NANO LETTERS
Size Effects in Mechanical Deformation and Fracture of Cantilevered Silicon Nanowires
2009 Vol. 9, No. 2 525-529
Michael J. Gordon,*,† Thierry Baron,‡ Florian Dhalluin,‡ Pascal Gentile,§ and Pierre Ferret| Department of Chemical Engineering, UniVersity of California - Santa Barbara, Santa Barbara, California 93106-5080, LTM-CNRS, CEA-DRFMC, CEA-LETI/MINATEC, 17 AVenue des Martyrs, 38054 Grenoble, France Received August 22, 2008; Revised Manuscript Received December 17, 2008
ABSTRACT Elastic modulus and fracture strength of vertically aligned Si [111] nanowires (ø ) 100-700 nm) in an as-grown state have been measured using a new, multipoint bending protocol in an atomic force microscope. All wires showed linear elastic behavior, spring constants which scale with (length)3, and brittle failure at the wire-substrate junction. The “effective” Young’s modulus increased slightly (100 f 160-180 GPa) as wire diameter decreased, but fracture strength increased by 2-3 orders of magnitude (MPa f GPa). These results indicate that vapor-liquid-solid grown wires are relatively free of extended volume defects and that fracture strength is likely controlled by twinning and interfacial effects at the wire foot. Small wires (100 nm) grown with a colloidal catalyst were the best performers with high modulus (∼180 GPa) and fracture stress >1 GPa.
One-dimensional nano-objects (nanowires, tubes, rods, springs, etc.) have attracted considerable interest lately as building blocks for electromechanical systems (oscillators, sensors, actuators), circuit interconnects, and composite materials of the future. Manipulation and exploitation of these new structures for technological applications requires detailed knowledge of material properties at the single nanostructure level. Previous studies have shown that the “effective” elasticity, strength, and plasticity of materials can all be influenced by size, shape, and “surface effects” (surface stress, oxide layers, roughness, and defects) when nanometer dimensions are involved.1-5 Given the importance of such issues, it is no surprise that many interrogation techniques have been used to explore these effects: nanoindentation, tensile/bending (static and dynamic) tests, and resonant excitation.1-16 In particular, atomic force microscope (AFM)based bending experiments on nanobeams and nanowires (NW) are very popular. These approaches typically measure the force required to deform a “beam” fabricated via topdown techniques,6,7 NWs that have been artificially “fixed” to a surface with metallic pads,8 or NWs positioned across a gap9-12 (with and without surface pinning of the wire ends). * To whom correspondence should be addressed. E-mail: mjgordon@ engr.ucsb.edu. † University of California - Santa Barbara. ‡ Laboratoire des Technologies de la Microe´lectronique (LTM-CNRS). § CEA-DRFMC. | CEA-LETI/MINATEC. 10.1021/nl802556d CCC: $40.75 Published on Web 01/21/2009
2009 American Chemical Society
Most bending experiments measure NW deformation at a single point; however, this situation can often lead to uncertainties related to the boundary conditions of deflection,2 structural integrity of clamping points,10,12 and questions of whether the “real” deflection of the wire is being measured (i.e., deformation may occur in several directions, but the AFM only measures one). Lateral forcing experiments can also involve NW-substrate friction,8 tip slippage,13 and low force sensitivity12,13 (i.e., the torsional spring constant of an AFM cantilever . NW spring constant usually). To alleviate these uncertainties, we introduce a multipoint testing protocol where cantilevered Si NWs are elastically deformed at various positions along their lengths in pure bending. This approach allows direct testing of as-grown samples (alleviating postgrowth manipulation, fixation, etc.), applies to both short and long NWs, can examine the integrity of the NW-substrate junction, uniquely determines the boundary conditions of deformation, and has high sensitivity (i.e., it is easy to choose ktip∼kwire because all defections are vertical). Bending and fracture measurements on vertically oriented Si [111] NWs showed that (1) all wires deform elastically with a true cantilevered boundary condition; (2) NW modulus is single valued, irrespective of forcing location; (3) NW spring constant scales with wire length L3, (4) elastic moduli increase slightly (100 f 180 GPa), but fracture stresses increase significantly (σb ) 0.03 f 2-4 GPa) as diameter
