Acta Materialia 50 (2002) 3579–3595
`
`www.actamat-journals.com
`
`A reaction-layer mechanism for the delayed failure of
`micron-scale polycrystalline silicon structural films subjected
`to high-cycle fatigue loading
`C.L. Muhlstein a, E.A. Stach b, R.O. Ritchie a,∗
`
`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 of n+-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 fracture
`strength 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 using
`transmission 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 failure
`of thin-film silicon involves sequential oxidation and environmentally-assisted crack growth solely within the native
`SiO2 layer. This ‘reaction-layer fatigue’ mechanism is only significant in thin films where the critical crack size for
`catastrophic failure can be reached by a crack growing within the oxide layer. It is shown that the susceptibility of
`thin-film silicon to such failures can be suppressed by the use of alkene-based monolayer coatings that prevent the
`formation 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 products
`at small dimensions has fueled the rapid development
`
`∗ Corresponding author: Tel.: +1-510-486-5798; fax: +1-
`510-486-4881.
`E-mail addresses: cmuhlstn@uclink4.berkeley.edu (C.L.
`Muhlstein); roritchie@lbl.gov (R.O. Ritchie).
`
`of microelectromechanical systems (MEMS) and the
`enabling 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 adapted
`from the microelectronics industry, and are compatible
`with fabrication strategies for the integrated circuits
`necessary for actuation and control of the systems.
`
`1359-6454/02/$22.00  2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.
`PII: S 13 59 - 6 4 5 4 ( 02 )0 0 1 5 8 - 1
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`these
`long-term durability of
`the
`However,
`microsystems may be compromised by the suscep-
`tibility of thin-film silicon to delayed failure during
`cyclic 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
`quite
`different) [9]. The mechanistic understanding of
`fatigue together with the use of damage/fracture
`mechanics to describe its effect at continuum
`dimensions has allowed for the reliable design and
`operation of innumerable macro-scale structures,
`such as aircraft airframes and engines. At
`the
`micro-scale, the fatigue of ductile materials is attri-
`buted to cyclic plasticity involving dislocation
`motion that
`causes
`alternating blunting and
`resharpening of a pre-existing crack tip as it
`advances
`[10].
`In contrast, brittle materials
`invariably lack dislocation mobility at ambient
`temperatures, such that fatigue occurs by cycle-
`dependent degradation of the (extrinsic) toughness
`of the material in the wake of the crack tip that
`developed from preexisting material inhomogen-
`eities [11]. Prior to this work, the relevance of these
`fatigue mechanisms to silicon films had yet to be
`established.
`Silicon is generally regarded as a prototypical
`brittle material; dislocation activity is generally not
`observed at low homologous temperatures (below
`~500 °C) and there is little evidence of extrinsic
`toughening, such as grain bridging or microcrack-
`ing [12]. Moreover, silicon is not susceptible to
`environmentally-induced cracking (i.e., stress-cor-
`rosion cracking) in moist air or water [13–15] at
`growth rates measurable in bulk specimens. These
`observations strongly suggest that silicon should
`not fatigue at room temperature. Indeed, there has
`been 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 fail
`under cyclic loading was first reported by Connally
`and Brown a decade ago [1]. Since then,
`the
`present authors and others [2–7] have confirmed
`that 2 to 20 µm thick single crystal and polycrystal-
`
`line silicon films can fail in fatigue at stresses as
`low as half their (single-cycle) fracture strength
`after more than ~1011 cycles. Despite such results,
`the mechanistic origins of why thin-film silicon
`should apparently suffer
`fatigue failure have
`remained elusive. Early studies highlighted the
`importance of water vapor and speculated that the
`mechanism may be associated with static fatigue
`of the native silica layer [1,7]. Other proposed
`explanations have involved dislocation activity in
`compression-loaded silicon (e.g.,
`[17]), stress-
`induced phase transformations [4], and impurity
`effects [4], although in no instance has conclusive
`experimental evidence been presented to support
`any of these mechanisms. Moreover, until now
`there has never been any direct observation of
`fatigue 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 the
`crack initiation and growth processes involved in
`the apparent fatigue of silicon are confined to the
`amorphous SiO2 reaction layer that forms on sur-
`faces upon their exposure to air. In this paper, we
`present a mechanism for the apparent fatigue of
`silicon, termed reaction-layer fatigue, on the basis
`of prior stress-life fatigue data, a compliance tech-
`nique for monitoring the damage accumulation,
`and microstructural analysis using high-voltage
`transmission electron microscopy. Additionally,
`we suggest a method for suppressing the cyclic
`fatigue of silicon films through the use of alkene-
`based monolayer coatings that is validated with
`stress-life fatigue data.
