First stages of plasticity in nano- and micro-objects: simulations and experiments

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1 First stages of plasticity in nano- and micro-objects: simulations and experiments Sandrine BROCHARD, Jean-Luc DEMENET, Julien GODET, Julien GUENOLE (PhD student), Dominique EYIDI, Laurent PIZZAGALLI, Jacques RABIER, Ludovic THILLY Former PhDs: Pierre HIREL Collaborations Tristan ALBARET, LPMCN (Lyon, France) Michael J. DEMKOWICZ, MIT (Cambridge, USA) Rudy GHISLENI, Alex MONTAGNE, Johann MICHLER, EMPA (Thun, Switzerland) Vincent JACQUES, ESRF (Grenoble, France) Contacts Context The mechanical properties of nano- and micro-objects such as thin films, nanowires or micropillars, are attracting much attention, not only because of their technological interest (nano and micro-electronics, nano- and micro-electromechanical systems), but also because they are model systems for the study of the elementary mechanisms of plasticity. Moreover, the smallest objects often allow for an effective comparison between experiments and numerical simulations, now with comparable sizes, which make them attractive systems for such studies. The nano- and micro-objects generally exhibit amazing behaviour, often different from their bulk counterparts. Concerning the mechanical properties, their two most salient features when compared to bulk are an increase of both the elasticity limit for almost all materials, and of the ductility domain for semiconductor materials. These differences with bulk can be ascribed to a change of the deformation mechanisms when the size of the microstructure decreases. Indeed, plasticity in bulk crystals is most often governed by the multiplication of dislocations from bulk sources, such as Franck Read sources, and their subsequent glide; no size effect is expected to occur then. However, in nanostructures, because of the small dimensions and the low initial density of dislocations, such mechanisms are inhibited. Nucleation of dislocations, rather than their multiplication, then becomes a mechanism of prime importance, and consequently the elasticity limit become close to the theoretical one. In this framework, our goals in the Physics of defects and plasticity group are to identify the details of the mechanisms responsible for the first stages of plastic deformation in these small objects, to determine the associated elasticity limit, and to relate the plasticity mechanisms to specific behaviour (such as the brittle to ductile transition observed in semiconductors at room temperature when the system size decreases). To achieve this, we use both atomistic simulations and tailored experiments. On the one hand, atomistic calculations give the opportunity to explore size and time scales that remain inaccessible to experimental observations. On the other hand, in-situ deformation experiments are performed in collaboration with several recognized groups (EMPA, Switzerland; ESRF, France) to collect

2 experimental data that can be confronted to the different scenarios emerging from atomistic simulations. We are thus investigating the mechanical behaviour of materials which can be considered as model ones: metals and semiconductors. Regarding metals, numerical calculations are performed on face-centered-cubic (fcc) metals (aluminum and copper), for which reliable semi-empirical potentials are available. Furthermore, the plasticity of fcc metals being relatively simple and well known, it allows for the efficient comparison of numerical simulations results with elasticity models that are also developed in the group. Regarding semiconductors, silicon (Si), considered as the prototypical semiconductor crystallizing into the cubic diamond structure, is investigated with both simulations and experiments. Indium antimonide (InSb) is also experimentally studied. For both semiconductors bulk plasticity has been previously well characterized within the group (see notably Brittle-ductile transition and dislocation cores in semiconductors file on this web site); the plasticity mechanisms can hence be compared between macroscopic and microscopic samples, enabling the exploration of size effects. Atomistic simulations: fcc metals and Si thin films Nano-objects are characterized by a high surface to volume ratio, so that surfaces are expected to play a key role in the first stages of plastic deformation. In our group, the very first stages of dislocation formation at surfaces, and particularly at their defects, have been studied by simulations at the atomic scale, using both static relaxation and Molecular Dynamics (MD), and both semi-empirical potentials and first-principles (ab initio) calculations to model the forces between atoms. In both silicon and fcc metals, surface steps have been shown to be preferential sites for dislocation nucleation, reducing the nucleation stress. Figure 1 shows the typical outcome of a simulation using a classical semi-empirical interatomic potential for aluminum at 100 K as the applied strain reaches 6.6%. Several dislocation embryos form on monatomic steps, but quickly vanish, until one of them exceeds a critical radius and eventually expands in one of the {111} planes passing through the step. The first formed dislocation is a Shockley partial, because of the stress direction which yields the highest Schmid factor for this dislocation. Figure 1: evolution of an aluminum sample under 6.6% applied strain at 100 K. Atoms are colored according to their central symmetry parameter; only atoms which are not in a perfect fcc environment are drawn: surfaces (yellow green), stacking faults and dislocation cores (blue). (a) Dislocation embryos appear randomly on both steps (arrows), and retract rapidly to the surface. (b,c) Only when it reaches a critical radius will a dislocation half-loop propagate into the crystal. Such a mechanism can be rationalized by means of the activation parameters, which defines the energy barrier that the system has to cross for a given mechanism to occur. Among other techniques, we used the nudged elastic band method to determine the activation energy and dislocation critical radius for different applied strains for aluminum. Aluminum being almost isotropic, the results from atomistic simulations can be used to fit a custom elastic

