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Monitoring fatigue damage growth in polysilicon microstructures under different loading conditions
Sensors and Actuators A 159 (2010) 233–240
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Monitoring fatigue damage growth in polysilicon microstructures under different loading conditions Giacomo Langfelder ∗ , Antonio Longoni, Federico Zaraga Politecnico di Milano – Dipartimento di Elettronica e Informazione – via Ponzio 34/5 – I-20133 Milano, Italy
a r t i c l e
i n f o
Article history: Received 10 July 2009 Received in revised form 24 February 2010 Accepted 10 March 2010 Available online 18 March 2010 Keywords: Polysilicon MEMS Fatigue Damage accumulation Real time monitoring
a b s t r a c t Nucleation and accumulation of damage in polysilicon microstructures under fatigue loading cycles are investigated with respect to the maximum applied stress. Measurements are performed with negative load ratios on a 15 m thick notched MEMS specimen, with a notch radius of 0.5 m. The damage in the material is investigated by means of an elastic stiffness decrease monitoring during fatigue life, obtained through a low noise, low perturbing capacitive position readout of the MEMS moving mass. The system is capable to detect elastic stiffness changes with a resolution <20 ppm/Hz1/2 . Experimental results show the existence of different damage accumulation dynamics, with respect to the maximum applied stress: beneath a lower stress limit, damage accumulation is not observed (within the system resolution) up to 2 × 109 cycles; above an upper stress limit, the delayed device failure happens suddenly (it is not anticipated by any detectable stiffness decrease) after ∼105 cycles; between these conditions, a slow, stable damage growth is evidenced through the analysis of the stress dependent stiffness decrease prior to the device failure, which happens after more than 106 to 107 cycles. It is thus suggested the presence of two distinct damaging phenomena, which both lead to the device delayed rupture but with different temporal dynamics. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The fatigue behaviour of polysilicon microstructures is a much investigated issue. As a brittle material, with no known acting extrinsic toughening mechanism, it would not be expected to be subject to fatigue effects, which means to damage accumulation until a critical condition of instantaneous rupture, when stressed with loading cycles well below the monotonic rupture load [1–3]. Though the causes of this behaviour are still discussed, it is demonstrated and accepted that polysilicon microstructures with high surface-to-volume ratio are clearly prone to fatigue [4–11], which can be considered a severe reliability issue for micro-actuators and micro-sensors subjected to mechanical cycles during their life. In the literature two main models have been proposed to explain fatigue, the first (mechanical) assuming subcritical crack growth in the polysilicon itself [4–6], the second (environmental) involving the effects of the surface region, with a stress-assisted oxidation and an environmentally assisted subcritical cracking of the oxide layer [2,7–9]. Critical comparisons of these models have been recently published [2,6]. Evidences supporting the mechanical theory are a strong dependence of fatigue from the load ratio [4,5,14]; the dependence of the
∗ Corresponding author. Tel.: +39 0223993425. E-mail address: [email protected] (G. Langfelder). 0924-4247/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2010.03.011
fatigue from the number of cycles rather than on the elapsed time [1]; the observed polysilicon fatigue also in vacuum (even if with a much longer time dynamics); the absence of failures for devices with thin native oxide tested at constant applied stress even in humid environment [4–6]; the fact that many polysilicon samples failures were observed within less than 30 s, which is a short time interval for large oxidations to happen [6]. A mechanical model for this theory was proposed and discussed in [1,5]: it is believed that the native oxide roughness or oxide debris accumulation can give rise to local wedges within natively formed cracks. Under compression loading (that is why the dependence on the load ratio supports this theory) the wedge is assumed to amplify a driving force for further crack extension inside polysilicon due to a lever effect. The environmental theory is supported by the fact that either a slower damage accumulation or an absence of failure is observed on samples tested in low-humidity environment [1,4,7]; in addition, by post-mortem evidences of a SiO2 thickening in the stress concentration region, observed at the Transmission Electron Microscope (TEM) [2,7–10,19]. Almost every fatigue campaign so far discussed in the literature showed stress-life behaviours of tested samples in line with a Wöhler graph [1]. This representation of obtained experimental results does not definitely help in finding out the reasons of fatigue failure, which can be alternatively looked for by: (i) post-mortem analyses on the failed devices (through several instruments like TEM, HVTEM, EFTEM, XEDS, XPS [2,6]); (ii) monitoring of a macro-
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Fig. 1. Layout of the MEMS test structure used in this work: (a) overview of the device; (b) detail of the lever system which transfers the actuator force to the notch; (c) detail of one of the six springs used to constrain the seismic mass movement in the horizontal direction; (d) layout detail of the fingers of the capacitance; (e) overview of the sole seismic mass, suspended by means of six springs and of the notch (the beams used to form the sensor and actuator capacitance are not shown); (f) SEM image of the lever system and the notch (the dashed line represent the effective points where the structure is fixed).
scopic quantity of the device under test, which changes as a result of cumulative fatigue damage. The performed monitoring of the resonance frequency [7–10] showed a decrease in this quantity, whose amplitude can be reasonably related to damage accumulation in the form either of crack propagation or of an oxide thickening. These analyses however were unable to capture the device behaviour in the very initial period of fatigue lifetime. In this paper a systematic approach to fatigue investigation is presented, which tries to monitor, with a higher temporal resolution than previous works, the nucleation and propagation of microdamages under different maximum applied stresses during fatigue lifetime at negative load ratios R. A specific Micro Electro Mechanical System (MEMS) is used, which includes on-chip both an electrostatic actuator to apply the desired loading cycle and an electrostatic sensor for capacitive position detection [12]. The analysis is performed through a continuous electronic monitoring of the position of the MEMS movable part, from which the elastic stiffness of the specimen can be calculated as the applied stress is known [13,14]. The detected decrease in the elastic stiffness is ascribed
to damage growth in the notched region of the MEMS, where the stress concentration is expected to be the highest. Experimental results obtained at −0.5 < R < −0.4 (which means that the compressive stress is ∼half of the tensile stress) show the existence of different damage accumulation mechanisms (depending on the applied stress peak during fatigue cycles), leading to different behaviours in the notched region. For maximum applied tensile stresses below a certain value low (1.81 GPa) no elastic stiffness change is detected, within the system resolution up to 2 billion cycles, which is consistent with an absence of fatigue damage accumulation. For maximum applied tensile stresses above another value high (2.21 GPa) the fatigue damage nucleation is quickly critical, and the specimen catastrophically breaks, after a short lifetime (105 cycles), without any evident decrease in the elastic stiffness prior to failure. In intermediate conditions, for maximum applied tensile stresses between the said values, the damage accumulation is revealed by a stable and monotonic elastic stiffness decrease, beginning after ∼105 cycles and slowing down until the unstable end of
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the fatigue lifetime. In particular, the higher the maximum applied peak stress within this region, the higher is the damage accumulation rate. Two different failure phenomena are thus revealed: (i) the first leads to delayed ruptures without showing any decrease in the device stiffness; (ii) the second leads to an elastic stiffness decrease, followed by a delayed rupture. A possible interpretation of these results is given in the discussion.
