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Short Communication

Material selection for electrostatic microactuators using Ashby approach

Ojasvita Parate, Navneet Gupta ⇑

Electrical and Electronics Engineering Group, Birla Institute of Technology and Science, Pilani, Rajasthan, India

a r t i c l e i n f o

Article history:

Received 7 May 2010

Accepted 8 September 2010

Available online 21 September 2010

a b s t r a c t

Due to variety of materials available to any designer for a particular application, there is a need for a

proper technique to select. This paper focuses on the optimum selection of materials for electrostatic mic-

roactuators using Ashby approach. In this work, performance indices and material indices have been

developed for electrostatic actuators and thereafter material selection chart is plotted. The selection chart

shows that for high actuation voltage and high actuation force, diamond is the best possible candidate

followed by silicon carbide and silicon nitride. On the other hand, if high speed electrostatic actuator

is desired, then aluminum is the best possible candidate followed by nickel and copper.

Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Electrostatic actuation is the most widely used driving force in

the design of radio frequency microelectromechanical systems

(RF-MEMS) like microresonators, microswitches, micromirrors,tunable capacitors, accelerometers, etc. [1–4]. Almost every kind of

microactuator hasone or moreelectrostaticactuation based version.

Electrostatic actuator uses electrical energy to produce motion

(actuation). An electric charge creates an electric field around it,

which applies a force to the charged particle and this produces

motion. This is the basic principle behind electrostatic actuation.

Material selection is a critical step in the design of any engineer-

ing product. The set of materials available to any microsystem de-

signer is continuously increasing. Techniques now exist to

introduce and integrate a large number of metals, alloys, ceramics,

glasses, polymers, and elastomers into microsystems, motivating

the need for a rational approach for materials selection in micro-

systems design. The selection of materials for micromechanical

system is complicated by the highly integrated multifunctional

roles of the components. The conventional set of MEMS materials

like silicon compounds, metals and alloys, ceramics/glasses, poly-

mers and composites [5,6] although compatible with the tradi-

tional micro machining techniques, are not an optimal choice for

the maximum performance of the devices. The growing interest

in developing thin films of arbitrary materials on various substrate

presents an opportunity to improve the performance of MEMS de-

vice by optimal material selection. Hence, identifying and ranking

promising candidate materials give the best performance for actu-

ation, which is required as driving force in various MEMS devices.

As MEMS technology is evolving, new techniques for optimum

material selection techniques like knowledge based system (KBS)

[7] and decision making approach [8,9] can be thought. However

these techniques of material selections are limited to bulk design-

ing only. For MEMS based design the Ashby approach is widely ac-

cepted [5,6]. This paper present a detailed analysis of materialselection for the electrostatic microactuators based on the electro-

static actuation model compatible with Ashby approach and also

assesses the influence of various parameters on the achievable per-

formance of the device.

This paper is organized as follows; Section 2 presents a brief

description about the material and their properties, Section 3

explains the Ashby Approach, Section 4 gives a brief explanation

of electrostatic actuators, Section 5 include application of Ashby

approach for material selection in electrostatic microactuators.

Section 6 explains the discussion and finally section 7 gives the

conclusion of the study.

2. Materials and properties for MEMS devices

Many processing technologies exist today that have made it

possible to give materials shape and integrate a large number of

engineering materials into MEMS elements. These materials are

traditionally grouped under four classes: metals and alloys, glasses

and ceramics, polymers and elastomers, and composites. The prop-

erties of materials commonly studied while designing are Young’s

Modulus (Y ), Poisson’s ratio (m), fracture strength (rF ), yield

strength, fracture toughness, coefficient of thermal expansion

and residual stress (rR) [10]. Using Ashby approach, the designers

consider all the materials and study their properties to optimize

the design performance and reliability. Certain other properties

like electrical resistivity and conductivity are also considered while

dealing with the electrical aspects.

In comparison to the bulk properties, the properties of micro-

scale structures can differ in accordance to their length and

0261-3069/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.matdes.2010.09.012

⇑ Corresponding author. Tel.: +91 9772976336; fax: +91 1596244183.

E-mail addresses: [email protected] (O. Parate), [email protected] (N. Gupta).

Materials and Design 32 (2011) 1577–1581

Contents lists available at ScienceDirect

Materials and Design

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / m a t d e s





































































































































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processing techniques. However it is possible to relate between the

properties of bulk and micro structures. Sharpe [11] has tabulated

initial design values based on an extensive survey of such measure-

ments whose values are listed in Table 1 along with the nominal

bulk values tabulated by Ashby and Jones [12]. For initial stages

of microelectromechanical design, bulk values of these propertiescan be used. Based on this, Table 2 summarizes the initial design

values for various material properties.

