MEMS Mechanical Fatigue: Experimental Results on ... - IEEE Xplore

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 4, AUGUST 2009

MEMS Mechanical Fatigue: Experimental Results on Gold Microbeams Aurelio Somà and Giorgio De Pasquale

Abstract—This paper proposes a new strategy for detecting material strength loss under mechanical fatigue on the basis of the pull-in voltage of the test device. Gold microbeam specimens are tested for mechanical fatigue using an electrostatically actuated dedicated device. The design of the fatigue device is discussed, providing the analysis of stress distribution inside the specimen. The finite-element method is used to simulate the electromechanical coupling. The fatigue limit is estimated through the “staircase” method, and a Wöhler curve is obtained from experiments. The surface topography evolution is monitored by scanning electron microscope images; specimen failure modes and material degradation are discussed, revealing the local yield of the material on the upper surface of the beam. The type of degradation appears to be in agreement with the established literature as a consequence of fatigue. [2008-0313] Index Terms—Failure analysis, fatigue, microelectromechanical (MEM) devices.

I. I NTRODUCTION

T

HE RELIABILITY of microelectromechanical systems (MEMS) became a fundamental topic of investigation as a result of their widespread application in many day-to-daylife devices. Fatigue and a high number of cycle reliability strongly influence the proper working of microfluidic bioMEMS used for medical purposes; for instance, MEMS-based telecommunication devices are subjected to the action of microcomponents such as oscillators or switches, and inertial sensors for aerospace applications dictate very severe performance requirements to minimize repairs and replacements. Until recently, there were, on average, ten mechanical moving parts per MEM device, but the number of internal components is increasing. In particular, the advent of micromirrors caused a significant growth of moving parts. Reliability is important because statistically every component added increases the global chance of system failure [1]. In top–down analysis, reliability of MEMS must be considered on three different levels, namely, system reliability, component reliability, and material reliability. For example, proper functioning of a microengine (the system) is assured by the efficiency of microrotors, gears, bearings, etc. (the components), working inside it, whose reliability reflects the failure modes of the materials that they are made of [2]. The system is related to its components through subassembly design and internal interactions. Component reManuscript received December 19, 2008; revised April 21, 2009. First published July 15, 2009; current version published July 31, 2009. Subject Editor S. M. Spearing. The authors are with the Mechanical Engineering Department, Politecnico di Torino, 10129 Turin, Italy (e-mail: [email protected]; giorgio. [email protected]). Digital Object Identifier 10.1109/JMEMS.2009.2024796

liability is related to material reliability through the study of fatigue, creep, and other damage mechanisms for specific geometries, environmental conditions, stress levels, and strain rates. Electromechanical coupling often represents a crucial issue for system reliability, even if many other sources of collapse potentially involve reliability. By focusing on material failure, it emerges that mechanical damage represents the more relevant source of failure. Mechanical reliability issues include mechanical fatigue, thermal fatigue, mechanical strength, surface and contact failure. Fatigue failure test results that are traditionally presented in the literature as S−N curves need a high number of failures (single points on curve) to produce a single diagram. Another difficulty is that data from S−N curves also capture deviceto-device variability, affected by the uncertainties of material characteristics and fabrication processes. Frequently, each investigation involving specific devices tends to be device dependent. Fabrication processes, etching techniques, and substrate materials greatly affect film structure strength, as well as the occurrence of initial defects [2], [3]. Understanding failure processes due to fatigue for different types of materials is fundamental. The material that is more widely used for building MEMS is polysilicon, which is also the most studied and tested material, but several works were also presented about the fatigue behavior of metal microstructures. In [4], fatigue-testing methods for thin-film metals were described after observing the incidence of material length on damage relative to the bulk material. Espinosa et al. [3], [5] and Son et al. [6] evaluated the effect of size on the mechanical response of suspended thin gold membranes and described the effect of thickness on yield stress and failure of the membrane. Millet et al. [7] investigated the fatigue behavior of gold microbridges at resonant frequency and pull-in actuation voltage and monitored structural stiffness and changes in electrical resistance. Important parameters for the fatigue behavior of gold, such as strain-rate sensitivity, grain size, grain-boundary properties, and temperature gradients, were investigated and discussed [8]–[11]. Read et al. [12], [13] studied the fatigue behavior of metal thin films like Al and Cu, Hemker et al. [14], [15] tested nickel samples to fatigue, and Weiss et al. analyzed metallic foils [16] and microwires [17]; many works testing the fatigue behavior of gold using external actuations were also presented [8], [18]–[20]. It was widely documented that fatigue damage in bulk metals involves the comparison of characteristic dislocation structures whose dimensions are in the micrometer scale; in the case of thin films, these dimensions are comparable with structural dimensions and grain sizes, making the damage investigation