3 model; it then provides analytical equations describing forces and energy associated with a dislocation half loop in a semi-infinite medium. Besides, we analyzed the implication of the activation parameters in the lowering of the nucleation strain when temperature is increased [1]. In silicon, mainly because of the covalent bonding, the situation is more complex and the core structure of the dislocations is determinant. Also Si, like many semiconductors, crystallizes into the cubic diamond structure, which yields two possible sets of slip planes for the dislocations (glide and shuffle set planes). As for fcc metals, the step geometry has been shown to be determining in the elasticity limit for silicon, but because of the nature of bonding, not only the step height, but also the step structure (reconstructed or not) acts upon the onset of plasticity. Using first principles calculations, it has also been possible to investigate the effect of the Si surface passivation by hydrogen atoms: when all the surface dangling bonds are saturated, dislocation nucleation does no longer take place at surfaces, even when steps are present. Finally, in Si, we have confirmed the existence of two plasticity modes depending on temperature and stress intensity, as already evidenced experimentally in bulk (see notably Brittle-ductile transition and dislocation cores in semiconductors file on this web site). However, compared to bulk Si, the only source of dislocations comes from the surface in our simulations, suggesting that this mechanism can governed the plasticity of silicon, especially in nanostructures. Atomistic simulations: Si nanowires Recently, in the context of enhanced experimental control of the shape of these objects, we have considered the more complex geometries of silicon nanowires. Various shapes (cylindrical, parallelepipedic), orientations, kind of surfaces (in the case of parallelepipedic nanowires), as well as core-shell nanowires, have been studied with MD simulations. In our simulations, we have observed the activation of different modes of plasticity (see for example figure 2), which can be rationalized mainly by the analysis of the Schmid factors and the specificity of the different used interatomic potentials. No size effect has been observed for the spanned size range (5 to 50 nm), the yield strain being almost constant, and the plasticity mechanisms being identical for nanowires with the same geometry but different sizes. Figure 2: (a) formation of a perfect dislocation in a <123> NW in tension at 300K. The white arrows indicate the emergence points of the dislocation loop on the NW surfaces. (b) A NW slide is cut through the defect for visualization of atomic details. The atoms are colored according to their coordination number, with cyan, light brown, green, grey and red atoms for 1, 2, 3, 4 and 5-fold coordination respectively. In (a) top view, 4-fold coordinated atoms are not shown.

