is the mass of the liquid being transformed to

vapor, c the heat capacity of the liquid, Lv the latent heat of

vaporization and

DT ¼ Tc � Ti ð4Þ

where, Ti and Tc are the initial temperature and vaporiza-

tion temperature of the incoming fluid in the pressurized

chamber.

If Vc is the volume of the vaporizing chamber and q is

the density of the liquid propellant, the fluid filling the

chamber will escape through the exit nozzle over a time

period, s, given by

s ¼ qVc

m� ð5Þ

where m* is the mass flow rate of liquid or vapor through

the exit nozzle. Considering the conservation of mass under

steady state condition, m* is considered to be same for both

liquid and vapor at inlet and exit locations.

In writing down Eq. 1, the thermal energy consumed to

heat up the remaining amount of liquid filling the chamber,

viz. (qVc - m) to the temperature below the vaporizing

point was not considered. Let it be denoted by Q0. So

QT ¼ Qo þ Q1 þ Q2 ð6Þ

In the actual device, the temperature distribution inside

the chamber is highly nonuniform excepting for the region

where the liquid is boiling. It is rather difficult to estimate

Q0 analytically. For the sake of analytical simplicity, Q0

was not considered in Eq. 1. With increasing heater power,

Q0 will decrease and become zero at the point of complete

vaporization (m = qVc) or above. When the heater power

is increased above the value for which (m/qVc) = 1, the

additional energy supplied by the heater will be utilized to

increase the temperature of vapor (Tc) filling the chamber.

The Eq. 6 is thus further modified as

QT ¼ Q0 þ Q1 þ Q2 þ Q3 ð7Þ

where Q3 is the amount of thermal energy involved in

raising the temperature of vapor after complete

vaporization. It is may be noted that

Q3 ¼ 0 for 0� m

qVc� 1 and Q0 ¼ 0 for

m

qVc� 1

ð8Þ

Thus the average power is given by:

W ¼ m

qVcm � ðcDT þ LvÞ þ

m�qVc

Q3 þm�qVc

Q0 ð9Þ

Fig. 1 Schematic 3D view of thruster design with two microheater

configuration

Microsyst Technol

123

Equation 9 is the general relationship subject to the

condition imposed by Eq. 8. Q3 may be approximated as

Q3 ¼ qVcCv Tc � T0c� �

ð10Þ

where Cv is the specific heat of gas (vapor) at constant

volume and T0c is the chamber temperature at the point of

complete vaporization m=qVcð Þ ¼ 1. It may be noted that

the mass of vapor filling the chamber for Tc [ T0c is the

same as qVc in Eq. 5 for a given flow rate (m*) due to the

conservation of mass. It may also be noted that the maxi-

mum value of DT in Eq. 9 is limited to DTmax ¼ T0c � Ti.

The average power dissipation required for vaporization

of propellant may, therefore, be estimated as

W ¼ mðcDT þ LvÞs

ð11Þ

W ¼ m

qVcm � ðcDT þ LvÞ ð12Þ

mqVc

is the fraction of fluid filling the chamber which is

vaporized due to electrical heating. The above derivation

is, however, based on the assumption that there is no loss of

heat. In reality, there will be heat loss due to conduction,

convection and radiation.

In the present design two heaters located at the top and

bottom surfaces of micro chamber are considered having

similar geometrical configuration and located centrally at

the equal distance from the chamber surfaces. Moreover

same electrical power is fed to the heaters so that the

temperature distribution at the chamber top and bottom

surfaces be same. Since the heater is located at a depth d

from the chamber surface, and considering the one

dimensional heat flow, heat dissipated away by conduction

process through the top or bottom silicon layer is given by

qcond ¼KSiA

dðTH � TcÞ ð13Þ

where A is the average cross sectional area of silicon

chamber surface for heat conduction to occur, Ksi is the

thermal conductivity of silicon, TH is the temperature of

heater surface.

The bottom surface of top layer and top surface of the

bottom layer in the vaporizing chamber are exposed to the

liquid propellant. The heat energy available at these sur-

faces coming from heaters by conduction process will be

transferred to the propellant by convective process. The

heat loss by the convection process is given by

qconv ¼ hcAðTc � TiÞ ð14Þ

where hc is the average convective heat transfer co-efficient

and Ti is the inlet propellant temperature. For a given

experimental condition and assuming the radiation loss is

negligible, under steady state condition we may write

qcond ffi qconv ð15Þ

Using Eqs. 13 and 14, we obtain

TH � Tc

Tc � Ti¼ hc

KSid ð16Þ

This equation may be solved to obtain TH i.e. heater surface

temperature taking into account the chamber temperature (Tc)

is equal to the vaporizing temperature of liquid propellant.