3. Material selection – the Ashby method

The Ashby approach is design-led. It starts by asking ‘What is

the function of the component in the design?’, ‘What objectives

need to be optimized?’, and ‘What constraints must be satisfied?’

The advantage of this approach is that it is systematic and unbiased

as it focuses on the product objectives. Once the need of the appli-

cation is decided, the performance indices are discovered, all the

materials are considered and their material properties are studied

[13,14]. After that material selection charts are plotted and ana-

lyzed. The materials that meet the need are then taken into consid-eration and thus subset of the originally considered materials is

obtained.

The steps involved in the material selection using Ashby ap-

proach are illustrated in Fig. 1.

In the Ashby approach to material selection, a function is sought

to describe the performance ( p) of the element under consider-

ation. In general, this function has the form

p ¼ f fF ;G;M g ð1Þwhere F , G and M express the functional requirements, geometric

parameters and material indices respectively [5,15].

In many cases the variables in Eq. (1) can be separated to give

p ¼ f 1fF g f 2fGg f 3fM g ð2ÞEq. (2) permits great simplification. For all F and G, the perfor-

mance can be optimized by optimizing the appropriate material

indices. This optimization can conveniently be performed using

graphs with axes corresponding to different material properties

or material indices.

4. Electrostatic microactuator

The driving force of an electrostatic microactuator includes

electrostatic actuation system which can be of three types namely;

straight actuation; comb-drives actuation and microresonators. In

straight drive actuation the exact movement of the mobile parts

is ruled by the electric field path and the mechanical constrains

of the structure while in comb-drive actuation, the force is equally

and symmetrically applied on both the sides of the beams and the

mobile parts move along the beam direction. It is the lateral trans-

lation of the mobile parts. On the other hand microresonators are

structures that vibrate. In this work straight drive actuation is

considered.

Electrostatic force depends largely on the size of the structures

and the distance between electrodes. Electrostatic effect decreases

with the square of the distance between the two charged bodies.

An important parameter in the electrostatic actuation is the actu-

ation voltage which is often quite high ranging between ten to

hundreds of volt. High voltages are easy to be handled on a large

device, but not on a very compact integrated system. If the actua-

tion voltage becomes too high, the material used for the applica-

tion can get heated up and exhibit the temperature dependent

behavior and it can even lead to deformation of the substrate.

Table 1

Comparison of bulk and microscale properties.

Materials Y bulk (GPa) Ref. [9] Y l (Gpa) Ref. [8] rF , bulk (MPa) Ref. [9] rF ,l (MPa) Ref. [8]

Aluminum 69 70 200 150

Copper 124 120 400 350

Gold 82 70 220 300

Nickel 214 180 400 500

Ni–Fe alloy 130–234 120 400–2000 1600

Diamond-like carbon 700–1000 800 8000–10,000 8000

Poly Si 130–180 160 2000–4000 1200–3000

Single crystal Si 130–180 125–180 2000–4000 >1000SiC 430–445 400 4000–10,000 –

Silicon nitride 280–310 250 5000–8000 6000

Silicon oxide 50–80 70 800–1100 1000

Table 2

Recommended initial design values of material properties.

Property Recommendation

Density, q (kg/m3) ql = qbulk (approx)

Young’s Modulus, Y (GPa) 0.8 E bulk 6 E l 6 E bulk

Poisson’s ratio, m (–) 0.25Fracture strength, rF (MPa) rF ,l = rF ,bulk (approx)

Linear expansion coefficient, a (KÀ1) al = abulk (approx)

Specific heat, C p (J kgÀ1 KÀ1) C p,l = C p,bulk

Intrinsic loss coefficient, gi 10À2 < gi (polymers)

10À5 < gi (metals)

10À7 < gi < 10À4 (ceramics)

Residual stress, rR (GPa) À1 GPa < rR < 1 GPa

l indicates microscales.

All materials taken into

consideration (low precision)

According to the application

requirement, screen the materials

List the screened materials as per the

objectives and seek details based on

the analysis

Final material selection

(high precision)

Fig. 1. Steps involved in materials selection.

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Another factor to be considered is the nature of the material be-

tween capacitive plates: water, for example, is conductive at low

frequencies, so electrostatic actuation cannot be used in these con-

ditions. Void and neutral gases are the best environments sincethese gases do not conduct.