2. The test structure and the high resolution elastic stiffness monitoring The test structures used in this work are built with the ST Microelectronics ThELMATM (Thick Epitaxial Layer for Micro-actuators and Accelerometers) process. As shown in Fig. 1(a), the chip area is mostly occupied by a 15 m thick, rectangular shaped, perforated movable mass, which forms with the constrained parts two sets of comb fingers capacitors, one serving as the sensor and the other serving as the actuator. Thanks to a lever system designed at one end of the movable mass, the electrostatic force generated by the actuator is delivered to a notched constraint [Fig. 1(b)] anchored at one side to the substrate, with a 0.5 m initial curvature radius and a ligament of 8 m, further extended by a free-standing rectangular small protrusion. The effective anchor line of the notch fixed part is evidenced by the dashed line in the SEM picture of Fig. 1(f). The movable mass is suspended also by means of six springs [Fig. 1(c)], which constrain the movable mass to a movement which is horizontal with respect to Fig. 1(a). Their elastic stiffness in the horizontal direction is negligible with respect to the notch constraint: the design of the structure was done with the aid of two FEA software (Comsol Multiphysics and Ansys) in such a way that the elastic stiffness of the whole movable mass is mainly set by this notched constraint [13]. The force can be applied to the moving mass by means of the on-chip electrostatic comb fingers actuator, useful to apply both a monotonic load to rupture and fatigue cyclic loads. A further electrostatic comb finger capacitor allows the position measurement of the structure through capacitance readout, as extensively described by the authors in a previous paper [13]. The main features are the possibility of a real time, continuous, monitoring of the absolute position of the moving mass, and the low noise and low perturbing electrostatic readout obtained by means of a 1 MHz lock in technique. Each pair of comb fingers [Fig. 1(e)] has a measured facing length L0 = 2.1 m and a gap distance xgap = 2.0 m (including the process overetch). To verify the effect of the fringing fields when the movable mass is subjected to large displacements, a set of FEM electrostatic simulations were performed to evaluate the capacitance value with respect to the movable mass displacement, as described in [14]. The measurements of this work are performed in the working region where the percentage error from the theoretical linear behaviour is smaller than 1%. This small systematic error does not influence the system readout resolution. From the position readout, the elastic stiffness can continuously be monitored as the applied force is known. As the elastic stiffness is set by the notched constraint, and as the fatigue stress is concentrated in the mechanical notch, monitoring the elastic stiffness allows monitoring the status of polysilicon in the region where fatigue is expected to cause the largest damage accumulation. The system allows the position detection with a resolution of ∼0.9 nm averaging at 1 Hz of readout bandwidth, corresponding in the range of displacements applied to the structure to elastic stiffness percentage changes k/k < 0.02% at 1 Hz. To further increase the setup sensitivity to elastic stiffness changes, the chosen test frequency was ftest = 11.57 kHz. This value is advantageously below
Fig. 2. Simulink simulation result of the effect of a decrease in the stiffness k on the displacement (normalized to an applied force) spectral response of the MEMS of this work (nominal Q = 27, fres = 12.04 kHz). At low frequency there is only an increase of the displacement as a consequence of the elastic stiffness decrease (point a). On the rising edge of the resonance peak, the effect is amplified (point b).
the resonance frequency (fres = 12.04 kHz) but on the rising edge of the resonance peak. Fig. 2 reports the effect of a decrease in the elastic stiffness on the displacement (normalized to the applied force) spectral response. To study this behaviour close to resonating conditions in case of elastic stiffness changes, a Simulink model of the device, with the measured mean mechanical parameters (resonance frequency fres = 12.04 kHz, elastic stiffness k = 190 N/m, damping coefficient = 0.018) was developed. These mechanical parameters were evaluated through quasi-static and dynamic tests using the capacitive MEMS characterization setup described in [13]. A decrease in the elastic stiffness from k to k causes both an amplitude increase in the low-frequency response (whose initial value is equal to 1/k), and a decrease of the resonance frequency (which is proportional to the square root of the elastic stiffness) from fres to fres . As a consequence (see Fig. 2) the monitored displacement variation around 11.57 kHz (point b) is enlarged with respect to what would be obtained at low frequencies (point a). Through the aid of the Simulink model, it has been verified that the method allows improving the resolution in the elastic stiffness tracking by a factor G = 11, which has been taken into account in the experimental data reduction procedure. It should be remarked that if all tests are performed at the same frequency ftest , the method is sensible to the spreading of the original natural frequency fres of the device. For this reason we used for fatigue analyses only those devices whose resonance frequency deviation fres was within the 0.005 of the average resonance frequency fres (i.e. fres < 0.005 fres ). This action reduced the maximum offset from the mean resolution gain factor to Gos ∼0.1 (this offset is constant during the measures and does not affect the system resolution in terms of minimum measurable elastic stiffness change). During the experimental tests, the changes in the resonance frequency caused by the fatigue cumulative damage are <0.005 fres (see Section 4). From data reported in the literature [7–9] the obtained setup resolution (18 ppm/Hz1/2 ) is fine enough for fatigue accumulation detection and the chosen readout frequency is suitable for measuring the damage accumulation rates during fatigue life. A set of 31 specimens have been used to evaluate the average voltage for instantaneous rupture Vcr = 67 V and to evaluate the corresponding critical principal tensile stress in the notch as described for this and other devices in [15,16,21]: the resulting failure probability is >0.1 at = 3.550 GPa, it is equal to 0.5 at
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Fig. 3. (a) Stress-life plot of the devices used in this work: data of a previous campaign are reported in grey, data of the present work in black. MEMS fatigued with negative load ratios fit a Wöhler curve, while a clear fatigue trend is not observed for devices tested at 0 load ratio. Devices signed with an arrow were interrupted prior to failure. (b) Typical displacement (from the rest position) of the MEMS movable mass during a fatigue test at a load ratio close to R = −0.5.
cr = 3.622 GPa (assumed as the nominal tensile strength), and it is >0.9 at = 3.894 GPa. The oxide native thickness, measured with a TEM analysis by the foundry on unstressed devices, is t ≤ 20 nm. Prior to applying the fatigue cycles, each microsystem has been characterized and its main mechanical parameters have been evaluated in order to screen for abnormalities and to discard devices that did not respect the condition fres < 0.005 fres . 3. Fatigue test conditions The fatigue behaviour of polysilicon microstructures has been reported in the literature to be dependent on several testing parameters, mostly the stress amplitude, the load ratio, the native oxide thickness and the environmental conditions [2,4,10,11]. The device architecture previously described is such that, in quasi-stationary conditions (i.e. at frequencies far lower than the resonance), the electrostatic actuator can only load the notched specimen with a local tensile stress. On the contrary if the excitation frequency is set close to the resonance frequency, also local compressive stresses can be applied to the device, thanks to the overshoots obtained as a consequence of the structure quality factor (∼27). A previous work [14] showed that fatigue lifetime for the present device is strongly dependent on the load ratio and on the applied stress. The stress-life plot obtained by the authors in that work is reported (gray squares and circles) in Fig. 3(a), which evidences the importance of the negative load ratio: no clear fatigue trend is obtained at R = 0 (squares) while
a Wöhler curve well fits the experimental data at R < 0 (circles). The fatigue analysis of the present work was performed in a condition of R < 0: Fig. 3(b) reports the measured displacement of the movable mass of a test device during 12 fatigue cycles in the conditions reported in the figure box. The displacement in the tensile direction is higher with respect to that in the compressive direction, because of the unidirectional electrostatic force, the structure quality factor and the chosen actuation frequency (which is not the resonance frequency). The measured ratio R [5,11] between the compressive (taken as negative) and the tensile (taken as positive) displacement during the tests was always included between R = −0.4 and R = −0.5. This implies that the maximum compressive stress during each test was comprised between the 40% and half the maximum tensile stress. The maximum applied tensile stress in the different tests was between 45% and 72% of the critical tensile rupture stress (cr = 3.62 GPa), depending on the chosen maximum voltage applied between the actuator and the movable mass contacts. The experimental results were taken on wafer level, unpackaged devices in uncontrolled laboratory conditions. The tests were performed at a temperature between 23.6 ◦ C and 25.3 ◦ C, and a relative humidity between 33.5% and 44.1%. During each single test, maximum temperature changes of ±0.05 ◦ C and maximum relative humidity changes of ±0.2% were measured. As these variations are small, no effect of the environmental changes during a single test has been revealed on the structures displacement.