Once TH is known qcond may be computed using Eq. 13.

The electrical power required by the microheater is

given by

P ¼ VI ¼ I2R ð17Þ

where V is the applied voltage, I is the current and R is the

resistance of the microheater. A part of this power is lost by

conduction process through silicon layer and the remaining part

is utilized to heat up and vaporize the liquid propellant. Hence

P ¼Wþ qcond ð18Þ

where W is given by Eq. 12.

The above equation predicts a relationship between the

applied heater power, chamber temperature, the fraction of

liquid vaporized in the chamber and the mass flow rate through

the chamber. The resistance of microheater is calculated using

Eqs. 17 and 18 and the maximum operating voltage specified

for microthruster operation. Once R value is known, the length

and width of the resistor were estimated considering the

microfabrication facilities available at authors’ laboratory.

Meanderline configuration of heater was considered to

accommodate the total length of the resistor within the mini-

aturize vaporizing chamber surface area with a fixed pitch

value so that at least 70 % of the chamber surface area is

covered by the microheater for uniform heating of propellant.

From the above analysis the resistor dimensions were calcu-

lated to be of total length 17 mm, width 150 lm, thickness

1 lm and pitch value 1,000 lm for electro thermal simulation.

3 Simulation study

Electro-thermal analysis of the microheater was carried out

using CoventorWare� software. 3-D electro-thermal sim-

ulation was performed to characterize the thermal behav-

ior, temperature distribution of the heater and its transient

analysis for a given heater power using finite element

method. The 2-D mask layout and process sequence of

microheater were executed to build a solid model and

subsequently mesh generation was performed. The finite

elements and boundary elements technique are used to

solve the differential equations of each physical domain in

the simulation study. The differential equations are solved

by discretizing the solid model into a mesh that consists of

Microsyst Technol

123

a number of elements each with a specified number of

nodes. When the mesh model is generated, this information

is transferred for use by the electro-thermal solver with

boundary conditions. The 3D view of the meshed boron

diffused microheater and its surrounding silicon layer are

shown in Fig. 2a, b. Considering wide dimensional varia-

tion of heater and silicon layer the meshing was performed

separately for the two layers and then merged together for

simpler computation process and to achieve accuracy in the

results. The models were built based on the GDS-format

mask layout, process sequences, layer thickness and

material properties database. The geometrical dimension of

microheater as calculated in previous section was used for

simulation process. The total surface area occupied by the

resistor was adjusted to investigate its effect on the tem-

perature distribution in the reaction chamber. It was

observed that with the increase of surface area, the heat

transfer will improve but the conduction loss will also

increase. On the other hand the decreased heater surface

area will affect the temperature distribution uniformity on

the chamber surface.

Simulations have been performed to investigate the

temperature distribution of chamber surface using the fol-

lowing boundary conditions:

• The initial temperature of the microheater surface is

assumed to be 300 K.

• Radiation loss is neglected.

• The heater voltage varies between 5 and 65 voltages as

a parametric study.

3.1 Simulation results

3.1.1 Steady state analysis

The steady state temperature distribution provides informa-

tion to understand the temperature difference between the

chamber and the heater surface. This information is required

to improve the microthruster performance. Figure 3 shows a

typical temperature distribution of a microheater surface and

along the meanderline resistor for the applied voltage 42 V.

The result shows uniformly distributed temperature over the

Fig. 2 Meshed boron diffused layer of a a microheater and b embedded microheater in silicon layer

Fig. 3 Simulated temperature distribution of a the microheater surface b along the meanderline structure for 42 V heater voltage

Microsyst Technol

123

entire vaporizing chamber and a negligible increase of tem-

perature at the heater bond pad regions. For a diffused or thin-

film heater, a better thermal yield i.e. maximum temperature

per unit of electrical power consumption is achieved by

minimizing the thermal heat loss. Reduction of thermal loss is

accomplished by power heat confinement around the heater

region which is achieved in the boron diffused micro heater as

observed from Fig. 3a. The temperature at the boron heater

increases rapidly, whereas the temperature of the surrounding

heater region does not change appreciably. This is attributed

by the meanderline microheater as compared to other design.

