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In situ electron backscatter diffraction (EBSD) during the compression of micropillars
Materials Science and Engineering A 527 (2010) 4306–4311
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
In situ electron backscatter diffraction (EBSD) during the compression of micropillars C. Niederberger ∗ , W.M. Mook, X. Maeder, J. Michler Empa, Swiss Federal Laboratories for Materials Testing and Research, Laboratory for Mechanics of Materials and Nanostructures, Feuerwerkerstrasse 39, CH-3602 Thun, Switzerland
a r t i c l e
i n f o
Article history: Received 28 October 2009 Received in revised form 12 March 2010 Accepted 15 March 2010
Keywords: SEM in situ testing Micro-compression Micromechanics EBSD Dislocations Semiconductor
a b s t r a c t For the first time, in situ electron backscatter diffraction (EBSD) measurements during compression experiments by a modified nanoindenter on micron-sized single crystal pillars are demonstrated here. The experimental setup and the requirements concerning the compression sample are described in detail. EBSD mappings have been acquired before loading, under load and after unloading for consecutive compression cycles on a focused ion beam (FIB) milled GaAs micropillar. In situ EBSD allows for the determination of crystallographic orientation with sub-100 nm spatial resolution. Thereby, it provides highly localized information pertaining to the deformation phenomena such as elastic bending of the micropillar or the formation of deformation twins and plastic orientation gradients due to geometrically necessary dislocations. The most striking features revealed by in situ EBSD are the non-negligible amount of reversible (elastic) bending of the micropillar and the fact that deformation twinning and dislocation glide initiate where the bending is strongest. Due to this high spatial and orientation resolution, in situ EBSD measurements during micromechanical testing are demonstrated to be a promising technique for the investigation of deformation phenomena at the nano- to micro-scale. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The assessment of the mechanical behavior of small material volumes is becoming increasingly important since the miniaturization of micromechanical components is continuously progressing. Micro-compression testing [1] has recently emerged as a method of choice for the determination of mechanical properties of materials in the micrometer and sub-micrometer range. Since the deformation is limited to the volume of the structure in question [1–8], such experiments are particularly suitable in order to study mechanical behavior size effects which are dislocation-based. In recent years, micropillar compression experiments have been realized in situ inside scanning electron microscopes (SEM) [9,10], transmission electron microscopes (TEM) [11–13], in a synchrotron Laue X-ray diffraction (XRD) beamline [14,15] and in a micro-Raman spectroscopy setup [16]. SEM in situ compression enables the direct observation of the micropillars during the experiment, which provides information concerning deformation and failure modes such as the onset and location of where shear bands, cracks or buckling start to appear. TEM in situ compression experiments enable
∗ Corresponding author. Tel.: +41 33 228 4626; fax: +41 33 228 4490. E-mail addresses: [email protected]fl.ch (C. Niederberger), [email protected] (W.M. Mook), [email protected] (X. Maeder), [email protected] (J. Michler). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.03.055
the observation of the evolution of the dislocation structure during deformation and therefore provide valuable insight into deformation mechanisms. Synchrotron Laue XRD in situ experiments were demonstrated to give access to possible crystal orientation changes during the compression experiment and micro-Raman in situ compression experiments allow the observation of stressgradients and phase transformations in the compression sample. Electron backscatter diffraction (EBSD) [17] has previously been used ex situ after nanoindentation [18,19] and compression [20] experiments in order to identify orientation gradients due to plasticity. Additionally, EBSD in situ tension [21] and bending [22] tests on polycrystalline metal samples followed the plastic evolution of the sample. The aim of the present contribution is to propose and demonstrate the compression of micropillars in situ in an EBSD setup, thereby providing information that is complimentary to the above-mentioned in situ approaches. In the EBSD technique, backscatter Kikuchi patterns are visualized on a phosphor screen and then automatically indexed in order to determine the local crystallographic orientation under the electron beam. The Kikuchi lines are generated by electrons that first undergo scattering and then are diffracted on the lattice planes of the crystal according to Bragg’s law. The spatial resolution capabilities of the EBSD technique can be understood when looking at the trajectories of the electrons that contribute to the Kikuchi pattern. It has been shown experimentally that the Kikuchi pattern is mostly due to backscattered electrons that have lost only very little
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Fig. 1. (a) The standard geometry for micropillar compression is realized by FIB milling an annular cavity into a polished surface. Part (b) depicts a micropillar milled near the edge of the sample. These two configurations are unsuitable for EBSD in situ compression since much of the EBSD detector screen will be shadowed by the specimen. Pillars milled into wedge-shaped specimens (c) and milled at cleaved edges (d) can be used for EBSD in situ compression.
of the incident beam energy in scattering events [23]. Backscattered electrons that experience significant inelastic scattering contribute only to the background and the blurring of the recorded pattern. The low loss electrons responsible for pattern formation each undergo only a few scattering events. This scattering can be characterized by the scattering cross-section for events with a angle of scattering > ϑ [24]: = 1.62 × 10−24
Z 2 E0
cot2
ϑ 2
(1)
where Z is the atomic number of the material and E0 is the electron energy (in keV). From this, the mean free path of the electrons can be calculated: =
A NA
(2)
where A is the atomic weight, NA Avogadro’s number and the density. For the case of GaAs analyzed with an electron energy of 20 keV, the mean free path of the electrons is about 10 nm. Considering that only electrons with small energy loss and few scattering events contribute to the Kikuchi pattern, the EBSD signal originates from a volume that is a few 10s of nm in size. This high spatial resolution has been confirmed in Monte Carlo simulations [25] as well as in experimental studies, e.g. on platinum where resolutions of less than 10 nm were realized [26]. As compared to X-ray Laue diffraction, where the spatial resolution of the orientation measurement is in the order of microns [15], the higher resolution of the EBSD technique enables detailed mappings of the crystal orientation of micron-sized pillars with an orientation resolution better than 0.5◦ . Even higher orientation resolution of up to 0.01◦ could be reached with the recently developed cross-correlation EBSD technique [27,28]. However, the substantially higher EBSD pattern quality required for this technique makes it difficult to acquire mappings on micron-sized 3-dimensional structures due to the drift expected in the system. Therefore, only Hough transform-based EBSD can provide detailed mappings of the crystal orientation and hence the microstructure in the compressed micropillar. Eventually, the EBSD signal coming from a well-defined volume at the surface of the micropillar should allow the observation of crystal orientation gradients, twinning and phase transformations in situ in the micro-compression setup. 2. Experimental The experiment described in this contribution requires a specific sample geometry and orientation inside the SEM in order to enable EBSD in situ compression measurements. The shape of the sample needs to be such that the incident beam can reach the pillar and that the diffracted electrons have a line-of-sight path to the entire EBSD detector. Since the EBSD detector has a diameter of about 4 cm and needs to be brought close to the specimen at an angle roughly perpendicular to the incident electron beam, this condition cannot be met with the typical geometry of focused ion beam (FIB) milled pillars, which is displayed in Fig. 1a. Typically, a micropillar is produced by milling an annular cavity into a polished surface. Such
