a comparative study on material selection for micro-electromechanical systems

Materials and Design 41 (2012) 177–181

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Materials and Design

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Technical Report

A comparative study on material selection for micro-electromechanical systems

Aditya Chauhan b, Rahul Vaish a,⇑a School of Engineering, Indian Institute of Technology Mandi, Mandi 175 001, Indiab Galgotias College of Engineering and Technology, Greater Noida 201 306, India

a r t i c l e i n f o

Article history:Received 17 February 2012Accepted 20 April 2012Available online 8 May 2012

0261-3069/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.matdes.2012.04.037

⇑ Corresponding author. Tel.: +91 1905 237908; faxE-mail address: rahul@iitmandi.ac.in (R. Vaish).

a b s t r a c t

Material selection is an important task because large numbers of competitive materials are available forvarious technological applications. Numerous material selection techniques are reported whereas most ofthe techniques are knowledge based and require performance indices for material selection. In this con-text, Ashby approach is one of the efficient methods which rely on performance indices of materials inspecific application. However Multiple attribute decision making (MADM) approaches do not requireexact physical relation for material selection. We have investigated micro-electromechanical system’s(MEMS) material selection using MADM approaches and compared their results with that of Ashbyapproach. Almost similar materials ranking indicates that MADM approaches are also efficient and easeto apply without any prior mathematical calculation for materials properties-application relation.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Last decade has witnessed large scale commercialisation of var-ious new and innovative technologies. Micro-electro-mechanicalsystems (MEMSs) are one of the key areas of research and techno-logical application which has been speedily expanded in last dec-ade. MEMS refer to microscopic devices that have a characteristiclength of less than 1 mm but more than 100 nm and combine elec-trical and mechanical components. MEMS research will be contin-ued in the near future due to the highly untapped potential thatstill exists in this field [1]. MEMS technologies have been success-fully transformed into the variety of applications including sensors,actuators, power generating devices and bio-medical services.However, one of the main hurdles that lie in the path of furtherdevelopment of MEMS technology is the fact that the materialsare very limited as the set of requirements are very narrow. Thereare three basic requirements that the material must possess to beable to be used in MEMS, these are: (a) compatibility with semi-conductor fabrication technology, (b) desirable electromechanicalproperties and (c) low values of residual stresses. For this reasonthe early attempts at MEMS technology were highly restricted tothe silicon family. However, with the development of advancedfabrication techniques such as LIGA, stereo lithography and lasermicromachining the number of materials that can be used forMEMS devices have grown considerably and now include fourmain categories of materials which are: (a) metals such as nickeland aluminium, (b) non-metals such as silicon and germanium,

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(c) polymers such as polyimmide and (d) ceramics such as carbidesand diamond.

This growing set of materials has further increased the scope ofMEMS applications. However, now the designers are faced with theproblem of selecting the optimum material for specific MEMSapplication. To overcome such a problem various multiple criteriadecision making (MCDM) and optimisation techniques are re-ported and found to be efficient in various decision making appli-cations [2,3]. The Ashby [4] approach is one of the most populartechniques used for material selection problems. MEMS materialsselection has been studied using Ashby approach which is basedon multi-objective decision making (MODM) approach [5–9]. Thismethod is efficient in screening compatible materials from largedatabase of materials. However, MADM techniques are not em-ployed in selecting MEMS materials. Various MADM methods havebeen reported and found to be promising [10]. Through this paper,an attempt has been made to compare the results of these tech-niques (Ashby approach and MADM methods) when are appliedto two case studies including selection of MEMS materials for theapplication of (a) vibratory gyroscope and (b) capacitive micro-machined ultrasonic transducer (CMUT).

2. Materials and methods

2.1. Materials

The success of MEMS technology largely depends upon thematerials performance. The key materials used in MEMS devicesinclude Si-based materials, various conductors and insulators.Si-based materials are generally used for mechanical component.The basic MEMS mechanical components are diaphragms, beams,

Table 1Important MEMS materials and their properties.

