Subscriber access provided by UB + Fachbibliothek Chemie | (FU-Bibliothekssystem)
Communication
Micro-scale fracture behavior of single crystal silicon beams at elevated temperatures Balila Nagamani Jaya, Jeffrey Martin Wheeler, Juri Wehrs, James P. Best, Rafael Soler, Johann Michler, Christoph Kirchlechner, and Gerhard Dehm Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b03461 • Publication Date (Web): 02 Nov 2016 Downloaded from http://pubs.acs.org on November 7, 2016
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Nano Letters is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
Micro-scale fracture behavior of single crystal silicon beams at elevated temperatures Balila Nagamani Jaya1*#, Jeffrey M. Wheeler2*, Juri Wehrs3, James P. Best3, Rafael Soler1, Johann Michler3, Christoph Kirchlechner1,4, Gerhard Dehm1# 1. Max Planck Institut fuer Eisenforschung GmbH, Max Planck Strasse-1, 40237 Duesseldorf, Germany 2.
ETH, Department of Materials, 8093 Zurich, Switzerland
3. Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory of Mechanics, Feuerwerkerstr 39, CH-3602 Thun, Switzerland 4.
Department of Material Physics, University of Leoben, Leoben, Austria
*Both authors contributed equally to the work #Corresponding authors: B. N. Jaya: Email:
[email protected]; Phone: +91-22-2576-7626; G. Dehm: Email:
[email protected]; Phone: +49-211-6792-217 Abstract: The micro-mechanical fracture behavior of Si 100 was investigated as a function of temperature in the scanning electron microscope with a nanoindenter. A gradual increase in KC was observed with temperature, in contrast to sharp transitions reported earlier for macroSi. A transition in cracking mechanism via crack branching occurs at ~300 °C accompanied with multiple load drops. This reveals that onset of small-scale plasticity plays an important role in the brittle-to-ductile transition of miniaturized Si. Keywords: Micro-scale fracture; Brittle to Ductile Transition; Fracture toughness; Single crystal silicon 1. Introduction The brittle-to-ductile transition (BDT) represents the change in fracture behavior of a material from low energy cleavage to high energy ductile rupture as a function of temperature or size. The temperature corresponding to this transition is known to be sensitive to the material’s composition and microstructure [1]. Typically, BDTs have been observed in BCC metals, intermetallics and semiconductors, which have limited dislocation mobility at low homologous temperatures. For such materials with high lattice resistances (Peierls’ stresses), the thermal activation of dislocations is essential to surpass this transition. Accurate knowledge of this behavior allows design of tough, fracture-resistant components for appropriate application temperatures, avoiding brittle failure at temperatures below the BDT. Ignorance of this phenomenon has resulted in catastrophic failures in the past: e.g. breaking up of the Liberty ships during WWII and the Space Shuttle Challenger disaster. In predicting BDT across all material length scales, there are challenges that continue to drive research, for e.g., the development of micro-turbines and micro-combustors in microelectromechanical structures necessitates further investigation of the BDT in silicon. Silicon’s high strength and ability to be precision machined at small length scales using 1 ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
modern lithography techniques allows it to be used as a structural material for microapplications. However, the extreme brittleness of silicon requires careful design to avoid catastrophic fractures during service. On the other hand, maintaining dimensional consistency and linear elastic behavior is also important in such applications. Accurate determination of the fracture behavior and onset of plasticity in silicon at small length scales as a function of temperature is therefore important to allow engineers to ensure proper damage tolerance (defined here to imply an increase in fracture resistance). So far, it is unclear whether fracture toughness of Si shows a temperature dependence at small length scales that is different from that of the bulk. This question is at the core of the present study. Si displays elastic, brittle behavior at ambient temperatures under tensile stresses [2]. The absence of room temperature plasticity suggests that dislocation mobility is restricted in Si. Brittle to ductile transition temperature (BDTT) measurements on bulk, single crystalline (SC) Si, first reported by John [2] and later by several others [3-5], show sharp transitions from brittle to ductile behavior within only a few degrees change in temperature. The actual value of the reported BDTT itself has varied widely from 545 °C to 805 °C, depending on the test method, strain rate and crystal orientation. Seminal work on the BDTT of Si including its strain rate dependence has been carried out by Hirsch, Sammuels and Roberts [3, 6], and experimental values of activation energy and activation volume for dislocation movement in Si in terms of partial or full slip have been determined. More recent reports suggest a size effect in BDT of Si, pushing the BDTT to even lower temperatures, (200-300 °C) for microscale specimen [7-9] and down to room temperature in nano-scale pillars [10-12]. These works use micro-pillar compression or micro-cantilever bending [13] to determine the sizeaffected BDTT. Below the BDTT, micro-scale samples reveal catastrophic failure while above it, significant plastic deformation is observed. What is missing though is a direct measure of the fracture toughness as a function of temperature at the micron scale, which would precisely reflect changes in fracture behavior and serve as a classical BDTT measurement. In addition, miniaturized fracture experiments can be used to identify the onset of small scale plasticity by changes in crack path and/or load-displacement data. This study, to the best of our knowledge, is the first attempt to analyze the temperature dependence of fracture toughness KC for Si at the micron length scale. 2. Experimental Section Intrinsic, nearly dislocation free SC Si 100 supplied by Infineon Technologies, Villach, Austria, was used for the present study. In order to measure KC as a function of temperature T, we performed notched micro-cantilever bending experiments in situ inside a Vega 3 (Tescan a.s., Brno, Czech Republic) scanning electron microscope (SEM) between 25 and 600 °C using a modified Alemnis SEM Indenter (Alemnis AG, Thun, Switzerland). This system [14] features independent heating of both the indenter and sample with the indenter’s apex temperature calibrated to act as a referenced surface temperature probe [15]. Sample surface temperatures were determined with an accuracy of 1% of the applied temperature gradient, and thermal drift was minimized by careful matching of the tip and sample temperatures. A conospheroidal diamond indenter (Synton-MDP AG, Switzerland) with a radius of 5 µm radius was used to reduce any indentation plasticity during bending. Microbeam specimens were produced by focused ion beam (FIB) machining of a 100-oriented SC Si wafer using a Zeiss Auriga dual beam FIB workstation operated at 30 kV. Coarse milling was carried out at 4 nA, final surface polishing was carried out at 240 pA to remove re-deposition and milling 2 ACS Paragon Plus Environment
Page 2 of 17
Page 3 of 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
currents were minimized to 10 pA at the notching stage to avoid ion damage at the crack tip. The notch tip radius below 30 nm, mimicking a sharp pre-crack. Rectangular microbeams were machined with dimensions of 8.5 × 2 × 2 µm with notches machined from the top to the same depth and a root radius < 30 nm, maintaining a crack length to width (a/W) ratio of ~ 0.3 [16]. The cantilever microbeams were oriented along the 011 and the notches were aligned along the 011100. Testing was carried out in displacement control at 5 nm/s at 25, 150, 300, 400, 500 and 600 °C during the heating cycle and again at 25 °C after cooling to investigate possible effects of thermal exposure. Testing above 600 °C was wrought with instrument related challenges and was not carried out. A total of 50 microbeams were tested with a minimum of 6 microbeams tested at each temperature. Since the experiments were carried out in the SEM, vacuum conditions of better than 10-5 mbar were maintained throughout, preventing any significant oxidation of the Si during the fracture process. Conducting these tests in situ also allowed accurate placement of the indenter on the beams and determination of the precise bending moment applied. Figure 1 summarises the test conditions and specimen geometry used. Fracture loads were correlated to onset of cracking from the notch tip and used to quantify the fracture toughness in terms of KC using Eq. (1-2) [17].
1
1.46 24.36
47.21 75.18 2
where KC is the critical stress intensity factor (different from KIC corresponding to a standard fracture test geometry under plane strain), a is the crack length, σ is the applied stress, Pcrit is the fracture load, and L, B, and W correspond to the cantilever length, breadth and width respectively. Crack tip opening displacement measurements were not possible due to the limited resolution of the SEM, especially at elevated temperatures. Post-mortem imaging of the crack tip at high resolution was carried out using the Gemini electron column of the Zeiss dual beam FIB workstation.