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a geometry is not suitable for EBSD measurements since the trajectories of the backscattered and diffracted electrons are blocked by the surrounding material of the specimen. Even if the pillar is milled close to an edge of the specimen, as displayed in Fig. 1b, the EBSD signal originating in areas close to the root of the pillar can only reach a portion of the detector screen. In order to avoid such shadowing of the signal, the pillar must be as free-standing as possible. This can either be accomplished by a micropillar milled into a wedge-shaped specimen as is typically used for Laue XRD in situ compression experiments, Fig. 1c, or by milling a pillar directly into an edge of the specimen as it is displayed in Fig. 1d. For the experiments described in this contribution, this last geometry has been used. In order to obtain a micropillar of a well-defined prismatic shape, it is important to have a 90◦ edge which is as sharp as possible. For this purpose, a silicon doped (2 × 1018 cm−3 ) GaAs (1 0 0) wafer was cleaved along the [1 1 0] direction and a rectangular pillar with a cross-sectional area measuring 1.3 m by 0.5 m with an effective length of 2.7 m was milled from the cleaved surface with a focused ion beam (FIB) microscope. The cleaved fracture surface, which is oriented along (1 1 0), shows no signs of plasticity and was never exposed to the focused ion beam. It was not amorphized, damaged or contaminated, and is therefore an ideal surface for EBSD analysis. Any re-deposition of substrate material onto the cleaved surface during pillar formation was minimal since there is no line-of-sight trajectory from the milled area to the cleaved surface. However, a disadvantage of the chosen pillar geometry is its asymmetric root which may lead to an asymmetric stress state. The asymmetric root geometry was however chosen on purpose here since it is the only geometry which allows EBSD mappings not only on the pillar but also on the pillar root and the underlying substrate. For materials that cannot be cleaved as is done here, EBSD measurements on FIB-milled pillar surfaces are also possible if the FIB milling conditions are carefully chosen [29] and if the geometry of the sample is as the one visualized in Fig. 1c. In this case however, orientation mapping of both pillar and root is not possible. In the SEM, the specimen is positioned such that the incident electron beam is perpendicular to the compression axis of the pillar and that it includes an angle of 20◦ with the cleaved surface in order to generate a diffraction pattern of maximum intensity on the EBSD detector screen, see Fig. 2a. The sample is mounted inside a high-resolution cold field emission Hitachi S-4800 SEM capable of simultaneously recording EBSD patterns with an EDAX/TSL EBSD system while conducting instrumented mechanical tests. The SEM operating conditions, typical of EBSD measurements, used an acceleration voltage of 20.0 kV at a working distance of 17.4 mm. The in situ compression was conducted with a Hysitron PicoIndenter® having a displacement noise floor (RMS) of ∼0.4 nm and a load resolution of 0.1 N. Further details concerning the compression setup are reported elsewhere [10,30]. The compression tip was a boron-doped diamond that was FIB-milled to create a flat-punch geometry. The compression tests were conducted under displacement control using a closed feedback-loop at a rate of 2 nm/s. The feedback-loop enables the compression to be conducted under displacement control as long as the pillar does not exhibit large structural instabilities which would be recorded as displacement bursts. For the compressions here, large instabilities are not observed, however a detailed description of such behavior during micro-compression has shown that even the most ductile materials can be susceptible to these bursts depending on the abundance of mobile defects [31]. The crystallographic orientation of the pillar’s cleaved surface was mapped with EBSD before, during and after the compression experiments making this the first time an EBSD in situ compression test has been accomplished.
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Fig. 2. (a) Schematic drawing of the EBSD in situ compression setup within the SEM chamber. The cleaved surface of the micropillar is tilted by 70◦ towards the EBSD detector screen. The compression axis z is perpendicular to the incident electron beam. The EBSD detector screen and the SEM pole piece are not drawn to scale with respect to the micropillar and the flat-punch indenter. (b) SEM image taken in situ during the compression of a GaAs micropillar.
3. Results and discussion Two compression cycles have been conducted on the abovedescribed GaAs micropillar. In the first loading–unloading cycle (1 → 2 → 3), the pillar was loaded to a maximum value of 1460 N, corresponding to a uniaxial stress of 1.9 GPa when dividing load by the pillar’s cross-sectional area. At this point (2 in Fig. 3) the
displacement was held constant for a total of 220 s while an EBSD mapping was acquired. After unloading (3), a third EBSD mapping was acquired. As can be seen in Fig. 3a, after the first 25 nm, the load–displacement curve has a linear elastic character during the loading. The initial, non-linear portion of the curve is most likely due to a change in contact area suggesting the possibility of minor misalignments as will be discussed later. The three EBSD mappings recorded before loading (1), under load (2) and after unloading (3) are displayed in Fig. 3b–d, respectively. On the left of the mappings, conducted with a step size of 300 nm on a hexagonal grid, the root of the micropillar is visible. For all three mappings, the constant orientation in the root has been taken as the reference orientation for displaying the misorientation between this reference orientation and the crystal orientation for the specific beam location. Before compression, see Fig. 3b, the crystal orientation inside the pillar is uniform within the angular precision of the EBSD orientation measurement (<0.5◦ [26]). Under load however, crystal orientation gradients within the pillar become apparent. Fig. 3c illustrates that the crystal orientation in the root of the pillar remains constant whereas it gradually changes along the pillar. In the area towards the top of the micropillar the crystal orientation change is largest, reaching about 3◦ . Upon unloading, the crystal orientation gradients disappear and it is again uniform within the micropillar. The reversible character of the crystal orientation change in this first loading–unloading cycle indicates that it is due to elastic deformation of the micropillar. In order to develop a deeper understanding of the processes involved in the reversible orientation change during loading, the crystal orientation change along the micropillar has been analyzed in more detail. In order to reduce the noise in the orientation measurement, the crystal orientation at EBSD spots having the same z position, i.e. being at the same distance from the pillar top, have been averaged. In this way, it is possible to visualize and plot the crystal orientation change along the compression direction (z-axis) of the pillar. Fig. 4a–c shows the crystallographic unit cell of the diamond cubic structure along the micropillar before loading, under load and after unloading, respectively. The viewing direction is perpendicular to the compression axis and along the cleaved surface of the GaAs crystal, i.e. along the x-axis of Fig. 2. Fig. 4a visualizes the situation before compression where the crystal orientation is uniform. Under load, the unit cell cubes continuously undergo rotation
Fig. 3. (a) Load–displacement curves acquired during the micropillar compression. Engineering stress is calculated by dividing load by the cross-sectional area of the pillar. Numbers 1–5 indicate the times when EBSD maps were acquired. The arrows indicate at what point bending is initiated as observed in the video during loading. (b)–(d) EBSD orientation mappings acquired before, during and after the first loading cycle. Before compression, the orientation of the micropillar is uniform whereas an orientation gradient is present in the loaded state (c). The orientation gradient can be interpreted as an elastic bending of the pillar since it vanishes upon unloading. (e)–(g) EBSD orientation mappings acquired before, during and after the second loading cycle. Unlike in the first loading–unloading cycle, part of the orientation change is not reversible, but permanent. Some pixels are missing due to the degrading pattern quality upon plastic deformation.