Material Elastic modulus E (GPa) Failure strength (GPa) Thermal conductivity K (W/cm/C) Coefficient of thermal expansion a (10�6/C) Density (kg/m3)

3H–SiC 400 7 3.5 3.3 3200SCSi(110) 168 7 1.57 2.33 2300SCSi(100) 130 3.4 1.57 2.33 2300Diamond 800 8.5 6.9 1 3500Si3N4 250 6.4 0.19 0.8 3100Aluminium 70 0.17 2.36 25 2700Copper 120 0.25 3.98 16.6 8960Poly-Si 159 1.65 0.34 2.8 230SiO2 70 1 0.001 0.55 2500Polyimmide 8 0.04 0.001 20 1420Titanium 110 0.5 0.2 8.5 4510Nickle 185 0.4 0.899 13 8910Tungsten 410 0.7 1.78 4.5 19,300PVDF 2.3 0.05 0.002 140 1780

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cantilevers and disks. A variety of major issues concerning materi-als for the application of MEMS technology have been covered bySpearing [11,12]. An extensive survey of thin film mechanicalproperties has been done by Sharpe et al. [13]. Spearing [12] hasextended research on other mechanical properties of thin filmMEMS materials. A list of potential MEMS materials is mentionedin Table 1.

Fig. 1. Schematic sketch for the gyroscope.

2.2. Material selection methods

MCDM techniques have been used in various decision makingproblems in diverse technological applications. MCDM methodscan be categorised into multi-objective decision making (MODM)and MADM approaches. Ashby has proposed systematic materialselection procedure using MODM approach. MODM approachesare useful in screening large number of alternatives. Material selec-tion is a problem of optimising various conflicting objectives.According to Ashby approach, objectives can be clubbed togetherto form suitable performance indices. These indices form a basisof comparison for different materials and thus, the material withthe highest performance index is the most suitable candidate fora given application. Ashby divided performance index P of anyengineering component as P = f(F,G,M), where ‘f’ denotes functionof functional (F), geometric (G) and materials (M) parameters,respectively. These parameters are independent of each otherand their collective output determines the overall performance ofthe component. If there are more than one performance indices,material selection is compromised solution. Compromised solu-tions (Pareto-optimal) are the alternatives that have the besttrade-off between objectives and are not dominated by any otheralternative in the solution space. Various multi-objective evolu-tionary algorithms (MOEAs) are extensively investigated forPareto-optimal solution in multi-objective decision making prob-lems. Selection of a best material from all Pareto-optimal solutionsis not possible using Ashby approach. On the other hand MADMmethods can be used to rank finite number of materials. Twopopular methods (technique for order preference by similarity toideal solution (TOPSIS) [14] and VlseKriterijumska Optimisacija IKompromisno Resenje (VIKOR)) [15] are employed in present study.TOPSIS methodology is based on relative distance of an alternativematerial from ideal and negative ideal solution. The best materialis the one which is close to ideal solution and far from nadir solu-tion. The ideal solution is the collection of ideal scores in all attri-butes whereas nadir solution is the combination of the leastperformance values. Usually Euclidean distance is used for measur-ing distances between the alternative materials. The VIKOR meth-od is a compromise approach MADM model. Even though bothTOPSIS and VIKOR are essentially the same techniques both differ

in their approach on the following basis: (a) the normalisationtechnique used in TOPSIS is vector while that in VIKOR is linear,(b) the technique used in TOPSIS tries to evaluate the alternativewith the maximum distance from the negative ideal solution whileVIKOR tries to give the alternative closest to the positive ideal solu-tion, (c) VIKOR is a compromise approach and hence, allows differ-ent users to apply their own judgement to the evaluation processand (d) VIKOR (extended) can be used to evaluate the fitness ofthe final output thereby evaluating feasibility of the final outcome.Other methods (which are common in materials selection) arequestionnaire method, artificial neural network and Multiple Attri-butes Decision Making Approaches (AHP, SAW, WPM, Grey rela-tional analysis and ELECTRE, etc.). These methods are explainedin detail for materials selection viewpoint [2]. One of the simplestand efficient methods is Weighted Product Method (WPM) [16].This method is computationally simple and do not require normal-isation process. Each alternative is compared with the others bymultiplying a number of attributes. Each attribute is raised to thepower equivalent to the relative weight. It is very similar toweighted sum model (WSM).

