Investigation of the Onset Voltage for the Design of a ... - IEEE Xplore

66 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 11, NO. 1, FEBRUARY 2006 

Investigation of the Onset Voltage for the Design of a 

Microfabricated Colloid Thruster 

Jijun Xiong, Dong Sun, Member, IEEE, Zhaoying Zhou, Senior Member, IEEE, and Wendong Zhang, Member, IEEE 

Abstract—Onset voltage plays a crucial role in the design of a 

microcolloid thruster. This paper presents a methodology to estimate 

the onset voltage for the design of a new microfabricated 

colloid thruster. The basic idea of this method is to simplify the 

source emitter and the extractor of the microthruster as two hyperboloids 

of two sheets of a set of equal potential surfaces. The 

maximum electric field between electrodes is modeled using the 

Lamé method, on which a method to estimate the onset voltage is 

developed. To avoid the aberration of electric field caused by protuberances 

on the surface of the source emitter, the height of the 

source emitter must be much greater than that of protuberance. 

Experiments conducted on the homemade microcolloid thrusters, 

designed based on the proposed onset voltage estimation, verify the 

correctness of the approach. 

Index Terms—Colloid thruster, electric field, microfabrication, 

onset voltage. 

I. INTRODUCTION 

COLLOID thruster was firstly proposed and studied in 

1960s [1], [2], with a working principle of electrospraying 

[3]–[5]. A colloid thruster consists of a source emitter and an 

extractor, between which a high voltage is applied (Fig. 1). The 

minimum applied voltage to start the electrospraying is called 

the onset voltage of a colloid thruster. Due to high efficiency 

and high specific impulse ability, the colloid thruster appears to 

be an alternative to the conventional ion engine [2]. However, 

the thrust produced by the colloid thruster was not high enough 

to meet the needs of propulsions for spacecrafts in the past. Another 

drawback of the colloid thruster is that the onset voltage, 

with a typical value of 10 kV, was so high that serious packaging 

problems might be caused [2], [6]. As a result, the application 

of colloid thruster has not obtained considerable interest in the 

past. 

Motivated by micropropulsion of microspacecrafts, the microcolloid 

thruster has attracted increasingly more attention in 

recent years, for reasons of lower cost, smaller risk in launch, 

and ability of formation flight of the microspacecraft [7]–[11]. A 

significant requirement for the micropulsion system lies in the 

Manuscript received March 24, 2003; revised February 10, 2005. 

Recommended by Technical Editor K. Ohnishi. Recommended by Technical 

Editor K. Ohnishi. This work was supported in part by a grant from the Research 

Grants Council of the Hong Kong Special Administrative Region, Hong 

Kong, China (Reference CityU 1124/03E). 

J. Xiong and W. Zhang are with the Key Laboratory of the State Education 

Ministry on Instrumentation Science and Dynamic Measurement, North University 

of China, Shan’xi, China (e-mail: xiongjj@263.net; wdzhang@nuc.edu.cn). 

D. Sun is with the Department of Manufacturing Engineering and Engineering 

Management, City University of Hong Kong, Kowloon, Hong Kong (e-mail: 

medsun@cityu.edu.hk). 

Z. Zhou is with the Department of Precision Instruments and Mechanology, 

Tsinghua University, Beijing, China (e-mail: zhouzy@mail.tsinghua.edu.cn). 

Digital Object Identifier 10.1109/TMECH.2005.859843 

Fig. 1. 

Basic principle of colloid thruster. 

attitude control [12]–[15], in which the produced thrust must 

be so small that it is in the order of micrometer-Newton, and 

the specific impulse should be in the order of hundreds of seconds 

[7], [12]. The micro colloid thruster can meet these needs. 

Because of the modern microfabrication technique, the onset 

voltage required by a microcolloid thruster can now be reduced 

significantly. Other advantages of the microcolloid thruster include 

high efficiency of energy conversion and control flexibility. 

As a result, the microcolloid propulsion system has been 

regarded as the most suitable system among all microelectric 

primary propulsion systems for microspacecraft propulsion applications 

[9]. 

