a reaction-layer mechanism for the delayed failure of

Acta Materialia 50 (2002) 3579–3595www.actamat-journals.com

A reaction-layer mechanism for the delayed failure ofmicron-scale polycrystalline silicon structural films subjected

to high-cycle fatigue loading

C.L. Muhlsteina, E.A. Stachb, R.O. Ritchiea,∗

a Materials Sciences Division, Lawrence Berkeley National Laboratory, and Department of Materials Science and Engineering,University of California, Berkeley, CA 94720-1760, USA

b National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, Berkeley, CA 94720-1760, USA

Received 5 November 2001; received in revised form 18 March 2002; accepted 18 March 2002

Abstract

A study has been made to discern the mechanisms for the delayed failure of 2-µm thick structural films ofn+-type,polycrystalline silicon under high-cycle fatigue loading conditions. Such polycrystalline silicon films are used in small-scale structural applications including microelectromechanical systems (MEMS) and are known to display ‘metal-like’stress-life (S/N) fatigue behavior in room temperature air environments. Previously, fatigue lives in excess of 1011

cycles have been observed at high frequency (~40 kHz), fully-reversed stress amplitudes as low as half the fracturestrength using a surface micromachined, resonant-loaded, fatigue characterization structure. In this work the accumu-lation of fatigue-induced oxidation and cracking of the native SiO2 of the polycrystalline silicon was established usingtransmission electron and infrared microscopy and correlated with experimentally observed changes in specimen com-pliance using numerical models. These results were used to establish that the mechanism of the apparent fatigue failureof thin-film silicon involves sequential oxidation and environmentally-assisted crack growth solely within the nativeSiO2 layer. This ‘reaction-layer fatigue’ mechanism is only significant in thin films where the critical crack size forcatastrophic failure can be reached by a crack growing within the oxide layer. It is shown that the susceptibility ofthin-film silicon to such failures can be suppressed by the use of alkene-based monolayer coatings that prevent theformation of the native oxide. 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Keywords: Silicon; Fatigue; Thin films; MEMS; Self-assembled monolayer coatings

1. Introduction

The promise of revolutionary commercial productsat small dimensions has fueled the rapid development

∗ Corresponding author: Tel.:+1-510-486-5798; fax:+1-510-486-4881.

E-mail addresses: [email protected] (C.L.Muhlstein); [email protected] (R.O. Ritchie).

1359-6454/02/$22.00 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.PII: S1359 -6454(02 )00158-1

of microelectromechanical systems (MEMS) and theenabling technologies of surface micromachining. Sili-con-based structural films have emerged as the domi-nant material system for MEMS because the microma-chining technologies for silicon are readily adaptedfrom the microelectronics industry, and are compatiblewith fabrication strategies for the integrated circuitsnecessary for actuation and control of the systems.

3580 C.L. Muhlstein et al. / Acta Materialia 50 (2002) 3579–3595

However, the long-term durability of thesemicrosystems may be compromised by the suscep-tibility of thin-film silicon to delayed failure duringcyclic loading conditions in ambient air [1–8].

Cyclic fatigue is the most commonly encoun-tered mode of failure in structural materials, occur-ring in both ductile (metallic) and brittle (ceramic)solids (although the mechanisms are quitedifferent) [9]. The mechanistic understanding offatigue together with the use of damage/fracturemechanics to describe its effect at continuumdimensions has allowed for the reliable design andoperation of innumerable macro-scale structures,such as aircraft airframes and engines. At themicro-scale, the fatigue of ductile materials is attri-buted to cyclic plasticity involving dislocationmotion that causes alternating blunting andresharpening of a pre-existing crack tip as itadvances [10]. In contrast, brittle materialsinvariably lack dislocation mobility at ambienttemperatures, such that fatigue occurs by cycle-dependent degradation of the (extrinsic) toughnessof the material in the wake of the crack tip thatdeveloped from preexisting material inhomogen-eities [11]. Prior to this work, the relevance of thesefatigue mechanisms to silicon films had yet to beestablished.

Silicon is generally regarded as a prototypicalbrittle material; dislocation activity is generally notobserved at low homologous temperatures (below~500 °C) and there is little evidence of extrinsictoughening, such as grain bridging or microcrack-ing [12]. Moreover, silicon is not susceptible toenvironmentally-induced cracking (i.e., stress-cor-rosion cracking) in moist air or water [13–15] atgrowth rates measurable in bulk specimens. Theseobservations strongly suggest that silicon shouldnot fatigue at room temperature. Indeed, there hasbeen no evidence to date that bulk silicon is sus-ceptible to fatigue failure. However, there is sub-stantial evidence that cyclically-stressed, micron-scale, silicon films can fail prematurely under high-cycle fatigue loading [1–8,16].

The observation that silicon thin films can failunder cyclic loading was first reported by Connallyand Brown a decade ago [1]. Since then, thepresent authors and others [2–7] have confirmedthat 2 to 20 µm thick single crystal and polycrystal-

line silicon films can fail in fatigue at stresses aslow as half their (single-cycle) fracture strengthafter more than ~1011 cycles. Despite such results,the mechanistic origins of why thin-film siliconshould apparently suffer fatigue failure haveremained elusive. Early studies highlighted theimportance of water vapor and speculated that themechanism may be associated with static fatigueof the native silica layer [1,7]. Other proposedexplanations have involved dislocation activity incompression-loaded silicon (e.g., [17]), stress-induced phase transformations [4], and impurityeffects [4], although in no instance has conclusiveexperimental evidence been presented to supportany of these mechanisms. Moreover, until nowthere has never been any direct observation offatigue damage in micron-scale silicon, nor indi-cations on how it accumulates.

A recent study by the authors [18], however,provided the initial experimental evidence that thecrack initiation and growth processes involved inthe apparent fatigue of silicon are confined to theamorphous SiO2 reaction layer that forms on sur-faces upon their exposure to air. In this paper, wepresent a mechanism for the apparent fatigue ofsilicon, termed reaction-layer fatigue, on the basisof prior stress-life fatigue data, a compliance tech-nique for monitoring the damage accumulation,and microstructural analysis using high-voltagetransmission electron microscopy. Additionally,we suggest a method for suppressing the cyclicfatigue of silicon films through the use of alkene-based monolayer coatings that is validated withstress-life fatigue data.