decreases; and (4) wires fail via sudden brittle fracture at the NW-substrate junction. The low value for σb was attributed to twinning at the NW foot region and (possibly) surface roughness (i.e., saw-tooth facets); specifically, larger wires grown at low temperature (550 °C) or low SiH4 flux were the weakest. In contrast, large wires (400-700 nm) grown at 650 °C and high SiH4 flux could not be fractured, even under the maximum load limit of the AFM (∼4 µN). These experiments show that moduli are roughly constant with size (within a factor of ∼2), but fracture stress depends on wire size and (more importantly) growth conditions. Vertically aligned Si NWs were epitaxially grown on (111)-oriented Si substrates by CVD (SiH4/H2) using the Aucatalyzed, vapor-liquid-solid (VLS) technique at 450-750 °C.17,18 Catalyst particles for large wires were formed by dewetting an Au layer at high temperature (500-900 °C) and smaller wires were grown from 100 nm Au colloid. For this study, four NW samples were considered to test a wide range of wire diameters (100-700 nm), lengths (1-6 µm), and crystallinity; growth conditions were (1) 550 °C, high SiH4 flux; (2) 650 °C, low SiH4; (3) 650 °C, high SiH4; and (4c) 450 °C, high SiH4, Au colloid catalyst. An SEM image of a typical NW sample is shown in Figure 1a. AFM-based mechanical testing was carried out in a DI/ Veeco Enviroscope using different cantilever types (forcemodulation and tapping, ktip ) 1.5f12 N/m) and two scanning configurations (“forward” and “reverse” reading, refer to Figures 1b-d). This approach was taken to internally check the measurement procedure and reproducibility of mechanical property estimations. Since NW growth was perpendicular to the substrate, samples were cleaved along a 3-fold substrate axis and examined “on-end” with the substrate vertical. Wires were imaged in tapping mode and force-distance (F-d) curves were recorded with XY scanning off, static tip (no excitation), and z-axis approach-retract cycles of 100-300 nm at 10-30 nm/s (pushing on the nanowire). The z-axis AFM piezo was piloted with C-code while recording FN and FL (normal and lateral force) externally. Wires were specifically aligned parallel to the X-axis scanning direction; in this way, X-only and Y-only line scans could be used to accurately determine the wire length and diameter. Tip geometry and convolution effects were taken into account by measuring the tip radius (i.e., scanning a colloidal particle of known size) and the tip shape (forward, reverse, and side rake angles) was evaluated by profiling vertical steps and corners with different scan angles. The resulting tip shape was used to simulate an X or Y line scan; the wire geometry was adjusted until the calculated and experimental profiles were in agreement. Errors in determining the wire radius and forcing location were estimated at 5 and 2%, respectively (see ref 19). Additionally, the spring constant of each AFM cantilever was measured using the thermal noise method20 before and after mechanical testing. F-d curves measured at various locations along the length of an Si NW (φ ) 205 nm, sample no. 1) are shown in Figure 2, along with the F-d curve for the Si substrate (the ideal “hard” surface). Overall, the NW response is elastic (linear) 526
Figure 1. (a) SEM image of Si NWs. (b) AFM scanning configurations used to image NWs. In the forward (fwd) and reverse (rev) schemes, the topography is read using only the front-side or back-side of the tip. In all measurements, the substrate (hatched region) is standing on end. (c,d) Top-down AFM topography images of NWs obtained using the forward (c) and reverse (d) reading schemes, respectively. S and nw annotations refer to the substrate and nanowire, respectively.
Figure 2. Force-distance curves at various a values for a ø ) 205 nm Si NW (sample no. 1) compared to the Si substrate.
with the F-d curve slope decreasing as the loading point “a” moves further from the NW foot. This latter trend is expected because the effective spring constant of the NW Nano Lett., Vol. 9, No. 2, 2009
should decrease as the lever arm increases. Furthermore, deformation was reversible and reproducible. From elastic bending theory, the Young’s modulus of a cantilevered NW can be obtained from the differential equation,21 which describes the wire deflection w(x) as a function of applied force f in the limit of small deflection (see Figure 3a) EI
Figure 3. (a) Geometric parameters for a bent nanowire, showing the deflection w when a force f is applied at position a. (b) Highresolution TEM image of the SiO2 sheath surrounding the Si NW.
