Review Article Reliability and Fatigue Analysis in ...

Review ArticleReliability and Fatigue Analysis in Cantilever-BasedMEMS Devices Operating in Harsh Environments

Mohammad Tariq Jan12 Nor Hisham Bin Hamid1 Mohd Haris Md Khir1

Khalid Ashraf1 and Mohammad Shoaib1

1 Department of Electrical and Electronics Engineering Universiti Teknologi PETRONAS 31750 Seri Iskandar Tronoh PerakMalaysia2 Department of Physics Kohat University of Science and Technology (KUST) Kohat 26000 Pakistan

Correspondence should be addressed to Mohammad Tariq Jan tariqjankustedupk

Received 30 August 2013 Revised 1 December 2013 Accepted 1 December 2013 Published 12 January 2014

Academic Editor Adiel Teixeira de Almeida

Copyright copy 2014 Mohammad Tariq Jan et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The microelectromechanical system (MEMS) is one of the most diversified fields of microelectronics it is rated to be themost promising technology of modern engineering MEMS can sense actuate and integrate mechanical and electromechanicalcomponents of micro- and nano sizes on a single silicon substrate using microfabrication techniques MEMS industry is at theverge of transforming the semiconductor world into MEMS universe apart from other hindrances the reliability of these devicesis the focal point of recent research Commercialization is highly dependent on the reliability of these devices MEMS requires ahigh level of reliability Several technological factors operating conditions and environmental effects influencing the performancesof MEMS devices must be completely understood This study reviews some of the major reliability issues and failure mechanismsSpecifically the fatigue in MEMS is a major material reliability issue resulting in structural damage crack growth and lifetimemeasurements of MEMS devices in the light of statistical distribution and fatigue implementation of Parisrsquo law for fatigue crackaccumulation under the influence of undesirable operating and environmental conditions

1 Introduction

The microelectromechanical system (MEMS) is a rapidlyevolving technology that incorporates electrical andmechan-ical elements at the microlevel Due to the small size ofMEMS devices this technology has been widely appreci-ated in almost every field of life MEMS devices possessa simple principle of operation and are easy to fabricateThe electronic components are fabricated using traditionalintegrated circuits (ICs) fabrication technology while themechanical parts are fabricated by using silicon and othersubstrates utilizing micromachining processes Bulk [1] andsurface micromachining [2] are the two main processesadopted for the fabrication of the mechanical parts of MEMSdevicesThe fabrication techniques such asmicrofabricationmicromachining and ICs involve components that can rangein size from the submicrometer level to the millimeter level[3] The MEMS industries are constantly improving thedesign and fabrication techniques of these devices

MEMS by virtue of its nature corresponds to a distinctivetechnology that has transformed the entire MEMS industryBulky sensors and actuators can be replaced by miniaturizedMEMS devices MEMS accelerometers are frequently used inautomobiles for air bag deployment blood pressure sensorsmicrosyringes and implantable biosensors in the medicaland life sciences inkjet printer heads computer disks pro-jection displays and microvalves used in electronics com-munication and defense [4ndash7] Apart from these many otherMEMS products are manufactured for various industrial andconsumer applications

MEMS devices mainly consist of sensors and actuatorscollectively called transducers are capable of converting oneform of energy into another form MEMS technologiesare merged with microelectronics and optical systems toform themicrooptoelectromechanical system (MOEMS) andthe nanoelectromechanical system (NEMS) on a single sil-icon chip [8ndash10] Advancement in the MEMS technologyis on the move and is well recognized and respected by

Hindawi Publishing CorporationJournal of Quality and Reliability EngineeringVolume 2014 Article ID 987847 16 pageshttpdxdoiorg1011552014987847

2 Journal of Quality and Reliability Engineering

the academicians research laboratories and industry how-ever in spite of its global recognition the reliable designof MEMS devices is one of the main challenges in thecommercialization of these devices [11ndash13] The reliabilityof MEMS is neither well established nor recognized by theindustry and academia [14] and is accepted as a relatively newand challenging field for research In the long run MEMSmay support novel classes of exceptionally small fast self-managing and cost effective devices [14] In order to gain ahigh volume market place it is essential that MEMS devicesshould be of competitive reliability

The main goal of reliable MEMS designing is to comeup with devices having mechanical components as reliable asits electrical parts Since MEMS technology is growing andmany more applications are entering into the mainstream ofMEMS devices it is important to understand the reliabilityissues in these devices Research in MEMS is mainly focusedon the design methodologies and fabrication techniques inorder to produce miniature and effective MEMS devices[15ndash17] Because of the basic building structure of MEMSthe working environments of MEMS sensors and actuatorsmay not be suitable for the electronics counterpart of thewhole assembly and hence can affect its performance Thereliability of MEMS devices has not been addressed asa major degradation factor in the performances of thesedevices at commercial as well as at consumer levels [11] InMEMS technology the trend towards constantly reducingthe size and volume intercommunication and multipledimensions is making them as devices of choice Howeverthe failure of the mechanisms due to the introduction of newprocesses designs and materials as well as the fabricationtechniques is making MEMS devices unreliable [18 19]Product replacement costs have driven the need for improvedreliability which has led to design tradeoffs [20] On theother hand reliability is a challenge forMEMSmanufacturersdue to the growing market and stricter government safetyregulations [17] MEMS applications are expanding in factthe MEMS market is currently double that of ICs and isexpected to be US$20 billion in 2017 [21] All MEMS deviceshave dissimilar applications nevertheless they share somecommon requirements such as (1) time to market that leadsto success (2) stress reduction and (3) reliability of MEMSbeing critical [22]

Design optimization of MEMS sensors and actuatorsis critical due to high cost lengthy fabrication processesVagueness in the fabrication and etching processes used tomanufacture MEMS devices can lead to certain uncertaintiesin the performance of final product consequently obtaininglow yield and poor reliability [23] The reliability study ofMEMS devices is therefore essential Due to complex natureof MEMS devices the reliability must be considered as aseparate field of research The research on reliability willgrow as theMEMS technology attains its height Temperatureand humidity are reported as two major reliability issuesof MEMS devices [24] The reason is that there are manysensors and actuators that are exposed to the harsh environ-ments such as accelerometers gyroscopes thermal actuatorsand chemical sensors This paper mainly discusses fatiguegeneration and the operational and environmental effects

on the performances of cantilever-based MEMS devicesParticularly fatigue being a material reliability issue that hin-ders the performance of cantilevers-based MEMS is focusedon Fatigue induced due to the crack growth rate and thelifetime of MEMS devices can be modeled through statisticaldistribution functions and Parisrsquo law

This paper presents a review of the current literature onthe reliability of MEMS Section 2 discusses reliability andits importance Section 3 describes the failure mechanisms ofMEMS devices followed by fatigue and then the crack growthmodeling of fatigue A thorough review of the environmentaleffects on the cantilever-based MEMS devices is presented inSection 4

2 Reliability

Due to the most promising technology of the modernengineering sciences MEMS has brought revolution to thesilicon industry Most of the MEMS components are beingfabricated using silicon and its oxides However regardless ofthe brighter future ofMEMS itmaterializes to be in an alarm-ing state In order to underline MEMS reliability concernsit is endeavored that a complete knowledge of the failuremechanism (physics and statistics) is fully understood Dueto continued intensification of the MEMS family the overallcosts of manufacturing failure rates and its performancesover the accepted period of time (reliability) are the signifi-cant issues that can be resolved at the time of manufacturingBeing an emerging technology MEMS reliability is of primeimportance in applications where the failure can be fataland shocking [25] A variety of materials are used in thefabrication of MEMS devices Materials showing improvedtendency in the direction of high reliability and long termsurvivability are taken as the material of choice even if itincreases the overall cost of the device [26]

MEMS manufacturers are going to come across a chal-lenging task in addressing the reliability of MEMS devicesfor the reason of their versatility both at the production andapplication levels [17] Reliability is the ability of a MEMSdevice to perform its intended function without failureunder stated conditions for a particular period of time Theperformance of MEMS devices is highly dependent on thecompatibility of several static and moving parts the designand the selection of materials where the device can performthe desired function with long term repeatability and accu-racy [27] The growing density of MEMS products demandsfor multiple functions on the same chip and its operation inmultiple domains are indeed making the reliability of MEMSdevices a challenging task Traditional approaches are beingused for the design and fabrication ofMEMS devices and lessattention has been diverted to address the reliability issues[27] As reliability is becoming the subject of research for theupcoming MEMS generation emphasis on the identificationand rectification of the reliability issues of MEMS devices isa big issue for the researchers academicians and industryParticularly the mechanical reliability of the material ofwhich MEMS devices are being fabricated is one of themost important aspects when dealing with reliability of thesedevices Therefore it is being treated as a new phenomenon

Journal of Quality and Reliability Engineering 3

and at the eve of new developments in the evaluation ofexperimental procedures and analysis which have resultedin further enhancements in the field of reliability of MEMSdevices

Three challenges are considered in MEMS reliability

(1) finding the correct failure mechanism

(2) obtaining statistically significant data

(3) defining the physical model of MEMS

Research into the MEMS failure mechanism is in its veryearly stages and cannot be trusted [20 28] The electronicindustry also acknowledges the importance of reliability inMEMS across several consumer applications [29] The rootcauses of failure of reliability in MEMS devices are extremelyproduct dependent Sufficient technical data has not beenavailable on the basis of which specific and general failuremechanisms of MEMS devices can be targeted A standardtest method is needed for characterizing the mechanicalproperties of MEMS devices produced by the same processesand at the same scales as the intended application Furtherstudies on reliability suggest that it is the ability to sort outgood devices from bad ones [28] and quantitatively predictthe failure rate in devices before they are delivered to thecustomer [20] The commercialization of MEMS is directlyproportional to the reliability of MEMS Moreover MEMSproducts being well guarded trade secrets and restrictions onsharing knowledge and experience have resulted in the slowgrowth of theMEMS industry [11] On the other handMEMSismultifunctional which causes failures that vary significantlyfrom device to device Reliable MEMS devices are key to suc-cessful commercialization [11] In spite of extensive researchbeing in progress only the digitalmicromirror device (DMD)for digital projectors from Texas Instruments analog devicesaccelerometer for air bag deployment Gyroscope in iphonesfrom STMicroelectronics and Inkjet printer heads fromHewlett-Packard (HP) have made their way to successfulcommercialization [4ndash6] Some common MEMS devicesand their reliability issues are listed accelerometer suffersfrom mechanical wear fractures fatigue and charging andfriction Vibration shock fractures and fatigue were foundin pressure sensors whereas the gyroscopesrsquo reliability issuesinclude charging shock and vibrations [29ndash32] Variousreliability test methods and approaches have been adopted bymany researchers and research laboratories and can be seenin [28 33ndash40] An experimental model analysis methodologyhas been investigated for microsystems emphasizing theshortage of techniques required to quantify the reliabilityof MEMS [3] Research on reliability mainly focuses on theprediction of the failure mechanism in MEMS devices [41]Several reports were documented on the response times andlinearity of the output signal subjected to shock loads [42 43]MEMS microengines were exposed to harsh environmentsby testing shock pulses for various amplitudes [19 44] Themain emphases of these studies were to observe the impact ofshocks under loading conditions some wrecked mechanicalcomponents were found as a result of unbearable shocksduring loading cycles

Si

Initial crack

Crack propagation Fracture

SiO2F

Figure 1 SCC formation on the silicon substrate subjected to tensilestresses [46]

Corrosion has been identified as one of the reliabilitydegrading factors It can cause a mechanical fracture in theform of scratches inclusion and environmentally assistedcracks [45] Moisture and temperature have been found toenhance corrosion in metals such as aluminum where stresscorrosion cracks (SCC) occur on the surface of the materialon the area of the maximum stress SCC is also found insilicon which is covered with a thin oxide layer in air andresults in the crack initialization that is enhanced undervariations in stresses As cracks proceed the silicon interfacesthe oxides deep into the structure enhancing the crack growthuntil the final fracture occurs this phenomena can be seen inFigure 1 [46]

Wear plays a vital role towards the poor reliability ofMEMS devices it is associated with rubbing or impactingsurfaces and is responsible of four types of failure in MEMSdevices for example adhesion abrasion corrosion and sur-face fatigue [12 47] It has been experimentally observed thatthe adhered length rest time temperature relative humidityand sliding velocity are some common factors contributingto the poor reliability in MEMS devices specially thosecontaining microcantilevers [48 49] Wear in MEMS can beprevented from occurring by introducing protecting bordersto the MEMS structures These borders can be in the formof solid films antistiction coatings gas phase lubricationor diamond like coatings (DLC) [50 51] To protect thesurface of the MEMS structure from wear a thin film suchas perfluorodecyltrichlorosilane is coated on the surface ofthe MEMS structure [52] Contamination is another factorthat can hinder the performances of MEMS devices Theinduction of unintended materials and contamination altersthe mechanical movements of MEMS devices thus resultingin failure [15 53]