Figure 4 shows the variation of maximum temperature in

steady state condition for different applied voltage. The

maximum temperature can be controlled by varying the

supply voltage. The simulation results show that the achiev-

able maximum temperature is quite low at lower applied

voltage (up to 30 V). However at higher heater bias voltage

the simulated temperature is quite high and can attain more

than the required propellant vaporizing temperature

(*410 K) nearly at 45 V required for thruster operation.

Figure 5 shows the results of temperature distribution on the

heater surface and bottom/chamber surface along the mic-

rothruster length from inlet to outlet. The result shows only

2�–3� temperature difference between the top and bottom

surface of the silicon wafer having 200 lm separations

between them. The simulation study confirms the confinement

of heat energy around the heater region resulting minimum

heat loss and negligible temperature difference between the

two heater surfaces which is acceptable for the thruster

operation.

3.1.2 Transient analysis

Time required to reach the maximum temperature for an

applied heater power is an important factor which decides

the response time of the thruster under pulse mode opera-

tion. Thus, the transient response of the heater has also

been carried out to evaluate the thruster response time.

Figure 6 shows the temperature variation with time for

different applied heater voltage. The plots indicate that the

maximum temperature increases rapidly on the application

of power and then slowly gets saturated at a temperature

within 2–3 s time. The rate of increase is fast for higher

applied power but the time required to attain steady state

value is less dependent on the input power. This is attrib-

uted by reaching the equilibrium state between heat gen-

eration by the Joule effect and heat loss by conduction and

other processes.

4 Fabrication of microheater

Based on the above design and its simulation results, the

structural geometry of microheater was configured for its

realization in microthruster device (Kundu et al. 2012).

Further the microheater of same configuration located on

200 lm thick silicon layer as depicted in VLM was indi-

vidually processed using microfabrication technology and

its detailed testing was performed. In this process the

starting substrate was a 2-inch diameter, phosphorus

doped, \ 100 [ orientation, 4–6 X-cm resistivity, 270 lm

thick and double side polished silicon wafers. The wafers

were cleaned by the standard cleaning process followed by

growth of thermal oxide in a furnace at 1,100 �C by the

cyclic oxidation process. Thickness of the grown silicon

dioxide was measured by an ellipsometer and was found to

be approximately 1.0 lm. The thermally grown silicon

Fig. 4 Variation of temperature on the heater surface vs. applied

voltage

Fig. 5 Temperature distribution along the inlet to outlet of the

microthruster chamber for heater voltage 42 V

Microsyst Technol

123

dioxide was used as the protection mask during resistor

diffusion and anisotropic etching of silicon in TMAH

solution in subsequent steps. The front-side oxide was

photolithographically pattern, to open windows for resistor

diffusion. Boron doped resistors were formed by the two-

step thermal diffusion technique using boron nitride solid

source. Boron pre-deposition was carried out at 1,100 �C

for 60 min in (1.5 %) N2/O2 ambient using BN1100 planar

diffusion source, followed by low temperature oxidation at

750 �C for 30 min. The drive-in diffusion was carried out

at 1,100 �C during 10–60–10 min cyclic oxidation process.

The sheet resistance of diffused layer was measured by the

four probe technique and the values obtained after pre-

deposition and drive-in are 3.5 and 5 X/sq respectively.

After resistor fabrication, the back-side silicon dioxide was

photolithographically patterned to delineate the silicon

membrane area aligned with the resistor pattern located

centrally at the other side of silicon wafer and then etched

by buffered hydrofluoric acid (BHF) at room temperature.

During the backside silicon dioxide patterning, the front-

side of the wafer was protected by photoresist. Subse-

quently, the front side oxide was photolithographically

patterned, to open the window for interconnection of the

top heater. Aluminum was deposited on the wafer by

thermal evaporation technique at a pressure of 9 9 10-6

torr and subsequently patterned photolithographically to

provide the contact links of diffused resistor. The alumi-

num film was then sintered at 450 �C for 15 min in N2/

10 % H2 ambient. Finally, the processed wafer was

anisotropically etched in 5 wt% dual-doped TMAH at

Fig. 6 Transient response of microheater for different supply

voltage

Fig. 7 Microheater fabrication process flow

Microsyst Technol

123

70 �C to form the 200 lm thick silicon membrane. The

micro fabrication process as reported (Kundu et al. 2012) is

shown in Fig. 7. The optical photograph of the meanderline

boron diffused resistor is shown in Fig. 8. The total length

and width of meanderline microheater was about 17 mm

and 200 lm respectively and area of microheater covers

about 70 % of the VLM chamber area to achieve uniform

and fast heating of propellant.