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Fig. 4. (a)–(c) Schematic side view of the pillar visualizing the crystal orientation and the bending of the pillar for the first compression cycle of Fig. 3. Part (a) represents the uniform crystal orientation before loading (1 in Fig. 3), while (b) shows the crystal orientation upon elastic loading (2 in Fig. 3). The orientation is represented by unit cell cubes, which are bounded by {1 0 0} surfaces. For easier visualization, the rotation of the unit cell is amplified by a factor of 5. The rotation is associated with an elastic bending of the micropillar, which occurs predominantly along the y-axis, i.e. out of the cleavage plane. The pillar is drawn schematically with the bold line representing the surface on which the EBSD measurements were done. (c) Situation after unloading. (d) The rotation of the crystal around the x-axis plotted against the position along the pillar axis z (z = 0 at the root of the pillar) for the pillar under load, cf. Fig 4b.
along the micropillar as seen in Fig. 4b. For easier visualization, the rotation of the unit cell cubes is amplified by a factor of five. The majority of the rotation occurs around the x-axis, while smaller amounts take place around the y- and z-axes. The rotation around the x-axis under load (cf. Fig. 3c and Fig. 4b) is plotted in Fig. 4d. The maximum rotation of almost 2◦ around x is reached near the top of the micropillar. The error bars in the plot give the standard deviation of the rotation. Interestingly, the standard deviation is larger in areas where significant orientation changes were observed. The measured change in crystal orientation directly corresponds to a change of the macroscopic shape of the micropillar. In addition, the elastic bending associated with the crystal orientation change is also visualized in Fig. 4b. The pillar bends towards the y- and to a lesser extent also towards the x-direction. The amount of lateral displacement of the tip can be calculated from the crystal orientation data by assuming that the crystal orientation gradient leads to rigid body rotations of successive segments of the micropillar. Such calculations show that the tip movement along the y-axis should
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be about 48 nm. This lateral movement is confirmed by the SEM movie taken in situ during the compression in which the bending of the pillar becomes visible. The amount of lateral tip displacement visible in the movie is in the correct direction and on the same order of magnitude as the value calculated from the crystal orientation measurements. As indicated by the arrows in Fig. 3a; a frame-by-frame analysis of the SEM movie taken in situ shows that the onset of the lateral tip motion begins at a load of approximately 1 mN (1.3 GPa). Prior to this load, there was no observable lateral tip motion. After the first loading–unloading cycle (1 → 2 → 3), a second cycle was conducted. In this second cycle (3 → 4 → 5), a maximum load of 1885 N, corresponding to an average contact stress of 2.5 GPa was reached. Unlike the first loading–unloading cycle, the second cycle shows extended plasticity comparable to the behavior of ductile metals, see Fig. 3a. GaAs is known to exhibit very little room-temperature ductility at macroscopic dimensions; however, such ductile plasticity in GaAs micropillars has previously been reported in the literature [4] and it also has been shown that at room-temperature a size dependant brittle-to-ductile transition occurs for pillar diameters of less than 1 m [32]. As in the case of the first compression cycle, EBSD mappings have been recorded before loading (3), under load (4) and after unloading (5). They are displayed in Fig. 3e–g, respectively. Under load, the crystal orientation change in the micropillar is more pronounced than in the previous compression cycle. In addition, some individual measurement points show the existence of deformation twins within the micropillar. The most important difference with respect to the EBSD mappings of the first loading–unloading cycle is that the crystal orientation change is not completely reversible. After unloading, a portion of the crystal orientation gradient in the tip area of the micropillar remains as can be seen in Fig. 3g. This implies that the micropillar has been bent not only elastically but also plastically. More detailed EBSD mappings conducted after unloading but still in situ in the compression device reveal the presence of deformation twins near the tip of the micropillar, see the inversepole-figure map of Fig. 5a. A higher resolution mapping with a step size of 40 nm, Fig. 5c, shows that the thickest twin in the upper half of the mapping is about 150 nm wide. The twinned areas are also visible on the cleaved surface of the micropillar in Fig. 5e. By superimposing a misorientation map onto the inversepole-figure map in Fig. 5b, the non-reversible crystal orientation gradient in the tip area of the micropillar can be visualized. The non-reversible orientation gradient is due to geometrically necessary dislocations (GNDs), which are accumulated in the micropillar during dislocation-based plastic deformation. The twinned areas and the crystal orientation gradient indicate that plastic deformation starts in an area near the tip of the micropillar. As can be seen in Fig. 4b, this is also the area where the orientation gradient and hence the bending of the pillar during the first loading cycle is the most pronounced. The localization of the plastic deformation in this area may be due to the tapering of the pillar, which leads to higher effective stress values towards the tip of the micropillar. In the following, the possible deformation mechanisms of dislocation slip and twinning are discussed. SEM images such as the one displayed in Fig. 5e show bands, which are running around the micropillar along the two {1 1 1}-type planes shown schematically in the upper part of Fig. 5f. The SEM images show that these bands are associated with surface steps so that they could be mistaken as dislocation slip bands. However, the in situ EBSD measurements show clearly that they are related to twinning. The crystallographic orientation of the GaAs micropillar is such that the compression axis is aligned with the [0 0 1] direction and the lateral surfaces of the micropillar are of (1 1 0) and (1 1¯ 0) type. The dislocations involved in plastic deformation by either slip or twinning are supposed to move on {1 1 1}-type planes. In the given configuration
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Fig. 5. (a) Inverse pole figure (ipf) mapping showing the top area of the micropillar (step size 75 nm). The color code gives the crystal orientation of the surface normal while the black lines are twin boundaries. (b) Misorientation mapping superimposed onto the ipf-mapping showing the orientation gradient associated with the plastic bending in the micropillar. (c) ipf mapping of the twinned area at a higher spatial resolution of 40 nm allowing the determination of the width of the twinned area. (d) Pole figure illustrating the twin relationship. (e) SEM image of the tip area. (f) Schematic drawing the two apparent slip planes (top) and of the possible Burgers vectors of a dislocation lying along [1 1¯ 0] in the (1 1 1) plane. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
of the micropillar, all four {1 1 1} planes include the same angle with the compression direction. Two out of the four are visualized in the upper part of Fig. 5f, namely the ones for which slip/twin bands are detected. Supposing perfect alignment of the [0 0 1] crystal direction with the compression axis, 8 out of the 12 {1 1 1} 1 1¯ 0 slip systems exhibit the same Schmid factor of 0.408. One of these equivalent slip systems is shown in the lower part of Fig. 5f where a full 60◦ dislocation lying along [1 1¯ 0] in the (1 1 1) plane hav¯ is depicted. It is known that full 60◦ ing a Burgers vector a/2[1 0 1] dislocations in GaAs dissociate in two partial dislocations [33,34], ¯ i.e. in a 90◦ and a 30◦ partial having Burgers vectors of a/6[1 1 2] ¯ respectively in the depicted case. The driving force and a/6[2 1¯ 1], for movement is not the same for both partials, the Schmid factor for the 30◦ partial is 0.236, whereas it is 0.471 for the 90◦ partial. ¯ can therefore The 90◦ partial having a Burgers vector of a/6[1 1 2] move more easily than the 30◦ partial. In this way, the dissociation distance of the partial can exceed the pillar diameter under the applied stress. Therefore, it has been proposed that in micronsized structures such as GaAs micropillars, partial dislocations can move independently since a leading partial can cut through the entire pillar and finally annihilate at the pillar surface before the trailing partial starts to move [4]. The consequence of this is that a relatively large amount of plasticity is possible in GaAs at small length scales by repeated movement of individual partial dislocations. However, the movement of partial dislocations through the micropillar comes at the cost of creating an intrinsic stacking fault. By passing partial dislocations in neighboring (1 1 1) planes, a twin