`
`2. Experimental procedures
`
`The 2-µm thick silicon films were fabricated
`from the first structural polycrystalline silicon layer
`on run 18 of the MCNC/Cronos MUMPs pro-
`cess. This surface micromachining process utilizes
`low-pressure chemical vapor deposition (LPCVD)
`to manufacture n+-type (resistivity, r=1.9 × 10⫺3
`⍀·cm) polycrystalline silicon [19]. Wafer curvature
`measurements showed the film to have a compress-
`ive residual stress of about 9 MPa [19]; out-of-
`plane deformation due to a through-thickness
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`residual stress gradient could not be detected using
`white-light
`interferometry. Secondary ion mass
`spectroscopy (SIMS), referenced to known stan-
`dards, was used to quantify the concentration of
`hydrogen,
`carbon, oxygen,
`and phosphorous
`present.
`The elastic properties of polycrystalline silicon
`thin films approach the average behavior of ideal-
`ized polycrystalline materials. An average of the
`Voigt 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 estimate
`the elastic behavior of the material. The fracture
`strength of polycrystalline silicon typically ranges
`from 3 to 5 GPa depending on loading condition,
`specimen size, and test
`technique. The fracture
`toughness, 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 were
`glued together face-to-face, mechanically thinned,
`dimpled, and ion milled to the desired electron
`transparency. 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 voltage
`of 800 kV and a JEOL 3010 TEM operating at 300
`kV. Analytical characterization was accomplished
`using a Philips CM200 Field Emission microscope
`equipped with a Link Energy Dispersive Spec-
`trometer (EDS) and a Gatan Image Filter for elec-
`tron energy loss spectroscopy (EELS) and energy
`filtered imaging (EFTEM). Plan view observations
`of the grain morphology and oxide structure were
`accomplished using both the ARM and the Kratos
`High Voltage Electron Microscope (HVTEM)
`operating at 0.8–1.0 MeV. Plan view samples were
`prepared by simply lifting the micromachined
`structures off of the substrate using a tungsten
`probe tip and placing them onto 100 mesh clam
`shell grids. For HVTEM studies, no additional
`thinning was necessary to image through the entire
`2 µm thick samples.
`The stress-life (S/N) fatigue behavior of the
`polycrystalline silicon films was determined using
`
`a ~300-µm square, ~2-µm thick, surface microma-
`chined
`fatigue
`characterization
`structure,
`as
`described in ref. [5] (Fig. 1). Briefly, the notched
`cantilever beam specimen (~40-µm long, 19.5-µm
`wide, with a 13-µm deep, ~1 µm root radius notch)
`is attached to a large, perforated, plate-shaped mass
`and is electrostatically forced to resonate. On
`opposite sides of the resonant mass are interdigi-
`tated ‘fingers’ commonly known as ‘comb drives’;
`one side is for electrostatic actuation, the other pro-
`vides capacitive sensing of motion. The specimen
`is attached to an electrical ground, and a sinusoidal
`voltage (with no direct-current (DC) offset) at half
`the natural frequency is applied to one comb drive,
`thereby inducing a resonant response in the plane
`of
`the figure. These conditions generate fully
`reversed, constant amplitude, sinusoidal stresses at
`the notch, i.e., a load ratio (ratio of minimum to
`maximum load) of R=⫺1, that are controlled to
`better than 1% precision with a resolution of ~5%.