Further research on the microcolloid thruster was motivated 

by advances in electrospray science, which has been driven by 

mass spectrometry in recent years [6], [16]–[18]. Taylor [19] 

predicted that the semiangle of the cone was 49.3 ◦ . Mora 

and Loscertales [20] proposed the spraying current law of the 

Taylor cone, which was one of the theoretical foundations for 

designing colloid thrusters. Jaworek and Krupa [18] clarified 

the electrospray into dripping, spindle, oscillating, jet, precession, 

and cone-jet modes. Hartman et al. [21], [22] proposed a 

global hydrodynamic model to predict the behavior of electrospray. 

Although progress has been made, detailed mechanics of 

electrospray and the mechanics of the colloid thruster are still 

far from being well understood. 

Microelectromechanical systems (MEMS) technology makes 

the micromation and performance improvement of the colloid 

thruster possible [23], [24]. An array with thousands of emitters 

can now be fabricated in a silicon wafer by a microfabrication 

process [25], [26]. The size of the emitter can be in the order 

of micrometer. The extremely small size of the microcolloid 

thruster is also helpful in decreasing the onset voltage, which 

is verified in Section II. Both micromation and low operating 

voltage are urgently demanded by the microcolloid propulsion 

system [7]. A colloid thruster prototype with 100 nozzles was developed 

in [4] and [10]. This small colloid thruster, however, was 

1083-4435/$20.00 © 2006 IEEE

XIONG et al.: INVESTIGATION OF THE ONSET VOLTAGE FOR THE DESIGN OF A MICROFABRICATED COLLOID THRUSTER 67 

Fig. 2. 

Typical shape of conventional colloid thrusters. 

Fig. 4. 

Electrostatic field of electrodes of microthruster. 

microthruster are regarded as two hyperboloids of two sheets 

of a set of equal potential surfaces. The maximum electric field 

between electrodes is derived by Lamé method, based on which 

a method to estimate the onset voltage is proposed. The condition 

to eliminate the influence of protuberances produced in microfabrication 

is also discussed in this paper. Four microthrusters 

are designed according to the onset voltage estimation. Testing 

results of these thrusters show that the proposed onset voltage 

estimation works effectively. 

Fig. 3. 

Surface of silicon after ICP etching. 

not based on the microfabrication. Further work on microcolloid 

thruster array was performed by Fernando. 1 Paine [27] designed 

another addressable microcolloid thruster array, in which a minimum 

thrust of 0.1 µmN was expected. 

It is noted that the fabrication process of a microcolloid 

thruster is largely different than that of a conventional thruster. 

To obtain the high electric field, the source emitter of the conventional 

colloid thruster usually employs a tapered tip [1], [2], 

as shown in Fig. 2. However, it is difficult to fabricate the tapered 

source emitter in the microfabrication process. A typical shape 

of the microfabricated source emitter looks like a hollowed 

cylinder with dimensions in the order of tens of micrometer, 

formed by deep dry etching on the silicon such as inductively 

coupled plasma (ICP) or deep reactive ion etching. Due to the 

long-time deep dry etching, many protuberances exist on the 

surface of silicon. Fig. 3 shows the surface of silicon at 40 min 

after ICP etching, from which 2-µm-high protuberances can be 

found. These protuberances may result in a serious coarseness 

problem. 

To solve problems of the electrode shape and coarseness, we 

need to reconsider the electric field distribution between electrodes 

and the onset voltage of the microcolloid thruster. This 

paper presents a new method for estimating the onset voltage 

through analyzing the surface tension stress and the force of 

the electric field at the tip of the source emitter of the microcolloid 

thruster. The source emitter and the extractor of the 

1 Online. Available: http://web.mit.edu/aeroastro/www/labs/SPL/Research/ 

colloid.htm 

II. ONSET VOLTAGE ESTIMATION 

The onset voltage is estimated based on the balance between 

the surface tension and the force of the electrostatic field on the 

surface of droplet at the tip of source emitter of a microcolloid 

thruster. In this section, the electrostatic field between the source 

emitter and the extractor of the microcolloid thruster, as well as 

an estimation for the onset voltage estimation, are discussed. 