is formed and its thickening is not associated with the expense of additional interface energy. This mechanism of twin formation has previously been observed experimentally in TEM studies by Ning et al. in GaAs, GaSb and Si [35,36]. They observed the nucleation of individual partial dislocations at the surface of the sample. The glide of such a partial dislocation leads to a surface step having the length of the Burgers vector of the partial dislocation. The surface step can subsequently serve as a preferential site for the nucleation of a partial dislocation half loop on the adjacent (1 1 1) plane [36]. The EBSD results of Fig. 5 and the bands visible in the SEM images show that the micropillar deforms plastically by the formation of such twins, which have a thickness of more than 100 nm. The in situ crystal orientation measurements during the compression of the GaAs micropillar show crystal orientation gradients. The bending of the micropillar, which is associated with the crystal orientation gradient, should not occur in a perfect compression experiment on short (low aspect ratio) micropillars. This indicates that the stress/strain state in the micropillar is not completely uniaxial and is most probably due to some asymmetry in the microcompression setup. Several sources of misalignment can occur for this testing configuration. First of all, the base of the compressed pillar for this geometry is not symmetric. Additionally, the pillar axis and the compression axis of the indenter may be misaligned by reason of inaccurate mounting of the specimen on the compression device or due to a micropillar, which is not FIB milled exactly perpendicular into the specimen. In addition, the FIB-milled surface of the diamond flat-punch may not be exactly perpendic-
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ular to the compression axis due to difficulties in controlling its orientation during FIB milling. Even though these misalignments are small, it is much more difficult to control them in a microcompression setup than in a macroscopic compression experiment. Such asymmetries, alone or in combination, can be responsible for the bending of the micropillar during the compression experiment. The measured crystal orientation change resulting from the bending is relatively small, only about 3◦ , however, it is remarkable that twinned areas and GNDs, which are signs of plastic deformation, are detected in the areas where the elastic bending was strongest. The bending modifies the stress state in the pillar. The bending stress formula = Ey/ı (y = 0 at the neutral fibre of the bent pillar) allows an estimation of the bending stress in the pillar. For a nominal pillar length of 2.7 m and a maximum bending of 3◦ , a radius of curvature of about ı = 50 m is calculated, assuming uniform bending. This leads to maximum compressive and tensile bending stresses of about 400 MPa at the front and back surfaces of the pillar, respectively. The bending stresses add to the supposedly uniaxial stresses plotted in Fig. 3. Together with the tapering of the pillar, which increases the effective stress in the tip area of the pillar, the elastic bending of the pillar triggers the onset of plasticity and determines the location where it occurs. The small misalignments, which are responsible for the bending, are difficult to avoid, but the resultant bending during the compression is equally difficult to detect unless an in situ technique can be performed during the compression experiment. For this reason, the effect of misalignments has in general been overlooked in many previous studies on the compression of micropillars. The consideration of bending effects by in situ EBSD during micropillar compression can provide valuable insight into the onset of plasticity and the deformation behavior of micropillars in general. By demonstrating the feasibility of EBSD measurements in situ during micromechanical testing, in situ strain (and accordingly stress) measurements by cross-correlation-based high-resolution EBSD [27] become conceivable in the future. Cross-correlation EBSD can provide the complete strain/stress and rotation tensors within a crystal, thereby giving access to the true strain/stress as compared to the engineering strain and stress that are in general calculated from the load–displacement data. However, detailed mappings are difficult to perform by cross-correlation EBSD on small threedimensional objects such as micro-compression pillars. Therefore, conventional Hough transform-based EBSD is the method of choice for the mapping of orientation gradients and twins in deformed structures. 4. Summary and conclusions For the first time, in situ EBSD measurements during compression experiments on micron-sized pillars are demonstrated. For this purpose, a compact instrumented nanoindentation device has been adapted to be operational in a SEM under the geometrical constraints necessitated by simultaneous EBSD measurements. The experimental setup and the geometrical requirements on the compression sample are described in detail. For the present study, micropillars have been milled into the cleaved surface of a GaAs wafer. EBSD mappings have been acquired before loading, under load and after unloading for consecutive compression cycles involving both elastic and plastic deformation. The main findings of these initial EBSD in situ measurements can be summarized as follows:
and in part non-reversible. A permanent bending remains after unloading in the area where the orientation gradient under load was strongest. Besides this orientation gradient which can be associated with GNDs, deformation twins are identified by EBSD in the same region. These findings indicate that the plastic deformation in the GaAs micropillar occurs by dislocation glide and twinning. Since elastic bending precedes plasticity, the strain/stress state in the micropillar cannot be characterized as a purely unixial compression. This non-uniaxial compression and the associated bending of the micropillar, which is due to small but unavoidable misalignments in the micro-compression setup, influences the onset of plasticity and determines the location where it occurs. Acknowledgements The authors would like to thank the European Commission for their financial support through the FP7 projects “M3-2S”, Grant No: FP7-NMP-213600 and “High-Ef”, Grant No: FP7-ENERGY-213303. References [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]
• When loading the pillar in what appears to be a linear elastic regime, bending of the pillar by as much a 3◦ has been detected by EBSD. The process is reversible, i.e. the bending disappears upon unloading. • When loading the pillar to stress levels at which a behavior characteristic of ductile plasticity is shown, the bending is stronger
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[32] [33] [34] [35] [36]
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In situ electron backscatter diffraction (EBSD) during the compression of micropillars C. Niederberger ∗ , W.M. Mook, X. Maeder, J. Michler Empa, Swiss Federal Laboratories for Materials Testing and Research, Laboratory for Mechanics of Materials and Nanostructures, Feuerwerkerstrasse 39, CH-3602 Thun, Switzerland
a r t i c l e
i n f o
Article history: Received 28 October 2009 Received in revised form 12 March 2010 Accepted 15 March 2010
Keywords: SEM in situ testing Micro-compression Micromechanics EBSD Dislocations Semiconductor
