Plastic Deformation of InSb Micro-Pillars: A Comparative Study Between Spatially Resolved Laue and Monochromatic X-Ray Micro-Diffraction Maps

Indium Antimonide (InSb) single-crystalline micro-pillars were mechanically deformed by uniaxial compression loading-unloading cycles up to the beginning of the plastic regime. After deformation, 2D spatially resolved maps were collected via two X-Ray Diffraction (XRD) techniques: polychromatic micro-Laue and monochromatic micro-diffraction. In both techniques, the integrated diffracted intensity shows strong variations inside the pillar. Moreover, the shift and streaking of one spot in polychromatic XRD as well as the lattice strain and tilt components derived from monochromatic XRD reveal that the plastically deformed area is localized on the top of the pillar, in agreement with scanning electron microscopy images. The two XRD techniques are thus providing correlated but yet complementary information. Introduction Indium Antimonide (InSb) and other semiconductors are known to be crystalline materials with brittle behavior at room temperature in the bulk state, but become ductile in the form of microand nano-objects [1-2]. At room temperature, InSb micro-pillars plastically deform by the nucleation of partial dislocations at surfaces: after gliding through the pillar, they escape at opposite surfaces (creating slip traces forming a deformation band) but leave in the crystal parallel Stacking Faults (SFs). This mechanism has been verified by post-mortem Scanning Electron Microscopy (SEM) observations and destructive Transmission Electron Microscopy (TEM) characterization [1-2] but also by non-destructive post-mortem study based on coherent X-Ray diffraction [3]. In the latter case, the profile of coherent diffraction patterns of 202 reflection evolves significantly between pristine and plastically-deformed regions: the splitting and streaking of patterns arise from interferences induced by the presence of SFs that are phasedefects creating phase-shifted regions within the pillar [3]. The maximum intensity of diffraction patterns could be related to the number of SFs present in the illuminated volume, and also to the volume of defected region (i.e. the size of the band containing the SFs). This diffraction technique thus proved to be very interesting as a non-destructive way to detect and characterize the presence of plastic defects in nano-and micro-objects. Residual Stresses 2018 – ECRS-10 Materials Research Forum LLC Materials Research Proceedings 6 (2018) 21-26 doi: http://dx.doi.org/10.21741/9781945291890-4 22 In the present work, the same system (InSb micro-pillar) is used to further assess the capacities of micro-diffraction techniques to characterize the impact of plastic deformation (lattice rotation, residual strain, defects storage, etc.) and in particular compare two techniques, Laue and monochromatic micro-diffraction, via spatially resolved 2D maps that are compared and discussed. InSb micro-pillars – Mechanical tests InSb micro-pillars were fabricated by Ga Focused Ion Beam (FIB) milling from a bulk <123>oriented single-crystalline wedge: at all milling steps, the ion beam current and acceleration voltage were kept as low as possible to avoid creation of lattice defects and/or surface amorphisation; for instance, the last milling step was performed at a beam current of 24 pA. The resulting geometry is a series of free-standing micro-pillars on top of pedestals. Fig. 1 (a) shows a SEM micrograph of the InSb micro-pillar of interest, with a dimension of 2.5×2.5×7.5 μm. Fig. 1 (d) provides a 3D schematic view of the pillar on its pedestal as well as the relevant crystallographic directions (top view is also schematized, as discussed later). The <123> orientation was chosen to favor “single-slip” deformation during compression, i.e. partial dislocations will nucleate and glide only in a single glide plane, (1-11), resulting in the accumulation of SFs in parallel (1-11) planes [1-3]. Figure 1: (a) SEM image of studied InSb pillar before deformation. (b) Load versus displacement compression curves applied to the pillar; the (red) star illustrates the condition at which 2D XRD maps were collected. (c) SEM image of the same pillar after deformation. (d) 3D schematic of pillar on pedestal with crystallographic directions and top view with the two diffraction geometries: “A” refers to the incident beam direction for polychromatic Laue microdiffraction, “B” refers to the incident beam direction for monochromatic micro-diffraction A custom-designed micro-compression device (MCD), equipped with a diamond flat tip and a standard 1D Triboscope transducer from Hysitron Inc. for force and displacement readout (see [4] for details), was used to in-situ perform uniaxial compression tests combined with a Laue polychromatic micro-diffraction as well as monochromatic micro-diffraction. Here, we focus on the post-mortem study of one specific pillar deformed by a series of loading-unloading cycles until the early plastic regime was attained, as shown by the mechanical curves presented in Fig. 1 (b). After the mechanical test, SEM