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SOMÀ AND DE PASQUALE: MEMS MECHANICAL FATIGUE: EXPERIMENTAL RESULTS ON GOLD MICROBEAMS

important [21]. Zhang et al. [22], [23] investigated the influence of film thickness and grain size on the amount of damage for Cu and Al films; Schwaiger et al. studied the fatigue behavior of Ag thin microbeams [24] and Cu films [25], observing the comparison of extrusions and voids and deducing their relation to fatigue failure; and Boyce et al. [26] identified a surface oxide thickening mechanism as the source of crack initiation. The goal of this paper is to experiment a new strategy to investigate the fatigue behavior of gold thin films; the authors present a very simple device for testing, which reproduces the operative conditions of the material faithfully. This is achieved by developing an in situ configuration of the testing device and using an electrostatic actuation; external forces are avoided in order that the real functioning of common devices such as oscillators and filters or components such as suspensions for switches and varactors are reproduced. This strategy allows one to excite the specimen at a frequency that is close to some common applications of it and to reproduce the effects of strain rate, creep, and temperature on the gold material; an effective load cycle is also applied in terms of minimum and maximum stress rate and tension and compression stress distribution in the specimen cross section. A short discussion on the test structure design and modeling and a preliminary investigation on the fatigue behavior of fabricated samples are reported in [27] and [28], respectively. The upper surface of the gold film is analyzed after a different number of loading cycles, and its topography is documented by scanning electron microscope (SEM) images; the modality of damage is discussed, and it appears to be in agreement with the theories of plasticity present in the literature. The fatigue limit of the material is estimated using a statistical approach based on the “staircase” method [29], which is a well-known procedure used in the macroscale fatigue analysis. II. D ESIGN OF T ESTING D EVICE Each device for fatigue tests should have the following two features: 1) the possibility to generate variable amplitudes of alternate forces for specimen excitation to generate different stress levels inside the material and 2) the possibility to monitor material damage during the accumulation of loading cycles and to provide a criterion to establish the final collapse of the specimen. To identify the exact number of collapses for a given set of specimens, it is fundamental to represent the test results with the established fatigue diagrams as the S−N curve (also known as Wöhler diagram); the number of collapses is also used to estimate the fatigue limit through the “staircase” method. The final collapse is not always identified by the rupture of the specimen, but, depending on the specific application, it can be represented by the yielding point, the softening of the material, or other relevant events; in a fatigue test, the event determining the collapse of the specimen must be fixed in advance. A. Technology Testing devices were built by FBK (Trento, Italy) using the RF switch surface micromachining process [30]. Structural moving parts are obtained through the gold electroplating process; the material is deposited in two steps, allowing the

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Fig. 1. (a) Scanning electron microscope image of the testing device formed by the actuator (perforated plate) and the specimen (suspended beam). (b) Detail of the specimen. The device was fabricated using the gold electrodeposition technique.