Figure 1. a) Series of cantilevers micromachined by FIB on Si 〈100〉. b) Single cantilever showing beam dimensions and orientation with respect to the loading direction under in situ loading. Since the BDTT is sensitive to the doping concentration, sample purity and crystal orientation, we complemented the micro-scale tests with standard 4-point bending (4PB) 3 ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 17
experiments for fracture toughness evaluation at the macro-scale using notched specimen on equivalent wafer grade SC Si samples, details of which are given in the Supporting Information.
3. Results and Discussion Table 1 shows the KC measured as a function of temperature, along with the yield stress and elastic modulus data recorded for similar sized samples from earlier work [7, 14], as well as the average plastic zone size and fracture energy calculated for each test temperature. Linear elastic fracture mechanics (LEFM) was used to calculate the initiation KC, since the loaddisplacement (P-d) curves did not indicate any deviations from linear elastic behavior at all temperatures. Fracture energy, G, was calculated using Eq. 3, and the plane stress plastic zone size rp was determined using Eq. 4 considering yield strength values from micropillar compression reported for a similar pillar size [7]. 1 & '
( 3
1 )* , / 4 2+ -. where E is the elastic modulus, ν is the Poisson’s ratio, σy is the 0.2% flow stress in compression. Eq. 4 is derived from continuum mechanics and is only an approximation in the case of micro-scale single crystalline materials. Potentially, the method can be coupled to EBSD and this would allow analysis of the crack tip process zone in greater detail. However, adequate surface preparation on such samples has not yet been successfully performed due to inherent difficulties with the FIB preparation technique. The room temperature fracture energy calculated from Eq. 3 is considerably higher than that measured for the natural cleavage 0 or 1101100 under pure mode I conditions in bulk SC Si [18]. This systems of 111112 is because the crack deviates from the chosen notch plane into the nearest low energy cleavage system at 25 and 150 °C (Figure 2b & 2d) and does not maintain mode I conditions. Table 1. Micro-scale fracture toughness, plastic zone size and fracture energy measured in this study as a function of temperature. Corresponding yield strength and elastic modulus are listed from literature.
T
KC
rp
G
compression) [7]
E (microcompression) [14]
MPam
GPa
GPa
nm
J/m
25
1.00±0.15
5.8
129.5
5
7.2
150
1.23±0.12
5.3
129
9
10.8
300
1.32±0.09
4.0
127
11
12.6
400
1.44±0.30
3.0
125.5
35
15.2
o
σy (micro-
1/2
C
4 ACS Paragon Plus Environment
2
Page 5 of 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
500
1.55±0.32
2.0
125
96
17.7
600
1.81±0.41
1.0*
124*
526*
24.6
* Estimated values based on extrapolation of σy and E data for 600 °C from data available at 500 °C [7, 14] Unlike earlier reports on bulk Si [2, 3], the KC measured in our tests shows a smooth transition in fracture behavior from brittle to a more damage tolerant state. A single BDTT point was not identified within the tested temperature range, suggesting full ductility may require even higher temperatures. From the plastic zone size calculations, the zone remains within the cantilever width for all the samples, so plane strain fracture toughness requirements were met for all temperatures. Figure 2 shows representative typical crack trajectories and P-d responses of micro-scale SC Si at the test temperatures. Figure 3 compiles the fracture surfaces at different test temperatures. From these images, it is clear that there is a distinct change in fracture mechanism at temperatures of ~300 °C from singular cleavage (Figure 3a & 3b) to multiple faceted fracture surface morphology (Figure 3c & 3d). At 25 and 150 °C, a single large load drop (Figure 2a & 2c) is accompanied by catastrophic brittle fracture of the cantilever (Figure 2b & 2d), as expected below the BDTT in Si. Cracks are extremely sharp and close up upon unloading at 25 °C. At 150 °C, the crack tip opening becomes larger and single kinks begin to appear as the crack approaches the free surface of the cantilever. At 300 and 400 °C, multiple load drops and crack branching events occur (Figure 2e-h). These lead to crack arrest and stabilization. At 500 °C and above (Figure 2i-l), there is another change in fracture mechanism that results in extensive crack deflection and kinking and only at 600 °C, a clear deviation from linear elasticity in the P-d response is observed in 2 out of the 6 samples tested (Figure 2k). The branching event disappears, but the cracks no longer follow a single cleavage plane as at low temperatures. Accordingly, the discussion follows three categories into which fracture modes can be classified: low (25, 150 °C), intermediate (300, 400 °C) and high temperatures 500, 600 °C). Sharper cracks at low temperatures (Figure 2b & 2d) and larger crack openings at higher temperatures (Figure 2j & 2l) indicate that deformation is purely linear elastic in the former case and shows onset of plasticity in the latter. Table 1 shows that while the yield strength evaluated from micro-pillar compression [7] drops significantly beyond 300 °C, the elastic modulus only drops marginally [14]. Therefore, the plastic zone size increases sharply beyond 300 °C, while the increase in fracture energy is more gradual. It is important to note that for cases where profuse crack branching or kinking events occur, at intermediate and high temperatures, only a lower estimate of KC can be made since the calculations do not account for the change in fracture mode.