A. Electrostatic Field Distribution 

The potential between electrodes of the microcolloid thruster, 

denoted by V, can be described in a cylindrical coordinate frame 

[30],i.e., 

1 

r 

∂ 

∂r 

( 

r ∂V ) 

+ 1 ∂ 2 V 

∂r r 2 ∂θ 2 

+ ∂2 V 

=0 (1) 

∂z2 where r, θ, and z are three basic coordinates of the cylindrical 

coordinate system. The boundary conditions of (1) are 

V = V 0 (r = r 1 ,z =0) 

V =0 (R 1 ≤ r ≤ R 2 ,z = d + r) 

where r 1 is the inner radius of the source emitter, R 1 is the outer 

radius of the extractor, R 2 is the inner radius of the extractor, 

d is the distance between two electrodes, and V 0 is the applied 

voltage between two electrodes. Fig. 4 illustrates the electrostatic 

field of electrodes of the microthruster, where the origin 

of the inertia coordinate frame o-xyz is located in the center 

top of the cylinder. The droplet is supposed to be a cone with 

height of 2r 1 . To enhance electric field in the z direction, d ≫ r 1 

in the design.


The solution of (1) is [30] 

∞∑ 

V = 

i=0 

A i J 0 

( 

x i 

r 

r 1 

) 

sh 

( 

x i 

z 

r 1 

) 

where J 0 (·) is the zero-order Bessel function, and coefficients 

A i can be determined by the boundary conditions. Note that the 

coefficients A i are hard to determine exactly. 

Equation (2) is too complicated to be used for estimation of 

the electric field distribution between electrodes. An approximate 

solution of (1) is developed here, based on the Lamé 

method .[29]–[31] In the inertia coordinate frame o-xyz, the following 

equation represents a set of hyperboloids of two sheets: 

x 2 

λ + y2 

λ − 

z2 

c 2 = −1 (3) 

− λ 

where c denotes the distance between the focal point and the 

origin, λ is a variable, and λ


where δ denotes the surface tension coefficient of the liquid 

cone. The electrostatic stress is 

P E = 1 2 ε 0E 2 (15) 

where ε 0 is the permittivity of vacuum. Suppose P E = P δ ,we 

then have 

√ 

δ 

E =2 

r 1 ε 0 tan(a) . (16) 

Substituting (16) into (11) yields the onset voltage 

√ 

( 

1 √ 

V 0 = 

δr1 ln 2+2 d ε 0 tan(a) 

r 1 

√ ( 

− 2 d +1 

)(3+2 d ) ) 

r 1 r 1 

( 

=0.312 × 10 6√ δr 1 ln 2+2 d r 1 

√ ( 

− 2 d )( 

+1 3+2 d ) ) . (17) 

r 1 r 1 

Fig. 6. 

Meshing model of electrodes of microcolloid thruster. 

It can be seen from (17) that the onset voltage V 0 greatly 

depends on the design of the radius r 1 , via a relationship of √ r 1 

in the expression of V 0 . [The variation of r 1 in ln(·) has little 

influence to V 0 .] A small value of r 1 results in a small value of 

V 0 directly. In conventional colloid thrusters, the radius r 1 of 

the source emitter is in the scale of millimeter, whereas in the 

proposed MEMS-based thruster, the radius r 1 is in the scale of 

micrometer. This is the main reason why the onset voltage of 

the proposed microthruster can be reduced dramatically. 

III. SIMULATIONS AND DISCUSSIONS 

A. Simulations of Electric Field 

To verify the electric field in (11), a comparison between 

results obtained by (11) and results obtained by the finite element 

method was performed in simulations. The meshing model used 

by the finite element method is shown in Fig. 6. The units of all 

length variables (e.g., d and r 1 ) are micrometers. The electric 

field between electrodes in the z direction has the maximum 

value at the tip of the source emitter (as seen in Fig. 5), which 

has the great influence to the onset voltage. Fig. 7 illustrates 

the numerical solution of the electric field by the finite element 

method, where R 1 =30µm, R 2 =50µm, R =15µm, d = 

420 µm, h =80µm, V = 2000 V, and h denotes the height of 

the source emitter (see more details in Fig. 12). It is seen that the 

maximum value of the electric field between electrodes around 

the tip of the source emitter ranges between 55.2 V/µm and 

55.7 V/µm. By (11), the maximum electric field was estimated 

to be 57.26 V/µm. The results obtained by the two methods are 

quite similar. 