Electric short and open circuits are valid factors that con-tribute to poor reliability Unfortunately this phenomena hasbeen mixed with the semiconductor technology in treatingreliability issues in ICs whereas MEMS are different fromsemiconductor devices The dielectric properties of silicon inMEMS are still not fully understood [7] Dielectric degrada-tion charge injection Ohmic contacts electromigration andelectric stress are typical examples and causes of problems indevice performances An electrostatic discharge (ESD) causesalmost 25 of failures in MEMS devices that includes gateoxidation breakdown junction spiking and latchup [54] InMEMS the dielectric is involved in sacrificial structuraloptical masking passivation insulator and encapsulation


layers ESD related problems in the dielectric are fatal [55ndash57] Sources of ESD include the human body charge devicescharged environments and cosmic raysThehuman body canbuild up an electric potential more than 1000 volts whichcan prove to be fatal for MEMS devices [58] Numeroustest standards experimental procedures and processes havebeen demonstrated to overcome the open short circuit andESD problems [59 60] However this area still requiresmore attention from researchers and academicians in orderto rectify the reliability issues in these sophisticated MEMSdevices

The packaging of MEMS devices is an important factorthat also contributes to poor reliability due to the uniqueconstruction of MEMS devices and their interaction withthe surroundings in certain ways Therefore it requires anonstandard packaging Standard hermetic packaging usedfor microelectronic circuits is not useful for most of theMEMS devices [13] It has been observed that MEMS andNEMS having moving parts (for sensing and actuation) haveto be free but inside a package alternatively an unpackagedMEMS is a dead MEMS [61]

21 Mathematical Measures of Reliability Reliability is basi-cally the probability of the device performing properlyunder typical operating conditions for the expected lifetimeintended The classical statistics along with system reliabilityapproaches using series and parallel system of ldquo119899rdquo compo-nents and modern high performance computing (HPC) haveprovided ways to measure reliability of MEMS These areequally supported by experimental analysis theoretical andmathematical modeling and simulations These approacheseffectivelymeasure the reliability function failure ratesmeantime to failure and so forth [62] Consider the following

119877 (119905) = 1 minus 119865 (119905) (1)119877(119905) is the reliability (survival) function which is the prob-ability of operation without failure to time 119905 119865(119905) is thecumulative failure function (CDF) and is the probability thata randomly chosen part will fail at time 119905 119891(119905) is the lifetimedistribution model that serves as the probability densityfunction (PDF) over the time range from 0 to infin CDF andPDF can be correlated as [20]

119865 (119905) = int

119905

0

119891 (1199051015840) 1198891199051015840

119891 (119905) =

119889

119889119905

119865 (119905)

(2)

22 Reliability Distribution The distribution of the failureover the lifetime of the device population is significantlyessential to MEMS reliability With the help of these distribu-tions the functions can be developed and used for predictivepurposes [20 63] Another important property of probabilityis the hazard or the instantaneous failure rate denoted by ℎ(119905)It is the ratio of the failure in the next time interval and thereliability 119877(119905) of the device [64] Consider the following

ℎ (119905) =

119891 (119905)

119877 (119905)

=

119891 (119905)

1 minus 119865 (119905)

(3)

Wear outUseful life

Infant mortality

Time

Failu

re ra

te

Figure 2 Bathtub curve [54]

or

ℎ (119905) = minus

1

119877 (119905)

119889119877 (119905)

119889119905

(4)

or

ℎ (119905) = minus

119889

119889119905

ln119877 (119905) (5)

The integral of the hazard rate is the cumulative failure rateand is given by

119867(119905) = int

119905

0

ℎ (1199051015840) 119889119905 = minus ln119877 (119905) (6)

An essential reliability factor is how long a certain populationwill survive without failureThis phenomenon is calledmeantime to failure (MTTF) and is given by the following equationshowing the first mean time to failure [65]

MTTF = 1199051015840equiv int

infin

0

119905119891 (119905) 119889119905 (7)

With the help of these statistical distributions the devicelifetime can be predicted under its expected operating condi-tions Some of the most common statistical distributions arelisted below

(1) bathtub curve(2) exponential distribution(3) weibull distribution(4) lognormal distributions

221 Bathtub Curve The failure rate of MEMS that changesover the lifetime of the device starting high reducing andincreasing towards the end of the devicersquos life is namedbathtub curve and is shown in Figure 2

This bathtub curve shows the three stages over theMEMSlifetime the high initial failure due to infant mortality con-stant failure rate over the useful lifetime and increased failurerate as the device ages [58] The reliability at these pointsdepends on the competence of MEMS devices to survivedegradation that arises during the operation capturing thewhole lifetime of these devices [24] The bathtub curveis a good tool when there is a single population underconsideration however in the case of multiple populationsthe subsequent statistical analysis can be incorporated


222 Exponential Distribution The exponential distributionis the most simplest as compared to all lifetime distributionmodels where the failure rate or hazard rate ℎ(119905) is denoted by120582 and is treated as a constant It is appropriate for the constantfailure rate region in the bathtub curve In the exponentialdistribution the reliability the cumulative distribution func-tion and the probability distribution function are given as[20]

119877 (119905) = 119890minus120582119905

119865 (119905) = 1 minus 119890minus120582119905

119891 (119905) = 120582119890minus120582119905

(8)

The mean time to failure of the exponential function is theinverse of failure rate 120582 Consider the following

MTTF =

1

120582

(9)

223 The Weibull Distribution It is used to fit a variety ofshapes of reliability curves and can be expressed in multipleways The Weilbull distribution is basically the probability ofsurvival between time zero and time 119905 [66 67] Consider thefollowing

119877 (119905) = 119890minus(1120572)

120573

997904rArr

119891 (119905)

ℎ (119905)

(10)

when 120573 = 1 the above equation becomes the exponentialmodel (bathtub reliability equation) when 120572 = 1120582 itbecomes the MTTF equation Two-parameter fit modelsare commonly used in reliability lifetime prediction Theprobability density function of the two-parameter Weilbullrsquosmodel is given by

119891 (119905) =

120573

119905

(

119905

120572

)

120573

119890minus(119905120572)

120573

(11)

224 Lognormal Distribution It is a continuous probabilitydistribution of random variables whose log is normallydistributed and can model a random variable 119909 where log(119909)is normally distributed Lognormal time to failure is nameda log normally distributedThe probability distribution func-tion in time unit of 119879

50is given by the following equations

119891 (119905) =

1

120590119905radic2120587

119890(minus(ln(119905)minusln(11987950))221205902)

119865 (119905) int

119879

0

1

120590119905radic2120587

119890(minus(ln(119905)minusln(11987950))221205902)

119889119905

(12)

3 MEMS Failure Mechanism

Unlike ICs MEMS devices move and thus special tools andtechniques are required to measure the mechanical motionon a nanometer scale in all 6 degrees of freedomThese toolsare used to understand the devicersquos behavior in detail so asto provide feedback to the designer in order to improve the

Figure 3 Particle obstruction in inertial sensor (Courtesy SandiaNational Laboratories)

120120583m

Figure 4 Electrostatically driven polysilicon MEMS comb fingerswith a notch at the anchor (Courtesy Sandia National Laboratories)

reliability in the designThe reliability tool kit has to measureminute changes in the devicersquos behavior after acceleratedtesting (large number of cycles mechanical shock thermalcycling and so forth) to estimate the lifetime once the failuremechanism has been identified

Several kinds of MEMS devices are used in a rangeof applications across the globe MEMS devices were oncethought to be in the family of ICs and may carry the samefailure mechanism as the ICs However due to the uniquestructure and geometry of MEMS devices and its variousbiasing techniques the failure mechanism of these devices iscategorized based on the complexity of the MEMS devicesMEMS devices are divided into the following four groups

Group 1 contains MEMS devices with no moving partssuch as DNA sequencers microphones and chemical sen-sors Particle contamination stimulates failure in this groupof MEMS devices In fact particles tend to mechanicallyobstruct the operation of MEMS devices Due to their smallsize and being nonelectrical in nature it is difficult to detectparticle contamination as it will not electrically bridge thestructure that can result in short circuits A typical example ofparticle contamination is shown in Figure 3 Here the sensorcannot move and hence cannot create an output signal to beforwarded to the readout circuitry [53]

Group 2 consists of MEMS devices with some movingparts and no rubbing surfaces such as accelerometers gyro-scopes and comb drives Reports have suggested that hingesand microcantilever yoke regions are prone to fatigue asshown in Figure 4 To study the structural failure (fatigue)in this group electrostatically actuated comb fingers with aperforated proof mass and a microcantilever with a notch ispresented Stress levels at the notch initializes cracks on thesurface of the microcantilever that tend to reduce the life ofthe device and ultimately causes the failure of the device byfracture [18]


Figure 5 Wear debris on the surface of the microengine (CourtesySandia National Laboratories)

Group 3 includes MEMS devices having moving partswith impact surfaces such as thermal actuators valves andrelays These devices are susceptible to debris created on thesurfaces fracture components cracks and so forth Failurein the MEMS structure occurs due to a fracture as a resultof impacting forces on the opposite structure of the MEMSdevices [18]

Group 4 represents MEMS devices with moving impact-ing and rubbing surfaces for example optical shuttermicromirror geared devices and so forth Moving com-ponents create friction that results in wear material ordebris causing several failures such as (1) failure by particlecontamination (2) particles creating third body wear thatchanges the motion tolerance and (3) adhesion of rubbingor contacting surfaces These characteristics can be seen inFigure 5 [68] It is noticeable that particle contamination andstiction can cause failure in all kinds of MEMS devices It istherefore emphasized that the root causes of failure must beknown before jumping for remedies of the particular failure

MEMS sensors and actuators by their classifications intogroups and by their nature have different and unique failuremechanisms In ICs electrical parameters are measured totackle the failure whereas in MEMS both the electrical andmechanical parameters are endorsed to deal with the failureand to enhance reliability [51] Further details can be seenin Table 1 which summarizes the MEMS common causes offailures and its procurement

4 Mechanical Failure in MEMS

MEMS components consist of beams or membranes that areflexible or rigid one- or two-sided clamped with or withoutperforation on its surface It also contains conductive orinsulative flat layers hinges cavities and gears connectedto an electronic readout circuit [13] On the other handtraditional MEMS devices such as pressure sensors andcantilevers have been integrated into accelerometers contactswitches micromirrors micropumps valves and so forthMEMS structures oncemoving along a single axis have beenreplaced by multiaxes moments Structures and applicationsof MEMS devices are becoming more complex In order to

improve the performances of MEMS devices it is essentialto know at the very preliminary stage the fundamentalcauses of their failures These failure analyses can greatlyhelp in understanding the root causes of failures at the waferlevel to the final packaging of the device [77] The deviceintercommunication and compatibility to perform its desiredfunctions result in certain failure mechanisms Table 2 listssome of the major mechanical failures of MEMS devices

The rapid market growth of MEMS products is evidenceof the improved reliability of MEMS devices No doubtpoorly designed MEMS devices can carry multiple modes offailures circumspectly designedMEMSproducts can congre-gate the harsh reliability provision of MEMS applications Itis a general perception that most of the failures of MEMSdevices are related to their mechanical portions howeverelectrical reliability issues have been unnoticed over and overagain These are responsible for a high electric field appliedacross the dielectric of MEMS devices Some importantelectrical reliability issues that cause electrical failures inMEMS devices are listed in Table 3 [78]

MEMS devices work on the principle of mechanicalvibrations that generate an output from the device Thegenerated output can never be the same due to the variousMEMS structures that rely on the dynamic displacements andvariations in the stress levels hence resulting in an outputerror enough to disturb the sensitivity of the device [79]Sensitivity is the ratio of themagnitude of the output signal tothe input stimuli Sensitivity is an important factor in deviceselection [80 81] The sensitivity power consumption andfrequency ranges of MEMS sensors and actuators used inmedical automobile defense communication and seismol-ogy are listed in Table 4