observations were performed on the pillar, as presented in Fig. 1 (c): the top third of the pillar exhibits permanent bending as a sign of plastic deformation, as well as the presence of two cracks at the very top. Spatially resolved 2D micro-diffraction maps: comparison between polychromatic and monochromatic cases After plastic deformation, the pillar was spatially mapped with two different diffraction techniques: polychromatic Laue micro-diffraction and monochromatic micro-diffraction. Post mortem Laue micro-diffraction mapping was performed at the MicroXAS beamline from the Swiss Light Source (SLS) in Switzerland, with a 1×1 μm pink beam and energy range of [4Residual Stresses 2018 – ECRS-10 Materials Research Forum LLC Materials Research Proceedings 6 (2018) 21-26 doi: http://dx.doi.org/10.21741/9781945291890-4 23 23] keV. X-Ray Fluorescence (XRF) was used to localize each micro-pillar before and after deformation: XRF maps were obtained by summing the signals from In–Lα, Sb–Lα and Sb-Lβ emission yields. A 2D Eiger 4M detector with a pixel size of 75×75 μm was used to collect Laue patterns in transmission mode. The sample-to-detector distance was fixed at 86.81 mm. 47×24 patterns were collected from top to bottom of the pillar, with a step size 300 nm. The polychromatic incident beam was parallel to the [-451] direction, corresponding to configuration “A” in top view of Fig. 1 (d). All Laue micro-diffraction data presented here are related to one of the many diffraction spots available in the patterns: the 1-1-1 reflection, as presented in Fig. 2 (a) and (b). A computer code was developed to analyze the data (XRF and XRD) using Python. Post mortem monochromatic micro-diffraction mapping was performed at the ID01 beamline from the European Synchrotron Radiation Facility (ESRF) in France, with a 8 keV monochromatic beam. A 2D Maxipix detector with a pixel size of 55×55 μm was used to collect diffraction patterns obtained in reflection mode, with a beam size of about 0.2x0.2 μm. The sample-to-detector distance was fixed to 140 cm. 60x60 patterns were collected from top to bottom of the pillar, with a step size of 250 nm. Only the (11-1) reflection was considered (associated to lattice planes that are parallel to pillar and compression axes, see Fig. 1 (d)), as presented in Fig. 2 (c) and (d): constraints from the goniometer and setup imposed that the incident monochromatic beam was at 12° in opposite direction to [-451], corresponding to configuration “B” in top view of Fig. 1 (d). This will result in mirrored maps obtained from polychromatic and monochromatic micro-diffraction experiments. A rocking curve made of 20 ɸ-scans was performed to probe the 11-1 Bragg peak in reciprocal space: the ɸ-scans were done between 18.2° to 19.15° with a step size of 0.05°. Homemade programs written in Python and Mathematica were used to analyze collected patterns: in particular, the center of mass for diffracted intensity was calculated as well as the integrated intensity. The conditions of the experiments were such that a horizontal variation of the center of mass of the spot is proportional to a Bragg angle evolution Δθ (in degrees) that can be translated into a lattice spacing evolution Δa, or strain Δa/a; a vertical variation of the center of mass of the spot is correlated with a change of the lattice orientation Δ⍵ (in degrees) that can be understood as a tilt (perpendicular to the pillar axis) of the single-crystalline pillar. Note that the other twist component, with an axis aligned with the pillar, could be obtained since rocking curves have been recorded, but is not shown here. Figure 2: (a) zoom from the full Laue pattern on the 1-1-1 spot collected at the pedestal and (b) at the top of the deformed pillar; the dashed black rectangle is a mask used for analysis. (c) Zoom from the full monochromatic micro-diffraction pattern on 11-1 spot collected at the pedestal and (d) at the top of the pillar. All scales are logarithmic. All axes are in pixels. Fig. 2 illustrates the shape and intensity of the spots obtained respectively by Laue and monochromatic micro-diffraction at the pedestal (Fig.2 (a) and (c)) and at the top of the pillar (Fig. 2 (b) and (d)), after deformation. It is interesting to observe that in both cases, the shape and Residual Stresses 2018 – ECRS-10 Materials Research Forum LLC Materials Research Proceedings 6 (2018) 21-26 doi: http://dx.doi.org/10.21741/9781945291890-4 24 intensity of the spots are significantly different between the pedestal and the pillar’s top, with apparition of peak shift, streaking and splitting that are characteristic of permanent change in lattice strain and orientation, as well as storage of lattice defects: these features are obviously the result of the concentration of plastic deformation at the top of the pillar, as observed in Fig. 1 (c). Fig. 3 presents the different spatially resolved maps obtained by XRF (Fig. 3 (a)), Laue micro-diffraction (Figur


Introduction