2. Experimental procedures

The 2-µm thick silicon films were fabricatedfrom the first structural polycrystalline silicon layeron run 18 of the MCNC/Cronos MUMPs pro-cess. This surface micromachining process utilizeslow-pressure chemical vapor deposition (LPCVD)to manufacture n+-type (resistivity, r=1.9 × 10�3

�·cm) polycrystalline silicon [19]. Wafer curvaturemeasurements showed the film to have a compress-ive residual stress of about 9 MPa [19]; out-of-plane deformation due to a through-thickness

3581C.L. Muhlstein et al. / Acta Materialia 50 (2002) 3579–3595

residual stress gradient could not be detected usingwhite-light interferometry. Secondary ion massspectroscopy (SIMS), referenced to known stan-dards, was used to quantify the concentration ofhydrogen, carbon, oxygen, and phosphorouspresent.

The elastic properties of polycrystalline siliconthin films approach the average behavior of ideal-ized polycrystalline materials. An average of theVoigt and Reuss bounds for a random, polycrystal-line aggregate (Young’s modulus, E=163 GPa,Poisson’s ratio, n=0.23 [20]) were used to estimatethe elastic behavior of the material. The fracturestrength of polycrystalline silicon typically rangesfrom 3 to 5 GPa depending on loading condition,specimen size, and test technique. The fracturetoughness, Kc, is ~1 MPa√m [12,21].

The microstructure of the films was charac-terized using transmission electron microscopy(TEM). Cross-sectional TEM specimens were pre-pared from the patterned films using standard lab-oratory practices [22]. Pairs of patterned chips con-taining the surface micromachined structures wereglued together face-to-face, mechanically thinned,dimpled, and ion milled to the desired electrontransparency. Diffraction contrast and high-resol-ution microscopy of the these specimens was per-formed using the Berkeley JEOL Atomic Resol-ution Microscope (ARM) at an operating voltageof 800 kV and a JEOL 3010 TEM operating at 300kV. Analytical characterization was accomplishedusing a Philips CM200 Field Emission microscopeequipped with a Link Energy Dispersive Spec-trometer (EDS) and a Gatan Image Filter for elec-tron energy loss spectroscopy (EELS) and energyfiltered imaging (EFTEM). Plan view observationsof the grain morphology and oxide structure wereaccomplished using both the ARM and the KratosHigh Voltage Electron Microscope (HVTEM)operating at 0.8–1.0 MeV. Plan view samples wereprepared by simply lifting the micromachinedstructures off of the substrate using a tungstenprobe tip and placing them onto 100 mesh clamshell grids. For HVTEM studies, no additionalthinning was necessary to image through the entire2 µm thick samples.

The stress-life (S/N) fatigue behavior of thepolycrystalline silicon films was determined using

a ~300-µm square, ~2-µm thick, surface microma-chined fatigue characterization structure, asdescribed in ref. [5] (Fig. 1). Briefly, the notchedcantilever beam specimen (~40-µm long, 19.5-µmwide, with a 13-µm deep, ~1 µm root radius notch)is attached to a large, perforated, plate-shaped massand is electrostatically forced to resonate. Onopposite sides of the resonant mass are interdigi-tated ‘fi ngers’ commonly known as ‘comb drives’ ;one side is for electrostatic actuation, the other pro-vides capacitive sensing of motion. The specimenis attached to an electrical ground, and a sinusoidalvoltage (with no direct-current (DC) offset) at halfthe natural frequency is applied to one comb drive,thereby inducing a resonant response in the planeof the figure. These conditions generate fullyreversed, constant amplitude, sinusoidal stresses atthe notch, i.e., a load ratio (ratio of minimum tomaximum load) of R=�1, that are controlled tobetter than 1% precision with a resolution of ~5%.Specimens were cycled to failure at resonance (~40kHz) in ambient air (~25 °C, 30–50% relativehumidity) at stress amplitudes ranging from ~2 to4 GPa using the control scheme described inrefs. [4,5].

Specimens were prepared by removing the sacri-ficial oxide layer in 49% aqueous hydrofluoric acid(HF) for 21 / 2 or 3 min, drying at 110 °C in air,and subsequently mounting in ceramic electronicpackages for testing [5]. In an attempt to suppressformation of the native oxide and access of moist-ure to the silicon surface, specific specimens werecoated with an alkene-based monolayer of 1-octa-decene, C16H33CH=CH2, after removal of the sacri-ficial oxide. The monolayer was then applied tothe surface of the silicon in a reactor containinga solution of one part 1-octadecene in nine partshexadecane [23]. This hydrophobic monolayerbonds directly to the hydrogen-terminated surfaceatoms of the silicon film created by the exposureto hydrofluoric acid such that no oxide can form;it acts as an effective barrier to both oxygen andwater [23].

The experimentally-measured motion of theresonating fatigue characterization structure wasused to determine the applied stress amplitude,natural frequency, and to monitor the accumulationof fatigue damage prior to failure. The magnitude


Fig. 1. Scanning electron micrograph of the fatigue life characterization structure and notched cantilever beam specimen used inthis investigation. The (a) mass, (b) comb drive actuator, (c) capacitive displacement sensor, and (d) notched cantilever beam specimen(inset) are shown.

of the displacements was carefully calibrated, asdetailed in ref. [5]. Finite element models wereused to establish the relationship between the dis-placements and the maximum principal stress atthe notch. It was previously demonstrated thatmeasured changes in natural frequency may beattributed to damage accumulation in the specimen[7,24]. Thus, additional numerical models of struc-tures containing cracks were used to determine therelationship between crack length and naturalfrequency (i.e., compliance) and the stress-inten-sity factor, K. The models were constructed usinga commercial software package (ANSYS v. 5.7);full details are reported in ref. [25]. In the presentpaper, such methods were used to measure in situthe propagation of nanometer-scale cracks bymonitoring the change in natural frequency of thesample. Crack-growth rates were determined usinga modified secant method applied over ranges ofcrack extension of 2 nm with a 50% overlap withthe previous calculation window; the averagecrack-growth rate was calculated based on a linearfit of the experimental data. The maximum stressintensity immediately prior to failure was taken asan estimate of the fracture toughness of thematerial.

