Dislocation plasticity and phase transformations in Si-SiC core-shell ...
Int J Fract (2011) 171:177–183 DOI 10.1007/s10704-010-9566-6
ORIGINAL PAPER
Dislocation plasticity and phase transformations in Si-SiC core-shell nanotowers A. R. Beaber · S. L. Girshick · W. W. Gerberich
Received: 13 August 2010 / Accepted: 29 October 2010 / Published online: 16 November 2010 © Springer Science+Business Media B.V. 2010
Abstract Vapor-liquid-solid (VLS) Si nanotowers were coated with nanocrystalline SiC to form a Si-SiC core-shell composite. Due to a mismatch in the coefficients of thermal expansion (CTE), the Si core was under a compressive stress following the deposition. The composite tower was then cross-sectioned using focused ion beam milling, exposing the Si core. Indentation into the Si showed an increased toughness as a function of diameter compared to similar sized Si nanotowers and nanospheres. This result is explained through enhanced dislocation and phase transformation plasticity in the Si core from the CTE compressive stresses. Keywords Fracture toughness · Nanocomposite · Silicon · Silicon carbide · Core-shell
1 Introduction The β-Sn phase transformation of silicon has received much attention in the past 30 years by the indentation A. R. Beaber · W. W. Gerberich (B) Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave SE, Minneapolis, MN 55455, USA e-mail: [email protected] S. L. Girshick Department of Mechanical Engineering, University of Minnesota, 111 Church St SE, Minneapolis, MN 55455, USA
research community due to the presence of large stresses during nanoindentation. The transformation process under indentation loading has been studied with a range of complementary techniques, including confocal Raman microscopy (CRM) (Kailer et al. 1997; Domnich et al. 2000; Gerbig et al. 2009), TEM (both post indentation thin foils (Saka et al. 2002; Ruffell et al. 2007) and in situ indentation (Minor et al. 2005)), electrical measurements (Mann et al. 2000; Bradby 2003; Ruffell et al. 2007), and molecular dynamics (Kim and Oh 2006; Valentini et al. 2007). Together, these studies have developed a commonly accepted progression of events during the indentation process. During loading, the diamond cubic Si (Si I) immediately beneath the center of the indenter transforms to metallic β-Sn (Si II) at hydrostatic pressures near 12 GPa for Si(100) (Gerbig et al. 2009). As the load is increased, the Si II region under the indenter expands and can cause a pop-in event in the load-displacement due to the 22% volume decrease from Si I to Si II. This can also lead to the plastic flow (or extrusion) of material at the edges of the indent (Pharr et al. 1991; Callahan and Morris 1992), which after pressure relief reverts to a-Si (amorphous Si). During the unloading process, either a pop-out or elbow is usually observed depending on the rate of unloading. This is a product of the Si II expanding during the transformation into a combination of rhombohedral (Si XII) and body centered cubic (Si III) after a pop-out or a-Si after an elbow [17, 21]. While Si XII and Si III are the thermodynamically preferred phases upon unloading, the presence of a-Si is
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attributed to kinetic entrapment during rapid unloading (Bradby 2003). In addition to hydrostatic stresses, there are also significant deviatoric contributions under the indenter (Johnson 1985). Page et al. (1992) recognized that the deformation response of Si under indentation is governed by the magnitude of the hydrostatic and deviatoric components of the stress tensor relative to critical stresses for densification (or metallization) and dislocation plasticity, respectively. However, others have suggested that phase transformations and dislocation motion are not independent deformation mechanisms (Gilman 1992, 1993), as an increase in the deviatoric stress can also decrease the critical threshold for a phase transformation. This is most obvious in the decrease of the phase transformation pressure for Si(111) compared to Si(100) due to the ease of plastic deformation on certain crystallographic planes (Gupta and Ruoff 1980; Kim and Oh 2006; Gerbig et al. 2009). In the current study, the combined effect of the β-Sn phase transformation and dislocation plasticity on fracture toughness was studied in Si-SiC core-shell nanocomposites. This involved the deposition of SiC coated Si nanotowers and subsequent indentation of crosssectioned towers. Results presented here suggest that contributions of compressive stresses on the Si tower from a mismatch in coefficients of thermal expansion can enhance the composite tower fracture toughness through a combination of crack tip shielding, ductile phase pinning, and crack confinement.
2 Experimental Si-SiC core-shell composites were grown in a two-step process. First, Si nanotowers with diameters ranging from 200 to 500 nm were grown using a vapor-liquidsolid (VLS) method on Si(111) substrates. Details of the VLS growth process are described elsewhere (Sivakov et al. 2006). The Si nanotowers were then coated with nanocrystalline 3C-SiC using hypersonic plasma particle deposition (HPPD) (Beaber et al. 2007). HPPD is a thermal plasma based deposition technique that combines nanoparticle ballistic impaction and chemical vapor deposition (CVD). The plasma was operated at ∼ 8 kW with 30 slm Ar and 3–4 slm H2 , with reactant flowrates of 40 sccm for SiCl4 and 240 sccm for CH4 . Coatings were deposited for 10 min
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at an operating pressure of 2–3 torr and a substrate temperature of 530–630◦ C. The composite towers were cross-sectioned to expose the Si core of the tower for indentation using a focused ion beam (FEI Quanta 200 3D) operated at 30 kV and 1 nA. Samples were oriented such that the tower was normal to the ion beam and cut to a height such that the exposed tower cross section was in plane with the surrounding film. Nanoindentation experiments (Hysitron Triboindenter) were run with a cube corner (r = 120 nm) diamond. Indents were displacement controlled, at displacement rates of 2–5 nm/s that varied based on the total displacement (δmax = 50– 175 nm). Holds (constant displacement) of 5 sec were used after the peak displacement was reached and midway through the unloading to monitor drift. For each indent, the indenter was aligned with the center of the Si tower core by imaging the tower surface with the diamond tip. Following the indent, the residual impressions were imaged using SEM (JEOL 6700).