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4. Experimental results The experimental data presented in this section show the behaviour of the elastic stiffness of the MEMS specimens during fatigue stress cycles. As aforementioned, the elastic stiffness was calculated for each specimen from the continuously measured position and from the known applied force. An analysis with respect to the maximum applied stress during fatigue life is performed, assuming in the following that % corresponds to the percentage of the critical tensile monotonic rupture stress. For a group of 20 devices the elastic stiffness measurement was performed either up to the device fatigue rupture or to Nmax = 2 × 109 cycles [see Fig. 3(a)]. The data are further averaged where no important stiffness decrease is observed. The results can be split in three groups: (1) 5 devices were loaded at low peak stresses (% < %, low = 51%). Within them only a device failed [see Fig. 4(a)] after 25 millions of cycles, while the other did not show any decrease in the elastic stiffness (within the system resolution) and did not reach critical rupture conditions within the maximum established number of cycles Nmax = 2 × 109 . This behaviour is consistent
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with the presence of a lower stress limit for fatigue, which would be around low = 1.81 GPa for this process polysilicon (∼half of the measured monotonic rupture tensile principal stress). (2) 11 devices that were loaded at an intermediate maximum stress (%, low = 51% < % < %, high = 61%) showed a decrease of the elastic stiffness during fatigue life. Fig. 4(a) collects data from these 11 measurements, reporting the elastic stiffness percentage decrease k/k on the y axis with respect to the number of cycles on the x axis. Apart from a certain statistical spreading it can be observed that the damage accumulation rate increases with increasing the applied stress. The curves indicated by an asterisk represent devices driven to failure; the other curves represent devices whose fatigue cycles were interrupted prior to the device failure to perform surface analyses of the notch region [these devices are also indicated by an arrow in Fig. 3(a)]. Fig. 4(b), which reports the data for the two devices tested at % = 56% on a logarithmic x axis, underlines how damage accumulation starts to become significant only after ∼105 cycles. This delay in the beginning of the stiffness decrease is revealed also on the other devices tested in this stress range. (3) 4 devices that were loaded at high maximum stresses (% > %, high = 61%) survived for a short lifetime (105 cycles, two orders of magnitude less with respect to the devices of point n. 2 above) and did not show any evident decrease of k before the catastrophic collapse. It is useful to remark that such tests lasted less than 25 s: in agreement with the results of point 2 above, there is no stable damage accumulation. The devices failed suddenly, suggesting the presence of a different delayed failure mechanism which is evident beyond a peak stress level around 2.21 GPa. As a consequence of the experimental results described, a simplified scheme for the damage accumulation in our device with respect to the number of fatigue lifecycles is represented in Fig. 5. There is an initial phase that for every tested device lasts up to ∼105 cycles.
Fig. 4. (a) Elastic stiffness relative decrease during fatigue life for 11 devices tested with a peak normal tensile stress during each cycle between 1.81 GPa and 2.21 GPa. Apart from a statistical spreading, the higher the applied stress, the higher is the damage accumulation rate (the slope of the elastic stiffness decrease). Devices tested at maximum peak normal tensile stresses below 1.81 GPa (50% of the critical stress) do not show a decrease in the elastic stiffness and do not reach the rupture up to 2 billions of cycles (with the exception of a device here represented which failed after 25 millions of cycles). (b) A logarithmic x axis evidences how damage accumulation always starts to be significant only after ∼105 and 106 cycles.
Fig. 5. Schematization of the collected experimental results, representing on a broken linear scale the elastic stiffness relative decrease during fatigue life as a function of the number of fatigue cycles, at different applied peak tensile stresses. Results show: (i) an initial temporal interval where, for every tested device, damage accumulation is not observed within the system resolution, represented by the noise level; (ii) a following interval where damage can accumulate until the device failure in different ways as a function of the applied stress. For peak stresses beyond 2.21 GPa the temporal resolution of the system (represented by the sampling points) cannot capture the very fast stiffness change. For peak stresses smaller than 2.21 GPa the damage accumulation is more stable, in the sense that the system is capable to capture the stiffness decrease. If the stress is even lower than 1.81 GPa, either no damage accumulation happens or the system is not capable to capture these slow but very small stiffness changes.
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G. Langfelder et al. / Sensors and Actuators A 159 (2010) 233–240 Table 1 Summary of the experimental results. Peak stress [GPa]
# of cycles
End of the test
Stiffness relative decrease
1.63 1.81 1.81 1.81 1.81 1.88 1.88 1.88 1.88 1.88 2.03 2.03 2.17 2.17 2.17 2.17 2.25 2.25 2.25 2.61
2 × 109 2 × 109 2 × 109 2 × 109 25 × 106 8 × 106 37 × 106 18 × 106 17 × 106 11 × 106 18 × 106 36 × 106 11 × 106 12 × 106 9 × 106 5 × 106 1 × 105 3 × 105 3 × 105 9 × 104
Survived Survived Survived Survived Failed Failed Failed Interrupted Interrupted Interrupted Failed Failed Failed Interrupted Interrupted Interrupted Failed Failed Failed Failed
Not measurable Not measurable Not measurable Not measurable 3.7 × 10−4 <0.5 × 10−4 0.6 × 10−4 3.9 × 10−4 0.6 × 10−4 <0.5 × 10−4 3.9 × 10−4 5.2 × 10−4 4.0 × 10−4 8.6 × 10−4 8.0 × 10−4 5.9 × 10−4 Not measurable Not measurable Not measurable Not measurable
Fig. 6. SEM detail of the notch root of a device failed after 107 fatigue cycles at 2.20 GPa at R < 0. The probable crack initiation point is marked with a circle.
Fig. 6 shows a scanning electron microscopic view of the rupture surface for a device reported in Fig. 3(a), failed after ∼107 cycles at R < 0 and at a relative maximum applied stress during fatigue cycles % = 60%. Though the SEM picture is taken from the top surface, the river markings on the fracture surface suggest that the starting point of the final crack is at a certain distance from the top of the device, on the surface sidewall of the notch root [17,18]. After the initial phase, for small applied stresses (<%low) no damage accumulation is revealed within the system resolution (represented by the transparent grey rectangle) up to the maximum established number of cycles 2 × 109 cycles (horizontal bold line, labelled n. 3). Above this first stress value a stable damage accumulation is revealed and its effects start to become evident on a macroscopic quantity like the elastic stiffness, after the above-mentioned initial phase. The damage accumulation rate (which is the slope of the bold curve labelled 2 in Fig. 5) increases when increasing the stress peak during fatigue lifecycles. For large applied stresses (beyond a second stress value %high) a different failure (represented by the almost vertical line labelled n. 3 in Fig. 5) manifests suddenly without a previous measurable stiffness decrease, within the temporal system resolution (10−4 point/cycle, represented by the sampling points in Fig. 5). A summary of the experimental results is reported in Table 1. It can be noted that, as the maximum relative stiffness change is kmax = 8 × 10−4 , the maximum amplification of the movement during this test can be evaluated as (1 + G kmax ) = 1.0088, so that the applied stress does not change significantly during each experiment. 5. Discussion Measurements of damage accumulation during fatigue life have been performed in previous works by Muhlstein et al. [2,7,8,19,20]. In their extensive work they monitor the changes in the resonance frequency of 40 kHz, notched resonators, with a different thickness (2 m), a different curvature radius (0.9 m), a different load ratio (−1) and a different Young modulus (163 GPa) with respect to the device tested in this work. The monitoring was performed ∼once every minute, which (at a frequency around 40 kHz) corresponded to one point every ∼2 × 106 cycles. Their results showed a rela-
tive decrease in the resonance frequency (fres /fres ∼ 10−4 [8] to 10−3 [7]) during fatigue life for applied peak stresses as low as half the monotonic rupture stress. Beside this monitoring, with a post-mortem cross-analysis performed with different techniques (HVTEM, EFTEM) they observed up to five-fold thickening of the oxide layer after cycling, for processes with a native oxide thickness both of 5 nm and of 20 nm [2]. They thus attribute the damage accumulation to stress-assisted local oxidation in the notch root and subcritical crack propagation (reaction layer model). They found also that the monitored growth rates are found to be decreasing throughout most of the fatigue life. Kahn et al. [4–6] on the contrary never observed stress-assisted thickening of the native oxide layer. In general, the ability to monitor the accumulation of damage prior to failure allows getting an insight on mechanisms that cannot be gleaned from failure data alone (i.e. simply presented in terms of a stress-life plot). The experimental results of this work, obtained through the continuous monitoring of another macroscopic quantity, the elastic stiffness, show the probable concurrent presence of two distinct phenomena. They both have a stress threshold but they have different time dynamics. • For every tested sample, in the initial phase of fatigue life (up to 105 , 106 cycles), no stiffness variation within the system resolution is ever observed [see for instance Fig. 4(b)]. It is possible that this behaviour was not observed by Muhlstein et al., because their first monitored happened more than 106 cycles after the test beginning. • For applied stresses >60% of the monotonic rupture stress, after the described initial phase, there happens a delayed rupture caused by a first kind of cumulative damage which manifests no measurable effect on the device stiffness (within both the amplitude and the temporal resolution). • In a certain range of applied stresses (between half and the 60% of the critical rupture stress), after the described initial phase, a stable damage starts to accumulate (clearly revealed in form of an elastic stiffness decrease) at a rate that increases when increasing the applied stress level [see Fig. 4(a)]. The stiffness decrease is interpreted as a symptom of a second kind of material degradation. It is worth noting again that the stable damage accumulation begins only after a certain number of cycles [∼105 see Fig. 4(b)].