selective superimposition of two gold layers. This permits creation of thin films of small (1.8 μm) and large (4.8 μm) thicknesses, which can be used for the specimen and for the suspended actuation electrode, respectively. The thickness of the actuation electrode is higher than that of the specimen to increase its mechanical stiffness; many square holes are present on the suspended electrode to facilitate the chemical removal of the sacrificial layer used to obtain the suspended parts and provide a final 3-μm-thick air gap. The lower electrode consists of a polysilicon layer deposited on the substrate previously oxidized on the surface and covered with a thin lowtemperature oxide layer. The material parameters are Young’s modulus E = 98.5 GPa, Poisson ratio ν = 0.42, and specific density ρ = 19.32 · 10−15 kg/μm3 . The static yield stress of electroplated gold thin films was investigated in [3] and [5] at variable thicknesses and widths, showing how specimen size strongly influences this parameter. The average grain size of the suspended gold layer ranges between 0.5 and 1 μm, as measured from the SEM images of the specimen surface. B. Geometry and Actuation The testing device is shown in Fig. 1; both nominal and measured dimensions are listed in Table I for the specimen and the actuation electrode. Fig. 1(a) shows a SEM image of the device. The fatigue test device includes both the actuation electrode that is represented by a perforated plate and the specimen; the specimen is a double-clamped beam with rectangular cross section [Fig. 1(b)]. The specimen is fixed to a rigid constraint on one side and is connected to the moving plate on the opposite side; plate motion causes bending of the specimen in the out-ofplane direction. The plate is clamped on the side opposite the specimen. A stress distribution combining shear and flexural components affects the material of the film during its bending; this stress distribution is variable across the beam thickness. The device is supplied by an alternate voltage of actuation that causes the gold beam deflection; the amplitude of the alternate bending force is variable and is proportional to the amplitude of the input voltage. The number of loading cycles can easily be determined by the knowledge of the input voltage frequency and the loading time. The loading conditions of the gold specimen can be calculated by a simple model based on Euler–Bernoulli theory; the specimen can be represented as a cantilever having the free end loaded with vertical force F (Fig. 2). The model shows that higher stress levels are reached in correspondence with cross sections A and B where the beam is constrained. The stress

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TABLE I N OMINAL D IMENSIONS OF THE O RIGINAL D ESIGN AND D IMENSIONS M EASURED BY O PTICAL I NTERFEROMETRIC P ROFILOMETRY ( IN PARENTHESES ) OF THE T ESTING D EVICE . A LL M EASURES A RE IN M ICROMETERS

III. T EST P ROCEDURE A. Pull-In Voltage as Damage Detector

Fig. 2. Euler–Bernoulli model of the specimen and its deformed shape. The electrostatic force produced by the actuator is represented by the concentrated force F in the model. Cross sections A and B are situated at the beam external constraint and at the connection with the perforated plate, respectively. The loaded end is subjected to a 0.4◦ rotation.

direction is orthogonal to the cross-sectional surface. The stress in the material is a function of thickness, and the maximum level is reached at the upper and lower surfaces; depending on the deformed shape of the beam, the upper surface is loaded by a positive stress (tension) at cross section A and by a negative stress (compression) at cross section B, while the lower surface is instead loaded in compression at cross section A and in tension at cross section B. The stress value at the outer surfaces of cross sections A and B for both tension and compression cases is σmax = 3F l/wt2 , where l is the beam length, w is the beam width, and t is the beam thickness. This value is calculated assuming that the rotation of the free end of the beam (that is equal to 0.4◦ ) is negligible. C. FEM Simulations The specimen design activity was supported by numerical simulations implemented using a commercial-type tool (Ansys TM) for optimizing test device geometry. The nonlinear relationship between structural and electrical domains, due to electrostatic force depending on the local gap width, was modeled by 1-D multiphysics elements trans126 [31]. The static relationship between the applied voltage and specimen tip displacement was measured on actual samples, as shown in Fig. 3(a). The internal stress of the material was estimated using structural FE models where the specimen tip displacement was imposed on the basis of the measured values. This estimation refers to an ideal geometry with surfaces unaffected by microdefects; stress distribution in actual specimens depends on crack nucleation points where local stress intensity is amplified, resulting in fatigue-induced failure. Modal analysis of the unloaded structure was performed to evaluate the modal shape and first resonant frequency of the testing device, which was found to be 26.3 kHz; in Fig. 3(b), the measured frequency response function (FRF) of the structure [32] is represented.