3 Results Figure 1 shows a representative image of the Si nanotower before (a) and after (b) deposition of the SiC coating. The coating thickness was 250–350 nm and was conformal to the Si nanotower structures based on images of tower cross sections (Fig. 2b, d). The SiC RMS roughness was less than 10 nm from tapping mode AFM scans while the average SiC grain size, as measured by image processing of a SEM micrograph, was 14.4 ± 5 nm. The dimensions of the Si core and SiC shell in each of the examples shown in Fig. 2 can be determined based on the presence of Au. The Au catalyst (darker contrast at the top of the Si tower in Fig. 1a) used in the VLS growth process of the Si towers was not removed from the tower before depositing the SiC coating. Due to the high substrate temperature (∼ 600◦ C) during the SiC coating process, there was likely rapid surface diffusion of the Au. Studies at similar temperatures have shown Ostwald ripening of catalyst droplets on Si nanowires (Hannon et al. 2006) and the agglomeration of Au nanoparticles on the nanowire walls (Sivakov et al. 2009). Thus, the core-shell interface after the deposition of SiC film is likely either coated with an Au thin film or agglomerated nanoparticles of Au. This is evident in the bright dotted ring in the SEM images of the tower cross sections (highlighted
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Fig. 1 VLS Si nanotowers a before (TEM) and b after deposition of the SiC coating (SEM, 30◦ tilt)
Fig. 2 Load-displacement (P − δ) and post indentation SEM imaging (plan view of the cross-sectioned tower) for displacement controlled indents to 75 nm (a, b) and 125 nm (c, d). A power-law unloading function is fitted to each data set (red, dashed line). Arrows indicate a,c deviations from the power-law, b Si-SiC core-shell interface, and d cracks extending from the indenter vertices. Note that the sample in Fig. 2d was slightly tilted (∼1◦ ) during the indentation testing, leading to a higher stress concentration (and fracture) at the top indent edges relative to the bottom edge
by arrows in Fig. 2b). Using these Au agglomerates as an indicator of the SiC shell-Si core interface, the Si core diameter in Fig. 2b is ∼488 nm while the core in Fig. 2d is ∼475 nm. For the indentation experiments that follow, composite towers with a Si core diameter of 400–500 nm were selected.
A series of cross sectioned composite towers were indented to depths ranging from 50 to 175 nm, with a single indent per tower. In each case, the tip of the indenter was aligned with the center of the Si core. Based on the maximum contact depth and the indenter area function (Oliver and Pharr 1992), the projected
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contact area of the indenter for an indent to 50 nm gives a contact diameter of approximately 151 nm. Similarly, the indenter contact diameter for an indent to 175 nm is approximately 376 nm. Considering that the core diameters were between 400 and 500 nm, the contact area of the indenter was confined to the Si core for all depths. Figure 2 shows two examples of load-displacement results along with their corresponding post indentation SEM image for 75 nm (Fig. 2a, b) and 125 nm (Fig. 2c, d) indents. The 75 nm indent shows no signs of fracture, either in load-displacement data (signified by load drops) or cracking from the post indentation SEM images (originating from the indenter vertices). Similar responses were found for indents up to 100 nm. However, substantial plastic yielding typically occurred, as suggested by the residual displacement between the loading and unloading curves (see Fig. 2a). In addition, the white areas surrounding the indenter impression suggest plastic pile-up (see Fig. 2b). Figure 3 shows a contact mode AFM scan of the 75 nm indent from Fig. 2a, b along with a line trace over indenter impression and suspected pile-up region. This result confirms that the bright contrast from the SEM data surrounding the indent is related to height. This is surprising, as the extent of plasticity required to produce ∼15 nm of pileup (as shown in Fig. 3) is much larger than expected for Si given its high Peierl’s barrier (Haasen and Alexander 1968). One possible explanation is the metallization and flow of Si from a phase transformation. The load-displacement data in Fig. 2 shows a distinct elbow in each of the unloading curves. This is labeled with a horizontal arrow and was present in all of the indents (50– 175 nm) regardless of depth. A power law function was fitted to the upper ∼60% of the unloading curve (dashed red line) in both the load-displacement curves shown in Fig. 2. The unloading response for elastic-plastic indentation can be approximated by a power law function of the form P (δ) = α (δ − δr )m ,
(1)
where P is the load, δ is the displacement, δr is the residual displacement, and α and m are material constants (Oliver and Pharr 1992). In the present case, the unloading curve deviates abruptly from elastic-plastic behavior near the end of the unloading, creating an elbow. As discussed in the introduction, this type of feature is commonly seen during the indentation of silicon and has been attributed to the transformation of the