Indium Antimonide (InSb) and other semiconductors are known to be crystalline materials with brittle behavior at room temperature in the bulk state, but become ductile in the form of microand nano-objects [1][2].At room temperature, InSb micro-pillars plastically deform by the nucleation of partial dislocations at surfaces: after gliding through the pillar, they escape at opposite surfaces (creating slip traces forming a deformation band) but leave in the crystal parallel Stacking Faults (SFs).This mechanism has been verified by post-mortem Scanning Electron Microscopy (SEM) observations and destructive Transmission Electron Microscopy (TEM) characterization [1][2] but also by non-destructive post-mortem study based on coherent X-Ray diffraction [3].In the latter case, the profile of coherent diffraction patterns of 202 reflection evolves significantly between pristine and plastically-deformed regions: the splitting and streaking of patterns arise from interferences induced by the presence of SFs that are phasedefects creating phase-shifted regions within the pillar [3].The maximum intensity of diffraction patterns could be related to the number of SFs present in the illuminated volume, and also to the volume of defected region (i.e. the size of the band containing the SFs).This diffraction technique thus proved to be very interesting as a non-destructive way to detect and characterize the presence of plastic defects in nano-and micro-objects.
In the present work, the same system (InSb micro-pillar) is used to further assess the capacities of micro-diffraction techniques to characterize the impact of plastic deformation (lattice rotation, residual strain, defects storage, etc.) and in particular compare two techniques, Laue and monochromatic micro-diffraction, via spatially resolved 2D maps that are compared and discussed.

InSb micro-pillars -Mechanical tests
InSb micro-pillars were fabricated by Ga + Focused Ion Beam (FIB) milling from a bulk <123>oriented single-crystalline wedge: at all milling steps, the ion beam current and acceleration voltage were kept as low as possible to avoid creation of lattice defects and/or surface amorphisation; for instance, the last milling step was performed at a beam current of 24 pA.The resulting geometry is a series of free-standing micro-pillars on top of pedestals.Fig. 1 (a) shows a SEM micrograph of the InSb micro-pillar of interest, with a dimension of 2.5×2.5×7.5 µm 3 .Fig. 1 (d) provides a 3D schematic view of the pillar on its pedestal as well as the relevant crystallographic directions (top view is also schematized, as discussed later).The <123> orientation was chosen to favor "single-slip" deformation during compression, i.e. partial dislocations will nucleate and glide only in a single glide plane, (1-11), resulting in the accumulation of SFs in parallel (1-11) planes [1][2][3].schematic of pillar on pedestal with crystallographic directions and top view with the two diffraction geometries: "A" refers to the incident beam direction for polychromatic Laue microdiffraction, "B" refers to the incident beam direction for monochromatic micro-diffraction A custom-designed micro-compression device (MCD), equipped with a diamond flat tip and a standard 1D Triboscope transducer from Hysitron Inc. for force and displacement readout (see [4] for details), was used to in-situ perform uniaxial compression tests combined with a Laue polychromatic micro-diffraction as well as monochromatic micro-diffraction.Here, we focus on the post-mortem study of one specific pillar deformed by a series of loading-unloading cycles until the early plastic regime was attained, as shown by the mechanical curves presented in Fig. 1  (b).After the mechanical test, SEM observations were performed on the pillar, as presented in Fig. 1 (c): the top third of the pillar exhibits permanent bending as a sign of plastic deformation, as well as the presence of two cracks at the very top.

Spatially resolved 2D micro-diffraction maps: comparison between polychromatic and monochromatic cases
After plastic deformation, the pillar was spatially mapped with two different diffraction techniques: polychromatic Laue micro-diffraction and monochromatic micro-diffraction.
Post mortem Laue micro-diffraction mapping was performed at the MicroXAS beamline from the Swiss Light Source (SLS) in Switzerland, with a 1×1 µm 2 pink beam and energy range of [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] keV.X-Ray Fluorescence (XRF) was used to localize each micro-pillar before and after deformation: XRF maps were obtained by summing the signals from In-Lα, Sb-Lα and Sb-Lβ emission yields.A 2D Eiger 4M detector with a pixel size of 75×75 µm 2 was used to collect Laue patterns in transmission mode.The sample-to-detector distance was fixed at 86.81 mm.47×24 patterns were collected from top to bottom of the pillar, with a step size 300 nm.The polychromatic incident beam was parallel to the [-451] direction, corresponding to configuration "A" in top view of Fig. 1 (d).All Laue micro-diffraction data presented here are related to one of the many diffraction spots available in the patterns: the 1-1-1 reflection, as presented in Fig. 2 (a) and (b).A computer code was developed to analyze the data (XRF and XRD) using Python.