5 ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Figure 2. Load-displacement response and corresponding crack trajectories recorded for different test temperatures. *Not representative at 600 °C: only 2 out of 6 specimen showed significant plasticity.
6 ACS Paragon Plus Environment
Page 6 of 17
Page 7 of 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
Figure 3. Fracture surfaces at the various test temperatures showing cleavage fracture at 25 °C and 150 °C and evidence of plastic deformation and multiple branches at 400 °C and larger kinks at 500 °C. (a) and (b) were broken subsequent to the tests to observe the fracture surface during which some contamination near the notched regions could not be avoided. Figure 4 shows the average KC and the associated standard deviations measured from the micro-scale tests as a function of temperature. Within the error bar, the fracture toughness remains fairly constant up to 300 °C and then increases gradually without reaching a plateau value at 600 °C, suggesting onset of BDT at around 300 °C or lower. The fracture toughness increases by 81% from 25 to 600 °C. There is no sharp rise in KC at any given test temperature unlike in the bulk [2]. The increase in scatter at higher temperatures and a lack of a plateau value also indicates that the BDT may not yet be complete by 600 °C. The macroscale KIC values across this temperature range from [2], recorded at the displacement rate of 80 nm/s have been superimposed for comparison. It remains at a low value of ~1.1 MPam1/2 from 25 °C up to 701 °C and suddenly jump to above 4 MPam1/2 at 705 °C. The BDTT shifts to higher values at higher strain rates [2, 3] but the strain rate dependence studies at the microscale was not within the scope of our work. The micro-scale initiation KC is also comparable to the macro-scale KC as determined both previously as well as in the present work at room temperature, but differences in fracture mechanism begin to appear at elevated temperatures. Our macro-scale tests showed linear elastic deformation till the point of catastrophic fracture at all test temperatures up to 600 °C (see Figure S1 of Supporting Information). The crack propagated along a single cleavage plane up to 500 °C and did not branch out like in the micro-scale samples. At 600 °C, the sample fractured into multiple fragments with a much higher fracture load, recording a sharp transition in fracture behavior. The force-displacement behavior at this transition temperature continued to be linear elastic, suggesting that full ductility is not achieved yet. As against this, the KC increases steadily and smoothly above 300 °C in micro-scale sample and at no point shows a sharp change up to the maximum tested temperature of 600 °C. The damage tolerance in terms of propagation toughness (R-curve) at the micro-scale has not been quantified in the present work. The energy absorbed during fracture for micro-scale samples tested at 300 and 400 °C is clearly higher owing to the multiple load drops that follow. Observations of the crack trajectory also show extensive crack branching, kinking and crack arrest at temperatures ≥300 °C, pointing to enhanced resistance to crack growth, although the initiation fracture toughness rises only marginally. This shows that the damage tolerance of micro-scale samples is improved significantly at temperatures ≥ 300 °C with a clear change in fracture mechanism, while the initiation toughness increases steadily. Therefore, it can be concluded that the micro-scale specimen show a lower BDTT, while also displaying a more gradual transition to increasingly ductile behavior. These distinctions between macro- and micro-scale results point towards a clear size effect in fracture behavior of SC Si. 7 ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
While a BDTT ≥ 600 °C is confirmed from our macro-scale tests, we refrain from reporting the KIC here as they predominately represent a notch toughness and not the true fracture toughness of SC Si. It should be noted that the dicing process used for notching leads to a finite notch root radius (~25 µm) in our macro-scale specimens, and an accompanying heavily deformed region of amorphous-dislocation rich zone at the crack tip. This creates very different crack tip conditions compared to earlier work using controlled pre-cracks [2, 3] and hence makes a toughness comparison invalid.