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high pressure β-Sn phase of Si to an amorphous phase (a-Si) (Domnich et al. 2000; Bradby 2003; Gerbig et al. 2009). The presence of a phase transformation in the current study is to be expected as the average contact stress (or hardness) was 12.6±1.2 GPa, which is well in excess of the stress needed for the phase transformation in Si(111) (Gupta and Ruoff 1980). What is surprising is the transition pressure where the elbow occurs. During the indentation of Si(111) wafers, the transition pressure on unloading (i.e. location of the elbow) is at 6.1 ± 0.7 GPa (Gerbig et al. 2009). In the present study, an average transition pressure of 2.9 ± 1.2 GPa was found for a Si core diameter of 451.3 ± 48.2 nm. This suggests that the Si II within the Si tower is more thermodynamically stable during unloading than in Si(111) wafers. At the deeper displacements (125–175 nm), cracking is consistently observed in the post indentation SEM images. The cracks readily propagate through the SiC shell compared to the Si core, despite the fact that the Si core will experience the greatest stresses under load and should be much more brittle than the SiC shell. One explanation is the stress distribution in the composite tower established by the mismatch in the coefficients of thermal expansion (CTE). During the cooling process following the deposition of the SiC film, the CTE mismatch between the SiC and Si will leave the Si core under compression and the SiC in tension. Based on an elastic shrink fit (Timoshenko 1930), the Si core is under a peak radial compressive stress of ∼150 MPa. This compressive stress inhibits the growth of cracks within the Si. However, once the indentation driving stress at the Si-SiC interface is high enough, the residual tensile stress in the SiC shell will help drive the crack through the SiC. This is evident in Fig. 2d, where the cracks extend through the entire SiC shell and arrest at the interface between the SiC shell and the surrounding film. For the indentations that showed cracking, a fracture toughness was calculated using a standard Vickers crack measurement technique developed by Anstis et al. (1981) and extended to shallow penetration cube corner indentation by Pharr (1998). This is given as 1/2 P E , (2) KIc = α H c3/2 where α is an empirical factor accounting for the tip geometry (αcube corner = 0.040), E is the elastic modulus, H is the hardness, P is the maximum applied load,
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Fig. 3 Contact mode AFM scan of the indent shown in Fig. 2 (a,b) along with a line scan across the indentation impression
and c is the average crack length measured from the center of the indentation impression. The elastic modulus and hardness were obtained from the respective indentations. Figure 4 shows the fracture toughness for the Si-SiC composite towers as a function of the tower diameter along with TEM in situ indented nanospheres and nanotowers from Beaber et al. (2010) and ex situ indented nanospheres from Mook et al. (2007). For the nanosphere and nanotower data from Beaber et al., fracture toughness was calculated using a work per unit fracture area approach while the nanosphere data from Mook et al. approximated the crack size as the thickness of the oxide surrounding the sphere and used the Griffith criterion to evaluate the fracture toughness. The solid line (K I c ∝ d −1/2 ) is based on Eq. 5 while the dashed line (K I c ∝ d −3/2 ) is a guide to the eye without theoretical basis. Both are discussed below.
4 Discussion Enhanced ductility in silicon at small length scales has been described previously based on strengthening (Gerberich et al. 2003; Nowak et al. 2010) and toughening (Mook et al. 2007; Östlund et al. 2009; Beaber et al. 2010) effects. In Si nanospheres, the strengthening effect can be explained by dislocation interactions or pile-up within the sphere internally and/or at the oxide shell. The oxide prevents the release of dislocations and leads to the formation of a back stress due to dislocation pile-up. The applied shear stress, τ , needed to nucleate additional dislocations is thus increased and can be
described by an Eshelby dislocation pile-up mechanism as (Eshelby et al. 1951) μbN , (3) τ= π (1 − ν) d where μ is the shear modulus, b is the Burgers vector, N is the number of dislocations, ν is Poisson’s ratio, and d is the sample diameter. The length scale dependence on fracture toughness can be described by first including plasticity effects in the fracture of brittle materials as (Gerberich et al. 2007) 10 N μσ ys b 1/2 , (4) KIc = 9 1−ν where σ ys is the yield strength and ν is Poisson’s ratio. Assuming σ ys = 2τ and using ν Si = 0.218, Eq. 3 can then be used to relate Eq. 4 to the sample diameter as (Gerberich et al. 2007) 10 μN bd −1/2 . (5) KIc = 9 Equation 5 is shown in Fig. 4 as a solid line, using the number of dislocations (N = 60) as a fitting parameter. Together, these results suggest that dislocations trapped in small volumes generate large back stresses, which not only increase the yield strength, but also lead to crack tip shielding during fracture, thus increasing the toughness. The fracture toughness of the Si-SiC composites is controlled by the combined effect of three mechanisms. First, due to the length scale of the Si towers, the previously mentioned dislocation pile-up and crack tip shielding mechanism will be active. Unlike the nanospheres and nanotowers, though, the composite towers also have a compressive stress on the Si due to the CTE
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mismatch between the SiC shell and Si core. A maximal shear stress in the center of the tower will increase the extent of dislocation plasticity within the Si core. These deviatoric stresses will also increase the extent of phase transformation plasticity by lowering the critical threshold. This is evident by the decrease in the measured transition from Si II → I. While the role of Si II during fracture is not well understood, the presence of a metallic phase within the Si core will likely increase the toughness from either its inherent ductility if the entire core is transformed or as a source of ductile pinning (Lawn 1993) if it is dispersed within a predominantly Si I matrix. Together, these two sources of plasticity explain the large degree of plastic deformation shown in Fig. 3. Finally, the compressive stress on the core will inhibit crack growth within the Si. This was demonstrated by the absence of any cracking within the Si (due to the compressive stress) and the rapid propagation of the cracks in the SiC (due to the tensile stress). The combined effect of these three mechanisms leads to an enhanced toughening effect relative to the Si nanospheres and nanotowers, as shown in Fig. 4. Additional experiments are needed to explain the basis for the K I c ∝ d −3/2 and whether it holds for an extrapolation to smaller dimensions.