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Also this second phase of stable damage accumulation ends with a delayed rupture. • For applied stresses lower than approximately half the monotonic rupture stress no cumulative damage is observed within the system resolution and almost never the device failed in tests lasting up to 2 billion cycles. It can be inferred that there are at least two distinct phenomena leading to delayed damage accumulation and following failure of the tested devices: a fast (unstable) mechanism and a slow (stable) mechanism. In the following discussion, hypotheses will be given to put the obtained results in the scientific scenario concerning the fatigue behaviour of polysilicon microstructures. The fast damage phenomenon cannot be captured as an elastic stiffness decrease within the system resolution. As it is hard to believe that a damage accumulation does not affect the device stiffness, it is reasonable to think that there effectively is damage caused by this first phenomenon, but very small in the initial phase (as schematically shown in Fig. 5). This is the reason why no stiffness change is observed. Though small, this damage soon becomes critical at high applied stresses, with propagation dynamics even faster than our sampling time. A hypothesis is stated considering that: (1) FEM simulations by Muhlstein et al. [7], as well as simulations performed by our group, show that a crack propagation is an unstable phenomenon (in the sense that the damage accumulation rate increases with the number of cycles) while simple oxide thickening is a stable phenomenon (in the sense that the damage accumulation rate decreases with the number of cycles); (2) the failure observed within this time interval happens in a very short time (<10 s), thus it is unlikely that a large oxidation can develop in such a short time. As a consequence it is more likely that this first phenomenon is the result of an initial crack nucleation (not affecting significantly the stiffness) and of following crack propagation (very fast) inside polysilicon itself. Further supporting this hypothesis are the facts that: (i) the failures happen only at high applied stresses. In these conditions a small crack may soon become critical, as critical crack size strongly depends on the stress amplitude [8]; (ii) negative load ratios are used, as in other previous works in which delayed failures without evidences of oxidation were observed [4,5]. On the contrary, for small applied stresses, such a failure not anticipated by any stiffness decrease was never observed. The results show a slow and clearly visible damage accumulation, with a damage accumulation rate which decreases during fatigue life, which is consistent with a local oxidation at the notch root [7]. Supporting this theory is also the percentage change of the stiffness that can be related to the percentage change of the resonance frequency observed by Muhlstein et al. (k/k = 2 fres /fres ), who then present, through a post-mortem analysis, evidence of thickened oxide. The failure generated by a critical crack propagating inside the oxide may not be visible because of its rapid propagation (as in the case suggested above of a crack propagating inside the polysilicon). It is thus reasonable to think that, depending on the stress amplitude and on the fabrication process, different phenomena can lead to delayed device failure. In previous works [6], using devices with thin native oxide (∼3 nm), the stress-assisted oxidation was not revealed, while it was clearly evidenced when using devices with a thick native oxide, for applied stresses as small as the 50% of the nominal tensile strength (in the cited work [6], all samples were prepared using a Pd coating which, sputtered to ensure good electrical conductivity, prevented the oxide from being exposed to the
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environment). On the other side, subcritical crack propagation is difficult to observe as it is a fast phenomenon, which requires a very high temporal resolution and a high applied stress. Due to the unavailability of TEM instrumentation, a lack of the present work is that no post-mortem analysis of the devices was performed, which could confirm the proposed hypothesis. We believe that for a full comprehension of what is happening during fatigue lifetime a high temporal resolution monitoring together with electron-optical inspections, both for failed devices and for devices interrupted prior to failure, after the monitoring has revealed that changes are happening, are of paramount importance. These are the guidelines which will be followed in our future analyses. 6. Conclusion An analysis of damage nucleation and propagation mechanisms during fatigue life, as a function of the maximum applied principal tensile stress, has been performed on a set of 20 suitably designed MEMS specimens in ambient air. The devices have a notched constraint with a radius of curvature of ∼0.5 m and a native oxide thickness slightly lower than 20 nm. The devices were tested at negative load ratios (−0.5 < R < −0.4) with maximum applied peak stresses between 1.63 GPa and 2.61 GPa. The experimental results put in evidence the presence of two distinct phenomena leading to cumulative (delayed) rupture. One of them is measured for applied tensile peak stresses >1.81 GPa and is observed through the continuous monitoring of the elastic stiffness decrease. The damage accumulation rate slows down during fatigue lifetime, a behaviour that is consistent with the reaction layer theory. The second phenomenon determines delayed ruptures for applied tensile peak stresses >2.21 GPa. Even if it leads to device failures, it is not anticipated by any change in the elastic stiffness of the structure. Future work will include similar analyses as a function not only of the applied stress, but also of (i) the load ratio and (ii) the environmental conditions. Acknowledgments The authors would like to thank Prof. A. Corigliano and Dr. A. Ghisi of the Department of Structural Engineering, Politecnico di Milano, for the helpful discussions, and STMicroelectronics for the test structure production. The SEM photographs were taken at the NEMAS Laboratory of Politecnico di Milano thanks to the support of Fondazione Cariplo. References [1] D.H. Alsem, O.N. Pierron, E.A. Stach, C.L. Muhlstein, R.O. Ritchie, Mechanism for fatigue of micron-scale silicon structural films, Advanced Engineering Materials 9 (1–2) (2007) 15–30. [2] D.H. Alsem, C.L. Muhlstein, E.A. Stach, R.O. Ritchie, Further considerations on the high-cycle fatigue of micron-scale polycrystalline silicon, Scripta Materialia 59 (2008) 931–935. [3] J.A. Connally, S.B. Brown, Science 256 (1992) 1537. [4] H. Khan, R. Ballarini, J.J. Bellante, A.H. Heuer, Fatigue failure in polysilicon not due to simple stress corrosion cracking, Science 298 (2002), 8 Nov. [5] H. Kahn, R. Ballarini, A.H. Heuer, Dynamic fatigue of silicon, Current Opinion in Solid State and Materials Science 47 (7) (2004) 71–76. [6] H. Kahn, A. Avishai, R. Ballarini, A.H. Heuer, Scripta Materialia 59 (2008) 912–915. [7] C.L. Muhlstein, S.B. Brown, R.O. Ritchie, High-cycle fatigue and durability of polycrystalline silicon thin films in ambient air, Sensors and Actuators A 94 (2001) 177–188. [8] C.L. Muhlstein, E.A. Stach, R.O. Ritchie, A reaction layer mechanism for the delayed failure of micron-scale polycrystalline silicon structural films subjected to high-cycle fatigue loading, Acta Materialia 50 (2002) 3579–3595.