After testing, the crack path and fracture sur-faces of the specimens were characterized using

scanning electron microscopy (SEM) andHVTEM. To avoid corrupting any microstructuralor fractographic features, neither SEM conductivecoatings nor TEM thinning processes were used.

To evaluate the possibility of specimen heatingdue to the large amplitude, high frequency stressesand the induced electrical current used to measuremotion of the structure, high-resolution infrared(IR) imaging of the fatigue characterization struc-ture was performed in order to map temperaturechanges during testing. Thermal images were gen-erated by plotting the difference between IRimages (12-bit resolution) collected while thestructure was resonated at a constant stress ampli-tude, and at rest. Individual IR images were col-lected by averaging over 2 sec at an acquisitionrate of 50 Hz. Temperature changes as small as 20mK could be detected with a spatial resolution ofbetter than 8 µm.

3. Results

3.1. Microstructural analysis

The microstructural analysis of the 2-µm thickpolycrystalline silicon film, shown in the cross-sec-tional TEM image of Fig. 2a, revealed an equiaxed


Fig. 2. (a) Microstructure of the polycrystalline silicon structural film showing a typical cross-sectional TEM image of the through-thickness grain morphology. TEM images of defect types, showing: (b) 220 bright field image of the interior of the grain to highlightmicrotwins, stacking faults, and Lomer–Cottrell dislocation locks, (c) high resolution image of a Lomer–Cottrell lock (inset).

grain morphology (grain size of ~100 nm), withno evidence of strong texture (from correspondingselected-area diffraction). No variations in micro-structure were apparent near features such as theroot of the notch, as expected given the depositionand etching strategy used in the surface microma-chining process. The lack of a textured columnarstructure, which is routinely observed in thin-filmsilicon [26], may be a result of the 900°C annealingused to dope the silicon with phosphorous and

relax the residual stresses associated with growthof the film.

SIMS analysis of the contaminants presentrevealed the interior of the film to contain� 2 × 1018 atoms/cm3

hydrogen, 1 × 1018 atoms/cm3

oxygen, and 6 × 1017 atoms /cm3carbon [5], levels

which are consistent with the processing history ofthe film. In addition, 1 × 1019 atoms /cm3

of phos-phorous were detected from the phosphosilicateglass used to dope the film. The films were found


to be representative of materials used throughoutmicromachining and MEMS research and pro-duction. Oxygen concentrations in excess of� 1018 atoms/cm3

at room temperature can be asso-ciated with precipitation of amorphous and crystal-line Si-O phases [27], although EELS of theinterior of the grains revealed no segregation ofoxygen or carbon in the film. Similarly, EFTEMimaging revealed no segregation of oxygen, car-bon, phosphorous, or nitrogen within the detect-ability limits of the technique. We conclude thatthat no precipitation of secondary species exists inthe films.

Diffraction contrast imaging was used to charac-terize the defect structure of the film and to confirmthe absence of precipitation. A high magnification220 bright field image of the interior of a represen-tative grain, shown in Fig. 2b, reveals several dif-ferent types of lattice defects, including Lomer–Cottrell dislocation locks (a high resolution imageof which is depicted in Fig. 2c), microtwins, andstacking faults. All dark areas of contrast in thesecross sectional images, including polygonal fea-tures, were observed to correspond to one of thesetypes of lattice defects and not to the presence ofprecipitates.

3.2. Stress-life fatigue behavior

Stress-life (S/N) data for the polycrystalline sili-con films from ref. [5], based on a total of 28fatigue specimens tested in room air, is shown inFig. 3; fatigue lives, Nf, varied from ~10 sec to 34days (3 × 105 to 1.2 × 1011 cycles) for stress ampli-tudes ranging from ~2 to 4 GPa at R=�1. Twospecimens were interrupted prior to failure forexamination in the HVTEM. It is apparent that thepolycrystalline silicon films display ‘metal-like’S/N behavior, with an endurance strength at 109–1010 cycles of roughly half the (single-cycle) frac-ture strength. Similar behavior has been seen in 20-µm thick films of single-crystal silicon cycledunder similar conditions [4]. Stress-life fatiguetests were also conducted on specimens coatedwith the 1-octadecene monolayer. Thirteen speci-mens were tested to failure and five were interrup-ted prior to failure for examination in the HVTEM.Fatigue lives varied from ~7.5 sec to 25 days (3 ×

Fig. 3. Typical stress-life (S/N) fatigue behavior of the 2 µm-thick, polycrystalline silicon at �40 kHz in moist room air underfully reversed, tension–compression loading [5].

105 to 8.9 × 1010 cycles) for stress amplitudes rang-ing from ~1.4 to 3.3 GPa at R=�1 (Fig. 4a). Incontrast to the specimens without the monolayercoating, the behavior is reminiscent of bulkbrittle materials.

3.3. Fractography and crack-path analysis

SEM and TEM of both failed specimens andspecimens interrupted during testing were used toevaluate fatigue damage, including the nature ofthe crack trajectory and the fracture surface mor-phology. Previous work [5] established that crackpaths in polycrystalline silicon films during fatigueand subsequent overload failure are transgranular.Scanning electron microscopy at magnifications ashigh as 80,000× revealed a cleavage fracture modewith few distinctions in fracture surface mor-phology in the (presumed) fatigue and overloadregimes.