`Specimens were cycled to failure at resonance (~40
`kHz) in ambient air (~25 °C, 30–50% relative
`humidity) at stress amplitudes ranging from ~2 to
`4 GPa using the control scheme described in
`refs. [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 electronic
`packages for testing [5]. In an attempt to suppress
`formation of the native oxide and access of moist-
`ure to the silicon surface, specific specimens were
`coated with an alkene-based monolayer of 1-octa-
`decene, C16H33CH=CH2, after removal of the sacri-
`ficial oxide. The monolayer was then applied to
`the surface of the silicon in a reactor containing
`a solution of one part 1-octadecene in nine parts
`hexadecane [23]. This hydrophobic monolayer
`bonds directly to the hydrogen-terminated surface
`atoms of the silicon film created by the exposure
`to hydrofluoric acid such that no oxide can form;
`it acts as an effective barrier to both oxygen and
`water [23].
`the
`The experimentally-measured motion of
`resonating fatigue characterization structure was
`used to determine the applied stress amplitude,
`natural frequency, and to monitor the accumulation
`of fatigue damage prior to failure. The magnitude
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`Fig. 1. Scanning electron micrograph of the fatigue life characterization structure and notched cantilever beam specimen used in
`this 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, as
`detailed in ref. [5]. Finite element models were
`used to establish the relationship between the dis-
`placements and the maximum principal stress at
`the notch. It was previously demonstrated that
`measured changes in natural frequency may be
`attributed to damage accumulation in the specimen
`[7,24]. Thus, additional numerical models of struc-
`tures containing cracks were used to determine the
`relationship between crack length and natural
`frequency (i.e., compliance) and the stress-inten-
`sity factor, K. The models were constructed using
`a commercial software package (ANSYS v. 5.7);
`full details are reported in ref. [25]. In the present
`paper, such methods were used to measure in situ
`the propagation of nanometer-scale cracks by
`monitoring the change in natural frequency of the
`sample. Crack-growth rates were determined using
`a modified secant method applied over ranges of
`crack extension of 2 nm with a 50% overlap with
`the previous calculation window;
`the average
`crack-growth rate was calculated based on a linear
`fit of the experimental data. The maximum stress
`intensity immediately prior to failure was taken as
`an estimate of
`the fracture toughness of
`the
`material.
`After testing, the crack path and fracture sur-
`faces of the specimens were characterized using
`
`and
`(SEM)
`electron microscopy
`scanning
`HVTEM. To avoid corrupting any microstructural
`or fractographic features, neither SEM conductive
`coatings nor TEM thinning processes were used.
`To evaluate the possibility of specimen heating
`due to the large amplitude, high frequency stresses
`and the induced electrical current used to measure
`motion of the structure, high-resolution infrared
`(IR) imaging of the fatigue characterization struc-
`ture was performed in order to map temperature
`changes during testing. Thermal images were gen-
`erated by plotting the difference between IR
`images (12-bit
`resolution) collected while the
`structure was resonated at a constant stress ampli-
`tude, and at rest. Individual IR images were col-
`lected by averaging over 2 sec at an acquisition
`rate of 50 Hz. Temperature changes as small as 20
`mK could be detected with a spatial resolution of
`better than 8 µm.
`
`3. Results
`
`3.1. Microstructural analysis
`
`The microstructural analysis of the 2-µm thick
`polycrystalline silicon film, shown in the cross-sec-
`tional TEM image of Fig. 2a, revealed an equiaxed
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`3583
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`(a) Microstructure of the polycrystalline silicon structural film showing a typical cross-sectional TEM image of the through-
`Fig. 2.
`thickness grain morphology. TEM images of defect types, showing: (b) 220 bright field image of the interior of the grain to highlight
`microtwins, stacking faults, and Lomer–Cottrell dislocation locks, (c) high resolution image of a Lomer–Cottrell lock (inset).
`
`grain morphology (grain size of ~100 nm), with
`no evidence of strong texture (from corresponding
`selected-area diffraction). No variations in micro-
`structure were apparent near features such as the
`root of the notch, as expected given the deposition
`and etching strategy used in the surface microma-
`chining process. The lack of a textured columnar
`structure, which is routinely observed in thin-film
`silicon [26], may be a result of the 900°C annealing
`used to dope the silicon with phosphorous and
`
`relax the residual stresses associated with growth
`of the film.