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[9] C. Muhlstein, R. Howe, R. Ritchie, Fatigue of polycrystalline silicon for microelectromechanical system applications: crack growth and stability under resonant loading conditions, Mechanics of Materials 36 (1–2) (2004) 13–33. [10] O.N. Pierron, C.L. Muhlstein, The critical role of environment in fatigue damage accumulation in deep-reactive ion-etched single-crystal silicon structural films, Journal of Microelectromechanical Systems 15 (1) (2006) 111–119. [11] J. Bagdahn, W.N. Sharpe, Fatigue of polycrystalline silicon under long-term cyclic loading, Sensors and Actuators A 103 (2003) 9–15. [12] G. Langfelder, A. Longoni, F. Zaraga, A. Corigliano, A. Ghisi, A. Merassi, A polysilicon test structure for fatigue and fracture testing in micro electro mechanical devices, in: Proceedings of the IEEE Sensors 2008 Conference, IEEE Sensors Journal, 2008, 94-97. [13] G. Langfelder, A. Longoni, F. Zaraga, Low-noise real-time measurement of the position of movable structures in mems, Sensors and Actuators A 148 (2008) 401–406. [14] G. Langfelder, A. Longoni, F. Zaraga, A. Corigliano, A. Ghisi, A. Merassi, A new on-chip test structure for real time fatigue analysis in polysilicon MEMS, Microelectronics Reliability 49 (2009) 120–126. [15] A. Corigliano, B.D. Masi, C. Comi, A. Villa, M. Marchi, Mechanical characterization of polysilicon through on-chip tensile tests, Journal of Microelectromechanical Systems 13 (2004) 200–219.
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Monitoring fatigue damage growth in polysilicon microstructures under different loading conditions Giacomo Langfelder ∗ , Antonio Longoni, Federico Zaraga Politecnico di Milano – Dipartimento di Elettronica e Informazione – via Ponzio 34/5 – I-20133 Milano, Italy
a r t i c l e
i n f o
Article history: Received 10 July 2009 Received in revised form 24 February 2010 Accepted 10 March 2010 Available online 18 March 2010 Keywords: Polysilicon MEMS Fatigue Damage accumulation Real time monitoring
a b s t r a c t Nucleation and accumulation of damage in polysilicon microstructures under fatigue loading cycles are investigated with respect to the maximum applied stress. Measurements are performed with negative load ratios on a 15 m thick notched MEMS specimen, with a notch radius of 0.5 m. The damage in the material is investigated by means of an elastic stiffness decrease monitoring during fatigue life, obtained through a low noise, low perturbing capacitive position readout of the MEMS moving mass. The system is capable to detect elastic stiffness changes with a resolution <20 ppm/Hz1/2 . Experimental results show the existence of different damage accumulation dynamics, with respect to the maximum applied stress: beneath a lower stress limit, damage accumulation is not observed (within the system resolution) up to 2 × 109 cycles; above an upper stress limit, the delayed device failure happens suddenly (it is not anticipated by any detectable stiffness decrease) after ∼105 cycles; between these conditions, a slow, stable damage growth is evidenced through the analysis of the stress dependent stiffness decrease prior to the device failure, which happens after more than 106 to 107 cycles. It is thus suggested the presence of two distinct damaging phenomena, which both lead to the device delayed rupture but with different temporal dynamics. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The fatigue behaviour of polysilicon microstructures is a much investigated issue. As a brittle material, with no known acting extrinsic toughening mechanism, it would not be expected to be subject to fatigue effects, which means to damage accumulation until a critical condition of instantaneous rupture, when stressed with loading cycles well below the monotonic rupture load [1–3]. Though the causes of this behaviour are still discussed, it is demonstrated and accepted that polysilicon microstructures with high surface-to-volume ratio are clearly prone to fatigue [4–11], which can be considered a severe reliability issue for micro-actuators and micro-sensors subjected to mechanical cycles during their life. In the literature two main models have been proposed to explain fatigue, the first (mechanical) assuming subcritical crack growth in the polysilicon itself [4–6], the second (environmental) involving the effects of the surface region, with a stress-assisted oxidation and an environmentally assisted subcritical cracking of the oxide layer [2,7–9]. Critical comparisons of these models have been recently published [2,6]. Evidences supporting the mechanical theory are a strong dependence of fatigue from the load ratio [4,5,14]; the dependence of the
∗ Corresponding author. Tel.: +39 0223993425. E-mail address: [email protected] (G. Langfelder). 0924-4247/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2010.03.011
fatigue from the number of cycles rather than on the elapsed time [1]; the observed polysilicon fatigue also in vacuum (even if with a much longer time dynamics); the absence of failures for devices with thin native oxide tested at constant applied stress even in humid environment [4–6]; the fact that many polysilicon samples failures were observed within less than 30 s, which is a short time interval for large oxidations to happen [6]. A mechanical model for this theory was proposed and discussed in [1,5]: it is believed that the native oxide roughness or oxide debris accumulation can give rise to local wedges within natively formed cracks. Under compression loading (that is why the dependence on the load ratio supports this theory) the wedge is assumed to amplify a driving force for further crack extension inside polysilicon due to a lever effect. The environmental theory is supported by the fact that either a slower damage accumulation or an absence of failure is observed on samples tested in low-humidity environment [1,4,7]; in addition, by post-mortem evidences of a SiO2 thickening in the stress concentration region, observed at the Transmission Electron Microscope (TEM) [2,7–10,19]. Almost every fatigue campaign so far discussed in the literature showed stress-life behaviours of tested samples in line with a Wöhler graph [1]. This representation of obtained experimental results does not definitely help in finding out the reasons of fatigue failure, which can be alternatively looked for by: (i) post-mortem analyses on the failed devices (through several instruments like TEM, HVTEM, EFTEM, XEDS, XPS [2,6]); (ii) monitoring of a macro-
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Fig. 1. Layout of the MEMS test structure used in this work: (a) overview of the device; (b) detail of the lever system which transfers the actuator force to the notch; (c) detail of one of the six springs used to constrain the seismic mass movement in the horizontal direction; (d) layout detail of the fingers of the capacitance; (e) overview of the sole seismic mass, suspended by means of six springs and of the notch (the beams used to form the sensor and actuator capacitance are not shown); (f) SEM image of the lever system and the notch (the dashed line represent the effective points where the structure is fixed).
scopic quantity of the device under test, which changes as a result of cumulative fatigue damage. The performed monitoring of the resonance frequency [7–10] showed a decrease in this quantity, whose amplitude can be reasonably related to damage accumulation in the form either of crack propagation or of an oxide thickening. These analyses however were unable to capture the device behaviour in the very initial period of fatigue lifetime. In this paper a systematic approach to fatigue investigation is presented, which tries to monitor, with a higher temporal resolution than previous works, the nucleation and propagation of microdamages under different maximum applied stresses during fatigue lifetime at negative load ratios R. A specific Micro Electro Mechanical System (MEMS) is used, which includes on-chip both an electrostatic actuator to apply the desired loading cycle and an electrostatic sensor for capacitive position detection [12]. The analysis is performed through a continuous electronic monitoring of the position of the MEMS movable part, from which the elastic stiffness of the specimen can be calculated as the applied stress is known [13,14]. The detected decrease in the elastic stiffness is ascribed
to damage growth in the notched region of the MEMS, where the stress concentration is expected to be the highest. Experimental results obtained at −0.5 < R < −0.4 (which means that the compressive stress is ∼half of the tensile stress) show the existence of different damage accumulation mechanisms (depending on the applied stress peak during fatigue cycles), leading to different behaviours in the notched region. For maximum applied tensile stresses below a certain value low (1.81 GPa) no elastic stiffness change is detected, within the system resolution up to 2 billion cycles, which is consistent with an absence of fatigue damage accumulation. For maximum applied tensile stresses above another value high (2.21 GPa) the fatigue damage nucleation is quickly critical, and the specimen catastrophically breaks, after a short lifetime (105 cycles), without any evident decrease in the elastic stiffness prior to failure. In intermediate conditions, for maximum applied tensile stresses between the said values, the damage accumulation is revealed by a stable and monotonic elastic stiffness decrease, beginning after ∼105 cycles and slowing down until the unstable end of
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the fatigue lifetime. In particular, the higher the maximum applied peak stress within this region, the higher is the damage accumulation rate. Two different failure phenomena are thus revealed: (i) the first leads to delayed ruptures without showing any decrease in the device stiffness; (ii) the second leads to an elastic stiffness decrease, followed by a delayed rupture. A possible interpretation of these results is given in the discussion.