a b s t r a c t For the first time, in situ electron backscatter diffraction (EBSD) measurements during compression experiments by a modified nanoindenter on micron-sized single crystal pillars are demonstrated here. The experimental setup and the requirements concerning the compression sample are described in detail. EBSD mappings have been acquired before loading, under load and after unloading for consecutive compression cycles on a focused ion beam (FIB) milled GaAs micropillar. In situ EBSD allows for the determination of crystallographic orientation with sub-100 nm spatial resolution. Thereby, it provides highly localized information pertaining to the deformation phenomena such as elastic bending of the micropillar or the formation of deformation twins and plastic orientation gradients due to geometrically necessary dislocations. The most striking features revealed by in situ EBSD are the non-negligible amount of reversible (elastic) bending of the micropillar and the fact that deformation twinning and dislocation glide initiate where the bending is strongest. Due to this high spatial and orientation resolution, in situ EBSD measurements during micromechanical testing are demonstrated to be a promising technique for the investigation of deformation phenomena at the nano- to micro-scale. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The assessment of the mechanical behavior of small material volumes is becoming increasingly important since the miniaturization of micromechanical components is continuously progressing. Micro-compression testing [1] has recently emerged as a method of choice for the determination of mechanical properties of materials in the micrometer and sub-micrometer range. Since the deformation is limited to the volume of the structure in question [1–8], such experiments are particularly suitable in order to study mechanical behavior size effects which are dislocation-based. In recent years, micropillar compression experiments have been realized in situ inside scanning electron microscopes (SEM) [9,10], transmission electron microscopes (TEM) [11–13], in a synchrotron Laue X-ray diffraction (XRD) beamline [14,15] and in a micro-Raman spectroscopy setup [16]. SEM in situ compression enables the direct observation of the micropillars during the experiment, which provides information concerning deformation and failure modes such as the onset and location of where shear bands, cracks or buckling start to appear. TEM in situ compression experiments enable
∗ Corresponding author. Tel.: +41 33 228 4626; fax: +41 33 228 4490. E-mail addresses: [email protected]fl.ch (C. Niederberger), [email protected] (W.M. Mook), [email protected] (X. Maeder), [email protected] (J. Michler). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.03.055
the observation of the evolution of the dislocation structure during deformation and therefore provide valuable insight into deformation mechanisms. Synchrotron Laue XRD in situ experiments were demonstrated to give access to possible crystal orientation changes during the compression experiment and micro-Raman in situ compression experiments allow the observation of stressgradients and phase transformations in the compression sample. Electron backscatter diffraction (EBSD) [17] has previously been used ex situ after nanoindentation [18,19] and compression [20] experiments in order to identify orientation gradients due to plasticity. Additionally, EBSD in situ tension [21] and bending [22] tests on polycrystalline metal samples followed the plastic evolution of the sample. The aim of the present contribution is to propose and demonstrate the compression of micropillars in situ in an EBSD setup, thereby providing information that is complimentary to the above-mentioned in situ approaches. In the EBSD technique, backscatter Kikuchi patterns are visualized on a phosphor screen and then automatically indexed in order to determine the local crystallographic orientation under the electron beam. The Kikuchi lines are generated by electrons that first undergo scattering and then are diffracted on the lattice planes of the crystal according to Bragg’s law. The spatial resolution capabilities of the EBSD technique can be understood when looking at the trajectories of the electrons that contribute to the Kikuchi pattern. It has been shown experimentally that the Kikuchi pattern is mostly due to backscattered electrons that have lost only very little
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Fig. 1. (a) The standard geometry for micropillar compression is realized by FIB milling an annular cavity into a polished surface. Part (b) depicts a micropillar milled near the edge of the sample. These two configurations are unsuitable for EBSD in situ compression since much of the EBSD detector screen will be shadowed by the specimen. Pillars milled into wedge-shaped specimens (c) and milled at cleaved edges (d) can be used for EBSD in situ compression.
of the incident beam energy in scattering events [23]. Backscattered electrons that experience significant inelastic scattering contribute only to the background and the blurring of the recorded pattern. The low loss electrons responsible for pattern formation each undergo only a few scattering events. This scattering can be characterized by the scattering cross-section for events with a angle of scattering > ϑ [24]: = 1.62 × 10−24
Z 2 E0
cot2
ϑ 2
(1)
where Z is the atomic number of the material and E0 is the electron energy (in keV). From this, the mean free path of the electrons can be calculated: =
A NA
(2)
where A is the atomic weight, NA Avogadro’s number and the density. For the case of GaAs analyzed with an electron energy of 20 keV, the mean free path of the electrons is about 10 nm. Considering that only electrons with small energy loss and few scattering events contribute to the Kikuchi pattern, the EBSD signal originates from a volume that is a few 10s of nm in size. This high spatial resolution has been confirmed in Monte Carlo simulations [25] as well as in experimental studies, e.g. on platinum where resolutions of less than 10 nm were realized [26]. As compared to X-ray Laue diffraction, where the spatial resolution of the orientation measurement is in the order of microns [15], the higher resolution of the EBSD technique enables detailed mappings of the crystal orientation of micron-sized pillars with an orientation resolution better than 0.5◦ . Even higher orientation resolution of up to 0.01◦ could be reached with the recently developed cross-correlation EBSD technique [27,28]. However, the substantially higher EBSD pattern quality required for this technique makes it difficult to acquire mappings on micron-sized 3-dimensional structures due to the drift expected in the system. Therefore, only Hough transform-based EBSD can provide detailed mappings of the crystal orientation and hence the microstructure in the compressed micropillar. Eventually, the EBSD signal coming from a well-defined volume at the surface of the micropillar should allow the observation of crystal orientation gradients, twinning and phase transformations in situ in the micro-compression setup. 2. Experimental The experiment described in this contribution requires a specific sample geometry and orientation inside the SEM in order to enable EBSD in situ compression measurements. The shape of the sample needs to be such that the incident beam can reach the pillar and that the diffracted electrons have a line-of-sight path to the entire EBSD detector. Since the EBSD detector has a diameter of about 4 cm and needs to be brought close to the specimen at an angle roughly perpendicular to the incident electron beam, this condition cannot be met with the typical geometry of focused ion beam (FIB) milled pillars, which is displayed in Fig. 1a. Typically, a micropillar is produced by milling an annular cavity into a polished surface. Such