Fatigue tests of MEMS reported in the literature show that several different parameters for monitoring material damage can be used. Resonant frequency, quality factor, and electrical resistance are widely used parameters for this purpose. This paper proposes a new strategy for detecting structural stiffness loss, based on the pull-in voltage of the fatigue test device. Because of its sensitivity and ease of setting up the associated experimental equipment, this can be a very significant parameter. The fatigue test procedure includes the following: 1) measuring and storing the pull-in voltage and 2) applying cyclical load by means of an alternate voltage at the desired level of amplitude for a specific time interval and at a specific frequency. The combination of time and frequency yielded the number of cycles of the current excitation block. The procedure was repeated up to a specimen failure. The event establishing the specimen failure was not associated to the rupture of the specimen but was related to a considerable change in a significant parameter of the device; the failure event was defined in advance as a drastic reduction (at least 10% of the previous value) of the pull-in voltage value, reflecting a reduction of the structural stiffness. The pull-in voltage [step 1)] was measured by a static actuation (using a dc voltage), which was progressively increased in steps. Pull-in was detected optically using the interferometer microscope ZoomSurf3D (Fogale Nanotech) [33]; this microscope provides profile measurements from a minimum area of 100 μm × 100 μm to a maximum area of 2 mm × 2 mm with 20× objective magnification. A lateral resolution of 0.6 μm and a vertical resolution of 0.1 nm were reached. Alternating excitation [step 2)] was obtained by means of a 20-kHz alternate voltage; the frequency of actuation was set to a value that was significantly lower than the mechanical resonance of the device, which is 28 kHz approximately [as highlighted by the FRF of Fig. 3(b)]. The two main reasons for this are given as follows: 1) resonant amplification involves additional problems when evaluating material internal stresses, and 2) progressive damage to the material could cause a shift in resonance peak or alter the device quality factor as a consequence of possible changes in structural stiffness and damping. B. Cyclic Excitation System dynamics must carefully be considered when supply voltage frequency is converted to a number of cycles of alternate load. The force that is responsible for specimen oscillation is generated by the potential difference between suspended


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Fig. 3. (a) Vertical displacement of the specimen loaded tip measured using the optical interferometric technique with respect to static input voltage. Measures are affected by an error introduced by surface roughness, particularly at small displacements. (b) Experimental FRF measured with interferometric dynamic detection using the sine seep technique.

and lower electrodes. Two periods TL ’s of the loading curve correspond to one period TV of the alternating voltage curve. This is due to the electrostatic force that acts always in the attractive direction for both possible polarizations of the electrodes; a consequence is that the current mode of deflection does not allow oscillation around the undeformed shape. The resulting number of load cycles NL is related to the number of cycles of alternating voltage NV according to NL = 2NV .

TABLE II R ESULTS OF FATIGUE L OADING ON S IX S PECIMENS FOR THE FATIGUE L IMIT E STIMATION U SING THE “S TAIRCASE ” M ETHOD . T HE S PECIMEN FAILURE I S I NDICATED AS 1, W HILE THE S PECIMEN N ONFAILURE I S I NDICATED AS 0

(1)

The curves of alternate displacement and local stress have the same frequency as the loading curve. The alternate excitation was maintained for 10 s during the tests between two consecutive measurements of the pull-in voltage; each block of excitation was composed of 4 · 105 cycles of loading, displacement, and local stress curves. The number of cycles to failure is indicated as N . Some basic parameters of fatigue loading must be defined: The maximum stress (σmax ) and the minimum stress (σmin ) are the stress levels that are locally reached in the material at the higher and lower points of the stress curve, respectively; the mean and alternate stresses can be calculated as σm = (σmax + σmin )/2 and σa = (σmax −σmin )/2, respectively. The parameter R = σmin /σmax defined as the “stress rate” is also important to distinguish stress cycles that are always in tension, always in compression, or composed of a combination of these states. It was demonstrated that the tension and compression cycles determine different fatigue behaviors in metal materials, and usually, pure tension cycles produce faster degradation. In correspondence to cross section A, the upper surface is subjected to a pure tension stress cycle; the minimum stress is σmin = 0, and the stress rate is R = 0. At the lower surface of cross section A,

the material is subjected to a pure compression cycle; the maximum stress is σmax = 0, and the stress rate is R = ∞. IV. E XPERIMENTAL R ESULTS The fatigue limit was estimated using the “staircase” method; this procedure is largely used in the macroscale to estimate the fatigue limit through a limited number of tests and is widely described in [29]. The “staircase” method is based on a few parameters: the reference number of cycles (Nref ), the starting load level (F ), and the load step (ΔF ). The procedure can briefly be described in a few steps: The first specimen is loaded at the starting load level (F ) for Nref cycles; if the specimen collapses during fatigue loading, then the second specimen will be loaded at load level F − ΔF for Nref cycles. Instead, if the first specimen does not collapse during fatigue loading, then the second specimen will be loaded at load level F + ΔF for Nref cycles. The procedure must be repeated for many specimens, increasing the load level after a nonfailure. The reference number of cycles used was Nref = 2 · 106 , the starting load level was F = 15 V, and the load step was

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Fig. 4. Pull-in voltage of different testing devices during the accumulation of fatigue loading, with alternate load being provided at 20-kHz frequency at the amplitude indicated for each curve. The pull-in voltage was measured and stored at specific time intervals. The specimen failure is indicated by the strong pull-in reduction (ranging from 12.9% and 22.7% of its last value).