The same analysis was further performed when electrodes 

have different sizes. Results are listed in Table I, where Ea denotes 

the value of the maximum electric field calculated by the 

Fig. 7. 

Results obtained by finite element analysis. 

TABLE I 

MAXIMUM ELECTRIC FIELD BETWEEN ELECTRODES 

finite element method, and Es denotes the value of the maximum 

electric field calculated by (11). It is seen that all values of Es 

are close to those of Ea, which indicates that the proposed simple 

electric field estimation is comparable to the finite element 

method. Note that the extractor is simplified as a plane when 

using (11), which enhances the electrical field of the source 

emitter. In the meshing model used by the finite element analysis, 

the extractor is a hollowed cylinder with the inner and outer 

radius. This is why Es is slightly larger than Ea in Table I. 

B. Influence of Aberration of Electric Field 

As mentioned in Section I and illustrated in Fig. 3, deep dry 

etch results in protuberances on the silicon surface. Heights of


TABLE II 

ESTIMATED ONSET VOLTAGES 

Fig. 8. 

Model of electrodes with protuberances. 

To eliminate the influence of the aberration of electric field, 

the height of the source emitter should be more than 75 µm. 

Therefore, we conclude that when (11) and (17) are used to 

design the microcolloid thruster, it is necessary to ensure the 

height of the source emitter is great enough compared with that 

of protuberances. Otherwise, the aberration of the electric field 

caused by the protuberances has to be taken into account. Further 

analysis has been given when H P =1µm, R P =0.5 µm, and 

H P =0.5 µm, and R P =0.25 µm, and it was found that the 

values of the electric field stabilize around 55.5 V/µm at smaller 

values of h (i.e., 60 and 48 µm, respectively). It will be helpful 

to reduce the influence of the aberration of electric field induced 

by protuberances, if microfabrication is improved and the height 

of protuberance is decreased. 

Fig. 9. 

Electric field versus height of source emitter. 

protuberances are not identical and increase as the ICP etching 

time increases. Protuberances affect the distribution of the 

electric field between electrodes, but this influence can be eliminated 

if the source emitter of the microcolloid thruster is high 

enough. In the following, a finite element analysis model of the 

microthruster with protuberances is developed for investigation 

of the relationship between the aberration of the electric field 

caused by protuberances and the height of the source emitter. 

Fig. 8 illustrates the finite element model, in which the height 

of the protuberance, denoted by H P ,is2µm, and the radius R P 

is 1 µm. The other parameters are R 1 =30µm, R 2 =50µm, 

r 1 =15µm, and d = 420 µm. For simplicity, only eight protuberances 

were considered in the model. These protuberances 

are identical in height and located in the axial symmetry 

positions. 

The relationship between the electrical field and the height 

of the source emitter is shown in Fig. 9. It can be seen that 

the maximum value of the electrical field between electrodes 

increases as the height of the source emitter increases. When 

the height of the source emitter is more than 75 µm, the value 

of the electric field stabilizes around 55.5 V/µm. In the case of 

H P =2µm and R P =1µm, protuberances weaken the electric 

field obviously when the source emitter is shorter than 70 µm. 

C. Onset Voltage Estimation 

We now estimate the onset voltages of the microcolloid 

thrusters listed in Table I by (17). The onset voltage relates to the 

surface tension coefficient of the propellant. When formamide 

doped with 30% NaI in weight is used as the propellant, δ is 

about 0.058 N/m. Using the same parameters as in Table I, the 

onset voltages of the microthrusters were predicted and given 

in Table II, where the numbers 1–4 correspond to the numbers 

in Table I. The values of the onset voltage in Table II are significantly 

smaller than those of conventional colloid thrusters. 

The correctness of such estimation and the design followed is 

verified in the experiment in Section IV. 

IV. EXPERIMENTS 

To verify the correctness of (17), four microcolloid thrusters 

with the same parameters as given in Table I, were fabricated and 

used in the tests. The thrusters were fabricated by bulk silicon 

process. 

A. Fabrication 

The fabrication of the microthruster includes fabrication of 

the source emitter and the extractor, as shown in Figs. 10 and 11. 