3.3.1. Overload fracturesOverload fracture surfaces were

(unambiguously) created by manually loading thefatigue test structure with a fixed (non-cyclic) dis-placement under an optical microscope; these con-ditions generate cracks that arrest due to thedecreasing stress gradient associated with displace-


Fig. 4. Comparison of the fatigue behavior of uncoated andmonolayer-coated polycrystalline silicon thin films, showing (a)the respective S/N curves and (b) accumulated fatigue damagein terms of the change in natural frequency of the sample, fcrack,normalized by the natural frequency at the start of the test, f0.Note the reduced susceptibility of the coated polycrystallinesilicon films to fatigue failure in (a), and the significantlyenhanced life (by two orders of magnitude) compared to unco-ated polycrystalline silicon at comparable applied stress ampli-tudes in (b).

ment-control in this configuration. Cracking in thesilicon was confirmed to be transgranular cleavage(Fig. 5), with evidence of secondary cracking andmicrocracking consistent with the ‘slivers’ whichappear on fracture surfaces (Fig. 5c).

3.3.2. Fatigue fracturesAlthough SEM studies were inconclusive in dis-

cerning any differences in the fatigue and overloadfractures, the distinct nature of these two processes

was clearly evident in the HVTEM. Examinationof failed fatigue specimens and untested controlsamples revealed a stark difference in the nativeoxide found at the notch root. In the controlsamples, a native oxide of ~30 nm in thickness wasuniformly distributed over the surfaces of the sam-ple, including the notch. 30-nm thick native oxidelayers were also present on the tested fatigue sam-ple, except in the vicinity of the notch where theoxide layer was significantly thicker. Specifically,up to a three-fold increase in oxide thickness at theroot of the notch was observed on samples that hadbeen exposed to cyclic stresses (Fig. 6), a resultconfirmed on three different fatigued samples.Such enhanced notch-root oxidation was notobserved in monotonically-loaded samples. Fur-thermore, no evidence of misfit dislocations due toa compressively-induced phase transformation wasobserved. As it is conceivable that the high loadingfrequency and induced electric currents may causeheating in the notch region, the role of thermaleffects in the oxidation process was experimentallyevaluated (Fig. 7), as discussed below.

By interrupting fatigue specimens prior to fail-ure after testing at various stress amplitudes andexamining them with HVTEM, several smallcracks (on the order of tens of nanometers inlength) were observed within the native oxide atthe notch root (Fig. 8). The fact that these crackswere partially through the oxide layer indicates thatthey are stable cracks; indeed, this is the first evi-dence of stable fatigue cracking ostensibly in sili-con. Moreover, the size of the cracks was consist-ent with the compliance change of the samplepredicted from the finite element modeling

3.3.3. Infrared microscopyHigh-resolution (20 mK) infrared images were

taken of the test structure during cyclic loading;results at rest and at increasing stress amplitude areshown in Fig. 7. Each image was created by plot-ting the difference between the IR image at restand while resonating; the vertical scale representstemperature changes less than 1 K. The slightwarming of the mass originates from friction of thesilicon with air as the structure resonates at ~40kHz. However, the temperature of the structuredoes not rise significantly (�1 K) above ambient,


Fig. 5. Fractography of failures in polycrystalline silicon films, showing (a) SEM and (b) HVTEM image of the crack trajectoryout of the notch (in an unthinned specimen). (c) SEM images of the transgranular cleavage fracture surfaces of a long-life fatiguetest (Nf=3.8×1010 cycles at σa=2.59 GPa). Horizontal arrow in (c) indicates the direction of crack propagation. Note the fine, needle-like features and debris on the fracture surface in (c).


Fig. 6. HVTEM image of the notch region in an unthinned polycrystalline silicon test sample, showing enhanced oxidation at thenotch root that failed after 3.56×109 cycles at σa=2.26 GPa

and there is no measurable change in the notchedregion. The absence of heating in the cantileverbeam section clearly indicates that the enhancednotch-root oxidation is not thermally induced. Asthe notch root is (initially) the most highly stressedregion of the structure, the process appears to bemechanical in origin. Furthermore, since oxidethickening is not observed under quasi-static load-ing, the phenomenon is associated with thecyclic loading.

3.4. Fracture mechanics analysis

The change in resonant frequency of the cantil-ever beam was monitored during each test to pro-vide a continuous measure of the specimen com-pliance. This frequency decreased monotonically(by as much as 50 Hz in the long-life tests) beforeeventual specimen failure at the notch (Fig. 9).This behavior suggests that the failure of the filmoccurs after progressive accumulation of damage,e.g., by the stable propagation of a crack. Indeed,

the longer the life of the specimen, the larger thedecrease in beam stiffness. A method for relatingsuch changes in resonant frequency and damageprocesses was analyzed in refs. [5] and [25]; in thecurrent work, we utilize this technique to monitorcompliance changes quantitatively throughout thefatigue test.

The frequency change, which from experimentalobservation was reasoned to be due to localizedoxidation and cracking at the notch root, was ana-lyzed using plane-stress finite element modalanalyses with ANSYS [5]. The model suggestedthat for ~1 nm of crack extension, a 1 Hz changein natural frequency should be observed. The cor-responding model for local notch root oxidationpredicted an initial decrease in frequency withincreasing oxide layer thickness (at a rate verysimilar to that induced by cracking) due to the rela-tively low elastic modulus of the SiO2; specifically,a 1 nm increase in oxide thickness resulted in a~0.5 Hz decrease in resonant frequency. Thenumerical models imply that the measured changes


Fig. 7. High resolution (20 mK) infrared (IR) images of the fatigue characterization structure at rest and at increasing stress amplitudeat ~40 kHz. Maximum temperature variations were less than 1 K above ambient and were not measurable in the notched cantileverbeam specimen.

in resonant frequency are consistent with processesoccurring on length scales commensurate with thenative oxide thickness. Accordingly, in the presentwork, estimates of the crack length were made dur-ing the tests and are plotted in Fig. 9; these esti-mates reveal crack sizes that were less than 50 nmthroughout the entire fatigue test. As described pre-viously, HVTEM studies provided direct confir-mation for these damage processes.