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a geometry is not suitable for EBSD measurements since the trajectories of the backscattered and diffracted electrons are blocked by the surrounding material of the specimen. Even if the pillar is milled close to an edge of the specimen, as displayed in Fig. 1b, the EBSD signal originating in areas close to the root of the pillar can only reach a portion of the detector screen. In order to avoid such shadowing of the signal, the pillar must be as free-standing as possible. This can either be accomplished by a micropillar milled into a wedge-shaped specimen as is typically used for Laue XRD in situ compression experiments, Fig. 1c, or by milling a pillar directly into an edge of the specimen as it is displayed in Fig. 1d. For the experiments described in this contribution, this last geometry has been used. In order to obtain a micropillar of a well-defined prismatic shape, it is important to have a 90◦ edge which is as sharp as possible. For this purpose, a silicon doped (2 × 1018 cm−3 ) GaAs (1 0 0) wafer was cleaved along the [1 1 0] direction and a rectangular pillar with a cross-sectional area measuring 1.3 m by 0.5 m with an effective length of 2.7 m was milled from the cleaved surface with a focused ion beam (FIB) microscope. The cleaved fracture surface, which is oriented along (1 1 0), shows no signs of plasticity and was never exposed to the focused ion beam. It was not amorphized, damaged or contaminated, and is therefore an ideal surface for EBSD analysis. Any re-deposition of substrate material onto the cleaved surface during pillar formation was minimal since there is no line-of-sight trajectory from the milled area to the cleaved surface. However, a disadvantage of the chosen pillar geometry is its asymmetric root which may lead to an asymmetric stress state. The asymmetric root geometry was however chosen on purpose here since it is the only geometry which allows EBSD mappings not only on the pillar but also on the pillar root and the underlying substrate. For materials that cannot be cleaved as is done here, EBSD measurements on FIB-milled pillar surfaces are also possible if the FIB milling conditions are carefully chosen [29] and if the geometry of the sample is as the one visualized in Fig. 1c. In this case however, orientation mapping of both pillar and root is not possible. In the SEM, the specimen is positioned such that the incident electron beam is perpendicular to the compression axis of the pillar and that it includes an angle of 20◦ with the cleaved surface in order to generate a diffraction pattern of maximum intensity on the EBSD detector screen, see Fig. 2a. The sample is mounted inside a high-resolution cold field emission Hitachi S-4800 SEM capable of simultaneously recording EBSD patterns with an EDAX/TSL EBSD system while conducting instrumented mechanical tests. The SEM operating conditions, typical of EBSD measurements, used an acceleration voltage of 20.0 kV at a working distance of 17.4 mm. The in situ compression was conducted with a Hysitron PicoIndenter® having a displacement noise floor (RMS) of ∼0.4 nm and a load resolution of 0.1 N. Further details concerning the compression setup are reported elsewhere [10,30]. The compression tip was a boron-doped diamond that was FIB-milled to create a flat-punch geometry. The compression tests were conducted under displacement control using a closed feedback-loop at a rate of 2 nm/s. The feedback-loop enables the compression to be conducted under displacement control as long as the pillar does not exhibit large structural instabilities which would be recorded as displacement bursts. For the compressions here, large instabilities are not observed, however a detailed description of such behavior during micro-compression has shown that even the most ductile materials can be susceptible to these bursts depending on the abundance of mobile defects [31]. The crystallographic orientation of the pillar’s cleaved surface was mapped with EBSD before, during and after the compression experiments making this the first time an EBSD in situ compression test has been accomplished.
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Fig. 2. (a) Schematic drawing of the EBSD in situ compression setup within the SEM chamber. The cleaved surface of the micropillar is tilted by 70◦ towards the EBSD detector screen. The compression axis z is perpendicular to the incident electron beam. The EBSD detector screen and the SEM pole piece are not drawn to scale with respect to the micropillar and the flat-punch indenter. (b) SEM image taken in situ during the compression of a GaAs micropillar.
3. Results and discussion Two compression cycles have been conducted on the abovedescribed GaAs micropillar. In the first loading–unloading cycle (1 → 2 → 3), the pillar was loaded to a maximum value of 1460 N, corresponding to a uniaxial stress of 1.9 GPa when dividing load by the pillar’s cross-sectional area. At this point (2 in Fig. 3) the
displacement was held constant for a total of 220 s while an EBSD mapping was acquired. After unloading (3), a third EBSD mapping was acquired. As can be seen in Fig. 3a, after the first 25 nm, the load–displacement curve has a linear elastic character during the loading. The initial, non-linear portion of the curve is most likely due to a change in contact area suggesting the possibility of minor misalignments as will be discussed later. The three EBSD mappings recorded before loading (1), under load (2) and after unloading (3) are displayed in Fig. 3b–d, respectively. On the left of the mappings, conducted with a step size of 300 nm on a hexagonal grid, the root of the micropillar is visible. For all three mappings, the constant orientation in the root has been taken as the reference orientation for displaying the misorientation between this reference orientation and the crystal orientation for the specific beam location. Before compression, see Fig. 3b, the crystal orientation inside the pillar is uniform within the angular precision of the EBSD orientation measurement (<0.5◦ [26]). Under load however, crystal orientation gradients within the pillar become apparent. Fig. 3c illustrates that the crystal orientation in the root of the pillar remains constant whereas it gradually changes along the pillar. In the area towards the top of the micropillar the crystal orientation change is largest, reaching about 3◦ . Upon unloading, the crystal orientation gradients disappear and it is again uniform within the micropillar. The reversible character of the crystal orientation change in this first loading–unloading cycle indicates that it is due to elastic deformation of the micropillar. In order to develop a deeper understanding of the processes involved in the reversible orientation change during loading, the crystal orientation change along the micropillar has been analyzed in more detail. In order to reduce the noise in the orientation measurement, the crystal orientation at EBSD spots having the same z position, i.e. being at the same distance from the pillar top, have been averaged. In this way, it is possible to visualize and plot the crystal orientation change along the compression direction (z-axis) of the pillar. Fig. 4a–c shows the crystallographic unit cell of the diamond cubic structure along the micropillar before loading, under load and after unloading, respectively. The viewing direction is perpendicular to the compression axis and along the cleaved surface of the GaAs crystal, i.e. along the x-axis of Fig. 2. Fig. 4a visualizes the situation before compression where the crystal orientation is uniform. Under load, the unit cell cubes continuously undergo rotation
Fig. 3. (a) Load–displacement curves acquired during the micropillar compression. Engineering stress is calculated by dividing load by the cross-sectional area of the pillar. Numbers 1–5 indicate the times when EBSD maps were acquired. The arrows indicate at what point bending is initiated as observed in the video during loading. (b)–(d) EBSD orientation mappings acquired before, during and after the first loading cycle. Before compression, the orientation of the micropillar is uniform whereas an orientation gradient is present in the loaded state (c). The orientation gradient can be interpreted as an elastic bending of the pillar since it vanishes upon unloading. (e)–(g) EBSD orientation mappings acquired before, during and after the second loading cycle. Unlike in the first loading–unloading cycle, part of the orientation change is not reversible, but permanent. Some pixels are missing due to the degrading pattern quality upon plastic deformation.