3. Case studies

For the comparison of our results, we here study materialselection for two MEMS applications. Pratap and Kumar [5] havereported MEMS materials selection using Ashby approach. Materi-als indices are evaluated for MEMS gyroscope and capacitivemicromachined ultrasonic transducer (CMUT) [5]. We have furtherstudied the MEMS material selection using TOPSIS and VIKORmethod and compared with that of results obtained from Ashbyapproach [5].

Table 2MEMS materials ranking based on Ashby, TOPSIS and VIKOR approaches for vibratorygyroscope applications.

Materials Area (sq. units) Ashby ranks TOPSIS ranks VIKOR ranks

ScSi(100) 83892.47662 1 5 3ScSi(110) 80028.43982 2 2 2Si3N4 22793.96725 3 6 5Diamond 21472.58846 4 3 43H–SiC 6589.380338 5 1 1Poly-Si 3336.88908 6 8 7SiO2 1806.620134 7 9 10Copper 391.6963383 8 4 6Aluminium 350.810943 9 7 8Titanium 194.9262995 10 10 12Tungsten 167.3507988 11 12 9PVDF 78.60438347 12 14 14Nickle 62.99471832 13 11 11Polyimmide 36.61140402 14 13 13

A. Chauhan, R. Vaish / Materials and Design 41 (2012) 177–181 179

3.1. Vibratory gyroscope

A gyroscope is used to sense and measure angular motion usingvibrating mechanical elements. It works on coriolis component ofapplied force to sense angular rates. A vibratory gyroscope hasone or more proof masses that are excited by means of a feed-backcontrol device. The amplitude of excitation is carefully controlledand frequency of vibration is set to natural resonant frequency.When the proof mass is made to rotate about an axis perpendicularto the plane of vibration, the coriolis component of the force setsthe proof mass into vibration along the axis perpendicular to theexcitation direction but in the plane of vibration. This secondaryvibration is dependent on the angular rate of rotation and thus,is employed to find out the angular rate. Schematic sketch of thegyroscope is shown in Fig. 1.

The two indices selected for performance measure are: (M1 = rf/E) [5] (maximisation of this index means that the component willpossess a higher cut-off frequency thereby increasing its upperlimit of functionality) and (M2 = k/Ea2) (maximisation of this indexmeans that the component will have a higher deflection for a givenfrequency) thereby improving its sensitivity. Hence desirablematerials require larger values of M1 and M2. In order to give quan-titative ranking to the materials, we combine the two indices tofrom a third index (M3 = M1 �M2). Thus, an overall higher valueof M3 indicates better performance of a given alternative. M3 canbe interpreted as area under the plot of M1 vs M2. This method issimilar to weighted product method (MADM approach) [16] whenwe assume unit weights for both the indices (M1 and M2). Therelative rank of materials based on the composite index (M3) ismentioned in Table 2.

Fig. 2. Cross-sectional sketch of CMUT devices.

Now the TOPSIS and VIKOR approach are applied to the givendata. The desirable properties for the selection of material for avibratory gyroscope are: a lower value of Young’s modulus andcoefficient of thermal expansion while a higher value of failurestrength and thermal conductivity are required. These are theproperties which form the positive ideal solution and vice versais done for negative ideal solution. The ranks of the materials usingTOPSIS and VIKOR methods are tabulated in Table 2.

3.2. Capacitive micromachined ultrasonic transducer (CMUT)

CMUTs consist of a fixed electrode on a surface and a membraneelectrode that can vibrate. It works on piezoelectricity and variablecapacitance. Ultrasonic waves generate by the vibration of the pie-zoelectric membrane. The application of CMUT’s ranges from sim-ple detection devices to integrated actuators in control systems tonon-destructive testing and bio-medical applications. Fig. 2 showsan illustration of typical CMUT cross-section.