Fig. 5. Pull-in voltage of different testing devices during the accumulation of fatigue loading, with alternate load being provided at 20-kHz frequency at the amplitude indicated for each curve. The pull-in voltage was measured and stored at specific time intervals. Specimens that failed immediately (21- and 22.5-V excitation amplitudes) or that did not fail (10-, 12-, and 13-V excitation amplitude) are reported. The curve labeled with 0-V excitation amplitude represents the pull-in variation during the application of a series of consecutive static actuations without alternate fatigue loading.

ΔF = 1 V. The procedure was repeated for six specimens; in Table II, each failure was then reported as 1, while each nonfailure was reported as 0. The fatigue limit estimated by the application of the “staircase” method is found to be FD = 13 ± 0.7 V. This value is used as an important reference when the alternate-load level is imposed in fatigue tests. According to the definition of fatigue limit, a failure at load levels higher than FD and a nonfailure at load levels lower than FD are expected. Fig. 4 shows the evolution of pull-in voltage for different test specimens during the accumulation of load cycles. Each curve refers to a different value of the alternate input voltage used. The failure is assumed to occur in the instant when the pull-in voltage shows a reduction that is equal to or higher than 10% of the previous value; only collapsed specimens are represented by the curves reported. The normal average pull-in voltage variation between two consecutive detections is around 2.3%, while the reduction after the specimen failure ranges from 12.9% to 22.7% of the last value before the failure. The curves shown in Fig. 5 indicate the pull-in voltage variation measured on other specimens; some of them failed instantly because of high loading amplitudes (21 and 22.5 V); other specimens did not fail after 200 million cycles because they were excited at a load level that is equal or lower than the fatigue limit (10–13 V). The number of cycles to failure (N ) and the corresponding amplitudes of input voltage were extracted from the curves shown in Figs. 4 and 5 and reported in Table III, where the

TABLE III FATIGUE T EST R ESULTS ON 13 S PECIMENS . T HE A MPLITUDE OF A LTERNATE I NPUT VOLTAGE , THE A MPLITUDE OF A LTERNATE A XIAL S TRESS C ALCULATED BY THE FEM M ODEL , AND THE N UMBER OF C YCLES TO FAILURE A RE I NDICATED

stress levels calculated by the finite-element (FE) model are also indicated; a Wöhler diagram (Fig. 6) was obtained by indicating the instant of failure for a specific amplitude of the actuation voltage at the corresponding number of cycles. The S−N curve confirms that the estimated value of the fatigue limit is consistent; in fact, it represents the load amplitude


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Fig. 6. S−N curve (Wöhler diagram) summarizing the results of fatigue tests. The number of cycles to failure is reported for each specimen in relation to the axial stress amplitude calculated by the FEM model.

threshold separating collapsed specimens from noncollapsed ones. V. S URFACE T OPOGRAPHY An SEM was used to evaluate some images of the specimen surface at its clamped end. Fig. 7(a) shows the surface of a specimen before the fatigue test. Fig. 7(b) shows a specimen surface that did not fail after 200 · 106 cycles at 10 V of actuation amplitude, while Fig. 7(c) is referred to a specimen that failed instantly under 30-V excitation amplitude. Fig. 7(d)–(i) shows the surface of many specimens that failed at different numbers of cycles under different levels of input voltage amplitude. VI. D ISCUSSION SEM images reveal the formation of intruded and extruded regions on the upper surface of the gold film. They are mainly located near the clamped end of the beam (cross section A). The location of the damaged regions can be explained considering the stress distribution in the material: At the upper surface of cross section A, the material is always subjected to pure tension stress distribution during alternate loading, and it was demonstrated that pure tension cycles produce faster degradation in metal materials during fatigue loading. The images show the presence of multiple striations and deformation areas near the clamped end of the beam; these regions are affected by local permanent deformations of the surface. As known from the fatigue literature in the microscale and macroscale, cracks propagate after their nucleation due to the motion of dislocations. At low temperatures, grain boundaries act as barriers to dislocation motion; this produces the macroscopic effect of material strengthening. This effect explains the behavior shown by gold specimens during the first cycles of fatigue tests, when an increase in the pull-in voltage of the test device was registered (Fig. 4). The dislocations are influenced by the grain boundaries in their movement, and their accumulation produces local yield on the material surface, as shown by Fig. 7(d)–(i). The local yield is usually isolated in only a few grains despite loading conditions being approximately identical on a wide area. In [34] is demonstrated that yield initiates only if proper conditions are verified. It was observed that the yield of gold films is nucleated at grain triple junctions that embody the following: 1) slip planes forming an