3.4.1. Crack-growth ratesAs noted above, in situ measurements of the

change in natural frequency during the fatigue testwere used to determine the crack length, a, as afunction of time or cycles [25]. From such data,crack-growth rates, da/dN, were calculated overincrements of 2 nm in crack extension; a represen-tative result in the form of da/dN as a function ofa is shown in Fig. 10. Crack lengths during the


Fig. 8. HVTEM image showing stable cracks, ~50 nm inlength, in the native oxide formed during cyclic loading of anotched, polycrystalline silicon beam. Testing of this samplewas interrupted after N=3.56×109 cycles at a stress amplitudeσa=2.51 GPa. Image was intentionally defocused to facilitatethe observation of the cracks.

Fig. 9. Representative damage accumulation in polycrystallinesilicon, shown by experimentally measured decrease in resonantfrequency, fcrack, with time during a fatigue test (Nf=2.23×1010

cycles at σa=3.15 GPa) and the corresponding computedincrease in crack length, a.

Fig. 10. Representative computed fatigue-crack growth rates,da/dN, as a function of the crack length, a, during a fatigue testof a polycrystalline silicon thin film (Nf=2.32×1010 cycles atσa=3.15 GPa). Growth rates were determined from the changein specimen compliance monitored throughout the test. Notethat the entire fatigue process of crack initiation and growthuntil the onset of catastrophic failure occurs for crack sizesbelow ~50 nm, i.e., within the native oxide layer.

fatigue process can be seen to remain under ~50nm, consistent with the fatigue process occurringin the oxide layer. Growth rates are vanishinglysmall1 and progressively decrease with increasingcrack length during the test.

3.4.2. Fracture toughness and critical crack sizeIf the crack-driving force at failure is taken as

an estimate of the fracture toughness, the resistanceof the material to unstable crack growth can bedetermined. The crack length estimates at failurewere used with plane-strain models of the stressintensity for the notched cantilever beam structure;the relationship between crack length, appliedforces, and the stress intensity are detailed in ref.[25]. Results from the polycrystalline silicon

1 The absolute values of these crack-growth rates are clearlyphysically unrealistic. However, the growth rates reported areaverage values associated with the number of cycles at the mea-sured natural frequency (~40 kHz) for the crack to grow over2 nm increments, assuming that the crack is growing continu-ously. Although this is the standard way of computing fatigue-crack growth rates [28], in reality the crack may not propagateevery cycle and the crack front may not advance uniformly.


fatigue tests (Fig. 11) give an average fracturetoughness of ~0.85 MPa√m, consistent with that ofthe native oxide [29]. However, it is important tonote the relationship between the critical crack sizeat final failure, ac, and the thickness, ho, of the SiO2

reaction layer when K=Kc. Such critical crack sizesare estimated in Fig. 12 for the range of maximumprincipal stresses used in this investigation. It isapparent that for applied stresses of 2 to 4 GPa,which caused failure in the present films after 105

to 1011 cycles, the critical crack sizes are less than50 nm, i.e., comparable to, or less than, theobserved oxide layer thicknesses (i.e., ac�ho). Thisindicates that the entire process of fatigue-crackinitiation, propagation, and the onset of cata-strophic (overload) failure all occur within theoxide layer.

4. Discussion

4.1. Reaction-layer fatigue

The cyclic fatigue of brittle materials is usuallyassociated with the degradation of (extrinsic)toughening mechanisms in the crack wake [9].Such toughening arises from crack-tip shielding,

Fig. 11. Computed fracture toughness, Kc, values determinedfrom the estimated crack length immediately prior to failure,i.e., from the critical crack size, ac, for the given applied stressamplitude. The average fracture toughness of 0.85 MPa√m isconsistent with failure within the native oxide on polycrystallinesilicon at room temperature.

Fig. 12. Computed estimates of the critical crack size, ac, asa function of the applied stress amplitude, σa, in the polycrystal-line silicon fatigue characterization structure. Critical cracksizes for the stress amplitudes used in the present tests (σa~2to 4 GPa) are less than ~50 nm, indicating that the onset offinal failure of the structure occurs at crack sizes within thenative oxide reaction layer.

which in brittle (non-transforming) ceramicmaterials generally results from mechanisms suchas grain bridging. Under cyclic loading, frictionalwear in the sliding grain boundaries can lead to aprogressive decay in the bridging stresses (e.g.,refs. [9,30,31]). The fatigue of brittle materials istherefore invariably associated with intergranularfailure. When such materials fail transgranularly,e.g., as in commercial SiC and sapphire [32,33],there is generally little or no susceptibility tofatigue failure. Since polycrystalline silicon alwaysfails transgranularly [5,21,34], and there has beenno reported evidence of extrinsic tougheningmechanisms, the material would not be expectedto be prone to cyclic fatigue. No precipitates weredetected in the silicon films that may also enableconventional, brittle material fatigue mechanisms.Furthermore, below ~500 °C, there is no evidenceof mobile dislocation activity [35,36], which couldcause fatigue failure as in a ductile material.

As the cracks observed in the oxide layerappeared to be quite stable, the cause of this crack-ing process was reasoned to be environmentallyassisted cracking due to the moist air environment.The toughness of the SiO2 oxide (Kc~0.8 MPa√m)


is comparable to that of the silicon (Kc~1 MPa√m);consequently, it is unlikely that the oxide wouldcrack prematurely and certainly not in the stablemanner shown in Fig. 8. However, unlike silicon,amorphous SiO2 is highly susceptible to environ-mentally-assisted cracking in moist environments;the threshold stress intensity, Kscc, for such crack-ing is much less than Kc, i.e., typically Kscc~0.25MPa√m, in contrast to silicon where Kscc�Kc [13–15]. Cyclic effects have also been suggested forsubcritical crack growth in borosilicate glass [37].Since no evidence of dislocation activity near thecrack or phase transformations in the vicinity of thenotch root were detected, the fatigue of structuralsilicon films in ambient air is deemed to be asso-ciated with stress-corrosion cracking in the nativeoxide layer that has been thickened under cyclicloading.