The first step of the source emitter fabrication process was that 

50% KOH etched the silicon wafer to create a square pyramidal 

pit. The etching depth was about 280 µm. SiO 2 /Si 3 N 4 was used 

as the mask. Second, the source emitter with a cylinder shape 

was built by ICP. Patterned photoresist mask was used for the 

ICP to form a round pit with 60 µm in depth. The outer wall of 

the source emitter was formed by the other ICP with aluminium 

layer as the mask, where the depth was 80 µm. Finally, the inner 

wall of the source emitter was formed, where the depth was


Fig. 12. 

SEM photo of source emitter. 

Fig. 10. 

Fabrication process steps of source. 

Fig. 13. 

SEM photo of extractor. 

Fig. 11. 

Fabrication process steps of extractor. 

Fig. 14. 

Packaged microcolloid thruster. 

140 µm, which was enough to make ICP penetrate through the 

silicon wafer. 

The fabrication process of the extractor was relatively simple. 

As shown in Fig. 11, the first step was similar to that of the 

source emitter, except that the etching depth was 360 µm. The 

following step was to form the aluminium electrode, and then 

ICP was used to penetrate through the silicon wafer and form 

the exiting channel of the spraying droplet. 

Two scanning electron microscope (SEM) photos of a source 

emitter and an extractor are shown in Figs. 12 and 13, respectively. 

The height of the source emitter is about 80 µm. In 

Fig. 12, the protuberances are about 2 µm in height and 1 µmin 

width. There is a glass spacer in the middle of the source emitter 

and the extractor. Epoxy was used to bond the structure. Fig. 14 

illustrates the photo of a packaged microcolloid thruster.


Fig. 15. 

Block diagram of test system. 

Fig. 17. 

Original output of displacement sensor (U =0V). 

Fig. 18. 

Output of displacement sensor after filtering (U = 1400 V). 

Fig. 16. 

Photo of test facility. 

TABLE III 

ONSET VOLTAGES IN TESTS. 

B. Tests 

Fig. 15 illustrates a testing structure used to verify the developed 

thruster. A cantilever beam with a thruster onboard was 

used as a sensor. When the force produced by the thruster acts 

on the cantilever beam, the beam deflects. The deflection was 

measured by a current vortex displacement sensor, which could 

translate the displacement into an electrical signal with a sensitivity 

of 8 mV/µm. The electrical signal was recorded by an 

A/D converter. The sensing system was placed in a high vacuum 

box with 10 −5 torr air pressure. Fig. 16 illustrates a photo of the 

testing system. 

The output of the displacement sensor includes two parts: 

the displacement of the cantilever beam caused by the external 

force, and the vibration superposed on that displacement. 

Because the displacement is so small that is in the scale of 

micrometer, the effect of the vibration to the output must be 

considered. The wave profile of the free vibration is shown in 

Fig. 17, where the vibration amplitude is about several micrometers. 

Vibration analysis shows that the main components of 

the vibration signal have frequencies of 1.95 and 13.67 Hz, respectively. 

To obtain the exact value of the displacement, the 

output components with frequencies of 1.95 and 13.67 Hz were 

removed from the signal. After removing these two components 

from Fig. 17, the displacement sensor appeared an output of 

−3.12 V when the external force is zero. 

Experimental results show that the onset voltage of the first 

microthruster is about 1260 V. When the applied voltage increases 

from 0 to 1300 V, the cantilever beam remains balanced, 

as shown in Fig. 17. When the applied voltage reached 

1300 V, the beam began to deflect. Removing components with 

the first- and the second-order natural frequencies from the signal, 

the output of the displacement sensor is plotted in Fig. 18. 

Compared with the output of the displacement sensor with zero 

input, there is an offset of about 0.49 V, which implies that the 

electrospray begins. 

The tests were further performed on the remaining three microthrusters. 

All results are listed in Table III. It can be seen 

that the testing results in Table III basically agree with those 

predicted by (17) in Table II. The slight difference is explained 

as follows: 1) the size of the extractor is neglected when using 

(17); 2) the size of the designed thruster is slightly different


from that of the actual one; and 3) there is a “voltage loss” due 

to the interaction of the charged droplets [5]. 