`the contaminants present
`SIMS analysis of
`revealed the interior of
`the film to contain
`苲 2 × 1018 atoms / cm3 hydrogen, 1 × 1018 atoms / cm3
`oxygen, and 6 × 1017 atoms / cm3 carbon [5], levels
`which are consistent with the processing history of
`the film. In addition, 1 × 1019 atoms / cm3 of phos-
`phorous were detected from the phosphosilicate
`glass used to dope the film. The films were found
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`to be representative of materials used throughout
`micromachining and MEMS research and pro-
`duction. Oxygen concentrations
`in excess of
`苲 1018 atoms / cm3 at room temperature can be asso-
`ciated with precipitation of amorphous and crystal-
`line Si-O phases [27], although EELS of
`the
`interior of the grains revealed no segregation of
`oxygen or carbon in the film. Similarly, EFTEM
`imaging revealed no segregation of oxygen, car-
`bon, phosphorous, or nitrogen within the detect-
`ability limits of the technique. We conclude that
`that no precipitation of secondary species exists in
`the films.
`Diffraction contrast imaging was used to charac-
`terize the defect structure of the film and to confirm
`the absence of precipitation. A high magnification
`220 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 image
`of which is depicted in Fig. 2c), microtwins, and
`stacking faults. All dark areas of contrast in these
`cross sectional images, including polygonal fea-
`tures, were observed to correspond to one of these
`types of lattice defects and not to the presence of
`precipitates.
`
`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 28
`fatigue specimens tested in room air, is shown in
`Fig. 3; fatigue lives, Nf, varied from ~10 sec to 34
`days (3 × 105 to 1.2 × 1011 cycles) for stress ampli-
`tudes ranging from ~2 to 4 GPa at R=⫺1. Two
`specimens were interrupted prior to failure for
`examination in the HVTEM. It is apparent that the
`polycrystalline 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 cycled
`under similar conditions [4]. Stress-life fatigue
`tests were also conducted on specimens coated
`with 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 苲40 kHz in moist room air under
`fully 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). In
`contrast to the specimens without the monolayer
`coating,
`the behavior
`is
`reminiscent of bulk
`brittle materials.
`
`3.3. Fractography and crack-path analysis
`
`SEM and TEM of both failed specimens and
`specimens interrupted during testing were used to
`evaluate fatigue damage, including the nature of
`the crack trajectory and the fracture surface mor-
`phology. Previous work [5] established that crack
`paths in polycrystalline silicon films during fatigue
`and subsequent overload failure are transgranular.
`Scanning electron microscopy at magnifications as
`high as 80,000× revealed a cleavage fracture mode
`with few distinctions in fracture surface mor-
`phology in the (presumed) fatigue and overload
`regimes.
`
`3.3.1. Overload fractures
`were
`surfaces
`Overload
`fracture
`(unambiguously) created by manually loading the
`fatigue test structure with a fixed (non-cyclic) dis-
`placement under an optical microscope; these con-
`ditions generate cracks that arrest due to the
`decreasing stress gradient associated with displace-
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`3585
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`was clearly evident in the HVTEM. Examination
`of failed fatigue specimens and untested control
`samples revealed a stark difference in the native
`oxide found at
`the notch root. In the control
`samples, a native oxide of ~30 nm in thickness was
`uniformly distributed over the surfaces of the sam-
`ple, including the notch. 30-nm thick native oxide
`layers were also present on the tested fatigue sam-
`ple, except in the vicinity of the notch where the
`oxide layer was significantly thicker. Specifically,
`up to a three-fold increase in oxide thickness at the
`root of the notch was observed on samples that had
`been exposed to cyclic stresses (Fig. 6), a result
`confirmed on three different
`fatigued samples.
`Such enhanced notch-root oxidation was not
`observed in monotonically-loaded samples. Fur-
`thermore, no evidence of misfit dislocations due to
`a compressively-induced phase transformation was
`observed. As it is conceivable that the high loading
`frequency and induced electric currents may cause
`heating in the notch region, the role of thermal
`effects in the oxidation process was experimentally
`evaluated (Fig. 7), as discussed below.