Fig. 7. SEM images of the specimen surface near the clamped end. (a) Before fatigue loading. (b) Did not fail after 200 · 106 cycles at 10-V amplitude. (c) Failed immediately at 30-V amplitude. (d) Failed after 1.2 · 106 cycles at 15-V amplitude. (e) Failed after 2.4 · 106 cycles at 20-V amplitude. (f) Failed after 4.8 · 106 cycles at 16-V amplitude. (g) Failed after 5.4 · 106 cycles at 13.5-V amplitude. (h) Failed after 5.4 · 106 cycles at 13-V amplitude. (i) Failed after 9 · 106 cycles at 14-V amplitude.

apex and 2) favorable grain boundaries for the formation of low-energy grain-boundary dislocations. The evidence showing that only a small fraction of triple junctions satisfy these

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Fig. 8. SEM image representing a surface detail of a specimen that failed after 2.4 · 106 cycles at 20-V amplitude. Typical damage structures like extrusions and intergranular cracks are clearly represented, and the grain boundaries are also visible.

conditions leads to a marked inhomogeneity of yielding despite the identical fatigue loading. Fig. 8 shows a detail of the surface of a specimen that failed after 2.4 · 106 cycles at 20-V loading amplitude; it is evident that the yield was reached selectively by some regions of the surface producing intrusions and extrusions on the material. Fig. 7(b) shows a specimen that did not fail after the fatigue test; its surface is quite similar to that of Fig. 7(a) representing a specimen before the test. This supports the relation between local surface yielding, loss of structural stiffness, and device pull-in voltage reduction. The association between the structural stiffness decrease and the degradation of the film, i.e., void and crack formation and crack propagation, was documented before [21], [24]; this allows one to use the stiffness parameter as an indicator of the material damage. The pull-in voltage measurement used in this paper is able to make an indirect estimation of the elastic force exerted by the structure, which is linearly proportional to the stiffness for small displacements. The static voltage input used to measure the pull-in of the device does not produce plastic deformations or local yield; this was verified by imposing a series of successive static actuations on the specimen and storing the corresponding pullin voltage. The resulting curve is shown in Fig. 5 and marked with a 0-V amplitude. The value of pull-in results is constant despite several static actuations, revealing that the mechanical characteristics of the device do not change significantly; this leads to the evidence that the material is loaded within the elastic field and, more specifically, that the structural stiffness of the specimen is not affected by the static actuation. Being the experimental strategy based on the correspondence between structural stiffness and material damage, it is evident that the sensitivity of the strategy used is related to the ability to detect the stiffness variation by means of the pull-in voltage. As a consequence, it is reasonable to assume that a constant pullin voltage means an absence of material damage in the context of the experimental strategy used. Previous works demonstrate that the mechanical behavior of gold thin films is strongly dependent on their dimensions when they are loaded in the plastic field [3], [5]. In particular, the yield stress of gold beams is inversely proportional to their width and thickness; instead, in the elastic field, there are no relevant differences varying the specimen dimensions, resulting in a constant value of the Young’s modulus. The elastic properties of