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Fig. 4. (a)–(c) Schematic side view of the pillar visualizing the crystal orientation and the bending of the pillar for the first compression cycle of Fig. 3. Part (a) represents the uniform crystal orientation before loading (1 in Fig. 3), while (b) shows the crystal orientation upon elastic loading (2 in Fig. 3). The orientation is represented by unit cell cubes, which are bounded by {1 0 0} surfaces. For easier visualization, the rotation of the unit cell is amplified by a factor of 5. The rotation is associated with an elastic bending of the micropillar, which occurs predominantly along the y-axis, i.e. out of the cleavage plane. The pillar is drawn schematically with the bold line representing the surface on which the EBSD measurements were done. (c) Situation after unloading. (d) The rotation of the crystal around the x-axis plotted against the position along the pillar axis z (z = 0 at the root of the pillar) for the pillar under load, cf. Fig 4b.
along the micropillar as seen in Fig. 4b. For easier visualization, the rotation of the unit cell cubes is amplified by a factor of five. The majority of the rotation occurs around the x-axis, while smaller amounts take place around the y- and z-axes. The rotation around the x-axis under load (cf. Fig. 3c and Fig. 4b) is plotted in Fig. 4d. The maximum rotation of almost 2◦ around x is reached near the top of the micropillar. The error bars in the plot give the standard deviation of the rotation. Interestingly, the standard deviation is larger in areas where significant orientation changes were observed. The measured change in crystal orientation directly corresponds to a change of the macroscopic shape of the micropillar. In addition, the elastic bending associated with the crystal orientation change is also visualized in Fig. 4b. The pillar bends towards the y- and to a lesser extent also towards the x-direction. The amount of lateral displacement of the tip can be calculated from the crystal orientation data by assuming that the crystal orientation gradient leads to rigid body rotations of successive segments of the micropillar. Such calculations show that the tip movement along the y-axis should
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be about 48 nm. This lateral movement is confirmed by the SEM movie taken in situ during the compression in which the bending of the pillar becomes visible. The amount of lateral tip displacement visible in the movie is in the correct direction and on the same order of magnitude as the value calculated from the crystal orientation measurements. As indicated by the arrows in Fig. 3a; a frame-by-frame analysis of the SEM movie taken in situ shows that the onset of the lateral tip motion begins at a load of approximately 1 mN (1.3 GPa). Prior to this load, there was no observable lateral tip motion. After the first loading–unloading cycle (1 → 2 → 3), a second cycle was conducted. In this second cycle (3 → 4 → 5), a maximum load of 1885 N, corresponding to an average contact stress of 2.5 GPa was reached. Unlike the first loading–unloading cycle, the second cycle shows extended plasticity comparable to the behavior of ductile metals, see Fig. 3a. GaAs is known to exhibit very little room-temperature ductility at macroscopic dimensions; however, such ductile plasticity in GaAs micropillars has previously been reported in the literature [4] and it also has been shown that at room-temperature a size dependant brittle-to-ductile transition occurs for pillar diameters of less than 1 m [32]. As in the case of the first compression cycle, EBSD mappings have been recorded before loading (3), under load (4) and after unloading (5). They are displayed in Fig. 3e–g, respectively. Under load, the crystal orientation change in the micropillar is more pronounced than in the previous compression cycle. In addition, some individual measurement points show the existence of deformation twins within the micropillar. The most important difference with respect to the EBSD mappings of the first loading–unloading cycle is that the crystal orientation change is not completely reversible. After unloading, a portion of the crystal orientation gradient in the tip area of the micropillar remains as can be seen in Fig. 3g. This implies that the micropillar has been bent not only elastically but also plastically. More detailed EBSD mappings conducted after unloading but still in situ in the compression device reveal the presence of deformation twins near the tip of the micropillar, see the inversepole-figure map of Fig. 5a. A higher resolution mapping with a step size of 40 nm, Fig. 5c, shows that the thickest twin in the upper half of the mapping is about 150 nm wide. The twinned areas are also visible on the cleaved surface of the micropillar in Fig. 5e. By superimposing a misorientation map onto the inversepole-figure map in Fig. 5b, the non-reversible crystal orientation gradient in the tip area of the micropillar can be visualized. The non-reversible orientation gradient is due to geometrically necessary dislocations (GNDs), which are accumulated in the micropillar during dislocation-based plastic deformation. The twinned areas and the crystal orientation gradient indicate that plastic deformation starts in an area near the tip of the micropillar. As can be seen in Fig. 4b, this is also the area where the orientation gradient and hence the bending of the pillar during the first loading cycle is the most pronounced. The localization of the plastic deformation in this area may be due to the tapering of the pillar, which leads to higher effective stress values towards the tip of the micropillar. In the following, the possible deformation mechanisms of dislocation slip and twinning are discussed. SEM images such as the one displayed in Fig. 5e show bands, which are running around the micropillar along the two {1 1 1}-type planes shown schematically in the upper part of Fig. 5f. The SEM images show that these bands are associated with surface steps so that they could be mistaken as dislocation slip bands. However, the in situ EBSD measurements show clearly that they are related to twinning. The crystallographic orientation of the GaAs micropillar is such that the compression axis is aligned with the [0 0 1] direction and the lateral surfaces of the micropillar are of (1 1 0) and (1 1¯ 0) type. The dislocations involved in plastic deformation by either slip or twinning are supposed to move on {1 1 1}-type planes. In the given configuration
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Fig. 5. (a) Inverse pole figure (ipf) mapping showing the top area of the micropillar (step size 75 nm). The color code gives the crystal orientation of the surface normal while the black lines are twin boundaries. (b) Misorientation mapping superimposed onto the ipf-mapping showing the orientation gradient associated with the plastic bending in the micropillar. (c) ipf mapping of the twinned area at a higher spatial resolution of 40 nm allowing the determination of the width of the twinned area. (d) Pole figure illustrating the twin relationship. (e) SEM image of the tip area. (f) Schematic drawing the two apparent slip planes (top) and of the possible Burgers vectors of a dislocation lying along [1 1¯ 0] in the (1 1 1) plane. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