Figure 4. Initiation fracture toughness plotted as a function of test temperature showing a fairly constant KC below 300 °C and a smooth rise above it for the micro-scale Si tested in the present work. Fracture toughness data of macro-Si from [2] showing a constant low value up to 700 °C followed by a single sharp transition above it is superimposed for comparison. It was previously shown that Ga ion damage does not affect the micro-scale fracture toughness of FIB notched Si at room temperature [16]. FIB induced damage and Ga ion implantation can play a detrimental role in fracture toughness measurements, especially at elevated temperatures. But FIB machined/notched structures will always contain some amount of Ga on the surface and a resulting amorphisation of the material. It has been shown that this damage zone does not extend beyond ~20 nm for milling conditions of 30 kV and 1 nA currents [19]. Furthermore, heating of Ga-implanted silicon results in desorption of the implanted Ga on the sample surface, since Si and Ga are immiscible at these temperatures [20]. Once Ga segregates to the surface, it begins to coalesce into beads. The Ga beads remain even after the sample is cooled (bright droplets in Figure 2). Fortunately, since we are testing SC Si, there are no internal grain boundaries where the Ga might enrich and alter fracture behavior. The similarity in KC measured at room temperature before and after heating to 600 °C (Figure 4) implies that Ga and heating induced changes has no adverse effect on the fracture experiments of SC Si. To the best of our knowledge, these are the first reports of true KC measurements at the microscale at elevated temperature for Si. Earlier reports analytically estimate KC for nano and micro-length scale samples within a limited temperature range of 60 to 80 °C [9, 11, 12]. Our 8 ACS Paragon Plus Environment
Page 8 of 17
Page 9 of 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
results show that crack tip shielding mechanism in the form of crack branching begins to operate in SC Si at intermediate temperatures between 300 and 400 °C (Figure 2f, 2h & 3c), which is considerably lower compared to the reported BDTT of macro-Si. This could be due to activation of partial dislocation slip at these temperatures [21]. Silicon has a diamond cubic structure, which is equivalent to two interpenetrating FCC lattices shifted by ⁄4 〈111〉. This results in loss of symmetry along the 21113 planes, the planes of easy slip in FCC materials, resulting in slip being accommodated by two asymmetric glide and shuffle planes [21]. The glide plane can accommodate slip via disassociated partials in addition to activating full dislocations at high temperatures, while the shuffle plane can only accommodate full dislocations. This would be consistent with the observed increase in crack opening displacement (Figure 2f & 2h) due to the formation of stacking faults from partial dislocations emitted from the notch tip. Curiously, the crack mechanism changes once again at high temperatures above 500 °C, suggesting a second transition from partial to full dislocation activity in Si. From the fracture surface observations (Figure 3), it is clear that at low temperatures, a single cleavage plane participates in the fracture process, while at intermediate and high temperatures, multiple cleavage planes seem to compete to accommodate fracture. Previous calculations by Hirsch et al. [6], showed that a sharp BDTT occurred in Si when there were no pre-existing dislocations in the material, so the transition was dependent on nucleation of dislocations from the surface to accommodate the deformation. Warren [22] showed experimentally that samples that were thermo-mechanically treated to contain dislocations close to the pre-crack showed a more gradual transition in fracture toughness. A smooth transition in our case can possibly be explained by facilitation of dislocation nucleation from the amorphised zone [23] at the notch tip due to the ion milling process. Electron channel contract imaging (ECCI) performed on the as-received Si wafer did not show any dislocation contrast within regions of 2*2 microns, confirming a low initial dislocation density. But ECCI and EBSD could not be performed on FIB machined structures at the crack milled region since it required high surface quality which was not possible to achieve. In the case of pre-existing dislocations, the fracture process is controlled by dislocation mobility in a material with a high Peierls’ stress. Li and Picu [21] carried out atomistic studies to determine possibilities of shuffle to glide dislocation transformation for different temperature and stress states. They showed that the transition was thermally activated and determined a stress dependent activation energy for such a transformation. The partials move by a propagation of kinks, which could result