d2w ) f(a - x) dx2
(1)
Here, E ) effective wire modulus, I ) πr4/4 is the moment of inertia (circular wire, radius ) r), and a ) position of the load. Additionally, the Si NWs in this study are composite coaxial structures, i.e., an Si wire surrounded by an SiO2 sheath of native oxide. In this case, the effective wire modulus22 can be calculated as E ) RESi + (1 - R)ESiO2 where R ) (Dc/Ds)4. ESi and ESiO2 are the moduli of Si (the wire) and SiO2 (∼73 GPa); Dc and Ds are the diameters of the wire core and sheath, respectively. Given that the SiO2 sheath is very thin (∼1.70 nm, see Figure 3b), its effect on the overall wire modulus is small; in fact, the wire modulus changes by 100 nm if the SiO2 layer is ignored. As such, wire modulus (E) was determined by neglecting the native oxide; however, error bars for E were adjusted to account for the SiO2 sheath (see ref 19 for details). Solving eq 1 using appropriate boundary conditions gives a stress-strain expression for the wire, where an effective wire spring constant (kwire) can be defined as f)
( )
3πr4E w ) kwirew 4a3
(2)
Since the wire deflection is indirectly measured using the deflection of the AFM cantilever, a system of two coupled springs must be considered to extract kwire. This analysis23 yields a rather simple result kwire ) ktip
mobs msubst - mobs
(3)
where msubst and mobs represent the slopes (FN per z-axis piezo stage movement) of the F-d curve when the AFM tip is in contact with the substrate (“hard” surface) and the wire (wire and AFM cantilever bend simultaneously), respectively. ktip is the spring constant of the AFM cantilever determined via the thermal noise method discussed earlier. A summary of spring constants measured at different forcing locations along various NWs of different diameter is shown in Figure 4a. The data can be analyzed further by linearizing eq 2 to extract the wire modulus via regression using F-d curves taken at different “a” positions along the nanowire length
( ) ( ) 1
kwire
Figure 4. (a) Spring constants for various Si nanowires measured at different forcing locations along their lengths. (b) Linearization of the data in panel a using eq 4. Nano Lett., Vol. 9, No. 2, 2009
1 3
)
1
4 3a 3πr4E
(4)
This approach allows one to check the consistency of E (one E value for all a), verify the a3 scaling that is indicative of pure bending (eq 2), and affirm that the wire base does not tilt during testing (otherwise, the intercept would not be zero). Figure 4b shows the result of this analysis; indeed, 527
Figure 5. Effective Young’s moduli of Si NWs. Moduli were determined by regression or at a single point as noted using different force-modulation (FM) and tapping (TAP) cantilevers with forward (fwd) or reverse (rev) reading. Spring constants (k) for each AFM cantilever are noted. Dashed lines are theoretical values for Si in the directions specified. See ref 19 for error bars. 1/3 one finds that 1/kwire versus a gives a straight line in every case with a hard zero intercept. Thus, as-grown NWs behave as cantilevered, elastic beams and the NW-substrate junction has reasonable mechanical integrity. Furthermore, the singlevalued modulus and a3 scaling of kwire suggests that VLSgrown wires from a mechanical point-of-view are relatively free of extended-volume defects. Elastic moduli determined via regression are summarized in Figure 5. Sample nos. 3 and 4c were tested at one forcing point only because wires were either very stiff (no. 3) or too flexible (no. 4c); large wires (no. 3) would not deform appreciably unless forced very near their ends (i.e., the AFM cantilever used was not stiff enough to prevent saturation of the position sensitive detector for small a); and small wires (no. 4c), when forced at a > 1 µm, would occasionally “slip” along the AFM tip during the F-d test cycle (FN had jumps, FN versus z-changed slope abruptly, or FL * 0). In general, the NW modulus increases slightly as the wire diameter decreases, irrespective of the AFM cantilever type (force-modulation versus tapping, low versus high spring constant) or scanning direction used to extract the wire geometry (forward versus reverse). Sample nos. 1, 2, and 4c exhibit similar trends with diameter, and E values saturate near ∼180 GPa for φ )100-200 nm, which is on par with the theoretical value for Si[111]. Sample no. 3, grown at high temperature and high SiH4 flux, shows similar behavior with diameter, except that saturation occurs at φ ) 400 nm. Failure characteristics of NWs were also investigated by forcing individual wires until snap-off occurred. Fracture stresses (σb) were determined from the following21
σb )
Mξ 4fa ) 3 I πr
(5)
where M ) bending moment (M ) fa) and ξ ) distance from the neutral axis to the NW circumference (≈r). An example force-deflection trace for a φ ) 190 nm wire is given in Figure 6a; wire response is linear elastic until catastrophic failure occurs at ∼2000 nN (σb ∼ 5 GPa). 528
Figure 6. (a) Force-deflection behavior for φ ) 190 nm Si NW. (b) Experimental fracture stresses (see ref 19 for error bars). Note, NWs from sample no. 3 could not be fractured and are therefore not shown. (c) TEM image of a NW from sample no. 2; annotations specify the substrate (S), twinning planes (T), a broken nanowire (bw), and the nanowire (nw) itself. Scale bar is 100 nm. (d) SEM image of saw-tooth facets sometimes found on larger nanowires.