5 Fatigue in MEMS

Fatigue plays amajor role inmaking theMEMS devices unre-liable Since 1992 after being discovered it has been widelystudied and observed bymany researchers and academiciansEach MEMS device has unique configurations therefore itcarries unique fatigue occurrences which by any means aredifferent from device to device [84]

Fatigue is the localized and structural damage that occurswhen a material is subjected to cyclic loading It starts with acrack that starts at an area of high stress and slowly propagatesthrough the material until there is a failure of the deviceThisis limited to the active components of MEMS devices thatis cantilevers membranes and comb drives [38] Howeverpassive structures are not physically exposed to mechanicalstress cycles enough to stimulate fatigue Formation of crackson the structures initiates fatigue which gradually spreads upthrough the material until there is a catastrophic failure ofthe device [17 85] Several changes on the surface of MEMSdevices have been observed during cyclic stress actuationsand interactions of water molecules with the silicon dioxidelayer It has also been reported that no fatiguewas observed insilicon when cyclic loading was 50 less than the total siliconfracture strength [86 87]

Initially researchers have emphasized on high frequenciesfor prediction of the fatigue lifetime of polysilicon MEMS


Table 1 Summarizes various MEMS groups their causes of failure and procurement of the failures

Group Causes of failurereliabilityissues Test Reference

Group 1

DNA sequencersMicrofludicnozzlesChemical sensor

Dielectric breakdown

2 times 4microfludic array X and Y directionelectrodes were shorted respectively the effects ofchanges on the electrodes were simulated andtransportation of droplets was observed by CCDCamera

[69]

Group 1 or 2

AccelerometerMechanical wear fracturefatigue charging change in

friction

(1) Built in self repairable tests within the devicewere reported Comparison of BISR andNon-BISR MEMS simulation of fatigue and S-N(no of cycles to failure) curve(2) Accelerated life time experimental tests wereperformed for 1000 hours at about 145∘ to 200∘C(3) Fatigue testing using Tytron 250 Theexperimental fatigue life lines were between778 times 10

4 to 148 times 107 cycles at the stress levels of

205 to 283GPa(4) Sandia National Laboratories have developedthe Sandia High volume Measurement ofMicromachine Reliability (SHiMMeR) to controland measure up to 256 MEMS partssimultaneously it is a Plexiglas enclosure with ahigh power optical microscope and cameras(5) Military Test Standard Device(MIL-STD-883F) for stiction Diamond LikeCarbon (DLC coating) for wear X-rays diffractionfor fatigue and creep and for contaminationScanning acoustic Microscope (SAM)

[28ndash30 33 34]

Group 2

Pressure sensorsFracture fatigue shockvibrations and change in

friction

Sensors were designed and manufactured wellbelow the stress level where fatigue was detectedin silicon fatigue in pressure sensor occurredwhen stress and fracture levels were almost equal

[35]

Gyroscopes Charging shock andvibrations

(1) Adhesion failure mode in lateral capacitivegyroscope was experimentally analyzed(2) Variations in noise and signal out as well astemperature degradations were reported

[36 37]

Group 3

Thermal actuator Mechanical wear shockand vibrations

(1) Fracture experimental tests were performed byapplying load on the beam usingWeibull statistics(2) Experimental methodology for the evaluationof creep in microswitches based on thedeformation of the switch due to charging anddue to creep(3) Pull-in voltages were observed in bend andtorsinol modes fatigue tests were carried out andthe predicted life time reported was 1011 cycles

[70ndash72]

ValvesMechanical wear fracture

fatigue shock andvibrations

(1) Design issues were classified more research isneeded for better understanding(2) Fatigue test of thick aluminum specimen wasobserved in liquid environment

[31 73]

Micro relaysMechanical wear fracturefatigue shock vibrations

and charging

109 onoff switching cycles without stiction andwelding induced failure were reported [32]


Table 1 Continued


Group 4

Electrostatic actuatorMechanical wear fracturefatigue shock vibrationsand charge in friction

Analysis of pull-in and pull-out voltages usingstochastic modeling for prediction of life time ofdevices

[39 74 75]

Optical shutterMechanical wear fracture


Imprecise data availability

Mirror deviceMechanical wear fracturefatigue shock vibrationsand optical degradation

Texas Instruments (TI) developed theMirrorMaster a custom optical inspection tool forDMD devices that inspects every pixel of theDMD array and determines the response of eachpixel to different electrical drive signals

[7]

Gear devicesMechanical wear fracturefatigue shock vibrationsand charge in friction

Simulations of sliding surfaces preventedadhesion and wear [76]

MicroturbinefanMechanical wear shockvibrations and charge in

frictionImprecise data availability

Table 2 Mechanical failures

Mechanical fractureFailure Overload Shock Corrosion Fatigue

Causes Excessive stress

Drops excessiveloading andmechanical

interference disorder

Chemical reactionoxidation

Structural damage atcyclic loading

StictionFailure Vander Waals forces Capillary forces Chemical bonding Electrostatic charging Residual stress

CausesInteraction of atomsor molecules at thesurface of close

contact

Monolayer of wateron all surfaces thatlubricates the surfaceinducing capillary

force

Chemical bondbetween contacting

surfaces

Two closed surfaces atdifferent potentials

During the releaseprocess structuretends to bend or

deform

WearFailure Adhesion Abrasion Corrosion Surface fatigue

Causes

Pulling off fragmentsof another surfacewhile sliding due to

surface forcesbetween them

Stripping awaymaterial from softsurface while slidingof harder surface

When two surfaceschemically interact

Smooth surfaces aresubjected to cyclicloading instead of

sliding

Creep and fatigueFailure Intrinsic stress Applied stress Thermal stressCauses Residual stress Input load Overheating

Table 3 Electrical failures

Electric short and open circuitFailure Dielectric material degradation ESD high electric field Electromigration OxidationCauses Capacitive discharges excessive load Mismatch load Environmental

ContaminationFailure Intrinsic (crystal growth) Manufacturing-induced Usage environmentCauses Environmental Rough handling in industry Low high temperature and humidity


Table 4 The sensitivity of various MEMS devices [82 83]

Fields ofapplication

Sensitivity invalue ldquogrdquo

Powerconsumption

Frequencyrange

Medical plusmn16 ge19mA 24MHz IEEE

Implantable plusmn2 plusmn4 plusmn8 plusmn16 25 uA 24 MH IEEEAutomobile plusmn35 plusmn50 plusmn70 ge13mA 250GHz

Defense Up plusmn70 20 A 20V 650KHz to15MHz

Communication plusmn20 to plusmn70 Fluctuates withapplications 27 to 10GHz

Seismology ge plusmn2 Fluctuates withapplications ge1 KHz

devices in the bend state [88ndash90] Not only testing thefatigue lifetime of polysilicon at lower frequencies is timeconsuming but also the mechanical loading has been con-fined to high frequencies only [91] There is a long list oftests and experimental procedures for predicting the fatiguelifetime using numerous approaches However there is noenough evidence of merging the existing experimental datain correlation to drawing a mathematical model for theprediction of the fatigue life cycle of MEMS References[92] reported a modeling approach for the prediction ofthe fatigue lifetime of polysilicon by taking the variationsin the thickness and creating a multiparameter expressionfor the prediction of the fatigue lifetime of polysilicon TheMEMS structure was subjected to various variations in thedesign rules This revealed that the devicesrsquo physical shapes(geometry) play an important role in changing the devicesrsquoperformances

In the failure analysis the process wreckage or debris issometimes not possible to examine using an optical micro-scope or SEM due to the fact that the rubbing surface restsbelow the other structure It is therefore recommended thatthe focused ion beam (FIB) is used for a clean observation ofthe cross-sectional area of the MEMS structures [93 94]

Many researchers have investigated the behavior offatigue in MEMS unfortunately there are no reputablemethods on the basis of which the fatigue behavior canbe explained for many uncertain factors which leads to theultimate failure of the MEMS device [72] Fatigue crackinitialization can be seen in Figure 6

In general the fatigue process involves (1) crack nucle-ation (2) short crack growth (3) long crack growth and (4)final fracture Cracks start at the localized shear plane at ornear high stress concentrations such as persistent slip bandsinclusions porosity or discontinuities Crack nucleation isthe first step in the fatigue process Once nucleation occursand cyclic loading continues cracks tend to grow along theplane of themaximum shear stress and through the boundaryof the component [95]

51 Crack Growth Model for Fatigue Analysis The crackgrowth model [41] that is used to describe fatigue is given as

119870119868= 120590119884119888

12 (13)

where 119870119868is the measure of intensity 120590 is the applied

stress 119884 is the crack shaped parameter and 119888 is the cracklength Failure will occur when 119870

119868exceeds a critical value

119870IC the intrinsic strength of the material is exceeded andcatastrophic failure occurs

A power law relationship between the crack growthratevelocity 119888 and the applied stress at the crack tip [41 4296 97] is given as

119889119888

119889119905

= 119888 = 119860(

119870119868

119870IC)

119899

(14)

This formof relation ismathematically convenient since staticand dynamic fatigue equations can be found in an analyticallyclosed form and it is mathematically compatible with theWeilbull distribution commonly used to describe the statis-tical variability in strength however it is not based on anyphysical model119860 is a preexponential term which representsthe overall crack growth depending on the environmentsand 119899 is the fatigue parameters (represents how sensitive therate is to the applied stress) [43] 119860 can be described by anArrhenius dependence on temperature The applied stresscauses the crack to extend which itself increases 119870

119868 leading

to an increase in the growth rate (13) Eventually 119870119868reaches

119870IC and failure occurs To determine the time to failure (13)and (14) can be utilized for given input parameters In mostreliability models the applied stress is assumed to be static(120590119886= constant) so that the time to failure 119905

119891 is given by [45]

119905119891=

2

1198601198842(119899 minus 2) 120590

119899

119886

(

120590119894

119870IC)

119899minus2

(15)

where 120590119894is the initial strength of the material in the absence

of the fatigue and can be referred to as the initial crack length119888119894 by (13)

119870IC119894 = 12059011989411988411988812

119894 (16)

Equation (15) is derived using the approximation that theinitial crack size 119888

119894 will be much smaller than the final crack

length 119888119891 when unstable crack growth occurs

119870IC119891 = 12059011988611988411988812

119891 (17)

52 Parisrsquo Law for Fatigue Crack Growth This law deals withthe stress intensity in association with the subcritical crackgrowth under a fatigue stressed area It is the commonlyused fatigue crack growth model in material science its basicformula corresponds with

119889119886

119889119873

= 119888Δ119870119898 (18)

where 119886 corresponds to the crack length and 119873 representsthe number of load cycles 119889119886119889119873 is the crack growth ratein other words the crack growth per increasing number ofload cycles 119888 and 119898 are the material constants and Δ119870 isthe range of the stress intensity factors which can be statedas the difference between the stress intensity factors at the


W

w

D

L

h

Comb drive

Torsional mass

Notched beam

Figure 6 SEM of the polysilicon fatigue characterization with details of notched cantilever [38]

maximum and minimum loading It can be written as Δ119870 =

119870max minus 119870min Consider the following

119870 = 120590119884radic120587119886 (19)

where 120590 is the uniform tensile stress perpendicular to thecrack plan and119884 is the dimensionless parameter that dependson the geometry The range of the stress intensity factors canbe given as

Δ119870 = Δ120590119884radic120587119886 (20)

whereΔ120590 is the range of the cycle stress amplitude and119884 takesthe value 1 for a center crack in an infinite sheet Consider thefollowing

119889119886

119889119873

= 119888Δ119870119898997904rArr 119888(Δ119884120590radic120587119886)

119898

int

119873119891

0

119889119873=int

119886119888

119902119894

119889119886

119888(Δ120590119884radic120587119886)119898997904rArr

1

119888(Δ120590119884radic120587)119898int

119886119888

119886119894

119886minus1198982

119889119886

119873119891=

2 (119886119888(2minus119898)2

minus 119886119894(2minus119898)2

)

(2 minus 119898) 119888(Δ120590119884radic120587)119898

(21)

119873119891is the remaining number of cycles to fracture 119886119888 is the

critical crack length at which instantaneous failure will occurand 119886119894 is the initial crack length at the fatigue growth thatstarts for a given stress range Δ120590 [98 99]

6 Effects of Humidity and Temperature onthe Reliability of MEMS

Single crystal silicon and polycrystalline silicon are the twomajor structural materials of MEMS devices The electricalproperties of these materials are well established howevertheir mechanical properties in analyzing the fatigue for theprediction of the lifetime of a MEMS device is still not wellunderstood Consequently the fatigue lives of silicon and

polysilicon by means of its reliance on the applied stressesunder various environmental effects have been explored[100ndash102]