in crack kinking and branching out. Interestingly, they showed that a second transition from a screw to 60° full dislocation on the shuffle set itself was possible at higher stresses and temperatures, albeit by surpassing a larger energy barrier. This could in part explain the two transitions seen in our experiments, one at intermediate and another at high temperature. Sen et al. [24], specifically looked into crack tip cleavage to dislocation emission transition in SC Si through ab initio molecular dynamics (MD) simulations. This case reflects our fracture experiments more closely. They confirm a sharp transition in fracture mode from brittle cleavage to enhanced crack tip plasticity and crack arrest between 577-627 °C. At lower temperatures, nanocracks develop along competing 111 cleavage planes, resulting in a brittle crack which is macroscopically straight. They showed that thermal activation creates disordered zones resulting in crack tip blunting and rotation at elevated temperatures, in turn creating ledges (local mode II shear) that can emit dislocations and increase plastic accommodation. 9 ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Size effects in Si have been studied by Kang and Saif [8], who showed a clear shift in BDTT to lower temperatures with decreasing sample width using bend tests. For a specimen of 1.5 µm width, which is in the same size range as our specimen, a clear transition from elastic to plastic behavior was recorded between 293 and 340 °C. This shifts to above 375 °C for samples of 8 µm width. The size effect was explained in terms of dislocation nucleation, which is controlled by the available surface-to-volume ratio for that sample size. In uniaxial loading, Korte et al. [7], showed a BDTT between 200 and 300 °C in compression of 2 μm diameter, 〈100〉-oriented Si pillars. They observed twinning, formation of partials and LomerCottrell locks at 500 °C, while twinning was absent and high stresses only lead to cracking at 100 °C. Östlund et al. [11] showed that this BDTT can be pushed down to room temperature by further decreasing the sample size to below 400 nm diameter. Their micro-pillar compression tests on SC Si to examine the size effect also revealed that their yield strength increases with decreasing pillar diameters. Despite this increase, the BDTT is seen to shift to lower temperatures with decreasing size. This occurs due to the reduced probability of preexisting flaws in smaller volume samples that otherwise initiate fracture. Hence yielding is promoted compared to fracture in intrinsically brittle systems like SC Si at smaller length scales. Gerberich et al. [12] inferred fracture toughness values as high as 8 MPam1/2 at room temperature, from compression tests of Si nano-spheres of 40 nm diameter. Such small length scales are not within the scope of a standard fracture toughness test, falling short of the requirements of continuum mechanics and therefore cannot be evaluated using the present test method. Gerberich et al. [12] report values from a compression based test geometry on unnotched samples while our case is that of micro-scale bend tests on notched samples in mode I. These differences in test geometries make comparison of absolute values of fracture toughness difficult. Despite them, for a micron-scale specimen, the fracture toughness reported at the room temperature in the present work matches that of the earlier studies discussed by Gerberich et al. Rabier et al. [10] observed that at room temperature, a single large slip offset occurred, which necessitates full dislocation operation. However, at 400 °C, they observed only small slip offsets and smooth stress-strain behavior, more consistent with partial dislocation motion. This explains the change in fracture mode we observe, from single cleavage plane to crack branching and multiple steps on the fracture surface (Figure 2 & Figure 3). A decrease in BDTT implies pronounced dislocation activity at the highly stressed crack tip process zone. Thermal activation of dislocation motion leads to relaxation of the high stresses at the crack tip, leading to an increase in both initiation and propagation toughness, bringing in features of an R-curve behavior in Si, seldom observed at low temperatures. Figure 4 shows the lower estimate of the fracture toughness, KC, once crack branching occurs at 300 and 400 °C, since the new crack length and loss of mode I fracture was not accounted for in the calculation. Small sizes typically suppress cracking due the statistically higher chance of being defect free. This favors nucleation of dislocations and associated onset of plasticity earlier than in macro samples. This explains the lowering of BDTT for small sample sizes and a consequent steady increase in the strain energy release rate, G (Table 1), impacting elevated temperature behavior of Si based MEMS and NEMS devices.