5 Summary
Fig. 4 a Fracture toughness as a function of diameter for Si-SiC composites (open squares) along with TEM in situ indented nanospheres (solid circles) and nanotowers (solid diamonds) from Beaber et al. (2010) and ex situ indented nanospheres (solid triangles) from Mook et al. (2007). The solid line represents a least-squares fitting of Eq. 5 while the dashed line is a guide to the eye for d−3/2 . b,c Representative post indentation SEM imaging of composite towers with diameters of 601 and 763 nm, respectively
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Si-SiC core shell composite nanotowers were deposited by first growing Si nanotowers via a VLS method and then coating the towers with SiC using HPPD. A CTE mismatch between the Si core and SiC shell generated a compressive stress in the Si core. Indentation of the FIB cross-sectioned tower revealed both a decrease in Si II → I phase transition stress and an increase in the fracture toughness with diameter compared to similarly sized Si. The superposition of the deviatoric component of the CTE mismatch stress on the Si tower enhances both dislocation plasticity and phase transformation plasticity during indentation. This leads to multiple toughening mechanisms, including crack tip shielding, ductile phase pinning, and crack confinement and an overall increase in the composite tower fracture toughness. These results demonstrate a synergistic toughening effect of multiple mechanisms for small volumes under compression that could be applied to other nanocomposite systems.
Dislocation plasticity and phase transformations in Si-SiC core-shell nanotowers Acknowledgments The authors would like to thank J.D. Nowak for TEM contributions and V. Sivakov and S. Christiansen for growing the Si nanotowers. This work was supported financially by the National Science Foundation (CTS-0506748) and the Air Force Office of Scientific Research (AOARD-08-4134). Parts of this work were carried out in the Characterization Facility, University of Minnesota, which receives partial support from NSF through the MRSEC program.
References Anstis GR, Chantikul P, Lawn BR, Marshall DB (1981) A critical evaluation of indentation techniques for measuring fracture toughness: I. Direct crack measurements. J Am Ceram Soc 64(9):533–538 Beaber AR, Nowak JD, Ugurlu O, Mook WM, Girshick SL, Ballarini R, Gerberich WW (2010) Smaller is tougher. Philos Mag A. doi:10.1080/14786435.2010.487474 Beaber AR, Qi LJ, Hafiz J, McMurry PH, Heberlein JVR, Gerberich WW, Girshick SL (2007) Nanostructured SiC by chemical vapor deposition and nanoparticle impaction. Surf Coat Technol 202(4–7):871–875 Bradby JE, Williams JS, Swain MV (2003) In situ electrical characterization of phase transformations in Si during indentation. Phys Rev B 67(8):9 Callahan DL, Morris JC (1992) The extent of phase-transformation in silicon hardness indentations. J Mater Res 7(7):1614–1617 Domnich V, Gogotsi Y, Dub S (2000) Effect of phase transformations on the shape of the unloading curve in the nanoindentation of silicon. Appl Phys Lett 76(16):2214–2216 Eshelby JD, Frank FC, Wills HH, Nabarro FRN (1951) Equilibrium of linear arrays of dislocations. Philos Mag A 42(327):351–364 Gerberich WW, Mook WM, Carter CB, Ballarini R (2007) A crack extension force correlation for hard materials. Int J Fracture 148(2):109–114 Gerberich WW, Mook WM, Perrey CR, Carter CB, Baskes MI, Mukherjee R, Gidwani A, Heberlein J, McMurry PH, Girshick SL (2003) Superhard silicon nanospheres. J Mech Phys Solids 51(6):979–992 Gerbig YB, Stranick SJ, Morris DJ, Vaudin MD, Cook RF (2009) Effect of crystallographic orientation on phase transformations during indentation of silicon. J Mater Res 24(3):1172–1183 Gilman JJ (1992) Insulator-metal transitions at microindentations. J Mater Res 7(3):535–538 Gilman JJ (1993) Shear-induced metallization. Philos Mag B 67(2):207–214 Gupta MC, Ruoff AL (1980) Static compression of silicon in the [100] and in the [111] directions. J Appl Phys 51(2): 1072–1075 Haasen P, Alexander H (1968) Dislocations and plastic flow in the diamond structure. Solid State Phys 22:27–158 Hannon JB, Kodambaka S, Ross FM, Tromp RM (2006) The influence of the surface migration of gold on the growth of silicon nanowires. Nature 440(7080):69–71 Johnson KL (1985) Contact mechanics. Cambridge University Press, Cambridge
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Kailer A, Gogotsi YG, Nickel KG (1997) Phase transformations of silicon caused by contact loading. J Appl Phys 81(7):3057–3057 Kim DE, Oh SI (2006) Atomistic simulation of structural phase transformations in monocrystalline silicon induced by nanoindentation. Nanotechnology 17(9):2259–2265 Lawn BR (1993) Fracture of brittle solids. Cambridge University Press, New York Mann AB, van Heerden D, Pethica JB, Weihs TP (2000) Sizedependent phase transformations during point loading of silicon. J Mater Res 15(8):1754–1758 Minor AM, Lilleodden ET, Jin M, Stach EA, Chrzan DC, Morris JW (2005) Room temperature dislocation plasticity in silicon. Philos Mag A 85(2–3):323–330 Mook WM, Nowak JD, Perrey CR, Carter CB, Mukherjee R, Girshick SL, McMurry PH, Gerberich WW (2007) Compressive stress effects on nanoparticle modulus and fracture. Phys Rev B 75(21):214112 Nowak JD, Beaber AR, Ugurlu O, Girshick SL, Gerberich WW (2010) Small