`By interrupting fatigue specimens prior to fail-
`ure after testing at various stress amplitudes and
`examining them with HVTEM, several small
`cracks (on the order of tens of nanometers in
`length) were observed within the native oxide at
`the notch root (Fig. 8). The fact that these cracks
`were partially through the oxide layer indicates that
`they 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 sample
`predicted from the finite element modeling
`
`3.3.3. Infrared microscopy
`High-resolution (20 mK) infrared images were
`taken of the test structure during cyclic loading;
`results at rest and at increasing stress amplitude are
`shown in Fig. 7. Each image was created by plot-
`ting the difference between the IR image at rest
`and while resonating; the vertical scale represents
`temperature changes less than 1 K. The slight
`warming of the mass originates from friction of the
`silicon with air as the structure resonates at ~40
`kHz. However, the temperature of the structure
`does not rise significantly (⬍1 K) above ambient,
`
`Fig. 4. Comparison of the fatigue behavior of uncoated and
`monolayer-coated polycrystalline silicon thin films, showing (a)
`the respective S/N curves and (b) accumulated fatigue damage
`in 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 polycrystalline
`silicon films to fatigue failure in (a), and the significantly
`enhanced 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 the
`silicon was confirmed to be transgranular cleavage
`(Fig. 5), with evidence of secondary cracking and
`microcracking consistent with the ‘slivers’ which
`appear on fracture surfaces (Fig. 5c).
`
`3.3.2. Fatigue fractures
`Although SEM studies were inconclusive in dis-
`cerning any differences in the fatigue and overload
`fractures, the distinct nature of these two processes
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`Fig. 5. Fractography of failures in polycrystalline silicon films, showing (a) SEM and (b) HVTEM image of the crack trajectory
`out of the notch (in an unthinned specimen). (c) SEM images of the transgranular cleavage fracture surfaces of a long-life fatigue
`test (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).
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`3587
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`Fig. 6. HVTEM image of the notch region in an unthinned polycrystalline silicon test sample, showing enhanced oxidation at the
`notch root that failed after 3.56×109 cycles at σa=2.26 GPa
`
`and there is no measurable change in the notched
`region. The absence of heating in the cantilever
`beam section clearly indicates that the enhanced
`notch-root oxidation is not thermally induced. As
`the notch root is (initially) the most highly stressed
`region of the structure, the process appears to be
`mechanical
`in origin. Furthermore, since oxide
`thickening is not observed under quasi-static load-
`ing,
`the phenomenon is associated with the
`cyclic 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) before
`eventual specimen failure at the notch (Fig. 9).
`This behavior suggests that the failure of the film
`occurs after progressive accumulation of damage,
`e.g., by the stable propagation of a crack. Indeed,
`
`the longer the life of the specimen, the larger the
`decrease in beam stiffness. A method for relating
`such changes in resonant frequency and damage
`processes was analyzed in refs. [5] and [25]; in the
`current work, we utilize this technique to monitor
`compliance changes quantitatively throughout the
`fatigue test.
`The frequency change, which from experimental
`observation was reasoned to be due to localized
`oxidation and cracking at the notch root, was ana-
`lyzed using plane-stress finite element modal
`analyses with ANSYS [5]. The model suggested
`that for ~1 nm of crack extension, a 1 Hz change
`in natural frequency should be observed. The cor-
`responding model for local notch root oxidation
`predicted an initial decrease in frequency with
`increasing oxide layer thickness (at a rate very
`similar 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. The
`numerical models imply that the measured changes
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`Fig. 7. High resolution (20 mK) infrared (IR) images of the fatigue characterization structure at rest and at increasing stress amplitude
`at ~40 kHz. Maximum temperature variations were less than 1 K above ambient and were not measurable in the notched cantilever
`beam specimen.
`
`in resonant frequency are consistent with processes
`occurring on length scales commensurate with the
`native oxide thickness. Accordingly, in the present
`work, 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 nm
`throughout the entire fatigue test. As described pre-
`viously, HVTEM studies provided direct confir-
`mation for these damage processes.
`
`3.4.1. Crack-growth rates
`As noted above, in situ measurements of the
`change in natural frequency during the fatigue test
`were used to determine the crack length, a, as a
`function of time or cycles [25]. From such data,
`crack-growth rates, da/dN, were calculated over
`increments of 2 nm in crack extension; a represen-
`tative result in the form of da/dN as a function of
`a is shown in Fig. 10. Crack lengths during the
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`3589
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`Fig. 8. HVTEM image showing stable cracks, ~50 nm in
`length, in the native oxide formed during cyclic loading of a
`notched, polycrystalline silicon beam. Testing of this sample
`was interrupted after N=3.56×109 cycles at a stress amplitude
`σa=2.51 GPa. Image was intentionally defocused to facilitate
`the observation of the cracks.