Silicon was deemed to be a perfect brittle and fatiguefree material at room temperature [103] However manyresearchers have declared that single crystal silicon andpolysilicon undergoe mechanical fractures due to the fatiguegrowth rate and cyclic stresses exposed to a range of temper-ature and humid environments [104ndash106]

Humidity plays a major role in the performances of theMEMS devices particularly on the active components Thefatigue test on humidity has been presented by [107] atvarious stress levels and at a fixed 50 relative humidity(RH) on polysilicon thin films This study has presentedthat the fatigue life was found to be 106 to 1011 cycles Alsothe fatigue damage accumulation is linked with the variouslevels of humidity and its respective changes in the resonancefrequencies of devices under observation

The effects of humidity on the surface of the polysili-con thin films revealed that surface oxide layers endure asubcritical and environmentally assisted crack alternativelythick oxide layers are responsible for the crack formation ornucleation [108 109] However fatigue behavior is typicallyan outcome of subcritical cracking on the surface roughnessof MEMS devices [110]

An unorthodox approach in evaluating the fatigue ofthe polycrystalline silicon membrane and its dependenceon humidity was adopted in [111] In this setup a circularweight of 12mm in diameter was placed at the center of themembrane to control the resonance frequency stress wasgenerated by deforming themembrane oscillating the weightin and out of the plane direction The fatigue damage growthwas observed by increasing the stress on the membraneThe fatigue damage rate was low at a lower humidity andincreased with an increase in the level of humidity

The correlated effect of the temperature and humidity onamicrofabricatedMEMS structure is not known andhas beenthe interest of this study However it is a wellaccepted factthat the fatigue of a bulk material is highly dependent on thetemperature and humidity It has been shown that the activity


at the crack tip is proportional to the relative humidity inthe ambient environment [42] The expected relationshipbetween the crack growth 119860 and the temperature 119879 andhumidity 119877119867 can be given as

119860 = V119891 (119877119867) exp(minus 119876

119877119879

) (22)

In the above expression the reaction rate constant is assumedto have an apparent activation energy119876 and some functionaldependence on the humidity activity119891

119868(119877119867) V is a frequency

factor119879 is the absolute temperature and119877 is the gas constantOver the last two decades the silicon-based

MEMS devices brought a revolution in the field ofmicronanoelectromechanical systems However there is agreat need to focus on the reliability of these devices both atthe structural (geometry) and design levels Environmentaleffects on the silicon thin film at room temperature wereevaluated by [112] Their study has demonstrated how anenvironmental effect can propagate fatigue in thin filmthrough oxidation by evaluating the nanometer scale surfaceoxide layersThe tensile stress test for the single crystal silicon(SCS) thin film was carried out in a humid environment by[113] Fatigue lifetime long term prediction was performed byWeibullrsquos statistics using the maximum likelihood methodhumidity effects were observed on the scale parameter whichdecreased the strength of the thin film affecting its long termreliability However no fatigue was observed in the vacuum

A polycrystalline silicon thin film structure was observedfor fatigue analysis at room temperature in ambient air and ata compressional loading of about 40KHz The transmissionelectronmicroscopy (TEM) of the surface test sample showedthe gradual thickening of the surface oxide layers thatincreased fatigue failure concentrations Interesting observa-tions in the fatigue mechanism were recorded The resultsshowed that moisture assisted the subcritical cracking withina cyclic stress An assisted thickened layer occurred untilthe crack reached a critical size to cause a sudden failureof the entire device The reaction layer fatigue mechanismis the leading mechanism for fatigue failure in microscalepolycrystalline silicon thin film [106] Reliability also dependson the quality and strength of the material used as reportedin [114]They conducted a thorough study and suggested thatsilicon and polysilicon have the essential mechanical robust-ness for microelectromechanical applications However nosuch study was reported about the fatigue lifetime in low andhigh temperatures operating in humid environments

Tensile and bending tests for the fatigue lifetime ofpolysilicon have been regularly used by researchers Suchinvestigations were carried out in [33] for determination ofthe fracture strength and fatigue lifetime of polysilicon Thesample was examined under the influence of a 1Hz cyclictensile frequency and showed that with the decrease in thefracture stress increases the lifetime of the sampleThe fatiguelifetime of polysiliconwas tested by [115 116] with a frequencyranging from 50Hz to 6KHz Their observations concludedthat the decrease in the fracture strength resulted in anincrease in the fatigue lifetime of polysilicon however nofrequency drift was observed during the process

A piezoelectric actuator was used by [117] for the inves-tigation of the tensile testing of the structure of a Polysil-icon thin film Their mechanical arrangement consists of astationary outer frame and a movable inner frame that wereconnected in parallel through a spring The gap betweenthe two frames was carefully filled by the structure of thepolysilicon The fatigue lifetime and fracture strength wereachieved when the movable inner frame was exposed to anexternal loading

The beam bending phenomena for the prediction of thefatigue lifetime has been demonstrated by [118]with the use ofan electrostatic comb drive as a notch sample at the frequencyof 20KHz Observations showed that low stress resulted inan increase in the fatigue lifetime of the material The fatiguelifetime of polysiliconwas studied and reported in [119] underhigh frequency (sim40KHz)The experimental setup containeda sample notch cantilever beam attached to a perforated plateserving as a resonant mass The outcome of their researchshowed that reducing the stress at the root of the notch willresult in a prolonged fatigue life

A microcantilever beam with an electrostatic load wasused for the prediction of the fatigue lifetime of polysilicon[84] The mechanical arrangements consisted of a copperplate with two pads a microcantilever and the sampleWith the applications of the voltage across the samplean electrostatic load was produced resulting in a bend inthe beam Fatigue was determined by the point where thepad wedged with the copper plate and did not return toits original position The automatic testing machine (MTSTytron 250) was used for the study of the fatigue lifetimeof the polysilicon microcantilever in the bend state Thefatigue life cycles calculated were 91 times 10

5 and 153 times 107

cycles with stresses of 237 to 37 Gpa at room temperatureIt was documented that high stresses reduced fatigue life[91] A similar study has been reported for fatigue testingin a micromirror using MTS Tytron 250 microforce systemThe experimental fatigue life cycle was between 778 times 10

4

and 148 times 107 cycles at the stress level of 205 to 283GPa

[34]A study of the fatigue of polysilicon in the bend position

[88] demonstrated with the help of an electrostatic combstructure beam and movable masses that with the suppliedvoltages the movable masses oscillated and tended to bendthe beam The fatigue fracture was calculated at the cyclicloading stress of 3Gpa

An on-chip test structure was developed by [120 121]for the fatigue analysis the experimental arrangements con-tained an electrostatically driven actuator sensor movablemass (responsible of delivering force to the notched beam)and a notched beam It was demonstrated that large stressreduces the fatigue life cycle High humidity will affect thefatigue life cycle of polysilicon thin film in harsh environ-ments as reported by [122] Effects of frequency on thefatigue lifetime were experimentally demonstrated with thehelp of an atomic force microscope nanoindentation andtensile tester They demonstrated that the sample size anddeformation mode can affect the fatigue lifetime References[123 124] reported the fatigue lifetime of single crystal


silicon in bendingThe experimental analysis showed that thefrequency altered the damage growth rate and hence thelower frequencies were held responsible for reducing thefatigue lifetime of single crystal silicon

A detailed study of the fatigue lifetime of polysiliconin the bend state has been reported [125] A piezoelectricmicrocantilever was actuated on 100Hz It was observed thatthe applied stresses were inversely proportional to the fatiguelifetime of polysilicon in the bend state They have utilizedthe effects of frequency on the fatigue lifetime however theyremained quiet on the effects of the fatigue lifetime of MEMSdevice operation in low and high temperatures and a humidenvironment

The effects of humidity and temperature on the fatigue ofpolysilicon thin film were tested and reported by [126] Theyobserved the fatigue behavior of polysilicon thin film in airrelative humidity of 80 at 22∘C and using inert nitrogen gasat 22∘C and 180∘C respectively Various stress amplitudes inassociation with the number of fatigue cycles were combinedusing the statistical analysis Parisrsquo law was incorporated inorder to observe the fatigue crack extension The outcome ofthis research suggested that fatigue damage is due to repeatedloading even in inert environments they further reportedthat high temperatures increase the fatigue damage rates

In reference with the literature it has been found thatthe fatigue behavior a major reliability issue has not beenobserved at the point of clarity at high and low temperaturesThe fatigue analysis of the MEMS under the impact ofhumidity and frequency requires some attention Anotherimportant point of observation is that the correlation betweenthe temperature humidity and frequency in the fatigueanalysis has not yet been observed Standard reliability testmethods and approaches are much needed in order to bridgethe failure mechanism of MEMS devices Root causes of fail-ure of reliability in MEMS are extremely product dependentSufficient technical data has not been available on the basisof which specific and general failure mechanisms of MEMSdevices can be targeted

7 Summary

It is a fact that the MEMS market is gaining momentumReliability of MEMS devices is a well known upcomingchallenge for academia and industry It is viable to understandthe failure mechanism of MEMS devices One of the obviousfactors affecting the reliability of MEMS devices is fatigueBased on the complex nature of MEMS devices an in-depthunderstanding of the reliability both at the technologicaland environmental operational levels is essential This studyreviewed the reliability issues that have been reported inMEMS devices and mathematically measured the reliabilityin order to predict the lifetime of MEMS devices undertesting The various MEMS groups causes of failure and theprocurement of the failures were discussed

MEMS mechanical failures in light of fatigue damageaccumulation were reviewed Fatigue crack growth andits dependency on harsh environments were presented indetail Additionally apart from fatigue several approachesto improve the reliability of MEMS were enclosed these

included creep wear contamination and electrostatic dis-charges

MEMS devices were once thought to be a class of theintegrated circuits family as many of its fabrication andtesting methods were utilized in traditional ICs technologyHowever due to the unique nature of the MEMS devicesinteraction with the environment their intercomponentcommunication and identification of imminent failure theprocurement of failures are still unknown at the degree ofclarity

Most MEMS devices consist of a membrane cantileversand comb drives that present common failure mechanismsfor example fatigue and stiction Consequently a completeunderstanding of these failure mechanisms can provide aplatform to design and fabricate MEMS devices againstpotential failures Hence academicians research laboratoriesand industry can brainstorm with lifetime efficient andreliable MEMS devices This will develop the consumersrsquoconfidence on MEMS devices and thus enhance their com-mercialization

Conflict of Interests

The authors have no conflict of interests

Acknowledgment

This research is partially supported by theMinistry of HigherEducation (MOHE) under cost center 15-8200-3250135AB-124

References

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[2] S M Spearing ldquoMaterials issues in microelectromechanicalsystems (MEMS)rdquo Acta Materialia vol 48 no 1 pp 179ndash1962000

[3] O B Ozdoganlar B D Hansche and T G Carne ldquoExper-imental modal analysis for microelectromechanical systemsrdquoExperimental Mechanics vol 45 no 6 pp 498ndash506 2005

[4] R M Boysel T G McDonald G A Magel G C Smith andJ L Leonard Jr ldquoIntegration of deformable mirror deviceswith optical fibers and waveguidesrdquo in Proceedings of the 1stConference on Integrated Optics and Microstructure vol 1793pp 34ndash39 September 1992

[5] W Kuehnel and S Sherman ldquoA surface micromachined siliconaccelerometer with on-chip detection circuitryrdquo Sensors andActuators A vol 45 no 1 pp 7ndash16 1994

[6] M R Douglass ldquoDMD reliability a MEMS success storyrdquo inProceedings of SPIE vol 4980 pp 1ndash11 January 2003

[7] H Yunhan A Vasan R Doraiswami et al ldquoMEMS reliabilityreviewrdquo IEEE Transactions on Device and Materials Reliabilityvol 12 pp 482ndash493 2012

[8] S Farhad D A Hutt and D C Whalley ldquoApplication ofadhesives in MEMS and MOEMS assembly a reviewrdquo in Pro-ceedings of the 2nd International IEEE Conference on Polymers


and Adhesives inMicroelectronics and Photonics (POLYTRONICrsquo02) pp 22ndash28

[9] S T Walsh ldquoRoadmapping a disruptive technology a casestudy The emerging microsystems and top-down nanosystemsindustryrdquo Technological Forecasting and Social Change vol 71no 1-2 pp 161ndash185 2004

[10] X Li and B Bhushan ldquoFatigue studies of nanoscale structuresfor MEMSNEMS applications using nanoindentation tech-niquerdquo Surface and Coatings Technology vol 163-164 pp 521ndash526 2003