size strength dependence on dislocation nucleation. Scripta Mater 62(11):819–822 Oliver WC, Pharr GM (1992) Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7(6):1564–1580 Östlund F, Rzepiejewska-Malyska K, Leifer K, Hale LM, Tang Y, Ballarini R, Gerberich WW, Michler J (2009) Brittle-to-ductile transition in uniaxial compression of silicon pillars at room temperature. Adv Funct Mater 19(15): 2439–2444 Page TF, Oliver WC, McHargue CJ (1992) Deformation behavior of ceramic crystals subjected to very low load (nano) indentations. J Mater Res 7(2):450–473 Pharr GM (1998) Measurement of mechanical properties by ultra-low load indentation. Mater Sci Eng A A253(1–2): 151–159 Pharr GM, Oliver WC, Harding DS (1991) New evidence for a pressure-induced phase-transformation during the indentation of silicon. J Mater Res 6(6):1129–1130 Ruffell S, Bradby JE, Williams JS, Munroe P (2007) Formation and growth of nanoindentation-induced high pressure phases in crystalline and amorphous silicon. J Appl Phys 102(6):8 Saka H, Shimatani A, Suganuma M, Suprijadi (2002) Transmission electron microscopy of amorphization and phase transformation beneath indents in Si. Philos Mag A 82(10):1971–1981 Sivakov V, Andrä G, Gösele U, Christiansen S (2006) Epitaxial vapor-liquid-solid growth of silicon nano-whiskers by electron beam evaporation. physica status solidi (a) 203(15):3692–3698 Sivakov VA, Scholz R, Syrowatka F, Falk F, Gosele U, Christiansen SH (2009) Silicon nanowire oxidation: the influence of sidewall structure and gold distribution. Nanotechnology 40:405607 Timoshenko S (1930) Strength of materials: part II, advanced theory and problems. D. Van Nostrand, Princeton Valentini P, Gerberich WW, Dumitrica T (2007) Phase transformation plasticity in silicon nanospheres. Phys Rev Lett 99:175701
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ORIGINAL PAPER
Dislocation plasticity and phase transformations in Si-SiC core-shell nanotowers A. R. Beaber · S. L. Girshick · W. W. Gerberich
Received: 13 August 2010 / Accepted: 29 October 2010 / Published online: 16 November 2010 © Springer Science+Business Media B.V. 2010
Abstract Vapor-liquid-solid (VLS) Si nanotowers were coated with nanocrystalline SiC to form a Si-SiC core-shell composite. Due to a mismatch in the coefficients of thermal expansion (CTE), the Si core was under a compressive stress following the deposition. The composite tower was then cross-sectioned using focused ion beam milling, exposing the Si core. Indentation into the Si showed an increased toughness as a function of diameter compared to similar sized Si nanotowers and nanospheres. This result is explained through enhanced dislocation and phase transformation plasticity in the Si core from the CTE compressive stresses. Keywords Fracture toughness · Nanocomposite · Silicon · Silicon carbide · Core-shell
1 Introduction The β-Sn phase transformation of silicon has received much attention in the past 30 years by the indentation A. R. Beaber · W. W. Gerberich (B) Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave SE, Minneapolis, MN 55455, USA e-mail: [email protected] S. L. Girshick Department of Mechanical Engineering, University of Minnesota, 111 Church St SE, Minneapolis, MN 55455, USA
research community due to the presence of large stresses during nanoindentation. The transformation process under indentation loading has been studied with a range of complementary techniques, including confocal Raman microscopy (CRM) (Kailer et al. 1997; Domnich et al. 2000; Gerbig et al. 2009), TEM (both post indentation thin foils (Saka et al. 2002; Ruffell et al. 2007) and in situ indentation (Minor et al. 2005)), electrical measurements (Mann et al. 2000; Bradby 2003; Ruffell et al. 2007), and molecular dynamics (Kim and Oh 2006; Valentini et al. 2007). Together, these studies have developed a commonly accepted progression of events during the indentation process. During loading, the diamond cubic Si (Si I) immediately beneath the center of the indenter transforms to metallic β-Sn (Si II) at hydrostatic pressures near 12 GPa for Si(100) (Gerbig et al. 2009). As the load is increased, the Si II region under the indenter expands and can cause a pop-in event in the load-displacement due to the 22% volume decrease from Si I to Si II. This can also lead to the plastic flow (or extrusion) of material at the edges of the indent (Pharr et al. 1991; Callahan and Morris 1992), which after pressure relief reverts to a-Si (amorphous Si). During the unloading process, either a pop-out or elbow is usually observed depending on the rate of unloading. This is a product of the Si II expanding during the transformation into a combination of rhombohedral (Si XII) and body centered cubic (Si III) after a pop-out or a-Si after an elbow [17, 21]. While Si XII and Si III are the thermodynamically preferred phases upon unloading, the presence of a-Si is