We therefore propose that the apparent fatigue

Fig. 13. Schematic illustrations of the reaction-layer fatigue mechanism at the notch of the polycrystalline silicon cantilever beam.(a) Reaction layer (native oxide) on surface of the silicon. (b) Localized oxide thickening at the notch root. (c) environmentally-assisted crack initiation in the native oxide at the notch root. (d) Additional thickening and cracking of reaction layer. (e) Unstablecrack growth in the silicon film.

of thin-film silicon occurs by a conceptually differ-ent mechanism to those cited above for ductile andbrittle solids. Specifically, by monitoring thegrowth of nanoscale cracks with direct HVTEMobservation and in situ stiffness changes we con-clude that such delayed failures are caused bysubcritical cracking of the silica surface layer. Theapparent fatigue of thin-film silicon involves thesequential mechanically-induced oxidation andenvironmentally-assisted cracking of the surfacelayer, a mechanism that we term reaction-layerfatigue (Fig. 13). The native oxide initially formson the exposed silicon surface with a thickness andcomposition dictated by the environment and pro-cessing history. This native oxide then thickens inhigh stress regions during subsequent fatigue load-ing and becomes the site for environmentallyassisted cracks which grow stably in the oxidelayer. The process then repeats itself until a critical


crack size is reached, whereupon the silicon itselffractures catastrophically by transgranular cleav-age. The rate-dependence of thin-film siliconfatigue failures is thus dictated by the cycle-depen-dent oxide thickening process and the time-depen-dent, environmentally-assisted, subcritical crackgrowth in this oxide layer.

While thick compared to the native oxide thatwill typically develop on single crystal silicon atroom temperature [38–41], the presence of heavyphosphorous doping and elevated temperatureexposure during drying of the film created a sig-nificantly thicker reaction layer. However, the pre-cise nature of the mechanically-enhanced oxidationis at present unclear. The notion of a mechanicaldriving force for oxidation is already a central fea-ture of models for the oxidation of silicon [42–47].The presence of a compressive stress in the oxide,primarily due to lattice and thermal mismatches, isthought to be responsible for the details of shapeeffects in oxidation as well as the initially high oxi-dation rates observed during the early stages of theprocess [42–47]. However, as most studies havebeen performed at a high temperature, the role ofstress in room temperature oxidation and theimportance of cyclic loading are far less clear.Studies of the effect of geometry on oxidationwould suggest that the oxide at the notch rootshould be thinner than that found on flat surfaces[46,47]; this further implies the critical role ofstress. Furthermore, it is generally accepted thatstress can modify the diffusivity of a species in agiven material [48]; indeed, high-temperature oxi-dation studies in silicon suggest contributions onthe order of 5–10% of the stress-free activationenergy for thermally grown oxides [42–45]. Atroom temperature, these changes in activationenergy would lead to a change in oxidation rate ofmore than 40 times. As the residual stress distri-bution in the oxide is dependent on the growth con-ditions, including the applied stress, it is conceiv-able that the time-varying stresses encounteredduring fatigue loading play a role in the oxidethickening. Additionally, the presence of the stressinduces cracks within the oxide layer at the notchroot which permit the further ingress of moistureand continued oxidation in this region.

The decreasing crack growth-rate behavior

observed (Fig. 10) is akin to behavior associatedwith microstructurally-small cracks, cracks grow-ing under displacement control, cracks growinginto residual stress fields, and cracks approachinginterfaces. In the present case, the effect is likelyrelated to several of these factors acting in concert,as the cracks are certainly small in size, conditionsdo pertain to displacement control, some degree ofresidual compression will exist in the SiO2 layer,and the crack advancing in the oxide is approach-ing the SiO2/Si interface where the elastic mis-match between the relatively compliant oxide andthe three-fold stiffer silicon substrate will cause thecrack to decelerate [49,50].

It is interesting to note that, in principle, thereaction-layer mechanism applies equally to bulkas well as thin-film silicon, even though bulk sili-con is generally not considered to be susceptibleto either stress-corrosion cracking or fatigue.Cracking in the nano-scale native oxide film has anegligible effect on a macroscopic sample of sili-con under load since crack sizes in the oxide couldnever reach the critical size, i.e., ac�ho, where ho

is the native oxide thickness. In contrast, the sur-face-to-volume ratio is far larger in micro- andnano-scale samples. Consequently, the oxide layerrepresents a large proportion of the sample andcracks within the oxide film are readily able toexceed the critical crack size, i.e., ac�ho, as shownquantitatively in Fig. 12. Thus, cracking in theoxide layer alone can lead to failure of the entiresilicon component.

This behavior provides insight into the observedS/N behavior of thin-film silicon. In metals, thegradual increase in life with decreasing stressamplitude is a direct consequence of the relativelywide range of stable crack growth characterized bya low crack-growth rate exponent of m�3–5 in theParis law, da/dN=�Km (where �K is the stress-intensity range). The appearance of a wide rangeof lives for bulk brittle materials tested at the samestress amplitude (e.g. [51]) is a natural result of thesize distribution of flaws and the limited range forstable fatigue-crack growth in the material, i.e., alarge crack-growth rate exponent, m�10 [9]. It isbelieved that the metal-like S/N behavior of siliconis a direct consequence of the decreasing crack-growth rates observed as the crack extends in the


oxide layer. In thin-film silicon the decreasingdriving force leads to a range of stable crackgrowth and failures that change monotonicallywith decreasing applied stress amplitudes in ameasurable timeframe. Although arising from dif-ferent mechanisms, the correlation between stressamplitude and fatigue life in metals and siliconfilms is ultimately due to the range of stable crackgrowth within the timeframe of the tests.

4.2. Suppression of reaction-layer fatigue

The central treatise of this paper is that thefatigue of thin-film silicon is environmentally-induced. Thus, the obvious test of this mechanismis to conduct experiments in an environment wherethe native oxide cannot form. This poses certaindifficulties with the present system, as the removalof the atmosphere affects the damping of the sys-tem, causing a mechanical as well as an environ-mental effect on cracking behavior [25]. An alter-native strategy is to use monolayer coatings tosuppress the formation of the native oxide with theexpectation that such samples would not be suscep-tible to fatigue in air.