4. Conclusion The micro-mechanical fracture behavior of SC silicon was investigated as a function of temperature. A smooth transition in KC was observed with temperature beyond 300 °C, in contrast to the sharp transitions observed in macro-scale Si. A sharp BDTT could not be 10 ACS Paragon Plus Environment
Page 10 of 17
Page 11 of 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
identified, but a clear change in fracture mechanism occurs at ~300 °C from simple cleavage to multiply branched cracking. This demonstrates the influence of small scale plasticity on fracture behavior at temperatures significantly lower than the BDTT of macro-Si. Although the increase in initiation toughness is marginal between 150 and 300 °C, the damage tolerance is improved significantly due to crack branching and stable crack growth, revealing that small scale plasticity becomes important in miniaturized Si samples.
Supporting Information Available: **Experimental procedure; force-deflection curves and fracture surface of macro-Si tested at elevated temperatures (Figure S1).** This material is available free of charge via the internet at http://pubs.acs.org. Acknowledgements J.M.W. acknowledges the financial support through the Swiss National Science Foundation (SNF Grant: 200021_166094). B. N. J acknowledges Dr. Kurt Matoy, Infineon Technologies, Austria, for supplying high purity Si wafers for these experiments. B. N. J and G. D are also thankful to Prof. Dov Sherman, Tel Aviv University, for useful discussions.
References: [1] Courtney TH. Mechanical Behavior of Materials. 2 ed: Waveland Press; 2005. [2] John CS. The brittle-to-ductile transition in pre-cleaved silicon single crystals. Philosophical Magazine 1975;32:1193-212. [3] Samuels J, Roberts SG. The Brittle-Ductile Transition in Silicon. I. Experiments. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 1989;421:1-23. [4] Brede M. The brittle-to-ductile transition in silicon. Acta Metallurgica et Materialia 1993;41:21128. [5] Hsia KJ, Argon AS. Experimental study of the mechanisms of brittle-to-ductile transition of cleavage fracture in Si single crystals. Materials Science and Engineering: A 1994;176:111-9. [6] Hirsch PB, Roberts SG, Samuels J. The Brittle-Ductile Transition in Silicon. II. Interpretation. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 1989;421:25-53. [7] Korte S, Barnard JS, Stearn RJ, Clegg WJ. Deformation of silicon – Insights from microcompression testing at 25–500°C. International Journal of Plasticity 2011;27:1853-66. [8] Kang W, Saif MTA. In Situ Study of Size and Temperature Dependent Brittle-to-Ductile Transition in Single Crystal Silicon. Advanced Functional Materials 2013;23:713-9. [9] Nakao S, Ando T, Shikida M, Sato K. Effect of temperature on fracture toughness in a singlecrystal-silicon film and transition in its fracture mode. Journal of Micromechanics and Microengineering 2008;18:015026. [10] Rabier J, Montagne A, Wheeler JM, Demenet JL, Michler J, Ghisleni R. Silicon micropillars: high stress plasticity. physica status solidi (c) 2013;10:11-5. [11] Östlund F, Rzepiejewska-Malyska K, Leifer K, Hale LM, Tang Y, Ballarini R, et al. Brittle-toDuctile Transition in Uniaxial Compression of Silicon Pillars at Room Temperature. Advanced Functional Materials 2009;19:2439-44. [12] Gerberich WW, Stauffer DD, Beaber AR, Tymiak NI. A brittleness transition in silicon due to scale. Journal of Materials Research 2011;27:552-61. [13] Armstrong DEJ, Tarleton E. Bend Testing of Silicon Microcantilevers from 21°C to 770°C. Jom 2015;67:2914-20. [14] Wheeler JM, Michler J. Elevated temperature, nano-mechanical testing in situ in the scanning electron microscope. Rev Sci Instrum 2013;84:045103. [15] Wheeler JM, Brodard P, Michler J. Elevated temperature,in situindentation with calibrated contact temperatures. Philosophical Magazine 2012;92:3128-41. [16] Jaya BN, Kirchlechner C, Dehm G. Can microscale fracture tests provide reliable fracture toughness values? A case study in silicon. Journal of Materials Research 2015;30:686-98. 