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attributed to kinetic entrapment during rapid unloading (Bradby 2003). In addition to hydrostatic stresses, there are also significant deviatoric contributions under the indenter (Johnson 1985). Page et al. (1992) recognized that the deformation response of Si under indentation is governed by the magnitude of the hydrostatic and deviatoric components of the stress tensor relative to critical stresses for densification (or metallization) and dislocation plasticity, respectively. However, others have suggested that phase transformations and dislocation motion are not independent deformation mechanisms (Gilman 1992, 1993), as an increase in the deviatoric stress can also decrease the critical threshold for a phase transformation. This is most obvious in the decrease of the phase transformation pressure for Si(111) compared to Si(100) due to the ease of plastic deformation on certain crystallographic planes (Gupta and Ruoff 1980; Kim and Oh 2006; Gerbig et al. 2009). In the current study, the combined effect of the β-Sn phase transformation and dislocation plasticity on fracture toughness was studied in Si-SiC core-shell nanocomposites. This involved the deposition of SiC coated Si nanotowers and subsequent indentation of crosssectioned towers. Results presented here suggest that contributions of compressive stresses on the Si tower from a mismatch in coefficients of thermal expansion can enhance the composite tower fracture toughness through a combination of crack tip shielding, ductile phase pinning, and crack confinement.
2 Experimental Si-SiC core-shell composites were grown in a two-step process. First, Si nanotowers with diameters ranging from 200 to 500 nm were grown using a vapor-liquidsolid (VLS) method on Si(111) substrates. Details of the VLS growth process are described elsewhere (Sivakov et al. 2006). The Si nanotowers were then coated with nanocrystalline 3C-SiC using hypersonic plasma particle deposition (HPPD) (Beaber et al. 2007). HPPD is a thermal plasma based deposition technique that combines nanoparticle ballistic impaction and chemical vapor deposition (CVD). The plasma was operated at ∼ 8 kW with 30 slm Ar and 3–4 slm H2 , with reactant flowrates of 40 sccm for SiCl4 and 240 sccm for CH4 . Coatings were deposited for 10 min
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at an operating pressure of 2–3 torr and a substrate temperature of 530–630◦ C. The composite towers were cross-sectioned to expose the Si core of the tower for indentation using a focused ion beam (FEI Quanta 200 3D) operated at 30 kV and 1 nA. Samples were oriented such that the tower was normal to the ion beam and cut to a height such that the exposed tower cross section was in plane with the surrounding film. Nanoindentation experiments (Hysitron Triboindenter) were run with a cube corner (r = 120 nm) diamond. Indents were displacement controlled, at displacement rates of 2–5 nm/s that varied based on the total displacement (δmax = 50– 175 nm). Holds (constant displacement) of 5 sec were used after the peak displacement was reached and midway through the unloading to monitor drift. For each indent, the indenter was aligned with the center of the Si tower core by imaging the tower surface with the diamond tip. Following the indent, the residual impressions were imaged using SEM (JEOL 6700).
3 Results Figure 1 shows a representative image of the Si nanotower before (a) and after (b) deposition of the SiC coating. The coating thickness was 250–350 nm and was conformal to the Si nanotower structures based on images of tower cross sections (Fig. 2b, d). The SiC RMS roughness was less than 10 nm from tapping mode AFM scans while the average SiC grain size, as measured by image processing of a SEM micrograph, was 14.4 ± 5 nm. The dimensions of the Si core and SiC shell in each of the examples shown in Fig. 2 can be determined based on the presence of Au. The Au catalyst (darker contrast at the top of the Si tower in Fig. 1a) used in the VLS growth process of the Si towers was not removed from the tower before depositing the SiC coating. Due to the high substrate temperature (∼ 600◦ C) during the SiC coating process, there was likely rapid surface diffusion of the Au. Studies at similar temperatures have shown Ostwald ripening of catalyst droplets on Si nanowires (Hannon et al. 2006) and the agglomeration of Au nanoparticles on the nanowire walls (Sivakov et al. 2009). Thus, the core-shell interface after the deposition of SiC film is likely either coated with an Au thin film or agglomerated nanoparticles of Au. This is evident in the bright dotted ring in the SEM images of the tower cross sections (highlighted
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Fig. 1 VLS Si nanotowers a before (TEM) and b after deposition of the SiC coating (SEM, 30◦ tilt)
Fig. 2 Load-displacement (P − δ) and post indentation SEM imaging (plan view of the cross-sectioned tower) for displacement controlled indents to 75 nm (a, b) and 125 nm (c, d). A power-law unloading function is fitted to each data set (red, dashed line). Arrows indicate a,c deviations from the power-law, b Si-SiC core-shell interface, and d cracks extending from the indenter vertices. Note that the sample in Fig. 2d was slightly tilted (∼1◦ ) during the indentation testing, leading to a higher stress concentration (and fracture) at the top indent edges relative to the bottom edge
by arrows in Fig. 2b). Using these Au agglomerates as an indicator of the SiC shell-Si core interface, the Si core diameter in Fig. 2b is ∼488 nm while the core in Fig. 2d is ∼475 nm. For the indentation experiments that follow, composite towers with a Si core diameter of 400–500 nm were selected.