5 Testing of microheater

The performance characteristics of fabricated the mi-

croheater has been experimentally evaluated by using

data acquisition system for acquiring temperature and

current–voltage reading using the setup as shown in

Fig. 9. The die having the heater configuration on silicon

membrane of thickness 200 micron is glued on a PCB.

The electrical connection to the heater has been estab-

lished by soldering electrical wires and the other end of

wires were connected to the voltage source. Two heater

configurations located at top and bottom surfaces of the

chamber have been designed in the actual thruster device

and accordingly the electrothermal simulation has been

carried out as discussed in previous sections. However,

in the present study experimentally micromachined sili-

con chip having only one heater has been considered for

temperature measurement. The purpose of this mea-

surement is to observe chamber temperature for varying

input heater power under wet condition by flowing the

propellant through the chamber. It is extremely difficult

to place a thermocouple and taking out its electrical leads

to monitor the output through a closed miniaturized

chamber under a propellant flow condition. Thus in this

study a miniature thermocouple (T-type) has been used

for sensing the temperature of silicon surface of thruster

chamber under dry condition. The testing of microheater

was carried out in such a way that the applied input

heater power was sufficient enough to produce the

chamber temperature much above the vaporization tem-

perature of the propellant. A fine-wire copper-constantan

thermo-couple tip was pressed against the electrically

insulated heater surface. The generated thermo emf due

to raise of temperature of VLM chamber was measured

for different voltages applied across the heater terminals.

The voltage output of the sensor has been feed to the

DAC (MW100-E-1D) system to record the temperature.

The heater current was also measured and hence the

power consumption of the heater was calculated. In the

present case the total heater resistance is about 818 X.

The silver epoxy used for contacting the electrical leads

imposed a limit of the maximum temperature to 200 �C

but far above the vaporizing point of water required for

VLM operation. The above experimental results help in

estimating and controlling the heater power for VLM

operation very accurately.

6 Results and discussion

In the present study the realization of boron diffused

resistor in single crystal silicon was aimed for its deploy-

ment as a microthruster which can deliver sufficient

amount of thermal energy to its bottom surface located at

200 lm below the heater surface for evaporation of liquid.

The fabricated resistor was electrically characterized to

obtain the temperature profile of its surrounding surface at

dry condition i.e. without any propellant flow. In these

measurements single heater located either at top or bottom

surface of the 200 lm thick silicon membrane was used to

measure the temperature of wafer surface for various input

heater power. The average resistance value of the fabri-

cated meander line microheater was about 810 ± 20 X.

For a particular device a minimum heater power of 1.4 W

was required to raise the temperature to 373 K without any

water flow. Figure 10 shows the distribution of potential

drop across the entire microheater region obtained from

electro thermal simulation using CoventorWare� software

for a supply voltage of 42 V. It is observed that almost

entire voltage drop occurs in the meander line part of the

boron diffused resistor region and negligible drop across

the aluminum metal interconnecting lines and the bond pad

portions. This result is expected due to much lower elec-

trical resistivity of metal line as compared to the boron

diffused region and thus metal line resistance can be

neglected. This simulation result ensures localized heating

of a surface region surrounded by only diffused resistor

area. Consequently the average temperature of the boron

diffused zigzag path obtained from electro thermal

Fig. 8 Optical photo graph of the fabricated microheater

Microsyst Technol

123

simulation can be used for comparison with the experi-

mental results.

Figure 11 shows a typical measured temperature profile

at the heater surface with respect to time for applying

potential across the resistor terminal. The transient

response shows that the temperature of the surface

increases very rapidly immediately on applying the heater

voltage and then it slowly saturates over a time span. For

higher applied voltage the rate of increase is quite high and

also the steady state temperature is higher than the lower

heater voltage. For applied voltage of 45 V the steady state

temperature is about 390 K that reaches within 2 s time

and for 42 V applied the values are 380 K and 3 s

respectively. The simulated transient response for 45 V is

also included in Fig. 11. The simulation result depicts that

the rate of increase and also the absolute value of the

temperature are higher as compared to measured data. This

variation is attributed due to heat loss by conduction pro-

cess as well as there will be radiation loss which was not

considered in the simulation.