the gold material instead show relevant differences in the case of variable strain rates, as documented by [8] and [11]; however, this effect does not affect the results of fatigue tests because they were all performed at the same driving frequency that gives the same strain rate. In Fig. 8, it is possible to recognize some of the typical dislocation structures and damage features that was documented before; for instance, the extrusions and intergranular cracks observed are very similar to those described by Kraft et al. [21], Zhang et al. [22], and Schwaiger and Kraft [24] on ductile material films like Cu and Ag. The cited authors explained the formation of extrusions as a consequence of dislocation motion and irreversible slip bands; this suggests that the density of dislocations in the region affected by plasticstrain accumulation is high. VII. C ONCLUSION This paper has proposed a new strategy for detecting the structural stiffness loss due to mechanical fatigue based on the pull-in voltage of the device. A dedicated testing device was designed and built to investigate the fatigue behavior of gold microbeams using the electrostatic actuation and in situ configuration. The specimen design procedure was performed by using FE simulations. The nonlinear relationship between structural and electrical domains, due to electrostatic force depending on the local gap width, was modeled by 1-D multiphysics elements. The static and dynamic mechanical behaviors were experimentally verified and considered for the design of the experimental fatigue plan. The original procedure of the fatigue test includes monitoring of the pull-in voltage applying cyclical load by means of an alternate voltage at the desired level of amplitude for a specific time interval and at a specific frequency. The fatigue degradation of the specimen is experimentally correlated to the reduction in the pull-in voltage, representing a simple and fast indirect detection of the structural stiffness. The fatigue limit was estimated using the “staircase” method and compared to the value resulting from fatigue tests; experimental data were represented with a Wöhler diagram. The surface topography after fatigue tests was described and appeared to be in agreement with the yielding theories present in the literature. The gold material exhibited local yields at the upper surface as a consequence of fatigue loading; a loss of structural stiffness corresponds to surface degradation, as revealed by pull-in detection. R EFERENCES [1] S. M. Allameh, “An introduction to mechanical-properties-related issues in MEMS structures,” J. Mater. Sci., vol. 38, no. 20, pp. 4115–4123, Oct. 2003. [2] A. B. Soboyejo, K. D. Bhalerao, and W. O. Soboyejo, “Reliability assessment of polysilicon MEMS structures under mechanical fatigue loading,” J. Mater. Sci., vol. 38, no. 20, pp. 4163–4167, Oct. 2003. [3] H. D. Espinosa and B. C. Prorok, “Size effects on the mechanical behavior of gold thin films,” J. Mater. Sci., vol. 38, no. 20, pp. 4125–4128, Oct. 2003. [4] G. P. Zhang, C. A. Volkert, R. Schwaiger, R. Mönig, and O. Kraft, “Fatigue and thermal fatigue analysis of thin metal films,” Microelectron. Reliab., vol. 47, no. 12, pp. 2007–2013, Dec. 2007. [5] H. D. Espinosa, B. C. Prorok, and B. Peng, “Plasticity size effects in freestanding submicron polycrystalline FCC films subjected to pure tension,” J. Mech. Phys. Solids, vol. 52, no. 3, pp. 667–689, Mar. 2004.


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Aurelio Somà was born in Saluzzo, Italy, on July 3, 1964. He received the M.S. degree in aeronautical engineering and the Ph.D. degree in applied mechanics from the Politecnico di Torino, Turin, Italy, in 1989 and 1993, respectively. He was Assistant Professor of Machine Design from 1992 to 1998 and Associate Professor from 1998 to 2002 at the Politecnico di Torino. Since 2002, he has been Full Professor, Chair of Machine Design, at the Politecnico di Torino. He has been Deputy Director of the Mechanical Engineering Department since 2007. He is also Coordinator of the MEMS Mechanical Laboratory, Faculty of Engineering II, Politecnico di Torino. His research activities include numerical and experimental mechanics in the field of robotic applications, finite-element simulation, multibody simulation, vehicle and railway dynamics and microsystems, in particular, dynamic model updating of mechanical systems and contact mechanics. In the field of MEMS, main research topics are design and dynamic identification, simulation and modeling of MEMS, reliability, and fatigue. He has published several scientific papers in national and international conference proceedings and international journals. He also has more than 100 scientific publications and is the holder of four patents.

Giorgio De Pasquale was born in Biella, Italy, on July 5, 1982. He received the B.S. (“Methods for fatigue analysis of microsystems”) and M.S. degrees (“Dynamic behavior of microsystems under squeeze film damping”) in mechanical engineering from the Politecnico di Torino, Turin, Italy, in 2004 and 2006, respectively, where he has been working toward the Ph.D. degree in the Mechanical Engineering Department since 2007. From 2006 to 2007, he was a Designer with medium-size enterprises in the fields of heat generators for industry and injectors for polyurethane deposition. From 2005 to 2007, he participated in the Scientific Research Program of Relevant National Interest (PRIN) entitled “Modeling, design and characterization of RF-MEMS devices.” In 2007 he was involved in the SISA project for aerospace applications of microsensors. He has more than 20 scientific papers and is the coauthor of one patent. His main research topics include mechanical design, modeling, and characterization of MEMS.