A series of cross sectioned composite towers were indented to depths ranging from 50 to 175 nm, with a single indent per tower. In each case, the tip of the indenter was aligned with the center of the Si core. Based on the maximum contact depth and the indenter area function (Oliver and Pharr 1992), the projected
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contact area of the indenter for an indent to 50 nm gives a contact diameter of approximately 151 nm. Similarly, the indenter contact diameter for an indent to 175 nm is approximately 376 nm. Considering that the core diameters were between 400 and 500 nm, the contact area of the indenter was confined to the Si core for all depths. Figure 2 shows two examples of load-displacement results along with their corresponding post indentation SEM image for 75 nm (Fig. 2a, b) and 125 nm (Fig. 2c, d) indents. The 75 nm indent shows no signs of fracture, either in load-displacement data (signified by load drops) or cracking from the post indentation SEM images (originating from the indenter vertices). Similar responses were found for indents up to 100 nm. However, substantial plastic yielding typically occurred, as suggested by the residual displacement between the loading and unloading curves (see Fig. 2a). In addition, the white areas surrounding the indenter impression suggest plastic pile-up (see Fig. 2b). Figure 3 shows a contact mode AFM scan of the 75 nm indent from Fig. 2a, b along with a line trace over indenter impression and suspected pile-up region. This result confirms that the bright contrast from the SEM data surrounding the indent is related to height. This is surprising, as the extent of plasticity required to produce ∼15 nm of pileup (as shown in Fig. 3) is much larger than expected for Si given its high Peierl’s barrier (Haasen and Alexander 1968). One possible explanation is the metallization and flow of Si from a phase transformation. The load-displacement data in Fig. 2 shows a distinct elbow in each of the unloading curves. This is labeled with a horizontal arrow and was present in all of the indents (50– 175 nm) regardless of depth. A power law function was fitted to the upper ∼60% of the unloading curve (dashed red line) in both the load-displacement curves shown in Fig. 2. The unloading response for elastic-plastic indentation can be approximated by a power law function of the form P (δ) = α (δ − δr )m ,
(1)
where P is the load, δ is the displacement, δr is the residual displacement, and α and m are material constants (Oliver and Pharr 1992). In the present case, the unloading curve deviates abruptly from elastic-plastic behavior near the end of the unloading, creating an elbow. As discussed in the introduction, this type of feature is commonly seen during the indentation of silicon and has been attributed to the transformation of the
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high pressure β-Sn phase of Si to an amorphous phase (a-Si) (Domnich et al. 2000; Bradby 2003; Gerbig et al. 2009). The presence of a phase transformation in the current study is to be expected as the average contact stress (or hardness) was 12.6±1.2 GPa, which is well in excess of the stress needed for the phase transformation in Si(111) (Gupta and Ruoff 1980). What is surprising is the transition pressure where the elbow occurs. During the indentation of Si(111) wafers, the transition pressure on unloading (i.e. location of the elbow) is at 6.1 ± 0.7 GPa (Gerbig et al. 2009). In the present study, an average transition pressure of 2.9 ± 1.2 GPa was found for a Si core diameter of 451.3 ± 48.2 nm. This suggests that the Si II within the Si tower is more thermodynamically stable during unloading than in Si(111) wafers. At the deeper displacements (125–175 nm), cracking is consistently observed in the post indentation SEM images. The cracks readily propagate through the SiC shell compared to the Si core, despite the fact that the Si core will experience the greatest stresses under load and should be much more brittle than the SiC shell. One explanation is the stress distribution in the composite tower established by the mismatch in the coefficients of thermal expansion (CTE). During the cooling process following the deposition of the SiC film, the CTE mismatch between the SiC and Si will leave the Si core under compression and the SiC in tension. Based on an elastic shrink fit (Timoshenko 1930), the Si core is under a peak radial compressive stress of ∼150 MPa. This compressive stress inhibits the growth of cracks within the Si. However, once the indentation driving stress at the Si-SiC interface is high enough, the residual tensile stress in the SiC shell will help drive the crack through the SiC. This is evident in Fig. 2d, where the cracks extend through the entire SiC shell and arrest at the interface between the SiC shell and the surrounding film. For the indentations that showed cracking, a fracture toughness was calculated using a standard Vickers crack measurement technique developed by Anstis et al. (1981) and extended to shallow penetration cube corner indentation by Pharr (1998). This is given as 1/2 P E , (2) KIc = α H c3/2 where α is an empirical factor accounting for the tip geometry (αcube corner = 0.040), E is the elastic modulus, H is the hardness, P is the maximum applied load,
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Fig. 3 Contact mode AFM scan of the indent shown in Fig. 2 (a,b) along with a line scan across the indentation impression
and c is the average crack length measured from the center of the indentation impression. The elastic modulus and hardness were obtained from the respective indentations. Figure 4 shows the fracture toughness for the Si-SiC composite towers as a function of the tower diameter along with TEM in situ indented nanospheres and nanotowers from Beaber et al. (2010) and ex situ indented nanospheres from Mook et al. (2007). For the nanosphere and nanotower data from Beaber et al., fracture toughness was calculated using a work per unit fracture area approach while the nanosphere data from Mook et al. approximated the crack size as the thickness of the oxide surrounding the sphere and used the Griffith criterion to evaluate the fracture toughness. The solid line (K I c ∝ d −1/2 ) is based on Eq. 5 while the dashed line (K I c ∝ d −3/2 ) is a guide to the eye without theoretical basis. Both are discussed below.