[11] T-R Hsu ldquoReliability in MEMS packagingrdquo in Proceedings ofthe 44th Annual IEEE International Reliability Physics Sympo-sium (IRPS rsquo06) pp 398ndash402 San Jose Calif USAMarch 2006

[12] O Tabata and T Tsuchiya Eds Reliability of MEMS Wiley-VCH Cambridge UK 2008

[13] W M Van Spengen ldquoMEMS reliability from a failure mecha-nisms perspectiverdquoMicroelectronics Reliability vol 43 no 7 pp1049ndash1060 2003

[14] S Ghosh and M Bayoumi ldquoOn integrated CMOS-MEMSsystem-on-chiprdquo in Proceedings of the 3rd International IEEENortheast Workshop on Circuits and Systems Conference (NEW-CAS rsquo05) pp 31ndash34 June 2005

[15] J A Walraven ldquoFuture challenges for MEMS failure analysisrdquoin Proceedings International Test Conference (ITC rsquo03) pp 850ndash855 October 2003

[16] D P Vallett ldquoFailure analysis requirements for nanoelectron-icsrdquo IEEE Transactions on Nanotechnology vol 1 no 3 pp 117ndash121 2002

[17] D J Fonseca andM Sequera ldquoOnMEMS reliability and failuremechanismsrdquo International Journal of Quality Statistics andReliability vol 2011 Article ID 820243 7 pages 2011

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[19] D M Tanner J A Walraven K Helgesen et al ldquoMEMSreliability in shock environmentsrdquo in Proceedings of the 38thIEEE International Reliability Physics Symposium pp 129ndash138San Jose Calif USA April 2000

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[22] S GuptaMEMS Need Comprehensive Market-Ready SolutionsHenkel Electronic Materials Dusseldorf Germany 2013

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[24] A Broue J Dhennin F Courtade et al ldquoCharacterizationof AuAu AuRu and RuRu ohmic contacts in MEMSswitches improved by a novel methodologyrdquo in Proceedingsof the Reliability Packaging Testing and Characterization ofMEMSMOEMS and Nanodevices IX January 2010

[25] T-M Bajenescu and M Bazu ldquoMEMS Manufacturing andreliabilityrdquoManufacturing Systems vol 7 pp 77ndash82 2012

[26] A Soma ldquoMEMS design for reliability mechanical failuremodes and testingrdquo in Proceedings of the 7th International

Conference on Perspective Technologies and Methods in MEMSDesign (MEMSTECH rsquo11) pp 91ndash101 May 2011

[27] S Tadigadapa and N Najafi ldquoReliability of microelectrome-chanical systems (MEMS)rdquo in Proceedings of the ReliabilityTesting and Characterization of MEMSMOEMS vol 4558 pp197ndash205 October 2001

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[29] X Xiong Y Wu and W Jone ldquoReliability analysis of self-repairableMEMS accelerometerrdquo in Proceedings of the 21st IEEEInternational Symposium on Defect and Fault Tolerance in VLSISystems (DFT rsquo06) pp 236ndash244 October 2006

[30] X Xiong Y Wu and W Jone ldquoMaterial fatigue and reliabilityof MEMS accelerometersrdquo in Proceedings of the 23rd IEEEInternational Symposium on Defect and Fault Tolerance in VLSISystems (DFT rsquo08) pp 314ndash322 October 2008

[31] J Bejhed ldquoActivity SummaryReliability assessment of aMEMS-based isolation valve for propulsion systemsrdquo 2011

[32] H Kam V Pott R Nathanael J Jeon E Alon and T K LiuldquoDesign and reliability of a micro-relay technology for zero-standby-power digital logic applicationsrdquo in Proceedings of theInternational Electron Devices Meeting (IEDM rsquo09) pp 1ndash4December 2009

[33] M Bazu L Galateanu and V E Ilian ldquoReliability acceleratedtests for microsystemsrdquo in Proceedings of the 34th InternationalSpring Seminar on Electronics Technology ldquoNew Trends inMicroNanotechnologyrdquo (ISSE rsquo11) pp 182ndash187 May 2011

[34] J-N Hung H Hocheng and K Sato ldquoTorsion fatigue testing ofpolycrystalline Silicon cross-micro bridge structuresrdquo JapnaeseJournal of Applied Physics vol 50 no 6 Article ID 06GM07 pp1ndash5 2011

[35] A Bemis A Ned S Stefanescu N Wilson and A KaneldquoThe effect of silicon fatigue on Kulite silicon pressure sensorrsquosreliabilityrdquo Kulite Proprietary Information 2012

[36] X J Liang and S Q Gao ldquoThe adhesion failure analysis of theMEMS gyroscope with comb capacitorrdquo in Proceedings of the8th International Conference on Reliability Maintainability andSafety (ICRMS rsquo09) pp 1234ndash1236 July 2009

[37] C Patel P McCluskey and D Lemus ldquoPerformance andreliability of MEMS gyroscopes at high temperaturesrdquo in Pro-ceedings of the 12th IEEE Intersociety Conference onThermal andThermomechanical Phenomena in Electronic Systems (IThermrsquo10) pp 1ndash5 June 2010

[38] M Budnitzki M C Scates R O Ritchie E A Stach C LMuhlstein and O N Pierron ldquoThe effects of cubic stiffnesson fatigue characterization resonator performancerdquo Sensors andActuators A vol 157 no 2 pp 228ndash234 2010

[39] D Mardivirin A Pothier M E Khatib A Crunteanu OVendier and A Blondy ldquoReliability of dielectric less electro-static actuators in RF-MEMS ohmic switchesrdquo in Proceedings ofthe European Microwave Integrated Circuit Conference (EuMICrsquo08) pp 490ndash493 October 2008

[40] F A Boloni A Benabou and A Tounzi ldquoStochastic modelingof the pull-in voltage in a MEMS beam structurerdquo IEEETransactions on Magnetics vol 47 no 5 pp 974ndash977 2011

[41] G X Li and F A Shemansky Jr ldquoDrop test and analysis onmicro-machined structuresrdquo Sensors and Actuators A vol 85no 1 pp 280ndash286 2000

[42] A Beliveau G T Spencer K A Thomas and S L RobersonldquoEvaluation of MEMS capacitive accelerometersrdquo IEEE Designamp Test of Computers vol 16 no 4 pp 48ndash56 1999


[43] T G Brown B Davis D Hepner et al ldquoStrap-downmicroelec-tromechanical (MEMS) sensors for high-G munition applica-tionsrdquo IEEE Transactions on Magnetics vol 37 no 1 pp 336ndash342 2001

[44] X Fang Q Huang and J Tang ldquoModeling of MEMS reliabilityin shock environmentsrdquo in Proceedings of the 7th InternationalConference on Solid-State and Integrated Circuits TechnologyProceedings (ICSICT rsquo04) pp 860ndash863 October 2004

[45] Q Zhang X Guo Y Liu N Dai and P Lu ldquoCorrosion andfatigue in micro-sized Ni cantilever beamsrdquo Transactions ofNonferrous Metals Society of China vol 17 pp 213ndash217 2007

[46] ldquoMetals handbook (desk edition) chapter 32 (failure analysis)rdquoin American Society for Metals vol 32 pp 24ndash26 ASMInternational Novelty Ohio USA 1997

[47] T Yi and C Kim ldquoMeasurement of mechanical properties forMEMSmaterialsrdquoMeasurement Science and Technology vol 10no 8 pp 706ndash716 1999

[48] S M Ali and L M Phinney ldquoInvestigation of adhesion duringoperation ofMEMS cantileversrdquo inProceedings of the ReliabilityTesting and Characterization of MEMSMOEMS III pp 215ndash226 January 2004

[49] N S Tambe and B Bhushan ldquoScale dependence ofmicronano-friction and adhesion of MEMSNEMS materials coatings andlubricantsrdquo Nanotechnology vol 15 no 11 pp 1561ndash1570 2004

[50] J K Luo YQ FuHR Le J AWilliams SM Spearing andWI Milne ldquoDiamond and diamond-like carbon MEMSrdquo Journalof Micromechanics and Microengineering vol 17 supplement 7pp S147ndashS184 2007

[51] S A Smallwood K C Eapen S T Patton and J S ZabinskildquoPerformance results of MEMS coated with a conformal DLCrdquoWear vol 260 no 11-12 pp 1179ndash1189 2006

[52] Z Guo Z Feng S Fan D Zheng and H Zhuang ldquoResearchdevelopment ofmeasuringmethods on the tribology charactersfor movable MEMS devices a reviewrdquo Microsystem Technolo-gies vol 15 no 3 pp 343ndash354 2009

[53] J A Walraven ldquoFailure mechanisms in MEMSrdquo in ProceedingsInternational Test Conference (ITC rsquo03) pp 828ndash833 October2003

[54] C Duvvury and A Amerasekera ldquoESD A pervasive reliabilityconcern for IC technologiesrdquoProceedings of the IEEE vol 81 no5 pp 690ndash702 1993

[55] G M Rebeiz and J B Muldavin ldquoRF MEMS switches andswitch circuitsrdquo IEEEMicrowaveMagazine vol 2 no 4 pp 59ndash71 2001

[56] J DeNatale R Mihailovich and J Waldrop ldquoTechniques forreliability analysis of MEMS RF switchrdquo in Proceedings ofthe 2002 40th annual IEEE International Relaibility PhysicsSymposium pp 116ndash117 April 2002

[57] M Kaynak F Korndorfer M Wietstruck et al ldquoRobustnessand reliability of BiCMOS embeddedRF-MEMS switchrdquo inPro-ceedings of the IEEE 11th Topical Meeting on Silicon MonolithicIntegrated Circuits in RF Systems (SiRF rsquo11) pp 177ndash180 January2011

[58] B Stark Ed MEMS Reliability Assurance Guidelines for SpaceApplications JPL Publication Pasadena Calif USA 1999

[59] S S McClure L D Edmonds R Mihailovich et al ldquoRadiationeffects inmicro-electromechanical systems (MEMS) RF relaysrdquoIEEE Transactions on Nuclear Science vol 49 no 6 pp 3197ndash3202 2002

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IEEEMicrowave andWireless Components Letters vol 18 no 2pp 100ndash102 2008

[61] I D WolfMEMS Reliability Testing Micro and Nano SystemsLanchaster UK 2007

[62] R Pathak S Joshi and D K Mishra ldquoDistributive computingfor reliability analysis of MEMS devices using MATLABrdquo inProceedings of the International Conference on Advances inComputing Communication and Control (ICAC rsquo09) pp 246ndash250 January 2009

[63] Q Sun Y Tang J Feng and P Kvam ldquoStress-lifetime jointdistributionmodel for performance degradation failurerdquo inPro-ceedings of the International Conference on Quality ReliabilityRisk Maintenance and Safety Engineering (ICQR2MSE rsquo11) pp308ndash311 June 2011

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[68] D M Tanner J A Walraven L W Irwin et al ldquoEffectof humidity on the reliability of a surface micromachinedmicroenginerdquo in Proceedings of the 1999 37th Annual IEEEInternational Reliability Physics Symposium pp 189ndash197 SanDiego Calif USA March 1999

[69] F Su W Hwang A Mukherjee and K Chakrabarty ldquoDefect-oriented testing and diagnosis of digital microfluidics-basedbiochipsrdquo in Proceedings of the IEEE International Test Confer-ence (ITC rsquo05) pp 487ndash496 November 2005

[70] H Kapels R Aigner and J Binder ldquoFracture strength andfatigue of polysilicon determined by a novel thermal actuatorrdquoIEEE Transactions on Electron Devices vol 47 no 7 pp 1522ndash1528 2000

[71] M van Gils J Bielen and G McDonald ldquoEvaluation of creepin RF MEMS devicesrdquo in Proceedings of the International Con-ference on Thermal Mechanical and Multi-Physics SimulationExperiments in Microelectronics and Micro-Systems (EuroSimersquo07) pp 1ndash7 April 2007

[72] QMin J Tao Y Zhang and X Chen ldquoA parallel-plate actuatedtest structure for fatigue analysis of MEMSrdquo in Proceedingsof the International Conference on Quality Reliability RiskMaintenance and Safety Engineering (ICQR2MSE rsquo11) pp 297ndash301 June 2011

[73] S M Ali S C Mantell and E K Longmire ldquoExperimentaltechnique for fatigue testing of MEMS in liquidsrdquo Journal ofMicroelectromechanical Systems vol 21 no 3 pp 520ndash522 2012