The two indices used to measure the performance of a CMUTare: (M4 = k/a); a higher value of this index essentially means thatthe materials chosen for the vibrating membrane are thermallymore stable. This is done because change in operational tempera-ture causes dimensional change which causes a shift in the funda-mental frequency. Thus, thermal stability becomes an importantcriterion while selecting material for the membrane. The secondperformance index is, M5 ¼ r3=2

f =ðE � qÞ1=2. This is composite indexcreated by combining two separate indices [5] (E/q)1/2 and (r3=2

f =E)which are responsible for maximising flexural rigidity and sensitiv-ity under a specified pressure, respectively. In order to rank studiedmaterials, we combine the two indices to from a third index(M6 = M4 �M5) similar to M3 (in vibratory gyroscope). Thus, anoverall higher value of M6 indicates better performance of a givenalternative. The relative rank of materials based on the compositeindex is mentioned in Table 3.

In order to study material selection using MADM approaches,TOPSIS and VIKOR methods are applied to the given data. Thedesirable properties for the selection of material for CMUT devicesare: lower value of Young’s modulus, coefficient of thermal expan-sion and density while higher value of failure strength and thermalconductivity are desirable. Ranks obtained from MADMapproaches (TOPSIS and VIKOR) are mentioned in Table 3.

4. Results and discussions

It is clear from Tables 2 and 3 that ScSi (100) and diamond arethe best materials (based on Ashby approach) for the applicationof vibratory gyroscope and CMUT applications respectively

Table 3MEMS materials ranking based on Ashby, TOPSIS and VIKOR approaches for CMUTapplications.

Materials Area (sq. units) Ashby ranks TOPSIS ranks VIKOR ranks

Diamond 138.3577915 1 4 4ScSi(110) 27.1817485 2 2 23H–SiC 23.50722353 3 1 1ScSi(100) 10.45999965 4 3 3Si3N4 5.914089343 5 5 5Poly-Si 1.822172463 6 8 6Tungsten 0.11150366 7 13 14Copper 0.039133215 8 7 8Aluminium 0.020607231 9 6 7Nickle 0.018449592 10 12 12Titanium 0.015991405 11 11 11SiO2 0.005884688 12 9 9Polyimmide 5.08131E�06 13 10 10PVDF 3.37978E�06 14 14 13

Fig. 3. TOPSIS and VIKOR materials ranks plotted against Ashby materials ranks forvibratory gyroscope applications.

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understudy. 3H–SiC, ScSi (110) and diamond are found to be bestmaterials using TOPSIS and VIKOR methods. The results from twoMADM approaches (TOPSIS and VIKOR) are in good agreementand quite similar to that of given by Ashby approach. Significantlyhigh linear correlation coefficients are observed between the ranksobtained from Ashby-TOPSIS (+0.82), Ashby-VIKOR (+0.88) andTOPSIS–VIKOR (+0.94) in case of vibratory gyroscope application(Fig. 3). Similarly for CMUT application, linear correlation coeffi-cients are Ashby-TOPSIS (+0.81), Ashby-VIKOR (+0.80) andTOPSIS–VIKOR (+0.98) as shown in Fig. 4. It indicates that theMADM techniques deliver the very similar result as that of Ashbyapproach. Results of MADM methods can be further improved byconsidering subjective weights (for all the properties under study)based on expert opinion. In the present study equal weights are as-signed for all properties under study in both the case studies. How-ever, Ashby technique is an efficient method and directly correlatesthe effect of various physical parameters on the overall performanceof a device. However, the formulation of indices can be a cumber-some and difficult task based on the fact that each application isinherently different from another application and also, exact func-tional relation between the parameters must be known and requireexpert decision. The constraints imposed on different category of

Fig. 4. TOPSIS and VIKOR materials ranks plotted against Ashby materials ranks forCMUT applications.

similar components could be different and hence different indicesare supposed to be used in it. Ashby approach is a highly reliabletechnique and its results are highly accurate. Originally the Ashbyapproach was extended to the MEMS materials by Srikar and Spear-ing [11]. Spearing has extended the performance indices to MEMSdevices by approximating various MEMS component as beams,plates, diaphragms, disks and springs. Additionally various issuesregarding application of materials in MEMS application have beencovered by Spearing [12], which included detailed analysis of effectsof scaling, processing, fabrication, material characteristics and de-sign issues. Thus, a comprehensive approach was established toevaluate the material suitability for a given MEMS application usingthe well established Ashby approach.