Fig. 2 illustrates the schematic of an electrostatic actuator that

could be used for successful design of RF MEMS devices. In this

one of the plate of the capacitor is fixed, other plate is attached

to a spring, having the spring constant k that is suspended from

a fixed support. However this fixed support can be a beam for in-

stance as shown in Fig. 3. The figure shows the representation of

an electrostatic actuator wherein the actuation voltage developed

due to electric charge provides displacement to the movable plate

of the capacitor such that the movable plate attains a stable posi-

tion and hence motion is achieved.

5. Ashby approach to electrostatic actuators

5.1. Performance indices

5.1.1. Actuation voltage

It is the voltage that is established between the two plates of the

capacitor. It is this voltage that leads to motion of the movable

plate as demonstrated in Fig. 1. If d1 is the final position attained

by the movable plate of the capacitor, then the spring force is given

by

F m ¼ kðd À d1Þ ð3Þ

Due to application of voltage between the electrodes the elec-trostatic force developed between the plates is given by

Fe ¼ E ed

¼ 1

2dCV 2

where C ¼ 2 Ad

is the capacity of capacitor. Hence,

Fe ¼ 2 AV 2

2d2

ð4Þ

To find the stable position of the movable plate at any instant,

we can equate the spring force with the electrostatic force to find

the balanced position of the plate i.e.,

F m ¼ F e

2 AV 2

2d2

¼ kðd À d1Þ

V ¼ d

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2kðd À d1Þ

2 A

r ð5Þ

Fig. 2. Schematic of an electrostatic actuator. (a) Spring is attached to the fixed

support; (b) spring is attached to the fixed beam.

Fig. 3. Actuation voltage ( ffiffiffiffi Y

p ) vs. speed

ffiffi ffi Y q

q for different class of materials.

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The above relation implies that the actuation voltage (V ) is di-

rectly proportional to the square root of the spring constant (k)

which means that if we use a material with a higher spring con-

stant, and then a higher actuation voltage will be generated which

is not desired. On the other hand high value of k is desired as a stiff

structure lead to a mechanically more robust device.

5.1.2. Speed of actuation (s)

This performance index relates the motion of movable plate of

the capacitor to the motion of spring. In other words, it is a mea-

sure of the speed of the spring to undergo expansion or compres-

sion. Speed of actuation (s) is directly proportional to the natural

frequency of vibration of the spring ( f ) which in turns is related

to the spring constant by following relation

f ¼ 1

2p

ffiffiffiffiffik

m

r ð6Þ

The above relation implies that the speed of actuation is directly

proportional to ffiffiffi k

p which means that if we want an electrostatic

microactuator with fast response then we need to select a materialwith higher stiffness constant.

In most of the applications, low actuation voltage and higher

speed is desired but the above two performance metrics indicate

that both can not be attained simultaneously and hence there is

a trade-off. The designer needs to decide which out of both is more

important according to the application.

In addition to the above performance metrics, there are few

other performance metrics like mechanical energy which depends

on spring stiffness as follows,

E ðmechanical energy storedÞ ¼ 1

2kx

2 ð7Þ

Electrical resistivity is purely application based. If we require

heat production in the application, then we need a material with

higher resistivity.

5.2. Material indices

(i) Spring constant (k): It is a measure of stiffness of the spring. It

is given by the ratio of the force applied (F) on the spring to

the displacement undergone ( x).

k ¼ F

xð8Þ

Young Modulus ðY Þ ¼ Stress

Strain

Now as stress is directly proportional to the force applied (F )

and strain is directly proportional to the displacement ( x),

then it implies that stiffness (k) Young’s /Modulus (Y )(Material index M1)

(ii) Actuation voltage (V): As we have already shown, actuation

voltage is directly proportional to the square root of stiffness

of the spring. But spring stiffness is directly proportional to

the Young’s Modulus (Y ) as above.

Hence; actuation voltage / ffiffiffiffiY

p ðMaterial Index M2Þ

(iii) Frequency of vibration for the moving plate or equivalently a

beam:

As; f ¼ 1

2p

ffiffiffiffiffik

m

r ð9Þ

But k is directly proportional to Young’s Modulus (Y ) and m is

directly proportional to density of the material (q). Hence

f / ffiffiffiffiY

q

s ðMaterial Index M3Þ

(iv) Energy: It is the mechanical energy stored in the spring due

to the electrostatic actuation.

E ¼ 1

2kx

2

Since stiffness is directly proportional to the Young’s Modu-

lus, we can conclude that

E / Young’s Modulus ðY Þ ðMaterial Index M4Þ(v) Actuation force: It is the same as mechanical force exerted on

the spring or the electrostatic force by the capacitor i.e.