It is also verified in the test that the onset voltage of the microcolloid 

thruster can be reduced dramatically compared with that 

of conventional colloid thrusters. In our test, the microcolloid 

thruster could work under 1300 V, whereas the working voltage 

of a conventional colloid thruster is usually at least 5000– 

10 000 V. The advantage of the low onset voltage required by 

our microcolloid thruster makes it easier to be integrated with 

the other colloid system components. 

V. CONCLUSION 

This paper presents a new method to analyze the electric field 

distribution between the source emitter and the extractor, and 

an estimation of the onset voltage of the microcolloid thruster. 

The basic idea is to regard two electrodes as two equal potential 

surfaces. To avoid the aberration of the electric field caused by 

protuberances on the surface of the source emitter, the height 

of the source emitter must be great enough compared with that 

of protuberances. Several microcolloid thrusters are designed 

and fabricated based on the proposed onset voltage estimation. 

Testing results show that the actual onset voltages of the newly 

designed thrusters match the estimated values. Meanwhile, it 

has been shown that the micromation of the colloid thruster 

helps decrease the operating voltage dramatically. 

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Jijun Xiong received the B.S. and M.S. degrees from 

the North China Institute of Technology in Shanxi, 

China, in 1993 and 1998, respectively, both in electrical 

engineering. He received the Ph.D. degree from 

Tsinghua University, Beijing, China, in 2003. 

From 2002 to 2003, he was a Research Assistant 

with the Department of Manufacturing Engineering 

and Engineering Management at the City University 

of Hong Kong, Kowloon, Hong Kong, China. He was 

an Associate Professor in the Department of Electrical 

Engineering of the North University of China. He 

is currently with the Key Laboratory of the State Education Ministry on Instrumentation 

Science and Dynamic Measurement, North University of China, 

Shan’xi, China. His recent research interests lie in the fields of measurement 

and MEMS. 

Dong Sun (S’95–M’00) received the B.Sc. and M.Sc. 

degrees from Tsinghua University, Beijing, China, in 

1990 and 1994, respectively, both in mechatronics. 

He received the Ph.D. degree in robotics and automation 

from the Chinese University of Hong Kong, 

Hong Kong, in 1997. 

He was a Postdoctoral Researcher with the University 

of Toronto and a Research and Development Engineer 

with Ontario Industry. Since 2000, he has been 

with the Department of Manufacturing Engineering 

and Engineering Management at the City University


of Hong Kong, Kowloon, Hong, Kong, China, where he is now an Associate 

Professor. He is also an Adjunct Professor at the University of Toronto. His 

research interests lie in robotics and automation, motion controls, and mechatronics. 

Dr. Sun is a Professional Engineer in the Province of Ontario, Canada. 

Since 2004, he has served as an Associate Editor for IEEE TRANSACTIONS ON 

ROBOTICS. 

He is an Editor of the International Journal of Micromechatronics and Sensors 

and Actuators A: Physical. He also serves as Vice President of the China 

Instrument Society. He has received 30 patents, three national awards, and ten 

Ministry Awards of Science and Technology Invention and Achievement. 

Zhaoying Zhou (SM’02) graduated from the Department 

of Precision Instruments of Tsinghua University, 

Beijing, China, in 1961. 

From 1979 to 1981, he was a Visiting Scientist 

at the Department of Automatic Control of Lund 

University, Lund, Sweden. He is currently a Professor 

in the Department of Precision Instruments 

and Mechanology and Chairman of the Academic 

Committee of the Micro/Nano Technology Research 

Center, Tsinghua University, Beijing, China. He has 

published more than 300 scientific and technical papers. 

His recent research interests lie in the fields of measurement, control, and 

micro/nano technology. 

Wendong Zhang (M’02) received the Ph.D. degree 

from Beijing Institute of Technology, Beijing, China, 

in 1995. 

From 1996 to 1998, he was a Postdoctoral Researcher 

at Tsinghua University, Beijing, China. 

From 1998 to 2001, he conducted his research at 

the University of California at Berkeley and at the 

National Measurement Laboratory, Japan. He is currently 

the President of North University of China, 

Shan’xi, China, where he is also with the Key Laboratory 

of the State Education Ministry on Instrumentation 

Science and Dynamic Measurement. His recent research interests lie in 

the fields of instrumentation science and MEMS.

Investigation of the Onset Voltage for the Design of a ... - IEEE Xplore

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