In the present study the requirement of heater power was

limited to the achievable temperature of the system up to

400 K required to vaporize the water. However the fabri-

cated microheater can be used for higher heater power

which was subsequently tested by varying the input heater

power. Figure 12 shows the microheater maximum

Fig. 9 Temperature measurement set up of microheater

Fig. 10 Potential distribution over the boron diffused microheater

Fig. 11 Measured variation of temperature with time and its

comparison with electro-thermal simulation results

Microsyst Technol

123

saturated temperature as a function of the electrical power

under dry condition. It may be observed from the figure

that the saturated heater temperature varies linearly with

input power except below 1.8 W. The heater power of

3.4 W is sufficient to increase the temperature nearly

470 K at dry condition which can satisfactorily produce

superheated dry stream required in the operation of VLM

(Kundu et al. 2012). The measurement was limited to

3.4 W to avoid overheating of the chip leading to unpre-

dictable failure of wire bonding located near to the heater

region.

7 Infrared imaging

Apart from the temperature measurement of silicon surface

using a tiny thermocouple, infrared (IR) imaging technique

has also been performed to acquire the thermal images of

the heater surface. The IR images were obtained for dif-

ferent input heater power supply by using FLUKE Ti32

camera of temperature resolution 0.05 �C. Figure 13a

shows a typical IR images of silicon top surface where a

boron diffused microheater of resistance 820 X is located

and powered by 2.4 W. Figure 13b represents the IR image

of the bottom silicon surface located at 200 lm thickness

below the top heater surface. The delineated portion around

the heater area consisting of a small rectangular microflu-

idic channel, a chamber and a converging–diverging in-

plane nozzle fabricated at the bottom surface of silicon

wafer by micromachining process for VLM application

(Kundu et al. 2012). The images reveal that a maximum

heater temperature reaches about 425 K and is uniform

throughout the meanderline area. However a uniform

temperature distribution at 415 K was observed at the

adjacent surface area of the heater location as observed in

Fig. 13a. The average temperature at the bottom silicon

surface located 200 lm thickness below the heater surface

is about 405 K as observed in Fig. 13b. Thus a temperature

variation of about 10 K was observed between heater

surface and its bottom surface. The measured variation is

slightly more as compared to the simulation results shown

in Fig. 5 which is attributed for radiation loss in the silicon

surface which was not considered in simulation. Since the

silicon chip was mounted on a PCB board by adhesive glue

and electrical connection to metal bond pads were estab-

lished for the temperature measurement the heater energy

was confined in these location resulting slight increase of

its temperature as observed in both the figures due to

thermal insulation characteristics of the bonded peripheral

boundaries. The measured absolute temperature and its

distribution for a boron diffused microheater in silicon

wafer matches closely with the simulation results discussed

in the previous section.

8 Conclusions

This paper presents the details of electro-thermal analysis

of microheater applicable for thruster operation. Initially

the total power required for vaporizing the liquid propellant

Fig. 12 Microheater maximum temperature versus electrical power

Fig. 13 IR images of a the silicon surface at microheater location

and b inner surface of silicon wafer located 200 lm below the topheater surface

Microsyst Technol

123

was analytically estimated considering various heat loss

and propellant mass flow rate. The geometrical dimensions

of the microheater was designed from the total power

requirement and its details electro-thermal analysis under

steady state and transient conditions were carried out to

obtain thermal characteristics. Boron diffused meanderline

resistor in silicon wafer can generate uniform temperature

distribution over the heater surface area with good heat

confinement. A supply voltage of 45 V is required to

achieve 410 K chamber temperature with 2–3 oC variation

between heater surface and chamber surface. Transient

analysis shows 2–3 s time requirement to achieve steady

state temperature under different bias supply. The boron

diffused microheater on 200 lm thick silicon diaphragm

was realized by microfabrication process. A 820 X resistor

can generate temperature up to 460 K for applied power

3.4 W. The IR imaging of the heater surface confirms

uniform distribution of temperature at 405 K with 10 K

variation between its two surfaces separated by 200 lm

thickness. The measured temperature vs electrical power

and the transient analysis matches closely with simulated

results.

Acknowledgments The work presented here is supported by Indian

Space Research Organization, Govt. of India. The authors would like

to express their gratitude to Professor S. K. Lahiri for his valuable

suggestions. The authors acknowledge the staff members of the

MEMS laboratory, IIT Kharagpur, for their help at various stages in

realization of the microthruster.

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