11 ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
[17] Matoy K, Schönherr H, Detzel T, Schöberl T, Pippan R, Motz C, et al. A comparative microcantilever study of the mechanical behavior of silicon based passivation films. Thin Solid Films 2009;518:247-56. [18] Gleizer A, Sherman D. The cleavage energy at initiation of (110) silicon. International Journal of Fracture 2014;187:1-14. [19] Rubanov S, Munroe PR. FIB-induced damage in silicon. Journal of Microscopy 2004;214:21321. [20] Olesinski RW, Kanani N, Abbaschian GJ. The Ga−Si (Gallium-Silicon) system. Bulletin of Alloy Phase Diagrams 1985;6:362-4. [21] Li Z, Picu RC. Shuffle-glide dislocation transformation in Si. Journal of Applied Physics 2013;113:083519. [22] Warren PD. The brittle-ductile transition in silicon: The influence of pre-existing dislocation arrangements. Scripta Metallurgica 1989;23:637-42. [23] Godet J, El Nabi FA, Brochard S, Pizzagalli L. Surface effects on the mechanical behavior of silicon nanowires: Consequence on the brittle to ductile transition at low scale and low temperature. physica status solidi (a) 2015;212:1643-8. [24] Sen D, Thaulow C, Schieffer SV, Cohen A, Buehler MJ. Atomistic study of crack-tip cleavage to dislocation emission transition in silicon single crystals. Phys Rev Lett 2010;104:235502.
12 ACS Paragon Plus Environment
Page 12 of 17
Page 13 of 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
Fig. 1. a) Series of cantilevers micromachined by FIB on Si 〈100〉. b) Single cantilever showing beam dimensions and orientation with respect to the loading direction under in situ loading. 44x13mm (300 x 300 DPI)
ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Fig. 2. Load-displacement response and corresponding crack trajectories recorded for different test temperatures. *Not representative at 600 °C: only 2 out of 6 specimen showed significant plasticity. 115x190mm (300 x 300 DPI)
ACS Paragon Plus Environment
Page 14 of 17
Page 15 of 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
Fig 3. Fracture surfaces at the various test temperatures showing cleavage fracture at 25 °C and 150 °C and evidence of plastic deformation and multiple branches at 400 °C and larger kinks at 500 °C. (a) and (b) were broken subsequent to the tests to observe the fracture surface during which some contamination of the notched regions could not be avoided. 35x8mm (300 x 300 DPI)
ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Fig. 4. Initiation fracture toughness plotted as a function of test temperature showing a fairly constant KC below 300 °C and a smooth rise above it for the micro-scale Si tested in the present work. Fracture toughness data of macro-Si from [2] showing a constant low value up to 700 °C followed by a single sharp transition above it is superimposed for comparison. 107x83mm (300 x 300 DPI)
ACS Paragon Plus Environment
Page 16 of 17
Page 17 of 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
TOC Graphic 35x22mm (300 x 300 DPI)
ACS Paragon Plus Environment