[76] P Yang and N Liao ldquoSurface sliding simulation in micro-gear train for adhesion problem and tribology design by usingmolecular dynamics modelrdquo Computational Materials Sciencevol 38 no 4 pp 678ndash684 2007

[77] J A Walraven ldquoFailure analysis issues in microelectromechan-ical systems (MEMS)rdquo Microelectronics Reliability vol 45 no9ndash11 pp 1750ndash1757 2005

[78] H R Shea A Gasparyan H B Chan et al ldquoEffects of electricalleakage currents on MEMS reliability and performancerdquo IEEETransactions onDevice andMaterials Reliability vol 4 no 2 pp198ndash207 2004

[79] S W Yoona S Leea and K Najafia ldquoVibration-induced errorsinMEMS tuning fork gyroscopesrdquo Sensors and Actuators A vol180 pp 32ndash44 2012

[80] O Matviykiv and M Lobur ldquoDesign principles and sensitivityanalysis of MEMS cantilever sensorsrdquo in Proceedings of the6th International Conference of Young Scientists ldquoPerspectiveTechnologies and Methods in MEMS Designrdquo (MEMSTECH rsquo10)pp 230ndash232 April 2010

[81] P S Thakur K Sugano T Tsuchiya and O Tabata ldquoAnalysisof acceleration sensitivity in MEMS tuning fork gyroscoperdquoin Proceedings of the 16th International Solid-State SensorsActuators and Microsystems Conference (TRANSDUCERS rsquo11)pp 2006ndash2009 June 2011

[82] G Baeten and H van der Heijden ldquoImproving SN for highfrequenciesrdquo Leading Edge vol 27 no 2 pp 144ndash153 2008

[83] M T Jan A Iqbal andM Shoaib ldquoAn unconventional methodfor exploration of oil and gasrdquo in Proceedings of the InternationalConference on Emerging Technologies (ICET rsquo12) pp 1ndash5 2012

[84] Y C Lin H Hocheng W L Fang and R Chen ldquoFabricationand fatigue testing of an electrostatically drivenmicrocantileverbeamrdquoMaterials and Manufacturing Processes vol 21 no 1 pp75ndash80 2006

[85] P Shrotriya S M Allameh and W O Soboyejo ldquoOn the evo-lution of surface morphology of polysilicon MEMS structuresduring fatiguerdquoMechanics of Materials vol 36 no 1-2 pp 35ndash44 2004

[86] T Tsuchiya A Inoue J Sakata M Hashimoto A Yokoyameand M Sugimoto ldquoFatigue test of single crystal silicon res-onatorrdquo in Proceedings of the Technical Digest of the 11th SensorSymposium pp 277ndash280 Tokyo Japan 1998

[87] T Ikehara and T Tsuchiya ldquoLow-cycle to ultrahigh-cyclefatigue lifetime measurement of single-crystal-silicon speci-mens using a microresonator test devicerdquo Journal of Microelec-tromechanical Systems vol 21 no 4 pp 830ndash840 2012

[88] R E Boroch R Muller-Fiedler J Bagdahn and P GumbschldquoHigh-cycle fatigue and strengthening in polycrystalline sili-conrdquo Scripta Materialia vol 59 no 9 pp 936ndash940 2008

[89] G Langfelder A Longoni F Zaraga A Corigliano A Ghisiand A Merassi ldquoA new on-chip test structure for real timefatigue analysis in polysilicon MEMSrdquo Microelectronics Relia-bility vol 49 no 2 pp 120ndash126 2009

[90] H Kahn R Ballarini and A H Heuer ldquoDynamic fatigue ofsiliconrdquo Current Opinion in Solid State and Materials Sciencevol 8 no 1 pp 71ndash76 2004

[91] H Hong J Hung and Y Guu ldquoVarious fatigue testing of poly-crystalline silicon microcantilever beam in bendingrdquo JapaneseJournal of Applied Physics vol 47 no 6 pp 5256ndash5261 2008

[92] K Bhalerao A B O Soboyejo and W O Soboyejo ldquoModelingof fatigue in polysiliconMEMS structuresrdquo Journal of MaterialsScience vol 38 no 20 pp 4157ndash4161 2003

[93] B Jalalahmadi F Sadeghi andD Peroulis ldquoA numerical fatiguedamage model for life scatter of MEMS devicesrdquo Journal ofMicroelectromechanical Systems vol 18 no 5 pp 1016ndash10312009

[94] S M Allameh B Gally S Brown andW O Soboyejo ldquoSurfacetopology and fatigue in Si MEMS structuresrdquo in Proceedingsof the Mechanical Properties of Structural Films pp 3ndash15November 2000

[95] Y-l lee J Pan RHathaway andM Barkey Eds Fatigue Testingand Analysis (Theory and Practice) Butterworth-HeinemannElsevier New York NY USA 2005

[96] WW van Arsdell and S B Brown ldquoSubcritical crack growth insilicon MEMSrdquo Journal of Microelectromechanical Systems vol8 no 3 pp 319ndash327 1999

[97] R Zheng and A Pendharkar ldquoObstacle discovery in distributedactive sensor networksrdquo in Proceedings of the 28th Conference onComputer Communications (IEEE INFOCOM rsquo09) pp 909ndash917April 2009

[98] N Pugno M Ciavarella P Cornetti and A Carpinteri ldquoAgeneralized Parisrsquo law for fatigue crack growthrdquo Journal of theMechanics and Physics of Solids vol 54 no 7 pp 1333ndash13492006

[99] S J Chu and C Liu ldquoFinite element simulation of fatigue crackgrowth determination of the Paris exponentrdquo in Proceedings ofthe 6th International Forum on Strategic Technology (IFOST rsquo11)pp 15ndash19 August 2011

[100] A D Romig Jr M T Dugger and P J McWhorter ldquoMaterialsissues in microelectromechanical devices science engineeringmanufacturability and reliabilityrdquoActaMaterialia vol 51 no 19pp 5837ndash5866 2003

[101] Z Stanimirovic and I Stanimirovic ldquoMechanical characteriza-tion ofMEMSmaterialsrdquo inProceedings of the 28th InternationalConference on Microelectronics (MIEL) pp 177ndash179 2012

[102] A B O Soboyejo K D Bhalerao and W O SoboyejoldquoReliability assessment of polysilicon MEMS structures undermechanical fatigue loadingrdquo Journal of Materials Science vol38 no 20 pp 4163ndash4167 2003

[103] K E Petersen ldquoSilicon as a mechanical materialrdquo Proceedings ofthe IEEE vol 70 no 5 pp 420ndash457 1982

[104] T Ikehara and T Tsuchiya ldquoHigh-cycle fatigue of microma-chined single-crystal silicon measured using high-resolutionpatterned specimensrdquo Journal of Micromechanics and Micro-engineering vol 18 no 7 Article ID075004 pp 1371ndash1386 2008

[105] C L Muhlstein R T Howe and R O Ritchie ldquoFatigueof polycrystalline silicon for microelectromechanical systemapplications crack growth and stability under resonant loadingconditionsrdquo Mechanics of Materials vol 36 no 1-2 pp 13ndash332004

[106] D H Alsem R Timmerman B L Boyce E A Stach J TM De Hosson and R O Ritchie ldquoVery high-cycle fatiguefailure in micron-scale polycrystalline silicon films effects ofenvironment and surface oxide thicknessrdquo Journal of AppliedPhysics vol 101 no 1 Article ID 013515 2007

[107] O N Pierron and C L Muhlstein ldquoNotch root oxide formationduring fatigue of polycrystalline silicon structural filmsrdquo Jour-nal of Microelectromechanical Systems vol 16 no 6 pp 1441ndash1450 2007

[108] C L Muhlstein E A Stach and R O Ritchie ldquoA reaction-layermechanism for the delayed failure of micron-scale polycrys-talline silicon structural films subjected to high-cycle fatigueloadingrdquo Acta Materialia vol 50 no 14 pp 3579ndash3595 2002


[109] H Kahn R Ballarini J J Bellante and A H Heuer ldquoFatiguefailure in polysilicon not due to simple stress corrosion crack-ingrdquo Science vol 298 no 5596 pp 1215ndash1218 2002

[110] S M Allameh P Shrotriya A Butterwick S B Brown and WO Soboyejo ldquoSurface topography evolution and fatigue fracturein polysilicon MEMS structuresrdquo Journal of Microelectrome-chanical Systems vol 12 no 3 pp 313ndash324 2003

[111] S Yamashita H Wado Y Takeuchi T Tsuchiya and OTabata ldquoFatigue characteristics of polycrystalline silicon thin-film membrane and its dependence on humidityrdquo Journal ofMicromechanics and Microengineering vol 23 no 3 pp 1ndash112013

[112] p olovier ldquoEnvironmental contributions to fatigue failure ofmicron-scale silicon films used in microelectromechanicalsystem (MEMS) devicesrdquo Intercollege Graduate Program inMaterials The Pennsylvania State University University ParkPa USA 2005

[113] Y Yamaji K Sugano O Tabata and T Tsuchiya ldquoTensile-modefatigue tests and fatigue life predictions of single crystal siliconin humidity controlled environmentsrdquo in Proceedings of the20th IEEE International Conference onMicro ElectroMechanicalSystems (MEMS rsquo07) pp 267ndash270 January 2007

[114] P M Sousa V Chu and J P Conde ldquoReliability and stabilityof thin-film amorphous silicon MEMS resonatorsrdquo Journal ofMicromechanics and Microengineering vol 22 no 6 pp 1ndash82012

[115] W N Sharpe Jr J Bagdahn K Jackson and G ColesldquoTensile testing of MEMSmaterials-recent progressrdquo Journal ofMaterials Science vol 38 no 20 pp 4075ndash4079 2003

[116] J Bagdahn and W N Sharpe Jr ldquoFatigue of polycrystallinesilicon under long-term cyclic loadingrdquo Sensors and ActuatorsA vol 103 no 1-2 pp 9ndash15 2003

[117] S Kamiya S Amaki T Kawai et al ldquoSeamless interpretation ofthe strength and fatigue lifetime of polycrystalline silicon thinfilmsrdquo Journal of Micromechanics and Microengineering vol 18no 9 Article ID 095023 2008

[118] H Kahn R Ballarini R L Mullen and A H Heuer ldquoElectro-statically actuated failure ofmicrofabricated polysilicon fracturemechanics specimensrdquo Proceedings of the Royal Society A vol455 no 1990 pp 3807ndash3823 1999

[119] C L Muhlstein S B Brown and R O Ritchie ldquoHigh-cyclefatigue and durability of polycrystalline silicon thin films inambient airrdquo Sensors and Actuators A vol 94 no 3 pp 177ndash1882001

[120] A M Fitzgerald D M Pierce B M Huigens and C D WhiteldquoA general methodology to predict the reliability of single-crystal silicon MEMS devicesrdquo Journal of Microelectromechani-cal Systems vol 18 no 4 pp 962ndash970 2009

[121] T Ikehara and T Tsuchiya ldquoHigh-cycle fatigue of microma-chined single crystal silicon measured using a parallel fatiguetest systemrdquo IEICE Electronics Express vol 4 no 9 pp 288ndash2932007

[122] M Budnitzki andO N Pierron ldquoHighly localized surface oxidethickening on polycrystalline silicon thin films during cyclicloading in humid environmentsrdquo Acta Materialia vol 57 no10 pp 2944ndash2955 2009

[123] E K Baumert P-O Theillet and O N Pierron ldquoInvestigationof the low-cycle fatiguemechanism formicron-scalemonocrys-talline silicon filmsrdquo Acta Materialia vol 58 no 8 pp 2854ndash2863 2010

[124] T Namazu and Y Isono ldquoFatigue life prediction citerion formicro-nanoscale single-crystal silicon structuresrdquo Journal ofMicroelectromechanical Systems vol 18 no 1 pp 129ndash137 2009

[125] J-N Hung and H Hocheng ldquoFrequency effects and life predic-tion of polysilicon microcantilever beams in bending fatiguerdquoJournal of MicroNanolithography MEMS and MOEMS vol 11no 2 Article ID 021206 2012