Post mortem monochromatic micro-diffraction mapping was performed at the ID01 beamline from the European Synchrotron Radiation Facility (ESRF) in France, with a 8 keV monochromatic beam.A 2D Maxipix detector with a pixel size of 55×55 µm 2 was used to collect diffraction patterns obtained in reflection mode, with a beam size of about 0.2x0.2µm 2 .The sample-to-detector distance was fixed to 140 cm.60x60 patterns were collected from top to bottom of the pillar, with a step size of 250 nm.Only the (11-1) reflection was considered (associated to lattice planes that are parallel to pillar and compression axes, see Fig. 1 (d)), as presented in Fig. 2 (c) and (d): constraints from the goniometer and setup imposed that the incident monochromatic beam was at 12° in opposite direction to [-451], corresponding to configuration "B" in top view of Fig. 1 (d).This will result in mirrored maps obtained from polychromatic and monochromatic micro-diffraction experiments.A rocking curve made of 20 ɸ-scans was performed to probe the 11-1 Bragg peak in reciprocal space: the ɸ-scans were done between 18.2° to 19.15° with a step size of 0.05°.Homemade programs written in Python and Mathematica were used to analyze collected patterns: in particular, the center of mass for diffracted intensity was calculated as well as the integrated intensity.The conditions of the experiments were such that a horizontal variation of the center of mass of the spot is proportional to a Bragg angle evolution Δθ (in degrees) that can be translated into a lattice spacing evolution Δa, or strain Δa/a; a vertical variation of the center of mass of the spot is correlated with a change of the lattice orientation Δ⍵ (in degrees) that can be understood as a tilt (perpendicular to the pillar axis) of the single-crystalline pillar.Note that the other twist component, with an axis aligned with the pillar, could be obtained since rocking curves have been recorded, but is not shown here.Fig. 2 illustrates the shape and intensity of the spots obtained respectively by Laue and monochromatic micro-diffraction at the pedestal (Fig. 2 (a) and (c)) and at the top of the pillar (Fig. 2 (b) and (d)), after deformation.It is interesting to observe that in both cases, the shape and intensity of the spots are significantly different between the pedestal and the pillar's top, with apparition of peak shift, streaking and splitting that are characteristic of permanent change in lattice strain and orientation, as well as storage of lattice defects: these features are obviously the result of the concentration of plastic deformation at the top of the pillar, as observed in Fig. 1 (c).
Fig. 3 presents the different spatially resolved maps obtained by XRF (Fig. 3 (a)), Laue micro-diffraction (Figure 3 (b)) and monochromatic micro-diffraction (Fig. 3 (c)) on the deformed pillar.The XRF map allows to entirely see the pillar on its pedestal and localize (star symbol) where reference patterns will be taken for the different data analyses.Fig. 3 (b) presents the Laue map of integrated intensity of the 1-1-1 spot (same region as in Fig. 2 (a) and (b)) normalized to the integrated intensity of the same spot at reference position in the pedestal: an unexpected increased normalized integrated intensity is observed in the upper part of deformed pillar, in a region of about 5µm in height.Fig. 3 (c) displays the monochromatic microdiffraction map of integrated intensity of the 11-1 spot normalized to the integrated intensity of the same spot at reference position in the pedestal.The plotted normalized integrated intensity has been obtained from the summation on the 20 rocking curves, or ɸ-scans, previously described.Again, an increased normalized integrated intensity is observed at top of the pillar; this increase of intensity is more localized than for Laue micro-diffraction, probably because of smaller beam size in monochromatic micro-diffraction.Considering the SEM observations made on the deformed pillar, it seems reasonable to correlate this region of increased diffracted intensity (observed in both maps) to the plastically deformed region at pillar's top.