Tapping mode images after fracture (not shown) confirm that NWs snap at or very near to the NW-substrate junction where the bending stress is largest. A summary of fracture results is given in Figure 6b. Despite the scatter in the data for each sample (1, 2, 4c), fracture stresses tend to increases as wires become smaller. This effect could be due to fewer defects or decreasing surface roughness24 as the wire diameter becomes smaller. TEM studies (Figure 6c) on low-strength samples (no. 2) showed significant twinning in the NW foot region as well as wires that preferentially fracture at twinning planes (i.e., during TEM sample preparation). In addition, larger diameter wires frequently exhibited a characteristic25 saw-tooth pattern (see Figure 6d) along their sidewalls; these areas may act as crack initiation sites during bending experiments, resulting in lower values for the fracture strength. In summary, we have used multipoint bending tests to evaluate the modulus and fracture stress of as-grown Si[111] nanowires. Orienting the substrate vertically so that NWs are in a cantilevered configuration is an easy method to Nano Lett., Vol. 9, No. 2, 2009
measure deflection behavior, moduli, and fracture characteristics of as-grown wires under well-defined boundary conditions. Multipoint bending tests showed that wires have linear elastic behavior, followed by brittle fracture, and that the wire spring constant scales with (length)3. Elastic moduli were relatively constant (100-180 GPa) with respect to diameter, but fracture stress increased dramatically (σb ) 0.03 f 2-4 GPa) as wires became smaller. Such trends agree with results for top-down fabricated structures.7 Moduli were comparable to theoretical values and do not appear to be strongly affected by different growth conditions. However, for the same growth conditions, smaller wires exhibited higher moduli; this observation is contrary to the expected increasing importance of the SiO2 sheath for smaller wire diameter (i.e., ESiO2 ) 73 GPa < ESi and the sheath represents a higher percentage of the overall wire diameter). Low values for σb, as compared to top-down fabricated structures (σb ) 10-20 GPa)7 and other VLS-grown Si wires (σb ) 7-18 GPa),26 can be attributed to twinning and less-than-perfect epitaxy in the NW foot region. Surface roughness associated with saw-tooth faceting in larger wires may also contribute to lower fracture strength. Therefore, careful control of NW epitaxy in the beginning stages of growth is a high priority for mechanical applications involving “as-grown” wires. Finally, smaller wires (∼100 nm) grown with a colloidal catalyst were the most mechanically sound with high modulus (160-180 GPa) and high fracture stress (>1 GPa). Acknowledgment. M.J.G. would like to thank Dr. Olivier Joubert and LTM-CNRS for support. The authors also thank C. Ternon for TEM work. References (1) Cuenot, S.; Fre´tigny, C.; Demoustier-Champagne, S.; Nysten, B. Phys. ReV. B 2004, 69, 165410. (2) He, J.; Lilley, C. M. Nano Lett. 2008, 8, 1798. (3) Uchic, M. D.; Dimiduk, D. M.; Florando, J. N.; Nix, W. D. Science 2004, 305, 986. (4) Zhou, L. G.; Huang, H. C. Appl. Phys. Lett. 2004, 84, 1940. (5) Duan, H. L.; Wang, J.; Huang, Z. P.; Karihaloo, B. L. Proc. R. Soc. London, Ser. A 2005, 461, 3335.
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