Such coatings have been developed by Maboud-ian et al. [23,52] to reduce the friction coefficientbetween contacting silicon surfaces. In the presentwork, an alkene-based coating of 1-octadecene wasused; the 3 nm thick monolayer on the polycrystal-line silicon at the root of the notch is shown in Fig.14. These coatings are applied directly after thesilicon is removed from the HF and bond directlywith the hydrogen-terminated silicon surface;accordingly, they suppress the formation of thenative oxide (Fig. 14). Moreover, they are hydro-phobic, stable up to 225 °C, and provide an effec-tive surface barrier to both moisture and oxygen.

The fatigue behavior of thin films of siliconcoated with this and other coatings is currentlyunder study. However, initial results on the alkene-based films do show fatigue lifetimes that areessentially unaffected by cyclic stresses (Fig. 4a).Indeed, comparisons of coated and uncoatedsamples indicate that damage accumulation is dra-matically altered and fatigue lives are significantlyextended in the coated samples (Fig. 4b). This

Fig. 14. HVTEM image showing a 1-octadescene self-assembled monolayer (SAM) coating the root of the polycrys-talline silicon notch. The lattice fringes of the silicon are clearlyvisible under the ~3 nm layer that has suppressed the formationof the native oxide layer on the silicon surface.

result clearly provides strong support for the pro-posed mechanism of silicon fatigue.

5. Conclusions

Micron-scale polycrystalline silicon thin filmscan degrade and prematurely fail by high-cyclefatigue in room air environments. Measuredstress/life behavior at ~40 kHz appears to be‘metal-like’ , with failures occurring at stresses aslow as half the (single-cycle) fracture strength forlives in excess of 1011 cycles. This presents a sig-nificant limitation for the long-term stability anddurability of silicon-based MEMS. Based on astudy of this high-cycle fatigue phenomenon using2-µm thick, LPCVD structural films of n+-typepolycrystalline silicon for MEMS applications, thefollowing conclusions can be made:

1. High-voltage transmission electron microscopy(HVTEM) of the polycrystalline silicon thin-film samples revealed a native SiO2 oxide layersome 30 nm thick. However, during fatigue cyc-ling, this layer was thickened by a factor ofroughly three in the immediate vicinity of the


notch root. As high-resolution IR measurementsrevealed that the temperature of the notch didnot exceed 1 K above ambient, such enhancednotch-root oxidation was considered to be prim-arily mechanically-induced.

2. By stopping fatigue tests for microscopic exam-ination, HVTEM also revealed the presence ofstable cracks, tens of nanometers in length,within the enhanced oxide layer. Such subcrit-ical crack growth was reasoned to occur bymoisture-induced stress-corrosion cracking inthe amorphous SiO2.

3. In situ monitoring of the change in natural fre-quency of the fatigue characterization structureduring testing was found to be consistent withprogressive evolution of damage in the form ofoxide formation and subcritical cracking of theoxide. Fracture mechanics-based calibrationsusing finite element methods revealed cracksizes not exceeding 50 nm, comparable withthose imaged directly with HVTEM. Thisimplies that the entire process of fatigue crackinitiation, subcritical cracking, and the onset ofcatastrophic failure, occurs wholly within thenative oxide layer.

4. Accordingly, the apparent fatigue of thin-filmpolycrystalline silicon is ascribed to a ‘surfacereaction-layer’ mechanism involving mechan-ically-induced oxide thickening and stress-cor-rosion cracking of the resulting oxide film.

5. Such reaction-layer fatigue is also applicable tobulk silicon although in comparison to thin-filmsilicon, its effect will be negligible. This isbecause the high surface-to-volume ratio of themicron-scale films means that the critical cracksize for the onset of catastrophic fracture (whenK=Kc) will occur for cracks within the oxidefilm. In contrast, the corresponding critical cracksize for bulk silicon will be much larger thanthe native oxide thickness.

6. The susceptibility of thin-film polycrystallinesilicon to premature failures under high-cyclefatigue loading can be suppressed through theuse of alkene-based monolayer coatings. Suchhydrophobic coatings, which bond directly tothe hydrogen-terminated silicon surface (createdafter exposure to HF), inhibit the formation of

the oxide layer and further act to prevent theingress of both moisture and oxygen.

Acknowledgements

This work was funded by the Director, Office ofScience, Office of Basic Energy Research,Division of Materials Sciences and Engineering ofthe US Department of Energy under Contract No.DE-AC03-76SF00098. Additional funding forequipment was provided by Exponent, Inc., Natick,MA, and the New Energy and Industrial Tech-nology Development Organization (NEDO),Tokyo, Japan. The authors wish to thank Dr. S.B.Brown for his initial support, Dr. W. Van Arsdellfor the original specimen design, Prof. R. Maboud-ian and W.R. Ashurst for assistance with the self-assembled monolayer technologies, Drs. M.Enachescu and S. Belikov for help with the IRimaging, and Prof. R.T. Howe and Dr. J.M.McNaney for helpful discussions.

References

[1] Connally JA, Brown SB. Science 1992;256:1537–9.[2] Brown SB, Van Arsdell W, Muhlstein CL. In: Senturia S,

editor. Proceedings of International Solid State Sensorsand Actuators Conference (Transducers ‘97). 1997. p.591–3.

[3] Muhlstein C, Brown S. Proceedings of theNSF/AFOSR/ASME Workshop on Tribology Issues andOpportunities. In: Bhushan B, editor. MEMS. KluwerAcademic; 1997. p. 80.

[4] Muhlstein, CL, Brown, SB and Ritchie, RO. J. Micrelec-tromech. Sys., 2001, 10, 593-600.

[5] Muhlstein CL, Brown SB, Ritchie RO. Sens Actuators A2001;94:177–88.

[6] Kahn H, Ballarini R, Mullen RL, Heuer AH. Proc RoySoc A 1999;455:3807–23.