[126] S Kamiya Y Ikeda J Gaspar and O Paul ldquoEffect of humidityand temperature on the fatigue behavior of polysilicon thinfilmrdquo Sensors and Actuators A vol 170 no 1-2 pp 187ndash195 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



the academicians research laboratories and industry how-ever in spite of its global recognition the reliable designof MEMS devices is one of the main challenges in thecommercialization of these devices [11ndash13] The reliabilityof MEMS is neither well established nor recognized by theindustry and academia [14] and is accepted as a relatively newand challenging field for research In the long run MEMSmay support novel classes of exceptionally small fast self-managing and cost effective devices [14] In order to gain ahigh volume market place it is essential that MEMS devicesshould be of competitive reliability

The main goal of reliable MEMS designing is to comeup with devices having mechanical components as reliable asits electrical parts Since MEMS technology is growing andmany more applications are entering into the mainstream ofMEMS devices it is important to understand the reliabilityissues in these devices Research in MEMS is mainly focusedon the design methodologies and fabrication techniques inorder to produce miniature and effective MEMS devices[15ndash17] Because of the basic building structure of MEMSthe working environments of MEMS sensors and actuatorsmay not be suitable for the electronics counterpart of thewhole assembly and hence can affect its performance Thereliability of MEMS devices has not been addressed asa major degradation factor in the performances of thesedevices at commercial as well as at consumer levels [11] InMEMS technology the trend towards constantly reducingthe size and volume intercommunication and multipledimensions is making them as devices of choice Howeverthe failure of the mechanisms due to the introduction of newprocesses designs and materials as well as the fabricationtechniques is making MEMS devices unreliable [18 19]Product replacement costs have driven the need for improvedreliability which has led to design tradeoffs [20] On theother hand reliability is a challenge forMEMSmanufacturersdue to the growing market and stricter government safetyregulations [17] MEMS applications are expanding in factthe MEMS market is currently double that of ICs and isexpected to be US$20 billion in 2017 [21] All MEMS deviceshave dissimilar applications nevertheless they share somecommon requirements such as (1) time to market that leadsto success (2) stress reduction and (3) reliability of MEMSbeing critical [22]

Design optimization of MEMS sensors and actuatorsis critical due to high cost lengthy fabrication processesVagueness in the fabrication and etching processes used tomanufacture MEMS devices can lead to certain uncertaintiesin the performance of final product consequently obtaininglow yield and poor reliability [23] The reliability study ofMEMS devices is therefore essential Due to complex natureof MEMS devices the reliability must be considered as aseparate field of research The research on reliability willgrow as theMEMS technology attains its height Temperatureand humidity are reported as two major reliability issuesof MEMS devices [24] The reason is that there are manysensors and actuators that are exposed to the harsh environ-ments such as accelerometers gyroscopes thermal actuatorsand chemical sensors This paper mainly discusses fatiguegeneration and the operational and environmental effects

on the performances of cantilever-based MEMS devicesParticularly fatigue being a material reliability issue that hin-ders the performance of cantilevers-based MEMS is focusedon Fatigue induced due to the crack growth rate and thelifetime of MEMS devices can be modeled through statisticaldistribution functions and Parisrsquo law

This paper presents a review of the current literature onthe reliability of MEMS Section 2 discusses reliability andits importance Section 3 describes the failure mechanisms ofMEMS devices followed by fatigue and then the crack growthmodeling of fatigue A thorough review of the environmentaleffects on the cantilever-based MEMS devices is presented inSection 4

2 Reliability

Due to the most promising technology of the modernengineering sciences MEMS has brought revolution to thesilicon industry Most of the MEMS components are beingfabricated using silicon and its oxides However regardless ofthe brighter future ofMEMS itmaterializes to be in an alarm-ing state In order to underline MEMS reliability concernsit is endeavored that a complete knowledge of the failuremechanism (physics and statistics) is fully understood Dueto continued intensification of the MEMS family the overallcosts of manufacturing failure rates and its performancesover the accepted period of time (reliability) are the signifi-cant issues that can be resolved at the time of manufacturingBeing an emerging technology MEMS reliability is of primeimportance in applications where the failure can be fataland shocking [25] A variety of materials are used in thefabrication of MEMS devices Materials showing improvedtendency in the direction of high reliability and long termsurvivability are taken as the material of choice even if itincreases the overall cost of the device [26]

MEMS manufacturers are going to come across a chal-lenging task in addressing the reliability of MEMS devicesfor the reason of their versatility both at the production andapplication levels [17] Reliability is the ability of a MEMSdevice to perform its intended function without failureunder stated conditions for a particular period of time Theperformance of MEMS devices is highly dependent on thecompatibility of several static and moving parts the designand the selection of materials where the device can performthe desired function with long term repeatability and accu-racy [27] The growing density of MEMS products demandsfor multiple functions on the same chip and its operation inmultiple domains are indeed making the reliability of MEMSdevices a challenging task Traditional approaches are beingused for the design and fabrication ofMEMS devices and lessattention has been diverted to address the reliability issues[27] As reliability is becoming the subject of research for theupcoming MEMS generation emphasis on the identificationand rectification of the reliability issues of MEMS devices isa big issue for the researchers academicians and industryParticularly the mechanical reliability of the material ofwhich MEMS devices are being fabricated is one of themost important aspects when dealing with reliability of thesedevices Therefore it is being treated as a new phenomenon








Si

Initial crack


SiO2F










119865 (119905) = int

119905

0

119891 (1199051015840) 1198891199051015840

119891 (119905) =

119889

119889119905

119865 (119905)

(2)


ℎ (119905) =

119891 (119905)

119877 (119905)

=

119891 (119905)

1 minus 119865 (119905)

(3)

Wear outUseful life

Infant mortality

Time

Failu

re ra

te


or

ℎ (119905) = minus

1

119877 (119905)

119889119877 (119905)

119889119905

(4)

or

ℎ (119905) = minus

119889

119889119905

ln119877 (119905) (5)


119867(119905) = int

119905

0

ℎ (1199051015840) 119889119905 = minus ln119877 (119905) (6)



infin

0

119905119891 (119905) 119889119905 (7)







119877 (119905) = 119890minus120582119905

119865 (119905) = 1 minus 119890minus120582119905

119891 (119905) = 120582119890minus120582119905

(8)


MTTF =

1

120582

(9)


119877 (119905) = 119890minus(1120572)

120573

997904rArr

119891 (119905)

ℎ (119905)

(10)


119891 (119905) =

120573

119905

(

119905

120572

)

120573

119890minus(119905120572)

120573

(11)



119891 (119905) =

1

120590119905radic2120587

119890(minus(ln(119905)minusln(11987950))221205902)

119865 (119905) int

119879

0

1

120590119905radic2120587

119890(minus(ln(119905)minusln(11987950))221205902)

119889119905

(12)




120120583m
















5 Fatigue in MEMS







Group 1




[69]

Group 1 or 2


friction




[28ndash30 33 34]

Group 2


friction


[35]



[36 37]

Group 3



[70ndash72]




[31 73]


and charging



Table 1 Continued


Group 4



[39 74 75]






[7]














contact


force


surfaces



deform


Causes






sliding









Powerconsumption

Frequencyrange











119870119868= 120590119884119888

12 (13)






119889119888

119889119905

= 119888 = 119860(

119870119868

119870IC)

119899

(14)


119868 leading



119891 is given by [45]

119905119891=

2

1198601198842(119899 minus 2) 120590

119899

119886

(

120590119894

119870IC)

119899minus2

(15)



119870IC119894 = 12059011989411988411988812

119894 (16)




119870IC119891 = 12059011988611988411988812

119891 (17)


119889119886

119889119873

= 119888Δ119870119898 (18)



W

w

D

L

h

Comb drive

Torsional mass

Notched beam




119870 = 120590119884radic120587119886 (19)


Δ119870 = Δ120590119884radic120587119886 (20)


119889119886

119889119873

= 119888Δ119870119898997904rArr 119888(Δ119884120590radic120587119886)

119898

int

119873119891

0

119889119873=int

119886119888

119902119894

119889119886

119888(Δ120590119884radic120587119886)119898997904rArr

1

119888(Δ120590119884radic120587)119898int

119886119888

119886119894

119886minus1198982

119889119886

119873119891=

2 (119886119888(2minus119898)2

minus 119886119894(2minus119898)2

)

(2 minus 119898) 119888(Δ120590119884radic120587)119898

(21)













119860 = V119891 (119877119867) exp(minus 119876

119877119879

) (22)


119868(119877119867) V is a frequency








5 and 153 times 107


4










7 Summary








Acknowledgment


References








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















Si

Initial crack


SiO2F










119865 (119905) = int

119905

0

119891 (1199051015840) 1198891199051015840

119891 (119905) =

119889

119889119905

119865 (119905)

(2)


ℎ (119905) =

119891 (119905)

119877 (119905)

=

119891 (119905)

1 minus 119865 (119905)

(3)

Wear outUseful life

Infant mortality

Time

Failu

re ra

te


or

ℎ (119905) = minus

1

119877 (119905)

119889119877 (119905)

119889119905

(4)

or

ℎ (119905) = minus

119889

119889119905

ln119877 (119905) (5)


119867(119905) = int

119905

0

ℎ (1199051015840) 119889119905 = minus ln119877 (119905) (6)



infin

0

119905119891 (119905) 119889119905 (7)







119877 (119905) = 119890minus120582119905

119865 (119905) = 1 minus 119890minus120582119905

119891 (119905) = 120582119890minus120582119905

(8)


MTTF =

1

120582

(9)


119877 (119905) = 119890minus(1120572)

120573

997904rArr

119891 (119905)

ℎ (119905)

(10)


119891 (119905) =

120573

119905

(

119905

120572

)

120573

119890minus(119905120572)

120573

(11)



119891 (119905) =

1

120590119905radic2120587

119890(minus(ln(119905)minusln(11987950))221205902)

119865 (119905) int

119879

0

1

120590119905radic2120587

119890(minus(ln(119905)minusln(11987950))221205902)

119889119905

(12)




120120583m
















5 Fatigue in MEMS







Group 1




[69]

Group 1 or 2


friction




[28ndash30 33 34]

Group 2


friction


[35]



[36 37]

Group 3



[70ndash72]




[31 73]


and charging



Table 1 Continued


Group 4



[39 74 75]






[7]














contact


force


surfaces



deform


Causes






sliding









Powerconsumption

Frequencyrange











119870119868= 120590119884119888

12 (13)






119889119888

119889119905

= 119888 = 119860(

119870119868

119870IC)

119899

(14)


119868 leading



119891 is given by [45]

119905119891=

2

1198601198842(119899 minus 2) 120590

119899

119886

(

120590119894

119870IC)

119899minus2

(15)



119870IC119894 = 12059011989411988411988812

119894 (16)




119870IC119891 = 12059011988611988411988812

119891 (17)


119889119886

119889119873

= 119888Δ119870119898 (18)



W

w

D

L

h

Comb drive

Torsional mass

Notched beam




119870 = 120590119884radic120587119886 (19)


Δ119870 = Δ120590119884radic120587119886 (20)


119889119886

119889119873

= 119888Δ119870119898997904rArr 119888(Δ119884120590radic120587119886)

119898

int

119873119891

0

119889119873=int

119886119888

119902119894

119889119886

119888(Δ120590119884radic120587119886)119898997904rArr

1

119888(Δ120590119884radic120587)119898int

119886119888

119886119894

119886minus1198982

119889119886

119873119891=

2 (119886119888(2minus119898)2

minus 119886119894(2minus119898)2

)

(2 minus 119898) 119888(Δ120590119884radic120587)119898

(21)













119860 = V119891 (119877119867) exp(minus 119876

119877119879

) (22)


119868(119877119867) V is a frequency








5 and 153 times 107


4










7 Summary








Acknowledgment


References








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














119865 (119905) = int

119905

0

119891 (1199051015840) 1198891199051015840

119891 (119905) =

119889

119889119905

119865 (119905)

(2)


ℎ (119905) =

119891 (119905)

119877 (119905)

=

119891 (119905)

1 minus 119865 (119905)

(3)

Wear outUseful life

Infant mortality

Time

Failu

re ra

te


or

ℎ (119905) = minus

1

119877 (119905)

119889119877 (119905)

119889119905

(4)

or

ℎ (119905) = minus

119889

119889119905

ln119877 (119905) (5)


119867(119905) = int

119905

0

ℎ (1199051015840) 119889119905 = minus ln119877 (119905) (6)



infin

0

119905119891 (119905) 119889119905 (7)







119877 (119905) = 119890minus120582119905

119865 (119905) = 1 minus 119890minus120582119905

119891 (119905) = 120582119890minus120582119905

(8)


MTTF =

1

120582

(9)


119877 (119905) = 119890minus(1120572)

120573

997904rArr

119891 (119905)

ℎ (119905)

(10)