`
`Fig. 9. Representative damage accumulation in polycrystalline
`silicon, shown by experimentally measured decrease in resonant
`frequency, fcrack, with time during a fatigue test (Nf=2.23×1010
`cycles at σa=3.15 GPa) and the corresponding computed
`increase 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 test
`of a polycrystalline silicon thin film (Nf=2.32×1010 cycles at
`σa=3.15 GPa). Growth rates were determined from the change
`in specimen compliance monitored throughout the test. Note
`that the entire fatigue process of crack initiation and growth
`until the onset of catastrophic failure occurs for crack sizes
`below ~50 nm, i.e., within the native oxide layer.
`
`fatigue process can be seen to remain under ~50
`nm, consistent with the fatigue process occurring
`in the oxide layer. Growth rates are vanishingly
`small1 and progressively decrease with increasing
`crack length during the test.
`
`3.4.2. Fracture toughness and critical crack size
`If the crack-driving force at failure is taken as
`an estimate of the fracture toughness, the resistance
`of the material to unstable crack growth can be
`determined. The crack length estimates at failure
`were used with plane-strain models of the stress
`intensity for the notched cantilever beam structure;
`the relationship between crack length, applied
`forces, and the stress intensity are detailed in ref.
`[25]. Results
`from the polycrystalline silicon
`
`1 The absolute values of these crack-growth rates are clearly
`physically unrealistic. However, the growth rates reported are
`average values associated with the number of cycles at the mea-
`sured natural frequency (~40 kHz) for the crack to grow over
`2 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 propagate
`every cycle and the crack front may not advance uniformly.
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`fatigue tests (Fig. 11) give an average fracture
`toughness of ~0.85 MPa√m, consistent with that of
`the native oxide [29]. However, it is important to
`note the relationship between the critical crack size
`at final failure, ac, and the thickness, ho, of the SiO2
`reaction layer when K=Kc. Such critical crack sizes
`are estimated in Fig. 12 for the range of maximum
`principal stresses used in this investigation. It is
`apparent 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 than
`50 nm,
`i.e., comparable to, or
`less than,
`the
`observed oxide layer thicknesses (i.e., acⱕho). This
`indicates that the entire process of fatigue-crack
`initiation, propagation, and the onset of cata-
`strophic (overload) failure all occur within the
`oxide layer.
`
`4. Discussion
`
`4.1. Reaction-layer fatigue
`
`The cyclic fatigue of brittle materials is usually
`associated 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 determined
`from the estimated crack length immediately prior to failure,
`i.e., from the critical crack size, ac, for the given applied stress
`amplitude. The average fracture toughness of 0.85 MPa√m is
`consistent with failure within the native oxide on polycrystalline
`silicon at room temperature.
`
`Fig. 12. Computed estimates of the critical crack size, ac, as
`a function of the applied stress amplitude, σa, in the polycrystal-
`line silicon fatigue characterization structure. Critical crack
`sizes for the stress amplitudes used in the present tests (σa~2
`to 4 GPa) are less than ~50 nm, indicating that the onset of
`final failure of the structure occurs at crack sizes within the
`native oxide reaction layer.
`
`ceramic
`(non-transforming)
`brittle
`in
`which
`materials generally results from mechanisms such
`as grain bridging. Under cyclic loading, frictional
`wear in the sliding grain boundaries can lead to a
`progressive decay in the bridging stresses (e.g.,
`refs. [9,30,31]). The fatigue of brittle materials is
`therefore invariably associated with intergranular
`failure. When such materials fail transgranularly,
`e.g., as in commercial SiC and sapphire [32,33],
`there is generally little or no susceptibility to
`fatigue failure. Since polycrystalline silicon always
`fails transgranularly [5,21,34], and there has been
`no reported evidence of extrinsic toughening
`mechanisms, the material would not be expected
`to be prone to cyclic fatigue. No precipitates were
`detected in the silicon films that may also enable
`conventional, brittle material fatig