Fig. 4 (a) displays the Laue map of integrated intensity of the 1-1-1 spot, calculated outside the masked region defined in Fig. 2 (a): this region is defined from the pattern at pedestal position, i.e. in a non-deformed region.As a first crude approximation, we consider that the diffracted intensities inside the mask are mainly contributions from the pristine crystal: all intensities outside the mask may then be considered as mainly resulting from plastically deformed regions, inducing shift, streaking and splitting of the 1-1-1 spot.As a result, the obtained map reveals that the most intense region corresponds indeed to the top of the pillar, where plasticity has taken place.Interestingly, this region is more localized than the one revealed previously without any mask (Fig. 3 (b)) and similar to the one revealed by monochromatic micro-diffraction (Fig. 3 (c)).A more in-depth analysis of the Laue spot profile should bring additional information on the origin of observed lattice strain and rotation (incl.lattice defects density) [5].The monochromatic case, based on a powerful XRD technique [6], has been studied in more details to obtain more quantitative information: Fig. 4 (b) maps the variation in Bragg angle, Δθ (°), deduced from the horizontal shift of center of mass (see above) in patterns collected at a ɸ angle equal to 18.2°.Again here, a reference pattern is taken in the pedestal.The Bragg angle variation is then transformed into lattice spacing variation Δa, and lattice strain Δa/a, with strain-free InSb lattice being taken as a=6.479Å [1][2].The resulting strain map is presented in Fig. 4 (c): the region with largest residual strain is, without surprise, at the top of the pillar where lattice strain of the order of 0.01 is observed.One should recall that this strain has been calculated from 11-1 spot and is thus associated to the lattice planes parallel to pillar axis (see Fig. 1 (d)): this strain is thus smaller than axial strain by a factor of about 1/3 (Poisson ratio) and of opposite sign.A similar approach has been applied to the vertical shift of the center of mass to obtain a map of lattice orientation variation Δ⍵ (°), or lattice tilt, compared to reference in the pedestal.The map shows that the residual tilt is rather small in the pedestal and in all the bottom part of the pillar: it is only the very top that exhibits relatively large residual tilt values (-0.06°) that are footprints of the plastically bent regions (as observed in SEM) but also the tilted regions between cracks at very top of the pillar.The micro-Laue gives access to a quantification of the tilt.
Overall, these spatially resolved maps are in good agreement with recent results obtained by Laue micro-diffraction combined with compression to investigate the deformation mechanisms in [001]-oriented single crystal MgO cylindrical pillars: a reduction in diffracted intensity was recorded along the vertical direction, moving from the top towards the bottom of the MgO micro-pillars, and associated to gradual reduction of the strain along the pillars height [7].In our case, both micro-diffraction techniques maps reveal a localized region at the top of the pillar where the integrated diffracted intensity is higher.This can be explained by the fact that in Laue configuration, a broader part of the pink spectrum is selected in the distorted areas.For the monochromatic case, a similar reasoning can be applied considering the summation over the 20 ɸ-scans.Moreover, this region is correlated to the volume where residual lattice strain and tilt were induced by plastic deformation

Figure 1 :
Figure 1: (a) SEM image of studied InSb pillar before deformation.(b) Load versus displacement compression curves applied to the pillar; the (red) star illustrates the condition at which 2D XRD maps were collected.(c) SEM image of the same pillar after deformation.(d) 3Dschematic of pillar on pedestal with crystallographic directions and top view with the two diffraction geometries: "A" refers to the incident beam direction for polychromatic Laue microdiffraction, "B" refers to the incident beam direction for monochromatic micro-diffraction

Figure 2 :
Figure 2: (a) zoom from the full Laue pattern on the 1-1-1 spot collected at the pedestal and (b) at the top of the deformed pillar; the dashed black rectangle is a mask used for analysis.(c) Zoom from the full monochromatic micro-diffraction pattern on 11-1 spot collected at the pedestal and (d) at the top of the pillar.All scales are logarithmic.All axes are in pixels.

Figure 3 :
Figure 3: spatially resolved maps from (a) normalized fluorescence of the InSb pillar, (b) normalized integrated intensity of the 1-1-1 spot in Laue micro-diffraction and (c) normalized integrated intensity of the 11-1 spot in monochromatic micro-diffraction.The stars localize the positions for reference patterns.The axes are in µm.

Figure 4 :
Figure 4: spatially resolved maps of (a) the normalized integrated intensity of the 1-1-1 Laue spot outside a masked region (mask shown on pattern at pedestal in Fig. 2 (a)), (b) the Bragg angle variation Δθ (°) of the 11-1 reflection in monochromatic micro-diffraction and (c) associated lattice strain Δa/a; (d) the variation Δ⍵ (°) of lattice tilt in the pillar from 11-1 spot monochromatic micro-diffraction.The stars localize the positions for reference patterns.The axes are in µm.