119891 (119905) =

120573

119905

(

119905

120572

)

120573

119890minus(119905120572)

120573

(11)



119891 (119905) =

1

120590119905radic2120587

119890(minus(ln(119905)minusln(11987950))221205902)

119865 (119905) int

119879

0

1

120590119905radic2120587

119890(minus(ln(119905)minusln(11987950))221205902)

119889119905

(12)




120120583m
















5 Fatigue in MEMS







Group 1




[69]

Group 1 or 2


friction




[28ndash30 33 34]

Group 2


friction


[35]



[36 37]

Group 3



[70ndash72]




[31 73]


and charging



Table 1 Continued


Group 4



[39 74 75]






[7]














contact


force


surfaces



deform


Causes






sliding









Powerconsumption

Frequencyrange











119870119868= 120590119884119888

12 (13)






119889119888

119889119905

= 119888 = 119860(

119870119868

119870IC)

119899

(14)


119868 leading



119891 is given by [45]

119905119891=

2

1198601198842(119899 minus 2) 120590

119899

119886

(

120590119894

119870IC)

119899minus2

(15)



119870IC119894 = 12059011989411988411988812

119894 (16)




119870IC119891 = 12059011988611988411988812

119891 (17)


119889119886

119889119873

= 119888Δ119870119898 (18)



W

w

D

L

h

Comb drive

Torsional mass

Notched beam




119870 = 120590119884radic120587119886 (19)


Δ119870 = Δ120590119884radic120587119886 (20)


119889119886

119889119873

= 119888Δ119870119898997904rArr 119888(Δ119884120590radic120587119886)

119898

int

119873119891

0

119889119873=int

119886119888

119902119894

119889119886

119888(Δ120590119884radic120587119886)119898997904rArr

1

119888(Δ120590119884radic120587)119898int

119886119888

119886119894

119886minus1198982

119889119886

119873119891=

2 (119886119888(2minus119898)2

minus 119886119894(2minus119898)2

)

(2 minus 119898) 119888(Δ120590119884radic120587)119898

(21)













119860 = V119891 (119877119867) exp(minus 119876

119877119879

) (22)


119868(119877119867) V is a frequency








5 and 153 times 107


4










7 Summary








Acknowledgment


References








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119877 (119905) = 119890minus120582119905

119865 (119905) = 1 minus 119890minus120582119905

119891 (119905) = 120582119890minus120582119905

(8)


MTTF =

1

120582

(9)


119877 (119905) = 119890minus(1120572)

120573

997904rArr

119891 (119905)

ℎ (119905)

(10)


119891 (119905) =

120573

119905

(

119905

120572

)

120573

119890minus(119905120572)

120573

(11)



119891 (119905) =

1

120590119905radic2120587

119890(minus(ln(119905)minusln(11987950))221205902)

119865 (119905) int

119879

0

1

120590119905radic2120587

119890(minus(ln(119905)minusln(11987950))221205902)

119889119905

(12)




120120583m
















5 Fatigue in MEMS







Group 1




[69]

Group 1 or 2


friction




[28ndash30 33 34]

Group 2


friction


[35]



[36 37]

Group 3



[70ndash72]




[31 73]


and charging



Table 1 Continued


Group 4



[39 74 75]






[7]














contact


force


surfaces



deform


Causes






sliding









Powerconsumption

Frequencyrange











119870119868= 120590119884119888

12 (13)






119889119888

119889119905

= 119888 = 119860(

119870119868

119870IC)

119899

(14)


119868 leading



119891 is given by [45]

119905119891=

2

1198601198842(119899 minus 2) 120590

119899

119886

(

120590119894

119870IC)

119899minus2

(15)



119870IC119894 = 12059011989411988411988812

119894 (16)




119870IC119891 = 12059011988611988411988812

119891 (17)


119889119886

119889119873

= 119888Δ119870119898 (18)



W

w

D

L

h

Comb drive

Torsional mass

Notched beam




119870 = 120590119884radic120587119886 (19)


Δ119870 = Δ120590119884radic120587119886 (20)


119889119886

119889119873

= 119888Δ119870119898997904rArr 119888(Δ119884120590radic120587119886)

119898

int

119873119891

0

119889119873=int

119886119888

119902119894

119889119886

119888(Δ120590119884radic120587119886)119898997904rArr

1

119888(Δ120590119884radic120587)119898int

119886119888

119886119894

119886minus1198982

119889119886

119873119891=

2 (119886119888(2minus119898)2

minus 119886119894(2minus119898)2

)

(2 minus 119898) 119888(Δ120590119884radic120587)119898

(21)













119860 = V119891 (119877119867) exp(minus 119876

119877119879

) (22)


119868(119877119867) V is a frequency








5 and 153 times 107


4










7 Summary








Acknowledgment


References








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















5 Fatigue in MEMS







Group 1




[69]

Group 1 or 2


friction




[28ndash30 33 34]

Group 2


friction


[35]



[36 37]

Group 3



[70ndash72]




[31 73]


and charging



Table 1 Continued


Group 4



[39 74 75]






[7]














contact


force


surfaces



deform


Causes






sliding









Powerconsumption

Frequencyrange











119870119868= 120590119884119888

12 (13)






119889119888

119889119905

= 119888 = 119860(

119870119868

119870IC)

119899

(14)


119868 leading



119891 is given by [45]

119905119891=

2

1198601198842(119899 minus 2) 120590

119899

119886

(

120590119894

119870IC)

119899minus2

(15)



119870IC119894 = 12059011989411988411988812

119894 (16)




119870IC119891 = 12059011988611988411988812

119891 (17)


119889119886

119889119873

= 119888Δ119870119898 (18)



W

w

D

L

h

Comb drive

Torsional mass

Notched beam




119870 = 120590119884radic120587119886 (19)


Δ119870 = Δ120590119884radic120587119886 (20)


119889119886

119889119873

= 119888Δ119870119898997904rArr 119888(Δ119884120590radic120587119886)

119898

int

119873119891

0

119889119873=int

119886119888

119902119894

119889119886

119888(Δ120590119884radic120587119886)119898997904rArr

1

119888(Δ120590119884radic120587)119898int

119886119888

119886119894

119886minus1198982

119889119886

119873119891=

2 (119886119888(2minus119898)2

minus 119886119894(2minus119898)2

)

(2 minus 119898) 119888(Δ120590119884radic120587)119898

(21)













119860 = V119891 (119877119867) exp(minus 119876

119877119879

) (22)


119868(119877119867) V is a frequency








5 and 153 times 107


4










7 Summary








Acknowledgment


References








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Group 1




[69]

Group 1 or 2


friction




[28ndash30 33 34]

Group 2


friction


[35]



[36 37]

Group 3



[70ndash72]




[31 73]


and charging



Table 1 Continued


Group 4



[39 74 75]






[7]














contact


force


surfaces



deform


Causes






sliding









Powerconsumption

Frequencyrange











119870119868= 120590119884119888

12 (13)






119889119888

119889119905

= 119888 = 119860(

119870119868

119870IC)

119899

(14)


119868 leading



119891 is given by [45]

119905119891=

2

1198601198842(119899 minus 2) 120590

119899

119886

(

120590119894

119870IC)

119899minus2

(15)



119870IC119894 = 12059011989411988411988812

119894 (16)




119870IC119891 = 12059011988611988411988812

119891 (17)


119889119886

119889119873

= 119888Δ119870119898 (18)



W

w

D

L

h

Comb drive

Torsional mass

Notched beam




119870 = 120590119884radic120587119886 (19)


Δ119870 = Δ120590119884radic120587119886 (20)


119889119886

119889119873

= 119888Δ119870119898997904rArr 119888(Δ119884120590radic120587119886)

119898

int

119873119891

0

119889119873=int

119886119888

119902119894

119889119886

119888(Δ120590119884radic120587119886)119898997904rArr

1

119888(Δ120590119884radic120587)119898int

119886119888

119886119894

119886minus1198982

119889119886

119873119891=

2 (119886119888(2minus119898)2

minus 119886119894(2minus119898)2

)

(2 minus 119898) 119888(Δ120590119884radic120587)119898

(21)













119860 = V119891 (119877119867) exp(minus 119876

119877119879

) (22)


119868(119877119867) V is a frequency








5 and 153 times 107


4










7 Summary








Acknowledgment


References








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table 1 Continued


Group 4



[39 74 75]






[7]














contact


force


surfaces



deform


Causes






sliding









Powerconsumption

Frequencyrange











119870119868= 120590119884119888

12 (13)






119889119888

119889119905

= 119888 = 119860(

119870119868

119870IC)

119899

(14)


119868 leading



119891 is given by [45]

119905119891=

2

1198601198842(119899 minus 2) 120590

119899

119886

(

120590119894

119870IC)

119899minus2

(15)



119870IC119894 = 12059011989411988411988812

119894 (16)




119870IC119891 = 12059011988611988411988812

119891 (17)


119889119886

119889119873

= 119888Δ119870119898 (18)



W

w

D

L

h

Comb drive

Torsional mass

Notched beam




119870 = 120590119884radic120587119886 (19)


Δ119870 = Δ120590119884radic120587119886 (20)


119889119886

119889119873

= 119888Δ119870119898997904rArr 119888(Δ119884120590radic120587119886)

119898

int

119873119891

0

119889119873=int

119886119888

119902119894

119889119886

119888(Δ120590119884radic120587119886)119898997904rArr

1

119888(Δ120590119884radic120587)119898int

119886119888

119886119894

119886minus1198982

119889119886

119873119891=

2 (119886119888(2minus119898)2

minus 119886119894(2minus119898)2

)

(2 minus 119898) 119888(Δ120590119884radic120587)119898

(21)













119860 = V119891 (119877119867) exp(minus 119876

119877119879

) (22)


119868(119877119867) V is a frequency








5 and 153 times 107


4










7 Summary








Acknowledgment


References








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Powerconsumption

Frequencyrange











119870119868= 120590119884119888

12 (13)






119889119888

119889119905

= 119888 = 119860(

119870119868

119870IC)

119899

(14)


119868 leading



119891 is given by [45]

119905119891=

2

1198601198842(119899 minus 2) 120590

119899

119886

(

120590119894

119870IC)

119899minus2

(15)



119870IC119894 = 12059011989411988411988812

119894 (16)




119870IC119891 = 12059011988611988411988812

119891 (17)


119889119886

119889119873

= 119888Δ119870119898 (18)



W

w

D

L

h

Comb drive

Torsional mass

Notched beam




119870 = 120590119884radic120587119886 (19)


Δ119870 = Δ120590119884radic120587119886 (20)


119889119886

119889119873

= 119888Δ119870119898997904rArr 119888(Δ119884120590radic120587119886)

119898

int

119873119891

0

119889119873=int

119886119888

119902119894

119889119886

119888(Δ120590119884radic120587119886)119898997904rArr

1

119888(Δ120590119884radic120587)119898int

119886119888

119886119894

119886minus1198982

119889119886

119873119891=

2 (119886119888(2minus119898)2

minus 119886119894(2minus119898)2

)

(2 minus 119898) 119888(Δ120590119884radic120587)119898

(21)













119860 = V119891 (119877119867) exp(minus 119876

119877119879

) (22)


119868(119877119867) V is a frequency








5 and 153 times 107


4










7 Summary








Acknowledgment


References








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










W

w

D

L

h

Comb drive

Torsional mass

Notched beam




119870 = 120590119884radic120587119886 (19)


Δ119870 = Δ120590119884radic120587119886 (20)


119889119886

119889119873

= 119888Δ119870119898997904rArr 119888(Δ119884120590radic120587119886)

119898

int

119873119891

0

119889119873=int

119886119888

119902119894

119889119886

119888(Δ120590119884radic120587119886)119898997904rArr

1

119888(Δ120590119884radic120587)119898int

119886119888

119886119894

119886minus1198982

119889119886

119873119891=

2 (119886119888(2minus119898)2

minus 119886119894(2minus119898)2

)

(2 minus 119898) 119888(Δ120590119884radic120587)119898

(21)













119860 = V119891 (119877119867) exp(minus 119876

119877119879

) (22)


119868(119877119867) V is a frequency








5 and 153 times 107


4










7 Summary








Acknowledgment


References








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119860 = V119891 (119877119867) exp(minus 119876

119877119879

) (22)


119868(119877119867) V is a frequency








5 and 153 times 107


4










7 Summary








Acknowledgment


References








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














7 Summary








Acknowledgment


References








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation








































































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Review Article Reliability and Fatigue Analysis in ...

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