2. The test structure and the high resolution elastic stiffness monitoring The test structures used in this work are built with the ST Microelectronics ThELMATM (Thick Epitaxial Layer for Micro-actuators and Accelerometers) process. As shown in Fig. 1(a), the chip area is mostly occupied by a 15 m thick, rectangular shaped, perforated movable mass, which forms with the constrained parts two sets of comb fingers capacitors, one serving as the sensor and the other serving as the actuator. Thanks to a lever system designed at one end of the movable mass, the electrostatic force generated by the actuator is delivered to a notched constraint [Fig. 1(b)] anchored at one side to the substrate, with a 0.5 m initial curvature radius and a ligament of 8 m, further extended by a free-standing rectangular small protrusion. The effective anchor line of the notch fixed part is evidenced by the dashed line in the SEM picture of Fig. 1(f). The movable mass is suspended also by means of six springs [Fig. 1(c)], which constrain the movable mass to a movement which is horizontal with respect to Fig. 1(a). Their elastic stiffness in the horizontal direction is negligible with respect to the notch constraint: the design of the structure was done with the aid of two FEA software (Comsol Multiphysics and Ansys) in such a way that the elastic stiffness of the whole movable mass is mainly set by this notched constraint [13]. The force can be applied to the moving mass by means of the on-chip electrostatic comb fingers actuator, useful to apply both a monotonic load to rupture and fatigue cyclic loads. A further electrostatic comb finger capacitor allows the position measurement of the structure through capacitance readout, as extensively described by the authors in a previous paper [13]. The main features are the possibility of a real time, continuous, monitoring of the absolute position of the moving mass, and the low noise and low perturbing electrostatic readout obtained by means of a 1 MHz lock in technique. Each pair of comb fingers [Fig. 1(e)] has a measured facing length L0 = 2.1 m and a gap distance xgap = 2.0 m (including the process overetch). To verify the effect of the fringing fields when the movable mass is subjected to large displacements, a set of FEM electrostatic simulations were performed to evaluate the capacitance value with respect to the movable mass displacement, as described in [14]. The measurements of this work are performed in the working region where the percentage error from the theoretical linear behaviour is smaller than 1%. This small systematic error does not influence the system readout resolution. From the position readout, the elastic stiffness can continuously be monitored as the applied force is known. As the elastic stiffness is set by the notched constraint, and as the fatigue stress is concentrated in the mechanical notch, monitoring the elastic stiffness allows monitoring the status of polysilicon in the region where fatigue is expected to cause the largest damage accumulation. The system allows the position detection with a resolution of ∼0.9 nm averaging at 1 Hz of readout bandwidth, corresponding in the range of displacements applied to the structure to elastic stiffness percentage changes k/k < 0.02% at 1 Hz. To further increase the setup sensitivity to elastic stiffness changes, the chosen test frequency was ftest = 11.57 kHz. This value is advantageously below
Fig. 2. Simulink simulation result of the effect of a decrease in the stiffness k on the displacement (normalized to an applied force) spectral response of the MEMS of this work (nominal Q = 27, fres = 12.04 kHz). At low frequency there is only an increase of the displacement as a consequence of the elastic stiffness decrease (point a). On the rising edge of the resonance peak, the effect is amplified (point b).
the resonance frequency (fres = 12.04 kHz) but on the rising edge of the resonance peak. Fig. 2 reports the effect of a decrease in the elastic stiffness on the displacement (normalized to the applied force) spectral response. To study this behaviour close to resonating conditions in case of elastic stiffness changes, a Simulink model of the device, with the measured mean mechanical parameters (resonance frequency fres = 12.04 kHz, elastic stiffness k = 190 N/m, damping coefficient = 0.018) was developed. These mechanical parameters were evaluated through quasi-static and dynamic tests using the capacitive MEMS characterization setup described in [13]. A decrease in the elastic stiffness from k to k causes both an amplitude increase in the low-frequency response (whose initial value is equal to 1/k), and a decrease of the resonance frequency (which is proportional to the square root of the elastic stiffness) from fres to fres . As a consequence (see Fig. 2) the monitored displacement variation around 11.57 kHz (point b) is enlarged with respect to what would be obtained at low frequencies (point a). Through the aid of the Simulink model, it has been verified that the method allows improving the resolution in the elastic stiffness tracking by a factor G = 11, which has been taken into account in the experimental data reduction procedure. It should be remarked that if all tests are performed at the same frequency ftest , the method is sensible to the spreading of the original natural frequency fres of the device. For this reason we used for fatigue analyses only those devices whose resonance frequency deviation fres was within the 0.005 of the average resonance frequency fres (i.e. fres < 0.005 fres ). This action reduced the maximum offset from the mean resolution gain factor to Gos ∼0.1 (this offset is constant during the measures and does not affect the system resolution in terms of minimum measurable elastic stiffness change). During the experimental tests, the changes in the resonance frequency caused by the fatigue cumulative damage are <0.005 fres (see Section 4). From data reported in the literature [7–9] the obtained setup resolution (18 ppm/Hz1/2 ) is fine enough for fatigue accumulation detection and the chosen readout frequency is suitable for measuring the damage accumulation rates during fatigue life. A set of 31 specimens have been used to evaluate the average voltage for instantaneous rupture Vcr = 67 V and to evaluate the corresponding critical principal tensile stress in the notch as described for this and other devices in [15,16,21]: the resulting failure probability is >0.1 at = 3.550 GPa, it is equal to 0.5 at
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Fig. 3. (a) Stress-life plot of the devices used in this work: data of a previous campaign are reported in grey, data of the present work in black. MEMS fatigued with negative load ratios fit a Wöhler curve, while a clear fatigue trend is not observed for devices tested at 0 load ratio. Devices signed with an arrow were interrupted prior to failure. (b) Typical displacement (from the rest position) of the MEMS movable mass during a fatigue test at a load ratio close to R = −0.5.
cr = 3.622 GPa (assumed as the nominal tensile strength), and it is >0.9 at = 3.894 GPa. The oxide native thickness, measured with a TEM analysis by the foundry on unstressed devices, is t ≤ 20 nm. Prior to applying the fatigue cycles, each microsystem has been characterized and its main mechanical parameters have been evaluated in order to screen for abnormalities and to discard devices that did not respect the condition fres < 0.005 fres . 3. Fatigue test conditions The fatigue behaviour of polysilicon microstructures has been reported in the literature to be dependent on several testing parameters, mostly the stress amplitude, the load ratio, the native oxide thickness and the environmental conditions [2,4,10,11]. The device architecture previously described is such that, in quasi-stationary conditions (i.e. at frequencies far lower than the resonance), the electrostatic actuator can only load the notched specimen with a local tensile stress. On the contrary if the excitation frequency is set close to the resonance frequency, also local compressive stresses can be applied to the device, thanks to the overshoots obtained as a consequence of the structure quality factor (∼27). A previous work [14] showed that fatigue lifetime for the present device is strongly dependent on the load ratio and on the applied stress. The stress-life plot obtained by the authors in that work is reported (gray squares and circles) in Fig. 3(a), which evidences the importance of the negative load ratio: no clear fatigue trend is obtained at R = 0 (squares) while
a Wöhler curve well fits the experimental data at R < 0 (circles). The fatigue analysis of the present work was performed in a condition of R < 0: Fig. 3(b) reports the measured displacement of the movable mass of a test device during 12 fatigue cycles in the conditions reported in the figure box. The displacement in the tensile direction is higher with respect to that in the compressive direction, because of the unidirectional electrostatic force, the structure quality factor and the chosen actuation frequency (which is not the resonance frequency). The measured ratio R [5,11] between the compressive (taken as negative) and the tensile (taken as positive) displacement during the tests was always included between R = −0.4 and R = −0.5. This implies that the maximum compressive stress during each test was comprised between the 40% and half the maximum tensile stress. The maximum applied tensile stress in the different tests was between 45% and 72% of the critical tensile rupture stress (cr = 3.62 GPa), depending on the chosen maximum voltage applied between the actuator and the movable mass contacts. The experimental results were taken on wafer level, unpackaged devices in uncontrolled laboratory conditions. The tests were performed at a temperature between 23.6 ◦ C and 25.3 ◦ C, and a relative humidity between 33.5% and 44.1%. During each single test, maximum temperature changes of ±0.05 ◦ C and maximum relative humidity changes of ±0.2% were measured. As these variations are small, no effect of the environmental changes during a single test has been revealed on the structures displacement.