F m = kx. Actuation force is directly proportional to stiffness

and stiffness is proportional to Young’s Modulus (Y ). Hence,

Actuation force / Young’s Modulus ðY ÞÂ ðMaterial Index M5Þ

(vi) Stroke/displacement: The maximum displacement of the

beam (d) is restricted by the fracture strength (rF

) of the

material.

Fracture strength is the normal stress at the beginning of

fracture.

Youngs Modulus ðY Þ ¼ Stress

Strain¼ rL

dð10Þ

At the time of fracture, r = failure strength (rF ), d = dmax

dmax / rF

Y ðMaterial Index M6Þ

dmax / L

This relation shows that dmax also depends on temperature be-cause length of a material varies with temperature.

dmax / Temperature ðMaterial Index M7Þ

6. Discussion

The optimum performance of a material varies with applica-

tion. For example, low actuation voltage is desired in applications

involving switches and displays whereas high actuation voltage is

desired in high force applications. Some performance metrics

may have conflicting demands. For example actuation voltage

and speed both directly depend on square root of Young’s Mod-

ulus. If low actuation voltage and high speed is desired, we haveto make an optimum choice according to the need. The selection

charts are used to compare and select the materials. These charts

are not only used for identifying appropriate candidates for

materials but also to identify optimal trade-offs when we have

conflicting metrics.

The Fig. 3 shows a plot of actuation voltage ( ffiffiffiffi Y

p ) vs. speed (

ffiffiffi Y q

q )

for different types of materials. It is known that high speed devices

need high actuation voltage. It can be concluded from the graph

that for high actuation, diamond is the best possible candidate fol-

lowed by silicon carbide and silicon nitride. While for high speed

actuation, aluminum is the best possible candidate followed by

nickel and copper.

Fig. 4 shows a plot of actuation force (proportional to Y ) vs.

displacement (proportional to ffiffiffiffi rF

Y

q ) for different types of materials

and it shows that for high actuation force, diamond is the best pos-

sible candidate out of all the materials taken into consideration.

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7. Conclusion

Material selection for MEMS design of electrostatic microactua-

tor following the Ashby approach of material indices has been dis-

cussed in this paper. As the material set is rapidly expanding, new

co-ordinates can be added to the existing material selection chart

and then optimum material can be chosen based on the need. In

this work we have developed the performance and material indicesfor electrostatic microactuators. Using material selection chart it

was observed that for high actuation voltage and high actuation

force, diamond is the best possible candidate followed by silicon

carbide and silicon nitride. For high speed electrostatic microactu-

ators, aluminum is the best possible candidate followed by nickel

and copper.

References

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[2] Hassanzadeh A. Design consideration for basic MEMS electrostatic actuators.In: 41st Southeastern symp on sys theory, Tullahoma (USA); 15–17 March2009.

[3] Chu CGH et al. A low actuation voltage electrostatic actuator for RF MEMSswitch applications. J Micromech Microeng 2007;17:1649–56.

[4] Tilmans HAC, Raedt WD, Beyne E. MEMS for wireless communications: fromRF-MEMS components to RF-MEMS-SiP. J Micromech Microeng 2003;13:S139–63.

[5] Srikar VT, Spearing SM. Material selection in micromechanical design: anapplication of Ashby approach. J MEMS 2003;12:3–19.

[6] Reddy GP, Gupta N. Material Selection for microelectronic heat sinks: Anapplication of the Ashby approach. Mater Des 2010;31:113–7.

[7] Sapuan SM. A knowledge-based system for materials selection in mechanical

engineering design. Mater Des 2001;22:687–95.[8] Rao RV, Patel BK. A subjective and objective integrated multiple attribute

decision making method for material selection. Mater Des 2010;31:4738–47.[9] Rao RV. A decision making methodology for material selection using an

improved compromise ranking method. Mater Des 2008;29:1949–54.[10] Senturia SD. Microsystem design. 1st ed. Norwell (MA): Kluwer Academic

Publishers; 2001.[11] Sharpe WN. Mechanical properties of MEMS materials. In: Gad-el-Hak M,

editor. The MEMS handbook. Boca Raton (FL): CRC Press; 2001. p. 3.1–3.25.[12] Ashby MF, Jones DRH. Engineering materials: an introduction to their

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Fig. 4. Actuation force (proportional to Y) vs. displacement (proportional to ffiffiffiffi rF Y

q ) for different class of materials.

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