4 Discussion Enhanced ductility in silicon at small length scales has been described previously based on strengthening (Gerberich et al. 2003; Nowak et al. 2010) and toughening (Mook et al. 2007; Östlund et al. 2009; Beaber et al. 2010) effects. In Si nanospheres, the strengthening effect can be explained by dislocation interactions or pile-up within the sphere internally and/or at the oxide shell. The oxide prevents the release of dislocations and leads to the formation of a back stress due to dislocation pile-up. The applied shear stress, τ , needed to nucleate additional dislocations is thus increased and can be
described by an Eshelby dislocation pile-up mechanism as (Eshelby et al. 1951) μbN , (3) τ= π (1 − ν) d where μ is the shear modulus, b is the Burgers vector, N is the number of dislocations, ν is Poisson’s ratio, and d is the sample diameter. The length scale dependence on fracture toughness can be described by first including plasticity effects in the fracture of brittle materials as (Gerberich et al. 2007) 10 N μσ ys b 1/2 , (4) KIc = 9 1−ν where σ ys is the yield strength and ν is Poisson’s ratio. Assuming σ ys = 2τ and using ν Si = 0.218, Eq. 3 can then be used to relate Eq. 4 to the sample diameter as (Gerberich et al. 2007) 10 μN bd −1/2 . (5) KIc = 9 Equation 5 is shown in Fig. 4 as a solid line, using the number of dislocations (N = 60) as a fitting parameter. Together, these results suggest that dislocations trapped in small volumes generate large back stresses, which not only increase the yield strength, but also lead to crack tip shielding during fracture, thus increasing the toughness. The fracture toughness of the Si-SiC composites is controlled by the combined effect of three mechanisms. First, due to the length scale of the Si towers, the previously mentioned dislocation pile-up and crack tip shielding mechanism will be active. Unlike the nanospheres and nanotowers, though, the composite towers also have a compressive stress on the Si due to the CTE
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mismatch between the SiC shell and Si core. A maximal shear stress in the center of the tower will increase the extent of dislocation plasticity within the Si core. These deviatoric stresses will also increase the extent of phase transformation plasticity by lowering the critical threshold. This is evident by the decrease in the measured transition from Si II → I. While the role of Si II during fracture is not well understood, the presence of a metallic phase within the Si core will likely increase the toughness from either its inherent ductility if the entire core is transformed or as a source of ductile pinning (Lawn 1993) if it is dispersed within a predominantly Si I matrix. Together, these two sources of plasticity explain the large degree of plastic deformation shown in Fig. 3. Finally, the compressive stress on the core will inhibit crack growth within the Si. This was demonstrated by the absence of any cracking within the Si (due to the compressive stress) and the rapid propagation of the cracks in the SiC (due to the tensile stress). The combined effect of these three mechanisms leads to an enhanced toughening effect relative to the Si nanospheres and nanotowers, as shown in Fig. 4. Additional experiments are needed to explain the basis for the K I c ∝ d −3/2 and whether it holds for an extrapolation to smaller dimensions.
5 Summary
Fig. 4 a Fracture toughness as a function of diameter for Si-SiC composites (open squares) along with TEM in situ indented nanospheres (solid circles) and nanotowers (solid diamonds) from Beaber et al. (2010) and ex situ indented nanospheres (solid triangles) from Mook et al. (2007). The solid line represents a least-squares fitting of Eq. 5 while the dashed line is a guide to the eye for d−3/2 . b,c Representative post indentation SEM imaging of composite towers with diameters of 601 and 763 nm, respectively
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Si-SiC core shell composite nanotowers were deposited by first growing Si nanotowers via a VLS method and then coating the towers with SiC using HPPD. A CTE mismatch between the Si core and SiC shell generated a compressive stress in the Si core. Indentation of the FIB cross-sectioned tower revealed both a decrease in Si II → I phase transition stress and an increase in the fracture toughness with diameter compared to similarly sized Si. The superposition of the deviatoric component of the CTE mismatch stress on the Si tower enhances both dislocation plasticity and phase transformation plasticity during indentation. This leads to multiple toughening mechanisms, including crack tip shielding, ductile phase pinning, and crack confinement and an overall increase in the composite tower fracture toughness. These results demonstrate a synergistic toughening effect of multiple mechanisms for small volumes under compression that could be applied to other nanocomposite systems.
Dislocation plasticity and phase transformations in Si-SiC core-shell nanotowers Acknowledgments The authors would like to thank J.D. Nowak for TEM contributions and V. Sivakov and S. Christiansen for growing the Si nanotowers. This work was supported financially by the National Science Foundation (CTS-0506748) and the Air Force Office of Scientific Research (AOARD-08-4134). Parts of this work were carried out in the Characterization Facility, University of Minnesota, which receives partial support from NSF through the MRSEC program.
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