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4. Experimental results The experimental data presented in this section show the behaviour of the elastic stiffness of the MEMS specimens during fatigue stress cycles. As aforementioned, the elastic stiffness was calculated for each specimen from the continuously measured position and from the known applied force. An analysis with respect to the maximum applied stress during fatigue life is performed, assuming in the following that % corresponds to the percentage of the critical tensile monotonic rupture stress. For a group of 20 devices the elastic stiffness measurement was performed either up to the device fatigue rupture or to Nmax = 2 × 109 cycles [see Fig. 3(a)]. The data are further averaged where no important stiffness decrease is observed. The results can be split in three groups: (1) 5 devices were loaded at low peak stresses (% < %, low = 51%). Within them only a device failed [see Fig. 4(a)] after 25 millions of cycles, while the other did not show any decrease in the elastic stiffness (within the system resolution) and did not reach critical rupture conditions within the maximum established number of cycles Nmax = 2 × 109 . This behaviour is consistent
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with the presence of a lower stress limit for fatigue, which would be around low = 1.81 GPa for this process polysilicon (∼half of the measured monotonic rupture tensile principal stress). (2) 11 devices that were loaded at an intermediate maximum stress (%, low = 51% < % < %, high = 61%) showed a decrease of the elastic stiffness during fatigue life. Fig. 4(a) collects data from these 11 measurements, reporting the elastic stiffness percentage decrease k/k on the y axis with respect to the number of cycles on the x axis. Apart from a certain statistical spreading it can be observed that the damage accumulation rate increases with increasing the applied stress. The curves indicated by an asterisk represent devices driven to failure; the other curves represent devices whose fatigue cycles were interrupted prior to the device failure to perform surface analyses of the notch region [these devices are also indicated by an arrow in Fig. 3(a)]. Fig. 4(b), which reports the data for the two devices tested at % = 56% on a logarithmic x axis, underlines how damage accumulation starts to become significant only after ∼105 cycles. This delay in the beginning of the stiffness decrease is revealed also on the other devices tested in this stress range. (3) 4 devices that were loaded at high maximum stresses (% > %, high = 61%) survived for a short lifetime (105 cycles, two orders of magnitude less with respect to the devices of point n. 2 above) and did not show any evident decrease of k before the catastrophic collapse. It is useful to remark that such tests lasted less than 25 s: in agreement with the results of point 2 above, there is no stable damage accumulation. The devices failed suddenly, suggesting the presence of a different delayed failure mechanism which is evident beyond a peak stress level around 2.21 GPa. As a consequence of the experimental results described, a simplified scheme for the damage accumulation in our device with respect to the number of fatigue lifecycles is represented in Fig. 5. There is an initial phase that for every tested device lasts up to ∼105 cycles.
Fig. 4. (a) Elastic stiffness relative decrease during fatigue life for 11 devices tested with a peak normal tensile stress during each cycle between 1.81 GPa and 2.21 GPa. Apart from a statistical spreading, the higher the applied stress, the higher is the damage accumulation rate (the slope of the elastic stiffness decrease). Devices tested at maximum peak normal tensile stresses below 1.81 GPa (50% of the critical stress) do not show a decrease in the elastic stiffness and do not reach the rupture up to 2 billions of cycles (with the exception of a device here represented which failed after 25 millions of cycles). (b) A logarithmic x axis evidences how damage accumulation always starts to be significant only after ∼105 and 106 cycles.
Fig. 5. Schematization of the collected experimental results, representing on a broken linear scale the elastic stiffness relative decrease during fatigue life as a function of the number of fatigue cycles, at different applied peak tensile stresses. Results show: (i) an initial temporal interval where, for every tested device, damage accumulation is not observed within the system resolution, represented by the noise level; (ii) a following interval where damage can accumulate until the device failure in different ways as a function of the applied stress. For peak stresses beyond 2.21 GPa the temporal resolution of the system (represented by the sampling points) cannot capture the very fast stiffness change. For peak stresses smaller than 2.21 GPa the damage accumulation is more stable, in the sense that the system is capable to capture the stiffness decrease. If the stress is even lower than 1.81 GPa, either no damage accumulation happens or the system is not capable to capture these slow but very small stiffness changes.
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G. Langfelder et al. / Sensors and Actuators A 159 (2010) 233–240 Table 1 Summary of the experimental results. Peak stress [GPa]
# of cycles
End of the test
Stiffness relative decrease
1.63 1.81 1.81 1.81 1.81 1.88 1.88 1.88 1.88 1.88 2.03 2.03 2.17 2.17 2.17 2.17 2.25 2.25 2.25 2.61
2 × 109 2 × 109 2 × 109 2 × 109 25 × 106 8 × 106 37 × 106 18 × 106 17 × 106 11 × 106 18 × 106 36 × 106 11 × 106 12 × 106 9 × 106 5 × 106 1 × 105 3 × 105 3 × 105 9 × 104
Survived Survived Survived Survived Failed Failed Failed Interrupted Interrupted Interrupted Failed Failed Failed Interrupted Interrupted Interrupted Failed Failed Failed Failed
Not measurable Not measurable Not measurable Not measurable 3.7 × 10−4 <0.5 × 10−4 0.6 × 10−4 3.9 × 10−4 0.6 × 10−4 <0.5 × 10−4 3.9 × 10−4 5.2 × 10−4 4.0 × 10−4 8.6 × 10−4 8.0 × 10−4 5.9 × 10−4 Not measurable Not measurable Not measurable Not measurable
Fig. 6. SEM detail of the notch root of a device failed after 107 fatigue cycles at 2.20 GPa at R < 0. The probable crack initiation point is marked with a circle.
Fig. 6 shows a scanning electron microscopic view of the rupture surface for a device reported in Fig. 3(a), failed after ∼107 cycles at R < 0 and at a relative maximum applied stress during fatigue cycles % = 60%. Though the SEM picture is taken from the top surface, the river markings on the fracture surface suggest that the starting point of the final crack is at a certain distance from the top of the device, on the surface sidewall of the notch root [17,18]. After the initial phase, for small applied stresses (<%low) no damage accumulation is revealed within the system resolution (represented by the transparent grey rectangle) up to the maximum established number of cycles 2 × 109 cycles (horizontal bold line, labelled n. 3). Above this first stress value a stable damage accumulation is revealed and its effects start to become evident on a macroscopic quantity like the elastic stiffness, after the above-mentioned initial phase. The damage accumulation rate (which is the slope of the bold curve labelled 2 in Fig. 5) increases when increasing the stress peak during fatigue lifecycles. For large applied stresses (beyond a second stress value %high) a different failure (represented by the almost vertical line labelled n. 3 in Fig. 5) manifests suddenly without a previous measurable stiffness decrease, within the temporal system resolution (10−4 point/cycle, represented by the sampling points in Fig. 5). A summary of the experimental results is reported in Table 1. It can be noted that, as the maximum relative stiffness change is kmax = 8 × 10−4 , the maximum amplification of the movement during this test can be evaluated as (1 + G kmax ) = 1.0088, so that the applied stress does not change significantly during each experiment. 5. Discussion Measurements of damage accumulation during fatigue life have been performed in previous works by Muhlstein et al. [2,7,8,19,20]. In their extensive work they monitor the changes in the resonance frequency of 40 kHz, notched resonators, with a different thickness (2 m), a different curvature radius (0.9 m), a different load ratio (−1) and a different Young modulus (163 GPa) with respect to the device tested in this work. The monitoring was performed ∼once every minute, which (at a frequency around 40 kHz) corresponded to one point every ∼2 × 106 cycles. Their results showed a rela-
tive decrease in the resonance frequency (fres /fres ∼ 10−4 [8] to 10−3 [7]) during fatigue life for applied peak stresses as low as half the monotonic rupture stress. Beside this monitoring, with a post-mortem cross-analysis performed with different techniques (HVTEM, EFTEM) they observed up to five-fold thickening of the oxide layer after cycling, for processes with a native oxide thickness both of 5 nm and of 20 nm [2]. They thus attribute the damage accumulation to stress-assisted local oxidation in the notch root and subcritical crack propagation (reaction layer model). They found also that the monitored growth rates are found to be decreasing throughout most of the fatigue life. Kahn et al. [4–6] on the contrary never observed stress-assisted thickening of the native oxide layer. In general, the ability to monitor the accumulation of damage prior to failure allows getting an insight on mechanisms that cannot be gleaned from failure data alone (i.e. simply presented in terms of a stress-life plot). The experimental results of this work, obtained through the continuous monitoring of another macroscopic quantity, the elastic stiffness, show the probable concurrent presence of two distinct phenomena. They both have a stress threshold but they have different time dynamics. • For every tested sample, in the initial phase of fatigue life (up to 105 , 106 cycles), no stiffness variation within the system resolution is ever observed [see for instance Fig. 4(b)]. It is possible that this behaviour was not observed by Muhlstein et al., because their first monitored happened more than 106 cycles after the test beginning. • For applied stresses >60% of the monotonic rupture stress, after the described initial phase, there happens a delayed rupture caused by a first kind of cumulative damage which manifests no measurable effect on the device stiffness (within both the amplitude and the temporal resolution). • In a certain range of applied stresses (between half and the 60% of the critical rupture stress), after the described initial phase, a stable damage starts to accumulate (clearly revealed in form of an elastic stiffness decrease) at a rate that increases when increasing the applied stress level [see Fig. 4(a)]. The stiffness decrease is interpreted as a symptom of a second kind of material degradation. It is worth noting again that the stable damage accumulation begins only after a certain number of cycles [∼105 see Fig. 4(b)].