[7] Van Arsdell W, Brown SB. J. Micrelectromech. Sys1999;8:319–27.

[8] Komai K, Minoshima K, Inoue S. Micros. Tech1998;5:30–7.

[9] Ritchie RO. Int. J. Fract 1999;100:55–83.[10] Suresh, S., Fatigue of Materials. 2nd ed., Cambridge Uni-

versity Press, Cambridge, England, 1998.[11] Ritchie RO, Dauskardt RH. J. Ceram. Soc. Jap

1991;99:1047–62.[12] Kahn H, Tayebi N, Ballarini R, Mullen RL, Heuer AH.

Sens. Actuators A 2000;A82:274–80.


[13] Chen TJ, Knapp WJ. J. Am. Ceram. Soc 1980;63:225–6.[14] Lawn BR, Marshall DB, Chantikul P. J. Mater. Sci

1981;16:1769–75.[15] Wong B, Holbrook RJ. J. Electrochem. Soc

1987;134:2254–6.[16] Allameh SM, Gally B, Brown S, Soboyejo WO. In: Kahn

H, de Boer M, Judy M, Spearing SM, editors. MaterialsScience of Microelectromechanical System (MEMS)Devices III. MRS; 2000. p. EE2.

[17] Kato NI, Nishikawa A, Saka H. Advanced characterisationof semiconductor materials. Elsevier, 2000 pp. 113-115.

[18] Muhlstein CL, Stach EA, Ritchie RO, Appl Phys Let,2002, 80, 1532–1534.

[19] MCNC/Cronos, www.memsrus.com, 2000.[20] Simmons G, Wang H. Single crystal elastic constants and

calculated aggregate properties: a handbook, 2nd ed. Cam-bridge, MA: M.I.T. Press, 1971.

[21] Ballarini R, Mullen RL, Yin Y, Kahn H, Stemmer S,Heuer AH. Adv. Appl. Mech 1997;12:915–22.

[22] Bravman JC, Sinclair R. J. Electron. Micr. Tech1984;1:53.

[23] Ashurst WR, Yau C, Carraro C, Maboudian R, DuggerMT. J. Micrelectromech. Sys 2001;10:41–9.

[24] Van Arsdell W. Ph.D. dissertation, Massachusetts Instituteof Technology, 1997.

[25] Muhlstein CL, Howe RT, Ritchie RO. Mech. Mater.,2002, in review.

[26] Sharpe Jr. WN, Yuan B, Edwards RL. In: Suhling JC,Liechti KM, Liu S, editors. Proceedings of 1997 Inter-national Mechanical Engineering Congress and Expo-sition. ASME; 1997. p. 113–6.

[27] Mikkelsen JC. In: Mikkelsen JC, Pearton SJ, Corbett JW,Pennycook SJ, editors. Oxygen, Carbon, Hydrogen andNitrogen in Crystalline Silicon. MRS; 1986. p. 3–5.

[28] ASTM. E 647 standard test method for measurement offatigue crack growth rates. In: Annual Book of ASTMStandards, 03.01. West Conshohocken, PA: ASTM; 2001.

[29] Wiederhorn SM. In: Valluri SR, Taplin DMR, Ramo RaoR, Knott JF, Dubey R, editors. Advances in FractureResearch. Pergamon Press; 1984. p. 61-3.

[30] Dauskardt RH. Acta Metal Mater 1993;41:2765–81.[31] Lathabai S, Rodel J, Lawn BR. J Am Ceram Soc

1991;74:1340–8.[32] Gilbert CJ, Cao JJ, MoberlyChan WJ, DeJonghe LC, Rit-

chie RO. Acta Mater 1996;44:3199–214.[33] Asoo B, McNaney JM, Mitamura Y, Ritchie RO. J.

Biomed. Mater. Res., 2000, 488-491.[34] Chen CP, Leipold MH. Amer. Cer. Soc. Bull

1980;59:469–72.[35] Lawn BR, Hockey BJ, Wiederhorn SM. J. Mater. Sci.

Sci 1980;15:12.[36] Chiao YH, Clarke DR. Acta Metal 1989;37:203–19.[37] Dill SJ, Bennison SJ, Dauskardt RH. J. Am. Ceram. Soc.

1997;80:773–6.[38] Taft EA. J. Electrochem. Soc 1988;135:1022–3.[39] Lukes F. Surf. Sci 1972;30:91–100.[40] Raider SI, Flitsch R, Palmer MJ. J. Electrochem. Soc

1975;122:413–8.[41] Lu ZH, Sacher E, Yelon A. Phil. Mag. B 1988;58:385–8.[42] Fargeix A, Ghibaudo G. J. Appl. Phys 1983;54:7153–8.[43] Fargeix A, Ghibaudo G, Kamarinos G. J. Appl. Phys

1983;54:2878–80.[44] Fargeix A, Ghibaudo G. J. Phys. D 1984;17:2331–6.[45] Fargeix A, Ghibaudo G. J. Appl. Phys 1984;56:589–91.[46] Kao D, McVittie JP, Nix WD, Saraswat KC. IEEE Trans.

Elect. Dev. 1987;ED-34:1008–17.[47] Kao DB, McVittie JP, Nix WD, Saraswat KC. IEEE

Trans. Elect. Dev. 1988;ED-35:25–37.[48] Paul W, Warschauer DM. Solids under pressure. New

York, NY: McGraw-Hill, 1963.[49] Hutchinson JW, Suo Z. Adv. Appl. Mech 1992;29:63–

163.[50] Beuth Jr. JL. Int J Solids Struct 1992;29:1657–75.[51] Lathabai S, Yiu-Wing M, Lawn BR. J. Am. Ceram. Soc

1989;72:1760–3.[52] Ashurst WR, Yau C, Carraro C, Howe RT, Maboudian R.

Hilton Head Solid-State Sensor and Actuator Workshop.Transducers Res. Found, 2000 pp. 320-323.

a reaction-layer mechanism for the delayed failure of

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