On the other hand MADM techniques like TOPSIS and VIKORcan be used without prior knowledge of physical relations of mate-rials properties for their specific applications [17]. It offers the fol-lowing advantages when used: (a) it can be used to evaluate theranks of alternatives regardless of the number of attributes associ-ated with it, (b) the technique can be applied regardless of theinterdependence of the attributes, (c) no functional relationshipneeds to be established or used, (d) the user can apply weightsas necessary to prioritise different attributes as per the given de-sign constraints, (e) less computational time required, and (f)non-numeric attributes and weights can also be considered usingfuzzy techniques. However material selection requires moresophisticated methods since materials properties vary with fabri-cation methods and scale of study.

Even though it is an open question for the researchers to com-pare, differentiate, evaluate and critically analyse various MADMand MODM methods for material selection and screening proce-dures, during the study we come across an additional phase ofevaluation. Mostly it is the case that the various performance indi-ces associated with the overall performance of component may beat conflict with each other. As is the case in the second case studyof CMUT the composite index M5 ¼ r3=2

f =ðE � qÞ1=2 is made up oftwo separate indices which are (E/q)1/2 and (r3=2

f =E) [5]. As isobserved one tends to maximise Young’s modulus while other triesto minimise it to increase the overall performance of the samecomponent. It then becomes additional problem to evaluate orrank the materials based on these conflicting indices. Also, addi-tionally when the number of such indices increases to a large num-ber it becomes difficult to apply visual techniques to select orscreen the materials. In such cases additional techniques may berequired to come to conclusive results. Pratap and Kumar [5] hasreported two separate techniques to combine different indices togenerate a composite index. First is the value function approachin which a normalised performance index Pnorm is evaluated asPnorm = a1M1 + a2M2 + a3M3 where ai (i = 1,2,3) are the weights tobe decided by the designer (Ra = 1) and individual indices arenormalised as Mnorm = Mi/Mmax. However, this method has inher-ent drawback of masking the effect of weaker index. Therefore,WPM has been used to couple two indices to provide a more justi-fied approach of evaluating a composite index. In the original papervisual and graphical techniques have been used to screen the vitalmaterials, and the final selection is a qualitative approach. In orderto have a quantitative approach we have extended the WPM to cre-ate a single performance index which may be directly used forranking. It brings us to the discovery that a hybrid techniquemay be evolved which combines the best features of MADM andMODM methods for efficient analysis of material performancesfor designated applications. However, it requires extensive re-search. It is never ending challenge for researcher because of fastdevelopment of materials and their applications. Further compari-son studies are required to examine consistency. A sensitivity anal-ysis is essential for all MADM techniques to find out which methodis more appropriate for a specific problem.

A. Chauhan, R. Vaish / Materials and Design 41 (2012) 177–181 181

5. Conclusions

MADM approaches (TOPSIS and VIKOR) are employed in MEMSmaterials selection. Their results are in close agreement with thatof Ashby approach. Materials are selected for MEMS vibratorygyroscope and capacitive micro-machined ultrasonic transducerdevices. Good concurrence (significantly high linear-correlation)between results of Ashby approach and MADM techniques likeTOPSIS and VIKOR indicates that MADM techniques can be usedfor material selection without prior knowledge of exact physical/mathematical relations of materials properties for their specificapplication. However more work needs to be extended for examinerobustness of MADM techniques in material selection.

Acknowledgements

One of the authors (RV) acknowledges support from the IndianNational Science Academy (INSA), New Delhi, through a grant bythe Department of Science and Technology, (DST), New Delhi, un-der INSPIRE faculty award-2011 (ENG-01).

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