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Also this second phase of stable damage accumulation ends with a delayed rupture. • For applied stresses lower than approximately half the monotonic rupture stress no cumulative damage is observed within the system resolution and almost never the device failed in tests lasting up to 2 billion cycles. It can be inferred that there are at least two distinct phenomena leading to delayed damage accumulation and following failure of the tested devices: a fast (unstable) mechanism and a slow (stable) mechanism. In the following discussion, hypotheses will be given to put the obtained results in the scientific scenario concerning the fatigue behaviour of polysilicon microstructures. The fast damage phenomenon cannot be captured as an elastic stiffness decrease within the system resolution. As it is hard to believe that a damage accumulation does not affect the device stiffness, it is reasonable to think that there effectively is damage caused by this first phenomenon, but very small in the initial phase (as schematically shown in Fig. 5). This is the reason why no stiffness change is observed. Though small, this damage soon becomes critical at high applied stresses, with propagation dynamics even faster than our sampling time. A hypothesis is stated considering that: (1) FEM simulations by Muhlstein et al. [7], as well as simulations performed by our group, show that a crack propagation is an unstable phenomenon (in the sense that the damage accumulation rate increases with the number of cycles) while simple oxide thickening is a stable phenomenon (in the sense that the damage accumulation rate decreases with the number of cycles); (2) the failure observed within this time interval happens in a very short time (<10 s), thus it is unlikely that a large oxidation can develop in such a short time. As a consequence it is more likely that this first phenomenon is the result of an initial crack nucleation (not affecting significantly the stiffness) and of following crack propagation (very fast) inside polysilicon itself. Further supporting this hypothesis are the facts that: (i) the failures happen only at high applied stresses. In these conditions a small crack may soon become critical, as critical crack size strongly depends on the stress amplitude [8]; (ii) negative load ratios are used, as in other previous works in which delayed failures without evidences of oxidation were observed [4,5]. On the contrary, for small applied stresses, such a failure not anticipated by any stiffness decrease was never observed. The results show a slow and clearly visible damage accumulation, with a damage accumulation rate which decreases during fatigue life, which is consistent with a local oxidation at the notch root [7]. Supporting this theory is also the percentage change of the stiffness that can be related to the percentage change of the resonance frequency observed by Muhlstein et al. (k/k = 2 fres /fres ), who then present, through a post-mortem analysis, evidence of thickened oxide. The failure generated by a critical crack propagating inside the oxide may not be visible because of its rapid propagation (as in the case suggested above of a crack propagating inside the polysilicon). It is thus reasonable to think that, depending on the stress amplitude and on the fabrication process, different phenomena can lead to delayed device failure. In previous works [6], using devices with thin native oxide (∼3 nm), the stress-assisted oxidation was not revealed, while it was clearly evidenced when using devices with a thick native oxide, for applied stresses as small as the 50% of the nominal tensile strength (in the cited work [6], all samples were prepared using a Pd coating which, sputtered to ensure good electrical conductivity, prevented the oxide from being exposed to the
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environment). On the other side, subcritical crack propagation is difficult to observe as it is a fast phenomenon, which requires a very high temporal resolution and a high applied stress. Due to the unavailability of TEM instrumentation, a lack of the present work is that no post-mortem analysis of the devices was performed, which could confirm the proposed hypothesis. We believe that for a full comprehension of what is happening during fatigue lifetime a high temporal resolution monitoring together with electron-optical inspections, both for failed devices and for devices interrupted prior to failure, after the monitoring has revealed that changes are happening, are of paramount importance. These are the guidelines which will be followed in our future analyses. 6. Conclusion An analysis of damage nucleation and propagation mechanisms during fatigue life, as a function of the maximum applied principal tensile stress, has been performed on a set of 20 suitably designed MEMS specimens in ambient air. The devices have a notched constraint with a radius of curvature of ∼0.5 m and a native oxide thickness slightly lower than 20 nm. The devices were tested at negative load ratios (−0.5 < R < −0.4) with maximum applied peak stresses between 1.63 GPa and 2.61 GPa. The experimental results put in evidence the presence of two distinct phenomena leading to cumulative (delayed) rupture. One of them is measured for applied tensile peak stresses >1.81 GPa and is observed through the continuous monitoring of the elastic stiffness decrease. The damage accumulation rate slows down during fatigue lifetime, a behaviour that is consistent with the reaction layer theory. The second phenomenon determines delayed ruptures for applied tensile peak stresses >2.21 GPa. Even if it leads to device failures, it is not anticipated by any change in the elastic stiffness of the structure. Future work will include similar analyses as a function not only of the applied stress, but also of (i) the load ratio and (ii) the environmental conditions. Acknowledgments The authors would like to thank Prof. A. Corigliano and Dr. A. Ghisi of the Department of Structural Engineering, Politecnico di Milano, for the helpful discussions, and STMicroelectronics for the test structure production. The SEM photographs were taken at the NEMAS Laboratory of Politecnico di Milano thanks to the support of Fondazione Cariplo. References [1] D.H. Alsem, O.N. Pierron, E.A. Stach, C.L. Muhlstein, R.O. Ritchie, Mechanism for fatigue of micron-scale silicon structural films, Advanced Engineering Materials 9 (1–2) (2007) 15–30. [2] D.H. Alsem, C.L. Muhlstein, E.A. Stach, R.O. Ritchie, Further considerations on the high-cycle fatigue of micron-scale polycrystalline silicon, Scripta Materialia 59 (2008) 931–935. [3] J.A. Connally, S.B. Brown, Science 256 (1992) 1537. [4] H. Khan, R. Ballarini, J.J. Bellante, A.H. Heuer, Fatigue failure in polysilicon not due to simple stress corrosion cracking, Science 298 (2002), 8 Nov. [5] H. Kahn, R. Ballarini, A.H. Heuer, Dynamic fatigue of silicon, Current Opinion in Solid State and Materials Science 47 (7) (2004) 71–76. [6] H. Kahn, A. Avishai, R. Ballarini, A.H. Heuer, Scripta Materialia 59 (2008) 912–915. [7] C.L. Muhlstein, S.B. Brown, R.O. Ritchie, High-cycle fatigue and durability of polycrystalline silicon thin films in ambient air, Sensors and Actuators A 94 (2001) 177–188. [8] C.L. Muhlstein, E.A. Stach, R.O. Ritchie, A reaction layer mechanism for the delayed failure of micron-scale polycrystalline silicon structural films subjected to high-cycle fatigue loading, Acta Materialia 50 (2002) 3579–3595.
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