4 For nanowires with square section, we have analyzed the competition between the surfaces and the corners of the nanowires for the onset of plasticity. In general, the probability is larger for defect nucleation from the edges than from the flat surfaces, the surfaces being implied in a few cases only for appropriate surface geometries. Another interesting feature revealed by the simulations is the unexpected activation in Si of {011} slip planes when nanowires are under compression along [001], regardless of the temperature and the used interatomic potential. The occurrence of such an unexpected slip system can be explained by a careful investigation of the generalized stacking fault energy under different stress conditions, and the associated restoring forces, that we have determined and compared for the used interatomic potentials and from ab initio calculations. Finally, the activation of {011} planes is shown to be an indirect consequence of the small dimensions of the considered nanostructures [2]. In order to gain knowledge on the mechanical behavior of core-shell nanostructures on which nanotechnology is now focused, we are also performing atomistic calculations using nanowires with Si crystalline core and amorphous shell. Under compressive deformation, we observe plasticity mediated by dislocation nucleation, but in a very different way than that observed in systems without amorphous shell. During the elastic deformation, some interface defects behave like seeds that create dislocations cores, regardless of the local stress state. One of these cores will eventually be at the origin of the first plastic event. Therefore, in the case of the studied core-shell systems, the onset of plasticity is governed by the amorphous shell. Deformation experiments: InSb and Si To experimentally study the plasticity of Si and InSb micrometer-sized columns (so-called micropillars ), the micro-objects are fabricated by focused ion beam (FIB) milling at EMPA, with different diameters and different crystallographic orientations. In the case of InSb, micropillars with crystal orientation <123> to favor single slip and <111> to favor multiple slip were tested at EMPA by in situ compression tests in a scanning electron microscope (SEM), at a strain rate ranging between and s -1. Although InSb is a brittle material at room temperature (RT) at the macroscopic scale, the micropillars can be plastically deformed up to strains of 20%. The SEM videos taken during the compression allowed observing slip bands that appear at the top surface of the pillar and propagate to its base (figure 3a). TEM thin foils were cut out from deformed pillars to study the deformation microstructure in our group: the analysis of dislocations revealed that microscopic samples deform via nucleation and glide of partial dislocations, i.e. similarly to macroscopic samples. In micro-pillars, all the observed partial dislocations nucleated at free surfaces showing that increasing the surface-to-volume ratio of the semiconductor pillars modifies the dislocation nucleation conditions and favors plasticity even at room temperature. This result confirms that nucleation is one of the rate-limiting parameters that govern ductile versus brittle behavior in semiconductors [3]. The same experimental procedure has been applied to <123>-oriented Si micropillars: compressions have been performed at EMPA at RT, 200 C, 400 C in a SEM at a low strain rate ( s -1 ). Moreover, materials with different electronic doping were investigated: intrinsic (P, N n =10 14 cm -3 ), n type (P, N n # cm -3 ) and p type (B, N p # cm -3 ). Slip traces at micropillars surfaces show the activation of a ½<110>(111) glide system at RT. At 200 C and 400 C secondary systems are also activated (figure 3b). TEM observations after deformation at RT do not show any dislocation storage or stacking faults. This is consistent with plastic deformation controlled by perfect dislocations. Additionally, a doping effect has been evidenced on the micropillars yield stress which is different from that obtained at higher

5 temperature on bulk materials, suggesting an electronic effect on the dislocation nucleation mechanisms. Figure 3: (a) Typical compression stress-strain curve obtained at RT for a 3 µm diameter InSb pillar. Inset: snapshots of the SEM video recorded during compression with corresponding schematic of the pillar showing the observed slip traces (from [3]). (b) SEM micrograph showing a 1 µm diameter Si pillar deformed at 200 C along <123> orientation. (a) (b) Recent publications [1] S. Brochard, P. Hirel, L. Pizzagalli, J. Godet, Elastic limit for surface step dislocation nucleation in face-centered cubic metals: Temperature and step height dependence, Acta Materialia, 58 (2010) p [2] J. Guénolé, S. Brochard, J. Godet, Unexpected slip mechanism induced by the reduced dimensions in silicon nanostructures: Atomistic study, Acta Materialia, 59 (2011) p [3] L. Thilly, R. Ghisleni, C. Swistak, J. Michler, In-situ deformation of micro-objects as a tool to uncover the micro-mechanisms of the brittle-to-ductile transition in semi-conductors: the case of Indium Antimonide, Philosophical Magazine, in press (2012)