of the micropillar, all four {1 1 1} planes include the same angle with the compression direction. Two out of the four are visualized in the upper part of Fig. 5f, namely the ones for which slip/twin bands are detected. Supposing perfect alignment of the [0 0 1] crystal direction with the compression axis, 8 out of the 12 {1 1 1} 1 1¯ 0 slip systems exhibit the same Schmid factor of 0.408. One of these equivalent slip systems is shown in the lower part of Fig. 5f where a full 60◦ dislocation lying along [1 1¯ 0] in the (1 1 1) plane hav¯ is depicted. It is known that full 60◦ ing a Burgers vector a/2[1 0 1] dislocations in GaAs dissociate in two partial dislocations [33,34], ¯ i.e. in a 90◦ and a 30◦ partial having Burgers vectors of a/6[1 1 2] ¯ respectively in the depicted case. The driving force and a/6[2 1¯ 1], for movement is not the same for both partials, the Schmid factor for the 30◦ partial is 0.236, whereas it is 0.471 for the 90◦ partial. ¯ can therefore The 90◦ partial having a Burgers vector of a/6[1 1 2] move more easily than the 30◦ partial. In this way, the dissociation distance of the partial can exceed the pillar diameter under the applied stress. Therefore, it has been proposed that in micronsized structures such as GaAs micropillars, partial dislocations can move independently since a leading partial can cut through the entire pillar and finally annihilate at the pillar surface before the trailing partial starts to move [4]. The consequence of this is that a relatively large amount of plasticity is possible in GaAs at small length scales by repeated movement of individual partial dislocations. However, the movement of partial dislocations through the micropillar comes at the cost of creating an intrinsic stacking fault. By passing partial dislocations in neighboring (1 1 1) planes, a twin
is formed and its thickening is not associated with the expense of additional interface energy. This mechanism of twin formation has previously been observed experimentally in TEM studies by Ning et al. in GaAs, GaSb and Si [35,36]. They observed the nucleation of individual partial dislocations at the surface of the sample. The glide of such a partial dislocation leads to a surface step having the length of the Burgers vector of the partial dislocation. The surface step can subsequently serve as a preferential site for the nucleation of a partial dislocation half loop on the adjacent (1 1 1) plane [36]. The EBSD results of Fig. 5 and the bands visible in the SEM images show that the micropillar deforms plastically by the formation of such twins, which have a thickness of more than 100 nm. The in situ crystal orientation measurements during the compression of the GaAs micropillar show crystal orientation gradients. The bending of the micropillar, which is associated with the crystal orientation gradient, should not occur in a perfect compression experiment on short (low aspect ratio) micropillars. This indicates that the stress/strain state in the micropillar is not completely uniaxial and is most probably due to some asymmetry in the microcompression setup. Several sources of misalignment can occur for this testing configuration. First of all, the base of the compressed pillar for this geometry is not symmetric. Additionally, the pillar axis and the compression axis of the indenter may be misaligned by reason of inaccurate mounting of the specimen on the compression device or due to a micropillar, which is not FIB milled exactly perpendicular into the specimen. In addition, the FIB-milled surface of the diamond flat-punch may not be exactly perpendic-
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ular to the compression axis due to difficulties in controlling its orientation during FIB milling. Even though these misalignments are small, it is much more difficult to control them in a microcompression setup than in a macroscopic compression experiment. Such asymmetries, alone or in combination, can be responsible for the bending of the micropillar during the compression experiment. The measured crystal orientation change resulting from the bending is relatively small, only about 3◦ , however, it is remarkable that twinned areas and GNDs, which are signs of plastic deformation, are detected in the areas where the elastic bending was strongest. The bending modifies the stress state in the pillar. The bending stress formula = Ey/ı (y = 0 at the neutral fibre of the bent pillar) allows an estimation of the bending stress in the pillar. For a nominal pillar length of 2.7 m and a maximum bending of 3◦ , a radius of curvature of about ı = 50 m is calculated, assuming uniform bending. This leads to maximum compressive and tensile bending stresses of about 400 MPa at the front and back surfaces of the pillar, respectively. The bending stresses add to the supposedly uniaxial stresses plotted in Fig. 3. Together with the tapering of the pillar, which increases the effective stress in the tip area of the pillar, the elastic bending of the pillar triggers the onset of plasticity and determines the location where it occurs. The small misalignments, which are responsible for the bending, are difficult to avoid, but the resultant bending during the compression is equally difficult to detect unless an in situ technique can be performed during the compression experiment. For this reason, the effect of misalignments has in general been overlooked in many previous studies on the compression of micropillars. The consideration of bending effects by in situ EBSD during micropillar compression can provide valuable insight into the onset of plasticity and the deformation behavior of micropillars in general. By demonstrating the feasibility of EBSD measurements in situ during micromechanical testing, in situ strain (and accordingly stress) measurements by cross-correlation-based high-resolution EBSD [27] become conceivable in the future. Cross-correlation EBSD can provide the complete strain/stress and rotation tensors within a crystal, thereby giving access to the true strain/stress as compared to the engineering strain and stress that are in general calculated from the load–displacement data. However, detailed mappings are difficult to perform by cross-correlation EBSD on small threedimensional objects such as micro-compression pillars. Therefore, conventional Hough transform-based EBSD is the method of choice for the mapping of orientation gradients and twins in deformed structures. 4. Summary and conclusions For the first time, in situ EBSD measurements during compression experiments on micron-sized pillars are demonstrated. For this purpose, a compact instrumented nanoindentation device has been adapted to be operational in a SEM under the geometrical constraints necessitated by simultaneous EBSD measurements. The experimental setup and the geometrical requirements on the compression sample are described in detail. For the present study, micropillars have been milled into the cleaved surface of a GaAs wafer. EBSD mappings have been acquired before loading, under load and after unloading for consecutive compression cycles involving both elastic and plastic deformation. The main findings of these initial EBSD in situ measurements can be summarized as follows:
and in part non-reversible. A permanent bending remains after unloading in the area where the orientation gradient under load was strongest. Besides this orientation gradient which can be associated with GNDs, deformation twins are identified by EBSD in the same region. These findings indicate that the plastic deformation in the GaAs micropillar occurs by dislocation glide and twinning. Since elastic bending precedes plasticity, the strain/stress state in the micropillar cannot be characterized as a purely unixial compression. This non-uniaxial compression and the associated bending of the micropillar, which is due to small but unavoidable misalignments in the micro-compression setup, influences the onset of plasticity and determines the location where it occurs. Acknowledgements The authors would like to thank the European Commission for their financial support through the FP7 projects “M3-2S”, Grant No: FP7-NMP-213600 and “High-Ef”, Grant No: FP7-ENERGY-213303. References [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]
• When loading the pillar in what appears to be a linear elastic regime, bending of the pillar by as much a 3◦ has been detected by EBSD. The process is reversible, i.e. the bending disappears upon unloading. • When loading the pillar to stress levels at which a behavior characteristic of ductile plasticity is shown, the bending is stronger
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[32] [33] [34] [35] [36]
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